Laser Doppler Anemometry for Flow Measurement

8/3/2019 Laser Doppler Anemometry for Flow Measurement

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National Bureau of Standards Special Publicat ion 484 t Proceedings o f theSymposium on Flow in Open Channels and Closed Conduits held a t NBS,Gaithersburg M D t February 23-25, 1977. (Issued October 1977)

LASER DOPPLER ANEMOMETRY FORFLOW MEASUREMENT

William W. Durgin

Alden Research Laborator iesWorcester Polytechnic Institute

Holden, Massachusetts

Lawrence C. Neale

Charles T . Main, Inc.Boston, Massachusetts

Laser doppler anemometers are non-invasive, l inear, andinherently precise. Calibration, in the usual sense, is notnecessary; length and frequency measurements suffice toestablish velocity at a spatial point . Measurements weremade at points in th e cross-sect ions of tw o square ductscontaining water flow. The points were selected in conformance with a numerical integration scheme to be usedfo r volumetric flow rate determination from the velocitymeasurements. The experiments were per formed in aprimary calibration facil i ty at flows up to 1.25 m 3 / secusing ducts with sides 46 and 92 cm. The anemometer,operating in forward scatter differential mode with a 15mw He Ne l aser, was positioned with a special t raversingframe. Windows in th e ducts allowed t ransmission of th ebeams into th e flow and reception of scat tered l ight . Twogrid pat terns , 4 x 11 and 11 x 11 , were used so that 44 and

121 velocities were measured for each tes t . A total of eighttests were conducted covering a Reynolds number rangefrom 1 .1 to 3.9 X 10 8 After accounting fo r er rors due toth e discreet integration scheme of 0.61% and 0.13% fo r th e4 x 11 and 11 x 11 schemes, respect ively, comparieon withth e calibration facil i ty indicated extreme e r ro r s of +0.81/-0.16 and +0.84/-0.61. The major l imitation of the se t -upused was the time requi red to move th e anemometer andobtain a new velocity value. I t was pointed out that eitherbet ter mechanical positioning o r optical scann ing could beemployed to reduce the time requ i red for a flow determination.

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1. In t roduct ion

As par t of a tes t program to evaluate the performance of a four path acousticflow meter, i t was necessary to es tabl ish th e veloci ty distribution at themetering sect ion. The measurements were made using a laser doppleranemometer and a pa t t e rn which allowed numerical integration fo r volumetricflow ra te . The exper iments were s e t up in a pr imary flow calibration facilityusing gravimetric determination of wate r flow ra te . Square ducts were usedwi th windows provided for the anemometer. A t r avers ing mechanism wasused to posit ion the anemometer measur ing volume at spat ia l locations wherevelocity measurements were made. T he fac i l i t ies , procedures , and resul tsof the entire program are repor ted in [1 , 2J *, while th is paper discussesonly those aspects per ta ining to determinat ion of flow ra te from laserdoppler measurements .

2. Test Faci l i ty

Square ducts (4 6 and 92 em) were ins ta l led in the l a rge primary cal ibra t ionfacility at the Alden Research Laborator ies , Figure 1. This facili!y consis tedof a sump with a capacity of 760 rn 3 of wate r, which was maintain"ed at temperatures from 30C to 40C, a pumping capaci ty of 1.27 m 3 / s at a head of 37 m, ast ra ight pipe ru n of 25 m, and a weigh tank wi th capaci ty of 45,000 kg . Adiver ter was provided to allow s ta t ic weighing for a l l tes ts and a timing act ivato r fo r mid-s t roke operat ion. At th e maximum flow ra te , the filling time fo r aweigh tank ru n was approximately 30 seconds.

