Investigations of roughness-generated TBL sound using coupled physical-computational experiments in conjunction with theoretical development

Transcription

1 Investigations of oughness-geneated TBL sound using coupled physical-computational expeiments in conjunction with theoetical development W. Blake a, K.-H. Kim b, M. Goody a, M. Wang c, W. J. Devenpot d and S. A L Glegg e a Naval Suface Wafae Cente (Ret.), 6905 Hillmead Road, Bethesda, MD 0817, USA b Office of Naval Reseach, Randolph St., Alington, VA 0, USA c Univesity of Note Dame, Depatment of Aeospace and Mechanical Engineeing, Note Dame, MD 46556, USA d Viginia Tech, Aeospace and Ocean Engineeing, 4E Randolph Hall, Blacksbug, VA 4061, USA e Floida Atlantic Univesity, Depatment of Ocean Engineeing, Boca Raton, VA 33431, USA hydoacoustics@aol.com 1059

2 Sound poduced by tubulent-bounday layes (TBL) ove ough walls is being studied in a seies of physical-computational expeiments. At issue is the development of an undestanding of how the wall elements geneate flow dipoles which diectly detemines how the sound is descibed in tems of dependent vaiables. The consideed mechanisms include dipoles at the oughness elements due to thei shed wakes, distibuted suface dipoles due to convecting tubulence impinging onto elements, and Rayleigh-like scatteing into sound of aeodynamic pessues of hydodynamic wave numbes of flow above the oughness. The LES of ough-wall TBL consists of numeical expeiments being used to isolate the sepaate mechanisms. These simulations ae benchmaked with analysis and with matching physical expeiments on ough wall patches in which identical geometies of wall oughness and identical Reynolds numbes ae used. In the physical measuements, aay-based measuements of the adiated sound ae being used to chaacteize the diectivity and magnitude of the sound and to elate the sound to aeodynamic wall pessue and to classical chaacteistics of the tubulent bounday laye. The LES poduces fo compaison both adiated sound and detailed flow stuctue aound the oughness elements. 1 Intoduction Sound geneated by tubulent bounday laye (TBL) flow ove ough walls has been of continuing, yet intemittent, inteest fo nealy 40 yeas and a lage body of wok has been pesented and published ove that time. In spite of this thee is still no coheent view of the physics of sound geneation by ough-wall tubulent bounday layes. Space does not pemit a compehensive view of the liteatue extant on this subject aea and so only a few efeences shall be cited hee. Blake [1] has eviewed the body of wok though 1986; the fist elevant expeimental wok on the poblem of acoustic adiation was conducted by Hesh []. In that wok a small oughness patch was installed at the exit of a nozzle flow to povide the fist contolled evaluation of sound emitted. The esults cannot be usefully genealized to a boade context of engineeing application, but they did give the initial view of dependence on speed and oughness. Then in the time peiod Faabee and Geib [3] conducted a well-contolled measuement of sound adiated along the suface of a igid wall downsteam of a lage patch of oughness. They obtained measuements of sound emitted downsteam of the patch and along the wall fo a vaiety of oughness configuations. Unfotunately the popeties of the tubulent bounday laye wee not compehensively documented ove the entie development of the flow. At the same time Howe [4] pesented a theoy in which sound is poduced by inviscid scatteing of tubulent bounday laye pessue geneated by the bounday laye flow above, but not flowing aound the oughness. In this way subsonic hydodynamic wavenumbes ae scatteed into sound by the Rayleigh-like scatteing at the elements beneath the bounday laye. The mechanism did not conside the sound that might be poduced by the unsteady dag that is eaction at the wall due to the poduction of tubulence. This pape is a shot summay of the esults cuently in hand of a special-focus pogam to undestand to quantify the sound poduced by ough-wall tubulent bounday layes. Othe papes at this meeting go into futhe depth. The cuent eseach pogam includes new wind tunnel investigations [5,6], two analytical investigations [6,7,8] and a seies of Lage Eddy Simulations (LES) [9] which ae tailoed to undestanding the mechanisms of sound geneation by ough-wall tubulent bounday layes though a seies of physical-numeical expeiments that ae mutually tailoed. The concept used in developing these expeiments is to link numeical and physical execises into a common expeiment in which the geomety, Reynolds numbe, and dependent and independent vaiables ae common. This equies that the physical and numeical expeiments ae specified along the common equiements of that which is possible in the physical wind tunnel facility (speed, geomety, size) and that which is possible in the numeical modelling (gidding, bounday conditions, numeical capacity). Thus the execises ae designed along a seies of compomises which ae detemined jointly by the physical expeimente and the numeical analyst. A subset of esults of these will be outlined in the body of this pape. Physics oveview and expeimental configuations The sound fom ough-wall tubulent bounday layes is consideed due to thee physical pocesses that ae depicted in Fig. 1. Fist, at the top of the figue, intestitial flow in the immediate vicinity of a oughness element includes a gust esponse due to the incident tubulence that oiginates fom upsteam and is highly otational. The intestitial flow is then fed by a viscous wake that is shed fom the element; the upsteam gust influences the wake poduction in ways that will be made clea in the LES. Moving on to the next oughness element, this flow becomes the gust inflow to it. The second contibution of sound geneation is the inviscid scatteing of aeodynamic pessue into sound by the oughness elements in the wall. In this mechanism the incident pessues ae geneated by the flow that gazes the tops of the oughness and lies above them. Notionally, the souce of these pessue distubances is the oveall tubulent bounday laye as detemined by the mean upsteam shea. This incident pessue is chaacteized by subsonic convection wave numbe, ω/u c (y ), whee ω is adian fequency and U c is local mean convection velocity at position y above the wall. Both the fist and second contolling mechanisms geneate foces at the oughness elements, these foces constitute dipole souces at the wall. The thid mechanism that is involved with the geneation of sound is the eflection of the oughness dipoles due to the pesence of the suface. If the flow wee inviscid then it is well known that the eflection of nomal stesses geneates only quadupole sound; the addition of fluctuating wall shea, eithe by the intoduction of viscous wall stesses in the case of the smooth wall, o by the geneation of stesses by eithe of the above two mechanisms, geneates tangential dipole stesses which, unde, eflection by the bounding igid wall, become longitudinal quadupoles of essentially the same adiation efficiency as the constituent dipole, itself. 1060

