A Study on the Sound Noise Emission of Moving Vehicle by Using Proudman Model Kyoungsoo Lee; Ziaul Huque; Raghava Kommalapati

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1 A Study on the Sound Nose Emsson of Movng Vehcle by Usng Proudman Model Kyoungsoo Lee; Zaul Huque; Raghava Kommalapat Abstract Ths paper ams at predctng the sound nose generated by a movng vehcle usng the steady state Proudman volume ntegral broadband nose source (BNS) model consderng road ground surface n md-feld. The steady and unsteady state CFD were performed to get the SST-turbulent RANS and LES smulatons for Proudman BNS and unsteady pressure fluctuatons respectvely usng commercal CFD code STAR-CCM+. The approxmate sound pressure levels n volume term were obtaned and that nformaton s compared wth the pont sound pressure level n frequency spectral range n md-feld regon. After evaluatng the Proudman volume ntegral, the applcablty and accuracy of t s dscussed. Index Terms computatonal aero-acoustc, vehcle, Broadband nose source model, Proudman volume ntegral, CAA. I. INTRODUCTION Sound nose problem n a hgh speed vehcle s an mportant polluton near the hghway resdent envronment. The tonal and broadband noses are harmful to the human's ear heath condton. The hghway fence s an easy way to reduce the hghway nose. The man nose sources of vehcle are tre-road nteracton [1-4], power-tran mechancal parts, and aerodynamcs. The acoustc sound nose from the aerodynamc of sold body s defned as aero-acoustc nose [5-1]. Regardng the reducton of traffc vehcle nose, sgnfcant progress has been acheved wth respect to the sound radaton of the power tran of vehcles. As a result, the tre and aero-acoustc sources are more mportant than the engne and power-tran mechancal source wth the ncreasng vehcle speed and results n very complcated nose sources. The tre-road nteracton nose can be reduced by usng flexble and soft pavement materal for road surface [1,4]. It s well known that the pressure fluctuatons on the front sde wndow surface of a road vehcle are a major sound source for both the external and nteror wnd noses. The front sde wndow aero-acoustc nose from A-pllar flow separaton and reattachment was regarded as the man source of aerodynamc turbulent flow and rotatng vortex [5-7]. The aero-acoustc sound nose s drectly related to the aerodynamc of the vehcle body. Thus, t can be reduced by nnovatve vehcle desgn process. The wnd tunnel faclty for aerodynamc or aero-acoustc nose was equpped well to dentfy that. However, ths study s not avalable n pre-desgn stage and t requres tme schedulng and expensve cost. The computatonal flud dynamcs (CFD) and computatonal aero-acoustcs (CAA) [11-18] are wdely used for varous engneerng problems. The aerodynamc applcaton s one of the engneerng felds whch the CFD and CAA have successfully adopted even though they re challengng n developng numercal method. The CFD and CAA can be selected and used n substtuton of wnd tunnel tests n pre-desgn process of developng new body shape for a vehcle. There are approxmate broadband nose source (BNS) models for dpole and quadruple nose sources n CAA wthn combnaton of Reynolds Averaged Naver-Stokes (RANS) equatons turbulent model. The steady and unsteady RANS equatons are avalable. These dpole and quadruple models are attrbuted for surface and volumetrc sound nose sources respectvely and they can be used n vehcle desgn process successfully. In new vehcle desgn process, the aerodynamc characterstcs and resultng aero-acoustc propagatons are man desgn objectve. In ths study, the characterstcs and applcablty of approxmate broadband nose source of the Proudman model [13] s demonstrated by comparng the results wth ponts sound pressure level (SPL, db) obtaned from the unsteady transent CAA analyss. The pont pressure fluctuaton was recorded and transformed to the spectral frequency doman to calculate the acoustc SPL to be used for reference value usng the large eddy smulaton (LES) smulaton wth the Smagornsky-Subgrd Scale (S-SGS) sub grd scales model n unsteady CAA analyss. The commercal CFD code Star-CCM+ was used for CFD and CAA smulaton n ths study. II. AERODYNAMIC NOISE: NUMERICAL METHOD, CFD AND CAA In the frequency doman, the sound can be understood