The weighing system was a Toledo beam scale ar ranged with a direct read ingdia l and nine individual drop weights . Timing w as accomplished by a pho toelectric system mounted on the diver te r which activated a 100 KH countersynchronized with a precis ion time b a s e . Dead weight cal ibra t ion ot the scaleand load cell was car r i ed ou t on a rout ine basis every 6 months , while thetime base was checked on a cont inuing bas i s each week . The culmative e r r o rassociated with this facil i ty was known to be approximately 0.1% so tha t i tformed a good primary s tandard fo r th e LDA flow measurements .

3. Lase r Doppler Anemometer

A laser doppler anemometer (LDA) operat ing in the forward scat ter differential mode was used . The l ight beam from a 15 mw He Ne l a se r was spl i tinto tw o beams which passed into th e tes t sect ion through a plane window,Figure 2. The beams were b rough t to a focus at the cross ing point wherethe velocity measurement was made. A photomul t ip l ier on the opposite s ideof the duct detected l ight scat tered from par t ic les in the measur ing volumemodulated at the doppler f requency. Figure 3 shows the 46 cm tes t section,t ravers ing frame, l a se r, an d t ransmiss ion opt ics . The receiving optics werealso mounted on the frame, b ut out of v iew. Figure 4 shows the measur ingvolume jus t ins ide the window on the 92 em duc t .

*Figures in brackets indicate the l i tera ture references at the end of this paper.

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The instantaneous par t ic le velocity U I was given by the equat ion

u = 2 s in e/2

where A was the wavelength of the laser radiat ion, in w as th e doppler f requency, and e was th e beam angle , The radia t ion wavelength was knownaccurate ly, and th e beam angle was determined b y pro jec t ing the tw o beamsonto a dis tant screen and using careful geometrical measurements . The

accuracy ofa velocity measurement

thus hinged on measurement of thedoppler f requency, This measurement was made with a f requency t r ackerwhich uti l ized a voltage controlled oscil lator and an e r ro r detector to t r ackthe doppler signal. Either the control voltage o r the veo output could bemonitored as an indication of veloci ty, The measurem ents of mean veloci tyreported here were made using a digital voltmeter with var iable timeconstants , although i t was la ter found that a f requency meter monitoringth e veo gave bet ter resu l t s , In ei ther case , th e system was convenient lyand accurately calibrated using a crysta l f requency s o u r c e .

Thus , all quantit ies associated with a velocity measurement were accurate lyand easily traceable, Furthermore. th e velocity and s ignal output werel inear ly re la ted which simplified subsequent p r o c e s s i n g . An e r ro r analysis

indicated that th e accuracy of th e velocity measurements was approximatelyO .18%.

4. Integration fo r Flowrate

The t ravers ing mechanism provided for the LDA faci l i ta ted po si t ioning themeasur ing volume at specific locations in the cross - sec t ion . The posi t ionswere chosen as 4 x 11 and 11 x 11 matrices such that the .flow ra te couldbe obtained from th e mean velocities using Gaussian quadra tu re [3] ,

The volumetric flowrate was determined as

11

Q ;: 4A I u.,lJ

i

where

A ;: duct area

x i ' x.J= fractional10cation of point from center l ine

~ i ' ~ .J= weights

u ..lJ = measured velocity at i , j

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The Gaussian weights and fractional locations are given in Table I.

TABLE I

11 POINTS 4 POINTS

i , j x.1

Il1

x.J ~ j

1 0.978 0.056 0.861 0.3482 0.887 0.126 0.340 0.6523 0.730 0.186 0.340 0.6524 0.519 0.233 0.861 0.3485 0.269 0.2636 0.000 0.2737 0.269 0.2638 0.519 0.2339 0.730 0.186

10 0.887 0.12611 0.978 0.056

To the extent that velocity profiles could be represented by Legendre po lynominals, th e integration would be exact . F or more real is t ic prof i les , theaccuracy was checked by in tegrat ing over a theoretical velocity dist r ibut ionderived from a la w of th e wall . An exac t integrat ion was made an d comparedto th e 4 x 11 and 11 x 11 schemes corresponding to the measurements . Basedon this calculation, th e 4 x 11 and 11 x 11 schemes should have overestimatedth e flow rate by 0 .61% and 0 .13% , respect ively.

