Fiber-optic dual-cylindrical wavesensor for measurement of wall velocitygradient in a fluid flow

Amir A. Naqwi and Stanislav Petrik

A Young's fringe pattern created by two light waves emanating from a pair of slits has been used as thebasis of a fiber-optic device for measuring the velocity gradients of flows near solid surfaces. This deviceis a variant of a dual-beam laser Doppler velocimeter, specialized to direct measurements of wall velocitygradients. A compact version of the device is described in which a fiber-polishing technique is employedfor fabrication of a two-point optical source consisting of two fiber cores separated by 18 pm. The lightfrom this source is collimated and focused on two slits that are prepared through electron-beamlithography and that are 1 um wide and 10 p m apart. Preliminary testing of the compact probe has beensuccessful.

Introduction

The present technique is a variant of laser Dopplervelocimetry (LDV), which is a well-developed andwidely used nonintrusive method for measuring flowvelocity.1 In an LDV system, a fringe pattern isproduced by crossing two focused coherent laserbeams in a region referred to as the measuringvolume. Suitable particles are seeded into the flowunder investigation, so on passing through the mea-suring volume they scatter light that is collected by aphotodetector. The frequency (D) of the resultingelectrical signal at the photodetector is proportionalto the component of particle velocity normal to thefringes (u) and may be expressed by the followingrelation:

ufD = d ' (1)

df

whre df is fringe spacing. The frequency fD is usu-ally called the Doppler frequency because the phenom-enon may be described precisely in terms of theDoppler effect.

When this research was conducted, the authors were withLehrstuhl fur Stromungsmechanik, Universitdt Erlangen, Niirn-berg, Cauerstrasse 4, D-8520 Erlangen, Germany. A. A. Naqwi isnow with TSI, Inc., 500 Cardigan Road, P.O. Box 64204, St. Paul,Minnesota 55164.

Received 5 August 1992.

0003.6935/93/306128.04$06.00/0.© 1993 Optical Society of America.

If the frequency of one beam is shifted relative tothe other one (e.g., by a Bragg cell) then the fringesmove continuously, and hence the sign of the velocitycomponent u can also be determined, in addition to itsmagnitude.

Unfortunately, a conventional LDV system is veryproblematic for measuring the flow velocities near asolid surface. The fringes in the measuring volumeare parallel, as illustrated in Fig. 1(a), so in the regionof large velocity gradient near the wall, the frequen-cies of the Doppler signals have an undesirable depen-dence on the unknown particle location (distance y)within the measuring volume. The diameter of atypical LDV measuring volume is 100 Aim, which isnot small enough to provide the necessary spatialresolution for deducing the instantaneous flow infor-mation from the individual signals. Only the aver-age frequency of an ensemble of signals may beassociated with the center of the measuring volume,provided that the seed particles are uniformly distrib-uted. However, the variance of the measured en-semble exceeds the true variance in the flow, andhence turbulence measurements become erroneousnear the wall. Furthermore, interference of thebeams with the wall leads to distortion of the fringesand produces additional noise. Uncertainty in theknowledge of the location of the measuring volumealso causes errors in the estimates of the near-wallmean velocities.

Here the above-mentioned problems have beeneliminated by directly measuring the instantaneouswall velocity gradient instead of the near-wall veloci-

6128 APPLIED OPTICS / Vol. 32, No. 30 / 20 October 1993

VelocityProfile

MeasuringParticles Volume

Wall

VelocityProfile

MeasuringParticles Volume

Signal

(a)

Signal

Wall(b)

Fig. 1. Near-wall flow and the velocimeter response: (a) conven-tional laser Doppler signals and (b) signals from a DCW system.

ties. As shown in Fig. 1, the flow velocity is zero at astationary solid surface and increases linearly withthe distance from the wall within a thin layer, whichis known as viscous sublayer in the case of turbulentflows (see, e.g., Ref. 2).

Within the viscous sublayer the velocity profile istime dependent but remains linear and may be ex-pressed as

u = g(t)y, (2)

where g(t) is the instantaneous velocity gradient,which can be related directly to the signal frequency ifthe measuring volume consists of a Young's fanlikefringe pattern, as shown in Fig. 1(b). This fringepattern is produced by the interference of two coher-ent light waves emerging from two slits etched in thewall, and it results in a far-field fringe spacing thatincreases linearly with the distance from the wally, inaccordance with the following expressions:

at differenty locations are shown to produce the samesignal frequency as long as the velocity gradient isfixed. Linearity of the relationship between thevelocity gradient and the signal frequency may also beappreciated from Fig. 1(b) by imagining that thevelocity gradient is changed to a new value that is ktimes higher than the present one. In this case thesignal frequencies at all the y locations will be en-hanced by the factor k.

For measurements in a reversing flow, the lightbeam emerging from one of the slits may be shifted infrequency in order to obtain a rotating fan of fringes,which allows one to recognize sign of the velocitygradient in addition to its magnitude.