as the ntensty of ar pressure propagaton. The tme dependent frequency of ar pressure fluctuaton must be obtaned from the unsteady transent smulaton usng LES, unsteady RANS (URANS), or detached eddy smulaton (DES). Computatonal aero-acoustcs (CAA) nvestgates the aerodynamc generaton of sound by usng numercal method. Sr James Lght hll derved a theory for the estmaton of the ntensty of sound that radates from a turbulent flow [11]. He establshed the theoretcal background generally referred to when nvestgatng aerodynamc nose and frst ntroduced the concept of aero-acoustc analogy whch conssts of replacng the actual flow feld responsble for generatng nose wth an equvalent system of nose sources. The nose sources act on a unform stagnant flud that s governed usng standard acoustc propagaton equatons. The aerodynamc characterzaton of the sources then becomes the man ssue n nose predcton. Before ths, flow-generated nose studes 3

2 6.5m ISSN: were focused on the relaton between the frequency of the flud fluctuatons and the emtted sound. Thus, the CAA can be classfed nto two types, whch are aero-acoustc analogy whch models the propagaton of sound waves by usng ntegraton technques [11-18] and drect numercal smulaton (DNS) for near-feld propagaton, accordng to the numercal method and process. Actually, DNS type aero-acoustc propagaton can be smulated usng unsteady CFD method ncludng DNS, LES (Large Eddy Smulaton), unsteady RANS (Reynolds Averaged Naver-Stokes equatons), or DES (Detached Eddy Smulaton) wth the advantage of accuracy. LES can use the central dfferencng n spatal dscretzaton. In general, URANS s not guaranteed to account the broadband content arsng from turbulent n vortex sheddng. DES uses RANS only n the boundary layer. DES and LES perform smlarly n terms of pressure spectra usng bounded central dfferencng, where boundary layer structures do not drectly affect the aero acoustcs. When the hybrd BCD dscretzaton scheme s used n DES, some key regons, such as an A-pllar or separated shear layers, suffer from numercal dampng of the pressure fluctuatons. The ntegral method (IM) [11-18], whch uses the aero-acoustc analogy, s fundamentally lmted to near-feld accuracy. It reles on the near-feld flow data from CFD soluton. The steady or unsteady strateges can be used accordng to the problems. For md-to far-feld nose predcton, the Ffowcs Wllams-Hawkngs (FW-H) acoustcs ntegral formulaton s the preferred strategy [16-18] to predct small ampltude acoustc pressure fluctuatons at the locatons of each recever for the sound sgnal that s radated from near-feld flow. The results of steady or unsteady CFD analyss nvolvng Reynolds Averaged Naver-Stokes (RANS) equatons can be utlzed to fnd the turbulence quanttes. Consequently, these quanttes can be used n conjuncton wth sem-emprcal correlatons and Lghthll s acoustc analogy [11-13] to come up wth some measures of the source of broadband nose. Thus, these models are based on the assumptons mplct to RANS turbulence modelng. They are termed Broadband Nose Source (BNS) Models, whch are strctly appled to turbulence-generated flow-nose and can be attrbuted to the classcal aero-acoustc categorzaton of dpoles [12] and quadruples [13-15] n shear and jet flows respectvely. Although such analogcal methods make t possble to estmate sound at a low computatonal cost, ts accuracy does not seem to be so hgh, snce sound sources are assumed to be ncompressble or the analogcal model tself does not have enough relablty. Thus, the more accurate and drectve to the sound sources and wave propagaton drect smulatons are preferred. But they need comprehensve computatonal efforts and cost and make the analyss to be mpossble n performng n current hardware..5m Fg.1 Geometry and grd defnton of vehcle body Fg.2 Grd defnton of flud doman 25m Pont probes P1 P2 P3 P4 P5 P6 P7 P8 P9 P1 2m 2m 2m 1m 3m 3m 1m 2m 2m 2m Fg.3 Pont probes defnton The aero-acoustc nose source, the surface and volumetrc terms, whch were defned as dpole and quadruple, are notced. The volumetrc term s usually omtted n far-feld hybrd ntegral method n the low Mach number problem. And 31

