&EPA
United States
Environmental Protection
Agency
Environmental Monitoring and Support EPA-600 4-80-033
Laboratory June 1980
Cincinnati OH 45268
Research and Development
Thermal Analysis of
the ISCO 1680
Portable Wastewater
Sampler
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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 ENVIRONMENTAL MONITORING series.
This series describes research conducted to develop new or improved methods
and instrumentation for the identification and quantification of environmental
pollutants at the lowest conceivably significant concentrations. It also includes
studies to determine the ambient concentrations of pollutants in the environment
and/or the variance of pollutants as a function of time or meteorological factors.
This document is available to the public through the National Technical Informa-
tion Service, Springfield. Virginia 22161.
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EPA-600/4-80-Q33
June 1980
THERMAL ANALYSIS OF THE ISCO 1680
PORTABLE WASTEWATER SAMPLER
by
Philip C. L. Lin
Instrumentation Development Branch
Environmental Monitoring and Support Laboratory
Cincinnati, Ohio 45268
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DISCLAIMER
This report has been reviewed by the Environmental Monitoring and
Support Laboratory - Cincinnati, U.S. Environmental Protection Agency,
and approved for publication. Mention of trade names or commercial
products does not constitute endorsement or recommendation for use.
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FOREWORD
Environmental measurements are required to determine the quality of
ambient waters and the character of waste effluents. The Environmental
Monitoring and Support Laboratory - Cincinnati conducts research to:
Develop and evaluate techniques to measure the presence
and concentration of physical, chemical, and radiological
pollutants in water, wastewater, bottom sediments, and
solid waste.
Investigate methods for the concentration, recovery, and
identification of viruses, bacteria, and other microbio-
logical organisms in water. Conducts studies to determine
the responses of aquatic organisms to water quality.
Conduct an Agency-wide quality assurance program to assure
standardization and quality control of systems for moni-
toring water and wastewater.
The Instrumentation Development Branch of the Environmental Monitoring
and Support Laboratory provides functional designs relating to water quality
instrumentation systems. This report, on an investigation of the heat
transfer characteristics of an automatic wastewater sampler, provides a
mathematical model with which manufacturers can design a portable sampler
capable of preserving samples by icing under certain extreme environmental
conditions.
Dwight 6. Ballinger
Director
Environmental Monitoring and Support Laboratory
Cincinnati
m
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ABSTRACT
A mathematical model was developed to simulate the operation of the
ISCO 1680 automatic wastewater sampler. This study was similar to the one
carried out earlier with the Manning S-4000 sampler. The objective was
to determine the feasibility of developing an automatic sampler with an
adequate ice compartment for sample preservation. The model was used to
confirm the validity of sample cooling predictions under variable conditions,
Experimental measurements on the sample cooling process were also conducted.
Data obtained during operation of the ISCO sampler cooling system
under varying conditions indicated that the accuracy of the mathematical
model was within ±2°C. Also, the theoretical sample temperature history
was in phase with that of the corresponding test sample. Good agreement
between theoretical and experimental results was obtained.
The sampler has a cooling space equivalent to 10 kg of ice which can
keep 24 500-ml samples at an equilibrium temperature of 0 C from an initial
sample temperature of 66.2°C if no heat is absorbed from the surroundings.
However, only half of the cooling space can be packed with cube ice unless
the container is filled with water and placed in a freezer. Furthermore,
a large amount of heat transfer from the environment to the sampler was
fourid in the tests. About 70 to 80 percent of the cooling capacity of-the
sampler was lost to the surroundings. After an exposure of 24 hours at an
ambient temperature ranging from 30 to 35°C, the final lowest temperature
of the sample was in a range of 13-19°C for an initial sample temperature
of 20-30°C. Also, it took 6 to 8 hours for a sample to reach its lowest
temperature. It is therefore concluded that the sampler insulation is in-
sufficient, and the sample cooling rate is slow.
Based upon the mathematical model, two prototype redesigns of the ISCO
1680 sampler cooling system are proposed in this report. The first new
design would require 13.6 kg of ice to lower the temperature of 24 500-ml
samples to about 4°C at a cycle time of 1 hour and with a temperature of
30°C for both the environment and the initial sample during a 24-hour
period. The second design would require 9.6 kg of ice to keep the same
amount of sample to about 4°C under similar conditions to those above with
the exception that the temperature for both the environment and the initial
sample was 35°C.
This project verified the feasibility of using mathematical models
for the development of specifications for a sampler cooling system.
IV
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CONTENTS
Foreword iii
Abstract iv
Figures ..... vi
Symbols .vii
Acknowledgment x
1. Introduction 1
2. Conclusions 2
3. Recommendations 4
4. Description of Sampler . 5
5. Thermal Analysis of Sampler Cooling System 7
Heat transfer by convection and conduction in the sampler ... 7
Solar irradiation on a sampler. . 12
6. Numerical Analysis of Mathematical Model 13
Numerical technique 13
Boundary and initial conditions 15
7. Laboratory Setup and Test Procedures. . .- 18
8. Results and Discussion 20
Comparisons between experimental and theoretical results. . . .20
Modification study of sampler cooling system 27
References . 35
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FIGURES
Number Page
1 Photograph of sampler 6
2 Sample container 8
3 Top view of sample container 9
4 Recommended correlation for free convection around vertical
plane surfaces 17
5 Accuracy test of sample temperature predicted by mathematical
model 21
6 Comparison of predicted and observed sample temperatures,
Test No. 1 23
7 Comparison of predicted and observed sample temperatures,
Test No. 2 25
8, Comparison of predicted and observed sample temperatures,
Test No. 3 26
9 Predicted sample temperatures using the original sample con-
tainer charged with 9.6 kg of ice (20°C for initial sample). . 28
10 Predicted sample temperatures using the original sample con-
tainer charged with 9.6 kg of ice (30°C for initial sample). . 29
11 Modified design of sample container (modification 1) 31
12 Predicted sample temperatures in the redesigned sampler
(modification 1) 32
13 Predicted sample temperatures in the modified sampler
(modification 2) 33
VI
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SYMBOLS
A . Contact area between the inner coolant and the sampler bottom,
538 cm2 (0.58 ft2}.