Because the important flow information near thewall is contained in the velocity gradient, it suffices tomeasure the wall gradient and its temporal fluctua-tions in order to characterize the viscous sublayer.In the case of a Newtonian fluid, the wall velocitygradient is a direct measure of the shear stressexperienced at the wall. The advantage of the pre-sent approach lies in the fact that the instantaneouswall gradient, as opposed to near-wall velocities, maybe measured accurately in a variety of flows withoutexceeding the typical spatial resolution (i.e., 100Aim) provided by LDV.

The arrangement in Fig. 1(b) also eliminates theproblem of laser beams grazing the wall, as the light isintroduced through the wall. Furthermore, the spa-tial position of the fringe pattern is precisely defined,as the slits can be flush with the wall with a highaccuracy.

From the above concept an instrument, referred toas a dual-cylindrical wave (DCW) shear-stress meterwas designed and built by Naqwi and Reynolds,3 whoalso reported measurements of two orthogonal compo-nents of the wall velocity gradient at a given locationin a flat-plate turbulent boundary layer. The prob-ability distributions of the wall gradients that theypresented not only agree with the previous authorita-tive measurements but also provide new insights intothe structure of the viscous sublayer. More re-cently, Naqwi4 reported results of detailed simula-tions of the instrument by using electromagnetictheory and provided general guidelines for a reliabledesign of the device.

Xydf = X '(3)

where is the wavelength of laser light and S is thespacing between the slits. Hence, according to Eqs.(1)-(3), the frequency of the scattered light signal isgiven by

Sg(t) (4)fD=(4)X

Equation (4) shows that the signal frequency is adirect measure of the instantaneous velocity gradientg(t) and does not depend upon the particle location y.This situation is depicted in Fig. 1(b), where particles

Construction of a Compact Probe

The hardware of the DCW shear-stress meter used byNaqwi and Reynolds3 was based on bulk optics, so itcould not be easily transported and was prone tomisalignments caused by mechanical vibrations.Here we are concerned with the miniaturization ofthe instrument by using fiber optics, so that it isrobust, easily transportable, and requires less spacefor mounting.

The focusing optics of the device are based on twokey components: a pair of optical slits and a two-point optical source composed of the exiting ends oftwo fibers. The present hardware is illustrated inFig. 2. Two laser beams emerging from a fiber

20 October 1993 / Vol. 32, No. 30 / APPLIED OPTICS 6129

,AVAVAVAVAVAV W_

Flow

Fiber Spherical Cylindrical SlitsJunction Lens Lens

Fig. 2. Optical layout of the miniaturized shear stress meter.

junction are collimated by a spherical lens and thenfocused on the two slits by a cylindrical lens. The slitplane is flush with the wall of the flow channel duringshear-stress measurements. The pair of optical slitswas prepared by using electron-beam lithography.The slits were etched on a 0.1-pm-thick chromiumcoating on an optically flat glass substrate with adiameter of 12 mm. A 0.1-1im-thick layer of quartz(SiO2) was subsequently deposited over the chro-mium coating to protect the slits. The glass disk wascemented to an aluminum plug with a diameter of20 mm.

As indicated in Ref. 2, it is necessary to create aYoung's fringe pattern within 100-200 [lm of the wallin order to take measurements in a typical turbulentboundary layer. Hence in the present version of thedevice, both the slit width and slit spacing have beenkept small; i.e., 1 A~m and 10 um, respectively.Furthermore, the slit lengths are restricted to 0.5 mmin order to resolve adequately the flow structuresparallel to the wall.

The special fiber-optic component, referred to asthe fiber junction in Fig. 2, has been developed toproduce two point sources of laser light with anappropriate separation so as to focus them onto thetwo slits. For the desired slit spacing of 10 jim, thefiber core-to-core spacing was estimated to be 16.lm ± 3 [um. This estimate is based on the assump-tion that the central-beam path follows the geometri-cal optics and the free-space propagation of eachbeam may be computed on the basis of Gaussianbeam optics.

A polishing technique similar to the method re-ported by Bergh et al.5 was used for reducing thecore-to-core spacing of two single mode fibers (Fuji-kura SM-48-P, Panda-type, with a core diameter of 3Aim and a cladding diameter of 125 jim), in whichstress elements on the opposite sides of the core areemployed for preserving polarization. The fiberswere placed in grooves on two aluminum blocks.As shown in Fig. 3, the grooves were made by bonding75-jim-thick steel tapes to the aluminum substrate,and the fibers were aligned in the grooves prior toepoxying so as to orient the plane of stress elementsparallel to the block surface. The ends of the fiberswere cupped and polished to obtain a flat surface ofoptical quality perpendicular to the fiber axes. Thefibers were subsequently polished parallel to thesurface of the block, and the core-to-surface distancewas checked periodically by a microscope.