3 the road ground surface nteracton s also omtted n far-feld propagaton predcton because of the grd model complexty. Actually, the vortex sheddng nteracton to the road ground surface s not neglgble but mportant n md-to far-feld sound nose propagaton. To account the road ground surface contrbuton n aero-acoustc, the md-feld flud doman should be consdered. However, t s also not easy to smulate, but more numbers of grd are necessary. An approxmate BNS Proudman model [13] can be used for volumetrc source term n steady state analyss whch can drastcally reduce the smulaton cost wthn acceptable accuracy. The tral to use the Proudman model s worth of consderaton for desgn of the vehcle and envronmental quck soluton. The characterstcs and applcablty of approxmate broadband nose source Proudman model s demonstrated by comparng wth SPL (db) obtaned from the unsteady transent CAA analyss. The pont pressure fluctuaton was recorded and transformed to the spectral frequency doman to evaluate the sound nose quanttes n md-feld regon. III. GEOMETRY AND METHODOLOGY To account the effects of vortex sheddng nteracton between road ground surfaces, the grd model should extend to md-to far area. The effects of volumetrc grd resoluton for the Proudman BNS model are crtcal n md-to far-feld area. The prelmnary parametrc studes for grd resolutons were studes to determne the grd model. As a result, the geometry, grd models of vehcle and flud doman are llustrated as n Fg.1 and Fg.2 llustrate for CFD and CAA. Fg.3 explans the locatons of pont probes n flud doman to record the pont pressure fluctuaton. After recordng the pressure hstory, the Fourer transform wll be performed. As shown n Fg.1, the length, heght, and wdth of vehcle are 5.13m, 1.8m and 1.17m respectvely. The aero-acoustc characterstcs were studed for car type vehcle. The flud doman sze was defned n Fg.2 as 25m, 6.5m and 14m for length, heght and wdth respectvely. The grd unt length of surface of vehcle s defned as 25mm for trmmed grd model. The resultng total number of grds and nodes are 18,16, and 18,54, respectvely. The effects of grd resoluton of the Curle surface ntegral s not sgnfcant when the proper grd model s used, because t s not tme dependent to the tme or frequency doman but surface pressure dstrbuton to calculate n an overall surface nterest. However, the Proudman model needs hgher qualty volumetrc grd to dentfy the broadband nose source n md-to far-feld. Thus n general, more numbers of grds and computatonal cost are needed to perform quadruple Proudman BNS model than dpole Curle surface BNS model. Ths s the reason why many CAA research works are nterested n tryng to adopt the ntegral method of Ffowcs Wllams-Hawkngs (FW-H) acoustcs ntegral formulaton for md-to far-feld problem. The flud doman grd should account the sound wave length of requred frequency range n unsteady transent analyss because the sound energy s contnuously dstrbuted over a broad range of frequences. The hgher qualty grd resoluton must be used for quadrupole BNS model or unsteady CAA analyss. However, from the lmtaton of computaton resource of ths study, the lmted numbers of grds were consdered. More numbers of grd models for hgher qualty resoluton wll be adopted n the followng studes. The nose source s emtted from the vehcle body to the ar flow. The sound energy s contaned nto the turbulent flow and hghly nfluenced by the complex flow behavors. To account the turbulent flow for the Proudman BNS model, whch calculate the volumetrc nose source term usng aero-acoustc analogy, the shear stress transport (SST) turbulent model was selected for steady RANS soluton. After obtanng steady state turbulent flow results n CFD, the quadrupole nose source was calculated usng the Proudman BNS model. IV. PROUDMAN BROADBAND NOISE SOURCE MODEL The turbulent flow emtted from a sold vehcle body s often nterest for generatng far-feld regon. The Proudman's ntegral, based on acoustc analogy, can be used to approxmate the locaton and ntensty of nose source term n ar volume to the total acoustc power from turbulent flow. In ths paper, the Proudman model was used for quadruple sources of nose. Ths Lghthll Stress Tensor feature nterrogates the flow feld and comples velocty dervatves whch make up the Lghthll Stress Tensor. It s a scalar wth vector components. By observng Lghthll results, t s possble to dentfy the locaton of flow-generated aero-acoustcs sources. Lghthll s nhomogeneous wave equaton governng the sound propagaton s derved from conservaton of mass and momentum: v (1) t x t x v v v p where, : densty; p : the stress tensor. p j p p j v, (2) v j : the velocty components; (3) where, p : the thermal dynamc pressure of the flow feld; : the Kronecker delta; : the vscous stress tensor. v v j 2 v (4) x j x 3 x Usng Ensten notaton, Lghthll s equaton can be wrtten as: 2 2 T 2 2 c (5) 2 t x x j Where T s the "Lghthll turbulence stress tensor" for the acoustc feld, and t s denoted by substtutng stress tensor 32