Af .. Contact area between bottle i (odd number) and the inner coolant,
93 cm2 (0.1 ft2).
9 7
Au . Contact area between bottles i and k, 59 cm (0.065 ft ).
K. j 1
A . Contact area between bottle i (even number) and the sampler wall,
• o o
133 cm (0.143 ft ).
h Contact area between outer coolant i and the sampler wall, 75
or 99
cm- (0.08 fr).
A . Contact area between bottle i (odd.,number) and outer coolant
i, 84 cm2 (0.09 ft2).
A , . , Contact area between outer, cool ant, irl and bottle i (even
number), 84 cm2 (0.09 ft2).
Contact area between outer coolant i+1 and bottle i (even
99
number), 84 cm (0.09 ft ).
Cf • Thermal conductance between sample i (odd number) and the
' 2 o
inner water coolant, cal/hr-cm - C.
C, . Thermal conductance between samples i and k, cal/hr-cm - C.
sl o
C Specific heat of water, 1 cal/gm- C.
C . Thermal conductance between sample i (odd number) and outer
* ' 2 o
coolant i, cal/hr-cm - C.
C -, . , Thermal conductance between sample i (even number) and outer
' 2 o
coolant i-1, cal/hr-cm - C.
c™ -j.i Thermal conductance between sample i (even number) and outer
' 2 o
coolant i+1, cal/hr-cm - C.
dx Thickness of the bottle, 1.0 mm.
2
g Gravitational acceleration, 980 cm/sec .
h Surface film coefficient, cal/hr-cm -°C.
VII
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h, . Surface film coefficient between sample i (even number) and
o _
the sampler wall, cal/hr-cm - C.
hf 4 Surface film coefficient between sample i (odd number) and
2 o
the inner water coolant, cal/hr-cm - C.
h. Surface film coefficient between the ice and the inner water
9 n
coolant, cal/hr-cm - C.
r\
h. . Surface film coefficient between bottles k and i, cal/hr-cm - C.
K, 1
h Surface film coefficient between the environment and the sam-
o p
pier wall, cal/hr-cm - C.
h . Surface film coefficient between sample i (odd number) and
' 2 o
outer coolant i, cal/hr-cm - C.
j j th iteration.
jti j+i th iteration.
K Thermal conductivity of the sampler wall, 1.49 cal/hr-cm- C
(0.1 Btu/hr-ft-°F).
Kfl Thermal conductivity of air, 0.22 cal/hr-cm-°C (0.015 Btu/hr-
ft-°F).
Kb Thermal conductivity of the bottle, 3.72 cal/hr-cm-°C (0.25
Btu/hr-ft-°F).
kk Number of bottles filled with sample.
K ' Thermal conductivity of water, 5.21 cal/hr-cm-°C (0.35 Btu/hr-
ft-°F).
1 Bottle height, 17.78 cm (7 in.)
m Sample mass, gm.
M Mass of the inner water coolant, gm.
m Mass of outer coolant i, gm.
n n time steps.
Q. Heat gain (negative) through the ice to the inner water coolant,
I \f V-
cal/hr.
Q . Heat gain through the sampler wall to sample i (even number),
cal/hr.
Q Heat gain through the sampler wall to outer coolant i, cal/hr.
Radius of the ice (assume that the ice is a cylindrical body
with a height of bottle length), cm.
vm
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t Time, hr.
T^ Water temperature in the inner coolant in °C.
TV Ice temperature, 0°C.
1. Temperature in sample i in °C.
T. Temperature in sample k in °C.
Tm Mean surface temperature, °C.
T. Ambient temperature, °C.
T . Temperature in outer coolant i in °C.
r»i
w Relaxation factor, 1.5.
Ax< Thickness of the sampler bottom, 3.18 cm (1.25 in.).
At Time increment, 1/60 hr.
AX . Average thickness of the sampler wall at the location of sample
i (even number), 3.18 cm (1.25 in.).
Average air
wall, 5 mm.
Average thii
coolant i, 4.76 cm (1.87 in.).
AX . Average air gap between bottle i (even number) and the sampler
AX Average thickness of the sampler wall at the location of outer
AT Half of temperature difference between two fluids, C.
N Nusselt number.
nu
N Prandtl number, y Cp/Kw, or 13.37-0.2556 Tm for water.
Pr 322
N Grashof number, 1 p gBAT/p .
y Viscosity, 64.35-0.57 Tm gm/cm-hr, for water.
3
p Water density, 1 gm/cm .
B Thermal expansion coefficient, (8.379 Tm+54) xlO" /°C for water.
C, a Constants.
IX
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ACKNOWLEDGMENT
The author wishes to thank Mr. H. W. Chiang for conducting
the experimental measurement of the temperature in this study.
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SECTION 1
INTRODUCTION
As a result of a thermal analysis of the Manning1 sampler, now being
prepared for publication, a mathematical model was developed for predicting
the sample cooling process. In that study, it was found that the Manning
sampler was not capable of preserving the samples at 4°C under normal con-
ditions and that the sample cooling rate in the sampler was slow. However,
the mathematical model developed for the Manning sampler cooling system did
predict the sample cooling process well. A modification of that sampler
cooling system was therefore proposed based on the mathematical model.
According to the model, the redesign of the sampler cooling system could
preserve the samples at 4°C at a temperature of 35°C for both the environ-
ment and the initial sample over a 24-hour period. Since the model showed
promise for the development of the automatic sampler cooling system, a
further study to substantiate the validity of the mathematical model was
developed for the sample cooling process in the ISCO 1680 sampler. The
same numerical technique, the Crank-Nicolson Implicit, was utilized. A
laboratory test to confirm the accuracy of the model was also conducted.