_ Al-Substrate

Tape Steel *@Cladding

Tape 0 * @ ) 1 Stresselement

Epoxy : so_ 'Core

Fig. 3. Two-point source composed of two optical fibers.

After polishing, the blocks were placed together asin Fig. 3. The final adjustment of the core-to-corespacing and the alignment of the two fiber blockswere done by checking the quality of the interferencepattern created by the two divergent laser beamsemerging from the fiber ends and by measuring theresulting spacing between the fringes. This methodpermits the desired core-to-core spacing to be ob-tained with an accurcy better than ± 3% and providesa satisfactory angular alignment of the two fibers.The aligned blocks were bonded together with ametal-to-metal epoxy.

A two-point optical source composed of two opticalfiber cores separated by a distance of 18 jim ± 0.5 jimwas made by using the above technique (Fig. 3). Wehave not observed any measurable influence of polish-ing on the intensity profile or the polarization state ofthe output beam.

Preliminary Testing

The feasibility of using the instrument describedabove has been verified experimentally. The probewas mounted in the wall of a flow channel of squarecross section of 200 mm x 200 mm. To detect thescattered light from water droplets in the flow, weused a photomultiplier with a two-lens receivingoptics at a location perpendicular to the fan of fringes.A pinhole with a diameter of 150 jm was mounted infront of the photomultiplier in order to receive thescattered light from a region whose extent along theyaxis (see Fig. 1) was limited to 100 jim. An argon-ion laser (Spectra-Physics Model 171) operating inthe cw mode with an output power of 800 mW wasused to couple coherent light (X = 514 nm) into thetwo input fibers. Figure 4 shows a typical high-passfiltered signal that was generated by a water dropletpassing through the measuring volume.

The measuring volume was moved perpendicularto the wall (along the y axis) by moving the pinhole infront of the photomultiplier, and ensembles of fre-quency signals were collected at various locations.As Fig. 5 shows, the mean frequency is approximatelyconstant in a layer of thickness 300 jlm near the wall,which verifies the principle of the device, i.e., thesignal frequency is independent of the scatteringparticle location as long as the instantaneous velocityprofile is linear. In a standard flow application, theregion of linear profile would generally be thinner

6130 APPLIED OPTICS / Vol. 32, No. 30 / 20 October 1993

10 20 30 40Time (bts)

Fig. 4. Typical signal produced by awater droplet passing throughthe measuring volume.

than the present one. Nevertheless, the thickness ofthis region may be estimated by following the aboveprocedure of moving the effective measuring volumeperpendicular to the wall, prior to taking the velocitygradient measurements.

The lengths of the vertical bars in Fig. 5 representtwice the rms value of the measured ensemble of the

iuU -

125 -_N -N

:X4 100-

C) ,P 75-a,

P, -.

25

F

-tI

II

0 100 200 300 400 500D (,um)

6o

Fig. 5. Signal frequencies near the wall.

velocity gradients. The rms velocity gradient is40% of the mean value, which is in agreement with

the expected behavior of a standard turbulent bound-ary layer.3

Concluding Remarks

The DCW shear-stress probe has already been provento be a useful instrument for basic research in fluidmechanics.3 It allows one to nonintrusively mea-sure important parameters of the viscous sublayer ina turbulent flow, that cannot be recorded reliably byusing conventional techniques, such as LDV or instru-mentation based on analogy between the near-wallmomentum transfer and the heat or mass transfer.In the past, however, the probe was not used exten-sively because of its cumbersome construction. Inthe present study, modern construction elements andtechniques such as polarization-maintaining opticalfibers and electron-beam lithography have been usedto make the DCW system compact and robust. Thepreliminary tests have indicated that this versionoperates satisfactorily. It is now being used forshear-stress measurements in complex turbulentflows.

This work was partially funded by the GermanNational Science Foundation (DFG) through contractNa 189/2-1. S. Petrik is thankful to the Alexandervon Humboldt Foundation for providing a researchfellowship to support his year-long stay at the Univer-sity of Erlangen.

References1. F. Durst, A. Melling, and J. H. Whitelaw, Principles and

Practice of Laser-Doppler Anemometry (Academic, London,1976).

2. H. Tennekes and J. L. Lumley, A First Course in Turbulence(MIT, Cambridge, Mass., 1972).

3. A. Naqwi and W. C. Reynolds, "Measurement of turbulent wallvelocity gradients using cylindrical waves of laser light," Exp.Fluids 10, 259-266 (1991).

4. A. A. Naqwi, "Performance prediction of dual-cylindrical wavelaser devices for flow measurements," Exp. Fluids 14, 121-132(1993).

5. R. A. Bergh, G. Kotler, and H. J. Shaw, "Single-mode fiber opticdirectional coupler," Electron. Lett. 16, 260-261 (1980).

20 October 1993 / Vol. 32, No. 30 / APPLIED OPTICS 6131

t ---

I

k