4 p n T, ISSN: p p c T v v (6) j where, : the Kronecker delta; : the vscous stress tensor; : far feld densty. In lamnar flow, the stress tensor s gven by: v v j 2 v (7), lam x x 3 x j In turbulent flow, the stress tensor s gven by: v v j 2 v (8), lam, turb eff x x 3 x j where the effectve vscosty s, the sum of the lamnar and turbulent vscostes. In nvscd flow, the stress tensor s. Each of the acoustc source terms from the Lghthll stress tensor n T may descrbe a sgnfcant role n the generaton of sound as: v v : descrbe unsteady convecton of flow(or j Reynold's stress); eff 2 : descrbe sound shear; p t c : descrbe nonlnear acoustc generaton processes. The Proudman nose source model evaluates acoustc power per unt volume and the sound s from quadruples. Specfcally, ths model computes the acoustc power to evaluate the local contrbuton to the total acoustc power per unt volume from the turbulent flow. The Proudman model assumes sotropc turbulence. Ths model can be used for quadruple sources of nose, such as the areas around rear C-pllar or blunted body. Lke the Curle model, ths model can be used n steady and unsteady (transent) analyses. It s compatble wth all Reynolds-Averaged Naver-Stokes (RANS) models that can provde turbulence tme and length scales. However, t s preferable for steady-state solutons. The analytcal result of Proudman [13] estmated the local acoustc power generated by unt volume of sotropc turbulence havng no mean flow. Proudman consdered the generaton of nose by sotropc turbulence and usng statstcal models of varous two-pont moments, usng the Lghthll analogy. In Proudman s hgh-reynolds model for sotropc turbulence n near ncompressble flow, Llley [14] added the effects of retarded tme n the evaluaton of the two-pont covarance of Lghthll s tensor (an effect prevously neglected by Proudman), and obtaned the followng expresson for acoustc power, AP per unt volume: 3 5 u u AP (9) 5 l a where, : a constant related to the shape of the longtudnal velocty correlaton; u : the root mean square of one of the velocty components; l : the longtudnal ntegral length scale of the velocty; : the far-feld densty ; a : the far-feld sound speed. In Proudman s orgnal dervaton [13], s approxmately 13. In Proudman s paper, the terms of u and can be wrtten as: u 2 k, 3 1.5u 3 (1) l In terms of the turbulence velocty scale and of the turbulence length scale, the local acoustc power due to the 3 unt volume of sotropc turbulence (n W / m ) becomes: 3 5 U U AP c (11) 5 L a L wth: U,. 629, where : the far-feld c T densty; U : the turbulence velocty; L : the turbulence length scale; T : the turbulence tme scale and a s the far-feld sound speed. The rescaled constant s based on Drect Numercal Smulaton for sotropc turbulence done by Sarkar and Hussan [15]. The total acoustc power per unt volume can be reported n 3 dmensonal unts ( W / m ) and n db: P ref AP AP 1 (12) db log P ref Where P s the reference acoustc power. ref E W / m V. NOISE SOURCE OF HIGH SPEED VEHICLE The nose source of aero-acoustc s based on aerodynamc flow. Flow separaton and nduced turbulent flow s the source of flow fluctuaton whch can be vsble n vortex sheddng. The strong flow mpngng wll make hgher nose emsson. There are several nose sources whch produce the Vortcty n boundary layer near the body. The vortex sheddng or emtted ar flow makes the Vortcty, flow, and pressure fluctuaton. The ntensty of pressure fluctuaton s SPL for human ear. Thus, the hgher pressure of flow produces hgher nose. The Vortcty of ar flow wll be dstrbuted nto the ar and contans the sound energy n frequency spectra as low frequency tonal nose