WATER POLLUTION CONTROL RESEARCH SERIES , 16050DOW10/71
Multidirectional Turbulence
Probe Development
Phase 1: Unidirectional Turbulence
Sensor Development
U.S. ENVIRONMENTAL PROTECTION AGENCY
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WATER POLLUTION CONTROL RESEARCH SERIES
The Water Pollution Control Research Series describes the
results and progress in the control and abatement of pollution
in our Nation's waters. They provide a central source of
information on the research, development and demonstration
activities in the Environmental Protection Agency, through
inhouse research and grants and contracts with Federal,
State, and local agencies, research institutions, and
industrial organizations.
Inquiries pertaining to Water Pollution Control Research
Reports should be directed to. the Chief, Publications Branch
(Water), Research Information Division, R&M, Environmental
Protection Agency, Washington, D.C. 20*4-60.
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MULTIDIRECTIONAL TURBULENCE PROBE
DEVELOPMENT
PHASE I
UNIDIRECTIONAL TURBULENCE SENSOR
DEVELOPMENT
by
BATTELLE
Columbus Laboratories
505 King Avenue
Columbus, Ohio 43201
for
ENVIRONMENTAL PROTECTION AGENCY
PROJECT #16050 D0W
Contract #14-12-827
October, 1971
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EPA Review Notice
This report has been reviewed by the Environmental
Protection Agency and approved for publication.
Approval does not signify that the contents necessarily
reflect the views and policies of the Environmental
Protection Agency, nor does mention of trade names or
commercial products constitute endorsement of
recommendation for use.
Battelle is not engaged in research for advertising, sales
promotion, or publicity purposes, and this report may not
be reproduced in full or in part for such purposes.
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, B.C. 20402 - Price 65 cents
ii
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ABSTRACT
Development of a unidirectional-turbulence probe was undertaken to
investigate the feasibility of a small-diameter strain-gaged diaphragm-
type pressure transducer and a self-adjusting depth compensation air
reservoir for use in the follow-on development of a small (1/2-inch
diameter) multidirectional-turbulence probe. A unidirectional probe
has been developed which is capable of monitoring water velocities
over a range of 0.5 to 5 ft/sec in turbulence frequencies of 0 to over
100 Hertz and which will automatically operate in water up to 10-feet
deep.
Sealing inadequacies in both the air reservoir membrane and the pressure
diaphragm permit mositure entry into the air volume covering the strain
gages. This has given rise to balance drift and circuitry ground
problems that have resulted in the placing of limitations on the water
exposure and turbulence monitoring times for the unidirectional probe.
These problems also suggested that the concepts cannot be immediately
incorporated into a multidirectional probe design.
The undirectional turbulence probe was released to the Environmental
Protection Agency for use and further evaluation with recommendations
for analysis of data obtained with the probe. This report was submitted
in fulfillment of Contract Number 14-12-827 under the sponsorship of
the Environmental Protection Agency.
iii
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CONTENTS
Section Page
I CONCLUSIONS 1
II RECOMMENDATIONS 3
III INTRODUCTION 5
IV DISCUSSION 7
V DEVELOPMENT PHASE I 11
VI PERFORMANCE 17
VII CALIBRATION 23
VIII ACKNOWLEDGMENTS 33
IX APPENDICES 35
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FIGURES
PAGE
1 PARTIALLY ASSEMBLED PROBE 12
2 UNIDIRECTIONAL PROBE 12
3 ORIFICE END OF PROBE 13
4 DIAPHRAGM WITH STRAIN GAGES 13
5 MOUNTED DIAPHRAGM 14
6 SELF-ADJUSTING DEPTH COMPENSATION 15
7 AIR-RESERVOIR MEMBRANE 16
8 DRIFT IN AIR 19
9 INITIAL DRIFT IN WATER 20
10 LONG TERM DRIFT IN WATER 21
11 STATIC CALIBRATION EXPERIMENT 23
12 STATIC CALIBRATION, PRESSURE 25
13 STATIC CALIBRATION, VELOCITY 26
14 FLOW PERFORMANCE CHECK 27
15 DYNAMIC PERFORMANCE PROBE HORIZONTAL 29
16 DYNAMIC PERFORMANCE PROBE VERTICAL 30
17 DEPTH COMPENSATION DEVIATION 31
vi
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SECTION I
CONCLUSIONS
1. Reliable water-velocity monitoring with the undirectional probe
can be expected over a range of approximately 0.5 to 5 ft/sec. The
actual output voltages, with 3 volts bridge excitation, corresponding
to these velocities are approximately 0.1 to 10 millivolts, a range
of 100 to 1. The device is at least partially successful. Acceptability
of the threshold velocity of 0.5 ft/sec or slightly less will have
to be determined by the Environmental Protection Agency.
2. Using a collapsible air-reservoir membrane for automatic-depth compen-
sation appears to be a workable concept in itself. Modifications in
the membrane's size and geometry should produce even better
compensation than that found acceptable for the undirectional probe.
3. Based on the diaphragm's high natural frequency (6600 Hz) indicated
by calculation, the unidirectional probe should have excellent frequency
response in the relatively low range desired, i.e., 100 Hz or less.
4. A probe to be used for long periods of immersion will have to have
a thicker air-reservoir membrane and possibly a thicker sensing
diaphragm, therefore, both these members will have to be larger in
order to maintain their response sensitivity. The twin concepts of
a thin-air reservoir membrane for compensation response and a thin
membrane-like diaphragm for velocity response appear, in the case of
the unidirectional probe, to have a very negative effect on the water
tightness of the air environment of the strain gages. Water, at
least in vapor form, seems to be penetrating these two membranes
causing wide drift in the zero balance of the unidirectional probe
(20 to 30 millivolts with 3 volts bridge excitation) and drastically
reducing the integrity of the circuitry's insulation to ground (from
33 x 10° ohms resistance to less than 200,000 ohms over three days
of immersion).
5. The unidirectional probe is a useful device even with the drift and
ground problems described above. The differential output of the
probe with a given impinging water velocity is only slightly different
(2 to 5 percent lower) with a high output balance point than with a
zero voltage balance point.
6. The diaphragm and air reservoir membrane designs as embodied in the
unidirectional probe are not suitable for direct incorporation into
a multidirectional turbulence probe design. The problem of output
drift observed with only the one diaphragm on the unidirectional
probe can only be multiplied in a multidirectional probe where three
or more diaphragms may be required. In the latter case corrective
balancing procedures would be likely to become so ponderous as to
be impractical.
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SECTION II
RECOMMENDATIONS
The unidirectional probe should be used in laboratory and possible field
tests both to provide further information on the functionality of the
concepts involved and to generate, through use, more specific performance
requirements for the probe. Specific instructions for operating the
probe are provided in Appendix B. These instructions should be closely
followed to avoid damage to the probe.
It is suggested that the performance of the unidirectional probe be
first monitored either directly with a sensitive oscilliscope or with
amplification and subsequent oscilliscope or chart recording display.