3 Pevious theoetical modelling of Howe [4] addesses this souce. The theoetical modelling of Glegg, appeaing in [6,11] addesses the geneation of elemental dipole foces by convected voticity and wake poduction; Matinez [7,8] futhe addesses the effect of local shea fluctuation and unsteady convection on the intestitial flow acoustics. The expeimental pogam of physical measuement coupled with the LES is devoted to claifying these mechanisms and to quantifying thei elevance. The LES detemined on the basis of a seies of peliminay physical expeiments that disclosed the attainable signal to noise fo one of the ough-wall TBLs. The paallel physical expeiment will exactly eplicate the LES Reynolds numbe, oughness configuation and oughness fetch size. It will also mio seveal of the computational iteations in tems of included numbes of oughness elements. This physical aangement will be pat of a lage seies of Fig. 3 Illustation of expeimental aangement of the NSWCCD goup. Fig. 1 Illustation of flow-acoustic featues of ough-wall flow. expeiments [9] will be conducted fo patches of hemispheical oughness elements with a finite steamwise fetch that is entiely confined to a contol volume as shown. The distibution of the oughness elements in this patch will evolve in stages fom the single-element building block. The computation adds a second element in the wake of the fist, then othes to constuct a total distibution of 40 elements. The LES will povide the details of flow among the intestices, the mean popeties of the TBL as it Fig. Illustation of the LES contol volume shown hee enclosing the single-element building block of a distibuted oughness. The volume occupies 5δxδx3δ with a smoothwall inflow TBL which has momentum thickness Reynolds numbe of 7500, oughness element size is h + =95. develops ove the fetch, and the sound adiated. Roughness sizes of h + =95 and ~190 will be examined fo compaison with wind-tunnel esults fom identical physical patches. The contol volume and oughness used in the LES was Fig. 4. Illustation of expeimental aangement of the Va Tech goup. geometies that ae examined. The physical expeiments equie facilities that meet thee equiements: measuements of bounday laye chaacteistics (mean and statistical) in ode to elate nomalize sound to TBL popeties and to compae with the LES expeiments; ability to measue sound in a fee field and to define its diectivity with espect to the oughness patch; measuement of the wall pessue fluctuations as a expedient metic of the TBL aeodynamic souce stength. The expeiments ae being conducted by complementay goups. The wok of Goody et al [5] is in n acoustic wind tunnel with the aangement shown in Fig. 3. This study will focus on lage oughness elements. The open-jet of the wind tunnel is bounded on one side with a igid wall bounday on which is mounted the vaious physical oughness panels. Positioned opposite the wall is a diective acoustic aay of 63 micophoness that is situated to measue the adiated sound to the nea-nomal to the plate. A wall-mounted linea micophone aay which is situated in the wall plane just downsteam of the oughness patch is used to measue the sound emitted in the plane of the wall. These two aays ae used to detemine diectivity of the sound in two citical diections. Aays of flush-mounted pin-hole micophones ae intespesed among the elements in ode to chaacteize the aeodynamic wall pessue field. Extensive TBL measuements ae used to chaacteize and 1061

