A laser velocimeter technique was used to measure the mean velocity and the frequency characteristics of an oscillatory flow component generated with a rotating flapper in liquid flow system at Reynolds numbers approximating 93,000. The velocity information was processed in the frequency domain using a tracker whose output was used to determine the flow spectrum. This was accomplished with the use of an autocorrelator/Fourier transform analyzer and a spectrum averaging analyzer where induced flow oscillations up to 40 Hz were detected. Tests were conducted at a mean flow velocity of approximately 2 m/s. The experimental results show that the laser velocimeter can provide quantitative information such as liquid flow velocity and frequency spectrum with a possible application to cryogenic fluid flows

Gartrell, L. R.

English

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NASA Technical Memorandum 78702
( y AS A —Ta-78702)	 LASER VF.LOCL,14 1b d	 N78-26189
APPLICATION TO OSCILLATORY 1!jJt,, FLOWS
(NASA)	 24 p HC A02/MF A01	 CSCL 20D	 Unclds
G3/34 21704
LASER VELOCIMETER APPLICATION TO OSCILLATORY
LIQUID FLOWS
LUTHER R, GARTRELL
MAY 1978	
g101^ej^?^^
41L ^
LO
RLASA
National Aeronautics and
Space Administration
Langley Research Gender
Hampton Virgini& 23665
i
SUMMARY
A laser velocimeter technique has been used to measure the mean velocity
and the frequency characteristics of an oscillatory flow component generated
with a rotating flapper in a liquid flow system at Reynolds numbers approxi-
mating 93,000. The velocity information was processed in the frequency domain
using a tracker whose output (analog form) was used to determine the flow
spectrum. This was accomplished with the use of an auto-correlator/Four.ier
transform analyzer and a spectrum averaging analyzer where induced flow
oscillations up to 40 Hz were detected. Tests were conducted at a mean flow
velocity of approximately 2 m/s. The experimental results show that the laser
velocimeter can provide quantitative information such as liquid flow velocity
and frequency spectrum with a possible application to cryogenic fluid flows.
A proposed final system is discussed in the appendix.
INTRODUCTION
The spontaneously occurring longitudinal vibrations, nicknamed POGO,
have been experienced in many liquid propellant rocket vehicles. The
frequency and the intensity of these vibrations, which occur typically for
10 to 40 seconds, are in the order of 5 to 60 Hz and 17 to 34 g's, respectively.
The structural vibrations can produce an intolerable environment to astronauts,
equipment, and vehicle structure. In addition, it can cause adverse effects
to the performance of the propulsion system (ref. 1).
In order to obtain a better understanding of the propellant fluid
dynamics contributing to these oscillations through quantitative means, a
technique for determining the mean velocity and the flow spectrum is needed.
References 1 and 2 discuss the use of piezoelectric transducers for propagating
^i	
ultrasonic waves in a moving fluid for determining the velocity. The velocity
measurement is determined from the time or phase variations resulting from
ultrasonic waves traveling across the flow from opposite points of a path
inclined at some angle to the flow. These variations are inversely proportional
to the square of the fluid sound velocity which is a function of temperature
and pressure. Since the sound velocity for a given fluid is dependent on
temperature and pressure, a simultaneous measure of the variations for waves
propagating in the same direction (and opposite direction) of the flow and
proper relative phasing of the trans,Atted waves can compensate for the
effects of these parameters, thus allowing the velocity to be obtained completely
independent of the sound velocity in the fluid. There are two significant
drawbacks in using the ultrasonic wave technique. They are stated as (1) the
system suffers from signal dropout when gas bubbles contaminate the fluid
sample region and (2) the long term reliability of the piezoelectric trans-
ducers operating in cryogenic fluids is uncertain.
With the current progress in laser velocimeter (LV), many types of
fluid measurements have been made possible. The present work study was
undertaken to investigate the feasibility of using laser velocimetry for
measuring the velocity flow field and frequency characteristics of fluid
flow having oscillatory structure. The results from this study could possibly
serve as a basis for future experiments featuring dynamic cryogenic flows such
as those related to the space shuttle program.
Fluid flow measurements have been made under controlled laboratory
conditions. A brief description of the measurement principle (LV) and a
discussion of the experimental results are presented.
SYMBOLS
f 	 Doppler frequency, Hz
NR	= Reynolds number
R(T)	 = correlation function
5 f	= fringe spacing, meter
T	 = period, seconds; integration time
V	 = velocity, meters/sec
= wavelength of laser light, meter
9	 = angle between intersecting laser beams, degrees
T	 = delay time
= phase angle
W	 = angular frequency
W 	 = Doppler angular frequency
2
k
APPARATUS AND PROCEDURLS
Laser Velocimetry Technique
Shown in figure 1 are two intersecting laser beams of wavelength a
with an included angle 0	 At the point of intersection of the two beams,
a stationary fringe pattern is formed, which is designated as the sample
volume. The fringe pattern is a combination of alternating light and dark
regions of equal spacing. The fringe spacing S f , is given by
A
S f = 2 sin 02
Particles suspended in a moving fluid, with a diameter less than the fringe
spacing will cause light to be scattered, according to the Mie theory, with
a resultant burst signal whose period, T, is equal to the inverse Doppler
frequency shift of the incident laser radiation. The Doppler frequency, fD>
is linearly proportional to the velocity component of the particle normal
to the fringe pattern. That is
f  = V	 (2)
f
where S 	 is the fringe spacing.
Test Apparatus
The water flow system in figure 2 is a recircu l ating type unit that
provides flow rates up to 2 m/s, depending on a manual controlled reservior
head level. There were overflow sections located at various levels that
provided additional head-level control. The local Reynolds number was
approximately 93,000. Axial velocity measurements within a 4.7-cm-diameter
pipe were made approximately 5 meters downstream of the flow entrance section.
A flapper used to produce known flow oscillations in the flow up to 60 Hz was
located at the exit section. The rotational speed of the flapper was monitored
electronically. Naturally occurring and seeded 1-pm-diameter alumina particles
in the flow were used as scattering centers.