With this procedure a period of familiarization will take place in which
the probe's capabilities will be more clearly defined and the type of
water environment to be subjected to analysis will be indicated.
As described in Appendix C, characterization of the water turbulence
monitored by the probe may be best obtained by spectral density analysis.
One method of obtaining such an analysis is to convert the probe's signal
from analog to digital form for analysis by one of several digital
computer techniques. Another method is to use Battelle's graphic level
recorder and frequency analyzer which provides a quasi-rms amplitude
spectrum down to about 2.5 Hz in frequency.
Two procedures can be followed to apply this analysis device to the probe's
output. Battelle personnel could bring the equipment to the area where
the probe is in use and perform direct spectral density analyses. Another
method would be to have the probe's output amplified to a minimum-nominal
voltage of 1-volt root mean square (this is a gain of 10,000 for a minimum
signal of Ool millivolt or 0.5 ft/sec) for recording on a magnetic tape
compatible with a Hewlett Packard Model 3960 tape recorder with a carrier
center frequency of 27 kilohertz at 15 in/sec or 5.4 kilohertz at 3 in/sec.
This tape can then be sent to Battelle1s-Columbus Laboratories where its
information can be processed on the graphic level frequency analyzer and/or
digitized for additional processing with Battelle's autocorrelation or
Fourier transform computer programs.
Following the familiarization and preliminary analysis procedures described
above, a re-evaluation of the concepts employed in the unidirectional-
probe design and usage should be made with the purpose of formulating the
direction of further development on a multidirectional probe.
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SECTION III
INTRODUCTION
As part of the mission of the Environment Protection Agency is to conduct
research directed at the expansion of scientific and technical knowledge
relating to pollution control, the need exists for appropriate instrumentation
and analysis procedures to characterize the relationship of bacteria growth
to turbulence in streams of the United States.
The overall objectives of the research reported herein are to develop a
device for monitoring the magnitude and direction of three-dimensional water
turbulence, under laboratory and field conditions, and to devise procedures
for analyzing the data obtained by this device. Existing devices for this
purpose are limited in low velocity sensitivity, which is the case with
conventional diaphragm-type dynamic pressure transducers, are not suitable
for the field requirements of ruggedness and resistance to fouling, a pro-
blem with hot wire anemometers, or do not facilitate highly localized three-
dimensional measurements, most devices are unidirectional.
Past research at Battelle has produced significant advances in miniature
diaphragm type low-pressure transducers. This type of transducer features
the electronic output from strain gages mounted on the back of a diaphragm
which is strained by the pressure differential to be measured. Knowle'dge
of this art combined with the inherent fouling resistance of a diaphragm
transducer suggested the development of a device featuring an array of
sensitive diaphragm-type dynamic (stagnation) pressure transducers mounted
on a small common housing for the purpose of measuring three-dimensional
turbulence.
To obtain a multidirectional probe using the diaphragm transducer concept,
a two phase development program was begun. In the first phase the problems
of design, fabrication, and operation of a diaphragm transducer capable of
meeting Environmental Protection Agency requirements would be investigated
by developing a unidirectional probe around a single diaphragm transducer.
The second phase would be the extension of the first phase experience into
the design of a multidirectional device. To meet the specific needs of the
Environmental Protection Agency, a number of requirements have been placed
on such a device. These requirements along with certain problems related
to the concept and the requirements are outlined in the following discussion.
The actual developments of Phase I are described in the sections following
the discussion section.
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SECTION IV
DISCUSSION
Size and Turbulence
The entire housing size for the multidirectional probe has been tentatively
set at 1/2-inch diameter or less. This limit arises from the need to
measure what might be somewhat inaccurately called microturbulence.
Turbulence or current eddies can occur on the truly microscopic scale.
Since the output of the device is an integration of the dynamic pressures
acting on the monitoring surface (the diaphragm), the minimum coherent
eddy size that can be identified can be no less than the diaphragm
diameter. The multidirectional device permits the identification of a
turbulence vector, i.e., the magnitude and direction of an eddy, the
size of which is limited to something greater than the total probe diameter.
The problems caused by the need for a miniature device are discussed below.
Sensitivity
The most immediate requirement is sensitivity. The monitoring of average
water velocities over a range of from 0.1 to 5 ft/sec is desired. In
terms of equivalent stagnation pressure this range is from 0.000067 to
0.168200 psi. The low pressure is an extreme requirement for any diaphragm
transducer but particularly so for one that is miniaturized. The above low
pressure acting on the 1/2-inch housing cross section would only produce a
force of 0.00021 ounces or 5.9 x 10~3 grams.
Frequency Response
Another requirement placed on the device is that it respond to water
turbulence frequencies of at least 100 Hz. Given the requirement of small
size, any resulting diaphragm automatically has a very high natural fre-
quency (several thousand Hertz). There is, however, one liability associated
with this requirement. The diaphragm must be unrestrained or undamped on
the side not in contact with the turbulent water, i.e., it must be free to
respond to the turbulence. To allow this response then, the back of the
diaphragm must be exposed to a relatively low viscosity environment such as
air. This necessity has one advantage in that air is highly desirable as
a medium in which the strain gages are to function.
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Static Pressure Compensation
Since the diaphragm is to respond, that is deflect, in proportion to
the fluctuating pressure of water impinging on its outside surface, some
relatively stable or known reference pressure must be maintained on its
back side. A sealed fixed volume of air behind the diaphragm would
essentially provide such a reference pressure but there are two negative
features borne with this practice. The probe is to operate in water depths
up to 100 feet. At any given depth the diaphragm, with a fixed air
pressure on its backside, would deflect under the static water pressure
in addition to the dynamic pressure. This static pressure could be sub-
tracted from all readings but this would be cumbersome. However, the main
drawback with a fixed backside pressure system is that a low-pressure
sensing diaphragm is not strong enough to withstand a static-pressure
differential of more than a foot or so of water. Therefore, it is impera-
tive that the air pressure on the backside of the diaphragm be within
approximately 0.5 psi of the static water pressure outside the diaphragm,
which at the 100-foot depth in water is approximately 43.3 psi.
Readout and Analysis
For the device to be of use, a means for monitoring, interpreting, and
analyzing its electronic output signals must be provided. The main problem
in monitoring the signals is the detection of those weak signals produced
by low-water velocities. There are practical limits to the minimum signal
that can be discerned, by conventional electronic equipment„
Given sufficient strength so as to be readable, the output signals may
have to be interpreted (processed) in preparation for analysis. The
electronic output from the diaphragm strain gages is in direct proportion
to the stagnation pressure which is a square function of the actual water
velocity. To obtain a direct indication of the water velocity impinging
on a diaphragm, the magnitude of the output signal must be reduced to its
square root. However, since a function of the velocity squared is required
for one type of turbulence analysis (power spectral density) the probe's
signal may be used directly.
