EPA
TVA
United States
Environmental Protection
Agency
Industrial Environmental Research
Laboratory
Research Triangle Park NC 27711
EPA-600/7-81-106a
July 1981
Tennessee Valley
Authority
Office of Power
Energy Demonstrations
and Technology
Chattanooga TN 37401
TVA/OP/EDT-81/47a
Testing and Analysis of a
Wet-Dry Crossflow
Cooling Tower
Volume I:
Test Program and Results
Interagency
Energy/Environment
R&D Program Report
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the INTERAGENCY ENERGY-ENVIRONMENT
RESEARCH AND DEVELOPMENT series. Reports in this series result from the
effort funded under the 17-agency Federal Energy/Environment Research and
Development Program. These studies relate to EPA's mission to protect the public
health and welfare from adverse effects of pollutants associated with energy sys-
tems. The goal of the Program is to assure the rapid development of domestic
energy supplies in an environmentally-compatible manner by providing the nec-
essary environmental data and control technology. Investigations include analy-
ses of the transport of energy-related pollutants and their health and ecological
effects; assessments of, and development of, control technologies for energy
systems; and integrated assessments of a wide range of energy-related environ-
mental issues.
EPA REVIEW NOTICE
This report has been reviewed by the participating Federal Agencies, and approved
for publication. Approval does not signify that the contents necessarily reflect
the views and policies of the Government, nor does mention of trade names or
commercial products constitute endorsement or recommendation for use.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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TESTING AND ANALYSIS
OF A WET-DRY CROSSFLOW COOLINJ3 TOWER,
VOLUME I: TEST PROGRAM & RESULTS
by
D. L. Ayers, M. R. Hogan, A. E. Hriba
Westinghouse Electric Corpo
Research & Development Cejiter
1310 Beulah Road
Pittsburgh PA 15235
, R. A. Lucheta
ration
TVA Contract No. TV4626
TVA Project Director: Hollis B
7
. Flora II
-y
Tennessee Valley Authori
Division of Energy Demonstrations and Technology
Chattanooga, Tennessee 37fr01
EPA Interagency Agreement No. D<5-E721-BE
Program Element No. INE624A
EPA Project Officer: Theodore
Industrial Environmental Research
Office of Environmental Engineering
Research Triangle Park, NC
Prepared for
U.S. ENVIRONMENTAL PROTECTION
Office of Research and Devel
Washington, DC 20460
Chi
G. Brna
Laboratory
,md Technology
27711
AGENCY
jpment
F'-'./'-onri-ntri! Protection Agency
•"i V, Mx;v.ry ,'
;. ,...-: i.:...-bcrn Si
iiigo, iliinuis 60604
-------
DISCLAIMER
This report was prepared as an account of work sponsored by the United
States Government. Neither the United States nor the Tennessee Valley
Authority, nor any of their employees, makes any warranty, express or
implied, or assumes any legal liability or responsibility for the ac-
curacy, completeness, or usefulness of any information, apparatus, pro-
duct, or process disclosed, or represents that its use would not infringe
privately owned rights. Reference herein to any specific commercial
product, process, or service by trade name, mark, manufacturer, or other-
wise, does not necessarily constitute or imply its endorsement, recom-
mendation, or favoring by the United States Government or any agency
thereof. The views and opinions of authors expressed herein do not
necessarily state or reflect those of the United States Government or
any agency thereof.
U,S. Environments! Protection
ii
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TESTING AND ANALYSIS OF A
WET-DRY CROSSFLOW COOLING TOWER,
TVA Contract No. TV46267
and
Interagency Agreement EPA-IAG-D8-E721-BE
ABSTRACT
This program was initiated with the objective of measuring and analyz-
ing mass transfer, heat transfer, fluid flow, plume formation and
acoustic characteristics of a wet/dry crossflow cooling tower, under
contract from the Tennessee Valley Authority.
The test apparatus was a fully instrumented mechanical draft cooling
tower constructed by Westinghouse Electric Corporation at the Cliffside
Plant of Duke Power Company, Cliffside, North Carolina. Data were
acquired at the test site by personnel from Westinghouse Power Generation
Services Division and analyzed by Westinghouse Research and Development
Center.
Results of the analysis of test data are generally in the form of cor-
relations or predictive computer codes. Data on mass transfer coef-
ficient, water loss, heat exchanger air-side convective heat transfer
coefficient, fan system efficiency, acoustic propagation and plume
formation are presented.
This report also describes the facility itself, its operational proce-
dure, instrumentation, data acquisition techniques and data reduction
procedures.
iii
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TABLE OF CONTENTS
VOLUME I
Abstract
List of Illustrations ix
List of Tables xii
1.0 INTRODUCTION 1
2.0 CONCLUSIONS 6
2.1 Thermal and Flow Tests 6
2.2 Acoustics Tests 9
2.3 Plume Tests. 10
3.0 RECOMMENDATIONS 11
3.1 Thermal and Flow Tests 11
3.2 Plume Tests 12
4.0 THERMAL PERFORMANCE TESTS 13
4.1 Thermal and Flow Instrumentation 15
4.1.1 Instrument Calibration Procedures 22
4.2 Data Acquisition and Transfer. 23
4.3 Thermal and Flow Data Reduction 31
4.3.1 Tower Heat and Mass Transfer 31
4.3.1.1 Wet Fill Heat and Mass Transfer Coef-
ficients 38
4.3.1.1.1 Computation of Ka 38
4.3.1.1.2 Calculation of Grid Size. . 45
4.3.1.2 Heat Exchanger Heat Transfer Analysis. 47
4.3.1.3 Heat Exchanger Air-Side Heat Transfer
Coefficient Computation 53
4.3.1.4 Airflow Rate Analysis and Computation. 54
4.3.1.5 Water Flow Rate Analysis and Compu-
tation 60
4.3.2 Data Reduction Computer Code 67
4.3.2.1 Data Reduction Main Program Functions. 67
(Continued)
v
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Table of Contents (cont'd) Page
4.4 Analysis of Thermal and Flow Data. 69
4.4.1 Correlation Forms 69
4.4.2 Statistical Analysis of Data. . 75
4.4.3 Linear Regression ............... 77
4.5 Results of Correlations 80
4.5.1 Mass Transfer Coefficient Ka. ......... 80
4.5.2 Rate of Water Loss Due to Evaporation (AL/L) . . 87
4.5.3 Dry Heat Exchanger Air-Side Convective Heat
Transfer Coefficient H 91
4.5.4 Fan Efficiency 95
4.6 Nomenclature ... ............ 109
4.7 References ............. 116
5.0 ACOUSTICS TESTS 117
5.1 Description of Acoustic Instrumentation. ....... 117
5.1.1 Data Acquisition Equipment. . 117
5.1.2 Data Analysis Equipment ............ 123
5.2 Acoustic Data Acquisition Techniques .... 123
5.3 Acoustic Data Reduction Techniques ... 127
5.4 Analysis of Data 127
5.4.1 Experimental Design , 129
5.4.2 Observed Noise Levels 131
5.4.3 Statistical Model 131
5.4.4 Examination of Model Fit 135
5.5 Noise Prediction Computer Code ..... 139
5.5.1 Program Code Modifications. . 139
5,5.1.1 Atmospheric Absorption ........ 141
5.5.2 Program Code Operation. . 144
5.6 Discussion of Results. ................ 146
5.6.1 Experimental Data ...... 146
5.6.2 Regression Analysis .............. 147
5.6.3 Noise Prediction Code 148
5.6,3.1 Ground Absorption. ........ . . 148
5.6.3.2 Wind and Temperature Fluctuations. . . 150
(Continued)
vi
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Table of Contents (cont fd) Page
5.7 Acknowledgements ........ ... 150
5.8 Acoustics References 150
5.9 Acoustics Nomenclature ................ 151
6.0 PLUME TESTS 153
6.1 Plume Instrumentation. ................ 153
6.2 Plume Data Acquisition Technique at the Cliffside Site 159
6.2.1 Data Handling at Westinghouse Fluid Systems
Laboratory. .................. 161
6.2.2 Data Handling at Westinghouse R&D Center. . . . 161
6.3 Plume Modeling 164
6.4 Analysis of Plume Data ...... ..,...,... 165
6.5 Discussion of Results. , 166
6.5.1 Validation of the Rubin Model 166
6.5.2 Compilation of Plume Data 167
6.5.3 Possible Further Studies 167
6.6 References ............. . 167
7.0 ACKNOWLEDGEMENTS. . 169
VOLUME II
List of Illustrations vii
List of Tables xi
APPENDICES 1
A. Description of Tower Test Facility 1
A.I Introduction 1
A.2 Tower Construction 1
A.3 Water System 11
A.4 Air Supply 11
A. 5 Controls 13
B. Cooling Tower Startup, Operating and Shutdown Pro-
cedures 15
(Continued)
vii
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Table of Contents (cont'd) Page
B.I Startup Procedures 15
B.2 Shutdown Procedure 18
B.3 Operation Procedure 19
C. Data Reduction Program 23
D. Data Correlation Computer Codes 117
D.I Input Data Files 117
1
D.2 Ka Correlation Code 119
D.3 Water Loss Correlation Code 122
D.4 Heat Exchanger Air-Side Heat Transfer Coefficient
Correlation Code 123
D.5 Fan Efficiency Correlation Code 124
E. Cooling Tower and Background Noise Data 179
F. Noise Prediction Computer Model Documentation 185
F.I Program Structure 185
F.2 Summary of Programs 185
F.3 Input Data Format 187
F.4 Sample Output Listings 191
G. Noise Prediction Computer Code 195
H. Basic Plume and Cooling Tower Data 207
I. Rubin's Program and Input Data 251
J. Comparison of Computed and Observed Plume Parameters. . £65
viii
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LIST OF ILLUSTRATIONS
VOLUME I
Figure No. Title Page
1.0-1 Side View of Tower Showing Location of Dew Cells, 2
Thermocouples, and Velocity Probes
1.0-2 Schematic of One-Half the Cooling Tower Cell, Showing 4
Water Flow Control and Measurement System
4.1.1 Mercury Manometer Used to Calibrate the Ellison Annubar 14
Water Flow Meter
4.1.2 Ellison Annubar Water Flow Meter in its Insulated and 14
Heated Housing
4.1-3 Photograph of the Kiel Probe Rake at the Fan Stack 16
Inlet
4.1-4 Photograph of the Wafer Switch Control for Kiel Probe 16
Pressures (See Figure 4.1-6 for Schematic)
4.1-5 Electromanometer Used for Pressure Measurement 18
4.1-6 Schematic Diagram of the Fan Stack Air Velocity Measur- 19
ing System's Probe/Wafer Switch/Purge Air/Pressure
Transducer System
4.1-7 Fluke Model 2240B Digital Data Acquisition System 18
4.3-1 Wet Fill Heat and Mass Transfer Control Volume 30
4.3-2 An Illustration of the Two-Dimensional Representation 40
of the Wet Fill and its Grid Structure
4.3-3 Typical Wet Fill Grid and Nomenclature Employed in 42
Defining the Temperature of the Grid i,j
4.3-4 Error in Mass Transfer Coefficient as a Function of 48
Computation Time and the Experimental Multiplication
Factor
4.3-5 Tower Heat Exchanger Tube and Fin Geometry, and Nomen- 49
clature Employed in the Heat Transfer Analysis
4.3-6 Stack Velocity as a Function of Distance Across the 56
Stack at the Velocity Pressure Probe Station
4.3-7 Fan-Stack Model and Nomenclature Employed for the 58
Calculation of Air Flow Rate from the Fan Curve
(Continued)
ix
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List of Illustrations (cont'd)
Figure No. Title Page
4.3-8 Schematic of Dry Heat Exchanger Hydraulic System with 62
the Manometer Employed to Measure the Frictional Pres-
sure Drop
4.3-9 Dry Heat Exchanger Water Flow Rate Calibration. The 64
Pressure Drop-Water Density Ratio is Shown as a Func-
tion of Water Flow Rate. Also Indicated is the Least
Squares Curve Used to Represent the Calibration in the
Data Reduction
4.3-10 Heat Exchanger Pressure Transducer Voltage as a Func- 66
tion of Dry Heat Exchanger Water Flow Rate. Also
Shown is the Second Order Least Squares Polynomial
used to Represent the Calibration in the Data Reduc-
tion Program
4.5.4-1 Airflow System Efficiency as a Function of Airflow 94
Rate
4,5.4-2 Airflow System Efficiency as a Function of Airflow 96
Rate for a Rotational Speed of 60 RPM
4.5.4-3 Airflow System Efficiency as a Function of Airflow 98
Rate for a Rotational Speed of 90 RPM
4.5.4-4 Airflow System Efficiency as a Function of Airflow 99
Rate for a Rotational Speed of 101 RPM
4.5.4-5 Airflow System Efficiency as a Function of Airflow 100
Rate for a Rotational Speed of 113 RPM
4.5.4-6 Airflow System Efficiency as a Function of Airflow 101
Rate for a Rotational Speed of 119 RPM
4.5.4-7 (a) Fan Pressure Rise and System Characteristic as 102
a Function of Volumetric Flow Rate. Each Fan Curve
Represents a Unique Pitch (X).
(b) Fan Efficiency for Three Blade Angles as a Func- 102
tion of Volumetric Flow Rate. Also Shown is Antici-
pated Fan Efficiency Behavior While Coupled to the
System Characteristic Shown in Figure 6-7a.
4,5.4—8 Airflow System Efficiency as a Function of Airflow 104
Rate for an 8-Degree Blade Pitch
4.5.4-9 Airflow System Efficiency as a Function of Airflow 105
Rate for a 10-Degree Blade Pitch
4.5.4-10 Airflow System Efficiency as a Function of Airflow 106
Rate for a 12-Degree Blade Pitch
(Continued)
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List of Illustrations (cont'd)
Figure No. Title Page
4.5.4-11 Airflow System Efficiency as a Function of Airflow 107
Rate for a 14-Degree Blade Pitch
4.5.4-12 Airflow System Efficiency as a Function of Airflow 108
Rate for a 16-Degree Blade Pitch
4.5.4-13 Airflow System Efficiency and Approximating Straight 110
Line as a Function of Volumetric Flow Rate
5.1-1 Data Acquisition Equipment 118
5.1-2 Frequency Response Calibration of the B&K 4l45 Micro- 120
phone. Upper Curve - Free— Field Normal Incidence
Response; Lower Curve - Pressure Response
5.1-3 Free-Field Corrections for the B&K 4145 Microphone 121
with Protective Grid as a Function of Incidence Angle
5.1-4 Free-Field Response Corrections for the B&K 4145 122
Microphone When Used with the B&K UA 0207 Windscreen
5.1-5 Measured Frequency Response at 15 ips of the Stella- 119
vox SP-7 Recording Channels
5.1-6 Data Reduction Equipment 124
5.2-1 Ground Level Measurement Locations 126
5.5-1 Source-Receiver Geometry 141
6.1-1 (a) Tethersonde Instrument Package 154
(b) Tethersonde Balloon in Flight 154
6.1-2 Sample Theodolite Data 158
VOLUME II
A-l
A-2
A-3
A-4
A.-5
A-6
Aerial View of the Cliffside Experimental Cooling 2
Tower
Photograph of the Cliffside Tower Showing the Control 2
House
Schematic of Hot Water Supply and Cold Water Return 3
Systems for the Tower Test Facility
View of Tower Showing Precast Side Wall Construction 4
View of Dry Heat Exchangers on the Tower Inlet Face 4
Photograph of the Wet Fill Elements in Their Wire Mesh 6
Spacer Grid
(Continued)
xi
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List of Illustrations (cont'd)
Figure No. Title Page
A-7 View of Inlet Fill Elements Being Installed 7
A-8 View of the Rear of the Fill Section Showing the Drift 8
Eliminator Assembly
A-9 Distribution Nozzles in the Hot Water Basin at the Top 8
of the Tower
A-10 Fan Deck and a Portion of the Fan Stack 9
A-ll View of the Hot Water Distribution Header at the Top 9
of the Tower
A-12 Tower Hot Water Supply Piping 10
A-13 Tower Hot Water Circulating Pump 10
A-14 Tower Hot Water Supply Pump with Bypass Line 12
A-15 Tower Air Circulating Fan 12
A-16 View into the Bottom of Fan Stack, Showing the Fan 14
Drive Assembly
A-17 Motor Controls for the Fan Drive System 14
F-l Flow Diagram for Main Program TOWER 184
F-2 Flow Diagram for Subroutine ABSORB 186
F-3 Flow Diagram for Subroutine GRND 187
F-4 Flow Diagram for Subroutine SOURCE 188
F-5 Flow Diagram for Subroutine TITLE 188
1-1 Format of Data Prepared for Rubin's Program £50
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LIST OF TABLES
VOLUME I
Table No. Title Page
4.1-1 Locations of Thermocouples, De-wcells and Thermo- 20
meters
4,2-1 Sample of Raw Tower Data from a Dry Heat Exchanger 24
Test
4,2-2 Delineation of Input Paper Tape Data by Channel for 28
Thermal and Flow Data
4,4-1 Thermal and Flow Test Grid 70
4.5.1-1 Mass Transfer Coefficient Correlation Data 82
4.5.2-1 Water Loss Correlation Data 88
4.5.2-2 Comparison of All Wet and Winter Wet Correlations of 90
Water Loss AL/L
4.5.3-1 Dry Heat Exchanger Heat Transfer Coefficient Cor- 92
relation Data
5.1-1 Measurement Equipment Models 118
5.1-2 Data Reduction Equipment Models 124
5.4-1 Independent Variables and Corrected Noise Levels 128
5.4-2 Fitted Coefficients for Surviving Model Terms 132
A
5.4-3 Comparison of Measured (Y) and Predicted (Y) Noise 134
Levels* with Standard Error (S)
5.4-4 Estimates of Standard Deviation 140
6.2.1-1 Sample Data, as Received 162
VOLUME II
C-l
C-2
C-3
Sample Input Listing for Nonplume Tests 26
Delineation of Input Paper Tape Data by Channel 28
Tower Diffuser Throat Static and Velocity Pressure 30
Data
(Continued)
xiii
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List of Tables (cont'd)
Table No. Title Page
C-4 Listing of the Tower Data Reduction Computer Code 30
C-5 Sample Output Listing 110
D-l Examples of Punched Card Output from the Data Reduc- 126
tion Program (Appendix C) Used as Input to Cor-
relation Programs
D-2 Listing of the Mass Transfer Coefficient Correlation 127
Computer Code
D-3 Sample Output from the Mass Transfer Coefficient Cor- 136
relation Code
D-4 Listing of the Water Loss Correlation Computer Code 141
D-5 Sample Output from the Water Loss Correlation Code 152
D-6 Listing of the Colburn j Factor Correlation Computer 157
Code
D-7 Sample Output from the Colburn j Factor Correlation 161
Code.
D-8 Listing of the Fan System Efficiency Correlation 167
Computer Code
D-9 Sample Output from the Fan System Efficiency Cor- 169
relation Code
E-l Measured Octave Band Noise Levels, dB* 180
E-2 Measured Overall Noise Levels, dB* 183
F-l Sample Output from Program Tower 190
H-l Sample of Raw Data File for Plume Tests 208
1-1 The Rubin Plume Prediction Computer Code 252
J-l Comparison of Predicted and Observed Plume Character- 269
istics
xiv
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TESTING AND ANALYSIS
OF A WET-DRY CROSSFLOW COOLING TOWER,
VOLUME I: TEST PROGRAM & RESULTS
D. L. Ayers, M. R. Hogan, A. E. Hribar, and R. A. Lucheta
Heat Transfer and Fluid Dynamics
SECTION 1.0
INTRODUCTION
In 1973-1974 Westinghouse Electric Corporation designed and constructed
a fully-instrumented wet/dry counterflow cooling tower with the aim of
using the facility to acquire tower performance data while operating
under typical power plant conditions. The tower facility was located
at the Cliffside plant of Duke Power Company and acted as an adjunct
to the cooling tower system which had previously serviced this plant.
Subsequently the tower test facility was purchased by the Tennessee
Valley Authority under contract number TV46267. The aim of TVA was to
use the tower test facility to obtain operating performance data in
order to better understand cooling tower dynamics and to verify tower
performance parameters in a cooling tower design computer code also
obtained from Westinghouse under the contract. Under the terms of this
contract Westinghouse Power Generation Services Division was to operate
the test facility to obtain raw data while Westinghouse Research Lab-
oratories were to reduce and analyze the data. The purpose of this
report is to document the cooling tower data acquisition, reduction
and analysis.
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Dwg. 7722A97
Dry Heat Exchanger
Plane 1 - 10 Dew Point
10 Dry Bulb
9 Velocity Probe
Plane 2 - 8 Dry Bulb - Air
Plane 3 - 4 Water Temperature
Plane 4 - 8 Water Temperature
Plane 5-8 Water Temperature
Plane 6-8 Water Temperature
Plane 7-4 Water Temperature
Plane 8 - 10 Dew Point
10 Dry Bulb
Plane 9 - 10 Velocity Probe
Plane 10 - 5 Dew Point
5 Dry Bulb
2 Dew Cells_^K,, ^
& Thermocouples! Jl01str1
Plane 10
Plane 9
butor
Basin
Two Thermo-
couples
Fill
Dry Heat Exchangers-
Drift Eliminators
Figure 1.0-1
Side View of Tower Showing Location of Dew Cells, Thermocouples,
and Velocity Probes.
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The cooling tower test facility was equipped to acquire data on airflow
rate and distribution, water flow rate and distribution, fan speed and
power, air pressure, air dry bulb and dew point temperatures and water
temperatures. Figure 1.0-1 shows schematically the location of the
instrumentation used to measure air properties in the test facility.
Velocity probes were located in inlet and discharge planes to measure
the distribution of airflow and total airflow. As explained later,
these probes could not be used as intended. Also, due to the adverse
environment, air dry bulb and dew point temperatures could not be measured
in the fill volume, but were measured in the fill inlet and discharge
planes, with considerable care taken to shield sensors from flowing water.
Airflow was induced by a variable speed, variable pitch axial fan within
the stack at the top of the tower. Figure 1.0-2 shows the water flow
control and measurement system. Total water flow was measured with an
Ellison Annubar flow meter, and the water was balanced between the two
sides of the tower by remote control valves. Flow was balanced by
equalizing water level in the two distributor basins at the top of the
tower, and the flow into each basin could also be measured, each basin
having been calibrated for water flow versus water depth in the basin.
For the measurement of water flow through dry heat exchangers, the static
pressure difference between top header and bottom header was used, since
this pressure difference is a function of the square of the water velo-
city in the exchanger tubes.
From the acquired data thermodynamic and flow parameters such as mass
transfer coefficient, water loss, dry heat exchanger heat transfer coef-
ficient and fan efficiency may be reduced. Further, by operating the
tower under a wide variety of conditions (weather, water inlet tempera-
ture, airflow rate, water flow rate, fan speed and fan blade pitch) it
is possible to ascertain how the thermodynamic and flow parameters vary
with these independent variables, by way of data correlations.
-------
Dwg. 7722A98
Remote Control Shut-off and
Flow Control Valves
Wet Fill
Distribution
Basin
"East-West"
Balance
Valve
Pump
Annubar Flow Meter
Drain to Basin
-Dry Heat Exchanger
Manual Shut-off
and Flow Control
Valves
Figure 1.0-2 Schematic of One-Half The Cooling Tower Cell, Showing Water
Flow Control and Measurement System.
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In addition to the thermodynamic and flow instrumentation previously
installed at the facility, instrumentation necessary to acquire acoustic
and plume data were installed. The acoustics and plume data were also
analyzed to determine their sensitivity to the tower independent parameters,
This report contains details of the tower instrumentation, techniques
used to acquire test data, the data reduction procedure, analyses of
data and discussion of results. The appendices contain a detailed de-
scription of the test facility, the data reduction computer program,
computer programs used to analyze reduced data, plume data and a math-
ematical model for plume formation.
Section 4.0 of this report contains details of thermal and flow tests,
while Sections 5.0 and 6.0 cover acoustics and plume tests, respectively.
Since each section represents disparate technologies, each contains its
own set of nomenclature and references, where necessary.
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SECTION 2.0
CONCLUSIONS
The cooling tower test program as delineated in TVA contract TV46267
was completed and all significant test results are presented in this
report. Based on the findings of this program the following conclusions
may be drawn.
2.1 THERMAL AND FLOW TESTS
1. While all scheduled tests were performed, out of a total of 2760
runs made, only 1399 runs were recoverable by the analyst. The unre-
coverable data were caused by instrument error, operator error, faulty
instruments in inaccessible areas of the tower, data logging equipment
failure and the generally hostile environment in the tower. The re-
covered data were sufficient to obtain adequate correlations of data
for fill mass transfer coefficient, percent water loss, dry heat ex-
changer air-side heat transfer coefficient and fan system efficiency.
2. The mass transfer coefficient data are best correlated by the
equation:
Ka = .2615 L.875G.683T-1.392 ^^
where Ka is mass transfer coefficient per unit volume of fill (Ibm/hr-
ft3), L is water loading (Ibm/hr-ft2), G is air loading (lbm/hr-ft2)
and T is average outlet water temperature. Use of this correlation in
tower design is iterative because of the use of average exit water temp-
erature. This correlation was obtained by using all wet fill test data
points where water loading was 10,000 lbm/hr-ft2 or less, a total of 498
data points. For this correlation the coefficient of multiple
6
-------
determination, R2, was .961, so that the multiple correlation coef-
ficient R is .980, a reasonably good fit. All other attempts to cor-
relate Ra with L, G and other representative system temperatures, or with
other limits on L or G resulted in smaller multiple correlation coef-
ficients (see Table 4.5.1-1) and, thus, Equation (2.1-1) should be used
in tower designs having fill elements like those in this tower (see
Appendix A for a description of the fill). It should be noted that
Equation (2.1-1) predicts a degradation in Ka with increasing water exit
temperature and, thus, tower performance should suffer correspondingly
with increasing ambient temperature.
A slightly less accurate correlation which ignores temperature effects:
Ka = .00029 L*83° G'838 (2.1-2)
may be used as a first estimate in utilizing Equation (2.1-1) or for
preliminary work. Equation (2.1-2) was also obtained using all wet fill
test data with water loading less than 10,000 lbm/hr-ft2, but with no
water temperature dependency. The multiple correlation coefficient
here is .969.
3. Percent water loss may be computed from the correlation:
AL/L = 367.8 L~'767 G*396 Au>*457 (2.1-3)
where L and G are as before and AL/L is percent water loss and Ato is the
log-mean specific humidity difference as defined in Equation (4.4.1-8).
Again this correlation requires iterative solution in tower design. The
coefficient of multiple correlation R is .961 for Equation (2.1-3).
This equation was obtained by linear regression using only wet fill test
data taken in the spring. Comparable correlations, restricted to other
seasons or combining all wet test data, were inferior to Equation (2.1-3)
for various reasons, including smaller values of R.
-------
For less accurate work the equation:
AT /T /QQ Q T-' n-467 A -800 ft 1 /\
AL/L = 488.8 L G Ato (2.1-4)
may be used, where Ato is the specific humidity difference between air
saturated at the inlet water temperature and air at the inlet of the
tower fill. The multiple correlation coefficient R is .918 for Equation
(2.1-4). This equation resulted from correlating all wet fill test data,
with no seasonal or water loading limitations.
4. The correlation that best fits the dry heat exchanger air-side heat
transfer coefficient data, in the form of Colburn j factor, is:
j = .2853 R§"^JJ (2.1-5)
However, the data scatter here is quite large and caution in using this
equation is urged (see Section 4.5). The correlation coefficient for
Equation (2.1-5) is -.606, which is quite poor. Section 4.5 presents
another correlation (Run 2, Table 4.5.3-1) where the correlation coef-
ficient was -.783, a significant improvement. As stated there, however,
the coefficient and exponent in the correlation are grossly different
from those found in the literature for comparable heat transfer surface.
Thus we caution the reader in using .any dry heat transfer surface cor-
relations in Section 4.5.
5. Fan system efficiency is defined as
- o i f
f E— (2.1-
where nf is efficiency, Q is airflow through the fan in ft /mln, Ap is
fan pressure rise in inches of water, E is electrical input to the fan
motor in kilowatts and a is the appropriate units conversion factor to
-------
make n,. dimensionless. This airflow system efficiency includes the
losses inherent in the drive motor and gear box, as well as the fan it-
self. It was found that fan system efficiency correlates quite simply
with total airflow rate by
nf = -1.004xlO~2 + 2.4xl
-------
4. The noise prediction code predicts linear, A-weighted and octave band
noise levels.
5. The ground absorption calculation assumes that the terrain is flat
and the ground cover is essentially uniform between the tower and re-
ceiver. The code is set up assuming a grass-covered surface—it can be
readily changed to accommodate other types of cover.
6. The noise prediction model has been verified only in the near field.
The high background noise level at the test site precluded making
measurements which could be used for verification of the far—field
predictions.
2.3 PLUME TESTS
1. The apparatus described in Section 6.0 seems capable of gathering
atmospheric boundary layer data, with the exception that the wind di-
rection measurements fluctuate widely.
2. The plume dispersion model evaluated in this report is unsatisfactory.
10
-------
SECTION 3.0
RECOMMENDATIONS
Based upon the work conducted in this program and discussed in detail in
the body of this report, the following recommendations are made.
3.1 THERMAL AND FLOW TESTS
1. In future experimental programs of this nature, it is recommended
that all instrumentation and data acquisition be directly linked and
the data automatically logged, with man removed from the loop. Al-
though this costs more at the outset, the time and expense saved in not
having to rectify human error will more than offset equipment cost.