and hgh frequency broadband nose. The vortex sheddng mpngng produces secondary Vortcty from the road ground surface. Thus, the exstence of road surface can be not gnorable but must be consdered n md-feld regon. Flow s generally dvded nto dfferent groups dependng on the propertes of the flud partcles n the flow as lamna or turbulent. There s also a transtonal flow, whch descrbes the case when lamnar flow s becomng turbulent but s not yet fully turbulent. Both lamnar and turbulent flows are generally unsteady, meanng that the velocty at a gven pont n space vares wth tme. A flow s steady f there s no change n the velocty feld through tme. Therefore, t s not possble to have a steady turbulent flow. The nose source s drectly related n pressure fluctuaton n tme doman, and t means the unsteadness fundamentally. 33

5 The steady nose source can be hghly dfferent from unsteady nose source because of unsteadness. Q-crteron: 2 Steady state volumetrc vortcty: SST, 1 (/sec) Q-crteron: 1 (a) Steady state (RANS) Usteady volumetrc vortcty: LES, 1 (/sec) (a) steady state(rans) Q-crteron: 2, LES Q-crteron: 1, LES (b) unsteady state(les) Fg.4 Volumetrc Vortcty for steady and unsteady state: 1(/sec) From Fg4, Fg.5, the turbulent flow can be recognzed by usng Vortcty or Q-crteron to vsualze the vortex. Q-crteron s the second nvarant of the velocty gradent tensor, often used for the detecton of vortces. Vortcty s defned as the curl of the velocty and t s equal to twce the rotaton of the flud at (x, t). As a result of ths, the Vortcty can be used drectly to dentfy vortces whch are often thought of as regons of hgh Vortcty. But there s no unversal threshold over whch Vortcty s to be consdered hgh. A problem assocated wth ths method s that Vortcty cannot dstngush between swrlng motons and shearng motons. Nevertheless of ther smlarty and dfference, both of them represent the velocty feld of flow. (b) unsteady state(les) Fg.5 Q-crteron for steady and unsteady state: 2, 1 There are not specfc quanttes of turbulent flow n velocty feld. But t can be assumed that hgher gradent or curl of velocty may contan the hgher turbulent flow on them. From Fg.4, and Fg.5, even though same values for steady state, the so-surface of Q-crteron and Vortcty n steady state are hghly dfferent from unsteady LES soluton n rear vehcle or wake whch related far-feld. From those results, the large scale of vortex sheddng s expected n unsteady flow rather than steady, and also smlar pattern n sound nose propagaton. 34

6 (a) Steady state(rans) Fg.6 Unsteady pressure fluctuaton: LES Fg.6 llustrates the turbulent fluctuaton and acoustcal fluctuaton n the near and far feld respectvely. There are hgher unsteady turbulent fluctuatons at the bottom of the front wndsheld and rear vehcle than the sde wndow or A-pllar. And the acoustcal fluctuaton has large sphercal volume than small turbulent fluctuaton. Fg.7 and Fg.8 show the comparatve demonstratons for surface wall shear stress and pressure. The mean pressure was selected for the unsteady LES case. The surface wall shear stress can explan the flow separaton or turbulent flow n boundary layer. The overall results of wall shear are smlar, both of steady and unsteady cases except the road ground surface. The nteractng flow of vortex sheddng to the road ground surface makes the turbulent on the road surface. There are consderable quanttes on the road ground surface for potental nose source. When the steady BNS models are used, those effects can be gnorable. In general far-feld CAA case, the md feld area s usually not consdered, but only near feld of vehcle body s the man nterest. Thus, f the road surface under the vehcle s omtted, the mportance nose source also can be gnored. (b) Unsteady state (LES) Fg.7 Wall shear stress for steady and unsteady state As explaned before, Fg.8 shows the surface pressure n steady and unsteady case. To take nto account the smlar meanng of steady state, the mean pressure s consdered for unsteady state. Thck contour lnes are located on A-pllar and the rear vehcle on specally rear trunk edge n unsteady case. The hgh negatve sucton pressure s caused by hgher flow velocty. That surface area can be dpole nose source, whch s more mportant n the low Mach number problem and they produce strong rotatng vortex to vehcle wake and vortex sheddng nteracton. 35