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SECTION 2
CONCLUSIONS
The laboratory tests ihdicate that the sample cooling rate in the ISCO
1680 sampler is slow. Also, the sampler cooling capacity is inadequate for
sample preservation under normal operating conditions. Conclusions from the
test include:
- The contact area between the coolant and the sample bottles is not
enough,
- The ice capacity is insufficient. It is not possible to fill the
coolant compartment with the designed capacity of ice unless it is
filled with water and placed in a freezer.
- The sampler insulation is insufficient to reduce the heat transfer
from outside the sampler.
Accuracy of the mathematical model verified by experimental measure-
ments of sample temperatures indicates that the following conclusions can
be drawn from the simulation model:
v.
- The maximum temperature difference for any sample between experimental
and predicted results at any given time is within 2 C.
- The corresponding temperature histories for each sample are in phase
with respect to time.
- Both results show the same trend of temperature-time histories for all
samples.
In general, they are in good agreement. The computer simulation model
developed for the sampler cooling system is generalized. The applications
of the model, which are also included in Reference 1, are:
- The mathematical model can provide a design guideline for the sampler
cooling system and minimize experimental work and manpower in evalu-
ating the sampler cooling capability.
- The computer program can be applied to different combinations of sam-
pler material, bottle thickness, number of bottles, number of samples,
ice mass, sample mass, cycle time, duration time, etc. provided the
sampler geometry is similar.
-------
Temperature-time histories of samples can be calculated and plotted
directly from the program.
Experimental data of sample temperatures can be fed into the program
for plotting.
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SECTION 3
RECOMMENDATIONS
The ISCO 1680 sampler cooling system is not acceptable under normal
operating conditions. Several recommendations which are suggested in the
study of the Manning1 sampler are also applicable to the ISCO sampler.
They are:.
- Improve the sampler insulation.
- Increase the cooling space.
- Increase the contact area between the coolant and the bottle.
- Increase the ice capacity by placing the container in a freezer.
Two prototype designs of the cooling system are proposed based on the
above. The first redesign of the container is based on the following modi-
fications in the design specifications:
- The sampler bottom thickness is increased to 7.62 cm (3 in.).
- The capacity of the coolant is increased to 13.6 kg of ice.
- The contact area is increased by 32 cm2 (0.034 ft2).
- The thermal conductivity of the sampler bottom with loose polyurethane
foam inside is less than 0.744 cal/hr-cm-°C (0.05 Btu/hr-ft-°F).
In the second design, the bottle radius is reduced from 3.18 cm (1.25 in.)
to 2.79 cm (1.1 in.), and the bottle length is increased from. 17.78 cm
(7 in.) to 20.83 cm (8.2 in.). The contact area is therefore increased by
14 percent. The container wall thickness is increased by 3 cm (1.2 in.)
and that of the sampler bottom is 7.62 cm (3 in.). It is assumed that the
thermal conductivity of the container wall with polyurethane foam inside is
less than 0.744 cal/hr-cm-°C (0.05 Btu/hr-ft-°F) and that the ice capacity
is about 9.6 kg. Both designs can reduce the temperature of a sample from
30°C to about 4°C in 3 hours and hold it at 4°C during a 24-hour period
under testing conditions.
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SECTION 4
DESCRIPTION OF SAMPLER
The ISCO 1680 sampler as shown in Figure 1 is equipped with a
peristaltic pump with a pumping rate of 1400 ml/min for a typical pump
and 5000 ml/min for a superspeed pump. The controls and electronics are
housed in a watertight stainless steel container. The power source is
either a line source of 117 volts AC or a 12-volt battery.
The sampler casing is constructed of double-walled plastic separated
with polyurethane foam insulation. The sample bottles have a capacity
of 500 ml and are made of high density polyethylene.
The sampler is designed to collect up to 28 separate sequential sam-
ples of a predetermined volume. Also, it is possible to fill 4 consecutive
bottles during each sampling period and allow each discrete bottle to be
composed of 1 to 4 samples for the optional multiplexing controls. Samples
are collected from either a time mode or a flow mode. In the time mode,
samples are taken at intervals from 1 to 999 minutes; or in the flow mode,
they are collected at intervals of 1 to 999 flow pulses. The interval
between samples is displayed with a light emitting diode (LED) either in
minutes or pulses.
Ice can be stored in the central section of the sampler for sample
preservation. The cooling space has an approximate capacity of 10 kg of
solid ice.
The sequence of operation of the sampler is described as follows:
1. The sampling interval is set for either minutes or flow pulses.
2. The peristaltic pump runs in the reverse direction to purge the intake
line.
3. The pump then runs in the forward direction to deliver the preset
volume. This is measured with the revolution of the pump and the lift
of the sample from the source. This sample is then channeled to the
sample bottle through the funnel spout onto the distributor plate.
4. The pump direction again changes to purge the intake line, and then
the pump shuts off.
5. The distributor funnel moves to the next bottle to be filled.
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6. This completes a cycle. This process continues until the 28th bottle
is filled, at which time the sampler automatically shuts off.
Figure 1. Photograph of sampler.
6
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SECTION 5
THERMAL ANALYSIS OF SAMPLER COOLING SYSTEM
The ISCO 1680 sampler has an ice compartment in its central section
and has 28 cylindrical bottles arranged as shown in Figure 2. The unusual
.arrangement of the bottles presents a thermal problem which cannot be solved
in as straightforward a manner as in the Manning sampler. To facilitate the
thermal analysis of the sampler, sample bottles are labelled from 1 to 28 as
shown in Figure 3. The outer bottles are even-numbered and the inner ones
are odd-numbered. The sampling sequence of the sampler is the same as the
.number sequence in Figure 3. The number of outer coolant (not shown in
Figure 3) is also labelled corresponding to that of the inner bottles.