2. In future experimental programs of this nature it is recommended
that the data reduction capability be located at the test site and the
data reduced when available so that problems in data logging may be pin-
pointed and corrected immediately when they occur. This will tend to
reduce the need for costly retest and subsequent program delays. In
this program logged data were mailed to a remote facility for reduction
and data logging errors that developed were not discovered until they
had spoiled many subsequent test runs.
3. It is recommended that all suggested correlation equations be used
for the design of cooling towers of the kind used here, except for the
dry heat exchanger air-side heat transfer coefficient (Colburn j factor)
correlation. In the design of finned-tube heat exchangers like those in
the Cliffside wet/dry tower, it is recommended that the designer obtain
air-side heat transfer coefficients from the exchanger manufacturer or,
if such data are not available, that Reference 8 of Section 4.0 be used
11
-------
or, as a last resort, that the data be obtained in another experiment
conducted in a more controllable environment. The designer is warned
that the recommended correlations are valid only for the same or similar
equipment.
4. It is recommended in future wet fill cooling tower testing that
pitot tubes not be used to measure air velocities downstream of the fill.
The sensing system tubing cannot be maintained free of liquid water, the
presence of which renders acquired data meaningless. It is recommended
that some other means, not sensitive to the accumulation of water, be
used to measure air velocity.
3.2 PLUME TESTS
1. The mathematical model for plume dispersion evaluated in this report
should not be used.
2. In planning further field studies of cooling tower plumes, it would be
desirable to seek a wider range of atmospheric conditions than were
available during this study, which is limited to mostly stable, early
morning hours in the spring. Also, in planning plume studies for wet/dry
cooling towers, a program should be set up to study the conditions
necessary to eliminate the plume, and this study should be independent of
the plume trajectory study.
12
-------
SECTION 4.0
THERMAL PERFORMANCE TESTS
The cooling tower test facility described in Appendix A was operated
from December 1977 to November 1978 to obtain data on thermal, acoustic
and plume performance. The nearly one-year test period provided test
data under a variety of weather conditions, hopefully representative of
the wide swings in ambient dry bulb and dew point temperatures that
such a tower would see in a typical year. In this section the thermal
performance is described. The acoustics results are presented in
Section 5.0 and plume studies are given in Section 6.0.
The tower test facility has the capability of acquiring thermal data
leading to the deduction of wet fill mass transfer coefficient, water
loss rate, dry heat exchanger air-side heat transfer coefficient and
fan performance. The tower is also equipped to measure airflow dis-
tribution at the inlet (dry heat exchanger) face and at the outlet
(drift eliminator discharge) face of the energy transfer portion of
the tower. During tests it was found that the air velocity measuring
instrumentation (Kiel probes) were inadequate to accurately measure
the airflow and so plans to study airflow distribution were abandoned
early in the program.
So that the reader may properly understand the tests performed and
their significance, this section includes a description of thermal and
flow instrumentation, data acquisition techniques, data reduction pro-
cedures and a thorough analysis of the reduced data.
13
-------
Dwg. 7697A65
Figure 4.1-1. Mercury Manometer Used to Cali-
brate the Ellison Annubar Water
Flow Meter.
Figure 4.1-2.
Ellison Annubar Water Flow Meter
in its Insulated and Heated
Housing.
-------
4.1 THERMAL AND FLOW INSTRUMENTATION
Total flow of water to the tower was measured with an Ellison Annubar
flow meter. This instrument outputs a pressure signal which is related
to total water flow. This pressure was measured in two ways. The first
was via a Taylor Instrument electronic flow meter housed in an insulated
and thermostatically-controlled instrument box adjacent to the inlet
piping containing the sensor. The 10 to 50 ma signal from the electronic
flow meter was automatically logged by the Fluke model 2240B data logger
located in the control trailer. The second measurement was made with a
50-inch "U" tube manometer with a 2.95 specific gravity fluid. This
manometer was located in the control shed (see Appendix A) adjacent to
the inlet flow pipe. Leads from the sensor to the instruments were
heat taped and insulated. The manometer was used to calibrate the
electronic flow meter and was used as a backup instrument in case of
failure of the electronic instrument. The manometer and electronic
flow meter are shown in Figures 4.1-1 and 4.1-2, respectively.
Water flow to either side of the tower was balanced by maintaining the
same water depth in both basins above the wet fill. For wet/dry testing,
where part of the water flow in each side was diverted to the dry heat
exchangers, the flow split was first balanced in the wet fill basins.
Then portions of the water were diverted to each dry heat exchanger,
adjustments being made to this diversion until the wet fill basins
showed identical, lower water depths. The volumetric flow of water
through the dry exchangers was measured with a Statham model PM230
strain gage differential pressure transducer connected between the
upper and lower headers of the exchangers. A second "U" tube manometer
was used to calibrate this transducer and as a backup instrument. Cal-
ibration of this flow was obtained by diverting all flow to the dry
exchangers and then using the total water flow instrument, the Ellison
Annubar, as the primary instrument for water flow in the exchangers.
15
-------
Figure 4.1-3. Photograph of the Kiel Probe Rake
at the Fan Stack Inlet.
Dwg. 7697A66
Figure 4.1-4. Photograph of the Wafer Switch Con-
trol for Kiel Probe Pressures (See
Figure 4.1-6 for Schematic).
-------
The total airflow measuring system consisted of two 17-feet-long pressure
rakes mounted on the intake of the fan, as shown in the upper center left
of Figure 4.1-3. Each rake held five Kiel probes which were connected
by tygon tubing, wrapped in heat tape and insulated in a conduit, to an
electrically-operated fluid wafer switch, shown in Figure 4.1-4. The
tygon leads were connected to a single pressure transducer through the
wafer switch which was stepped from one pressure port to the next by a
signal from manual controls in the control trailer where the data logging
equipment was located. The transducer output was displayed on a Data-
metrics model 1014A electromanometer located in the control trailer,
shown in Figure 4.1-5. To maintain the tygon lines clear of conden-
sate and sediment, a second stepped fluid wafer switch was connected
between the tubing and a 9 psig air supply. For 10 seconds prior to a
pressure being measured through the first wafer switch, the second
switch opened and allowed the supply air to clear the tygon line of
contaminants. When the 10 second purge had ended the second wafer
switch closed to isolate the sensor probe from the purge air and the
first wafer switch opened to connect the probe to the sensing transducer.
A 10 second settling time was allowed before the transducer pressure
signal was logged. Figure 4.1-6 is a schematic diagram of the probe/
wafer switch/purge air system.
Most temperature measurements in this system were obtained with copper-
constantan thermocouples, while air moisture content was measured with
Foxboro model 2711TG dewcells. A thermocouple in the wet fill had its
junction located at the throat of a small plastic water-collecting
funnel to isolate the junction from the airstream. Thermocouples used
to measure air dry bulb temperature were located in short sections of
plastic piping whose axis was aligned with the direction of airflow.
The piping contained a baffle system which intercepted and removed water
droplets before they could impinge on the junction. It was very impor-
tant that the airstream did not impinge on the wet fill water junctions
and that water droplets did not collect on the airstream dry bulb
17
-------
00
Figure 4.1-5. Electromanometer Used for Pressure Figure 4.1-7. Fluke Model 2240B Digital Data Ac-
Measurement. quisition System.
-------
Dwg. 7697A68
VD
To Rake
(Total)
Barometer
Cell
Electro
Manometer
To Rake
(Static)
Figure 4.1-6. Schematic Diagram of the Fan Stack Air Velocity Measuring System's Probe/Wafer Switch/
Purge Air/Pressure Transducer System.
-------
TABLE 4..1-1
LOCATIONS OF THERMOCOUPLES, DEWCELLS AND THERMOMETERS
32 Thermocouples in the fill
10 Thermocouples on the west heat exchanger
10 Dewcells on the west heat exchanger
2 Thermocouples on east heat exchanger
2 Dewcells on the east heat exchanger
10 Thermocouples at the drift eliminator exit, west
10 Dewcells at the drift eliminator exit, west
5 Thermocouples at discharge of fan stack
5 Dewcells at discharge of fan stack
1 Thermocouple in hot water inlet pipe
1 Thermocouple in hot water basin
2 Thermocouples in heat exchanger outlet, west
1 Thermocouple in cold water return
10 Thermocouples at inlet louvers, air discharge from HX
2 Thermocouples at inlet louvers, air discharge from HX, east
2 Thermocouples on pole near test trailer for ambient
2 Dewcells on pole near test trailer for ambient
2 Mercury bulb thermometers, one at each manometer
20
-------
junctions as both perturbations produce significant error in the measur-
ed temperature. A few temperature measurements were made with mercury
bulb thermometers. Table 4.1-1 gives the number and location of thermo-
couples, dewcells and thermometers. The thermocouples and dewcells were
connected directly to a Fluke model 2240B data logger located in the
control trailer and shown in Figure 4.1-7. Thermometer readings were
hand typed on the data logger tape when all automatically-acquired data
had been logged (see Section 4.2).
Fan motor current and supply voltage were monitored in the control shed
on an ammeter and voltmeter, respectively. A 20:1 current transformer
and 35:1 potential transformer reduced the current and voltage to 1.8
amperes and 120 volts, respectively, thus allowing the use of an Ester-
line Angus model AW, 0 to 1000 watt, recording, two-element A.C. watt-
meter. The wattmeter was located in the control trailer. Values taken
from the current, voltage, and wattage indicating instruments were hand
tabulated, then typed onto the data tape after automated data logging
was complete.
Fan speed was measured with a proximity sensor, amplifier, and a Veeder
Root electronic counter. The proximity sensor was triggered once per
revolution of the fan and the counter integrated those triggers for 60
seconds. Values from the speed counter were tabulated and then typed
onto the data tape.
The primary measuring instrument was a Fluke 2240B data logger. The
microprocessor controlled data logger was programmed through front panel
push button switches to execute an exact measurement routine. The Fluke
instrument measures voltage to 1 microvolt (lUv) and temperature to
one-tenth degree (.1°) Celsius or Fahrenheit. Measurements are displayed
on light-emitting diode front panel digits, printed copy, and through a
teletype on punched paper tape. An internal digital linearization module
permits temperature to be recorded directly in degrees. The final system
21
-------
configuration allowed 120 channels of analog data to be input to the
data logger.
4.1.1 Instrument Calibration Procedures
Gross flow calibration is discussed in Section 4.1. The Ellison Annubar
was calibrated by the manufacturer. The Datametrics electronic mano-
meter and Fluke data acquisition systems were calibrated by their manu-
facturers at the time of delivery. Fluke specifies "system accuracy"
(includes all instrument errors such as A/D error, scanner error, power
supply internal warm-up, etc.) at:
90 days (20° to 30°C) +.01% RDG + .005% RNG + 3 yV (slow speed)
1 year (15°C to 35PC) +.02% KDG + .01% RNG + 5 yV (slow speed).
Reference stability is +.003%/°C and +.003%/hr.
The temperature and scaling option when used with the high resolution.
A/D converter produces a system specification of .1°F resolution. For
type T (copper-constantan) thermocouples operating in the temperature
range of 32°F to 750°F worst case resolution is .1°F, NBS nonconformity
is ,1°F, 90-day system accuracy is ,6°F, and one-year system accuracy
is .8°F. No attempt was made to recalibrate the data acquisition system.
The Datametrics Electromanometer was calibrated daily using an internal
reference for range and zero. Manufacturer's specifications indicate
linearity: +.01% F.S., zero coefficient: +5PPM/°F, sensitivity coef-
ficient: +30PPM/°F. These specifications apply only to the 1014-A
power supply and signal conditioner.. The "barocell" is calibrated at
10 TORR F.S. Worst case linearity (from the barocell calibration re-
port) is .01% at 1 mm Hg. System accuracy is therefore +.0002 mm Hg.
Dew cells were calibrated by the manufacturer. No attempt at recalibra-
tion was made during the test.
22
-------
Fan motor current and supply voltage were measured on standard analog
meters. These meters are accurate to +2% F.S. No calibration was
attempted. Fan power was measured on an Esterline-Angus wattmeter which
was calibrated at the factory. Stated accuracy is +1% F.S. over the
temperature +20° to 120°F.
The fan speed was measured on a digital electronic counter which used
power line frequency for a reference. Since power line stability is
better than .05% and digital resolution is 1 RPM, fan speed error was
less than +1 RPM.
4.2 DATA ACQUISITION AND TRANSFER
The procedures used to start up, shut down and run the tower test facility
are quite detailed. They are not truly germaine to data acquisition but
in the event the test facility is ever used again, they would be of great
value. Therefore the startup and shutdown procedures are listed in
Appendix B. Likewise, the detailed procedure used to run the facility
during data acquisition is presented there.
When the facility operators had ascertained that the proper test condi-
tions were set, the actual procedure for acquiring thermal and flow
data was initiated by taking the data on fan stack pressures. The wafer
switches which connected the Kiel probe signals to their pressure trans-
ducer were stepped through 11 positions, each time waiting 10 seconds
for the decay of pressure line transients. The output was displayed on
the electromanometer and entered into the Fluke data logger. One chan-
nel of the 11 was the null signal from the transducer, one was a static
pressure in the fan stack entrance and the remainder were velocity
pressures (total minus static pressure) from each of nine Kiel probes.
After logging air velocity data the data logger was allowed to sequence
through the automated acquisition of temperature and water flow pressure
drop data, a total of 110 channels. Finally, when the automated se-
quence was complete, facility operators hand-typed 18 channels of data
23
-------
TABLE 4.2-1
SAMPLE OF RAW TOWER DATA FROM A DRY HEAT EXCHANGER TEST
u 322 12
119:03:50 '.22
322121
0 - 0.001 *
us :oq:5o:32
322121
0 * 1.525 J
322121
0 * 1.762 V
322121
o + 5.i?2 y
i is: 08:5i : 06
322121
0 + 2.348 ^
ii5:c.n:5i: 12
322121
0 •* 2.050 V
ns:os:5i:i7
322121
0 + 1.552 V
us: cs:5i;22
322121
0 + 1.542 V
119108:51:32
322121
0 + 2.277
-------
Table 4.2-1 (cont'd)
322121
0 * 2.175 y
119:C8t5l:52
322121
10 +
14 •*
18 +
22
26 •*
30 +
24 4
38 4
42 +
46 +
50 4
54 *
58 +
62 +
66 +
70 *
74 +
78 •»
82 •#
86 *
SO +
S4 4
58 +
102 +
106 *
110 +
114 +
lie +
81,4 F
60,3 F
86,0 F
QL F
60,9 F
61.1 F
81,8 F
103.2 F
104,6 f
67.6 F
68,8 F
70,4 F
66,9 F
67.2 F
66.2 F
68.6 F
77.9 F
77,8 F
74.0 F
76.4 F
107.1 F
78,3 F
77,1 F
80.0 F
106,9 f
103,9 F
75.0 F
1.98HV
11
15
IS
23
27
31
35
39
43
47
51
55
63
67
71
75
79
83
87
91
95
Q O
s j
103
107
111
115
4-
4
4
4
*
4
4-
4
+
4-
4
4
4
4-
4
4
4
4
4
4
4
4
4
4
4
4
4
104,1 F
61,4 F
107.4 F
105.5 F
50,0 F
61.4 F
104,6 F
115.3 F
103,6 F
69,6 F
76.6 F
77.6 F
66.9 F
67, C F
66,6 F
69,9 F
65.8 F
77,5 F
72.2 F
55,5 F
110.0 F
78.7 F
74, S F
79,0 F
108.6 F
104.1 F
74.9 F
12
16
20
24
28
32
36
40
44
48
52
55
60
64
63
72
76
80
81
88
92
96
100
104
103
112
116
4-
4
-4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
,4
4
102.3
105,6
117,7
104,0
50.9
61.2
107,8
117,0
104.4
69.6
67.1
69,2
69.0
67,9
67.2
70.?
67.7
78.3
78,0
112,8
8T
77,4
78.0
74.2
67,3
50.0
63.2
F
F
p
F
F
F
F
F
F
F
F
F
p
F
F
F
F
F
F
F
F
F
F
F
F
F
F
13
17
21
25
29
33
37
41
45
49
53
57
61
65
69
73
77
81
85
89
93
97
101
105
109
113
117
•«•
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
105.1 F
104.3 F
104.3 F
60. ,« F
€1.4 F
82.0 F
15.6 F
105,4 c
€8.1 F
78.2 F
77.5 F
65.3 F
62.5 F
59.4 F
69.7 F
65.8 F
78.7 F
77,8 F
77.5 F
111.6 F
104.1 F
75.7 f
77.7 F
58.3 f
67,3 F
63. c F
BT F
119:03:54:43
322
118 +
118 4
118 4
118 +
118 *
121
l,64Htf
1.82NV
1.94MV
2,04f«y
1.76MV
118
118
118
118
118
4
4
4
4
4
1.83MV
1.84MV
1.70MV
2.14HV
1.99HV
118
118
118
118
118
4
4
4
4
4
1.92HV
1 .79
1,80
2.0£
1»91
y V
N V
FV
HV
118
118
118
118
118
4
4
4
4
4
1.73MV
1.85FV
1.97FV
1.92PV
2.Q7PV
(Continued)
25
-------
Table 4.2-1 (cont'd)
ns:oa:55:i6
322121
119
119
119
119
119
12C
126
132
+ 42.
+ 43.
+ 44.
•» 46.
+ 42.
4090.
35.5
15.0
57P y
03MV
35P.V
22MV
69PV
121
127
133
119
IIS
119
119
119
44.
7.2
60.0
* 41.
+ 44.
+ 44.
+ 46.
+ 42.
0 122
128 5
134
52MV
22MV
03?*V
91MV
30 KV
44.
.5
127.
119
119
119
119
119
0 123
129 65
135
+ 42
+ 39
+ 45
+ 44
+ 44
43.
.0
12.
• 54P1V
• 54^V
»9°WV
• 39VV
,67MV
0 124
130 2.
136 .
119
119
119
119
119
36.5
95 1
20D
* 44.
+ 43.
+ 43.
+ 43.
+ 43.
125
31 15
137 3
53WV
37f*\(
80I«V
72(«\l
16^V
36.0
.0
0.22
iis:oe:57:29
26
-------
which had been read from isolated instruments. This sequence was
followed for five sets of data at every set of test conditions.
Table 4.2-1 is a listing of a typical run. The figure 322121 which
appears throughout the data is the test number; the first digit indi-
cating this was a dry heat exchanger test, the second indicating it was
run in the spring, the third, fourth and fifth digits indicating test
conditions (water flow rate, airflow rate) and the last digit indicating
this is the first of five runs under these conditions. Also scattered
throughout the data are the characters 119:xx:yy:zz, where 119 indicates
data was acquired on the 119th day of 1978 and xx:yy:zz is the time of
day in hours, minutes and seconds. As for other entries in the sample
data, Table 4.2-2 lists their definitions. Note that channel 118, the
output from the pressure transducer between the top and the bottom of
the dry heat exchanger, and channel 119, the output from the Ellison
Annubar flow meter, are logged 20 times so that they may be averaged. The
data for channels 120 through 137 were hand-typed, the data having been
previously logged manually from separate individual instruments. When
all five runs at a given set of conditions had been logged, a duplicate
punched paper tape was made to insure its availability when the master
punched tape was forwarded by mail to Westinghouse Fluid Systems Lab-
oratory (WFSL) for analysis.
Before describing the reduction and correlation of data, mention should
be made of the condition of the raw data as received by the analyst and
how it was processed. Recall that thermal and flow data were acquired
at the test site using a combination of automated acquisition and hand-
typed input of visual readings of instruments. The data for a given run
were transferred to the analyst on punched paper tape. The control
characters generated by the data acquisition equipment were not compat-
ible with the computer (Purdue University CDC6500) used to reduce the
raw data. Consequently, each raw data tape received from the tower site
had to be processed by a minicomputer (PDP-8E) which read raw tapes,
sensed control characters and produced a new data tape with CDC-compatible
control characters. The translated tapes were then used with the
27
-------
TABLE 4.2-2
DELINEATION OF INPUT PAPER TAPE DATA BY CHANNEL
FOR THERMAL AND FLOW DATA
Channel Description
0 11 repetitions of time, run ID, and fan stack Kiel probe
pressure transducer output. The first grouping contains the
transducer's zero, Group 2 and 3 are velocity pressures, 4 is
a static pressure, and the remaining are velocity pressures.
10 Tower basin cold water return temperature
11-13 Heat exchanger air inlet dewcell temperature
14-15 Heat exchanger inlet air temperature
16-17 Heat exchanger inlet air dewcell temperature
18 Tower hot water inlet temperature
19-21 Heat exchanger inlet air dewcell temperature
22 Not used
23-24 Heat exchanger inlet air dewcell temperature
25-32 Heat exchanger inlet air temperature
33-34 Heat exchanger outlet water temperature
35-44 Wet fill outlet air dewcell temperature
45-57 Fill water temperature
58-59 Ambient air temperature
60-76 Fill water temperature
77-86 Wet fill outlet air temperature
(Continued)
28
-------
Table 4.2-2 (cont'd)
Channel Description
88 Not used
89-93 Stack exit air dewcell temperature
94-98 Stack exit air temperature
99-105 Fill inlet air temperature
106-107 Ambient air dewcell temperature
108-109 Fill water temperature
110-117 Not used
118 Dry heat exchanger pressure drop transducer
119 Annubar element transducer
120 Tower voltage (v)
122-126 Tower pump amperage (a)
127 Annubar manometer column rise above datum (in)
128 Annubar manometer column fall below datum (in)
129 Annubar manometer ambient temperature (°F)
130 Manometer fluid specific gravity
131 Dry heat exchanger manometer column fall below datum (in)
132 Dry heat exchanger manometer column rise above datum (in)
133 Dry heat exchanger manometer temperature (°F)
134 Fan rotational speed (rpm)
135 Fan pitch (degrees)
136 Fan power (reading x 700 = kw)
137 Barometric pressure (in Hg)
29
-------
Dwg. 7697A69
dx
L
T
w
dy
dz
T.
Figure 4.3-1. Wet Fill Heat and Mass Transfer Control Volume.
30
-------
reduction program described in Section 4.3. The reduction program pro-
duced both paper output and punched cards containing reduced data.
These data cards were segregated and sorted as to test type (wet, wet/
dry, dry, fan, short fill) and test number so that ultimate correlations
could be obtained without unnecessarily handling extraneous data.
As for the condition of the raw data, it left a lot to be desired from
the standpoint of completeness and usability. In particular, a run
contained 137 pieces of test data, the first 119 coming from automated
acquisition and the remaining 18 from hand-fed data. The last 18 pieces
were generally so inconsistent that each had to be scanned by the ana-
lyst and, in almost all cases, corrected because of some obvious error.
This could be done because each test point was repeated five times and
visual scanning showed that, perhaps in one run, the data in question
was incorrect, possibly due to digit transposition or dropping of a
digit. In many cases, the data were so inconsistent from run to run
that it all had to be thrown out. In many cases, one or two runs out
of five were deleted because of the very large number of incorrect or
missing pieces of data in each set. As a consequence, although the
test schedule (Section 4.4) shows that a total of 2760 separate runs
were to be made, only 1399 or 51 percent were recoverable by the analyst.
4.3 THERMAL AND FLOW DATA REDUCTION
4.3.1 Tower _Hea_t and Mass Transfer
Consider the control volume in Figure 4.3-1. Water enters the top of
the volume at L lbm/hr-ft2 and some temperature, Tw. Air with specific
humidity wa and temperature Ta enters from the side with a mass velocity
of G. The energy entering the control volume is
Ghadzdy (4.3-1)
Using a first order Taylor series to estimate the energy out of the
control volume yields,
31
-------
3L 9Tw
E = Cp (L + |^ dy) (T + r-2 . , . .
o w 3y w 9y dy) dxdz
3h
~^dx) dydz (4.3-2)
and steady state requires that
EQ - Ei " ° • (4.3-3)
Substitution of (4.3-1) and (4.3-2) in (4-3.3) gives
3T 9h 3T
CPW^ - -[6j^+<*A^] (4.3-4)
where second order terms have been dropped. The last term on the right-
hand side of (4.3-4) is usually neglected. This can be justified by first
recalling the definition of moist air specific enthalpy,
ha = Cp T + w h . (4.3-5)
a ra a a v
Differentiation yields,
3h 3T
The 9Cp /3x and 3h /3x terms have been neglected since they are very
small relative to the other terms in (4.3-6). From conservation of mass
it is known that,
at 3t°a
Substitution of (4.3-6) and (4.3-7) into the right-hand side of (4.3-4)
results in,
32
-------
9h 3T 9u)
*T + CPwTw If = G [Cpa fcT + *T (hv + CPwV] ' (^3-8)
Since the water vapor specific enthalpy is at least an order of magni
tude greater than the specific enthalpy of the water, CpwTw can be
dropped from (4.3-8). With this simplification it becomes
9h .T 9Ta
G + G K G
It can be seen that the right-hand side of (4.3-9) is the space deriva-
tive of the air specific enthalpy [refer to (4.3-6)]. Equation (4.3-9)
can, therefore, be rewritten as,
3h a, 9h
G —- + Cp T ~ * G ^-S. . (4.3-10)
9x rw w 9y 9x '
Replacement of the right-hand side of (4.3-4) with that of (4.3-10)
yields the desired simplified result.
9T 9h
CpwL-9 = "G9lT ' (4.3-11)
To get an expression for the mass transfer coefficient or tower transfer
units in terms of measurable variables consider a deformable control
volume whose surface corresponds to that of a water droplet. Conserva-
tion of energy requires
3U
9~ = q (4.3-12)
where U is the water's internal energy. Using the chain rule of dif-
ferentiation on (4.3-12) yields the more useful expression,
33
-------
3U 3U ,
w w dy
~ = ' (4.3-13)
Recall that
U = m Cp (T - T ,) (4.3-14)
w w *w v w ref '
where Tre£ is some reference temperature. Substituting (4.3-14) in
(4.3-13) and performing the required differentiation results in.
3U 8m 3T
at2 =
Usually the water loss term (9m /3y) is neglected since it is small
W
relative to the other terms. This can be seen by casting (4.3-15) into
a different form. First, note that
3m 3d)
-— - = -m r-3- . (4.3-16)
3y a 3x
Using
g
m = — m (4.3-17)
a L w
in (4.3-16), and that result in (4.3-15) gives the desired expression,
3U 3T (T - T
"
_ W
3y
An order of magnitude analysis on the second term within the braces in
(4.3-18) shows it to be on the order of .05. Hence, it can be dropped
from (4.3-18),
34
-------
3U 3T ,
T-^ = m Cp -r-£ SZ. . (4.3-19)
3t w *w 3y dt
Equation (4.3-19) can be made more useful by realizing that,
V = L (4.3-20)
w dt
and, as a result, (4.3-19) can be written as,
3U 3T
^~ = mwCpwVw^T ' (4.3-21)
As a means of eliminating the need for details of the water droplets
(4.3-21) can be put into a per unit volume basis. Substitution of the
result into (4.3-12) yields,
m 3T
Now since
m
w
= P V = T~
w w V
(4.3-22) can be rewritten as,
3T
q'" = CpL^-2. . (4.3-24)
The expression for q111 must account for both sensible and evaporative
heat transfer. A Newtonian type of expression is commonly assumed,
q'" = Kg • a •• (Ta - Tw) + Ka (wa - MW) hfg (4.3-25)
35
-------
where a is the droplet surface area per unit volume, Kg the sensible
heat transfer coefficient, and K the mass transfer coefficient. Note
that the water droplet temperature is assumed uniform. The subscript
w on CD and T indicates conditions at the air-water interface, assumed
saturated.
Heat and mass transfer may be related under certain conditions . This
presumes the heat and mass transfer to be related in the following
fashion,
Kg = LenCpmaK (4.3-26)
where Len is the Lewis number to some power (approximately two-thirds
for turbulent flows). For water vapor-air mixtures at moderate temp-
eratures the Lewis number is approximately unity; as a result, (4.3-26)
can be approximately written as
Kg - Cp K . (4.3-27)
ma
Substitution of (4.3-27) into (4.3-25) yields
Ka ^ma (Ta " V + (t°a ~ V> V
Substituting
in (4.3-28) and expanding yields,
[(CpaTa + «oCpwTa + a,ahfg)
(4.3-30)
36
-------
The to which appears in (4.3-30), and originally in (4.3-29), is the re-
sult of applying the heat and mass transfer analogy. It is a property
which describes the transport process across the boundary layer. It is
not clear whether the freestream (cua), interfacial (o>w), film (w +ui )/2,
or any other fraction between the freestream and interfacial specific
humidity is the characteristic specific humidity. A common, and usually
satisfactory estimate is the film specific humidity,
w - 2 . (4.3-31)
If (4.3-31) is used in (4.3-30) and the result rearranged, one finds
that,
q"1 = Ka [Cp T + u Cp T + w h£ ]
ra a a rwv a a fg
-Ka [Cp T + u) Cp T + to h. ]
aw w *wv w w fg
+2 CPwv [Ta + Tw][a)w - wa] Ka ' (4.3-32)
The first two bracketed terms on the right-hand side of (4.3-32) are
the air freestream and interfacial enthalpy, respectively. As a result,
q'" = Ka [ha - hw][l + e] (4.3-33)
where
Cp [T + T ][co - o> ]
2 *wv a w'L j
a w
w
. (4.3-34)
e is dominated by the difference in specific humidities. An order of
magnitude analysis of (4.3-34) indicates e to be on the order of .03.
