Journal of Wind Engineenng and Industrial Aerodynarracs, 50 (1993) 129-138 129 Elsevier

VORTEX SHEDDING FROM F L A T P L A T E S U N D E R

T H E I N F L U E N C E O F A N A C O U S T I C F I E L D .

R. Parker, A.H. Hammoud and S.A.T. Stoneman.

Department of Mechanical Engineering, University College of Swansea, Singleton Park, Swansea. SA2 8PP. United Kingdom

Abstract Experhnental data obtained with two flat plates in tandem in a wind tunnel are

presented. Attention is concentrated on the phase of the vortex shedding from the upstream plate relative to the acoustic field when a resonance is excited. At some plate spacings a resonance was excited over two ranges of flow velocity, at the lower velocities the relationship between phase and velocity was found to be similar to that with a single plate but, at the higher velocities, it was quite different. The implications regarding resonances in axial-flow compressors are discussed.

1. INTRODUCTION

The excitation of sound and vibration due to flow around bluff bodies has been studied in many different contexts for many years. Despite a great deal of experimental and theoretical investigation there is, as yet, no complete quantitative model of the processes involved in the feedback loop responsible for the excitation which includes

(a) the generation of acoustic or vibrational energy due to vortex shoaling,

(b) the correlating effect of sound and/or vibration on the vortex shedding process

and (c) the responses of the various posmble resonances which may be mechanical, acoustic or combinations of these.

A simple configuration which has been used for many investigations 1s a single plate spanning a closed passage in which the first transverse acoustic mode (the [~ mode [1]), is excited. Parker [2], Cumpsty and Whitehead [3] and Archibald [4], all examiued tins case and the latter described a linear feedback model of the excitation generated by the shedding of vortices from the plate. Since these early investigations, progressively more complex situations, including acoustic resonances in axial-flow compressors, have been examined and some of the results were sl~ ...... arised in reference [5].

0167-6105/93/$06.00 © 1993 - Elsevier Sctence Pubhshers B.V. All rights reserved.

130

One feature of vortex excitation wluch has proved to be of particular interest m connection voth turbo-machines is the fact that, as vortices shed ~om one row of blades convect downstream, their passage through succeeding blade rows creates a further source of acoustic energy The authors' first experience of th~s effect was an experimental investigation of the excitation of acoustic resonances in a single stage axial flow compressor in which vortex shedding from the thick trailing edges of the inlet guide vanes excited a series of acoustic resonances of the annulus [6] & [7]. Variation of the axmJ spacing between the guide vanes and the rotor was found to have a marked effect on the acoustic amplitudes and on the flow velocity ranges at which the various resonant acoustic modes of the compressor annulus were excited_ An analogous situation occurs when vortices shed fi'om one immg'xvogtt body convect past a second i m m g ~ d body in an enclosed passage and this, relatively simple situation has been used for several investigations of the mechanisms involved.

Theoretical and experimental investigations of the generation of acoustic energy associated with vortex shedding and with the convection of vortices past flat plates and aerofoil section blades in the presence of an acoustic field have been reported in references [8] to [11] and the energy generauon part of the feed-back loop is now well understood. The part of the feed-back loop which requires further eincidafion is the link between the resulting acoustic and/or mechanical oscillations and the vortex sbe~dlng.

The present paper reports an experimeutal contribution to this aspect of the problem As m much of the previous work the simplest possible configurauon was chosen, i.e. a pair of plates in tandem spanning a rectangular flow passage designed so that all resonances excited were purely acoustic. Attention was concentrated on the frequency, amplitude and phase relationships as fimctions of the flow velocity with various spacings between the plates.

2. TEST F A C I L I T Y

The tests were performed in the working section of an open return wind tunnel w~th a rectangular cross section. The general arrangement and relevant dimensions are shown m Figure 1.

Both plates spanned the entire width of the worldng section and the only variables were the axial spacing between the plates and the flow velocity. A pitot-static tube was used to measure the flow velocity and the acoustic ampfimdes were measured ruth a 1/2 inch B&K microphone mounted with the diaphragm flush with the surface of the lower wall of the munel in the position shown. Vortex shedding was detected by means of a hot wire anemometer "X" probe fxom which the longitudinal (u) and normal (v) components of velocity were obtained. This was mounted on a traversing mech~ni-sm to f ~ i t a t e inltial checking to ensure that the variations observed were entirely due to the passage of vortices and, for the tests reported in this paper the probe was then fixed st the position just above the plane of the plate surface and a little way downstream of the wafting edge as shown in Figure 1.