In this study, three phases of heat transfer, i.e., radiation, conduc-
tion, and convection, are investigated.
HEAT TRANSFER BY CONVECTION AND CONDUCTION IN THE SAMPLER
In addition to the assumption of transient response of the sample with
negligible internal resistance to the heat, the following hypotheses also
proposed in the Manning! study are made:
- Heat transfer in the sample occurs only in the r- and e- directions.
- No heat transfer exists for bottles without samples.
- Heat transfer to the coolant comes from the samples in the r-direction
and from the top and bottom of the sampler in the axial direction.
Four heat transfer equations were then derived, each of which is as follows:
i. Heat Transfer Equation for (Odd Numbered) Samples in Inner Bottles
dT,
™CP dT-= Cf,i Af,i(Tf-Ti)+Cr,iAr,i(Tr,i 'V
k=i+2
* £ Ck i Ak T(Tk - Ti} (5-1}
!,_.: O *» *
kfi"
where
i - sample number, 1, 3, 5 27.
7
-------
V
Figure 2. Sample container.
-------
Figure 3. Top view of sample container.
9
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In this equation, the first term is the transient temperature response of
sample i. The second, third, and fourth terms represent heat gain of sample
i through the inner water coolant, outer coolant i, and the neighboring sam-
ples, respectively. Symbols in equation (5-1) and following subsequent
equations are explained in the "SYMBOLS" section for convenience.
By introducing:
r fi
= f.i f,i
Tf,i mC
_ cr.1 Ar,i
Tr,i ' mC
Ck -A. .
Tk i = mC (5"2)
K,I mtp
The transformed equation becomes:
~rr= Tf ,uf - V f T a i . - i.; i- I
dt T,I T i r,i r,i i k=i_2
kft
ii. Heat Transfer Equation for (Even Numbered) Samples in Outer Bottles
dTi
mCp dFT = Crl,i-l AH ,i-l(Tr,i-l " V + Crr,i+l Arr,i+l
k=i>l
kfi'
(Tr ,+1 - T.) + I C, . A. . (T. - T.) + Q (5-4)
I % t' X I 1 • 1 ^5' "^»l i>- '" W 1
7 l/~ n _ r •* *
where
i = sample number 2, 4, 6, ,28.
On the right hand side of equation (5-4), the first and second terms are
heat gain from outer coolants i-1 and i+1 to sample i, respectively. The
third term is the total heat contribution from the neighboring samples and
the last term is the heat gain from outside the sampler to sample i. By
similar transformations introduced in equation (5-2), equation (5-4) becomes
10
-------
.
~dt
-l " V + Trr,i+l (Tr,i+l " V
k=i+l Q .
z Vi(Tk - V +ir (5-5)
k=i_l «,i k i mC
kfi
Hi. Heat Transfer Equation for the (Odd Numbered) Outer Hater Coolants
dTr 1
-------
In this equation, the first term on the right hand side is the total heat
transfer between the inner samples and the inner water coolant. The second
and third terms are heat gain from the sampler bottom and top, and the ice,
respectively. The total heat, obtained from the right hand side of the
equation, leads to the temperature response of the inner water coolant. By
the similar transformations as in i, equation (5-8) becomes:
dTo kk OA
r T /T T } 1 + ____2A__/T
Ht u f iv'i 'f' M Av 1 ^'n 'f>
OL • i -> I, 1 1 T PI / AX, 1 \ «i^ 0 T
1=1,3 (rX)MCP
'ice
MC v '
Equations (5-3), (5-5), (5-7), and (5-9) may be solved simultaneously for T-j
Trjl-, and Tf in terms of time t, if the boundary and initial conditions are
provided.
SOLAR IRRADIATION ON A SAMPLER
A surface used as a heat rejection surface in the solar environment
should have a low value of solar absorptivity and a high value of infrared
emissivity, since the surface radiates mainly in the infrared band. Refer-
ence 1 presents a detailed discussion of this subject.
12
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SECTION 6
NUMERICAL ANALYSIS OF MATHEMATICAL MODEL
NUMERICAL TECHNIQUE
Numerical solutions were obtained by transforming the mathematical
expressions as shown in the previous section through a numerical technique,
the Crank-Nicolson Implicit,2 into finite difference forms.
Four corresponding finite difference equations are:
j+1 j n n j n j k=i+2 n j
T. = T. + w [a, (T- . T~ + T . T . + i T. . T. +
i 1 7 T 1 T v* i v* i ]f "} tf
I i *- ' 9 * ' * S ' '5* I—,40 f^ 3 ' *^
kfi"
n j
ax) - T,-] (6-1)
where
k=i+2
j; Ti, • (T - T. )
kfl'"2
At At k=1+2
a2 = 2~ / [1 + -p ^Tf,i + Tr,i + _z. Tk,i^]
kkf]"2
j+1 j n n j n j
Ti = Ti +w [52(Trl,i-l Tr,i-l + Vr,i+lTr
k=i+l n j n j
I T, - T. + b.) - T,] (6-2)
k=i-l Kjl K ] n
kfi
13
-------
where
T \ + Trr,i+l ,T T x +
r 2 v r.i+1 i'
k=i+l 2 Q .
k=1+1
k_f
kfi
j+l j n n j n j n j
Tr,i = Tr,i * w[c2
-------
where
_ kk
dl = M z Tf i (Ti " Tf5 + Ax i (2T0 - V
If
MCp - ' At
, _ At , r, , At ,m
dp - -y / [1 + J~ (TT
'- *. c nj_i
1-
Equations (6-1) to (6-4) were solved simultaneously for T-j , Tr}j, and Tf
for the n+1 th time step by a successive overrelaxation technique. The
same procedure was repeated for solutions of the successive time steps
until all bottles were filled with sample or until the specified duration
time was reached. Equations (6-1) to (6-4) cannot, however, be solved
without the boundary and initial conditions provided.