As a result, e can be neglected relative to unity, and, consequently,
Equation (4.3-33) simplifies to,
37
-------
q'" = Ka [ha - hw] . (4.3-35)
Substitution of (4.3-35) into (4.3-24) yields the expression for the
tower mass transfer coefficient,
3T
= Ka (h- • (4-3-36)
The number of transfer units (NTU) can be calculated from,
NTU = /l . (4.3-37)
Jj
o
If Ka is assumed constant throughout the tower, then
NTU - ~L . (4.3-38)
Since the functional relationship between Ka (or NTU) and Tw, ha, h^
is unknown, Equations (4.3-11) and (4.3-36) must be solved implicitly
for Ka. The data obtained from the tower provides the lacking process
information so that Ka may be determined.
4.3.1.1 Wet Fill Heat and Mass Transfer Computation
4.3.1.1.1 Computation of Ka
Since neither the air nor the water thermodynamic process is known
analytically in the wet fill, it is necessary to start in one corner of
a two-dimensional representation of the fill, where the air and water
states are known, and numerically march across the tower. The tower
is first divided into small rectangles. A Ka is then assumed. Inlet
air enthalpy and water temperature are known. An average water temper-
ature, air enthalpy, and a saturated air enthalpy corresponding to the
38
-------
average water temperature is estimated. Equation, (4.3-36) is solved for
the vertical water temperature gradient. That result is used in (4.3-11)
to calculate the air specific enthalpy gradient (with respect to the
air streamwise coordinate) . Knowledge of the water temperature and air
enthalpy gradients enables the outlet states from the rectangle to be
computed, as well as new averages. With the new averages available, the
solution of (4.3-36) and (4.3-11) is repeated. The solution is consider-
ed complete when the water exit temperatures of two iterations are
essentially identical. The entire procedure is repeated for each grid.
After all of the grids have been solved, an average fill water outlet
temperature is computed and compared to the actual recorded outlet
temperature. If they are not within the desired accuracy a new Ka is
assumed, a solution for all grid points obtained, and a new average
outlet water temperature acquired. This new temperature is compared
to the experimentally acquired value, hopefully with less error than the
first. If necessary, the process is repeated until the calculated value
is sufficiently close to the actual temperature. The Ka which enables
convergence to occur is the sought-after value. In the remainder of
this section the numerical technique will be developed mathematically.
Consider Figure 4.3-2. Since the air and water flow rates, as well as
their properties, are assumed uniform across their respective inlets,
the wet fill can be considered two dimensional. Consider now a Taylor
expansion about some point (x,y)
f (x + Ax,y) = f (x,y)
where e is the remainder of the Taylor expansion. It represents an
error which is of Ax2 order. (4.3-39) can be rearranged to,
jf (*.y) _ f (x + Ax.y) - f (x,y) _ £ 3
3x Ax '
39
-------
Dwg. 7697A70
1
Tw,i
i J-l
2,1
1,1
Figure 4.3-2. An Illustration of the Two-Dimensional Representation of
the Wet Fill and its Grid Structure.
40
-------
It can be seen in (4.3-40) that a derivative can be approximated by a
ratio of finite differences within an error of order A2. To use this
result (4.3-36) must first be solved for the water temperature gradient,
3T Ka (h . . - h . .)
w a, 1,3 w,i,3 .
(4.3-41)
and then (4.3-40) applied to the result,
Similarly for (4.3-11),
3T
(x,y + Ay) = ~- Ay + Tw(x,y) (4.3-42)
3T
3h Cp L -T--
-i . - wp *? (4.3-43)
9x G
h& (x + Ax,y) = —• Ax + ha (x,y) . (4.3-44)
h - h , the driving potential for mass transfer, is a function of the
a w
spatial coordinates. Since the finite difference technique jumps from
one point to another A away, the driving potential must be representa-
tive of conditions between points. Consider, for example, Figure 4.3-3.
Assume for the sake of argument that the integration process is proceed-
ing from coordinates (x.,y.) to (x.,y. + Ay) across element i,j. Con-
ditions are known at (x.,y. + Ay) after the solution is complete. Con-
"*• J
ditions within the element, however, are unknown. The properties of
element i,j are best approximated by some average of the boundary values,
In this work the driving potential appropriate for element i,j was
taken to be the difference in average enthalpies, computed as follows:
41
-------
Dwg. 7697A71
Node
Node
AX
6
6
Node
J*. v
i 2 ' yj
Node
(x. ^
Figure 4.3-3.
Typical Wet Fill Grid and Nomenclature Employed
in Defining the Temperature of the Grid i,j.
42
-------
T (x.,y. + Ay) + T (x.,y.)
T = *...-* 13 11 w * °J (4.3-46)
hw -
Equations (4.3-41) through (4.3-47) constitute the set of equations which
must be solved for each element. The integration starts with element
(1,1) [Figure 4.3-2] and proceeds downward until all elements in that
column are used. It then continues with the top of the next column,
(2,1), and works its way down again. The only restriction on the step-
by-step progression through the tower is provided by the boundary con-
ditions. The upper and right-hand side edge of each element must have
T and h , respectively, specified for a solution to be possible. The
W 3,
following steps were followed in calculating Ka:
1. Ka is assumed based on experience.
2. The boundary values for Tw and ha are set. (Tw = Tw -^
on y = 0 and ha = ha>in on x = 0) .
3. Start grid solution: i = 1, j = 1.
4. An estimate of Tw (x£,yj+Ay) and ha (x-j+Ax/2, y^+Ay/2)
is assumed (refer to Figure 4.3-3). J
5. Based on Tw (x. ,y-s+Ay), h^ (x. ,y.+Ay) is calculated from
(4.3-46). X * J
6« ha,i,j is calculated from (4.3-45).
7. Equation (4.3-41) is evaluated for 3T ./9y.
w, 1, j
8. Equation (4.3-42) is calculated for a refined value of the
exit water temperature, T1 (x£,y.+Ay)
w j
9. 9ha>i j/9x is calculated from (4.3-43).
43
-------
10. (4.3-44) is evaluated for a refined version of the exit
air enthalpy, h^ (x.j+Ax/2, yj+Ay/2).
11. A check is made as to whether
TW
or (4.3-48)
- T' (x-»y,+Ay)
< •°0001
c.)
Three actions can result from (4.3-48).
(a) True. Convergence has been obtained, the grid solution
is complete. Let
T- / • Ax , Ay-. . , , , Ax . Ay,.
ha (xi + T ' yj + 2 } = ha (xi + ~» 7j + 2 }
(4.3-49)
Tw ^i'
Increment j if possible. If not, then increment i and re
index j to 1 (i.e., start again at top of next downstream
column.) Repeat steps 4 through 11.
(b) False. Convergence has not been achieved yet. A better
estimate1 of TW (xi?yj+Ay) and ha (x^H- x/2,y.+Ay/2) is
made. Steps 5 through 11 are repeated.
(c) True. Convergence has been achieved at all grid points.
If M is the maximum number of i increments and N the max-
imum j, then the average fill outlet water temperature is
calculated from
44
-------
If
M
T1 — •— £
w,o,avg " M . .
lTw,o,avg * Tw,o,avg' < '01 C4.3-50)
or
w,o,avg
where TWjQjavg is the actual water temperature obtained
by ' ' experiment*, then the assumed version of
Ka is considered correct and the tower solution complete.
If (4.3-50) is false, then a better estimate of Ka is per-
formed and steps 2 through 11 repeated. The Secant
method2 is employed in obtaining the correct Ka for a given
Tw,o,avg-
4.3.1.1.2 Calculation of Grid Size
Since this data reduction program was to be used a great many times, it
was important that the grid size be no finer than necessary for the
desired accuracy in Ka. This section presents the technique utilized
in calculating the grid size. In fallowing the derivation, first con-
sider Figure 4.3-2 and the following approximation for the water temp-
erature gradient,
- T(Xl,y2)
w
3y Ay
(Ay) (4.3-51)
*The fill outlet water temperature was acquired by averaging the bottom
fill thermocouples, whereas the inlet water temperature was taken to be
the measured distribution basin temperature. Air-side inlet conditions
were computed from the average of the fill inlet dry-bulb and dewcell
temperatures, from which specific enthalpy can be calculated.
45
-------
where e is the truncation error (or order Ay), and x , y , y arbitrary
vertical coordinates, (4.3-51) can be obtained from a Taylor's expan-
sion, e.g., solve (4.3-39) for 3f/3x. Using (4.3-36) in (4.3-51) to
eliminate the temperature gradient yields,
Ka[h (xltyi) -
Ay
Solving for e (Ay),
- T (x1>y2) Ka[h (x1>yi) - h (x1>yi)] (4.3-53)
e(Av) = ~ _ v
For the error to be zero, the following must be true,
, Ka[h (Xl,yi) - h (Xl,
_ (4.3-54)
Ay LCp
or since Ay = Y/N,
KaY [ha(Xl,yi) - hw(Xl,yi)]
[Tw(Xl,yi) - Tw(Xl,y2)] (4.3-55)
The number of air streamwise divisions (M) can be calculated in a
similar fashion,
Tw(xi,yi) - T (xi,y2) LCp dN
M = [ 7—r- c ~f r 1 —~r~ (4.3-56)
) GY
To allow for more flexibility (4.3-55) was multiplied by an experimental
multiplication factor Xmf,
46
-------
Xmf K-a-Y [ha(Xl,yi) -
-Tw(Xl,y2)] (4-3-57)
Figure 4.3-4 shows the effect of Xmf on computation time and accuracy.
Note that the error in the figure is dimensional and relative to a Ka
calculated for Xmf = 2.0, a value for which subsequent increases produced
only small and random perturbations to Ka. Clearly the accuracy improves
very little for Xmf > 1, and at great expense. All data reduction for
this work was performed with Xmf = 1, considered to be a good tradeoff
between accuracy (approximately 2 percent) and run time (about 7 seconds) .
For each set of data both M and N were calculated. To evaluate N, Ka
was estimated from
.599_.438
T._.
Ka = '° 2.04- - (4.3-58)
Tw,i '
which is an expression developed in previous years by the Fluid Systems
Laboratory. hw(xi,yi) [Equation (4.3-57)] was based on inlet water con-
ditions, h (xj,yi) on fill inlet conditions, h (x^.yi) on the air state
at the fill outlet, and the water temperature difference in the denom-
inator of (4.3-57) and numerator of (4.3-56) were taken to be the difference
in the inlet water temperature and the average of the first array of
fill thermocouples. M and N were calculated for each Ka. In this way
accuracy as well as good utilization of computer time was maintained.
4.3.1.2 Heat Exchanger Heat Transfer Analysis
This section presents the heat transfer analysis utilized to determine
the heat exchanger air-side heat transfer coefficient from the tower test
data. Figure 4.3-5 should be referred to for tube and fin nomenclature.
The total heat transfer rate from the tower heat exchanger can be cal-
culated from
47
-------
Curve 717153A
1.0--0 Xmf = .7
8
10 11 12
Run Time (sec)
13 14 15 16
Xmf =2.0
{O—~
Figure 4,3-4, Error in Mass Transfer Coefficient as a Function of Compu-
tation Time and the Experimental Multiplication Factor.
= Ka (Xmf = 2.0) - Ka (Xmf)
48
-------
Dwg. 7697A72
'of
DL D
o,t
/ /
/ /
Figure 4.3-5. Tower Heat Exchanger Tube and Fin Geometry, and Nomenclature
Employed in the Heat Transfer Analysis.
49
-------
F • AT
N
q - Z R± (4.3-59)
where
N to[D /D ] *n[D /D J
y p 1 i ___ Q-yt ***•_ c o,t
i H A ?c ^ —
1=1 1 w i,t 2TrktLt
co fa
Solving for the unknovrn H ,
Si
w i,t
Txr^-rX > } (4.3-61)
:L c o,t
F, the crossflow temperature correction factor, can be calculated from
A
the work of Bowman, et. al. ,
(4.3-62)
ccf
where
and
50
-------
- T
w.o
(4.3-64)
T - T .
^ _ a,o a,i
q " T . - T .
w,z a,i
and
oooo r . \ i m^n
= £ E (-l)m (nHti)I
m=0 n=0
The solution of (4.3-65) for r f is necessarily numerical but once it is
determined, F can be easily calculated from (4.3-62) in conjunction with
(4.3-63) and (4.3-64).
AT ,, the driving potential for heat transfer, is determined from,
(T — T ) — (T — T )
AT = w.i a.o' w.o a.r (4.3-66)
£mtd T . - T
The fin efficiency, n, can be calculated from the work of Gardner1*,
(4.3-67)
where I and I are zeroth and first order modified Bessel functions of
0 1
the first kind, K and K zeroth and first order modified Bessel functions
o i
of the second kind, and
Ii OJ.)
* - <4-3-68>
51
-------
D - D 2H 1/2 D , ~l
r O.t C-, r a-, r O.I n1
[_^_ ] [_] [-^-1] (4.3-69)
k t c
°o f
Ue = Ub HH (4.3-70)
c
Eckels5 provides a means of estimating the collar-to-tube-surface con-
tact resistance,
i .6422
H = 4.51 x 105 { — - £— - } (4.3-71)
Since the water-side heat transfer coefficient is also unknown, it too
must be estimated. The following expression from Sieder and Tate6 was
used to estimate the water-side film coefficient,
All water properties in (4.3-72) are evaluated at the freestream or bulk
temperature, except for y .. which is evaluated at the tube wall.
w,wall
The bulk water temperature was considered to be the arithmetic average
of the inlet and outlet temperature (T ). The wall temperature was
found from,
fT I> J. 'T1 D
T = w.avg o a,avg 1 (4.3-73)
w,wall R + R
where T is the arithmetic average of the air inlet and outlet temp-
a»av§
erature, R , the first term on the right-hand side of (4.3-60), and R ,
52
-------
the sum of the remaining terms on the right-hand side of (4.3-60). q,
the heat transfer rate from the water to the air, is known from,
q = m Cp (T . - T ) (4.3-74)
H a ra a,i a,o
where m , T ., and T are measured values.
B. 3, j 1 3. j O
With Equations (4.3-62) through (4.3-74), the air-side heat transfer
coefficient can be calculated from (4.3-61). Since the fin efficiency
[Equation (4.3-67)] via (4.3-69), and the water-side film coefficient
[Equation (4.3-72)] via (4.3-73) are functions of the air-side heat
transfer coefficient, the solution of Equation (4.3-61) is iterative
with respect to itself, (4.3-67) and (4.3-72).
4.3.1.3 Heat Exchanger Air-Side Heat Transfer Coefficient Computation
The calculation of the air-side heat transfer coefficient is complicated
by the fact that it is a function of the fin efficiency (a function of
the air-side heat transfer coefficient) and the water-side film coef-
ficient (a function of the tube wall temperature and thus a function
of the air-side film coefficient). Nevertheless, the computation is
relatively straightforward. The procedure is as follows:
1. All air properties are computed at the average air
temperature.
2. The heat exchanger heat transfer rate is calculated
from (4.3-74).
3. An average wall temperature and air-side film coef-
ficient is assumed.
4. Fin efficiency (4.3-67), water-side heat transfer coef-
ficient (4.3-72), and the log mean temperature difference
(4.3-66) are calculated.
5. The cross-flow correction factor (4.3-62) is calculated.
[Equation (4.3-65) is solved numerically with the
Secant method2.)
53
-------
6. A refined estimate of the air-side heat transfer coef-
ficient is computed via (4.3-61). Although the air-side
heat transfer coefficient is, in effect, a function of
itself, the dependency is very weak. As a result, only
two iterations on wall temperature (steps 3-6) are usually
necessary to obtain closure. For this work, three
iterations were used to insure a high degree of
computational accuracy.
7. After the required three iterations, the Stanton, Nusselt,
Reynolds, etc. numbers are computed for later correlation.
4.3.1.4 Airflow Rate Analysis and Computation
The tower air flow rate was calculated from velocity pressure measure-
ments at the throat of the stack, conservation of energy considerations,
and from a static pressure measurement at the fan inlet. The objective
was to supplant the velocity pressure data if it was determined to be
unreliable. This can occur because water is often ingested by the probes
as a result of the stack environment. If the water is not purged from
the signal-conveying tubing , it will drastically alter the sensed
pressure. Initially the purging system was unreliable and the alter-
native energy conservation technique for calculating air flow rates was
employed. After the purging system was operating satisfactorily the
velocity pressure measurements were utilized, with the other methods
held as backups.
As noted in Section 3.0, ten pairs of Kiel and static pressure probes
were installed across the throat of the stack. They were circuited such
that velocity pressure was sensed in nine of them, while the remaining
one was set up for a static pressure measurement. The velocity was
calculated from the velocity pressure measurement according to the
following relationship,
(4.3-75)
54
-------
Figure 4.3-6 is a graph of four velocity data sets taken a few moments
apart under steady state conditions. It illustrates two important points.
First, any water trapped in the signal tubing can be readily discerned
by the resulting anomalous velocities, e.g., data points near the stack
wall and centerline. Second, it illustrates the problem of determining
the air flow rate by this method. Under ideal conditions all of the
velocity pressure measurements would be free of error and a simple
radial integration of the velocity profile would yield an air flow rate.
This, however, is not the case in this wet environment. Despite purg-
ing before each measurement, erratic readings did occur periodically in
a given traverse. In almost all instances the bad reading was confined
to one probe station, though the particular station was random. As a
result, the air flow rate was calculated by averaging the measured
velocities. Even though this is not as rigorous as an integral technique,
it tended to dampen the effect of one erroneous reading rather than
amplifying it, as would radial integration.
The second method of determining air flow rate, used for the first tests
during which time the purging system was being perfected, was based on
conservation of energy. Considering the tower as a control volume,
conservation of energy requires that,
m (h - h .) = m (T . - T ). (4.3-76)
a. ^ a,o a, i/ w v w,i w,o'
Solving for the air mass flow rate yields the desired final result,
m (T . - T )
^ - — w w,i w'
m -
- — - r - >r
a ( h - h . )
v a,o a,i
This technique is considered viable because of the very good accuracy
obtainable in measuring water flow rate and the inlet and outlet air
states. Contrarywise, utilization of this method precluded the use of
energy conservation in checking the quality of the data.
55
-------
50--
40.-
30--
20--
10 -
O First Run
D Second Run
A Third Run
O Fourth Run
Velocity (ft/sec)
4-
Curve 717154A
6 9 12 15 18 21 24
Distance Across Stack Throat (ft)
27
30
Figure 4.3-6. Stack Velocity as a Function of Distance Across the Stack
at the Velocity Pressure Probe Station.
56
-------
The third method by which air flow rate was calculated uses the fan in-
let static pressure, a diffuser loss model, and the available fan curve.
It was retained only as a limited check, and was never used in the heat
and mass transfer calculations. The method of solution is based on
obtaining the fan pressure rise, via diffuser loss calculations, and
then obtaining the air flow rate for the given pressure rise from the
manufacturer's fan curves.
Shown in Figure 4.3-7 is an illustration of the fan stack system. Note
that the station at the fan inlet will be denoted by subscript (i),
the fan outlet by (o), and the stack discharge by (e). Conservation of
energy and momentum from the fan outlet to the stack discharge yields,
r 2 £
Pe - Po + KVB,o [1 - & 1 + kVa,o [1 ~ <^>
*• A
e e
-iK£ p V2
2 o a,o
where the subscripts (s) and (a) denote the swirl and axial velocity
component, respectively. K& is the stack loss coefficient and P is
e
atmospheric pressure. The static pressure rise across the fan is,
APr = P - P. (4.3-79)
o i
or upon substitution of (4.3-79) in (4.3-78),
i\f O
Y»
APr = P + ±K*p V2 - 4> V2 [1 - (-£) ]
e 2 ro a,o 2 o s,o v^ ' J
e
57
I 2
C^T) 1 - Pi (4.3-80)
A
e
-------
Dwg. 7697A73
Figure 4.3-7.
Fan-Stack Model and Nomenclature Employed for
the Calculation of Air Flow Rate From the Fan
Curve.
58
-------
Assume the fan inlet flow to be axial,
AP
V = -fc. (4.3-81)
' p oj r
o
where r is the mean radius and can be calculated from,
* a, 2 1/2
r = [ _Ji tip_ j (4.3-82)
Substituting (4.3-81) in (4.3-80), and then applying the definition of
volume flow rate to V in (4.3-80) results in,
Si f O
p KAQ2 A_2 £ 2
APT - P - P. + - — [1 -
e i 2A2 2p
o o
P Q2
0
_ __ (4.3-83)
2A2 A
o e
Idel'Chik7 presents correlations for calculating KA for common diffuser
geometries. For a conical diffuser, such as is the case here,
«// * 2 * 2
5/4 A A
KA = 3.2 (tan ~] [1 - -^-] + [1 - (•—) ] . (4.3-84)
A 8 sin -pr A
e 2 e
where a is the diffuser included angle, and X the wall friction coef-
ficient. X was calculated from smooth wall correlations based on the
axial Reynolds number.
59
-------
The fan curve can be represented by
Q - f(APr,0,u>) = 0 (4.3-85)
where 0 is the blade angle and co the rotational speed. Equation (4.3-85)
existed in subroutine form and could reproduce the manufacturer's data.
The different operating rotational speeds were taken into account by the
fan scaling laws.
Written in a more generalized form, (4.3-83) becomes
APr - f(APr,Q,yi) = 0 (4.3-86)
where f is a generalized function and y. represents the known parameters
in (4.3-83). Equations (4.3-85) and (4.3-86) represent a system of non-
linear algebraic equations which were solved via the Secant method2 for
determining the roots of an equation.
4.3.1.5 Water Flow Rate Analysis and Computation
Since the flow to the tower was divided into two equal streams, half to
each cell, and each stream could be diverted to its respective heat ex-
changer in any amount, at least two streams had to be monitored during
tests. Total flow to the tower was measured by an Annubar flow meter
whereas the flow diverted through the dry heat exchanger was determined
from its known flow versus pressure drop characteristics.
The Annubar is a device which is constructed in such a way that a given
flow rate generates a known pressure drop across two pressure taps.
For this work the signal was measured by both a manometer and a pressure
transducer. If the manometer measurement was being used, then the total
water flow rate was calculated from
60
-------
(4.3-87)
1/2
where C = 18962.615 gal-lbf /in-min (a constant which is a result of
the calibration, the particular pipe diameter in use, and the Annubar
design), p is the metered water density, p ,_ is the density of water
at 60°F, and y the Annubar element differential pressure in lb^/in2. y
was calculated from
y - -^fP" [- — _ —2—J 7g (4.3-88)
1728 Pw,39.2 pw,39.2
where y is the manometer column height, p _ the density of the manometer
fluid, p ~Q , the density of water at 39.2°F (4°C). The reason that
v* • J./ • £*
two different standard water densities are used is due to the different
standards followed by the Annubar manufacturer (60°F) and the manometer
fluid manufacturers (4°C) in defining specific gravity. Equations
(4.3-87) and (4.3-88) could be rewritten more simply in terms of specific
gravity (p/p ,) but could be misapplied if one did not realize that
Vv • o LCL
two different standard water densities were employed.
To calculate the water flow rate from the pressure transducer output
it must be noted that its output was in percent of full scale, and full
scale was defined as the transducer output (proportional to the Annubar
differential pressure [y}) at a flow rate of 25,468 gpm. With Equation
(4.3-87) it can be written that,
Qfs - C 1—^- /'fo (4.3-89)
or
61
-------
Dwg. 7697A74
Upper Water Box
TT
Heat
Exchanger
Tubes
Water
Filled'
Lower Water
Box
Ambient
Environment
Manometer Fluid
Figure 4.3-8.
Schematic of Dry Heat Exchanger Hydraulic System with the
Manometer Employed to Measure the Frictional Pressure Drop.
62
-------
w,60
Substitution of C in (4.3-87) with (4.3-90) yields,
Q = n /-IS- /-I- (4.3-91)
or since the measurement is recorded as percent of full scale, Pfg,
* * ' '" ' *" (4.3-92)
_, _ * n nn
w,fs
The water flow rate was calculated from the manometer measurement (i.e.,
Equation [4.3-87]) for all tests in which it was available. The pressure
transducer measurement (i.e., Equation [4.3-92]) was utilized as a backup
only. As a continuing check, the difference between the two flow rate
computational measurement techniques was always computed and printed for
each run. Usually the difference was less than 3 percent.
By knowing the frictional pressure drop through the dry heat exchanger
as a function of water flow rate, the amount of water diverted to it
could be determined. In other words, the dry heat exchanger was used
much in the same way as an orifice plate except the calibration was
initially unknown. Consider the equation for viscous pressure losses
between the upper and lower water boxes shown in Figure 4.3-8,
P - P = AP. .
3 1 htx
> . r _2 i f + ± Rep £— + £ KoprT *— ] (4.3-93)
••LJ.-,. L f\t _ T* 9 "T.T '\J— / TJ 'u**
63
-------
Curve 717155A
1.4-
1.2
1.0--
0.8
O.6..
0.4 .-
0.2-
AP
htx
w
o Dry Heat Exchanger
Calibration Points
12
Water Flow Rate (gpm x 10 )
Figure 4.3-9. Dry Heat Exchanger Water Flow Rate Calibration. The
Pressure Drop-Water Density Ratio is Shown as a
Function of Water Flow Rate. Also Indicated is the
Least Squares Curve Used to Represent the Calibration
in the Data Reduction.
64
-------
Ke and Ko are entrance and exit loss coefficients respectively, A is
the total tube cross-sectional area, 73 the heat exchanger tube length,
D the diameter, Q the total water flow rate through the dry heat ex-
changer, and f the Moody friction factor. (4.3-93) can be rewritten as
(4.3-94)
Since the friction factor and the loss coefficients are functions of the
Reynolds number, and subsequently a function of temperature via the fluid
properties, Equation (4.3-94) is only an approximation since AP, /p
is shown only as a function of flow rate. However, for the relatively
narrow temperature range encountered by the heat exchanger water, Equation
(4.3-94) is only negligibly in error.
Calibration of the heat exchanger was accomplished by diverting all the
tower flow through the dry heat exchanger. In this way the Annubar mon-
itored the flow rate while the dry heat exchanger pressure drop was
noted.
For computational purposes Equation (4.3-94) was rearranged and cast into
second order polynomial form,
(4.3-95)
where C , C , and C are constants determined from a least squares analy-
sis. Figure 4.3-9 shows the heat exchanger calibration and the least
squares curve.
The dry heat exchanger pressure drop (AP. ) was measured with both a
manometer and a pressure transducer. Figure 4.3-8 shows the heat
65
-------
Curve 717156A
Water Flow Rate (gpm'x io~3)
12 -
10
8 --
4 •'
2 ..
o Calibration Point
H h
1 2
Voltage (v x 103)
0
Figure 4.3-10.
Heat Exchanger Pressure Transducer Voltage as a Function of
Dry Heat Exchanger Water Flow Rate. Also Shown is the
Second Order Least Squares Polynomial Used to Represent
the Calibration in the Data Reduction Program.
66
-------
exchanger and manometer system. From Figure 4.3-8 it can be shown that
the heat exchanger pressure drop can be calculated from,
APhtx = tpw(Thtx) - Pw(Tamb)] 8y3 + ^mf (Tamb) ' pw(Tamb)]
where the density dependence on temperature is indicated by the paren-
thesis. Note that the first term in braces on the right-hand side of
(4.3-96) is the hydrostatic correction for the difference in heat ex-
changer and manometer tubing fluid density, resulting from different
temperatures. Although inclusion of this correction is rigorously cor-
rect, its effect on the flow rate was very small.
The pressure transducer was connected in parallel with the manometer.
Its output was calibrated against the Annubar. Figure 4.3-10 presents
the calibration and the least squares quadratic polynomial employed in
the computations. The manometer measurement was used in the data re-
duction for all runs in which it was available.
4.3.2 Data Reduction Computer Code
This section is intended to be a brief overview of the data reduction
program. The interested reader is referred to the program listing
(Appendix C) which contains sufficient comment cards to be self-
explanatory. A sample input and output can also be found in Appendix C.
Most of the calculations are performed within subroutines; as a result
the main program is composed almost entirely of call statements and the
routing logic. A brief description of the nine main program fundamental
units or functions follows.
4.3.2.1 Data Reduction Main Program Functions
A. Set Geometry and Program Parameters - Here the geometry
of the fan, fill, heat exchanger, instrumentation, etc.
are set. Various options such as preference for manometer
67
-------
or transducer sensed pressure drop for flow calculation,
solution convergence maximum errors, etc. may be selected.
B. Read Input - A subroutine which decodes the Fluke and
manually-typed data is called (refer to Appendix C for
additional information). All of the input is passed to
the main program via common blocks. The six-digit run
identifier is also decoded.
C. Water Flow Rate Determination - Water flow rate to the
wet fill and/or dry heat exchanger is calculated. This
calculation depends on the first digit of the six-digit
run identifier. If it indicates a wet/dry test, then
the logic knows there must be an accounting of two water
streams. If it is all wet or all dry, then the program
must account for only one water stream.
D. Air and Water State Determination - All of the necessary
state properties of the air and water streams are cal-
culated at every point of interest, i.e., tower inlet,
fill inlet and outlet, stack outlet, distribution basin,
heat exchanger inlet and outlet, fill outlet, etc.
E. Airflow Rate Computation - As described in previous
sections, the airflow rate could be calculated by several
methods. This section of the program computes the air-
flow rate by the three methods and then utilizes the one
selected by the program option for the heat and mass
transfer calculations.