131

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FIGURE I WIND TUNNEL WORKING ~CTION AND PLATE COI~FIGU]ATION SHOWING INSTRUMENTATION Pf~]TIOI~ FOR PHASE MF.~D]U~C.]~'q'IS

A double beam oscilloscope and a two channel I-Iewlett Packard type 3582a specu'um analys~r were used for iniual checks and run time monitoring and all the ~ m presented in this paper were recorded .~ing a Masscomp 5450 computer fitted with a 12 bit analogue m digital converter. Frequency and amplin~:le d~m fzom the microphone and hot wire signals were processed and displaycd n~ng mchniques which have been described previously [6, 7, 10 & II], and a re~resentaxivc example of the results derived f~m the microphone signal is shown in Figure 2. For the phase mcasuremems, ~3e histories of the acoustic pressure and the u and v components of velocity were obtained using condiuonal s~mpling m ellminstc noise by averaging 20 ~mple~. Typical results are shown in Figure 3. from which it may be seen that the velocity variations are compatible with vortices shed fzvm the plate convecting along a line near m the probe position. The method of calc~d~6ng the phase is shown and it should be noted that an increasing phase angle represents an increasing delay in the acoustic cycle relanve to convection of the vortices past the hot-wire anemometer position. No attempt was made to calibrate the absolute phase differences as interest was concentraued on the varianon of phase with flow velocity.

3. TESTS AND RESULTS

3.1 Single Plate

Initial tests were performed ovcr the full speed range of the tunnel with the downsn'eam plate removed and the amplimdc, phase and fz~quency results are shown at the left hand end of Figure 4. The resonance was excited from approximately 25 to 35 m/s; th~'C was a Sm~11 incl"e, asc in freqtlt~llcy with increasing velocity through this range and it can be seen fi'om the figure that there is also a change in the relative phase of nearly half a cycle. These feann~s are ~n~logous m vibration of a lightly d~mped,

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single degree of freedom, spring mass system ff it is assumed that there is no change in the phase of the excitation relative to the vortex sh_~ding. In the present data the narrow ~cquency band covered by the resonance indicates a comparatively low level of damping.

3.2 Tandem Plates

Tests were carried out over a range of plate spacings up to 90 rnrn The frequencies of the principal peaks in the acoustic signal which coincided with the vortex passing firequencies are summarised in Figure 5. It can be seen that at spacings of 25, 28 and 32 mm thel"c ~ two clearly defined resonances with the firequcncy tending to rise at the higher velocities towards the end of the first resonance but with very little change taking place in the second (higher velocity) resonance. From 35 to 50 mm only one resonance occurs within the available flow range but from 60 to 70 mm there are again two resonances although the break between them is not very distinct. At 74 there seems to only be one resonance but well correlated vortex sb~dl,g at a progessively increasing fiequency was found at the highest velocities and, at 77 ram. thCl'C are two clear resonances with low amplitudes at a higher bequency in between. Spacings of 20, 28, 60 and 77 mm were chosen for more detailed e)~amlnation including measurement of the phase angles and the results are shown in Figure 4, along with those for the single plate. At 20 mm and 50 mm no second resonances were fo, nd within the available velocity range and, in both cases, the phase changes are essentially similax to those found with the single plate. In the other three cases the first resonances (occurring at the lower velocity range) again show progressive phase changes similar to that with the single plate but, in each case, the second resonance shows much less variation and the phase does not come

within the range of the first resonance.

To facilitate comparison between the curves, the phase results for all cases have been superimposed in Figure 6. The most important conclusions are:

(a) the variation in phase is within a band of between ~/2 and x with the single plate and during the first resonances with tandem plates, in all cases the phase increases progressively with increasing velocity.

and (b) during the second resonances with tandem plains the phase is always in a narrow band approximately z/2 below the mean of the first resonance phases.

4. DISCUSSION AND CONCL USIONS

Nicasurement of the ~ at which the vortices are shed ~s subject to a small error because, to detect the passage of a vortex, the sensor had to be placed downstream of the region in which the voruces form and it is difficult m define exactly when a vortex is "shed". Bearing this in mind, the results obtained are companble with the following hypothesis:

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With two plates in tandem, the excitauon process in the lower velocity resonance is the same as for a single plate, the conversion to acoustic energy due to vortex interaction with the downstream plate having a small effect on the velocity range and the amplitudes but always being a minor effect compared wath the energy conversion associated with vortex shodding.

In the second resonance the energy generamd m the vortex shedding process is negligible compared with that resulting f ~ m intera~tion of the vortices with the downsu'eam plate. This is eon.~t~at with the fact that vortex shedding is, in relation to the acoustic cycle, approximately a quarter of a cycle away from the phase at which the largest amplitudes are excited by the shOdi.g process.