BOUNDARY AND INITIAL CONDITIONS
Boundary conditions for equations (6-1) to (6-4) are partially given
in Figure 3. The following are also required for equations (6-1) to (6-4).
Heat transfer, Q -, through the sampler wall to an (even numbered) outer
sample is:
Ir r\
(6~5)
^
01
AX
K
AX
f~I
a
1
ho
'h
1
bi
dx
K. p
D
Heat transfer, Q , through the sampler wall to outer caolant is:
(T° 0
°r
15
-------
Heat transfer, Qice> from the solid ice to the inner water coolant is:
= 2 Pi Rice ] hice
-------
in which
C, a = constants
M = pranc|f| number
N = Grashof number
•j
The Nusselt number for a vertical sample bottle was approximated by that of
a vertical plate. Values for a and C for a vertical plate free convection
were listed by Chapman.3 According to Chapman, the following approximations
can be used for a vertical plate:
qr
1C) < N
gr pr
: use Figure 4
: C = 0.59, a = £
1C)9 < V V < = l°12 '•c = °-129'a = i
(6-11)
Log { Ngr Npr
10
Figure 4. Recommended correlation for free con-
vection around vertical plane surfaces.
17
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SECTION 7
LABORATORY SETUP AND TEST PROCEDURES
The mathematical model on the ISCO sampler cooling system was
experimentally verified in three separate laboratory tests. The laboratory
facilities used in this study included:
- Environmental chamber, Zero-Temp Inc.
- Electronik 16 recorder, Honeywell Industrial Division
- Bath & circulator, Forma Scientific, Inc.
- Matheson thermometer, -1 to 51°C, 1/10 division.
A thermocouple was placed centrally in each of the 28 bottles in the
sampler and the wires were firmly taped to the sampler casing. The sampler
was then placed in the environmental chamber. The leads from the thermo-
couples were passed through a hole of the chamber and connected to the
Honeywell Electronik 16 recorder. However, the recorder would record only
24 discrete temperature readings at intervals of 6 seconds at a recording
speed of from 1 to 8 in./hr. It was found that to distinguish 24 discrete
temperature readings was difficult even at a maximum recording speed of
8 in./hr. Therefore, only about 12 randomly chosen thermocouples were
hooked to the recorder for each run. The accuracy of the recorder was
about" ±0.5°C in the testing range of 0 to 40°C. A temperature-controlled
water bath filled with sample was also placed in the chamber, completing
the setup of the laboratory test.
Test procedures for each run were as follows:
1. The bath and circulator were turned on and the temperature controller
was set to the desired temperature of the water sample to be taken.
2. The environmental chamber was turned on and its dry-bulb temperature
was set to the desired ambient temperature.
3. A Matheson thermometer was used to check the reading of the temperature
controller after the bath and circulator reached a steady state.
4. After the chamber reached a steady state, weighted ice and water were
placed in the sampler ice compartment. The initial water temperature
was measured.
5. The recorder was turned on.
18
-------
6. The sampler cycle time was set and the sampler began to collect the
first sample from the bath and circulator.
7. The run was stopped after the duration time was reached or the total
number of samples was taken.
19
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SECTION 8
RESULTS AND DISCUSSION
The thermal properties of the sampler were estimated in this study.
According to Brandrup and Immergut,* the thermal conductivity of polyethyl-
ene (high and low density) is 2.88 cal/hr-cm-°C (0.1935 Btu/hr-ft-°F), but
is 3.57 and 4.76 cal/hr-cm-°C (0.24 and 0.32 Btu/hr-ft-°F), respectively
for a density of 0.945 and 0.976 gram/cm^ as listed in Macromolecules, Vol-
ume 1 edited by Elias. In this study, the thermal conductivity of the
sample bottle, which is made of high density polyethylene, was assumed to
be 3.72 cal/hr-cm-°C (0.25 Btu/hr-ft-°F); that of the sampler wall, made of
double-walled plastic separated with compressed polyurethane foam, was as-
sumed to be 1.49 cal/hr-cm-°C (0.1 Btu/hr-ft-°F). Loose polyurethane foam
has a value of thermal conductivity ranging from 0.2-0.37 cal/hr-cm- C
(0.015-0.025 Btu/hr-ft-°F).
COMPARISONS BETWEEN EXPERIMENTAL AND THEORETICAL RESULTS
Accuracy of the computer simulation model was tested again as described
in Reference 1. An energy-balanced sample equilibrium temperature in the
sampler, without heat gain from surroundings, was compared with those
obtained by solving equations (6-1) to (6-4) using the assumptions as in
Reference 1, i.e., the thermal conductivity of the wall approached zero and
the bottle surface film coefficient was equal to 2976 cal/hr-cm2-°C (200
Btu/hr-ft2-°F).
Results shown in Figure 5 indicated that it took about 1 hour for the
temperature of sample 1 to drop from 30 to 0.03°C, and the final temperature
of all samples was about 3.72°C after 24 hours. By comparing the energy-
balanced equilibrium temperature of 3.43°C with 3.72°C, this program was
considered sufficiently accurate for the present purpose.
The experimental results and theoretical calculations are compared in
plots 6 to 8. Dashed lines on all plots represent results from experiments;
solid lines represent those theoretically predicted. For the reader's con-
venience, detailed testing conditions on the 1680 sampler are summarized in
Table 1.