F. Wet Fill Calculations - The tower mass transfer coef-
ficient and number of transfer units are calculated.
Note that this portion of the program is not entered
if the run identifier indicates a dry test.
G. Dry Heat Exchanger Calculations - This portion of the
program is activated if the run identifier indicates a
wet/dry or a dry test. All pertinent properties of the
dry heat exchanger such as air-side heat transfer coef-
ficient, Reynolds number, etc. are calculated.
H. Fan Calculations - Fan-motor-gear train efficiency as
well as the dimensionless pressure and flow coefficient
are computed.
I. Output - This final program function relies entirely on
the type of test being reduced. It was designed to glean
the maximum amount of information from a given test for
additional study at a later date. A good example is a
68
-------
wet/dry test. Clearly wet/dry type output is warranted
but, in addition, the fan calculations are also outputted
despite it not being a fan test. As another example,
consider a plume test. Not only was plume data printed
(and punched for later retrieval) but wet, dry (if avail-
able on this particular test), and fan data were also
retrieved.
4.4 ANALYSIS OF THEEMAL AND FLOW DATA
The main purpose of the entire cooling tower test program was to obtain
performance data which would allow interpretations of how critical tower
performance parameters are affected by operating conditions. The test
program had been set up so that the ranges of these operating conditions
spanned those that one typically finds in an operating tower. By operat-
ing the tower over a one-year time period it was hoped that weather-
dependent conditions would also undergo typical annual swings.
To insure statistical significance of the data, a large number of tests
were scheduled in blocks throughout the year. Table 4.4-1 lists these
test blocks and the ranges of significant operating variables for each
block. As was noted previously, only 1399 or 51 percent of these runs
ultimately reached a final reduced state.
4.4.1 Correlation Forms
There are four tower characteristics which can be obtained from the re-
duced thermal and flow data: mass transfer coefficient per unit volume
Ka, water loss AL/L, dry heat exchanger air-side heat transfer coef-
ficient H and fan drive efficiency n > each of which is a function of
various tower independent parameters such as water loading L and air
loading G.
For the fill-averaged mass transfer coefficient, a correlation of the
form:
69
-------
TABLE 4.4-1
THERMAL AND FLOW TEST GRID
Block
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Test
Type*
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
Season
**
1
1
1
1
7
2
2
2
3
3
3
3
3
3
3
3
3
3
No.
of
Runs
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
Range of L
(#/hr-ft2)
3750-7500
3750-7500
3750-7500
3750-7500
3750-7500
3750-7500
3750-7500
3750-7500
3750-7500
3750-7500
3750-7500
3750-7500
4500-9000
4500-9000
4500-9000
5600-11200
5600-11200
5600-11200
Range of G
(#/hr-ft2)
2575-5150
2575-5150
2575-5150
2575-5150
2575-5150
2575-5150
2575-5150
2575-5150
2575-5150
2575-5150
2575-5150
2575-5150
2575-5150
2575-5150
2575-5150
2575-5150
2575-5150
2575-5150
Fan
Angle
(deg)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
%Wet
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
%Dry
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Dry GPM
Each Side
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
*Types of Tests:
1 = all wet, 18 feet air travel
2 = wet/dry
3 = dry
4 = fan
5 = plume
6 = acoustics
7 = all wet, 14 and 10 feet air travel
**Season
1 = winter
2 = spring
3 = summer
4 = fall
(Continued)
-------
Table 4.4-1 (cont'd)
Block
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
Test
Type*
2
2
2
2
3
3
3
3
3
3
4
4
4
4
4
Season
**
1
1
1
1
2
2
2
3
3
3
2
2
2
2
2
No.
of
Runs
135
135
135
135
90
90
90
90
90
90
120
120
120
120
120
Range of L
(#/hr-ft2)
250-3750
250-3750
250-3750
250-3750
0
0
0
0
0
0
3750-7500
3750-7500
3750-7500
3750-7500
3750-7500
Range of G
(#/hr-ft2)
2575-5150
2575-5150
2575-5150
2575-5150
2570-5150
2570-5150
2570-5150
2570-5150
2570-5150
2570-5150
2570-5150
2570-5150
2570-5150
2570-5150
2570-5150
Fan
Angle
(deg)
0
0
0
0
0
0
0
0
0
0
0
+2
-2
+4
-4
%Wet
10-50
10-50
10-50
10-50
0
0
0
0
0
0
100
100
100
100
100
%Dry
50-90
50-90
50-90
50-90
100
100
100
100
100
100
0
0
0
0
0
Dry GPM
Each Side
3000-5400
3000-5400
3000-5400
3000-5400
6000-12000
6000-12000
6000-12000
6000-12000
6000-12000
6000-12000
0
0
0
0
0
-J
I-1
-------
Ka = C La Gb T° (4.4.1-1)
was used as equations of this form are the most commonly found in the
cooling tower mass transfer literature and physical arguments can be
made for the exponential dependence on L and G, Addition of the temper-
ature dependency Tc was examined in light of some past experience in the
literature which shows that mass transfer coefficient is a weak function
of water film temperature, perhaps due to the temperature dependency of
water transport properties. Correlations with and without temperature
effects were obtained.
Water loss, which can be expressed as a fraction of water inlet flow
rate (Am/m) and thus as AL/L, must be a function of the tower fill mass
transfer coefficient. Locally, within the fill, the rate of water loss
m from the liquid phase into the vapor phase within a volume (dx)(dy)(dz)
can be expressed as
dm = Ka (u> - w ) dx dy dz (4.4.1-2)
w a
and over the entire fill:
m = / / / Ka (u - CD ) dx dy dz (4.4.1-3)
w a
where Ka here is a distributed value, Ka . We are unable to
determine the distributed Ka and would have great difficulty in using it
if it could be determined. We thus, as shown in Section 4.3, determined
an average value over the entire fill volume. Using this value of
volume-averaged Ka we may write Equation (4.4.1-3) as
m = Ka / / / (ww - u>a) dx dy dz (4.4.1-4)
72
-------
Dividing this equation by fill width and depth Z and X we have:
I- = L = Ka / / / (u - a) ) ~ dy |£- (4.4.1-5)
XZ W "• A i-
Further, multiplying the right-hand side by Y and dividing both sides
by L we have
AL Ka Y . f f , , dx dy dz .. . 1 ,,
T = —f!f K-V XY — (4.4.1-6)
Equation (4.4.1-6) indicates that the fractional water loss should be a
function of the number of transfer units NTU, or Ka itself, and a fill-
volume-averaged humidity difference between the water surface and the
air free stream. In this experimental apparatus we were not instrumented
to measure co within the fill so the integration indicated in Equation
(4.4.1-5) was not possible. We only knew values at the fill extrema
(top, bottom, front and rear). Since we know Ka can be correlated by
C La G^ , we have attempted to correlate AL/L with the form
AL/L = qLd Ge At/ (4.4.1-7)
where Ao) is humidity difference based upon some combination of known
extrema states, one combination being the log-mean value across the fill:
AUK - Au>2
Aco. = •• . (4.4.1-8)
£m Aw..
This is the same approach which is used in expressing temperature dif-
ference in counterflow and crossflow heat exchangers. Further, from
prior arguments we would like to see d = a-1, e = b, f = 1 and C. = C Y.
73
-------
As for the dry heat exchanger air-side heat transer coefficient H, the
most common method of reporting these heat transfer coefficient data is
in terms of the dimensionless parameters, Nusselt number (H£/k), Prandtl
number (yc/k) and Reynolds number (V£p/y). Specifically, heat transfer
texts, e.g., References 1 and 2, report heat transfer coefficient data
in the form of the Colburn "j-factor", (Nu/Re Pr) Pr2/3, as a function
of Reynolds number. Reference 1, especially, presents the heat transfer
coefficient for externally-finned (circular fins) tubing in this manner
for many geometries. The data reported by Reference 1 are linear curves
on log-log plots, so one would expect correlations of the form
- C2 R" (4.4.1-9)
to fit our data. In order to compare our data with that of Reference 1,
their convention in expressing characteristic length H (for Nusselt and
Reynolds numbers) was adopted here. Reference 1 defines & as the volume
of air space in the heat exchanger divided by the air-side heat transfer
surface area in that volume. Their reason for adopting this convention
is that data for heat exchangers of disparate types may be handled with
a common characteristic length.
Fan efficiency data presented some severe problems in attempts to correlate
data (see Section 4.5.4). Parameters such as fan blade pitch angle,
speed and water loading should have some effect on the fan's operating
point, and thus fan efficiency. However, the simplest of correlations,
linear variation in fan drive efficiency with volumetric flow rate, was
found to fit the data best. The fan efficiency is reported here in the
form:
nf = C3 + C^ Q (4.4.1-10)
74
-------
4.4.2 Statistical Analysis of Data
In many instances there were several methods available for correlation
of a given set of test data, and some means was necessary to determine
which method produced the best fit or least error. The standard error
of estimate, similar to standard deviation, was used to evaluate the
validity of competing correlations. The correlation coefficient was
used to examine the degree to which candidate independent variables
correlate with the dependent variable.
To show how these parameters were used in evaluating each correlation,
let us use the expression for mass transfer coefficient:
Ka = C La Gb T° (4.4.2-1)
For each set of tower test data there are N subsets of corresponding
variables Ka., L., G. and T. and a corresponding Ka. from Equation
(4.4.2-1). Since Ka^ is not, and should not be, a constant (since it
varies with L, G and T, all of which varied from run to run) it is not
feasible to perform an analysis on the variation |Ka^ - Ka^| or |Ka^ -
™™ I 4e
Ka-jJ . Rather, for each data point Ka^, a ratio <|>.|_ = Ka^/Ka^ was formed
after the correlation, Equation (4.4.2-1), was obtained. If the data
correlated perfectly, then i = 1.0, i = 1,2,3...N. With the set of
N
(f)^, a population mean, = £ ./N, was formed and the standard error
i=l
of estimate a was formed from:
V
(4.4.2-2)
In addition, correlation coefficients and/or the coefficient of multiple
determination were obtained. The correlation coefficient r is a measure
of explained variation in relation to total variation through:
75
-------
= + J explained variation
- if
total variation
and indicates how well one parameter correlates with another. For per-
fect correlation r = +1, while for no correlation at all r = 0. When a
dependent parameter, such as Ka in Equation (4.4.1-1), is a function of
more than one independent parameter, then it is necessary to utilize
the coefficient of multiple determination to check on the validity of
correlation. Using the subscript system Ka=l, L = 2, G = 3 and T = 4
for Equation (4.4.2-1), then the coefficient of multiple determination10
R. gat. i-s defined as
(4.4.2-4)
where, for example r is defined as:
J_ J
rTT = (4.4. -5)
1J [NZI2 - (ZI)2] [NEJ2 - (ZJ)2]
and so, for example:
NSKa.T. - (SKa.) (ZT.)
rllt = ..... =*• X 11 __ (4.4.2-6)
2 - (ZKa±)2] [N^T? - (ZT,.)2]
The remaining factors in Equation (4.4.2-4) are defined as:
, - (4.4.2-7)
13-"
and
76
-------
= iHri ri3^ '23-** (4-4-2-8)
12.34
V (3-r?3.
The coefficient of multiple determination lies between 0 and 1, and the
closer it is to 1.0, the better is the correlation,
4.4.3 Linear Regression
Although the correlation equations for mass transfer coefficient, water
loss and heat exchanger air-side heat transfer coefficient are of ex-
ponential form, linear regression may be used to determine the unknown
correlation parameters simply by taking logarithms of the correlations
prior to regression. For example, taking the logarithm of Equation
(4.4.1-1) yields:
Hn Ka = Sin C + a Sin L + b Jin G + c to T (4.4.3-1)
Let Ka^ be the mass transfer coefficient as determined from data reduc-
tion for the ith test, in which test parameters !•£, G^ and T^ prevailed,
and let Ka* be the value of Ka from Equation (4.4.3-1) when L^, G^ and
T-^are applied. Then the coefficients CQ, a, b and c are determined for
least mean square error between Ka^ and Ka* for all N data sets when:
N
I (Jin Ka* - Hn Ka.)2 = minimum (4.4.3-2)
i=l X 1
This will occur when:
N *
£ (*,n Ka. - An Ka.T - 0 (4.4.3-3)
77
-------
N
~- E (to Ka - to Ka.)2 = 0 (4.4.3-4)
a
* 2 =
a N
|r- Z (Hn Ka* - Jin Ka.)2 = 0 (4.4.3-5)
9b i i
a
~- 2 (An Ka. - £n Ka.)2 = 0 (4.4.3-6)
dc 1=1 1 1
From Equation (4.4.3-1), the factor (Jin Ka* - In Ka.)2 is:
(JlnKa.-JlnKa.) 2 = (JlnC +a£nL.+bJlnG.+cJlnT.- JlnKa.)2 (4.4.3-7)
or
(Jin Ka* - Jin Ka..^)2 = (D + aW. + bX. + cZ. - Y.)2 (4.4.3-8)
Performing the square of the right-hand side of (4.4.3-8) yields
(Jin Ka* - Jin Ka±)2 = D2 + a2W? + b2X2 + c2Z2 + Y2 +
2DaW±
- 2DY - 2aWY - 2bXY - 2cZY (4.4.3-9)
Performing the differentiations indicated by Equations (4.4.3-3 through
6) on (4.4.3-9) gives four expressions:
, N N
~ E (JlnKa. - JlnKa.)2 = E (D + aW. + bX. + cZ. - Y.) = 0
3 1=1 x ! 1=1 1111
78
-------
a N N
4- E (£nKa* - £nKa.)2 = E (DW. + aW2 + bW.X. + cW.Z. - W.Y.) = 0
3a ._- i i ._, i i 11 11 11
a N N
|r- £ (JlnKa* - £nKa.)2 = E (DX. + aW.X. + bX2 + cX.Z. - X.Y.) - 0
OD ... 1 1 . - 1 11 1 11 11
1=1 1=1
a N N
~ Z (toKa. - £nKa.)2 = Z (DZ. + aW.Z. + bX.Z. + cZ2 - Z.Y.) = 0
9c ... i i ._- i 11 11 i li
This leads to four simultaneous equations in D, a, b and c, the coef-
ficients being summations of tower test data:
N N N N
ND + aZW. +bZX. + c E Z. = E Y. (4.4.3-10)
i-1 1-1 X i=l X i=l 1
N N N N N
D E W. + a S W2 + b Z W.X. + c Z W.Z. = 2 W.Y. (4.4.3-11)
1=1 1 1-1 X 1-1 X X 1-1 X 1 i-1 1 X
N N N N N
D Z + a I W.X. + b Z X2 + c Z X Z. = E X.Y. (4.4.3-12)
1-1 i=l 1-1 i-1 1 X 1-1 x 1
N N N N N
D E + a E W.Z. + b E X.Z. + c E Z? = E Z.Y. (4.4.3-13)
1-1 1-1 1 1 i-1 x X i-1 X i=l 1 X
For correlations in which no temperature effect is desired, the set of
all T. may be equated to 1.0. Then £n T. =0 and Equations (4.4.3-10
through 13) yield c = 0. Likewise, when the correlation for dry heat
exchanger air-side heat transfer coefficient is sought, Equations (4.4.3-10
through 13) can be used by letting W± = An Re.., Y = An j ., and X. = Z
= Jlnl = 0. For fan efficiency correlations, a linear form was assumed
79
-------
and no logarithms were necessary. Here Equations (4.4.3^10 and 11) are
used where Y. = TI , D = C , a = C , W. = Q., and Y. = Z. = 0.
1 1 . j ^)- 1 1 11
In order to use the prior four equations to obtain correlations for
mass transfer coefficient, water loss, heat transfer coefficient and
fan efficiency, a set of four computer codes were written. These cor-
relation programs a.re listed in Appendix D, which includes necessary
explanations of inputs, outputs and some internal logic explanations.
4.5 RESULTS OF CORRELATIONS
The correlations of four cooling tower parameters with their correspond-
ing independent parameters are reported in this section. The great bulk
of output data from the correlation programs precludes total inclusion
here. Samples of the four correlation detailed outputs are shown in Ap-
pendix D. Results are summarized in condensed tables in this section.
4.5.1 Mass Transfer Coefficient Ka
A total of 539 good data sets were obtained in WET fill tests. In ad-
dition, a total of 194 WET/DRY tests were run, each containing Ka data,
so that a total of 733 data sets for Ka were available. Note, however,
that in WET/DRY tests some water was diverted to the dry heat exchangers
and so the consequent water loadings L in the wet fill were much less
than in pure WET tests. This allows us to analyze the Ka data (a) for
all tests, (b) for WET tests only and (c) for low water loadings in
WET/DRY tests. This last condition is of some value since data for
these conditions (i.e., very low L) are not found in the literature and
they are necessary for the design of towers operating wet/dry. In
addition to the WET and WET/DRY tests, some WET tests were performed
with a fraction of the fill theoretically inactive. This was accomplished
by blocking flow nozzles in the top deck of the tower such that the
active fill depth was either 14 feet or 10 feet, rather than the full 18
80
-------
feet. In these cases the water -was truly loaded onto the first 14 or 10
feet of fill at the top of the tower, but it was not assured that the
water did not spread toward the rear four or eight feet of fill at
lower depths of fill. With this uncertainty, these tests were kept
separate from "full fill depth" tests and were correlated separately as
SHORT tests. There were 147 tests at 14 feet of air travel and 104
tests at 10 feet air travel.
Reference 11 reports data taken in 1974 in a small cooling tower test
facility using the same fill elements as in the Cliffside tower and
using water loadings L and air loadings G similar to those in the tests
reported here. In the prior work a correlation of the form (424 data
points):
Ka - 1188 L°'5" G°'438 T2'04 (4.5.1-1)
was obtained, where T was water inlet temperature. When temperature
was ignored a correlation of the form:
Ka = 0.0609 L°'649 G°'436 (4.5.1-2)
was obtained. The results were not subjected to statistical analysis.
Strong physical and mathematical arguments were made for the exponent
on L to be somewhat less than unity and the exponent on G to be somewhat
less than 0.6 (expected from heat transfer data) and about 0.45. The
consistency of the exponents in the two correlations and the fact that
they fell near predicted values was gratifying. We had hoped that there
would be similar results occurring in the analysis of the Cliffside
tower tests. Such was not entirely the case.
The results of all attempts to correlate WET, WET/DRY and SHORT test
data are presented in Table 4.5.1-1, a total of 39 program runs. Var-
iations were run to determine the effects of:
81
-------
TABLE 4.5.1-1
MASS TRANSFER COEFFICIENT CORRELATION DATA
"So.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Input
Data File and Correlation Conditions
All WET data; no effect of temperature
Winter WET data (llxxxx tests) ; no
temperature
Spring WET data (12xxxx tests) ; no
temperature
Summer WET data (13xxxx tests) no
temperature
All WET data; inlet water temperature
All WET data; outlet water temperature
All WET data; average water, temperature
All WET data; inlet air temperature
All WET data; outlet air temperature
All WET data; mean air temperature
All WET data; mean fluid temperature
All WET/DRY data; no effect of temp-
erature
All WET/DRY data; inlet water temp-
erature
All WET/DRY data; outlet water temp-
erature
All WET/DRY data; average water temp-
erature
All WET/DRY data; inlet air temperature
All WET/DRY data; outlet air temp-
erature
All WET/DRY data; average air temp-
erature
All WET/DRY data; mean fluid temp-
erature
WET + WET/DRY data; no effect of temp-
erature
WET + WET/DRY data; no temperature;
L < 10,000
Statistics
a
.183
.157
.085
.152
.152
.145
.148
.140
.164
.145
.145
.205
.191
.149
.172
.205
.200
.204
.189
.227
.229
5T
1.017
1.012
1.004
1.013
1.012
1.011
1.012
1.011
1.014
1.011
1.011
1.017
1.016
1.011
1.014
1.017
1.017
1.017
1.016
1.021
1.021
N
539
172
167
200
539
539
539
539
539
539
539
194
194
194
194
194
194
194
194
733
592
r!2
.592
.562
.408
.585
.592
.592
.592
.592
.592
.592
.592
.664
.664
.664
.664
.664
.664
.664
.664
.508
.474
r!3
.916
.863
.914
.926
.916
.916
.916
.916
.916
.916
.916
.845
.845
.845
.845
.845
.845
.845
.845
.786
.779
rll
-
-
-
-
-.370
-.676
-.568
-.357
-.488
-.441
-.510
-
.038
-.354
-.263
-.571
-.266
-.452
-.379
-
-
R'*
.926
.906
.973
.923
.946
.950
.948
.952
.938
.949
.949
.916
.919
.942
.927
.916
.917
.916
.920
.913
.909
Correlation Parameters
C
o
.00153
.00545
.00077
.00650
1.254
1.639
1.679
.0260
.1815
.1234
.5035
.0328
.4266
1085.
31.60
.0286
.1267
.0480
1.8919
.00645
,00577
a
.626
.596
.727
.487
.571
.700
.628
.598
.679
.637
.633
.433
.438
.711
.520
.433
.462
.437
.479
.497
.511
b
.852
.733
.823
.801
.831
.689
.766
.824
.776
.793
.778
.649
.650
.291
.549
.651
.615
.641
.578
.808
.807
c
0
0
0
0
-1.341
-1.473
-1.435
-.582
-1.053
-.946
-1.216
0
-.586
-2.369
-1.570
+.0278
-.3094
-.0826
-.9010
0
0
00
KJ
(Continued)
-------
Table 4.5.1-1 (cont'd)
00
OJ
No.
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
Input
Data File and Correlation Conditions
WET + WET /DRY data; no temperature;
L <_ 8,000
WET + WET/DRY data; no temperature;
L < 6,000
SHORT data (14 and 10 feet travel); no
temperature
SHORT data; 14 feet travel; no temp-
erature
SHORT data; 10 feet travel; no temp-
erature
SHORT data; 14 feet travel; exit water
temperature
SHORT data; 10 feet travel; exit water
temperature
WET data; no temperature; L < 10,000
WET data; no temperature; L < 8,000
WET data; no temperature; L < 6,000
WET data; exit water temperature;
L £ 10,000
WET data; exit water temperature;
L £ 8,000
WET data; exit water temperature;
L£ 6,000
WET + WET/DRY; exit water temperature
(See #20)
WET data; no temperature; G > 400
WET data; no temperature; G > 600
WET data; no temperature; G > 800
WET data; no temperature; G > 1,000
Statistics
a
.193
.193
.124
.082
.045
.081
.045
.159
.139
.118
.123
.115
.096
.185
.192
.193
.192
.196
X
1.016
1.016
1.008
1.004
1.001
1.003
1.001
1.013
1.011
1,008
1.008
1.008
1.006
1.016
1.019
1.019
1.018
1.018
N
540
408
251
147
104
147
104
498
346
214
498
346
214
733
454
396
7,92
261
r!2
.359
.287
.269
.322
-.038
.322
-.038
.586
.420
.227
.586
.420
.227
.508
,562
.599
.686
.727
r!3
.802
.831
.914
.927
.994
.927
.994
.909
.922
.940
.909
.922
.940
.786
.867
.831
.740
.750
rl.
_
-
-
-
-
-.437
-.780
-
-
-
-.704
-.613
-.831
-.235
-
-
_
-
R*
.909
.910
.938
.953
.994
.954
.994
.939
.931
.944
.961
.950
.959
.933
,883
.860
.820
.314
Correlation Parameters
C
o
.01457
.01898
.00222
.00622
.06514
.03823
.08893
.00029
.00091
.00014
.26145
.127?4
.07605
2.2159
.00182
.00172
.00228
.00218
a
.439
.406
.582
.508
.190
.551
.194
.830
.726
.914
.875
.855
.852
.671
.625
.632
.670
.645
b
.754
.751
.881
.815
.925
.787
.920
.838
.799
.839
.683
.680
.703
.618
.828
.827
.745
.781
c
0
0
0
0
0
-.4470
-.0699
0
0
0
-1.392
-1.188
-1.099
-1.377
0
0
0
0
-------
1. Including or excluding fluid temperature
2. Considering WET and WET/DRY data together and separately
3. Eliminating data with high water loading L
4. Eliminating data with low air loading G
5. Considering seasonal data separately
and combinations of these variations.
Consider runs 1 and 5 through 11 in Table 4.5.1-1 in which the effect of
fluid temperature is first ignored and then considered in terms of
specific or average water or air temperatures. First it should be noted
that in all cases the correlation coefficient between Ka and L (r,2) is
moderate (0.592) and between Ka and G (r,,) is high (0.916), Further,
the coefficient of multiple determination R2 is quite high. Note that
R2 is improved when any fluid temperature is considered and that the
standard error of estimate a is universally reduced when one includes
the effect of water temperature. When the correlation is based on fill
outlet average water temperaure, run 6, the correlation coefficient be-
tween Ka and T is -0.676. Also a is reduced from 0,183 to 0.145 and R2
is increased from 0,926 to 0.950. One must conclude that inclusion of
the effect of fluid temperature is warranted and fill outlet average
water temperature is superior to other fluid temperatures.
Analysis of runs 1 and 5 through 11 with runs 12 through 19 compares
corresponding correlations using first WET and then WET/DRY data. Table
4.5.1-1 shows all WET/DRY correlations to be inferior to corresponding
correlations using WET data. The standard error of estimate is univer-
sally slightly higher in the case of WET/DRY data, r is slightly higher
(0.664 versus 0.592) and r is slightly lower (0,845 versus 0.916).
As for the effect of temperature in the correlation, r.. is much lower
in all cases and, as a consequence, R2 suffers slightly. It must be
concluded that there is no advantage in using WET/DRY data to the ex-
clusion of WET data.
84
-------
Comparing run 20 with run 1, we see that when WET and WET/DRY data are
correlated together there is degradation in all the statistical parameters.
As a consequence of the above, only the WET data are considered in further
attempts to correlate the Ka data.
Comparing run 1 with runs 29 through 31 we see the effect of eliminating
from the correlation the data for very high water loadings, values some-
what above those commonly used in crossflow cooling towers. We see that
limiting data to L <_ 10000 Ibm/hr—ft2 improves a, only slightly reduces
rJ2 , slightly reduces r13 and slightly improves R2. Further, restrict-
ing L to values j< 8000 and then _< 6000 continues to improve a but has a
deleterious effect on ^ . ^-^ t^1686 comparisons are made when no effect
of temperature is included. When the effect of exit water temperature
is included in the correlation (compare run 1 with runs 32 through 34)
we see that a is improved, r,2 and r are as when no temperature is
considered and R2 is improved further. It would appear that restricting
data sets to those with L _<_ 10,000 and including the effect of exit water
temperature leads to a fairly good correlation (run 32).
When one systematically removes data sets with low air loading G (runs
1 and 36 through 39) we see that a is unaffected, r._ increases, r
decreases and R2 is reduced. There is no advantage in restricting the
correlation to data sets with higher G only.
There was some concern that the season in which wet fill tests were per-
formed would have an effect on the correlation. The argument ran that
winter tests would be superior to spring tests and particularly summer
tests since air-water temperature differences would be the greatest in
winter. In this case a given error in measuring air or water tempera-
ture would produce the least error in temperature difference and, con-
sequently, the least error in deducing Ka. Thus it was reasoned that
the scatter in Ka data due to temperature measurement error would be the
85
-------
least in winter tests. Run 1 compared with runs 2 through 4 shows the
effect of correlating all WET data with seasonally segregated WET data.
The results show a decided improvement in a (less scatter) but the cor-
relation coefficient r.. is reduced somewhat. One might be tempted to
elect to use the correlation obtained with spring WET data (lowest a,
greatest R2) except for the low r12 and the fact that only 167 data
points were considered.
As for the SHORT data, the correlations (runs 24 through 28) show a very
poor correlation coefficient r12- Also, the small number of available
data sets (147 for 14 feet air travel and 104 for 10 feet air travel)
make any conclusions on these data tenuous at best.
It is recommended that for the wet fill type tested in the Cliffside
cooling tower the correlation (run 32):
Ka = .2615 L.875G.683T-1.392 (4.5.1-3)
be used in design and performance calculations. Note that the temperature
in the correlation is average exit water temperature, a quantity not
known at the start of calculations. Thus any analysis using the cor-
relation must be iterative. For less precise work, the correlation (run
29):
Ka = .00029 L°-83° G°'838 (4.5.1-4)
which contains no temperature effect, may be used. As an alternative
spring test data (run 3) may be used:
777
Ka = .00077 L*' ' G' (4.5.1-5)
with the warning that it was obtained with limited data and shows a fairly
weak correlation coefficient between Ka and L.
86
-------
4.5.2 Rate of Water Loss Due to Evaporation (AL/L)
Again, there were 539 WET test runs and 194 WET/DRY test runs available
for analysis, or a total of 733 data sets. Table 4.5.2-1 lists a total
of 39 attempts at correlating AL/L with water loading L, air loading G,
and water-to-air humidity difference. The column headings in this table
are like those in Table 4.5.1-1. We are attempting to correlate water
loss with water loading L, air loading G and a humidity difference Aco
(between the air and water in the fill) with an equation of the form:
AL/L = G Ld Ge Auf (4.5.2-1)
As was the case in Ka correlation attempts, the results in Table 4.5.2-1
show that merging of WET and WET/DRY data for the correlation produces
a strong degradation in the scatter as predicted by the parameter a (cf
runs 1 and 8, 2 and 9, 3 and 10, etc.), although r12 and R2 are, at the
same time, strengthened. The correlation coefficient r is reduced
L J
slightly. Comparing WET data with WET/DRY separately (cf runs 1 and 15,
2 and 16, etc.) we again see more severe scatter in the WET/DRY data,
improvement in r12, an anomalous (negative) r and poor R2. Note that
the WET/DRY correlations show an inverse dependency, of AL/L on G, i.e.,
negative values of the exponent e, which does not stand to reason. We
conclude that there must be anomalies in the WET/DRY data and that only
the WET data should be used in further correlation attempts.