Two different methods of calibration and signal processing can be employed
for the multi-directional probe. The simpler method would be to interro-
gate and calibrate the particular sensing diaphragm(s) associated with each
primary axis on an axis-by-axis basis. With this type of calibration, the
device would be used in a passive manner with signal information being
processed in an after-the-fact program. A much more sophisticated approach
would be to electronically process the signals from all the diaphragms on a
real time basis. The resulting signal from the electronic logic unit would
be the velocity, in terms of magnitude and direction of the water impinging
on the whole probe. Such an electronic package would undoubtedly be complex
in conception, fabrication and calibration, but it would permit better control
of a laboratory setup and might be amenable to a more direct analysis procedure.
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The type of analysis applied to the velocity data will evolve with usage.
For preliminary analyses, random phenomena characterization techniques
would best be used. These are described in Appendix C. These results
coupled with specific Environmental Protection Agency experimental require-
ments will dictate the required analysis techniques and hardware.
Summary
The environmental and performance criteria require the use of a small-
diameter, thin, strain-gaged, diaphragm-type, differential pressure
transducer(s).
An air environment is required behind the diaphragm(s) to promote its
frequency response.
The' air pressure behind the diaphragm must be close to the ambient water
pressure at operational depths in order to prevent diaphragm collapse.
A self-pressure adjusting air volume would be greatly preferrable to one
that requires external measurement and adjustment control.
Electronic instrumentation, calibration procedure, and analytical methods
must be developed to permit meaningful monitoring and subsequent characteri-
zation of the water turbulence.
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SECTION V
DEVELOPMENT PHASE I
Since many of the technical problems are initially encountered in-the
small, depth compensated, pressure-sensing diaphragm concept, it was
decided to devote an initial phase in the probe's development to the
proving out of the critical points contained in this design concept.
This portion of the development was designated Phase I. Development
within Phase I would center around the design, fabrication, :and testing
of a unidirectional turbulence probe containing one diaphragm. The
performance objectives and specifications for this probe are:
1. A 3/8-inch maximum-housing diameter with a removable
orifice tip
2. Detect water velocities within the range of .1 to
5 ft/sec
3. Have a frequency response of up to 100 Hz
4. Operate in water depths up to 10 feet
5. Evaluate the system for application to a multi-
directional probe
To meet the requirements placed on either the multidirectional or uni-
directional probe, significant departures from existing diaphragm design
and manufacturing practices must be undertaken. These departures can
only be guided by approximating engineering calculations and heavy
extrapolations on experience.
The final design of the unidirectional probe evolved through several
engineering conceptual arrangements, discussions with Dr. Walter M0 Sanders,III
of the Southeast Water Laboratory, and through improvements discovered
during its fabrication and testing. This evolution is partially documented
in the monthly progress reports to the Southeast Water Laboratory. The
resulting form of the probe is shown in a partially disassembled condition
in Figure 1 and assembled in Figures 2 and 3. Complete drawings of the
probe details, assembly, and assembly instructions are contained in Apendix A0
Only the salient features of the design will be discussed here.
The heart of the device is the strain-gaged diaphragm. This assembly is
shown in Figure 4 and Drawing A-4 of Appendix A. The diaphragm derives
its sensitivity from its extreme thinness (0.00075 inch) and its arrangement
of silicon semiconductor strain gages. These gages have a very high gage
factor which permits the reading of very low strain levels. The arrangement
shown, particularly the notches at the rim, enable placement of the gages
in areas of highest possible reverse strain on the diaphragm's inner surface.
The fully mounted diaphragm is shown in Figure 5.
11
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FIGURE 1. PARTIALLY ASSEMBLED PROBE
FIGURE 2. UNIDIRECTIONAL PROBE
12
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FIGURE 3. ORIFICE END OF PROBE
FIGURE 4. DIAPHRAGM WITH STRAIN GAGES
13
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FIGURE 5. MOUNTED DIAPHRAGM
14
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The gages are wired and connected in a Wheatstone bridge circuit whose
diagram is presented in Drawing A-15 of Appendix A. The actual bridge
connections and temperature compensation and balancing elements are
made on a special mounting strip physically located in the wire leads
just outside of the probe body proper. This location of the connections
permits electronic adjustments and checking of the individual bridge
elements without a complex disassembly of the device. The strip is
partially protected inside a hard plastic sheath which can be seen in a
horizontal position at the top of Figure 1.
Self-adjusting depth compensation is probably the second most critical
feature of the device. It is accomplished by placing a reservoir of air
behind the diaphragm enclosed in a collapsible membrane. This reservoir
is exposed to the ambient water pressure under which it accordingly com-
presses or expands, depending on its previous condition, until the pressure
inside and outside the air volume are balanced at the ambient static water
pressure. In this manner the diaphragm sees no pressure differential from
its outside to its backside due to the operational water depth. This is
shown schematically in Figure 6.
Water
Diaphragm
Membrane
FIGURE 6. SELF-ADJUSTING DEPTH COMPENSATION
15
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In this concept the membrane must be highly flexible so that it will
not support water or air pressure but will act only as a divider between
the air and the water. The flexibility is achieved by fabricating a very
thin membrane, 0.002- to 0.004-inch thick, in a geometry that is susceptible
to collapse. The membrane is shown in Figure 7 and Drawing A-9 in
Appendix A.
The other features of the probe are evident in the assembly Drawings A-l
through A-3 in Appendix A.
FIGURE 7. AIR-RESERVOIR MEMBRANE
16
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SECTION VI
PERFORMANCE
Throughout the design, fabrication, and calibration processes of Phase I,
various characteristics of the unidirectional probe were noted and, in
some cases such as calibration, these were quantified. A discussion of
those characteristics that have a bearing on the operation of the device
follows.
Sensitivity
The device, though sensitive, is not sensitive enough to produce a
practical readable electronic signal at the specified minimum velocity
of 0.1 ft/sec. Though the minimum or threshold signal that can be,
discerned will depend on the actual electronic equipment used, conven-
tional amplifying and signal processing equipment will operate on minimum
signals of 0.1 millivolt or slightly lower. As presented in the
"Calibration" portion of this report (see Figure 13) 0.1 millivolts is
the probe output expected at approximately 0.5 ft/sec water velocity.
No operational equipment will function on the 0.0036 millivolt signal
produced by a water velocity of 0.1 ft/sec, therefore, the functional
water velocity detection range of the unidirectional probe is approximately
0.5 to 5 ft/sec.
Linearity
The device displays excellent linearity throughout its range with devia-
tions of less than 1 percent of the full scale output (9.1 millivolts at
5 ft/sec) observed during calibration. There was also no measurable
hysteresis encountered in the static calibrations.
Drift
The one major negative characteristic of the device is its lack of balance
stability. Balance stability, in the case of the probe is its ability
to maintain the same output reading over a period of time in which there
is no change in the velocity of the medium to which the probe's diaphragm
is exposed, e.g., with a lack of balance stability the probe, when lying
in a pool of motionless water, would show a gradual change in its output
voltage over a period of time. In the development of the unidirectional
probe two types of drift have been observed, one type occurs when the probe
is in air, and the other occurs when the probe is under water.
