Measurement of flow and turbulence distribution of a free jet by laser photon correlation spectroscopy

Volume

6, number

OPTICS

4

MEASUREMENT

OF FLOW AND TURBULENCE

BY LASER

PHOTON

C.T. MENEELY**,

December

COMMUNICATIONS

DISTRIBUTION

CORRELATION

1972

OF A FREE JET

SPECTROSCOPY

*

C.Y. SHE and David F. EDWARDS

Colorado State Universi(v, Fort Collins, Colorado 80511, USA Received

The flow and turbulence profile and photon correlation spectroscopy

5 September

of a free jet is reported

After the first demonstration by Yeh et al. [ 1J , the use of a laser Dopplermeter for flow measurements has been widely considered. The cross-beam (or real fringe) geometry investigated by many authors [ 21, has the clear advantage of maximizing sig* Sponsored in part by a contract with the Air Force Cambridge Research Laboratories, Office of Aerospace Research, USAF. under Contract No. F19628-70-C-0035. Project THEMIS. ** Present address: Air Force Cambridge Research Laboratories (OPL), Hanscom Field, Bedford, Massachusetts 01730. USA.

1972

by remote

sensing techniques

using laser Doppler

m&to-noise ratio for fixed available laser power 131. Using a spectrum analyzer, Rudd (41 has recently applied this technique to measure the turbulent pipe flow by sensing the forward-scattered signal. From the standpoint of the speed of signal processing and the practicality of remote sensing, photon correlation spectroscopy and a backward scattering configuration should be used. With this arrangement, Pike [5] has recently reported the observation of flow in an u11seeded laboratory wind tunnel. In this article. we rt’port the flow and turbulence profile measurement ot a free jet in laboratory by the backward scattering

LASER

L

APtRTURE

PIPE

HUMIDIFIER

T

Fig. 1. The experimental

380

effect

if

set;up.

I

I

1

100

.

200 r (P set)

Fig. 2. A typical

December 1972

OFTTICSCOMMUNICATIONS

Volume 6. number 4

measured photon correlation flow and turbulence.

function

of

techniques with cross-beam Doppler photon-correlation spectroscopy. The free jet was formed by a circular pipe of 3’ long and 3” in diameter in an up-right position. The

flow was generated by a commercial humidifier modified to provide a smaII amount of water-vapor seeding. The flow in the tube is very slow and the Reynolds number is about 8000. Due to the short pipe used, a significant amount of turbulence in the flow is visible. The jet system together with the whole light scattering set-up is shown in fig. 1. By moving the free jet relative to the cross-point of the laser beams, we can probe anywhere in the jet and measure its flow and turbulence profile. A 40 mW He-Ne laser at 0.6328 pm was used as the light source in our experiment. A Sacoir model 42 correlator was modified to operate in a double-clipped photon count mode [6] with mean count per sampling interval kept below 0.2. A typical photon correlation function obtained is shown in fig. 2. The decaying oscillatory Doppler signal can clearly be seen. The rate of decay which is caused by the random phase modulation of the Doppler signal, measures the degree of turbulence and velocity fluctuations. There is an additive slower background as indicated by the dotted curve in fig. 2, in the correlation function. We wish to

15( 3

2 c

2

E > <

IOC

d

I

50

I

I

5

I

r (inch] (a)

Fig. 3. Flow and turbulence

1.5

0

I

.5 r

15

(Inch)

.(b)

profile

of a free jet: (a) the velocity distribution and (b) the turbulence the exit of the pipe, r = distance from the pipe center.

distribution.

z = distance

from

381

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4

OPTICS

point out that this is the self-beat signal contribution from each of the beams used in the crossed-beam experiment. To our knowledge, this slower background has not been experimentally reported. This background can not be easily observed if a much faster time scale [5] is used, and, due to its low frequency, it is separated from the Doppler signal in frequency and it is usually ignored when a spectrum analyzer is used. To verify this is indeed the self-beat signal, experiments using a single beam (by blocking one of the double beams) were performed. This same slower spectrum was seen. The detailed study of the shape of the photon correlation function would provide valuable information on the statistics of the turbulent flow. One expects the correlation function envelope to change from exponential to gaussian, as a laminar (diffusive) flow becomes highly turbulent. For the purpose of this work, the correlation function envelope can be approximated by a gaussian function [7], from which the velocity fluctuations were determined. Fig. 3 shows the result of the profile of the velocity and its fluctuations. Several points in our results presented in fig. 3 are worth mentioning: ( 1) the flow near the exit of the pipe (z = l/4”) depicts essentially

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1972

the flow in the pipe as reported by Kudd ]4] , (2) near the edge of the free jet (r = I .S”), the flow is most turbulent near the pipe exit where maximum shear occurs, and (3) there definitely exists a core region in the center portion of the jet, All these are in agreement with the usual understanding of‘ a free jet and the theory of turbulence [8]. It demonstrates the unique value of using photon correlation spectroscopy in remote sensing of a jet flow with a laser Dopplermeter.

References [ I 1 Y. Yeh and 11.Z. Cummins,

Appl. Phys. Letters

4

(I 964)

116. 121W.M. Farmer and D.R. Brayton,

131 141 [5l 161 171 [S]

Appl. Opt. IO (I 97 1) 2319: R.J. Adrian and R.J. Goldstein, J. Phys. C 4 (1971) 505. L. Lading, Appl. Opt. 10 (1971) 1943. M.J. Rudd, J. Fluid Mech. 51 (1972) 673. E.R. Pike, J. Phys. D 5 (1972) L23. D.E. Koppel, J. Appl. Phys. 42 (1971) 3216. E.R. Pike, D.A. Jackson, P.J. Bourke and D.I. Page, Am. Inst. Chem. Engng. J. 3 (1968) 203. A.A. Townsend, The structure of turbulent shear tlow (Cambridge Univ. Press, London, 1956).