Comparing run 1 with runs 2 through 7 we see the effect of not applying
and then applying various humidity differences (air-to-water) in the
water loss correlation. It is apparent that addition of the effects of
humidity difference reduces correlation scatter a and generally improves
the coefficient of multiple determination R2. In all cases, however,
the correlation coefficients r12, r13 and rllt show a rather weak relation-
ship between AL/L and the independent parameters L, G and Am. The best
of the humidity-dependent correlations seems to be the one based on
87
-------
TABLE 4.5.2-1
WATER LOSS CORRELATION DATA
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Input
Data File and Correlation Conditions
All WET data;' no effect of humidity
difference (A between water out &
air out
Statistics
0
.271
.175
.177
.268
.179
.193
.190
.386
.365
.369
.384
.367
.341
.359
.346
.335
.304
.344
X
1.033
1.015
1.015
1.033
1.016
1.017
1.017
1.058
1.046
1.047
1.055
1.047
1.043
1.047
1.062
1.049
1.044
1.060
N
539
539
539
539
539
539
539
733
733
733
733
733
733
733
194
194
194
194
r!2
-.475
-.475
-.475
-.475
-.475
-.475
-.475
-.848
-.848
-.848
-.848
-.848
-.848
-.848
-.741
-.741
-.741
-.741
r!3
.445
.445
.445
.445
.445
.445
.445
.339
.339
.339
.339
.339
.339
.339
-.276
-.276
-.276
-.276
rm
0
.643
.530
.266
.878
-.233
.195
0
.330
.025
-.220
-.760
-.615
-.224
0
.253
.268
-.197
R2
.646
.838
.842
.650
.823
.815
.813
.811
.855
.857
.823
.851
.864
.853
.555
.667
.700
.579
Correlation Parameters
Cl
88.64
152.8
488.8
156.9
31.16
1678.
524.5
143.8
1321.
2176.
712.1
484.3
810.7
2229.
415.5
53420.
4438.
1228.
d
-.884
-.561
-.724
-.896
-.326
-1.06
-.798
-.846
-.807
-.881
-.915
-.682
-1.16
-.911
-.592
-.606
-.620
-.655
e
.452
.437
.467
.418
.204
.840
.607
.336
.354
.368
.279
.195
.750
—
-.064
-.101
-.110
-.066
f
0
.720
.880
.039
.419
.994
.847
0
.587
.725
.101
.324
1.02
—
0
.983
1.10
.089
co
co
(Continued)
-------
Table 4.5.2-1 (cont'd)
Innut
No. Data File and Correlation Conditions
19 WET/DRY data; Aw between water in &
air out
20 WET/DRY data; Aw between water out &
air in
21 WET/DRY data; Am between mean water
and air
22 WET data; L < 10,000; log-mean An)
23 WET data; L < 8,000; log-mean Aui
24 WET data; L < 6,000; log-mean Am
25 WET data; L <_ 10,000; no Aw
26 WET data; L < 8,000; no Aw
27 WET data; L < 6,000; no Aw
28 SHORT data; no AID
29 SHORT data; log-mean Am
30 SHORT 14-foot data; no Au>
31 SHORT 14-foot data; log-mean Au>
32 SHORT 10-foot data; no Aw
33 SHORT 10-foot data; log-mean Aw
34 WET data; winter (llxxxx), no A
39 WET data; summer (13xxxx), log-mean Aw
Statistics
a
.345
.323
.311
.170
.155
.156
.257
.254
.263
.181
.176
.159
.121
.141
.130
.129
.106
.136
.112
.241
.195
X
1.053
1.050
1.044
1.041
1.013
1.013
1.030
1.032
1.033
1.016
1.015
1.012
1.007
1.009
1.007
1.008
1.006
1.009
1.006
1.027
1.019
N
194
194
194
498
346
214
498
346
214
251
251
147
147
104
104
172
172
167
167
200
200
r!2
-.741
-.741
-.741
-.460
-.330
-.452
-.460
-.330
-.452
-.581
-.581
-.628
-.628
-.628
-.628
-.436
-.436
-.660
-.660
-.352
-.352
r!3
-.276
-.276
-.276
.503
.628
.569
.503
.628
.569
.668
.668
.639
.639
.732
.732
.747
.747
.646
.646
.553
.553
ru
.353
-.198
.104
.632
.666
.685
0
0
0
0
.472
0
.585
0
.283
0
.582
0
.775
0
,654
R*
.645
.654
.698
.835
.822
.790
.655
.579
.517
.741
.761
.817
,888
.836
.868
.9109
.939
.888
.924
.671
.759
Correlation Parameters
Cl
11.895
1.75x10
_
189.9
240.6
94.68
205.0
33.62
1122.
26.73
68.07
144.32
1868.
133.7
1830.
3.989
10.62
23.91
367.8
22.99
167.2
d
-.392
-1.09
_
-.600
-.529
-.322
-.979
-.749
-1.09
-.707
-.634
-.982
-.903
-.822
-.798
-.766
-.537
-1.01
-.767
-.759
-.596
e
-.354
.481
_
.434
.371
.329
.451
.428
.333
.431
.410
.533
.447
.36.1
.354
.705
.667
.462
.396
.516
.417
f
.611
1.35
_
.689
.785
.903
0
0
0
0
.325
0
.613
0
.613
0
.568
0
.457
0
.633
co
VO
-------
log-mean humidity difference, run 2, in terms of scatter, R2 and most
important, r •
Comparing run 2 with run 22 shows the effect of limiting data to tests
where L _< 10,000. There is little difference here, as one might expect,
since the L discrimination reduces the number of data sets only slightly,
from 539 to 498. Further discrimination in L has a mixed effect on
correlation coefficients, with no significant improvement.
The best correlations appear to occur when one segregates the WET data
into seasonal blocks. Comparing runs 2 (all WET data), 35 (winter WET),
37 (spring WET) and 39 (summer WET) we see an improvement, especially in
the winter and spring tests. Direct comparison of all WET data and
spring WET data is made in Table 4.5.2-2.
TABLE 4,5.2-2
COMPARISON OF ALL WET AND WINTER WET CORRELATIONS
OF WATER LOSS AL/L
Run a r12 rJ3 r^ R2 C^ d e f
2 .175 -.475 .445 .643 .838 152.8 -.561 .437 .720
37 ,112 -.660 .646 .775 .924 367.8 -.767 .396 .457
The spring WET data correlation is clearly superior to the all WET cor-
relation. Examination of runs 38 and 39 shows that it was probably the
summer WET test data that caused the problem in the correlation of all
WET data.
The SHORT data correlations show the same trends, i.e., inclusion of
humidity difference in the correlation improves correlation coefficients
and segregation into 10 foot and 14 foot air travel tests offers further
improvement.
90
-------
Overall we are somewhat disappointed in the scatter (a) in all correla-
tions. It is recommended that the correlation for spring tests (run 37):
AL/L = 367.8 L~'767 G*396 Au*457 (4.5.2-2)
(where Ao> is log-mean humidity difference) be used in design or perfor-
mance calculations. Again these calculations must be iterative because
we do not know the humidity of the air at discharge nor the saturation
humidity of air at the discharge water temperature at the start of cal-
culations. For a somewhat less accurate prediction of water loss, the
correlation based on humidity difference between air at the inlet air
state and saturated air at the water inlet temperature, run 3, may be
used:
AL/L = 488.8 L~'724 G'467Au)*88° (4.5.2-3)
All these independent parameters will be known at the start of design or
performance calculations.
4.5.3 Dry Heat Exchanger Air-Side Convective Heat Transfer Coefficient H
Based on a wealth of prior experience in the heat transfer literature on
heat exchanger surface, correlations of the form:
j = C2 Ren (4.5.3-1)
were used to relate the dry heat exchanger air-side convective heat
transfer coefficient H with airflow data. Table 4.5.3-1 presents the
limited number of correlation attempts, the number of runs being limited
by the simplicity of the correlation. Runs dealt with WET/DRY (194
runs) and DRY (415 runs) test data.
91
-------
TABLE 4.5.3-1
DRY HEAT EXCHANGER HEAT TRANSFER COEFFICIENT CORRELATION DATA
No.
1
2
3
4
5
Data File and Correlation Conditions
All DRY data
All WET /DRY data
All DRY + WET/DRY data
DRY data; summer (33xxxx) only
DRY data; spring (32xxxx) only
Statistics
a
.264
.338
.380
.123
.332
X
1.040
1.062
1.063
1.006
1.058
N
415
194
609
237
176
r!2
-.200
-.783
-.606
.0288
-.2622
Correlation
Parameters
C2
.0199
.8248
.2852
.0065
.0215
n
-.1672
-.6696
-.5335
-.0117
-.2057
VO
-------
We are extremely disappointed, but not surprised, by the large scatter
in these data, as indicated by the standard estimate of error a, and
by the low values of the correlation coefficient between Colburn j
factor and Reynolds number, r . These poor tendencies are expected in
light of the conclusions drawn in the analysis of Ka and AL/L, where
WET/DRY data were not used because of poor statistics. We surmise that
one of two problems caused the DRY and WET/DRY data to be poor. First,
the method used to measure water flow through the dry exchangers is
suspect . A more positive flow-measuring device such as an orifice or
venturi would have yielded a more accurate water flow. Water flow is
required to determine water-side convective heat transfer coefficient,
which is used in conjunction with heat exchanger core heat transfer rate
to calculate air-side heat transfer coefficient, and thus j . A second
problem in the exchanger core may have arisen because the tubes were
vertical, causing the inner tube surfaces to be nonuniformly wetted,
The method for determining water-side convective heat transfer coef-
ficient assumed completely wetted water surface in fully developed tur-
bulent flow. In any case, all j-Re correlations are suspect.
Reference 8 shows that for a finned heat exchanger bank similar to the
one in the Cliffside tower the Colburn j factor should correlate with
Reynolds number by:
j = .2130 Re~'384° (4.5.3-2)
Other circular finned heat exchangers with different tube pitches and
tube diameters in Reference 1 show similar exponents but different
coefficients.
Examination of Table 4.5.3-1 shows no correlation similar to Equation
(4.5.3-2). About the closest would be run 3 which uses all available
data and gives:
—
j = .2852 Re ' (4.5.3-3)
93
-------
Curve 717157A
i.OOO-
,833-
,667-
o
£=
-------
Rather than use Equation (4.5.3-3) or (4.5.3-2), it is recommended that
the designer contact the supplier of his finned surface. Suppliers
all provide data of this type for their products.
4.5.4 Fan Efficiency
It has been established that in all probability the velocity pressure
probes at the fan stack throat did not, for one reason or another, supply
good pressure measurements. Consequently, it would be misleading to base
the fan efficiency on erroneous airflow rate measurements. Instead, the
fan efficiency is based on the airflow rate required to conserve energy.
In other words, each fan test was reduced using Equation (4.3-77) to
determine airflow rate and the fan efficiency was calculated from,
qQAP ,. _ . .,
nf = -|— (4.5.4-1)
where AP is the measured fan inlet-to-stack outlet (atmospheric) pressure
difference and E the measured fan-motor energy consumption rate. Note
that this efficiency includes the motor and gear box losses as well as
any effects associated with the stack. For conciseness, this lumped
system efficiency will be referred to as the airflow system efficiency.
Figure 4.5.4-1 presents the results of the fan tests. As is evident in
the figure, the data are generally very good with only a few obvious
exceptions.
Before examining the results in any more detail, it is useful to review
the anticipated airflow system efficiency behavior. It is well known
that the efficiency of a given fan can be correlated with the specific
speed v, defined as
' 1/2
v = 9 .. (4.6.4-2)
95
-------
1.000 -i
.667-
c
OJ
4-
q-
.500-
.167-
.000-
Curve 717158A
.0000- .OHHO .0880 .132(1 .1760
Q(CFM) (X10 ")
.2200
Figure 4.5.4-2. Airflow System Efficiency as a Function of Airflow Rate
for a Rotational Speed of 60 RPM.
96
-------
where 9 is the rotational speed, Q the volumetric airflow rate, and AP
the fan head rise. From the 'fan laws', it is also known that
Q - C 0 (4.5.4-3)
3.
AP = C, 02 . (4.5.4-4)
D
Substitution of (4.5.4-3) and (4.5.4-4) into (4.5.4-2) yields the result
= constant . (4.5.4-5)
In other words, for any change in angular speed, the specific speed is
constant. One would, therefore, expect the fan efficiency to remain
constant for changes in angular speed. Clearly, however, Equations
(4.5.4-3) and (4.5.4-4) are oversimplified. They do not account for
Reynolds number effects — which would tend to increase the efficiency at
a constant specific speed — nor do they include the influence of the fan
stack, motor, or gear train. Nevertheless, the efficiency should be a
weak-to-moderate function of angular speed. Figures 4.5.4-2 through
4.5.4-6, when compared with one another, indicate a rather pronounced
influence of rotational speed on the airflow system efficiency. Some of
the data which appear in Figure 4.5.4-1 are not present in Figures 4.5.4-2
through 4.5.4-6. The measured angular speed was required to be within
+4 rpm of the plotted speed. Since there was some drifting of the actual
speed from the desired test value, several data points were culled for
this presentation.
The behavior of the airflow system efficiency to perturbations in blade
pitch can also be qualitatively predicted. Figure 4.5.4-7 illustrates
the interaction between fan and system. Figure 4.5.4-7a delineates
three fan curves, one for each blade pitch; the respective operating
97
-------
Curve 717159A
l.OOO-i
.833-
,687-
o
j! .500-
o
UJ
.167-
.000-
.0
A
A
M4^
1 1 1 1 1
000 .0440 .0880 .1320. .1760 .220C
Q(CFM) (X10 ?)
Figure 4.5.4-3. Airflow System Efficiency as a Function of Airflow Rate
for a Rotational Speed of 90 RPM.
98
-------
1.000 -i
.667-
CD
2 .500
.167-
.000
.0000
.OWO - .0880 .1
Q(CFM)
Curve 717160A
.1760 .2200
Figure 4.5.4-4. Airflow System Efficiency as a Function of Airflow Rate
for a Rotational Speed of 101 RPM.
99
-------
1.000 -i
.667-
o
O)
•r—
O
.500-
.167-
.000
.0000 .OHHO
.0880 .!<
QCCFM) (X10
Curve 717161A
.1760 .2200
Figure 4.5.4-5. Airflow System Efficiency as a Function of Airflow Rate
for a Rotational Speed of 113 RPM.
100
-------
1.000
0
c
O)
o
.667-
,500-
.167-
.000'
.0000 -
Curve 717162A
Q(CFM) (XIO
.132Q.
^
.1760
.2200
Figure 4 5.4-6. Airflow System Efficiency as a Function of Airflow Rate
for a Rotational Speed of 119 RPM.
101
-------
Curve 717163A
n
b. Fan Efficiency for Three Blade Angles as a Function
of Volumetric Flow Rate. Also Shown is Anticipated
Fan Efficiency Behavior While Coupled to the System
Characteristic Shown in Figure 6-7a.
System
Character!'sti
a. Fan Pressure Rise and System Characteristic as a
Function of Volumetric Flow Rate. Each Fan Curve
Represents a Unique Pitch (X).
Figure 4.5.4-7. Effect of Pitch on Fan Performance.
102
-------
points (labeled A, B, and C); and the system characteristic. For each
pitch, the fan manifests a unique efficiency versus flow rate perfor-
mance. Thus, the fan efficiency for a blade angle of A can be found
by noting the flow rate at the operating point A. Using this flow rate
in Figure 4.5.4-7b allows the efficiency of the fan with blade pitch \l
to be determined. The locus of such points, denoted as the dashed curve
in Figure 4.5.4-7b, represents the anticipated influence of pitch on fan
performance for a given system characteristic. It is important for the
reader to recognize that the dashed curve was synthesized from one system
characteristic. A variable system characteristic would hopelessly ob-
fuscate the preceding analysis, making any kind of discussion on the
fan-system performance academic. Despite the variable air and water
loadings of the fan tests, the system characteristic changed only slight-
ly and is only a second order effect relative to the fan speed and blade
pitch. The reader is reminded, however, that the airflow system ef-
ficiency is a lumped parameter manifesting the influence of the fan,
stack, motor, and gear train.
Figures 4.5.4-8 through 4,5.4-12, when compared to each other, show the
observed influence of pitch on the airflow system efficiency—negligible
within the limits imposed by the data scattering. The only discernible
trend (gradual monotonic increase in efficiency with flow rate) is the
previously discussed influence of rotation speed—observable for each
blade pitch. One can only conclude that the fan-system efficiency per-
formance for variable pitch conditions (dashed curve in Figure 4.5.4-7b)
is very flat over the range of blade angles tested. This result could
be a consequence of a very flat family of fan efficiency curves for a
fixed pitch (solid curves in Figure 4.5.4-7b) or the tested variations
in pitch (+4°) were simply too small to manifest any observable trends.
The latter is most likely and is aggravated by the dilution effect
attributable to the other (drive train, stack, and motor) system losses.
Any small change in fan efficiency could easily be overwhelmed by the
remaining system components.
103
-------
l.OOO-i
.833-
.667-
O)
o .500-1
£
,167-
.000
Curve 717164A
1
.0000 .onto
1 T
.0880 .1321
Q(CFM) (XIO
~~I 1
.1760 .2200
Figure 4.5.4-8. Airflow System Efficiency as a Function of Airflow Rate
for an 8-Degree Blade Pitch,
104
-------
1.000-n
.833-
.667-
£ .500 -
a
UJ
.167-
.000
* * p-
.0000 .OWO
.0880 .1320,
Q(CFM) (XIO ^
Curve 717165A
.1760 .2200
Figure 4.5.4-9. Airflow System Efficiency as a Function of Airflow Rate
for a 10-Degree Blade Pitch.
105
-------
l.OOO-i
.833-
.667-
o
O)
•I—
o
.500-
.167-
.000
z
.0000 .OHHO
—i r
.0880 .1
KCFM)
Curve 717166A
z
T
1
,1760 .2200
Figure 4.5.4-10. Airflow System Efficiency as a Function of Airflow Rate
for a 12-Degree Blade Pitch.
106
-------
l.OOO-i
.667-
o
E
OJ
2 ,500 -
q-
q-
,167-
.000
.0000 .OHHO
.0880 .132(1
QCCFM) (XIO
Curve 717167A
.1760 .2200
Figure 4.5.4-11. Airflow System Efficiency as a Function of Airflow Rate
for a 14-Degree Blade Pitch.
107
-------
(O
c:
o>
Efficiency
o
oo
en
no
-h
Qi — •
O
O^
i ,00
0
ro
ro 3
n>
m
oo -h
— • -h
O, _•.
Q. O
(D -••
n>
o
CU
3
n
o
o
o
n>
s
O)
-J
cn
§
o
o
o
o
o"
o
o
CD
X
I
*
e
-s
^1
__l
*-J
CO
-------
It is clear that the airflow system efficiency is a complex function of
several interacting components. The fan efficiency alone is a very com-
plex function of geometry and operating conditions. If just the fan
efficiency (no stack, gears, or motors) were available, it still could
not be correlated with any confidence in applying the result to a dif-
ferent fan. Fan efficiency, as it is defined and applied here, is
simply not a fundamental variable—the measured process is not basic
enough to allow confident generalizations or correlations. Consequently,
any quantitative relationship derived from the presented data will be
valid only for the tested system. Qualitative extrapolation to different
systems is less hazardous but should be done with caution. With these
warnings firmly established, Figure 4.5.4-13 is presented for the pur-
pose of visual establishment of the quality of the data. Compared is
the experimental airflow system efficiency data and a straight line
representing the best least squares fit of the data. The line manifests
a standard error of estimate of .2493 (refer to the heat and mass trans-
fer analysis for the development of the standard estimate of error) and
a correlation coefficient of .8872. The statistical information is pre-
sented to indicate the data quality—not the degree of confidence in the
generality of the approximating line.
Perhaps the most useful conclusion that can be drawn from this work is
the poor utilization of electrical power manifested by the airflow system.
Only 25 to 35 percent of the available electrical energy is ever used to
move air. Generally, a range of 50 to 70 percent (the latter value would
be very good) is reasonable for a fan efficiency. If the former value is
assumed reasonable for this application, then the motor and drive train
consume from 15 to 25 percent of the total electrical input power.
4.6 NOMENCLATURE
A Surface area (ft2) .
A Cross-sectional area (ft2) .
109
-------
1. OQO-i
.833-
.667-
o
QJ
,500-J
,333-
,167 J
Curve 717169A
n = -1.004 x TO'2 + 2.4 x TO'7 Q (CFM)
.0000
Q(CFM)
.1760 .2200
Figure 4.5.4-13. Airflow System Efficiency and Approximating Straight Line
as a Function of Volumetric Flow Rate.
110
-------
a Water droplet area per unit volume (ft *).
a Exponent of water loading L in the mass transfer coefficient cor-
relation (dimensionless).
b Exponent of air loading G in the mass transfer coefficient cor-
relation (dimensionless).
C A constant (gal-lbf^-'^/in-min).
Cp Specific heat at constant pressure (btu/lbm-°F) .
C Coefficient in the correlation of mass transfer co
o
Coefficient in the correlation of water loss AL/L.
C2 Coefficient in the correlation of heat exchanger air-side heat
transfer coefficient.
C Coefficient in the correlation of fan system efficiency.
«j
C. Coefficient in the correlation of fan system efficiency.
»
C Proportionality constant, Q with 9.
3.
C, Proportionality constant,, AP with 62 .
c Exponent of temperature T in the mass transfer coefficient correlation
(dimensionless) .
D Diameter (ft) .
D Logarithm of C in the regression analysis.
d Tower depth (ft) .
d Exponent of water loading L in the correlation for water loss AL/L
(dimensionless) .
E Electrical input to the fan motor (kW) .
E Energy flux (Btu/hr).
e Exponent of air loading G in the correlation for water loss AL/L
(dimensionless) .
F Cross-flow heat exchanger temperature difference correction factor
(dimensionless) .
f Exponent of air specific humidity difference Aw in the correlation
for water loss AL/L (dimensionless) ,
f A general function.
G Air loading or mass velocity (lbm/hr-ft2).
g Gravitational acceleration (ft/sec2) .
H Heat transfer coefficient (Btu/hr-f t2-°F) .
Ill
-------
h Specific enthalpy (Btu/lbm).
I Zeroth order modified Bessel function of first kind (dimensioness).
o
I First order modified Bessel function of first kind (dimensionless).
i Index (dimensionless).
2/3
j Colburn j factor (Nu/Re Pr) Pr (dimensionless).
K Mass transfer coefficient (lbm/hr-ft2)
Ka Mass transfer coefficient per unit volume of tower fill (lbm/hr-ft3)
' Entrance and exit loss coefficients (dimensionless).
Ko
K£ Stack loss coefficient (dimensionless).
Kg Sensible heat transfer coefficient (Btu/hr-ft2-°F).
k Thermal conductivity (Btu/hr-ft-°F).
K Zeroth order modified Bessel function of second kind (dimensionless)
K First order modified Bessel function of second kind (dimensionless).
L Water loading (lbm/hr-ft2).
Le Lewis number, Kg/K Cp (dimensionless).
IU3.
^
L Total tube length (ft).
H Tower height (ft).
M Maximum index in a summation.
m Mass (Ibm); index.
m Mass flow rate of water (Ibm/hr).
N Maximum index in a summation; number of data sets*
n Exponent of Reynolds number Re in the correlation of heat exchanger
air-side heat transfer coefficient (Colburn j factor) (dimension-
less) .
Nf Fin pitch (in-1).
Nu Nusselt number, HD/k (dimensionless).
NTU Number of transfer units (dimensionless).
P Pressure (Ibf/ft2).
P. Percent of full scale (dimensionless).
f s
Pr Prandtl number (dimensionless).
APr Pressure rise (Ibf/ft2).
112
-------
p Defined in Equation (4.3-64) (dimensionless).
Q Flow rate (ft /sec).
'V
Q Flow rate (gal/min).
q Heat transfer rate (Btu/hr).
a.
q Defined in Equation (4.3-64) (dimensionless).
q Defined in Equation (4.3-64) (dimensionless).
R Thermal resistance (°F-hr/Btu).
R.. Coefficient of multiple determination between parameters ± and j
1J (l=Ka, 2=L, 3=C, 4=T or Ato) (dimensionless).
Re Reynolds number (dimensionless).
r Defined in Equation (4.3-63) (dimensionless).
r.. Correlation coefficient between parameters i and j (l=Ka or AL/L,
1:1 2=L, 3=6, 4=T or Au>) (dimensionless).
r" Mean radius, defined in Equation (4.3-82) (ft).
^
r Radius (ft).
T Temperature (°F).
t Time (hr).
o>
t Fin thickness (in).
U Internal energy (Btu).
U, Defined in Equation (4.3-69) (dimensionless).
U Defined in Equation (4.3-70) (dimensionless).
V Velocity (ft/hr); (ft/sec) in Section 4.3.1.4.
v Electrical potential (v).
¥ Volume (ft3).
W. Logarithm of L for the ith data set.
X Fill total depth (ft).
rth
X. Logarithm of G for the icn data set.
Xmf Multiplication factor (dimensionless).
x Depth to a given point in the fill (ft).
Y Fill total height (ft).
Y. Logarithm of Ka for the ith data set.
113
-------
y Distance of vertical water travel in the fill (ft) .
Z Total width of tower fill (ft) .
Z. Logarithm of T in the i£h data set.
z Distance from one side of the fill to a given point in the fill
(ft).
Greek Symbols
a Dif fuser divergence angle (deg) .
3 Defined in Equation (4.3-68) (dimensionless) .
Y Differential pressure (lbf/in2).
Y Manometer column height (in) .
A Finite difference step size (ft) .
e An error term.
n Fin efficiency (dimensionless) .
nf Fan system efficiency (dimensionless).
6 Fan blade angle (degrees) .
•
0 Fan speed (rpm) .
A Wall friction coefficient (dimensionless).
y Dynamic viscosity (Ibm/ft-hr)
V Kinematic viscosity (f t2/hr) .
p Density (Ibm/ft3); (slugs/ft3) in Section 4.3.1.4.
cr Standard estimate of error (similar to standard deviation)
(dimensionless) .
Ratio of a test parameter from data to its value from a correlation
(dimensionless) .
<|> The mean value of for a data set.
oj Specific humidity (dimensionless) .
^ i
w Angular velocity (sec"1 ) .
Subscripts
a Air; axial.
amb Ambient .
114
-------
avg Average.
ax Axial.
c Collar.
cf Crossflow.
ccf Counter-current flow.
co Effective for convection.
d Diameter.
e Exit.
f Fin.
fg Latent.
fs Full scale.
htx Heat exchanger.
hub Hub.
i In; inside; index.
in In.
j Index
Imtd Log mean temperature difference.
ma Moist air.
mf Manometer fluid.
o Out; outside.
oc Tube-to-fin interface.
of Fin outer edge.
ref Reference.
s Swirl.
std Standard.
t Tube.
tip Tip.
v Velocity; vapor phase,
w Water.
wv Water vapor.
wall Wall.
1,2,3 Specific indices.
115
-------
Superscripts^
In Unit volume.
Time derivative.
1 Refined value.
* Value from a correlation.
4.7 REFERENCES
1. Wegstein, J. H., "Accelerating Convergence of Iterative Processes",
Communications for Association for Computing Machinery, Vol. I, No.
6, June 1958, pp. 9-13.
2. Hamming, R. W., Numerical Methods for Scientists and Engineers, 2nd
Ed., McGraw-Hill Book Company, New York NY, 1973.
3. Bowman, R. A., Mueller, A. C. and Nagle, W. M., "Mean Temperature
Difference in Design", Trans. ASME, May 1940.
4. Gardner, K. A., "Efficiency of Extended Surface", Trans. ASME,
November 1945, pp. 621-634.
5. Eckels, P. W., "Contact Conductance of Mechanically Expanded Plate
Finned Tube Heat Exchangers", ASME Paper 77-HT-24, 1977.
6. Sieder, E. N. and Tate, C. E., "Heat Transfer and Pressure Drop of
Liquids in Tubes", IEC, Vol. 28, 1936, p. 1429.
7. Idel'Chik, I. E., "Resistance Coefficients of Diffusers", Handbook
of Hydraulic Resistance, AEC-TR-360, 1966.
8. Kays, W. M. and London, A. L., Compact Heat Exchangers, 2nd Ed.,
McGraw-Hill Book Company, New York NY, 1964.
9. McAdams, W. H., Heat Transmission, 3rd Ed., McGraw-Hill Book Co.,
New York, 1954.
10. Spiegel, M. R., Statistics, McGraw-Hill Book Co., New York NY, 1961.
11. Ayers, D. L. and Hogan, M. R., "Mass Transfer Measurements in a
Wet Crossflow Cooling Tower Test Facility", Westinghouse Research
Report 75-1E9-TOTES-R1, December 2, 1975.