20
-------
GO
55
50
• — •
ej 45
• — •
LU
or 40
ID
a: 35
or
^ 30
CL
l i 1 -} tr
C J
1 —
LU ?r
_j
CL.
s: 15
a:
^ 10
5
0
_ ! ! II 1 ! 1 ! 1 „
- NO. OF SflMpLEb -20 z
- 5flM^LE Mfl55 -500 00 ML ~
- ICE Mfl55 ^3. 00 KG
-; COOLING WflTER ^5.00 KG -
Z flMBlENT TEMP ^30. 00 C
COOLING WflTER TEM^ -^0.00 C
Z INIT. 5flMPLE FEMP --30. 00 C Z
CYCLE TIME --1 . 00 HR.
I OURflTIQKi TIME -24.00 HR. Z
-
— —
-
~
z Sfl.MPLE NO, =
f 3 5 7 9 11
3 IS
719
- —
-
1
X
1
V]
\
VJVi
LKJ
U
U<;
^J
L/
u
,
^JM
b— p^""i
-
~
I
_
I
=
-
— j
1
-
L \
-
i 1 i ! 1 ~
0 2 4 G 3 10 12 14 16 18 20 22 2
ELflP5-ED T IME iHRJ
Figure 5. Accuracy test of sample temperature predicted by mathematical model.
-------
TABLE 1. TESTING DATA ON ISCO 1680 SAMPLER
Test number
Number of samples
Sample volume, ml
Ice Mass, kg
Cooling water, kg
Ambient temp. , °C
Initial sample temp., °C
Cooling water temp., °C
Cycle time, hr
Duration time, hr
Bottle height, cm
Bottle thickness, mm
Thermal conductivity of
bottle, cal/hr-cm-°C
Thermal conduct! tity of
sampler wall, cal/hr-cm-°C
24
500
4.57
5.00
35.00
25.00
11.00
1.00
24.00
17.78
1.00
3.72
1.49
24
500
4.65
5.00
30.00
30.00
13.00
1.00
24.00
17.78
1.00
3.72
1.49
24
430
4.43
5.00
30.00
20.00
10.00
1.00
24.00
17.78
1.00
3.72
1.49
•
Test 1
In this test, crushed ice was packed into the ice compartment, and
cooling water was poured over the ice to increase the contact area between-
the coolant and bottles. Results obtained from the test and the program
are shown in Figure 6. The experimental measurements shown in dashed lines
indicated that a minimum temperature of 6.5°C (first sample) was reached at
an elapsed time of 5 to 6 hours and persisted for about 2 to 3 hours. The
cooling rate for each sample was rapid at the beginning of the sampling
period. For example, the temperature in sample 1 dropped 18°C within 1 hour.
The cooling rate then decreased rapidly after the next sample was taken.
This is due to heat transfer from the latter sample to the former one. Fur-
thermore, the equilibrium temperature should theoretically be 0°C if no
heat transfer from the surroundings is assumed. However, the final tem-
perature of the first sample at 19.5°C after 24 hours indicated that heat
gain from surroundings to the sampler was extremely high. About 427 kcal
(1697 Btu) were absorbed by the coolant from outside the sampler and 66 kcal
(261 Btu) were extracted from the samples. Therefore, approximately 81 per-
cent of the cooling capacity of the sampler was lost to surroundings.
Comparisons between the experimental results and the values predicted
by the model indicated the following:
- The temperature-time histories for each corresponding sample are
closely in phase.
- A maximum temperature difference of 2°C is observed.
22
-------
50
or
or
rr
LLJ
Q..
s:
LU
a.
s:
a:
LO
40
35
—1
NO.
OF 5flMpLfb
ICE
COOL!NG
COOL ING
1 N ! T ,
CrCl.E TlMf
UJRflTlOM TlMf
-
-4,57 KG
•-S,00 KG
•-JS.OG1 C
-1 1 . 00 C
•-^5.00 C
•-i . 00 MR.
•-••24.00
ML
SflMPLE NO.
9 11 13 15
1 T ~
23
0
8 10 12 14 16 IS 20 22 24
FL flPSEQ TIME iHRJ
Figure 6. Comparison of predicted and observed sample temperatures, Test No. 1.
-------
- The difference between these values at the lowest temperature for the
first sample is 1-2°C.
- The predicted final temperatures are in a range of 20-24°C.
Test 2
Figure 7, which shows the results of Test 2 and the mathematical model,
indicates that a minimum temperature of 6.1°C was reached at an elapsed time
of 7 to 8 hours.
The final temperature of the first sample after 24 hours was 17.7°C,
which was 12.3°C below its initial temperature. Theoretically, the equilib-
rium temperature for all samples should be 2.57°C in an adiabatic condition.
However, during the 24-hour period, about 327 kcal (1298 Btu) of heat were
transferred to the coolant from outside the sampler and 147 kcal (585 Btu)
were transferred from the samples.
A temporary sharp increase in temperature for sample i was obtained
while sample i+1 or i+2 was being taken. This is due to a large tempera-
ture difference between samples i and i+1 or i+2. In general, the sample
cooling rate was similar to that of Test 1.
Comparisons between the values obtained in the test and the predicted
values indicate similar temperature-time histories for each corresponding
sample. The maximum temperature difference is about 2°C.
Test 3
Test 3 is similar to Tests 1 and 2. Results from both the model and
the test are plotted in Figure 8.
It took about 7 hours for the first sample to reach its lowest tempera-
ture (4.6 C) and 24 hours to reach the final temperature (13.1°C), which
would be 0°C in the perfectly insulated sampler. The heat transfer to the
coolant from outside the sampler and the samples was estimated at about 342
kcal (1358 Btu) and 83 kcal (328 Btu), respectively for 24 hours.
The model indicates that the minimum temperature occurs in about 8 hours
and that the final temperature of the first sample is 1°C higher than the
observed result. The maximum temperature difference between the observed
and the predicted results is about 2°C.
In summary, the results indicate that the cooling rate of a sample in
the 1680 sampler is rapid within a cycle time and then decreases rapidly
even though the cooling rate of the inner samples is generally faster than
that of the outer ones. In general, it takes about 6 to 8 hours for a sam-
ple to reach its minimum temperature. Also, the results show that the
sampler cooling capacity is inadequate and the sampler needs additional
insulation.