17
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When the probe has been resting in undisturbed air on a laboratory bench
with 3 volts excitation, its electronic output over a period of days
has drifted back and forth over a range of +9 millivolts. While this
range is high (double the operational range), the rate of this drifting
has been relatively low apparently never exceeding +0.030 millivolts/min.
A sample of this drifting in room air has been recorded and is presented
in Figure 8.
While the range of drift is excessive, its existence is not entirely
unexpected. The extreme thinness of the diaphragm coupled with the
highly strain-sensitive semiconductor gages renders the diaphragm assembly
susceptible to all of the negative factors normally affecting diaphragm
transducers plus factors unique to this assembly. The most common source
of drfit is environmental temperature effects on the transducer components..
Temperature compensation elements have been added within the bridge circuitry.
In this manner subsequent temperature excursions have been limited to less
than 1 millivolt over the environmental temperature range of 32 to 100 F.
Normally a diaphragm transducer can be temperature compensated to produce a
much lower excursion than this but again the coltish nature of this unique
diaphragm assembly is manifest. In any event the temperature excursion
does not appear to be the source of the wide drift range. A clue to the
true source of drift may be contained in the performance of the probe when
it has been immersed in stagnant (no flow) water.
In this case, the drift has consistently gone up scale, i.e., in the
direction seen with a positive impinging water velocity. The initial
drifting observed when only the diaphragm was exposed to 2 inches of water
is shown in Figure 9. The drift over a long term was observed when the
entire probe was immersed in 10 inches of water, this is shown as the upper
curve in Figure 10. The lower curve on this figure shows the long term
drift accompanying the immersion of only the rear, i.e., reservoir, portion
of the probe in 1-1/2 inches of water.
Prior to each of the water immersion experiments shown on Figures 9 and
10, the probe had been dry for some time, indeed, prior to the experiments
of Figure 10 the assembly had been baked in an over (curing of the reservoir
seal prior to the 10-inch immersion and drying up after the 10-foot support
tube leak prior to the 1-1/2 inch immersion). The baking, at 195 F, prior
to the 1-1/2 inch immersion may have affected the distribution of the air
reservoir's wax coating. When dried, the balance of the probe is less
than +8 millivolts.
The resistance between the strain-gage bridge and ground was checked
during the water immersion experiments. Prior to immersion, the resistance
was immeasurably high. Immediately after immersion, the resistance to
ground was 33 x 10" ohms. With increasing immersion time the resistance
continued to decrease; on the 1-1/2-inch immersion, the resistance was
13 x 10" ohms on the second day and fluctuating at 200,000 to 20,000 ohms
on the third day.
18
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VO
en
"5
0.080 r
0.060 -
0.040 -
- 0.020
5
o.
3
-0.020 -
-0.040
10
3 volts bridge excitation
20
Time, minutes
30
40
FIGURE 8. DRIFT IN AIR
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0.800
3 volt bridge excitation
20 40 60
Time, minutes
FIGURE 9. INITIAL DRIFT IN WATER
80
20
-------
N>
Probe fully immersed in 10 of water
air reservoir immersed in I-5 of water
1000
Immersion Time , minutes
FIGURE 10. LONG TERM DRIFT IN WATER
10000
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The key to the above described behavior seems to be exposure to water.
It is a well recognized fact that contact with water vapor causes
problems with any strain gage installation but this is particularly
true with semiconductor gages. Water vapor appears to be getting through
the neoprene reservoir membrane and even possibly the diaphragm. The
requirement of thinness in both parts introduces the likelihood of
molecular porosity. Whether the upward drift of the 1-1/2-inch immersion
(still in progress at this writing) will produce a vapor pressure
equilibrium or a condensate ground is not clear at this point.
It should be noted that the sensitivity of the probe does not seem to
be seriously affected when the zero balance is as high as the 20 to 30
millivolts range. Satisfactory static and dynamic experiments were performed
with the zero balance at these levels. It should also be noted that the
drift rate of the submerged probe is always less than 0.020 millivolts/min.
Depth Compensation
Depth compensation does take place in the unidirectional probe. As
described in the "Calibration" section of this report submersion in
ten feet of water produces less than one millivolt of shift. This
indicates a relatively minor pressure differential across the diaphragm,
whereas without the compensation the diaphragm would have seen a pres-
sure differential great enough to cause its permanent deformation.
Frequency Response
A simple calculation of the diaphragm's natural frequency yields the
value of 6627 Hz. This frequency is sufficiently higher than the required
maximum response frequency of 100 Hz that a considerable amount of
inaccuracy in the assumption that the diaphragm is a simple circular plate
with rigidly clamped edges can be tolerated. This margin of better than
60 to 1 between the theoretical natural frequency and the required response
frequency also indicated that no checking of the probe's performance in
this area is required, consequently no specific frequency response
experiments have been performed.
22
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SECTION VII
CALIBRATION
Several calibration and performance checking experiments were applied
to the unidirectional probe. In all of the experiments the Wheatstone
bridge on the device was supplied with three volts potential from a
constant current source and its output was read directly on a voltmeter
sensitive to +10"5 volts.
Static Calibration
This procedure consisted of applying an essentially static water pressure
to the outside of the diaphragm while maintaining atmospheric pressure
on the air reservoir. The experimental setup is shown schematically in
Figure 11.
Depth scale
Probe
Tank
water
Velocity baffle
Diaphragm
Air reservoir
Drain
FIGURE 11. STATIC CALIBRATION EXPERIMENT
23
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The experiment was begun with a half inch of water (0.01806 psi), measured
from the ceterline of the diaphragm, covering the diaphragm, This static
water pressure was then varied by filling the tank to a depth of six
inches (0.21667 psi) above the diaphragm centerline and then draining back
to a half-inch depth. The output of the probe was recorded at every half-
inch increment of depth. The elapsed time for each cycle, from one-half
to six and. back to one-half inch, was approximately 15 minutes. The
results of three of these cyclings are presented in terms of output
versus water level in Figure 12.
The deviation was slight, i.e., if the actual experimental points were
plotted on the above graph they would fall within the thickness of the
plotted line. The slope of the output curve is
1.964 millivolts = 54.388 millivolts
inch HO psi ,
or with the input voltage normalized,
0.655 millivolt/volt _ 16.129 millivolts/volt
inch HO psi
If these static pressure results are converted into an equivalent water
velocity by interpreting the static pressure as a velocity stagnation
pressure through the formula,
V2
P = P = JL-
s v 2g ,
and 1/2
V = «/2gP = 8.02496 P , ft/sec ,
where
P = static pressure, feet of HO
S 2.
P = stagnation pressure, feet of HO
_ 1 f\
g = acceleration due to gravity, 32.2 sec ,
24
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3 volts bridge excitation
12 3 4 5 6
Static Pressure , inches of water
FIGURE 12. STATIC CALIBRATION,
PRESSURE
25
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3 volts bridge excitation
IU
8
6
4
3
2
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0.8
0.6
0.4
£ 0.3
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* 0.2
5
1 °'
0 Q08
0.06
0.04
0.03
0.02
0.01
0.008
0.006
0.004
0003(
/
/
/
/
/
/
/
A
/
/
/
/
/
f
/
/
.