4 suppot the acoustic measuements; these yield TBL mean wall shea and thicknesses along the steamwise diection. The physical aangement of Devenpot et al [6], Fig. 4, was simila although with less focus on measuing fa field acoustic diectivity and geate focus on measuing the details of wall shea stess and tubulence statistics in the egions nea to the oughness elements. This goup will addess smalle patches and smalle oughness elements. Both Goody et al [5] (~100<h + <~1900, h +,= hu τ /ν,) and Devenpot et al (~<h + <~8) ae modelling andom distibutions of sand gain oughness as well as the deteministic distibutions of hemispheical elements that match the LES expeiments. 3. Initial measuements and simulations of sound fom distibuted andom oughness elements The initial exploatoy measuements of sound [5,6] wee conducted with vaious oughness sizes and distibutions with objectives that included the establishment of the facility limitations. Initial measuements with the oughe [5] wall patches will be discussed hee. A most essential step in establishing the physics of the ough-wall TBL sound is to unequivocally measue the sound emitted into the two diections nomal and paallel to the wall. Figue 5 discloses esults of thee test situations. In pat (a) of the figue is shown a baseline smooth wall souce distibution that is infeed fom the aay output; pat (b) shows the souce distibution fom ows of oughness elements aligned acoss the flow diection; pat (c) shows the souce distibution fom a complete patch of appoximate dimensions 813 mm (3 in) steamwise by 03 mm (8 in) span. The oughness size fo this measuement is in the vicinity of h + ~1800. These souce maps ae detemined by invesion of the aay output [5] and povide maps of meansquae sound pessue pe unit esolution aea (oughly 50 mm by 50 mm esolution at 000 Hz and popotional to fequency), with the mean-squae sound efeed to a efeence ange. Nomalization of the map on the esolution aea and then integation ove the entie map aea yields the oveall mean-squae sound at that efeence ange. We see in Figue [5] that the measued sound level inceases monotonically as oughness is added to the patch and that the geatest contibution to the sound is fom nea the leading edge of the patch. oientation of the patch and its instantaneous dipole distibution elative to the aay. The oveall magnitude of the shea stesses was tapeed to matched the obseved [10] evolution of wall shea along the patch s steamwise diection. The simulated souce map is compaed with the measued one in Figue 6. Results suggest that the leading oughness elements in a finite patch of oughness contibute heavily to the oveall sound adiated. Figue 7 shows the calculated diectivity patten of the sound as well as supeposition of the measued sound levels at 0 and 90 degees fom the flow diection. The diectivity patten was (a) (b) Figue 6 shows additional souce maps fo a patch of lesse oughness, h + = ~780. Again, flow is fom ight to left. These maps show simila distibutions of souces and also shows dominance by the leading edge elements. Note that the levels ae ~5dB lowe than fo the lage elements. An analytical simulation was conducted to calculate the sound fom a finite oughness aea in which the oughness dipoles wee given andom stength and oientation as well as being eflected by the igid wall plane. The oientations of the dipoles wee simulated to have vecto oientations aligned as if they wee flow-induced stesses that would occu on the elements of the oughness. These geneally oient themselves as shea fluctuations in the diection of the mean flow, but with diections vaying slightly elementto-element within some limit. The simulation thus mimicked the expeimental aangement in the size and (c) Fig. 5 Images of souce distibutions on oughness patch at ~4.7 m/s and 3000 Hz. (a) baseline smooth wall, (b) ows of oughness elements, (c) patch of continuous andom distibution of elements. The coloba in pat (c) applies to pat (b). 106

5 plotted by scaling the calculated level on the wall to match the measued value. It would appea that the measuements to this point geneally agee with the initial hypothesis of dominance of the sound in the plane of the wall and that the sound fom a finite patch of oughness with a developing TBL dominates at its leading edge. y b (in) (a) No Roughness Baseline Beamfoming, 3000Hz, SPL (db ef 0 μpa) x b (in) (b) Rough Patch, h = ~5mm. Fig. 6 Images of souce distibutions on oughness patch at ~4.7 m/s and 3000 Hz. (a) baseline smooth wall, (b) patch of continuous andom distibution of elements, h + ~550. Fig. 7. Measued and calculated images fo souce distibutions of oughness patch at 3000 to 4000 Hz Fig. 8 Diectivity patten of distibuted wall oughness at 6000 Hz; points ae measued using fee field (VT spial aay) and wall-mounted aays; line is calculated using the simulation then scaled to the value obtained by the wave vecto filte. 4 The elationship between the adiated sound and fluctuating wall pessue Devenpot [6] has examined the elationship between the fluctuating wall pessue and the adiated sound in the fee field egion above the wall. Figue 8 shows atios of the measued sound pessue and wall pessue fluctuation specta fo patches of distibuted oughness simila to that discussed above, but smalle, i..e. 305 mm steamwise (~0 δ) by 610mm span, with h + also smalle. It was found that futhe nomalization on the measued geometic size was equied to align the measuements into a single goup. This nomalization aises fom a dimensional analysis that of shea stess dipoles that has two altenative foms depending on whethe the dipole stength is detemined by Rayleigh-like scatteing o by aeodynamic dag at the oughness elements. Thus fo the dag mechanism, the elationship between the wall pessue and sound pessue involves an h and this is eflected in the scaling shown in Figue 8b. A dimensional analysis of the oughness-geneated sound discloses altenative paametic dependences depending on whethe the dipoles that ae attached to the elements ae geneated fom eactions to Rayleigh-like scatteing o to aeodynamic inteaction, thus, Φ ad ω cosθ A suface [ F ( ω) ] G(h,k l) + ( ω) = (1) c co l xl y whee the backeted tems epesent espectively the spatial aveage spectum of foces on the elements, the compact dipole Geen function, the statistical numbe of adiating elements, and a geomety-dependent function that epesents dependence on oughness size, h +,=hu τ /ν, and the pojection of the mean convection wave numbe on the oughness spacing vecto l. Fo the sound detemined by aeodynamic intestitial flow this becomes 1063