5. Results

Mean and rms velocity measurements were made at each of the 165 gr id points .Each measurement requ i red approximately tw o minutes to insure p roper timeaveraging. A flow rate determination was made after each 11 measurementsand slight temporal variations accounted fo r in subsequen t data reduct ion.Three useful r uns were made using th e smal ler duc t , while five were madefor the l a rger. The resul ts are summarized in Table II .

Test TestSize em No. Date

46 x 46 4 1/29/7546 x 46 5 2/05/7546 x 46 6 2/07/7592 x 92 7 5/06/759 2 x 9 2 8 5/12/759 2 x 9 2 9 5/19/759 2 x 9 2 10 5/20/7592 x 92 11 6/17/75

TABLE II

Flow m3

/ s

1.20131.20980.59551. 24700.63701.24180.62221.2498

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% l l x l l % 4 x 11 JR x 10- 6

+0.37 +0.70 3.5-0.01 +0.45 3.9+0.30 +0.73 1.9-0.24 +0.83 1.8-0.12 +0.68 1.0+0.97 +1.42 2. 0+0.65 +1.16

1.1-0.48 +0.59 1.8


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Keeping in mind that errors of 0.61% and 0.13% should be expected for the4 x 11 and 11 x 11 schemes, respect ively, because of th e integration method,i t can be seen that flow rate determinations using the LDA a re quite good.In fact, after accounting for the integration e r r o r , the maximum percentageflow rate error fo r th e 4 x 11 scheme was +0.81/-0.16 while the 11 x 11scheme was +0.84/-0.61. Similar ly, th e mean e r ro r s were +0.21% and -0.35%,respect ively.

6. Conclusions

The precis ion of the system, including the LDA and th e integrat ion, was good,The system required no calibration other than a tape measure to determinebeam angle and a frequency standard to calibrate the t racker, The poss ibi l i tyof using s tandards other than volume or mass in connection with flow meter ingis thus open. The major limitation i s seen to be the l eng th of time r equ i r ed tomake a flow rate determination, I t is speculated, however, that sui table ha rdware could be arranged to provide fast scanning of the flow cross-sect ion.

7, Acknowledgements

Much of th e work descr ibed herein wa s original ly suppor ted by th e OceanicDivision of Westinghouse Electric Corporation in connection with th e development of their LEFM flow meter. Matching funds from an internal development

fund enabled acquisit ion of th e laser Doppler sys tem.

8. References

[1] Tass inar i , P. J . , "Fluid Flow Characteristics in Square Ducts at HighReynolds Numbers, " M. S. Thesis , Worcester Polytechnic Inst i tute ,(May 1975),

[Zl Tassinar i , P, J , and W,W, Durgin, IlFlow Measurement in RectangularDucts," Report 87-75/M91F, Alden Research Laborator ies , WorcesterPolytechnic Institute, (November 1975).

[3] Benedict, R ,P . and J . Wyler. "Determining Flow Rate from VelocityMeasurements," Instruments and Control Systems, pp . 47 - 50 ,February 1974.

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BREAKDOWN VALVE

FIGURE 1 TEST FACILITY

+ + ;. + . ..+ + + ,+ ;. ;. + + ...

+ + + + + + + +

+ + + + + + +

4 x 11VELOCITY

MEASUREMENT

PATTERN

HEAD

FL = 60 CM

FIGURE 2 TEST SECTION

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45,000 kgWEIGHING TANK

SWITCHWAY

DISA

OPTIC

PHOTOMULTIPLIER

15 mw He Ne

46 x 46 CM D U ~ . ~ ~ .


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FIGURE 3 46 em DUCT, LOA, AND TRAVERSING FRAME

FIGURE 4 B.EAM CROSSING IN 92 em DUCT

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Laser Doppler Anemometry for Flow Measurement