/
'
.
/
/
/
).l 0.2 0.3 0.4 0.6 0.8
Velocity , ft
/
/
/
/
/
/
/
/
/
/
/
/
/
/
2 345
/sec.
FIGURE 13. STATIC CALIBRATION, VELOCITY
26
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then Figure 13 represents the relationship between the electronic output
and the velocity of the water impinging on the probe's diaphragm. The
slope of this curve is
365.960 microvolts
ftz/sec2
or
121.987 microvolts/volt
Flow Performance
The procedure described here is not strictly one of calibration but the
probe was subjected to it in order to approximately check the static
calibration results. The probe was pointed into the center of the opening
of a 0.815 inch internal diameter pipe discharging water at various flow
rates. The apparatus of this procedure is shown in Figure 14.
Deflector
Water
Flow discharge pipe (
Water
Drain supply
\
FIGURE 14. FLOW PERFORMANCE CHECK
27
-------
An individual run in this checking procedure consisted of opening the
control valve until the desired approximate flow rate was established.
The actual average flow rate was checked by timing 4he rise of the
water level, and thus the volume change, in the tank. The probe output
during this period was monitored through the voltmeter and an approximate
average value was recorded. The tank is 24 inches in diameter and the
timing was done over 4-inch and 8-inch level changes depending on the
flow rate used. The timing periods varied from 97 to 287 seconds.
The procedure does not provide an accurate calibration for several reasons;
chief among these is that the apparatus itself is not calibrated. For
example, the exact velocity profile of the water discharging from the
pipe is not known and can only be defined within theoretical limits.
A uniform velocity-flow profile is one limit and a laminar-flow profile
would be the other. A brief calculation of Reynolds number for the
average velocity of 1 ft/sec yields 5,600 which is just above the upper
limits for the laminar-flow region as normally encountered in engineering
applications, therefore, the flow is very likely to be turbulent. A
theoretical determination of the correct turbulent-flow profile is not
feasible as it would entail too many doubtful assumptions. It must
suffice to state that the velocities at the center of the pipe discharge
will be greater than those predicted by uniform flow and less than the
peak value (twice that of the average uniform flow) predicted by a laminar-
flow assumption. Additional factors such as a fluctuating pressure source,
approximation of the average voltmeter readings, and probe output drift
with time also detract from the quantitative accuracy of the results using
this procedure.
The results of numerous runs using the procedure are presented as individual
points in Figures 15 and 16. In these figures the average volumetric-
flow rate is plotted against the velocity at the center of the pipe dis-
charge as indicated by the probe and its static calibration shown in
Figure 13. Lower flow velocities were not run due to the difficulty of
obtaining accurately measurable flow volumes in reasonable periods of time.
Depth Compensation
An extension tube and wiring were fitted onto the probe's existing two
feet of support tube in preparation for depth-compensation tests. The
immediate probe portion of the assembly was then immersed beneath the
surface of Battelle-Columbus1 diving pool and allowed to stabilize for
six minutes. The probe, was then immersed in increments to a depth of ten
feet and the resulting deviations recorded. A total of eleven minutes
elapsed while moving the probe from the depth of two inches to the ten-
foot depth. The resulting point-by-point deviations are shown in Figure 17.
The maximum deviation of less than 1 millivolt took place at the ten-foot
depth (4.33 psi).' This shift is comparable to that observed when the
diaphragm alone was subjected to 1/2 inch of water pressure (0.01805 psi)
during the static calibration shown on Figure 12. After a short period at
the ten-foot depth, the support tubing developed a leak which grounded the
electronics and the probe was removed for repair. No further compensation
tests were performed.
28
-------
10
45
9
15
8
75
K Co K * ft
m So
7
65
*
I
O
X
i
X
o
- 3
«
1
1
u_
0>
to'
^
1$
Sferf
--
r v»
^
Tin
TE
4
iki
n'l '.
Att
in!
I? N S O) K *SoiBo)SviSlo>8ioi5o
Velocity ,ft./sec.
FIGURE 15. DYNAMIC PERFORMANCE PROBE HORIZONTAL
29
-------
tc Eg
g
x
5
X
o
a:
o
$
<
~ s u K
Velocity ,ft./sec.
FIGURE 16. DYNAMIC PERFORMANCE PROBE VERTICAL
30
-------
3 volts bridge excitation
10
9
8
«_ 7
•5 5
"5.
? 4
3
2
I
I
I
-0.2 0 0.2 0.4 0.6 Q8 1.0
Output Deviation .millivolts
FIGURE 17. DEPTH COMPENSATION DEVIATION
31
-------
SECTION VIII
ACKNOWLEDGMENTS
The majority of the fabrication and laboratory calibration experiments
on the unidirectional probe were performed by Battelle's senior
technician Mr. Donald H. Lyons.
Attachment of the semiconductor strain gages, compensation, and wiring
of the Wheatstone bridge were performed by the Sensotec Division of
Comtel.
The final air reservoir neoprene membrane used was fabricated by The
Qak Rubber Company.
The design of the unidirectional probe was assisted by Mr. Nelson A.
Crites, Mr. James E. Sorenson, Mr. Milton Vagins, and Mr. Jack J. Groom,
all of Battelle Columbus Laboratories.
All documentation covering the development of the unidirectional probe
is contained in Battelle Laboratory Record Book Number 27668.
This report was prepared by Mr. Thomas J. Atterbury, Mr. James E. Sorenson,
and Mr. Jack J. Groom.
The support of this project by the Environmental Protection Agency, and
the direction of Dr. Walter M. Sanders III, are acknowledged with sincere
thanks.
33
-------
SECTION IX
APPENDICES
Page No.
A. Unidirectional Turbulence Probe Detail and Assembly
Drawings, Assembly Instructions, and Operational Circuitry. 37
B. Unidirectional Turbulence Probe Operating Instructions ... 53
C. Characterization of Random Phenomena 57
35
-------
APPENDIX A
UNIDIRECTIONAL TURBULENCE PROBE
DETAIL AND ASSEMBLY DRAWINGS,
ASSEMBLY INSTRUCTIONS,
AND OPERATIONAL CIRCUITRY
37
-------
UNIDIRECTIONAL TURBULENCE PROBE ASSEMBLY
u>
oo
COAT THIS AREA WITH GAGEKOTE NO. 5
DIAPHRAGM FACE *
2.962
4-40 SKT. HD. CAP SCR. x£ LONG
(2 REQ'D.)