The laser velocimeter shown in figure 3 was used to measure the veloci-
ties and velocity fluctuations in the pipe flow. The system which incorporates
a 15-mw He-Ne laser (a = 632.8 mm) was operated in the forward-scatter mode
with a crossbeam angle of 11.6 degrees.
A schematic diagram of the signal processing electronics is shown in
figure 4. The signal from the photodetector is processed by a frequency
3
(1)
0
tracker. This signal processor, with an operational range of 2 kHz to 30 MHz,
converts the Doppler frequency into a proportional analog voltage. This unit
has the capability of measuring velocity fluctuations of better than 100:1,
thereby permitting velocity measurements in environments of very large
turbulence intensity. The input signal was nearly continuous, i.e., the
data rates were in the order of 10 5 samples per second. The output from the
tracker was low-pass filtered to about 1 kHz and fed into a correlator-Fourier
analyzer system and an averaging spectrum analyzer for determining the frequency
characteristics of the velocity flow field. The experimental results were
recorded on a film and by an x-y plotter.
Test Procedure
During each series of test, the mean velocity was measured and held
constant by controlling the height of the water level in the reservior tank.
Next, a rotating Flapper was used to interrupt the flow to create approximately
sinusoidal oscillations ranging from 10 to 40 Hz, depending on the flapper
speed. The frequency characteristics of the flow was measured using two
processing techniques both operating from the Doppler signal processor analog
output which is proportional to the detected flow velocity. The first method
entails averaging individually measured spectra using a digital recursion
process. The second method entails performing an autocorrelation of the
output signal and Fourier transforming the results.
RESULTS AND DISCUSSION
The estimated autocorrelation function, R(T) . , , a representation of
the similarity of a waveform and its replica as a function of a delay time
(T), can be expressed as
T
R(T)	 T o f(t) f(t + T) dt	 (3)
where T is the integration time, and T is the delay.
For a continuous input signal in the form
f(t)	 A Sin (wo t + fir)	 (4)
with a randomly varying phase ^, th , autocorrelation function is
R(T) 22 Cos wo t	 (5)
4
aTaking the Fourier transform of the autocorrelation function, R(T), yields
a one-sided power spectral density jr(w)I 2 of f(t), i.e.,
F [R(-r)] f R(r) a-)WT dT - JF(W) 12	 (6)
n
where
2
F ( W ) ° 2 [ 6 ( W—WA 	 (7)
Shown in figures 5, 6, 7, and 8 are the autocorrelation function and
the power spectral density for 10, 20, 30, and 40 Hz induced flow oscillations,
respectively. In each of these spectrum plots the frequencies indicated were
obtained from a position marker and digital display (a feature of the 'Vourier
transform analyzer).
The data from the averaging spectrum analyzer is shown in figures 9, 10,
and 11. The frequency spectrum of the overall flow without the flapper is
shown in figure 9. The amplitude of the flow oscillation varied approximately
inversely to the rotating flapper speed. As the oscillations were increased
to about 40 Hz, iL was difficult to distinguish the spectrum of the induced
oscillations from the background turbulence. However, with longer averaging
time (^60 sec) the 40 Hz oscillations were detectable (see figs. 8 and 11).
In general the auL-ocorrelation/Fourier transform method yields the
better results. These findings were particularly evident at the higher
induced frequencies. The fact that 40 Hz was the upper limit frequency
attempted for these experiments does not imply that this is the system's
maximum capability in distinguishing higher frequencies. The results were
limited to 40 Hz because of the inherent features of the oscillatory flow
system, i.e., the amplitude of the oscillations were coupled to the oscilla-
tory frequency and varied nearly inversely proportional to it. In other words,
at the higher frequencies (flapper speed) the amplitudes of the induced
oscillations decreased to the background turbulence level where they became
difficult to distinguish. However, in measurement situations where the
amplitude and induced oscillations are uncoupled, higher frequencies could
be detected using this measurement technique.
CONCLUSION
A laser velocimeter technique has been used to measure the mean velocity
and the power spectrum of a liquid flow system, with Reynolds numbers in the
5
Y Y A..v:
order of 93,000. The velocity information was processed in the frequency
domain wing a tracker whose output (analog form) was used to determine the
flow frequency characteristics. This was accomplished with the use of an
autocorrelator/Fourier transform analyzer and a spectrum averaging analyzer,
where induced flow oscillations up to 40 Hz were detected. Tests were
conducted at mean flow velocities in the order of 2 m/s. The experimental
results show that the laser velocimeter can provide quantitative information
such as flow velocity and frequency spectrum with possible transition to
cryogenic flows. A proposed final system is discussed in the appendix.
REFERENCES
1, Pedersen, N. E.; Lynnworth, L. C.; and Carnevale, E. H.: Nonintrusive
Dynamic Flowmeter. Final Report, NAS1-11756 and NASA CR-112313,
June 1973.
2. Alais, P. and Demarais, J. C.: Measurement of Rapidly Varying Hydraulic
Flow Rates by Ultrasonic Waves. Extrait de LaRecherche Aerospatiale,
no. 1972-2 (mars-avril), pp. 61-73, NASA TTF-14, 392.
Meyers, J. F. and Walsh, M. J.: Computer Simulation of a Fringe Type
Laser Velocimeter. Proceedings of Second International Workshop on
Laser Velocimeter, Vol. I, H. D. Thompson and W. H. Stevenson, eds.
Purdue Univ., pp. 471-510, March 1974.
APPENDIX
Proposed Laser Velocimeter System
J. M. Franke and L. R. Gartrell
A mini-laser velocimeter system is proposed as a final system. The
components for the system are small and can be housed very compactly. The
active devices are 1007 solid state for better reliability and power
consumption efficiency. The laser source characteristics are shown in Table 1A.
A computer program for theoretically evaluating laser velocimeters
(ref. 3) was used to examine the signal and signal levels as a function of
time at , fixed distance, 5.08 cm and fixed f-number, 2.54. The input
parameters in the program are given in Table 1A.' Results of an extension of
this program are shown in figure lA where she expected signal to noise is
plotted as a function. of f-number for a given particle size (0.5 - 5 micrometers).
The predicted signal-to-noise ratio as a function of bandwiuth, laser
power, and distance can be expressed as:
SNR = SNR graph + 10 log [KP 2^
	