6 claifies the impotance of viscous inteaction between the element and flow. Acknowledgments This poject is funded by the Office of Naval Reseach, Washington, D.C., USA. The authos wish to thank the many co-wokes and students that made this wok possible; most notably J. Andeson, D. Stewat, B. Smith and N. Alexande. (a) Nomalization on suface pessue alone. Refeences [1] W.K. Blake, Mechanisms of Flow Induced Sound and Vibation, Academic Pess, [] Hesh, A.S., 1983, Suface Roughness Geneated Flow Noise, AIAA [3] Faabee, T. and Geib, E., 1991, Measuements of Bounday Laye Pessue Fluctuations at Low Wavenumbes on Smooth and Rough Walls, Poceedings of the Int l. Mech. Eng. Cong. and Expo., NCA Vol. 11, pp Φ (b) Nomalization on suface pessue and oughness measued height. Fig. 8. Spectum of adiated sound nomalized on wall pessue spectum. ad Asuface ωh [ pp( )][ M] cos θ Gd (h,k + Φ ω l) ( ω) = c U and fo inviscid Rayleigh-like scatteing of convected TBL pessue 4 Asuface ωh ad( ) [ pp( )][ M] cos Gs(h,k + (3) Φ ω = Φ ω θ c l) U whee M is fee steam Mach numbe, is ange, U is fee steam velocity, [ Φ ( ω pp )] is the aea-aveaged wall pessue ove A suface. 5 Conclusion () Oveall, the data pesented hee suggests that the paametic equation () best defines the adiated sound fom ough walls in the fully-ough egime when the oughness elements ae evenly and andomly dispesed ove the aea. Additional on-going wok suggests equation (3) best defines sound in the tansitional anges of h + between hydaulically smooth and fully ough. This is suggested by a slight lack of collapse fo the smalle elements in Figue 8b. LES expeiments [9] on 1 and element micocosms of a ough wall cuently indicate that it is difficult to conclusively sepaate sound-geneation mechanisms, but that a second element in the wake of anothe is the dominant adiato of the two elements. Thus the LES [4] Howe, M.S., 1988, The Tubulent Bounday-Laye Rough-Wall Pessue Spectum at Acoustic and Subconvective Wavenumbes, Poceedings of the Royal Society of London A, Vol. 415, pp [5] Goody, M.C., Andeson, J.A., Stewat, D.O., and Blake, W.B., "Expeimental Investigation of sound fom flow ove a ough suface," Session: NS07/ Aeoacoustics, Pais- 08, 008. [6] Devenpot, W., Glegg, S., Alexande, N., Smith,B., The mechanisms of oughness noise, Session: NS07/1 Aeoacoustics, Pais-08, 008. [7] Matinez, R. Et al, Undestanding Roughness Noise: Pogess in Analytical Modelling and Testing, Pat : Compaison of Calculations to Data Poceedings of NCAD008 NoiseCon008-ASME NCAD July 8-30, 008, Deabon, Mi [8] Matinez, R. et al, Undestanding oughness noise: Pogess in analytical modelling and testing, Pat : Compaison of calculations to data Poceedings of of NCAD008 NoiseCon008-ASME NCAD July 8-30, 008, Deabon, Mi [9] Wang, M. and Yang, Q., Lage-eddy simulation of oughness-geneated bounday-laye noise Session NS07/1-Aeoacoustics, Pais-08, 008 [10] Yeh, Y.-F. and Nickeson, E.C. Ai flow ove oughness discontinuity, Coloado State Univesity Repot, CER70-71FFY-ECN6, July [11] Gissom,D., Smith,B., Devenpot, W., and Glegg,S., Rough-Wall Bounday laye Noise: An Expeimental Investigation AIAA pape