0-80 FLAT HD. CAP SCR.x^LONG
(6 REQ'D)
\
4.493
\
4.902 \
SEE ASSEMBLY NO.(A2>
OJ
0.375
•0.500
-0.375
DRAWING AND ASSEMBLY NUMBER Al
-------
VO
SOLDER GROUND WIRE TO TUBE AND PLUG
,
\
NO. 32 GAGE STRANDED TEFLON
FOUR CONDUCTOR CABLE
I. PRE-WIRE COMPENSATION MOUNTING CHIP,
RUN WIRES INSIDE /AI4NAND SOLDER TO PLUG
COMPENSATION CHIP
^2.SOLDER COMPENSATION MOUNTING CHIP,
ONTO LEADS FROM ASSEMBLY^
AMPHENOL 5 PRONG FEMALE PLUG
CONNECTOR .SERIES 126-1085
3. TEMPERATURE COMPENSATE THE BRIDGE
OVER THE RANGE OF 32-IOOF WITH THE
ELEMENT LOCATED ON THE CHIP
4. BALANCE THE BRIDGE WITH RESISTORS
MOUNTED ON THE CHIP
5. PRIME STAINLESS STEEL SHOULDER ON '
UNDER LARGE END OF THE MEMBRANE WITH
CHEMLOCK 205. COAT THIS AREA WITH C HEM LOCK
236 CEMENT. FIT MEMBRANE
-------
NOTE'.ORDER OF ASSEMBLY IS INDICATED BY INSTRUCTION NUMBERS
5.STRIP COATING FROM WIRES
IN THIS AREA PREPARATORY
TO INSTRUCTION 8.
IO.LOCATE (A9) ON ASSEMBLY
AND BONO~SMALL END ONLY
WITH CHEMLOCK CURED AT
200 F FOR 5 HOURS.LEAVE
LARGE END LOOSE
I.SOLDER @ INTO ^
(400 F SOLDER) ^
2. NO. 51 (0.067) DRILL THRU
TO CENTER
I HOLE
3. SOLDER @ INTO
@ (400FSOLDER)
^.THOROUGHLY REMOVE
ALL FLUX LEFT FROM
SOLDERING OPERATIONS
7. SCRAPE OUT EXCESS
EPOXY FROM GROOVE
AND FILL GROOVE
WITH 245F SOLDER:
8. BOND WIRES IN PLACE
WITH RTC EPOXY
6. BUN WIRES FROM
@) THROUGH ASSEMB
AND EPOXY @ TO
ON THIS FACE ONLY
USING EPY 500 CURING
AT 275F FOR 4 HOURS
INTERNAL ASSEMBLY
9.GOLD PLATE THE
EXPOSED PORTIONS
OF THE DIAPHRAGM (A4)
WITH A BRUSH TEMPOREX
PLATING SOLUTION WITH
A GOLD ANODE AT 10 VOLTS
DRAWING AND ASSEMBLY NUMBER A3
-------
RED
FORM AND SOLDER GAGE LEADS
SOLDER 5- POLYMIDE ENAMELED
WIRES (400-600 F), 34 GAGE x 12 INCHES
LONG TO TERMINALS
THOROUGHLY CLEAN ALL FLUX FROM
INSIDE OF DIAPHRAGM AFTER SOLDERING
WHITE
GREEN
NOTE : WIRE IS NOT COLOR CODED,
COLORS ARE GIVEN FOR
REFERENCE ONLY
uBLACK
WHITE
-6-TERMINALS CUT
FROM FIBERGLASS -
BACKED T125 STRIP
ATTACHED WITH EPY
500 CURED AT 350 F
FOR 2 HOURS
RED
L
WHITE
0.06
SECTION A-A
•4-BALDWIN LIMA HAMILTON#SP5-02-I2-UI/SEN
SEMICONDUCTOR STRAIN GAGES ATTACHED WITH NO
PRE-BOND OF EPOXY, E P Y 500 CURED AT 250 F FOR
15 HOURS.
DIAPHRAGM ASSEMBLY
DRAWING AND ASSEMBLY NUMBER A4
41
-------
DIAPHRAGM
MATERIAL:BRYLCO ALLOY 25 , FULL HARDENED (38-40 RC)AGED AND
LAPPED TO 0.038 THICKNESS
r
ELECTRON DISCHARGE MACHINE TO 0.004
THICK ,
FINISH NEAR SIDE WITH 600 GRIT SOLUTION,
ETCH NEAR SIDE SURFACE TO APPROXIMATELY
0.00175 THICK,
ETCH FAR SIDE SURFACE TO APPROXIMATELY
0.00075 WHICH IS THE FINISHED THICKNESS
OF THE DIAPHRAGM
0.015-*"
TYP.
, 0.030-H
r REF- 1
\
f
!
\
aisoDiAT1
^ ^
p0.038
SECTION A-A
DRAWING ANDPART NUMBER A5
42
-------
..^ 0.020-1
\ I
*» 1 '
"T "" T*" 'A
! ! '
00 *-•
1 cvi w
1 ' d oc
1
1— m— ' V. *
i :i: i
\
0.252 DIA. __
i
1
1
— J \
A 0.025-1
_O.I87 DIA._
\w
_^
x^
^
W
^
^N^^
L
0.031
DIA.
"" 0.249 DIA. ~~\
j
1
L 1
CO
d
F
ro
(\i
O
SECTION A- A
MATERIAL '. BRYLCO ALLOY 25 , FULL HARD
CAP
DRAWING AND PART NUMBER A6
43
-------
^ DIA. DRILL X 0.093 DEEP
#0-80 UNF BOTTOM TAP
J
!
'
c
i
i
rtDMI M^ fi 1 / /^ f"\^"7^ LJfM C T
HRU
1
j
O
s F3 o
P"
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0.468
0.156
>
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i> n
•41 vi-
H
ii '
J I"1"
i
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h
^ rf-'
:: !!
1) II
r 0.250
|| "-i:
0.1875
0.500 "~
0.562
1.186 REF.
w.wu^i
« — 0.025
P
CD
CD
l^^
^ .
p
K>
01
o
*
o
01
ro
g
i
MATERIAL: 316 STAINLESS STEEL
COUPLING
DRAWING AND PART NUMBER A7
-------
MATERIALI304 STAINLESS STEEL TUBING,-
16 GA. , 0.065 0.0. , 0.046 I.D.
NO. 69 (0.0292) DRILL THRU ONE WALL THICKNESS ONLY
3 PLACES
•P-
Oi
CENTER TUBE
DRAWING AND PART NUMBER A3
-------
r
T
L
^16 _ 8
r Blend
LITJ^J Rodius
1
- Less Than .003
Preferably .001
Blend -v
Radii Vv
^-W^
~~1*
1 ^^
iT
Collapse Region
Thicknesses in these areas may be
greater than .003
0.062-
Blend
Radius
(TYR)
Note: All dimensions are internal
MATERIAL! NEOPRENE RUBBER (mandrel dipped, two dips minimum ,must be airtight)
AIR RESERVOIR MEMBRANE
DRAWING AND PART NUMBER A9
-------
MATERIALI 316 STAINLESS STEEL
0.093 DRILL THRU, 2 HOLES AT 180°
DRILL THRU, 0.114DIA.x82°CSK
2 HOLES AT 180°
0375
-EW
SILVER SOLDER-
0.125
DIA.