116
-------
SECTION 5.0
ACOUSTICS TESTS
Measurement of the noise radiated by the TVA test cooling tower, at
Duke Power Company's Cliffside Station, was made and corrected for back-
ground noise. Data were obtained for 31 combinations of fan speed, fan
blade pitch, total water flow rate and water flow through the dry heat
exchangers. These combinations were chosen so that a second order cen-
tral composite experimental design could be fitted to the data. Re-
sulting empirical equations for the octave band, linear and A-weighted
sound levels at the top of the fan exhaust stack and in front of the
open louvered face of the tower are presented. These equations were
used to update an existing computer code for predicting the noise level
of such cooling towers as a function of observer location and tower
operating parameters. This computer code is presented along with suit-
able documentation for its use.
5.1 DESCRIPTION OF ACOUSTIC INSTRUMENTATION
All of the data acquisition and analysis equipment utilized were of
precision grade and meet all relevant national standards. This equip-
ment is described in the following subsections.
5.1.1 Data Acquisition Equipment
Figure 5.1-1 is a schematic diagram of the noise measurement equipment
used for the data acquisition. Table 5.1-1 identifies the equipment
by manufacturer and model number.
117
-------
Dwg. 7697A95
Sound Level Meter,
Microphone and
Wi ndscreen
Tape
Recorder
Voice
Microphone
Figure 5.1-1. Data Acquisition Equipment.
TABLE 5.1-1
MEASUREMENT EQUIPMENT MODELS
Bruel and Kjaer (B&K) Type 4145 one inch
condenser microphone
B&K Type 2204 sound level meter
Stellavox SP-7 professional tape recorder
B&K Type 4220 pistonphone
Voice microphones
Tripods, cables and miscellaneous items
118
-------
The B&K 4145 one-inch microphone is a design tailored for use in a free-
field environment. This microphone has the frequency response and
directivity characteristics illustrated in Figures 5.1-2 and 5.1-3*.
Figure 5.1-2 shows, in the upper curve, the free-field response at normal
incidence for the microphone with its protective grid. The lower curve
is the microphone pressure response. Figure 5.1-3 shows the free-field
corrections which must be added to the pressure response curve of Fig-
ure 5.1-2 in order to determine the microphone response at other angles
of incidence. The windscreen used with the microphone is a B&K UA 02C7
polyurethane sponge ball. Its effect on the microphone frequency
response is shown in Figure 5.1-4 as a function of the incidence angle.
In general, the windscreen produces a slight (0.0 - 0.7 dB) amplification
of the noise over frequencies from about 1 to 5 kHz and an attenuation of
about 0.6 to 1.4 dB at about 10 kHz. Since the random incidence response
of the B&K 4145 microphone is amplified by several dB at frequencies near
10 kHz, the use of the windscreen tends to give the microphone a "flatter"
frequency response.
The B&K 2204 sound level meter is a precision grade instrument whose
characteristics surpass those of the microphone. Hence, the sound
level meter conditions the input microphone signal without adversely
affecting the signal frequency or amplitude characteristics. The
Stellavox SP-7 is an exceptionally high quality two-channel portable tape
recorder. The frequency response of both channels of the recorder,
operating at 15 ips, is shown in Figure 5.1-5.
Curve 717170A
—
-
— — — I
/
1
1
—
' —
-
-
-
—
—
:.:
-
-
-
__
-
_
-
-—
.... __
—
_-
- —
OQ
-O
— CM
\t >
M*0 50 100 200 500 1000 2000 5000 10000 20000~*~" "°
ne i—
Figure 5.1-5. Measured Frequency Response at 15 ips of the Stellavox
SP-7 Recording Channels.
*This data is taken from B&K equipment manuals and calibration curves.
119
-------
Curve 717171A
| BrOel t
Meter Range'
dB >
+ 1 -
1 .
•10
20 •
•
t Kjcer
t
—
•
i
IB Rectif
-
-
•
_..
— .
er:
t 1
•
,
I I
BrUel & Kjcer
.ower Lim. Frt
—
-
i
•-
1
-
M
-
_
-
1 • ~ '
•q.: Hz
•
BBSS:
• i
•
w_
^v.
Wr. Speed:
rj1"™!
—
s
^v
^»
\
N
•••-
\
v
1
^M
v
•^
BrUel &
'• ,'i . '
*n
fs'
s
>
s
T:
-
1
\
•
*^i
i,
-V—
V
• ^v
(jeer
- j
fsec. Pap
• ••
A
\
\|
|
1
1
1
i
\~
>
\
V
\
20 Hz 50 100 " 200 500 1000 2000 5000 10000 20000 L
Frequency Scale by Zero Level: (1612/2112)
Figure 5.1-2. Frequency Response Calibration of the B&K 4145 Microphone.
Upper Curve - Free-Field Normal Incidence Response; Lower
Curve - Pressure Response.
120
-------
Curve 717172A
15
dB
10
-S
-10
Free field corrections for
Type 4K5 and Type 41W/46
with protecting grid
5 6 7 8 9 10 kHz 15 20 30 40 50
1 kHz
Figure 5.1-3. Free-Field Corrections for the B&K 4145 Microphone with
Protective Grid as a Function of Incidence Angle.
121
-------
Curve 717173A
0° OdB-
30 OdB-
60 OdB-
J_
IdB
90 OdB-
120 OdB-
150° OdB-
180 OdB-
^ —
' r
2 3 4 5678910
kHz "<"3S
Figure 5.1-4. Free-Field Response Corrections for the B&K 4145 Micro-
Phone When Used with the B&K UA 0207 Windscreen
122
-------
The entire measuring system was calibrated with a B&K 4220 pistonphone.
This unit allows proper amplitude calibration of the sound level meter
and tape recorder within +0.2 dB at a frequency of 250 Hz. To ensure
proper analysis of the data, the pistonphone calibration signal was
recorded on tape to provide a known reference signal level.
All of the recording equipment used is of precision grade and was util-
ized in a manner consistent with accepted measuring standards and the
equipment manufacturer's instructions.
In addition to the equipment listed in Table 5.1-1, a small Dwyer wind
speed indicator and a sling psychrometer were used to measure the wind
speed and wet and dry bulb temperatures respectively.
5.1.2 Data Analysis Equipment
The data analysis equipment is schematically represented in Figure 5.1-6
and identified in Table 5.1-2. The microphone amplifier and attenuator
were used to adjust the tape recorder output signal level to the proper
range for input to the real time analyzer. The analyzer consists of a
parallel set of octave and third octave filters followed by an rms de-
tector and averager. It allows simultaneous determination of all of the
octave and third octave band levels in a given signal. The PDF 11/10
computer is used to control operation of the analyzer and to store the
analyzed data in a disc file. The cathode ray tube (CRT) terminal was
used to input commands to the computer and to display analysis results.
A thermal copier was used to make hard copies of results displayed on
the CRT screen.
5.2 ACOUSTIC DATA ACQUISITION TECHNIQUES
Two measuring systems as shown in Figure 5.1-1 were used to acquire
the data. One system was located on the top deck of the tower—it was
123
-------
Dwg. 7697A75
Tape Recorder
Microphone
Amplifier
and
Attenuator
CRT/
Hard Copy
Output
Real
Time
Analyzer
Computer
Figure 5.1-6. Data Reduction Equipment.
TABLE 5.1-2
DATA REDUCTION EQUIPMENT MODELS
General Radio Type 1921 - octave and third
octave real-time analyzer
Stellavox SP-7 professional tape recorder
Digital Equipment Corp. PDF 11/10 Minicomputer
System
Tektronix 4010-1 CRT Display Terminal
Tektronix 4631 Thermal Copier
B&K 2608 Microphone Amplifier
124
-------
used to measure the noise level at the top edge of the fan discharge
stack. The second system was located at ground level to make measurements
around the tower. The use of two systems reduced the time needed to
obtain the data.
For each of the planned tests, measurements were made approximately five
feet above the ground at the locations shown in Figure 5.2-1 and at the
rim of the fan discharge stack. The measurements near ground level were
made at distances of 3, 6 and 12 ft from the louvered face of the tower.
The location 6 ft from the louvered face of the tower is labelled location #1
and the location at the fan stack discharge is labelled location #2. These
locations were well within the near-field of the tower. The louvered face
of the tower was about 40 ft wide and about 40 ft high. Measurements were
also made near to the enclosed sides of the tower. As had been expected
from Ref. 2, the noise levels near the enclosed sides were so low that they
could not be distinguished from the background noise levels measured at the
same positions. For this reason, these locations are not,shown in Fig-
ure 5.2-1 and the data are not presented.
The measurements at ground level were intended to document the noise
radiated from the louvered faces. The measurement at the fan stack
discharge was intended to determine the stack radiated noise level.
Measurements were not made at distances greater than shown in Figure
5.1-1 because previous work at the site (Reference 2) showed that the
background noise level is too high for accurate measurements to be made
at greater distances. Measurements of the background noise levels were
made at all of the measuring locations before the TVA tower was turned
on and again after the tower was turned off at the end of a day's
testing.
A windscreen was used on the microphone at all times to reduce the ef-
fect of wind gusts. A Dwyer wind speed indicator was used to monitor
wind speeds. No data were recorded during periods of excessive wind
125
-------
N>
Location #2
Broad River
Dwg. 7697A76
I 'v
X
/ Y =
X = 45° 55'
True Plant
North North
Single Cell
Demonstration
Tower
Storage
Shed
Storaae
Yard
Figure 5.2-1. Ground Level Measurement Locations,
-------
speeds. The operator stood to one side and behind the microphone, ap-
proximately five to 10 feet away, while data were being recorded.
During the recording periods, the sound level was monitored by the
operator to ensure that the microphone signal did not overload the sound
level meter and/or recorder. A voice microphone was used to record
identifying information about each test on the recording tapes. Data
were recorded for at least 40 seconds for each of the tests at each of
the test locations. A standard calibrator was used to check operation
of the sound level meters and to record a calibration signal at the
beginning of each reel of tape. This provided a means to accurately
reproduce the amplitude of the recorded data.
5.3 ACOUSTIC DATA REDUCTION TECHNIQUES
The field-recorded data were played back into the real-time analyzer
illustrated in Figure 5.1-2. The recorded calibration signal was used
to adjust the analyzer input gain to the proper value. Each of the
input data records was averaged for 32 seconds. The octave band,
A-weighted and linear sound pressure level values were then outputted
to the minicomputer. When the data analysis was complete, a data reduction
program was run on the minicomputer. This program formatted the analyzed
data, corrected the data for the effects of background noise and printed
out the results on a CRT terminal. The data from the real time analyzer for
the 31 tests and the background noise levels are listed in Appendix E.
The analyzed data corrected for the background noise were used as in-
put for the regression analysis to fit a model to the data (see Section
5.4).
5.4 ANALYSIS OF DATA
This section describes the statistical models formulated from the ex-
perimental data and the procedures utilized in their formulation.
127
-------
TABLE 5.4-1
00
INDEPENDENT VARIABLES AND CORRECTED NOISE LEVELS
Test
ID
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Seq
No.
9
10
11
12
13
14
15
16
18
19
20
21
22
23
24
25
1
3
5
7
28
30
17
26
2
4
6
8
29
27
31
Physical
FS
(%)
50
100
50
100
50
100
50
100
50
100
50
100
50
100
50
100
50
105
75
75
75
75
75
75
75
75
75
75
75
75
75
WFR
(gpm)
14000
14000
22000
22000
14000
14000
22000
22000
14000
14000
22000
22000
14000
14000
22000
22000
18000
18000
10000
26000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
Variables
DF
(%)
40
40
40
40
80
80
80
80
40
40
40
40
80
80
80
80
60
60
60
60
20
100
60
60
60
60
60
60
60
60
60
BP
(°)
~2
~2
~2
~2
"2
"2
"2
~2
2
2
2
2
2
2
2
2
0
0
C
0
0
0
"4
4
0
0
0
0
0
0
0
Coded Variables Octave Band Noise Levels (dB) and Locations
xl
j.
"l.O
1.0
~1.0
1.0
"l.O
1.0
~1.0
1.0
~1.0
1.0
"l.O
1.0
"l.O
_1.0
"l.O
1.0
"l.O
1.2
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
X
"1
"l
1
1
"l
~1
1
1
"l
~1
1
1
"l
"l
1
1
0
0
~2
2
0
0
0
0
0
0
0
0
0
0
0
xq
J
"l
"l
"l
~1
1
1
1
1
"l
"l
"l
"l
1
1
1
1
0
0
0
0
~2
2
0
0
0
0
0
0
0
0
0
XA
*t
"l
~1
"1
"1
"l
"l
"l
"l
1
1
1
1
1
1
1
1
0
0
0
0
0
0
~2
2
0
0
0
0
0
0
0
63
1
70.1
83.2
67.9
82.1
71.7
84.0
71.2
82.7
70.1
83.7
67.0
84.3
70.1
84.5
71.2
84.3
65.9
83.2
76.2
76.5
74.7
75.5
76.2
72.7
75.8
75.5
75.5
75.8
74.0
74.3
74.3
Hz
2
80.2
94.7
79.6
94.7
78.1
95.0
77.1
95.5
78.4
97.5
77.5
97.2
77.8
96.5
78.1
96.5
77.8
96.5
87.9
87.4
86.6
86.3
87.1
85.3
87.6
87.6
87.1
87.6
86.9
87.1
86.3
125
1
0.0
89.1
0.0
88.0
66.6
90.1
63.9
89.8
0.0
89.3
0.0
89.3
0.0
89.6
63.9
90.1
63.9
89.1
79.0
79.0
75.8
78.3
80.3
72.3
78.3
78.6
77.9
78.3
75.8
76.7
76.2
Hz
2
79.7
96.5
78.3
96.2
80.0
96.7
77.9
96.5
76.7
98.0
77.1
97.2
80.0
98.2
79.3
97.2
79.7
97.7
87.0
85.9
85.1
86.7
87.8
85.1
87.0
86.7
86.4
86.7
85.9
86.2
85.6
250
1
70.4
83.4
72.6
83.4
72.0
84.9
74.4
83.7
70.7
83.4
72.0
84.9
71.0
83.9
73.5
84.7
71.7
83.9
75.8
76.6
73.8
75.8
76.9
72.0
75.5
75.5
75.0
75.3
73.8
73.8
73.5
Hz
2
79.0
95.5
79.6
95.0
79.3
95.5
78.5
95.2
77.4
96.5
78.2
96.0
78.2
96.3
77.7
96.0
79.0
95.5
84.9
84.9
83.7
84.9
87.5
83.7
84.4
84.4
84.9
85.2
83.9
84.2
84.4
500
1
71.3
76.1
72.1
75.3
72.4
76.3
72.1
75.8
70.7
77.1
71.8
76.9
71.5
79.9
73.2
77.9
72.6
77.4
72.4
73.7
72.4
72.1
72.9
70.1
72. &
72.4
72.4
72.9
70.7
71.0
71.3
Hz
2
78.7
91.2
78.7
91.0
78.4
91.0
77.4
90.5
75.3
92.5
76.6
92.0
76.3
92.8
75.8
92.3
78.4
93.0
82.5
82.5
80.4
81.2
83.2
80.7
82.5
82.7
83.2
83.0
80.2
81.4
80.9
*dB re 20 yN/m2
-------
5.4.1 Experimental Design
A central composite experimental design in four independent variables
was selected to guide the data acquisition. The four physical indepen-
dent variables are the fan speed (FS), percent, total water flow rate
(WFR), gpm, blade pitch (BP), degrees, and dry flow percentage (DF)1.
For convenience in the analysis, the physical variables are expressed
in a standardized or coded form defined as follows:
x = (FS - 75)/25
x = (WFR - 18000)74000
(5.4-1)
x = (DF - 60) /20
a
BP/2
Table 5.4-1 lists the 31 tests required for this design, the correspond-
ing values of the physical and coded variables and the sequence in which
the tests were performed.
Column 1 gives the test number, which follows a standardized or "exper-
imental design" pattern that is evident in the coded variables of
columns 7-10. Column 2 lists the actual prespecified order in which
the tests were conducted; e.g., Test 17 was run first, Test 25 second,
etc. The experimental design consists of three kinds of combinations of
the coded independent variables. Tests 1-16 are all combinations of a
2k factorial design, where (x^x^x^xj = (±1,±1,±1,±1) . Tests 17-24
are eight so-called axial combinations, where one x. assumes extreme
values while the other three x.'s assume the center value zero. Tests
25-31 are repeat runs of the design's center point (0,0,0,0). Such
*The percent of the total water flow rate passing through the heat
exchangers.
129
-------
Table 5.4-1 (cont'd)
Test
ID Seq
No. No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
9
10
11
12
13
14
15
16
18
19
20
21
22
23
24
25
1
3
5
7
2b
30
17
26
2
4
6
8
29
27
31
Physical Variables
FS WFR DF BP
(%) (gpm) (%) ( )
50
100
50
100
50
100
50
100
50
100
50
100
50
100
50
100
50
105
75
75
75
75
75
75
75
75
75
75
75
75
75
14000
14000
22000
22000
14000
14000
22000
22000
14000
14000
22000
22000
14000
14000
22000
22000
18000
18000
10000
26000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
40
40
40
,40
80
80
80
80
40
40
40
40
80
80
80
80
60
60
60
60
20
100
60
60
60
60
60
60
60
60
60
"2
"2
~2
~2
~2
~2
~2
~2
2
2
2
2
2
2
2
2
0
0
0
0
0
0
~4
4
0
0
0
0
0
0
0
Coded Variables
Xl X2 X3 X4
"l.O
1.0
"l.O
1.0
"l.O
1.0
"l.O
1.0
"l.O
1.0
"l.O
1.0
"l.O
1.0
"l.O
1.0
"l.O
1.2
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
~1
~1
1
1
"1
~1
1
1
~1
~1
1
1
~1
~1
1
1
0
0
"2
2
0
0
0
0
0
0
0
0
0
0
0
~1
~1
~1
~1
1
1
1
1
"1
~1
"1
~1
1
1
1
1
0
0
0
0
~2
2
0
0
0
0
0
0
0
0
0
~1
"l
~1
~1
~1
~1
~1
~1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
~2
2
0
0
0
0
0
0
0
Octave Band Noise Levels (dB) and
1000 Hz 2000 Hz 4000 Hz
121212
70.6
75.6
71.4
74.3
71.7
75.6
72.0
73.8
70.9
75.4
71.2
75.9
69.5
82.0
72.0
77.2
71.2
74.9
71.7
72.8
70.9
70.9
73.0
69.8
72.5
72.3
72.3
72.5
70.1
69.8
70.6
75.6
90.8
75.4
90.0
75.6
90.5
74.3
89.8
73.6
90.0
73.3
89.5
73.6
90.5
73.8
89.5
73.8
90.0
82.5
82.0
81.2
83.5
86.5
80.0
82.5
82.5
82.5
82.0
82.0
82.0
81.2
66.9
70.1
68.7
69.5
67.1
70.3
67.7
69.5
67.1
68.7
67.9
68.5
66.6
68.2
68.7
68.7
67.4
69.5
67.1
68.5
67.7
64.9
68.2
60. 6
67.9
67.7
68.5
68.2
66.9
66.6
66.9
70.3
88.3
71.6
87.5
70.8
88.5
71.6
87.3
68.7
87.5
70.8
86.5
70.3
87.5
71.6
87.3
68.2
86.8
74.9
73.9
75.7
75.7
76.7
75.2
74.7
74.4
74.4
74.2
75.9
76.2
75.4
63.4
62.5
65.6
64.3
62.8
61.9
64.5
63.4
63.7
62.5
64.5
62.2
62.2
60.4
63.7
61.9
63.4
62.2
61.9
64.5
64.3
57.9
63.7
63.4
63.4
63.4
63.4
64.5
62.5
62.8
62.8
69.6
78.0
70.4
78.2
69.3
79.0
70.4
79.2
66.4
80.7
70.4
80.7
68.8
80.5
70.1
80.7
63.7
74.7
66.2
67.2
71.9
68.8
71.9
71.7
66.4
66.7
67.0
67.2
71.9
72.4
71.4
Locations
8000 Hz
1 2
61.2
58.8
63.6
61.2
59.9
57.7
62.3
60.2
60.7
57.4
61.8
58.2
58.2
55.0
60.7
57.1
60.7
58.5
57.9
60.4
62.3
52.2
61.5
60.7
60.4
61.0
61.5
61.8
60.4
61.0
61.0
66.7
73.0
69.5
74.0
66.9
73.2
69.5
74.2
65.4
75.2
70.5
76.0
66.9
74.5
69.5
75.5
56.5
65.1
57.9
59.9
70.2
62.8
69.5
69.5
58.8
58.8
60.4
58.5
69.5
68.9
68.9
-------
an experimental design yields a good estimate of a full second-order
statistical model in the x.1s, as described in Section 5.4-3.
5.4.2 Observed Noise Levels
An initial examination of the data obtained at the three measuring
locations near the ground showed that (1) the data at 3 and 6 ft. were
virtually identical and (2) the data at 12 ft. were more affected by
the background noise levels than that at 3 and 6 ft. Consequently the
data obtained at 6 ft. (Location #1) were chosen for use -in the re-
gression analysis along with the data obtained at the fan stack dis-
charge (Location #2).
Table 5.4-1 lists the measured noise levels corrected for the back-
ground noise (the dependent variables) for these two locations. The
data consist of octave band sound levels for the bands from 63 Hz to
8 kHz. The background noise data and the uncorrected data are presented
in Appendix E.
Several of the corrected data values in Table 5.4-1 for the 125 Hz
octave band at Location 1 are listed as zero. These are test conditions
for which the tower noise was less than 3 dB above the background. In
these cases no conclusion can be drawn about the true value of the tower
noise level and, hence, ztero values are listed. These values were not
included in the regression analysis.
5.4.3 Statistical Model
The general form of the statistical model, relating the dependent vari-
able, y, to the four independent variables, is
y - 3 + I 3.x, + I 3,,xJ + H 3,,x.x, (5.4-2)
131
-------
TABLE 5.4-2
FITTED COEFFICIENTS FOR SURVIVING MODEL TERMS
Octave Band Coefficients
Model
Term
Constant
1
2
3
4
11
22
33
44
12
13
14
63
1
74.87
6.92
~0.25
0.53
1.03
0.53
Hz 125 Hz
2 1
87.03 77.14
8.76 12.48
"0.10
0.04 ~1.11
~0.98
0.53
0.69 0.84
2
86.36
9.05
"0.34
0.40
"0.14
1.41
0.47
250 Hz
1
74.65
5.85
0.46
0.47
"0.43
2.80
0.47
"0.47
2
84.58
8.41
"0.37
2.07
0.32
0.52
500 H*
1
72.10
2.41
0.10
0.09
2.27
"0.43
0.55
2
82.10
7.10
"0.35
2.53
"0.29
0.93
Octave Band Coefficients
Model
Term
Constant
1
2
3
4
11
22
33
44
12
13
14
1000
1
71.56
2.35
"0.06
0.1C
1.94
"0.70
0.82
Hz 2000
2 1
81.97 67.54
7.76 0.79
0.29
"0.25
"0.89 "0.36
1.07
"0.28
0.30
"0.40
"0.33
Hz
2
74.75
8.29
0.01
0.15
"0.36
3.21
0.40
0.46
"0.55
4000
1
63.42
"0.69
0.66
~0.85
"0.33
"0.49
Hz
2
68.18
4.95
~0.11
0.16
3.66
0.86
1.21
8000
1
60.83
"1.38
0.88
"1.33
"0.72
"0.39
"0.87
Hz
2
61.84
3.09
"0.62
0.27
4.34
1.67
2.41
132
-------
The 8 and 3. terms denote the unknown model coefficients to be estimated
o i
by the method of least squares. This model has the obvious capability of
estimating the (x ,x ,x ,x.) combination associated with minimal (or
4- £, 3 *
maximal) y, should the experimental region contain such a combination.
Since there is no theoretical model for relating the noise, y, to the
x. terms, we use the above second-order model and assume that it is of
the correct form, with the unknown (3*s to be estimated by least squares.
If the assumed form is a poor approximation to the correct form for
one or more of the y's, the quality of interpolative y-predictions
(i.e., predictions of y at x-combinations between ones actually included
in the experimental design) will diminish somewhat and that of extrapo-
lative y-predictions even more. To fit and assess a more complex model
would require a much larger experiment.
In practice, most of the potential terms will be dropped from the model.
When we initially fit the full model to a particular y we generally find
several b's (least square estimates of the g's) do not differ signifi-
cantly from zero, as judged by an estimate of experimental error ob-
A
tained from the differences between observed y's and fitted y's cal-
culated from the fitted model. A process of iteration thus begins,
since dropping the $'s corresponding to the least significant b's from
the model will (1) always change and often decrease the estimated ex-
perimental error, and (2) may alter the relative Importance of the
remaining g's, although such alterations will be small in the case of
our symmetrical experimental design. We proceed in this way until all
surviving second-order b's are significant at the 10% level. There is
little basis for dropping any insignificant first-order term, say
^ixi' as -*-onS as xi *-s stiH present in at least one surviving second-
order term.
Table 5.4-2 lists the fitted coefficients corresponding to all surviv-
ing model terms. These coefficients may be used to predict noise level
133
-------
TABLE 5.4-3
COMPARISON OF MEASUBED (y) AND PREDICTED (y) NOISE LEVELS* WITH STANDARD ERROR (s)
63 Hz Octave Band
125 Hz Octave Band
Location 2
Location 1
Location 2
y
7U.1
83.2
67.9
82.1
71.7
84.0
71.2-
82.7
70.1
83.7
67.0
84.3
70.1
84.5
71.2
84.3
65.9
83.2
76.2
76.5
74.7
75.5
76.2
72.7
75.8
75.5
75.5
75.8
74.0
74.3
74.3
y
69.2
63.1
68.7
82.6
70.3
84.1
69.8
83.6
69.2
83.1
68.7
82.6
70.3
84.1
69.8
83.6
69.0
84.7
77.5
7b.5
73.8
75.9
74.9
74.9
74.9
74.9
74.9
74.9
74.9
74.9
74.9
e
0.8
0.1
~0.8
~0.4
1.4
"0.1
1.4
~1.0
0.8
0.7
~1.7
1.7
~0.2
0.4
1.4
0.6
"3.1
"1.5
~1.3
0.9
"0.5
1.3
"2.2
0.9
0.6
0.6
0.9
"0.9
"0.5
~0.5
s(y)
0.57
C.55
0.57
0.55
0.57
0.55
0.57
0.55
0.57
0.55
0.57
0.55
0.57
0.55
0.57
0.55
0.47
0.60
1.02
1.02
0.65
0.65
0.39
0.39
0.39
0.39
0.39
0.39
0.39
0.39
0.39
y
80.2
94.7
79.6
94.7
78.1
S5.0
77.1
95.5
78.4
97.5
77.5
97.2
77.8
96.5
78.1
96.5
77.8
96.5
87.9
87.4
86.6
86.3
87.1
85.3
87.6
87.6
87.1
87.6
86.9
87.1
86.3
y
78.9
95.1
78.9
95.1
78.9
95.1
78.9
95.1
77.6
96.5
77.6
96.5
77. 6
96.5
77.6
96.5
78.3
97.5
87.0
87.0
87. C
87.0
87.0
87.1
87.0
87.0
87.0
87.0
87.0
87.0
87.0
e
1.2
"0.3
0.7
"0.3
"0.8
"0.1
"1.8
0.4
0.8
l.C
"0.2
0.7
0.2
0.5
"0.5
"l.l
0.9
0.3
~0.4
~0.7
0.2
"1.8
0.6
0.6
0.1
0.6
~0.2
0.1
"0.7
s(y)
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.23
0.26
0.14
0.14
0.14
0.14
0.35
0.35
0.14
0.14
0.14
0.14
0.14
0.14
0.14
y
89.1
88.0
66.6
90.1
63.9
89.8
89.3
89.3
89.6
63.9
90.1
63.9
89.1
79.0
79.0
75.8
78.3
80.3
72.3
78.3
76.6
77.9
78.3
75.8
76.7
76.2
y
89.5
89.3
66.3
89.5
66.1
89.3
89.0
88.8
89.0
62.2
88.6
63.7
90.7
79.4
79.1
77.1
77.1
79.4
74.9
77.1
77.1
77.1
77.1
77.1
77.1
11. 1
e
~0.5
~1.3
0.3
0.6
"2.1
0.5
0.4
0.5
0.6
1.8
1.3
0.2
"1.6
"0.5
"0.1
"1.4
1.1
1.0
"2.6
1,1
1.5
0.7
1.1
"1.4
"0.5
"0.9
s(v)
0.71
0.69
0.90
0.71
0.89
0.68
0.69
0.71
0.69
1.06
0.71
C.72
0.63
1.12
1.11
0.41
0.41
0.79
0.79
0.41
0.41
0.41
0.41
0.41
0.41
0.41
y
79.7
96.5
78.3
96.2
80.0
96.7
77.9
96.5
76.7
98.0
77.1
97.2
80.0
98.2
79.3
97.2
79.-7
97.7
87.0
85.9
65.1
86.7
87.8
85.1
87.0
86.7
86.4
86.7
65.9
86.2
85.6
y
79.3
96.4
78.6
95.7
80.1
97.2
79.4
96.5
78.1
97.1
77.4
96.4
78.8
9*7.9
78.2
97.2
78.7
99.2
87. C
85.7
85.6
87.2
86.6
86.1
86.4
86.4
86.4
86.4
86.4
86.4
86.4
e
0.4
"0.3
0.5
"0.1
"0.5
"1.5
"0.1
~1.4
0.2
"0.3
0.8
1.2
0.3
1.2
1.0
"1.5
"0.1
0.2
"0.5
"0.5
1.1
"l.O
0.6
0.3
C.I
0.3
~0.5
"0.2
"0.7
s(yl
0.46
0.45
0.46
0.45
0.46
0.45
0.46
0.45
0.46
0.45
0.46
0.45
0.46
0.45
0.46
0.45
0.28
0.36
0.41
0.41
0.41
0.41
0.41
0.41
0.23
0.23
0.23
0.23
0.23
0.23
0.23
-------
at any combination of interest provided that the variables are properly
coded. An example follows:
Predict the 63 Hz octave band noise level at the fan stack discharge
Fan Speed = 70% xn = -0.2
Water Flow Rate = immaterial
> Te:
Terms did not survive
Dry Flow % = immaterial
Blade Pitch » +1 degree " x, = +0.5
Substitute x. » -0.2 and x, • +0.5 into
87.03
y * 85 dB
y - 87.03 + 8.76^ + 0.04x4 +
5.4.4 Examination of Model Fit
Table 5.4-3 lists the observed sound levels y, the corresponding fitted
A A
sound levels y, the differences or residuals e = y - y, and the standard
A
errors s(y) of the fitted y's. Clearly, the residuals must necessarily
exhibit whatever lack of fit there is between model and observed data;
hence, examination of model fit implies careful study of the residuals.