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The variations in phase may be relau~L to the corresponding Swouhal numbers (Sn = f-dr where f = frequency, t = plate thJclmess and v = flow ve.locity). In all cases, the lowest velocity at which the resonance was excited corresponds to a Stronhal number close to that for natural vortex sh_,~,t;-g from the upstream plate and, with increasing velocity, the S~,h~m number decreases because the actual sb~d~-g frequency locks on to the resonance faequency. In the first resommces, the decrease in Stro.h~d number coinc/des wi± the Im~n~ /ve inc~a.se in phase, in other words, as the Su'ouhal number dem-eascs the voruces are shed pn~rmsively earlier in the acoustic cycle. The present results suggest that, for the ~ used for these tes~ a ~ of about 20% in the SII"onhRI D::mh~ resnlts in a phase change approaching half a cycle and it is 131own that a greater phase change would result in a s/minion when: vortex shedd/ng in the

137

presence of the acoustic field would generate negative acoustic energy (acoustic energy would be absorbed). Therefore, with a single plate, the resonance is not possible at higher velocities (i.e. lower Strouhal numbers). With tandem plates, the second resonances are associated with greater reductions in Strouhal number and the vortex shedding appears to be controlled entirely by the acoustic velocities, and at a point in the acou~c cycle at which little or no acoustic energy is generated.

The objective of this investigation was to obtain clarification of some aspects of the vortex shedding processes which occur in full scale axial-flow compressors. In other investigations it has been observed that coherent vortex sh~a~ng rarely occurs with sections such as flat plates with asymmetrically chamfered ll'ailing edges (sce [5] section 2.3) unless there is either vibrational or acoustic stimulation to control the vortex shedding frequency and spatial correlation. It is logical to expect the ~ m e to be true of the blades in axial flow compressors when operating near to the surge line as, at high incidence, the separation point on the upper surface tends to be forward of the trailing edge. This is, however, the condition in which acoustic resonance excitation of blade vibration has been observed in a number of compressors and it now appears probable that, in a compressor, the acoustic energy which drives a resonance is generated entirely by vortex interaction with blade rows downslream of those from which the vortices are shed. In Otis situation, the necessary conelated vortex sheJcaing is stimulated by the acoustic field and, as she~alng at the fiequency of the resonance would not occur natm'aUy, the vortices are shed at a point in the acoustic cycle at which tittle or no acoustic energy is generated by the shedding process.

5. ACKNOWLEDGEMENTS

The authors are grateful to the Science and Engineering Research Council, the Mimstry of Defence and Rons-Royce plc. for their financial support of research at Swansea into the subject of flow excited acoustic and mechanical oscillations in un'bo-machines and other flow systems. This paper reports a small part of the programme of work which has been in progress for mary years.

REFERENCES

1.

2.

3.

4.

Parker, R. "Resonance Effects in Wake Sb,~daing from Parallel Plates: Calculation of Reson,m Frequencies." J.Sound and Vibration (1967)5(2), 330-343. Parker, P,_ ASME 69-WA/GT-13. "Disctete Frequency Noise Generation Due to Fluid Flow over Blades, Supporting Spokes and Similar Bodies." Ct~psty, N.A. and Whitehead D.S. "The Excitation of Acoustic Resonances by Vortex Sh¢~ddlng" J.Sound and Vibration (1971)18(3) 353-369. Archibald, F.S. "Self Excitation of an Acoustic Resonance by Vortex Sh_e~c,4i~g". J.Sotmd and Vibration (1975)38(1) 81-103.

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5. Parker, R. and Stoneman, S.A.T. "The Excxtation and Consequences of Acoustac Resonances in Enclosed Fluid Flow around Solid Bodies". Proc. Inst. Mech. Engrs. Part C, 1989, Vol 203, pp 9-19.

6 Parker, R. and Stoneman, S.A.T. "An Expertmental Investigation of the Generation and Consequences of Acoustic Waves in an Axial Flow compressor. Large Axial Spacings between Blade Rows." J.Sotmd and Vibration (1985)99(2), 169-182.

7. Parker, R. and Stoneman, S.A.T "An Experimental Invesugation of the Generation and Consequences of Acoustic Waves in an Axial Flow compressor: The Effect of Variations in the Axial Spacings between Blade Rows. "J. Sound and Vibration (1987)116(3) 509-525.

8. Stokes, A.N. and Parker, R. "The intea'aetion of flow and resonant sound m a compressor". Computational Techniques and Applications: Sydney 24-27 August 1987.

9. Stoncma,, S.A.T., Hourigan, K., Stokes, A.N. and Welsh, M.C., "Resonant sound caused by flow past two plates in tandem in a duet" J.Fluid Mech. (1988)192, pp 455-484.

10. Legerton M., Stoueman S.A.T. and Parker 1L "An experimental investigation into flow induced acoustic resonances in an annular cascade". Paper no C416/060, International conference on "Flow Induced Vibrations" Brighton, U/K. May 1991. (Inst. Mech.Engrs.)

11. Legerton M., Stoueman S.A.T. and Parker IL, "The effect of plate spacing and downstream plate length on the acoustic resonance excited by flow past two plates m tandem in a duct". Proc. Second World Conf. on Experimental Heat Transfer, Fluid Mechamcs and Thermodynamics. Dubrovnik, June 1991.