*33(O.I!3)DRILLTHRU,
DIA. SPOTFACE , 2 HOLES
O.I875_
0.375
0.813
*-0.297
0.328-*
2.625
-0.125
1.563 REF.
HOUSING
DRAWING AND PART NUMBER A10
-------
#50(0.700) DRILL THRU.2 HOLES AT 180°, 0.114 DIA.x 82 °CSK
CO
SHROUD
MATERIAL: sis STAINLESS STEEL
DRAWING AND PART NUMBER All
-------
0.062 RER—
i
i
CM
ro
C>
g
CM
d
t
_k
S\
o.3f5
DIA.
Hh-
1
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'H
-Nv
\*
^_^
I
^
r* *i
3.3I25_
• — NO. 51 (0.067) DRILL THRU
)
} 0.125
•A- f ft iF>R^ HRII i « ™ nPPP
r*DlA.-
•CTION A-A
DIA. DRILL THRU
BOTH SIDES
#0-80 UNF TAP THRU
BOTH SIDES
MATERIAL:316 STAINLESS STEEL
END PLUG.
DRAWING AND PART NUMBER A12
49
-------
Ln
O
0.1875-
0.500
0.250!!
10.3751 0.813
0.781:
0-1875 -
0.375
1.563
— BLEND RADIUS
N0.43 (0.089) DRILL,5 DEEP
4-40 UNC TAP 5 DEEP JLi
o •,«, r-« 16 |6 '
Q (0.332) DRILL.fg DEEP,
|-24UNFTAP jgDEEP,
i nni P .. . i L.
V
O3I2J
|
II
U.
I
n^
L-
f
.J3-USS-
-«--
f
IL
/
II
ll
f
j
-N
ii
T
NO.3{0.2130) DRILL,
^DEEP,i-28UNF 5
TAP, |L DEEP f | HOLE ~
p
^i
o>
\y\
MATERIAL: 304 STAINLESS STEEL
HOLDER
DRAWING AND PART NUMBER A13
-------
1-20 UNF SEMIFINISHED S.S.
HEX NUT
•«-|-24UNF
THREAD
DRAWING AND PART NUMBER AI4
0.245
LD.REF
51
-------
Ol
O.C. Power Supply
constont
voltoge/current
^ 0 to4 volls f
0 to 0.033 amps'
High Impedance
Readout
white
green
V
Support tube
•Amphenol 5 prong
female connector
126-1085
Compensation chip
3.1 > temperature
Possible readout
equipment combinations
(I) oscilloscope
(2) amplifier to oscilloscope
(3) amplifier to tape recorder t
compensation
I
Probe housing and holder
r—Diaphragm
green
black
•
lOfl
AA/V
balance
/^VNA
24 fl.
;*L
1
1
^ J
white
'*
fZ
red
Vacuum tube (connected only for momentary
ohmmeter ground readings)
OPERATIONAL CIRCUIT SCHEMATIC
DRAWING NUMBER AI5
-------
APPENDIX B
UNIDIRECTIONAL TURBULENCE PROBE
OPERATING INSTRUCTIONS
-------
APPENDIX B
UNIDIRECTIONAL TURBULENCE PROBE
OPERATING INSTRUCTIONS
General Notes
All referenced drawings are to be found in Appendix A.
The probe should be handled with care at all times. When it is being
moved in air or in water, it should be handled with reasonably slow
deliberate motions so as to avoid damage to the strain gages or their
compensation circuitry from dropping or jarring.
The unidirectional probe is a complete sealed assembly; any repair or
modification other than that described below must be made by Battelle-
Columbus technicians or under the close supervision of Battelle-Columbus
personnel.
The only field assembly or disassembly that can be performed is the
attachment of an extension support tube and wiring to the 2 foot support
tube (see drawings Al, A2, and A14) connection and/or removal and
replacement of the shroud over the diaphragm (see drawings All and Al).
If a support tube extension is to be used and its joint with the 2 foot
support tube is to be submerged, extreme care" should be taken to secure
a watertight joint. The entry of water into the two foot support tube
will short and cause corrosion in the circuit's compensation and wiring
elements.
Nothing but low pressure and low velocity fluids should touch the
surface of the diaphragm transducer. DO NOT use compressed air on any
part of the probe. A water meniscus over the diaphragm inside the
shroud or over the air reservoir membrane inside the probe housing can
be removed by air blown from a long-nosed plastic wash bottle.
Velocity Monitoring
The probe should be connected, as shown in drawing A15, to a good quality
constant voltage/constant current D.C. power supply for a few hours
(if possible) prior to usage. The circuitry input voltage should be 3
volts with a constant voltage setting and the bridge should be reasonably
zero balanced (as indicated by its high impedance readout instrumentation)
with the 50,000 ohm balance potentiometer (schematically shown in drawing
A15). After this warm up period the balance should be set at an exact
zero and the power supply should be switched from constant voltage to
constant current. The maximum voltage limit should then be adjusted to a
higher value of 4.0 volts. Note that the voltage to the bridge should
never exceed 4 volts.
54
-------
During all subsequent handling the readout instrumentation should be
adjusted such that a + full scale reading will represent + 10 milli-
volts output from the probe. If, during handling, the instrument shows
a reading approaching full scale (particularly any rapid change) a
potentially dangerous pressure on the diaphragm may be at hand, such
as collapse of the air reservoir membrane or excessive water velocity,
and corrective action should be taken. Excessive water velocity will
be obvious in the stream condition. A collapsed air reservoir membrane
will provide a steadily increasing reading to + 12 millivolts by the
time the probe is immersed in 6 inches of water (see Figure 12 in the
main body of this report). A water leak anywhere in the system will
change the output drastically and should show as a grounded circuit
condition.
The circuitry's resistance to ground should be checked periodically.
A vacuum tube ohmmeter has been used for this purpose connected to the
powered circuitry in the manner shown on drawing A15. A check on the
ground prior to wetting of the probe usually shows a value of over 60
megaohms. Immediately on wetting of the probe this value drops into
the 30 megaohm range and with extended immersion it deteriorates. The
probe should be removed from the water and dried in air (blow water out
of the housing from around the air reservoir membrane) if the ground
drops to less than 1 megaohm.
Before immersion the probe should be pointed up or down and filled with
water inside the housing around the air reservoir. This is done by
applying the snout of a water-filled plastic wash bottle to the bottom
most hole in the housing and, while covering the hole on the opposite
side of the housing with a finger, squeezing water into housing, thus
forcing the air out the top holes. Any air-water meniscus inside the
housing will be very tenacious and may affect the depth compensation
feature of the probe. The water should then be injected through every
hole in turn with two of the other holes covered and one left open for
relief. The probe should then be placed in the water to a shallow depth.
If any air bubbles stick inside the shroud they can be removed with
the wash bottle.