24
-------
ro
en
6(J
55 I
50
'45
LU
a: '40
or
cc
35 I
-i—i—i—r
i r
NO. QF
SflMPLE: MflSS
ICE Mfl55
COOL ING WflTER
flMBIENT TEMP.
COOLING WflTER
INIT. 5RMPL.E
CrCLE TIME
OURflTION TIME
TEMP
TEMP.
• 24
;5QO. 00 ML.
•4.65 KG
^5.00 KG
^30.00 C
'13.00 C
• 30.00 C
•I . 00 MR.
= 2.4. 00 HP..
5-
SflMPLE'NQ.
11 13 15
I 7
19
23
8 10 12 14 16
FLflPSED TIME (H.R)
19
20
22
_j
—i
_>
24
Figure 7. Comparison of predicted and observed sample temperatures, Test No. 2.
-------
LU
or.
-------
Comparisons between the tests and the calculations indicate that both
results show a similar trend of sample cooling process for all samples.
Accuracy of the model, in general, is within 0-2°C.
MODIFICATION STUDY OF SAMPLER COOLING SYSTEM
The 1680 sampler cooling system can technically hold up to 10 kg of
ice if it is filled with water and placed in a freezer for a period of time.
It can hold about 7 and 3 kg of ice respectively in the central and outer
portions of the container. Since this is rarely done, the cooling capacity
is generally less than the designed maximum. In this study, no experimental
test was conducted under such conditions; however, two theoretical results
under the maximum cooling capacity were obtained to determine the necessity
of the modification of the sampler cooling system. The results shown in
Figures 9 and 10 were obtained under the following conditions:
- Ambient temperature = 30°C.
- Initial sample temperature = 20 and 30°C.
- Ice in the central portion of the container =6.9 kg.
- Initial water in the central portion of the container = 0.2 kg.
- Ice in the outer portion of the container = 2.7 kg.
- Initial water in the outer portion of the container = 0.2 kg.
- Cycle time = 1 hour.
Figure 9 indicates that the first sample temperature drops rapidly to
3°C in 1 hour and then rises sharply to about 4.5°C. This is due to the
fillings of bottle 2. Temperature then drops again to 3°C within the next
hour. While sample 3 is being taken, the temperature in sample 1 rises
again to 4°C and then drops to 3°C at the third hour. The mutual effect
among samples 1,2, and 3 is very obvious. The temperature in sample 1
reaches a minimum of about 2°C at the sixth hour and then rises to 4°C
after 24 hours. The same phenomena occur for all other samples.
Two kg of ice remain and the final temperature of all samples is in
the range of 4-5°c after 24 hours which indicates that the cooling rate is
better than achieved in the experimental tests. At the same time, it also
shows that cooling capacity is sufficient under these conditions. The
cooling rate of outer samples is still slightly lower than that of the inner
ones (the initial sample temperature is assumed to be 20°C and the ambient
temperature is 30°C).
Figure 10 shows similar results to those shown in Figure 9. Final
temperatures of all samples are in the range of 5-6°C and 1 kg of ice
remains after 24 hours. One can therefore conclude that the cooling
capacity of the sampler is barely enough under these conditions (30°C for
27
-------
"i r
i r
r\D
CO
3S
30 :
NO
bflM
1GF
COOL
COOL
INIT
CrCL
DURfl
OF SflMPLEb -24
'LE M95S r-SQO.OO ML.
MP55 --9 GO KG
ING HflTER -0.40 KG
FNI TEMP. -30.00 G
ING WflTER TEMP. --0. 00 G
sflMPLE TEMP. -20.00 G
E TIME -i.00 HR.
TION TIME -24.00 HR.
SflMPLE NO.
9 11 13 15
9 10 12 14 16
ELflPSED TIME IHRJ
Figure 9. Predicted sample temperatures using the original sample container
charged with 9.6 kg of ice (20°C for initial sample).
-------
GO
55 t
50 I
45 E
0
NO. OF 3flMPLE5
bflM^LE MPSS
ICE Mfl55
COOL ING WflTER
PM61ENT TEMP.
COOLING WftTER TEMP
INIT. SflMPLE TEMP.
CTCLE TIME
DURATION TIME
--SQQ-OQ ML
-9.60 KG
-0.40 KG
-30-00 C
-0.00 C
•-30.00 C
--1 . 00 MR.
=24.00 HR.
8 10 12 14 16
fLflPSED TIME (HRJ
18
Figure 10.
Predicted sample temperatures using the original sample container
charged with 9,6 kg of ice (30° for initial sample).
-------
both the ambient and the initial sample); that the contact area between the
outer bottles and the coolant is not sufficient; and that the heat transfer
from outside the sampler to the outer samples is somewhat high.
The above results indicate that a redesign of the sample container is
necessary. Based on the mathematical model, a new bottle container is sug-
gested as shown in Figure 11. This new container has ,a bottom thickness of
7.62 cm (3 in.) instead of the original 3.175 cm (1.25 in.). Polyurethane
foam is then inserted between the double-walled plastic. Its thermal con-
ductivity is assumed to be 0.744 cal/hr-cm-°C (0.05 Btu/hr-ft-°F). The ice
capacity is increased to about 13.6 kg, but the other parameters remain the
same as in the original sampler. ''
Figure 12 shows the results from the computer program under an average
temperature of 30°C for both the surroundings and the initial sample for the
new container. The first sample temperature drops quickly below 4°C within
1 hour and increases sharply to about 6°C. It then drops again to 3°C in
the next hour. While sample 3 is being taken, temperature in sample 1 agaiii
rises rapidly to 6°C and then decreases below 4°C at the third hour. The
final temperature after 24 hours is below 4°C. This process repeats again
for all other inner samples. The same phenomena are observed as in the
inner samples for the outer ones, although their cooling rates are slower.