We find no evidence that the assumed second-order model fails to ade-
quately represent the effects of the four independent variables. Also,
we find no significant trends in the residuals (trends which would in-
dicate drift in the measurement process) with respect to the order of
measurement, although occasionally residuals of very large absolute
magnitude occur for which we have no explanation.
The most striking example of large absolute residuals occurs for Test
ID 28, 30 and 31 at Location 2 for the 8000 Hz octave band; Table 5.4-3
shows residuals of 7.6, 7.1, and 7.1 for these tests, respectively.
It is interesting to note that the noise levels for these tests (Table
5.4-1) are relatively low. It is possible that fluctuations in the
background noise were sufficiently large so that the average background
noise correction applied to the measured data was not adequate.
135
-------
Table 5.4~3 (cont'd)
250 Hz Octave Band
Location 1
Location 2
500 Hz Octave Band
Location 1
Location 2
Co
y
70.4
83.4
72.6
83.4
72.0
84.9
74.4
83.7
70.7
83.4
72.0
84.9
71.0
83.9
73.5
84.7
71.7
83.9
75.8
76.6
73.8
75.8
76.9
72.0
75.5
75.5
75.0
75.3
73.8
73.8
73.5
y
71.1
83.7
73.0
83.7
72.0
84.7
73.9
84.7
70.2
82.9
72.1
82.9
71.2
83.8
73.0
83.8
71.6
85.7
75.6
77.5
73.7
75.6
75.5
73.8
74.6
74.6
74.6
74.6
74.6
74.6
74.6
e
~0.7
"0.3
"0.3
"0.3
0.3
0.5
"1.0
0.5
0.6
~0.1
2.1
~0.1
0.1
0.5
0.9
0.1
"1.8
0.2
"0.8
0.1
0.2
1.4
"1.8
0.9
0.9
0.3
0.6
~0.8
"o.s
"l.l
s(y)
0.53
0.53
0.53
0.53
0.53
0.53
0.53
0.53
0.53
0.53
0.53
0.53
0.53
0.53
0.53
0.53
0.36
0.46
0.77
0.77
0.4S
0.49
0.49
0.49
0.29
0.29
0.29
0.29
0.29
0.29
0.29
y
79.0
95.5
79.6
95.0
79.3
95.5
78.5
95.2
77.4
96.5
78.2
96.0
78.2
96.3
77.7
96.0
79.0
95.5
84.9
84.9
83.7
84.9
87.5
83.7
84.4
84.4
84.9
85.2
83.9
84.2
84.4
y
79.5
95.2
79.5
95.2
79.5
95.2
79.5
95.2
77.7
95.5
77.7
95.5
77.7
95.5
77.7
95.5
78.2
97.7
84.6
84.6
84.6
84.6
86. 1
85.1
8H.6
84.6
84.6
84.6
84.6
84.6
84.6
e
"0.4
0.3
0.1
"0.2
"0.2
0.3
"0.9
"0.2
1.0
0.6
0.5
0.6
0.7
0.5
0.8
"2.2
0.4
0.4
"0.9
0.4
0.9
"1.5
"0.1
"0.1
0.4
0.6
"0.7
"0.4
~0.1
s(y)
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.28
0.36
0.23
0.23
0.23
0.23
0.60
0.60
0.23
0.23
0.23
0.23
0.23
0.23
0.23
y
71.3
76.1
72.1
75.3
72.4
76.3
72.1
75.8
70.7
77.1
71.8
76.9
71.5
79.9
73.2
77.9
72.6
77.4
72.4
73.7
72.4
72.1
72.9
70.1
72.6
72.4
72.4
72.9
70.7
71.0
71.3
y
71.9
76.5
73.0
75.8
71.9
76.5
73.0
75.8
71.0
77.7
72.0
77.1
71.0
77.7
72.0
77.1
72.0
78.3
71. £
72.3
72.1
72.1
71.9
72.3
72.1
72.1
72.1
72.1
72.1
72.1
72.1
e
"0.6
"0.4
"0.9
~0.5
0.5
"0.1
"0.9
"0.3
"0.6
~0.2
"0.2
0.6
2.2
1.2
0.8
0.7
"0.9
0.5
1.4
0.3
1.0
"2.1
0.5
0.3
0.3
0.8
"1.4
"1,1
"0.8
s(y)
0.57
0.56
0.57
0.56
0.57
0.56
0.57
0.56
0.57
0.56
0.57
0.56
0.57
0.56
0.57
0.56
0.33
0.44
0.49
0.49
0.28
0.28
0.49
0.49
0.28
0.28
0.28
0.28
0.28
0.28
0.28
y
78.7
91.2
78.7
91.0
78.4
91.0
77.4
90.5
75.3
92.5
76.6
92.0
76.3
92.8
75.8
92.3
78.4
93.0
82.5
82.5
80.4
81.2
83.2
80.7
82.5
82.7
83.2
83.0
80.2
81.4
80.9
y
78.5
90.9
78.5
90.9
78.5
90.9
78.5
90.9
76.0
92.0
76.0
92.0
76.0
92.0
76.0
92.0
77.5
S4.3
82.1
82.1
80.9
80.9
82.8
81.4
a2.i
82.1
82.1
82.1
82,1
82.1
82.1
e
0.2
0.4
0.2
0.1
"0.1
0.1
"l.l
"0.4
"0.7
0.5
0.6
0.4
0.7
"0.1
0.2
0.9
"1.3
0.4
0.4
"0.5
0.3
0.4
"0.7
0.4
0.6
1.1
0.9
"1.9
"0,6
"l.l
s(y)
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.29
0.37
0.24
0.24
0.63
0.63
0.40
0.40
0.24
0.24
0.24
0.24
0.24
0,24
0.24
(Continued)
-------
Table 5.4-3 (cont'd)
1000 Hz Octave Band
Location 1
Location 2
2000 Hz Octave Band
Location 1 Location 2
U)
y
70.6
75.6
71.4
74.3
71.7
75.6
72.0
73.6
70.9
75.4
71.2
75.9
69.5
82.0
72.0
77.2
71.2
74.9
71.7
72.8
70.9
70.9
73.0
69.8
72.5
72.3
72.3
72.5
70.1
69.8
70.6
y
71.2
75.7
72.5
74.2
71.2
75.7
72.5
74.2
69.8
77,5
71.1
76.0
69.8
77.5
71.1
76.0
71.1
77.2
71.7
71.4
71.6
71.6
71.4
71.6
71.6
71.6
71.6
71.6
71.6
71.6
71.6
e
"0.6
"0.1
"l.l
0.2
0.5
~0. 1
"0.5
~0.3
1.1
"2.1
0.1
~0.1
"0.2
4.4
0.9
1.2
"2.3
1.3
"0.6
"0.6
1.7
"1.9
1.0
0.7
0.7
1.0
"1.5
"1.7
~0.9
s(y)
0.84
0.83
0.84
0.83
0.84
0.83
0.84
0.83
0.84
0.83
0.84
0.63
0.84
0.83
0.84
0.83
0.50
0.65
0.73
0.73
0.41
0.41
0.73
0.73
0.41
0.41
0.41
0.41
0.41
0.41
0.41
y
75.6
90.8
75.4
90.0
75.6
90.5
74.3
89.8
y
75.4
90.9
75.4
90.9
75.4
90.9
75.4
90.9
e
0.2
"0.2
"0.9
0.2
"0.4
"1.1
"1.2
sCy)
0.29
0.29
0.29
0.29
0.29
G.29
0.29
0.29
73.6 73.6 "0.1 0.29
90.0 89.1 0.9 0.29
73.3 73.6 "0.3 0.29
89.5 89.1 0.4 0.29
73.6 73.6 "0.1 0.29
SO.5 89.1 1.4 0.29
73.8 73.6 0.2 0.29
89.5 89.1 0.4 0.29
73.8 74.2 ~0.4 0.26
90.0 91.3 "1.3 0.29
82.5 82.0 0.5 0.18
82.0 82.0 0.18
61.2 82.0 "0.7 0.18
83.5 82.0 1.5 0.18
86.5 84.9 1.6 0.60
80.0 81.4 "1.4 0.60
82.5 82.0 0.5 0.18
82.5 82.0 0.5 0.18
82.5 82.0 0.5 0.18
62.0 82.0 0.18
82.0 82.0 O.lb
82.0 82.0 0.18
81.2 82.0 "0.7 0.18
y y e s(y)
66.9 67.j. "0.3 0.36
70.1 70.2 "0.1 0.36
68.7 68.5 0.2 C.36
69.5 70.0 "0.4 0.36
67.1 66.6 0.5 0.36
70.3 69.7 0.7 0.36
67.7 68.0 "0.3 0.36
69.5 69.4 0.1 0.36
67.1 67.1 0.1 0.36
68.7 68.8 "0.1 0.36
67.9 66.5 "0.5 0.36
68.5 68.6 "0.1 0.36
66.6 66.6 0.36
68.2 68.3 "0.1 0.36
68.7 68.0 0.8 0.36
68.7 68.1 0.7 0.36
67.4 67.8 "0.4 0.22
69.5 70.0 ~0.5 0.28
67.1 67.0 0.2 0.31
68.5 68.1 0.3 0.31
67.7 66.9 0.7 0.48
64.9 65.9 "l.O 0.48
68.2 68.3 0.31
66.6 66.8 ~0.2 0.31
67.9 67.5 0.4 0.18
67.7 67.5 0.1 0.18
68.5 67.5 0.9 0.18
68.2 67.5 0.7 0.18
66.9 67.5 "0.7 0.18
66.6 67.5 "l.O 0.18
66.9 67.5 ~0.7 0.18
y y e s(y)
70.3 70.2 0.1 0.52
88.3 87.9 0.4 0.51
71.6 71.3 0.3 0.52
87.5 86.8 0.7 0.51
70.8 70.5 0.4 0.52
88.5 88.2 0.3 0.51
71.6 71.6 0.52
87.3 87.1 0.2 0.51
68.7 69.5 ~0.7 0.52
87.5 87.1 0.4 0.51
70.8 70.6 0.3 0.52
86.5 86.1 0.4 0.51
70.3 69.8 0.6 0.52
87.5 87'.4 0.1 0.51
71.6 70.9 0.8 0.52
87.3 86.4 0.9 0.51
68.2 69.7 "1.4 0.39
86.8 89.3 "2.6 0.48
74.9 74.7 0.2 0.49
73.9 74.8 "0.8 0.49
75.7 76.0 "0.3 0.75
75.7 76.6 "0.9 0.75
76.7 77.3 "0.6 0.75
75.2 75.9 "0.7 3.75
74.7 74.7 ~C.l 0.31
74.4 74.7 ~0.3 0.31
74.4 74.7 "0.3 0.31
74.2 74.7 ~0.6 0.31
75.9 74.7 1.2 0.31
76.2 74.7 1.5 0.31
75.4 74.7 0.7 0.31
(Continued)
-------
Table 5.4-3 (cont'd)
4000 Hz Octave Band
Location I
Location 2
8000 Hz Octave Band
Location 1
Location 2
y
63.4
62.5
65.6
64.3
62.8
61.9
64.5
63.4
63.7
62.5
64.5
£ 62.2
62.2
60.4
63.7
61.9
63.4
62.2
61.9
64.5
64.3
57.9
63.7
63.4
63.4
63.4
63.4
64.5
62.5
62.8
62. fe
y
64.1
62.8
65.5
64.1
62.4
61.1
63.8
62.4
63.5
62.1
64.8
63.4
61.8
60.4
63.1
61.7
64.1
62.6
62.1
64.7
63.2
59.8
64.1
62.8
63.4
63.4
63.4
63.4
63.4
b3.4
63.4
e
"0.7
"0.2
0.2
0.2
0.4
0.9
0.8
1.0
0.2
0.4
"0.3
"1.2
0.5
0.6
0.2
"0.7
"0.4
"0.2
"0.2
1.1
"1.8
"0.4
0.6
1.1
"0.9
"0.6
"0.6
s(y)
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.35
0.25
0.27
0.35
G.35
0.56
0.56
0.35
0.35
0.17
0.17
0.17
0.17
0.17
0.17
0.17
y
69.6
78.0
70.4
78.2
69.3
79.0
70.4
79.2
66.4
80.7
70.4
80.7
68.8
80.5
70.1
80.7
63.7
74.7
66.2
67.2
71.9
68.8
71.9
71.7
66.4
66.7
67. C
67.2
71.9
72.4
71.4
y
68.9
78.8
68.9
78.8
68.7
78.6
68.7
78.6
69.2
79.1
69.2
79.1
69.0
78.9
69.0
78.9
66.9
79.4
68.2
68.2
71.8
71.4
72.7
73.4
68.2
68.2
68.2
68.2
68.2
68.2
68.2
e
0.7
"0.8
1.5
"0.6
0.6
0.4
1.7
0.6
"2.8
1.6
1.1
1.6
"0.2
1.6
1.1
1.8
"3.2
"4.7
"2.0
"0.9
0.1
"2.6
"0.8
"1.7
"1.7
"1.5
"1.2
"0.9
3.7
4.2
3.2
s(y)
1.01
0.99
1.01
0.99
1.01
0.99
1.01
0.99
1.01
0.99
1.01
0.99
1.01
0.99
1.01
0.99
O.S4
1.16
0.75
0.75
1.82
1.82
1.82
1.82
0.75
0.75
0.75
0.75
0.75
0.75
0.75
y
61.2
58.8
63.6
61.2
59.9
57.7
62.3
60.2
60.7
57.4
61.8
58.2
58.2
55.0
60.7
57.1
60.7
58.5
57. S
60.4
62.3
52.2
61.5
60.7
60.4
61.0
61.5
61.8
60.4
61. C
61.0
y
62.1
59.4
63.9
61.1
59.5
56.7
61.2
58.5
60.7
57.9
62.4
59.7
58.0
55.3
59.8
57.0
62.2
59.2
57.5
61.0
60.0
54.7
62.3
59.4
60.8
60.8
60.8
60.8
60.8
60.8
60.8
e
"0.9
"0.6
"0.3
0.1
0.4
1.0
1.1
1.7
"0.5
"0.7
"1.4
0.2
"0.3
0.9
0.1
"1.5
"0.6
0.4
"0.6
2.3
"2.5
"0.8
1.3
"0.4
0.1
0.7
0.9
"0.4
0.1
0.1
sCy)
0.51
0.51
0.51
0.51
0.51
0.51
0.51
0.51
0.51
0.51
0.51
0.51
0.51
0.51
0.51
0.51
0.40
0.43
0.82
0.82
0.82
0.82
0.54
0.54
0.30
0.30
0.30
0.30
0.30
0.30
0.30
y
66.7
73.0
69.5
74.0
66.9
73.2
69.5
74.2
65.4
75.2
70.5
76.0
66.9
74.5
69.5
75.5
56.5
65.1
57.9
59.9
70.2
62.8
69.5
6S.5
58.8
58.8
60.4
58.5
69.5
68.9
68.9
y
67.5
73.7
67.5
73.7
66.3
72.5
66.3
72.5
68.1
74.2
68.1
74.2
66.8
73.0
66.8
73.0
63.1
71.8
61.8
61.8
69.8
67.3
70.9
72.0
61.8
61.8
61.8
61.8
61.8
61.8
61.8
e
"0.8
"0.7
1.9
0.3
0.6
0.8
3.2
1.8
"2.7
1.0
2.4
1.7
0.1
1.5
2.6
2.5
"6.6
"6.7
"3.9
~2.C
0.5
"4.5
"1.5
"2.6
"3.0
"3.0
"1.4
"3.3
7.6
7.1
7.1
s(y)
1.75
1.72
1.75
1.72
1.75
1.72
1.75
1.72
1.75
1.72
1.75
1.72
1.75
1.72
1.75
1.72
1.64
2.01
1.30
i.30
3.16
3.16
3.16
3.16
1.3G
1.30
1.30
1.30
1.30
1.30
1.30
-------
Estimates of a, the standard deviations due to experimental error, can
be obtained from the residuals and are listed in Table 5.4-4. The
quantity a is the standard deviation among sound level measurements
taken under fixed experimental conditions. Based on the estimate of
a, the form of the experimental design and the final form of the fitted
model, the standard error s(y) of each y can be obtained; see Table
5.4-3. This quantity is the standard error of the estimated average
sound level at the particular experimental conditions. The standard
error , s(y), is obviously small if a is small and if y is a prediction
corresponding to experimental conditions near the center of the experi-
mental design. As we depart from the experimental region s(y) increases
sharply, a consequence of extrapolation. If we recall the six relatively
remote axial combinations (Tests 19-24 of Table 5.4-1), we note that
* 2
these s(y)'s are higher whenever the term P^x^ is in the fitted model,
where x^ denotes the variable that assumes the extreme values +2 in
the axial combination.
5.5 NOISE PREDICTION COMPUTER CODE
The original prediction code is based on the material in Reference 7 .
This code was developed to predict the linear and A-weighted noise
levels radiated from the cooling tower without the dry flow heat exchangers,
5.5.1 Program Code Modifications
In the form described in Reference 7, the code did not include correct-
ions for either atmospheric absorption or ground attenuation. Thus the
major modifications that were made to this code were (1) incorporating
the regression equations from Section 5.4 to account for the effect of
the heat exchangers, (2) adding code to calculate the total atmosphere
absorption for any conditions, (3) adding code to calculate the
absorption of the ground surface between the tower and the receiver
and (4) rewriting much of the mainline code to accommodate
139
-------
TABLE 5.4-4
ESTIMATES OF STANDARD DEVIATION
Octave Band
Center Estimate of 0, dB
Frequency Location 1 Location 2
63 Hz 1.3 0.8
125 Hz 1.4 0.8
250 Hz 1.0 0.8
500 Hz 1.0 0.8
1000 Hz 1.5 0.8
2000 Hz 0.6 0.9
4000 Hz 0.8 2.3
8000 Hz 1.1 4.0
140
-------
calculations on an octave band rather than an overall frequency basis.
This last step was necessary because the atmospheric and ground attenu-
ations are frequency-dependent and, hence, cannot be applied directly
to the linear and A-weighted sound levels,
5.5.1.1 Atmospheric Absorption.
Correcting noise propagation over ground terrain has been a very dif-
ficult task because of the need to know the complex acoustic impedance
over the ground between the source and receiver. In the last few years,
considerable success has been achieved in modeling the ground surface
with the acoustic properties of fibrous absorbent materials. Delany and
Bazley6 determined expressions for the complex acoustic impedance of the
fibrous materials as a function of frequency and the flow resistance of
the material. Chessel1**5 was the first to show that use of these im-
pedance expressions along with either Rudnick's^ or Ingard's8 theory of
sound reflection from a finite impedance produced results for ground
absorption which agree very well with experimental data.
The geometry of the ground propagation problem is as shown in Figure
5.5-1.
Dwg. 7697A77
Receiver, R
Z! = poco
//////////eV
f Rs ) ' *H Rr
.HS
Rt
Image Source, Sl
Figure 5.5-1. Source-Receiver Geometry,
141
-------
Delaney and Bazley have shown that the impedance ratio, Z./Z.. can be
written as
Z /Zl = 1+ 9.08(f/0)~°'75 - 11.91(f/a)~°'73 (5.5-1)
and that the propagation coefficient ratio, k^/k. , can be written as
k/k - 10.3(f/a)~°'59 + i(l + 10.8(f/a)~°'70) (5.5-2)
Rudnick's expressions for the plane wave reflection coefficient, RP,
and the 'so-called* numerical distance, w, have been used rather than
Ingard's simpler expressions. Ingard's formulations are strictly valid
only for small grazing angles (small values of 9) which may not exist if
noise levels are calculated close to the cooling tower. The spherical wave
reflection coefficient is found from
RP = (sin 9 - 6Z /Z )/(sin Q + 6Z /Z ) (5.5-3)
where 6 - (1 - k2/^ cos2 6)"*
and the numerical distance from
w = 2ik r (Z /Z )262/[(l-RP) cos e] (5.5-4)
The image source strength can be expressed as
Q = RP + F(w) (1-RP) (5.5-5)
where F(w) is a boundary loss factor which can be evaluated from the
following expressions.
142
-------
- + i [6XP (-W)] (W) 2 u .n-1
F(w) = < for |w| < 10
o^« . . (5.5-6)
n-1 2 n!(2w)'
(or w, 10
Considering spherical spreading, the velocity potential at the source
can be given as
exp(ikr^)
$ = [i + (ri/r2)Q exp(ikAr]) (5.5-7)
The excess attenuation caused by the boundary surface alone is
A (dB) = 20 lOfe.Jl + (r /r )Q . xp(ikAr)| (5.5-8)
e -L'-' 1 2
On expressing Q as |ojexp(i3) and modifying the equation to account for
finite bandwidths, A can be written as
e
2 2 - sin(uAr/X^)cos(nAr/X_.
A (dB) = 10 lognn [1 + (1/r2) |Q.| 4
e lu i
where u = 2irAf/2f
1
iy
(5.5-9)
n = 2Tr[l + (Af/2f±)2]
Ar = r -
= Co/fi
Bi = tan'1 [Re(Qi)/Im(Q1)]
r1 = r /r
2 1
143
-------
The Q, , A.JL and 3^ are values corresponding to the respective octave
band center frequencies.
For large values of Q (e > 30°) the effects of the boundary loss factor,
F(w), become very small. In this case significant computational econ-
omics occur because Equation (5.5-5) reduces to
Q = RP (5.5-10)
and Ingard's expression for RP
RP = (sin 6 - Z1/Z2)/(sin 6 + Z^Z,,) (5.5-11)
can be used instead of Equation (5.5-3).
The equations presented here constitute the basis of subroutine GKND
with one exception. Oncley1" points out that the sign of the reactive
component of the ground impedance, Equation (5.5-1), is an arbitrary
choice. In acoustics this is conventionally taken to be negative. How-
ever, for this problem, an examination of the vector relationships of
the terms comprising the velocity potential, Equations (5.5-7) and
(5,5-5), indicate that the reactive impedance component must be positive
for the calculation of the attenuation to be valid. This has been done
in subroutine GRND.
5.5.2 Pr ogram- Code Operation
In terms of calculation, the program treats the noise radiated from the
fan stack and the louvered open faces of the tower separately. The
first step in the program is to calculate the octave band source sound
levels for the specified tower operating conditions from the fitted
regression equations. The atmospheric absorption is then calculated in
dB/ft for the given atmospheric conditions. Then, for each distance from
144
-------
the tower at which the receiver noise level is desired, the program cal-
culates the spherical spreading attenuation and the ground attenuation
for each of the two sources. The octave band noise levels at the receiver
from each source is determined by adding the atmospheric absorption
attenuation, the respective spherical spreading attenuation and the ground
attenuation to the calculated source levels. A directivity correction
factor is also applied to the fan stack source noise level. The "total"
noise level at the receiver is then found by summing, on a mean square
pressure basis, the octave band noise level at the receiver produced by
each of the two sources. The overall linear and A-weighted noise levels
at the receiver location are determined by summing (again, on a mean
square pressure basis) the corrected octave band levels.
The program assumes that the receiver is always located perpendicular
to one of the louvered faces of the tower, equidistant from either
side. The decrease in the louvered face noise level at the receiver
location from that six feet away from the tower is found from
10 log1(J [ir/(2 tan'l(h/d) tan~1(t/2d))] (5.5-12)
where
h = tower height, m
t = tower width, m
d = distance from tower base to receiver, m
This equation accounts for spreading 'losses'. It is discussed in more
detail in Reference 7. This reference also discusses how this equation
changes if the receiver is located either (a) perpendicular to the
louvered face of the tower at one of the tower edges, or (b) at an angle
Y away from a perpendicular line to the louvered face at one of the
tower edges.
145
-------
The decrease In the fan stack discharge noise level from the stack to
the receiver is calculated from Equation (5.5-13)
AL2(dB) - 10 Iog1() [s/11.2ffr2] (5.5-13)
where
S = area of the fan stack discharge, m2
r = distance from fan stack to receiver, m
This equation basically accounts for spherical spreading losses from the
finite sized fan stack discharge and is Valid regardless of the position
of the receiver (as long as r is several times larger than the fan stack
diameter).
5.6 DISCUSSION OF RESULTS
The project results can be separated into three categories for purposes
of discussion. These three categories are (1) the experimental data
and its acquisition, (2) regression analysis and (3) the noise pre-
diction computer model. Each of these are discussed below.
5.6.1 Experimental Data
No apparent problems occurred during the data acquisition at the TVA
tower site. Weather conditions were good: temperatures of 60-70°F,
sunny-overcast skies with no rain and wind speeds less than 10 miles/hr.
As shown in Figure 5.1-3 and noted in Section 5.1, the ground level
measurements were made at perpendicular distances of 3, 6 and 12 ft.
from the louvered face of the tower oriented away from the main plant.
All of the data from these locations were analyzed and corrected for
the effects of background noise. All of the data were louder than the
146
-------
background except for some of the 125 Hz octave band data. When the time-
averaged background noise exceeds the time-averaged tower noise, as in
this case, no information about the true tower noise level for these
conditions can be determined. Hence, for these cases a zero is listed
in the tables of corrected tower noise levels. (See Table 5.4-1 for
125 Hz data at Location 1, for example.)
Ten of the 31 noise levels measured at 12 ft. from the tower were in-
determinate because of the high average background noise levels. Five
of the 31 measured noise levels at 3 and 6ft. from the tower were
similarly indeterminate. The measured noise levels at 3 and 6 ft. for
the other 26 tests were virtually identical. From this information,
the data obtained at 6 ft. from the tower was chosen as being most
representative, and this measuring location was designated 'Location 1'.
No further use was made of the data at the other two distances.
The high 125 Hz octave band background noise levels were most likely
produced by several sources including (1) nearby multi-cell Marley
cooling towers, (2) main plant power transfer and (3) the main plant
turbine hall. An examination of the data in Table 5.4-1 at Locations
1 and 2 for those tests where the background noise exceeded the noise
level at Location 1 (zero entries in Location 1 data column) indicates
that this occurred when the tower fan speed was 50 percent, the lowest
value tested. The corresponding data in the Location 2 column indi-
cates that for 50 percent fan speed, the tower produces the lowest 125
Hz octave band fan noise levels. Hence, the zeros in the Location 1
column are explainable in terms of reduced 125 Hz band fan noise coupled
with a relatively high 125 Hz band background noise.
5.6.2 Regr ess ion Analysis
The regression analysis was a rather straightforward process for this
project because it was possible to choose tests optimally to fit the
desired experimental design. The only deviation from the optimal was
147
-------
the occurrence of the zero values in the 125 Hz octave band noise levels
at Location 1. The regression analysis for this case was performed
using the 26 valid test noise levels. The missing five test values did
not significantly affect the analysis because not all the terms of the
model [Equation (5.4-2)] appeared in the final fitted equation. Hence,
less than the 31 test noise levels were needed to successfully fit the
data.
Several interesting features of the fitted model coefficients in Table
5.4-2 are in agreement with our understanding of operation of the tower.
For example, the noise levels at the fan stack discharge (Location 2)
are dominated by the fan noise and this is apparent from the dominance
of the x1 and x terms in the Location 2 models. The size of the x
term diminishes at the higher frequencies (4 kHz and 8 kHz) because the
fan noise level is diminishing at these frequencies.
5.6.3 Npise_Predictipr^ Code
Operation of the prediction code is straightforward. However, there
are some cautions that must be exercised to ensure accuracy of the pre-
dicted results. These cautions apply in two areas; one is proper
characterization of the ground characteristics and the second is the
effect of variations in atmospheric turbulence.
5.6.3.1 Ground Absorption^
The ground absorption model incorporated into the code assumes that the
ground characteristics are the same over the entire area between the
tower and the receiver. In addition the terrain has been assumed to be
flat. Inclusion of means to account for uneven terrain is beyond the
current state of the art. Significant variations from either of these
assumptions can be expected to alter the calculated ground absorption.
148
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The ground absorption model Is based on the flow resistance ground
impedance model formulated by Chessel from the impedance results of
Delany and Bazley. This model relies on an empirical curve fitting
of the model impedance equations to field measurements. The fitting
parameter is the flow resistance, a. Values of a between 150 and 300 cgs
units have been found to fit existing data, acquired by other investi-
gations, for propagation over grass. The data indicate that a = 150 is
characteristic of shorter grass (15-25 mm) and a = 300 is characteristic
of taller grass. The prediction code uses a = 200 cgs units, and hence,
implicitly assumes grass covered ground.