The probe can then be immersed to the desired turbulence monitoring
position. Due to the drift of the zero balance point a procedure for
rebalancing must be followed just prior to each turbulence monitoring
period. This procedure consists of placing a baffle or cover across
the opening of the submerged probe in order to induce a zero impinging
water velocity on the diaphragm while the circuitry is being balanced
to zero. During this period the stability should be checked for
assurance that the drift rate has become fairly low (0.20 millivolts/
min) and consistent. The rate of drift determines the maximum period
or magnitude range over which reasonably accurate velocity readings can
be obtained after the zeroing procedure. A conservative velocity
monitoring period would not exceed five minutes at low velocities
(0.5 to 1.5 ft/sec) before repeating the balancing procedure. After
rezeroing, the cover is removed and differential voltages proportional
to the water velocities will be obtained.
55
-------
With the 3000 ohm resistor and 50,000 ohm potentiometer balancing
arrangement in the bridge circuitry as shown on drawing A15, the output
of the bridge will be 2 to 5 percent less, depending on the amount of
balance required, than the proportions presented in Figure 13 in the
main body of this report.
Unless some major improvement is effected in the probe's resistance
to water entry into the strain gage air volume, as manifested by a
lack of wide zero shift or a lack of ground deterioration, the probe
should not be left continuously under water for longer than two days.
To date the removal of the saturated probe from the water and drying
in air for a day has been sufficient to return the zero balance and
the circuitry ground to reasonable levels, e.g., less than +10 milli-
volts with no balance circuitry and greater than 60 megaohms to ground.
Refinements in the operating procedures for this probe will undoubtedly
turn up with its use. Any questions concerning its initial operation
should be directed to the authors listed in Section VIII Acknowledge-
ments.
56
-------
APPENDIX C
CHARACTERIZATION OF RANDOM PHENOMENA
57
-------
APPENDIX C
Characterization of Random Phenomena
A random signal is one whose amplitude or phase cannot be predicted by
a study of previous values of the signal. The signal can represent a
voltage, current, stress, pressure, strain, displacement, velocity,
acceleration, or almost anything. Such a signal, plotted as a function
of time, is represented in the sketch below.
Statistical methods are employed to analyze these random phenomena. The
following discussions is restricted to stationary, ergotic random processes.
Three important aspects of a random signal are
1. Autocorrelation function
2. Power-spectral density
3. Mean-square value
The autocorrelation function indicates the dependence of the signal upon
itself. If y(t) is some random function, the autocorrelation function is
A(T)
-T
y(t) y (t + T) dt
58
-------
where T is a variable time delay. A schematic of an electrical circuit
used to obtain the autocorrelation of an electrical signal is shown
below.
Time
Delay
Multiplier
y(t) y (t +
Integrator
and
Averager
A(T)
y (t +T)
The autocorrelation function describes, in a sense, the degree of random-
ness in a signal.
The power spectal density is the Fourier transform of the autocorrelation
function, and can be represented by the equation
S(co)
2 r °°
= — \ A(T) cos («T dr
J o
The power spectral density indicates the mean-square contribution in
each frequency interval, Aa>, and can also be represented by the equation
S(ou) = lim A (y )
Aw-*0 Au)
A schematic of a power spectral density analyzer is shown below.
y (t)
Filter
Aco
u) + Au)
y(t)]m
Square
Averager
S(u>)Au>
Division
by
AUJ
S(u>)
^ ^
59
-------
The mean square value of a random signal is
2 lira _1
y T „ 2T
Since a power spectral density plot of a random signal indicates the mean
square contribution in each frequency interval, the total area under the
curve is also the mean square value of the signal.
y = J o SO") du)
The root mean-square value is the square root f the area under the power
spectral density curve.
'RMS
Typical autocorrelation and power spectral density plots for three types
of signals are shown below.
y(t)
Signal
sine wave
fW1
Narrow Band
y(t)
\lf'"-\
Autocorrelation
A(T)
"o
A(T)
J
_ T
Power Spectral
Density
S(tu)
0) 1U
o
(I)
Wide Band
y(t)
f
.A(T)
K\.
S(B)
(U
60
-------
It is proposed to use these methods in characterizing turbulence in a
flowing stream. The turbulence detection whose output is proportional
to pressure, would be placed at a desired location in a stream. The
output would be recorded as a function of time. If the dynamic signals
are predominately in the low-frequency spectrum (5 cps or less) the
output would be recorded using some type of pen recorder. The analysis
of the data could be performed, using digital techniques. If the dynamic
signals are in the higher frequency range (greater than 5 cps) magnetic
tape could be used and the analysis performed using analog techniques.
It is anticipated that static signals (zero frequency) with essentially
constant magnitudes are characteristic of smoothly flowing streams,
while signals with widely varying magnitudes and frequencies are charac-
teristic of turbulent streams. These extremes and environments between
these limits should be clearly indicated by the spectral density and
root mean-square value of the pressure history.
61
-------
1
5
Accession Number
2
Subject Field & Group
02E
SELECTED WATER RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
Organization
Battelle Columbus Laboratories Columbus. Ohio
Applied Solid Mechanics Division
Title
MULTIDIRECTIONAL TURBULENCE PROBE DEVELOPMENT
Phase I - UNIDIRECTIONAL TURBULENCE SENSOR DEVELOPMENT
i Q Authors)
Atterbury, Thomas
Sorenson, James E.
Groom, Jack J.
16
21
Project Designation
EPA. Prni
Note
pri- ifinsn
nflw
22
Citation
23
Descriptors (Starred First)
*Turbulence, *Turbulent Flow, Non-Uniform Flow, Eddies, *Streamflow, Channel Flow,
Flow Profiles, Monitoring-Data collections, *Measuring Instrument Strain Gages
25
Identifiers (Starred First)
*Turbulence Sensing Devices, Measurement of large eddies
27
Abstract
Development of a unidirectional-turbulence probe was undertaken to investigate
the feasibility of a small-diameter strain-gaged diaphragm-type pressure
transducer and a self-adjusting depth compensation air reservoir for use in the
follow-on development of a small (1/2-inch diameter) multidirectional-turbulence
probe. A unidirectional probe has been developed which is capable of monitoring
water velocities over a range of 0.5 to 5 ft/sec in turbulence frequencies of
0 to over 100 Hertz and which will automatically operate in water up to
10"feet deep.
Sealing inadequacies in both the air reservoir membrane and the pressure diaphragm
permit moisture entry into the air volume covering the strain gages. This has
given rise to balance drift and circuitry ground problems that have resulted in
the placing of limitations on the water exposure and turbulence monitoring times
for the unidirectional probe. These problems also suggested that the concepts
cannot be immediately incorporated (into a multidirectional probe design.
The unidirectional turbulence probe was released to the Environmental Protection
Agency for use and further evaluation with recommendations for analysis of data
obtained with the probe.
Abstractor
Jack
J.
Groom
Institution
Battelle
Columbus
Laboratories
WR:I02 (REV. JULY 1969)
WRSIC
SEND TO: WATER RESOURCES SCIENTIFIC INFORMATION CENTER
U.S. DEPARTMENT OF THE INTERIOR
WASHINGTON. D. C. 20240
*D. S. GOVERNMENT PRINTING OFFICE : 1 972 — kBk-W2/2B
» GPO: 1969-359-339
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