In general, it takes about 3 hours for the outer samples to reach below 5°C.
At the end of 24 hours, about 2.56 kg of ice remain. It is therefore
clear that the cooling capacity is adequate under these conditions. How-
ever, the contact area between the outer bottles and the coolant should be
increased if the sampler is to be used at a higher environmental temperature,.
At the same time, the wall thickness of the sampler should also be increased
to reduce heat gain from the outside to the outer samples.
To further increase the contact area and the sampler wall thickness, a
further modification is suggested. If the bottle radius is reduced from
3.18 cm (1.25 in.) to 2.79 cm (1.1 in.) and the bottle length is increased
from 17.78 cm (7 in.) to 20.83 cm (8.2 in.), the contact area will be in-
creased by 14 percent. In this design, the bottle volume is not changed,
but the sampler wall thickness is increased by 3 cm (1.2 in.) It is assumed
that the thermal conductivity of the wall and the bottom filled with loose
polyurethane foam would be less than 0.744 cal/hr-cm-°C (0.05 Btu/hr-ft-°F).
The ice capacity would be 9.6 kg, which is similar to that of the original
container.
Figure 13 shows the predicted sample temperatures obtained with this
design using a temperature of 35°C for both the surroundings and the initial
sample. Similar results as in Figure 12 are obtained. It takes about 3
hours for an inner sample to drop and stay below 4°C and 5 to 6 hours for an
outer one to remain below 5°C. At the end of 24 hours, about 2.5 kg of ice
is not melted. Hence, the cooling capacity is sufficient for the sample to
stay at 4-5°C, although the cooling rates of the outer samples are still
slightly low.
30
-------
CO
_ 3".
Polyurethane Foam
.19.5"
Figure 11. Modified design of sample container (modification 1),
-------
CO
r-o
61'
55 I
50 L.
45 r
rr 40
ZD
T_ ! j | j ,_
"I T
NO. OF bRMPLEb
bflMPLE Mfl55
IGE MR55
GOQLING WflTER
8MB I ENT TEMP.
GQQLING WflTER TEMP
INIT. b'flMPLE TEMP.
GrGLE TIME
OURflTlQN TIME
T T
•500.00 ML
•13. GO KG
Q.i-lQ KG
•30.00 G
•0. 00 G
•30.00 G
•1 .00 MR.
00 MR.
SflMPLE NO,
9 11 13 15
1 7
2
8 10 12 14 16
FLfiPSED TIME (HRJ
18
20
22
H
24
Figure 12. Predicted sample temperatures in the redesigned sampler (modification 1).
-------
CO
CO
or
ID
or
or
UJ
70 ^
h
r~
60 E
h
_ 55 E
— 50 ~
45 =
NO. OF 5flMPLES
50MPLE M.Q55
ICE MP55
COOLING WflTER
flMBIENT TEMP,
COOL ING WflTER TEMP
INIT. SflMPLE TEMP,
CTCLE TIME
OURflTION TIME
-24
-500,00 ML
-9.60 KG
-0,40 KG
-35.00 C
--G. 00 C
-35,00 C
- 1,00 MR,
--24,00 H.R.
SflMPLE NO.
11 13 IS
1 7
19
-i
21
23
0 2
Figure 13.
18
20
22
8 10 12 14 16
ELflPSED TIME (HR)
Predicted sample temperatures, in the modified sampler (modification 2).
24
-------
This study concludes that by Icing it is possible to lower 24 samples
of 500 ml each to about 4°C during a 24-hour period under conditions men-
tioned above.
-------
REFERENCES
1. Lin, P. C. Thermal Analysis of a Manning S-4000 Portable Wastewater
Sampler. 1980 (in preparation).
2. Smith, G. C. Numerical Solution of Partial Differential Equations.
Oxford University Press, New York, 1965. 179 pp.
3. Chapman, A. J. Heat Transfer. The Macmillan Co., Mew York, 1967.
617 pp.
4. Brandrup, J. and E. H. Immergut. Polymer Handbook. John Willey
and Sons, Inc., New York, 1967. 341 pp.
5. Elias, H. G. Macromolecules, Vol. 1. Plenum Press, New York, 1977.
532 pp.
35
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/4-80-033
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
THERMAL ANALYSIS OF THE ISCO 1680 PORTABLE
WASTEWATER SAMPLER
5. REPORT DATE
JUNE 1980 ISSUING PATE.
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Philip C. L. Lin
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
SAME AS BELOW
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
12, SPONSORING AGJENCY NAME AND ADDR6S.S
EnvironmentaT Monitor!ng
and Support Lab. - Cinn, OH
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
13. TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
EPA/600/06
15. SUPPLEMENTARY NOTES
16. ABSTRACT
A.mathematical model was developed to simulate the operation of the ISCO 1680
automatic wastewater sampler. This study was similar to the one carried out earlier
with the Manning S-4000 sampler. The objective was to determine the feasibility of
developing an automatic sampler with adequate ice compartment for sample preservation.
The model was used to confirm the validity of sample cooling predictions under vari-
able conditions. Experimental measurements on the sample cooling process were also
conducted.
i.
Data obtained during operation of the ISCO sampler cooling system under varying
conditions indicated that the accuracy of the mathematical model was within ±2 C.
Also, the theoretical sample temperature history was in phase with that of the corre-
sponding test sample. Good agreement between theoretical and experimental results
was obtained.
This project verified the feasibility of using mathematical models for the
development of specifications for a sampler cooling system.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Sampling, Samplers, Automatic Samplers,
Mathematical Model, Sampler Cooling,
Sampler Cooling Process
68D
148
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RELEASE TO PUBLIC
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UNCLASSIFIED •
21. NO. OF PAGES
46
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22. PRICE
EPA Form 2220-1 (9-73)
36
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