(1A)
(BW) d 
2
where K = constant ^50 MHZ cm1
MW
BW = bandwidth (MHz)
d	 = distance (cm)
P	 = laser power (mw)
A prototype mini-LV system has been demonstrated in the laboratory
where mean flow velocity in the circular pipe was measured. The system was
operated in the forward-scatter mode, as shown in figure 2A. The proposed
final system is shown in figure 3A.
7
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TABLE 1A.- PROGRAM INPUT PARAMETERS
Laser wavelength
Laser power
Beam diameter
Transmission coefficient
Input lens focal length
Crossbeam angle
Collecting lens diameter
Receiving coefficient
Electronic input impedance
Electronics bandwidth
Fringe spacing
Beam waist
Sample volume length
76...0 am
0.015 watt
0.25 .mi
0.5P
5.08 cm
4.3730
Varied
0.50
50 ohms
29 MHz
10.0 micrometers
0.197 mm
3.66 mm
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_aser Velocimeter System for POGO Flow Diagnostic
System
^-
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PMT 1	 AMP 1	 FILTER I	 TRACKER
FOURIER	 BAND PASS
TRANSFORM	 CORRELATOR	 FILTERANALYZER
REAL TIME
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Figure 4. - A Block Diagram of'the Data Processing Electronics
TIME -------
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FREQUENCY ;HZ)
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Figure 6. - The Auto-Correlation Function and Corresponding Power
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FOURIER TRANSFORM FUNCTION
( POWER SPECTRUM)
Figure 7. - The Auto-Correlation Function and Corresponding Power
Spectrum for an Approximate 30 Hz Induced Flow Oscillation.
25
0
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Figure 8. • The Auto-Correlation Function and Corresponding Power
Spectrum for an Approximate 40 Hz Induced Flow Oscillation.
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FREULENCY (HZ/10)
FREQUENCY (HZ / 10)
Figure 11. - Power Spectrum for a 30 Hz (Upper) and 40 Hz (Lower)
Induced Flow Oscillation.
kk


Laser velocimeter application to oscillatory liquid flows

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