The computer code calculates the ground absorption assuming that the
noise sources are concentrated at individual points (at the fan stack
discharge nearest the receiver and at the center of the louvered tower
face). This assumption is reasonable for the fan stack noise, but
open to some question for the noise radiated from the louvered face.
This question arises because the predicted A-weighted noise levels as a
function of distance from the tower exhibit greater amplitude variations
than seen in some experimental data reported in the literature. Because
the louvered tower face is relatively large (40 ft x 40 ft), the actual
path length of the ground reflected wave reaching the receiver varies
depending on the source point selected on the louvered face. This
difference in path lengths has the same effect on the received noise
level as changes in phase of the arriving waves. These changes in phase
will probably reduce the amplitude of the "peaks and valleys" in the
ground attenuation vs frequency curves.
The ground absorption calculations should be repeated for several source
points on the louvered face and the results averaged. A comparison of
the average absorption values with the point source values currently
used would indicate how important this effect is. This has not been
done for this report because of project time and cost constraints.
149
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5,6.3.2 Wind and Temperature Fluctuations
The real world atmospheric conditions include random fluctuations of
wind and temperature which cause fluctuations in the amplitude and phase
of the tower noise at the receiver. These fluctuations, if included in
the model, are expected to reduce the ground attenuation from the values
calculated for a quiet atmosphere. However, the theory required to in-
corporate these effects is still in its infancy and is not adequate for
predictive purposes. Hence, the prediction model is restricted in
application to conditions with minimal wind over the region between the
tower and the receiver.
5.7 ACKNOWLEDGEMENTS
Our thanks to L. J. Harper and R. P. Martin for acquiring and analyzing
the experimental data and for providing many suggestions which contri-
buted to the successful completion of this project.
5.8 ACOUSTICS REFERENCES
1. TVA Cooling Tower Test Grid, November 28, 1977.
2. Hribar, A. E., "Noise Levels Generated by the PCSD Demonstration
Cooling Tower—West Configuration", Westinghouse Research Report
74-1E9-TOWNO-R1, Westinghouse Research Laboratories, October 1974.
3. "Standard Values of Atmospheric Absorption as a Function of Temper-
ature and Humidity", ARP 866A, Society of Automotive Engineers, Inc.,
March 1975.
4. Chessel, C. I., "Propagation of Noise Along a Finite Impedance
Boundary", J. Acoust. Soc. Am., Vol. 62, No. 4, October 1977, pp.
825-834.
5. Chessel, C. I., "Meteorological and Ground Effects on the Propaga-
tion of Aircraft Noise Close to the Earth's Surface", J. Sound Vib.,
Vol. 60, No., September 22, 1978, pp. 251-266.
6. Delany, M. E. and Bazley, E. N., "Acoustical Properties of Fibrous
Absorbent Materials", Applied Acoustics, Vol. 3, 1970, pp. 105-116.
150
-------
7. Hribar, A. E., "A Noise Level Prediction Procedure for Multi-Cell
Induced Draft Cooling Towers", Westinghouse Scientific Paper 75-
1E9-TOWNO-P1, Westinghouse Research Laboratories, May 12, 1975.
8. Rudnick, I., "The Propagation of an Acoustic Wave Along a Boundary",
J. Acoust. Soc. Am., Vol. 19, 1947, pp. 348-356.
9. Ingard, U., "On the Reflection of a Spherical Sound Wave from an
Infinite Plane", J. Acoust. Soc. Am.. Vol. 23, 1951, pp. 329-335.
10. Oncley, P. B., "Propagation of Jet Noise Near a Porous Surface",
J. Sound Vib.. Vol. 13, No. 1, 1970, pp. 27-35.
5.9 ACOUSTICS NOMENCLATURE
A Excess attenuation, dB.
BP Tower fan blade pitch, degrees.
c Speed of sound in air, m/sec.
d Ground distance between tower and receiver, m.
DF Percent of total tower water flow passing through the dry
heat exchangers, percent.
A
e Residual value = y-y, dB
f Frequency , Hz .
FS Tower fan speed, percent of maximum.
h Cooling tower height, m.
i
k Propagation coefficients in air, ground = 2irf/c, m
1 » 2
n Numerical index for summations, dimens ionles s.
Q Image source strength.
r Direct and reflected path length between source and receiver,
J. • £.
' m.
1 Ratio r2/r1.
R Receiver location.
Rr Ground distance defined in Figure 5.5-1.
Rs Ground distance defined in Figure 5.5-1.
Rt Ground distance = Rr + Rs, m.
151
-------
RP Spherical wave ground reflection coefficient, dimensionless.
s\
s(y) Standard error of fitted values, dB.
S Source location (also area of fan stack exhaust for Equation
[5.5-13] only, m2).
s1 Source image location.
w Complex numerical distance defined by Equation (5.5-4), m.
WFR Total tower water flow rate, gpm.
x1,...x. Coded form of the tower independent variables, dimensionless,
y Observed tower dependent variable (sound level), dB«
A
y Fitted tower dependent variable (sound level), dB.
Z Air and ground impedance, mks rayIs.
1»2
Greek SymbpIs
a Material flow resistance
6. Unknown model coefficients, i - 0,1,...,4
Af Octave band frequency bandwidth, Hz.
Ar Path length difference, r2 - r^, m.
T) Frequency parameter defined in Equation (5.5-9).
8 Angle of incidence (to ground) of reflected ray from source,
deg.
A. Wavelength of sound in air = c /f, m.
P Density of air, kg/m3.
CT Standard deviation of fitted variables, dB.
<(> Velocity potential of the source.
152
-------
SECTION 6.0
PLUME TESTS
The prediction of the spread and dissipation of cooling tower plumes is
a continuing matter of interest in the electric power industry. This
interest has engendered numerous methods for predicting plume behavior
using a small number of surface-based meteorological measurements and
cooling tower parameters. Of course, these analyses must be verified
with experimental data. This verification requires the use of a cooling
tower.
The wet/dry cooling tower at the Cliffside Power Station at Cliffside,
North Carolina, is a unique facility for collecting such data, because
of the-available wide range of control of the state of the air leaving
the cooling tower.
During the period March 18, 1978, to May 18, 1978, 60 measurements of
plume properties were made at Cliffside, mostly in the morning under
stable atmospheric conditions. These tests covered the following range
of parameters: stack exit relative humidity - 84.42 percent to 100 per-
cent; plume length - 0 to 235 feet; plume height - 0 to 257.2 feet. The
results of this investigation are described in this section.
6.1 PLUME INSTRUMENTATION
Study of the growth and dissipation of cooling tower plumes requires
both micro-meteorological measurements (in the vicinity of the plume)
and measurements of the plume dimensions.
153
-------
. 7697A78
Figure 6.1-1 a. Tethers.onde Instrument Package.
Figure 6-1-lb. Tethersonde Balloon in Flight.
154
-------
The originally proposed meteorological instrumentation was to be an
anemometer and an automatic psychrometer on a meteorological tower.
Several problems, however, made the use of a tower undesirable and forced
us to consider other alternatives:
1. The plant manager did not want to have a tower which might,
conceivably, fall onto some transmission lines near the
cooling tower.
2. Since the spread and dissipation of the plume would be
expected to be affected most by air temperature and wind
velocities at the level of the top of the cooling tower
and above, a meteorological tower would have to be much
higher than the cooling tower. Such a tower would be very
expensive.
3. Because the spread and dissipation of the plume depends
on the structure of the atmospheric boundary layer, data
on this structure up to the height of the top of the
plume (200-300 feet) would be desirable. Since a meteor-
ological tower of practical cost would normally be less
than 100 feet high, we can again see that a meteorological
tower would have been the wrong instrument platform for
the job.
Because of the foregoing considerations, a tethered balloon-mounted
meteorological sensor package was used instead of a meteorological tower.
This system (see Figure 6.1-1), comprising a balloon and winch, an air-
borne sensor package, and a ground receiver package, was produced by
the Atmospheric Instrumentation Research Company of Boulder, Colorado,
under the name of Tethersonde. The sensor package contained a wet and
a dry bulb thermometer (mechanically aspirated), an anemometer, a wind
direction indicator, and a differential barometric pressure transducer.
(This latter was an instrument which read the pressure difference—in
millibars—between the surface and the instantaneous balloon altitude.)
While the differential barometer itself had a potential resolution
equivalent to an altitude change of 21 feet, pressure fluctuations
equivalent to altitude changes of about 100 feet appeared on the Tether-
sonde output in the stronger winds, when no equivalent change of altitude
155
-------
was apparent from watching the balloon. These fluctuations may have
been caused by the effect of the dynamic pressure of the wind on the
static pressure port of the Tethersonde.
The sensor package also contained a small UHF telemetry transmitter
which transmitted the data to the receiver on the ground as five channels
of time-multiplexed data.
The plume program as furnished by Rubin (see Appendix I) contained a
prediction of visibility in the densest part of the plume, which was
intended to be correlated with subjective evaluations of plume density.
Earlier tests had apparently validated the significance of this pre-
dicted visibility as a measure of the perceived density of the plume1.
In the present tests, an attempt was made to check the quantitative
accuracy of this portion of the analysis by mounting a small transmitto-
meter in the exhaust plume one stack radius above the cooling tower out-
let. (The transmittometer is manufactured by Meteorology Research, Inc.
[MRI] of Altadena, California, as the model 1580 Fog Visiometer.) In
order to bring the range of the instrument more in line with the antici-
pated observations, the range was changed from a span of 256 to 25,600
feet to a range of 25.6 to 2560 feet by changing the reference calibra-
tion voltage on the Visiometer from 1.1 volts to 0.11 volts, in accord-
ance with the instructions on pages 4-10 and 4-11 of MRI Instruction
Manual IM-142. A tenfold reduction of the range is more than normally
recommended by the manufacturer, but MRI verified that such a reduction
in range could be done if the reference calibration was set with a suf-
ficiently accurate voltmeter.
Due to the turbulence in the jet leaving the cooling tower, a meaningful
measurement of visibility would most accurately be taken along a base-
line of length comparable to £he visibility to average—in space—the
turbulent fluctuations of the scattering coefficient in the plume.
156
-------
Since the turbulence in a free jet can be considered to be ergodic, an
average over a lengthy period of time would be equivalent to an average
over a long baseline. Scattering coefficients (or the proportionate
voltage output of the Visiometer) were averaged, rather than visibilities,
since scattering would be cumulative along a long light path, whereas
visibility would not be.
Examination of the plume photographs taken during the tests showed that
the Visiometer was always immersed in the plume. While there are severe
discrepancies between the calculated and measured visibilities, the
measured visibilities are always lower than the calculated (except in
test 511071 and 511072), so that the discrepancy could not be explained
as a result of the plume missing the Visiometer.
Plume height and length were measured by elementary surveying techniques.
Four observing points, designated as A, B, C, and D, were chosen, located
on generally perpendicular axes intersecting at the cooling tower. One
of these axes was parallel to the prevailing winds at Cliffside. The
distances of the observing points from the cooling tower were as follows:
point A, 545 feet; point B, 750 feet; point C, 390 feet; point D, 455
feet. The observing point chosen for any given run was always one for
which the line of sight from the observing point to the plume was most
nearly perpendicular to the axis of the plume, to assure the greatest
accuracy of the plume height and length measurements. Obviously, locat-
ing an observing point for each run to give a line of sight rigorously
perpendicular to the axis of the plume would have given a more accurate
measurement, but at the cost of an unaffordable increase in the time
required per run. Further, it would be difficult to define a unique
plume direction if there were a significant shift of wind direction over
the height of the plume, such as might exist under inversion conditions.
Once the direction of the axis of the plume had been determined, the
proper sighting point was chosen and the elevation and length of the
plume determined by sighting with a transit (see Figure 6.1-2).
157
-------
Dwg. 7697A79
I I
Figure 6.1-2. Sample Theodolite Data.
158
-------
The temperature, velocity, and humidity of the efflux from the cooling
tower were measured by the cooling tower instrumentation (see Section
4.0).
A complete study of plume spread and dissipation further requires that
the cloud cover be described for each test, and that the shape of the
plume be described. This was achieved, during these tests, by photo-
•p
graphing the plume with Polacolor type 108 film from the observing
point. (Polacolor is a trademarked name for a color film produced by
the Polaroid Company of Cambridge, Massachusetts.) Earlier studies had
shown that color photographs, much more than black and white photographs,
were capable of depicting the subtle differences between a plume and an
overcast background, and some trial runs at the start of these tests
verified this.
6.2 PLUME DATA ACQUISITION TECHNIQUE AT THE CLIFFSIDE SITE
In order to actually acquire the data, a combination of manual and auto-
matic methods were used. Plume tests were run only on days when a plume
was observed by the on-site personnel arriving in the morning, about
sunrise. (Obviously, plumes cannot be observed in the dark.)
Data were acquired and recorded on three different media:
a) punched paper tapes containing cooling tower, Visiometer,
and Tethersonde data
b) written sheets containing transit readings of plume
angular height and length
c) photographs of the plume.
The Tethersonde receiver package contained a microprocessor which auto-
matically synchronized the receiver with the airborne unit, decoded the
signal, and presented the data on a strip chart recorder. The five
variables were also formatted in 7-bit ASCII code for output on a male
159
-------
EIA-RS-232 connector. Further, one selected channel of data was also
routed to the second channel of the strip chart recorder mentioned
earlier and recorded continuously.
In order to record data from both a Fluke 2240-B data logger and from
the Tethersonde, the outputs of the Tethersonde and of the data logger
were connected to a teletype equipped with a paper tape punch. Thus,
during operation, data could be routed to the paper tape punch from the
TTY keyboard, from the Fluke data logger, or from the Tethersonde re-
ceiver unit.
At the start of any given run, cooling tower data were scanned by the
Fluke datalogger and automatically punched onto paper tape. Fifty read-
ings of the Visiometer were then punched manually onto the tape.
Following this, Tethersonde data were entered on the tape, as follows.
A pseudo-channel number was punched onto the tape through the TTY key-
board, after which four lines of Tethersonde data were punched onto the
paper tape (together with additional incomplete first and last lines).
The Tethersonde data were taken at several levels, each level being in-
dicated by a different pseudo-channel number, as follows:
Channel 200 - 30 feet above ground level (AGL)
Channel 201 - 75 feet AGL
Channel 202 - 125 feet AGL
Channel 203 - 175 feet AGL
Channel 204 - Top of plume
On days when the wind was too high to fly the balloon, the instrument
package was mounted on a pole near the trailer, and this situation was
identified by the pseudo-channel number 300.
160
-------
Concurrently with this, the observer with the transit was positioned at
the appropriate observing point. Typically, five to eight measurements
were made of the height and length of the plume while a set of cooling
tower and Tethersonde measurements were being taken. These measurements
were written down.
T>
The observer photographed the plume using a Polaroid Automatic 250
Land Camera, taking one photograph at the start of a set of data and
one at the end. Both the photographs and the transit data sheets were
mailed directly to the Westinghouse R&D Center, Pittsburgh, Pennsylvania.
6.2.1 Data Handling at Westinghouse Fluid Systems Laboratory
The contents of the punched paper tapes so produced were transmitted
via commercial telephone circuits to the Westinghouse Fluid Systems Lab-
oratory, where the cooling tower data were extracted to perform cooling
tower calculations, and the Visiometer and Tethersonde data were combined
with the results of the cooling tower data to produce input cards for-
matted for Rubin's plume analysis program. A sample is in Table 6.2.1-1.
6.2.2 tond-gtWestinghouse R&pCenter_
These cards were sent to the Westinghouse R&D Center where they were
loaded onto magnetic disc. A series of text processing programs then
extracted the input cards for Rubin's program and sorted them by test
number. Identifying headers were then attached to the data for each
test run. The card images were then used as input for Rubin's program.
The transit data (see Figure 6.1-2) were also analyzed (by elementary
triganometric formulae) to produce a tabulation of plume heights and
lengths .
Cloud cover was estimated from the plume photographs, using the termin-
ology of the National Weather Service "Manual of Surface Weather Obser-
vations", where "overcast" means a cloud cover of more than 90 percent,
161
-------
TABLE 6.2.1-1
SAMPLE DATA, AS RECEIVED
11*
128
13S
140
151
168
17s
188
193
210
213
.~. •% .-v
i.i.0
23f
2--0
25§
2i§
?7*
2o3
290
3I§
31*
H!
•:••;•'&
3*0
36i
37g
380
391
4§B
411
421
430
4*i
450
460
47§
4SJ
490
530
Sis
521
533
540
550
: RUNID
2,945
2,943
2.934
2,945
1.951
2,930
201
109,240
13M58
189=673
109,381
221
111.173
111.39*
111,. 188
111=320
2L32
113,330
113.540
113,760
113, 970
1 14.83S
115.05*
1.5,260
115,480
: HUNID
1,953
1.977
1.963
1,945
l.?3*
1.9*9
•m
12&.460
126.630
126,890
127.110
2& 1
128.400
128, o20
123,833
129,053
204
511821
2,945
2.941
2,934
2.948
2.951
2,928
9,370
9.951
9.978
ia.14*
1-3.210
10.11*
9.990
10 JSfc
1*.*2*
10.15*
9,98*
1*.160
11.370
10.460
10.480
10,421
51l!i22
1,953
1.976
1,965
1.945
1.913
1.911
11.59*
11.900
11.930
12.020
11.781
11.75*
11.83*
11,870
flRK 23 i
2=945
2.938
2.932
2.947
2,951
2.923
39JII
39.310
39, 3il
39.70*
39.7§i
40.338
39,711
39,508
39.940
39.320
40.291
4i,3«
41,290
41,6/3
41,350
HAR 23 i
1,954
-,,974
1,965
, 1.943
1.91?
1.9*9
46,613
47,383
46.981
47.213
46.548
46,740
47. Mi
46.619
197a
2,947
Z.-537
2.931
2,945
2,949
2-920
3,190
3,190
3,240
3.180
3,23i
3.223
3.23g
3.160
3.140
3.196
3,236
3.190
3,480
1.400
3.55S
1978
1,955
1.972
1,966
1.94S
1.908
1,906
3.86*
4.07*
4.09*
4,173
3,830
3.981
3.930
3.96*
2.949
2.936
2,931
2,948
2,946
2.918
84,87g
34,660
84,82i
84.98S
84.910
34,85§
84.790
84,710
84,730
84,850
34.848
84.540
84,720
84.810
84,821
34,790
1.957
1,971
1.959
1,937
1.907
1.904
84.640
84.78i
84,318
84.90*
84,688
84.81*
84.69i
84=3M
2.919
2,935
2.932
2.953
2,945
2,917
7.950
4.663
6.301
7,598
8,331
11,171
10.00*
9,331
11.750
11.660
11.01*
11.000
13.270
12.710
14.061
12,518
1.961
1.972
1,952
1,936
1.9*7
1.902
10J73
9,9g0
9.690
ll.il*
11,240
13.9*8
11.420
10.95*
2,947
2,C36
2.935
2.950
2.941
2.914
35,610
33.01*
27.210
37.848
41,380 ,
42.360
36,203
33,701
44,820
4i,67§
44,560
43.423
58.551
54.518
56.11*
68,440
1,966
1,971
1,949
1.937
1,907
l,98g
37.580
39,420
44.510
43.260
47.790
48.48g
44.930
53.098
2,946
2,937
2,938
2,949
2,937
.35*
.591
,590
.38*
1.12*
1.280
1,320
,97»
,88§
1.388
,728
.7*8
.*2«
1.11*
1.22S
1.250
1.971
1,968
1,947
1,938
1.908
.350
.560
,258
,33@
,888
.70S
,800
.61*
2
2
£
2
L
317
341
341
04-.
19
25
15
359
331
342
334
355
358
28
326
40
1
1
1
1
1
341
LL
18
13
356
16
339
334
,/45
,933
.941
.958
,932
.4*0
.30*
.8**
,288
.30*
,6§8
.818
.40*
JS9
,600
,708
.780
-2g0
,900
.m
.975
,964
.945
,939
.988
.901
,208
,10«
,100
.901
.300
.800
.000
^H
*•*
P
s
(Continued)
162
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PROCESSED DATA
RUBIN'S PROGRAM
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"broken" is 60 to 90 percent coverage, "scattered" is 10 to 50 percent
coverage, and "clear" is less than 10 percent coverage. A "thin" layer
is one through which the sun, moon, stars, or part of the celestial dome
can be seen.
The plume data are tabulated in three appendices as follows: Appendix
H contains the raw data from the Visiometer and Tethersonde. Appendix
I contains reduced data from the Visiometer and Tethersonde as well as
stack exit air conditions, all formatted for input to the Rubin plume
model, which is also included in this appendix. Appendix J tabulates
plume height and length, comparing actual values with those predicted by
Rubin's model. Also included in the tabulation are cloud cover and
vertical temperature gradient. In most cases, the vertical temperature
gradients were obtained between the temperature on pseudo-channel 200
(30 ft AGL) and the top of the plume (channel 204). In some cases, when
the wind was too strong to permit flying the balloon to the top of the
plume, the temperature gradient over a lesser range of heights was used.
6.3 PLUME MODELING
The Rubin plume program1, listed in Appendix I, was used to generate the
predicted values given in Appendix J. The program uses Briggs'2 formula
to calculate plume rise for five different vertical temperature gradients,
from -0.004 to +0.004°F/ft. A Gausian dispersion model3 is used to
calculate plume length for both stable and unstable air. No intermediate
stability categories were considered. No attempt was made to modify the
program to consider the actual temperature gradient or stability category.
Actual temperature gradients were often an order of magnitude greater
than those considered by Rubin's program. The highest gradient considered
by Rubin's program was 0.004°F/ft. If the actual gradient exceeded this
value, the 0.004 figure was used in the analysis.
164
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To determine the stability category for calculating plume length, stable
conditions were assumed whenever the vertical temperature gradient was
greater than -0.0055°F/ft (l°c/100 m). This is the "dry adiabatic lapse
rate", the temperature drop a parcel of air would experience due to ex-
pansion (or contraction) if raised (or lowered) with no heat loss or gain.
6.4 ANALYSIS OF PLUME MTA
A least-squares fit of the measured plume rise to the forecast plume
rise for a correlation of the form
(observed rise) = m x (computed rise) + b
yielded
m = 0.1248
b = 92.34
and a coefficient of correlation of 0.5616 indicating a poor correlation.
The Large intercept shows that when the computed plume rise was nearly
zero, the actual plume rise averaged 92 feet. This systematic error is
probably attributable to the use of the Briggs plume rise modelf which
is based solely on plume buoyancy and neglects its initial momentum.
The initial momentum of the plume from a mechanical draft cooling tower
is relatively large and results in significant plume rise even for non-
buoyant plumes.
The small slope, m = 0.1248, shows that for large predicted plume heights,
actual heights were significantly smaller than predicted. This systematic
error can be explained by two factors. First, the prediction ignores the
internal turbulence of the plume, which significantly enhances dispersion
and reduces buoyancy. Second, the computer program assumed a vertical
165
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temperature gradient of 0.004°F/ft whenever the actual gradient was
greater than this value. Since actual gradients were often much greater
than 0.004, this factor alone would produce large errors in predicted
plume heights.
A similar calculation of predicted and observed plume lengths yielded a
coefficient of correlation = -0.0164 and the correlation between observed
and forecast plume scattering coefficients was 0.191. These correlations
indicate such a weak relation that it is meaningless to cite the slope or
intercept of the regression lines.
This poor correlation can also be explained by two factors. Again the
prediction ignores the internal turbulence of the plume in enhancing
dispersion. During the early stage of plume growth the dilution of the
plume is dominated by this internal turbulence. It is probable that
many of these plumes were so short that they did not go beyond this stage.
Also, Rubin*s model considers only two atmospheric stability classes,
stable and unstable. Because predictions for these two classes are
generally separated by one or more orders of magnitude, common practice
is to use six stability classes^.
6.5 DISCUSSION OF RESULTS
The results of this study may be considered under three separate headings:
a) The validation of the Ruben model
b) The compilation of plume data
c) Suggestions for further work.
6.5.1 Validation of the Rubin Model
It can be fairly stated that Rubin's program has been shown to accurately
predict neither plume height, length, nor visibility under the conditions
encountered in this study.
166
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Although the Rubin model could certainly be improved by merely consider-
ing more categories of stability and by using the actual vertical temp-
erature gradients, this was not done since many models already exist
which are vastly superior to the Rubin model. It is hoped that data
from this work can be used by others to help verify or calibrate these
models.
6.5.2 Compilation of Plume Data
The plume data have been compiled in the appendices to this report, with
the exception of the plume photographs. Copies of these photos on trans-
parency film, as well as the numerical data in machine readable form,
will be available from the Division of Energy Demonstrations and Tech-
nology, Tennessee Valley Authority, Cattanooga, Tennessee 37401.
6.5.3 Recommendations for Further Research
The authors are not prepared to comment on future developments in plume
modeling except to recognize that the state of the art has advanced
greatly since the Rubin model was developed.
In planning further field studies of cooling tower plumes, it would be
desirable to seek a wider range of atmospheric conditions than were
available during this study, which is limited to mostly stable, early
morning hours in the spring. Also, in planning plume studies for wet/dry
cooling towers, a program should be set up to study the conditions neces-
<
sary to eliminate the plume, and this study should be independent of the
plume trajectory study.
6.6 REFERENCES
1. Rubin and Klanian, "Visible Plume Abatement with the Wet/Dry Cooling
Tower", Power Engineering, March 1975, pp. 54-57.
167
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2. Briggs, G. A., Plume Rise, AEG Critical Review Series TID-25075,
November 1969.
3. Somers, E. V., "Dispersion of Pollutants Emitted into the Atmosphere",
Air Pollution Control, Part 1, Edited by W, Strauss, John Wiley &
Sons, New York, pp. 1-33, 1971.
4. Slade, David H., Editor, Meteorology and Atomic Energy, U. S. Atomic
Energy Commission, July 1968, Available from NTIS as TID-24190.
168
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SECTION 7.0
ACKNOWLEDGEMENTS
Beside the listed authors of this report there were several individuals
in Westinghouse who contributed materially to the successful execution
of this program, and their splendid efforts are hereby acknowledged:
1. K. A. Oleson of the Steam Turbine Division acted as an
initial liaison with TVA and served as a source of histor-
ical information on the test facility,
2. K. A. Katzor and D, E, Gonya of Power Generation Services
Division took care of contract administrative details,
Mr. Gonya performed yeoman service as liaison between the
test facility and the Fluid Systems Laboratory.
3. L. H. Keeler of Power Generation Services Division did
an excellent job in reactivating the test facility and
conducting the tests. He was ably assisted by D. Hauser,
D. Scruggs, and M. Jolley at the test site.
4. Last, but definitely not least, we are indebted to M. R.
Sorton and K. H. Lee of the Fluid Systems Laboratory who
labored long and hard at data transfer and reduction.
Mr. Sorton also contributed materially to the restoration
and expansion of instrumentation and data acquisition
equipment at the test site when the program was initiated.
169
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing]
1. REPORT NO. 2.
EPA-600/7-81-106a
4. TITLE AND SUBTITLE Testing and Analysis of a Wet/Dry
Crossflow Cooling Tower; Volume I. Test Program
and Results
7. AUTHOR(S)
D. L. Ayers , M. R. Hogan , A. E . Hribar , and
R.A. Luceta
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Westinghouse Electric Corporation
1310 Beulah Road
Pittsburgh, Pennsylvania 15235
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
3. RECIPIENT'S ACCESSION- NO.
5. REPORT DATE
July 1981
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT N(
TVA/OP/EDT - 81/47a
10. PROGRAM ELEMENT NO.
1NE624A
EPmUmNE72l-BE
13. TYPE OF REPORT AND PERIOD COVEREC
Task Final; 7/77-5/81
14. SPONSORING AGENCY CODE
EPA/600/13
is. SUPPLEMENTARY NOTES IERL-RTP project officer is Theodore G. Brna; TVA project di-
rector is H.B. Flora, II (Div. of Energy Demonstrations and Technology, Chatta-
nooga. TN 37401).
16. ABSTRACTThe repOrj. discusses the test program and performance analysis of a single
cell mechanical-draft wet/dry cooling tower in Cliffside, NC. Objectives of the pro-
gram were to obtain performance data and results on mass transfer, heat transfer,
fluid flow, plume formation, and acoustic characteristics for comparison with mo-
dels/theories. Correlations are presented for the wet-fill mass transfer coefficient,
wet-fill water loss, Colburn j-factor for the finned tubes, and fan efficiency in terms
of one or more of the following: water loading in the tubes, air loading over the fins,
log mean humidity difference, outlet water temperature, Reynolds number, and air-
flow rate. Acoustic data were fitted to a series of curves for each of the eight octave
bands. Attempts to model plume data failed. The report also describes the test
facility, test procedures, instrumentation, data acquisition, and data reduction.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
Pollution Fluid Flow
Cooling Towers
Tests Plumes
Analyzing Acoustics
Mass Transfer
Heat Transfer
13. DISTRIBUTION STATEMENT
Release to Public
b.lDENTIFIERS/OPEN ENDED TERMS
Pollution Control
Stationary Sources
19. SECURITY CLASS (This Report)
Unclassified
20. SECURITY CLASS (This page)
Unclassified
c. COSATi Field/Group
13B 20D
13A,07A,13I
14B 21B
20A
14G
20M
21. NO. OF PAGES
184
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