7 Steady state surface pressure: SST (a) Steady state (RANS) Usteady surface mean pressure: LES (b) Unsteady state (LES) Fg.8 Surface pressure for steady and unsteady state (mean pressure) VI. VOLUMETRIC PROUDMAN NOISE SOURCE The turbulent flow of steady state has constant velocty feld. Thus, the vortex of steady state does not contan the pressure fluctuaton. To analyze the SPL n frequency spectra, the unsteady DNS or smlar numercal technque should be used. In ths study, the RANS SST-turbulent model and LES wth Smagornsky-Subgrd Scale (S-SGS) sub grd scales were used n steady and unsteady smulaton respectvely. As long as the volumetrc sound energy can be contaned n volumetrc vortex, the sound nose analyss can be understood as to fnd the vortex. However, the vortex s dffcult to defne clearly. In ths study, the Vortcty s selected n vsualzng the vortex rather than Q-crteron because the Vortcty s more clear and drect n velocty feld. The level of ntensty of Vortcty s not certan but tral. The SPL of volumetrc Proudman s valuated n comparson wth Vortcty. When consderng the acoustc fluctuaton whch s tme dervatve of pressure, there are many potental small parts of Vortcty whch contan the sound energy n broadband frequency regon. The SPL s dstrbuted along the low to hgh frequency spectra. Even though low speed, crusng vehcle produces vortex flow around the body nto the ar. There are more aerodynamc Vortcty, f the turbulent flow, whch s caused by the flow separaton n hgher speed, exsts. Among the Vortcty, the hgher pressure fluctuatng partcles can be emtted from the vehcle body to hgh frequency. And there are complex vortcal structures mpngng n local and global pressure fluctuatons on the body part and road ground surface ether whch feed the acoustc hgh frequency turbulence-structure nteracton. The buffetng nose, due to the open sunroof or sde wndow, can be caused by an unsteady shear flow whch was result n the perodc convecton of large-scale vortces over the cavtes. The tme varyng vortex sheddng on the vehcle body also can produce a low frequency sound nose. The tralng edge noses can occur due to the nteracton of the boundary layers nstabltes wth the surface edges. Ths s attrbuted to tme-varyng flow separatons and the breakng of large vortcal structures nto fne turbulent structures. The flow-nduced aero-acoustc nose has broadband spectral content rangng from tens of Hertz at low frequences to a few hundreds or thousands of Hertz at md-to-hgh frequences n near to far-feld doman. The BNS model can calculate the approxmate SPL n volumetrc turbulent flow for quadruple. The Proudman model can be used for BNS. As long as the turbulent flow s accurate or acceptable, the converted volumetrc SPL shows the sound nose nformaton of locaton and ntensty. Thus fundamentally, the applcablty and accuracy of Proudman BNS model deeply can rely on the steady or unsteady RANS soluton, not the aero-acoustc analogy tself. If the data for the Proudman model s close to that of tme varyng flow, the resultng nformaton of sound nose by the Proudman BNS model can be more accurate. But the fundamental soluton of steady RANS soluton, whch uses the turbulent model, can not be related to unsteady DNS, or smlar. Even though URANS s used, the turbulent flow of vortex s hghly dfferent from the others. The reason of approxmaton of BNS model s not dependent to the theory but the turbulent flow predcton whch obtaned from the approxmate CFD analyss. 36

8 Volumetrc vortcty: 3 (/sec) Volumetrc SPL: 2dB Volumetrc vortcty: 4 (/sec) Volumetrc SPL: 3dB Volumetrc vortcty: 5 (/sec) Volumetrc SPL: 4dB Volumetrc vortcty: 1 (/sec) Volumetrc SPL: 5dB Volumetrc vortcty: 2 (/sec) Volumetrc SPL: 6dB (a) Volumetrc Vortcty (b) Volumetrc sound pressure level Fg.9 Volumetrc quadrupole nose source: Proudman model 37

9 Pont5 ISSN: (a) Volumetrc Vortcty 2(s -1 ) 6dB Pont6 5dB 1(s -1 ) (b) Volumetrc sound pressure level Fg.1 Overlapped sound nose sources Pont1 Fg.9 shows the steady state Vortcty and volumetrc SPL obtaned from the Proudman BNS model n varous Vortcty and SPLs. The predcted volumetrc SPL means the volumetrc area of equal nose ntensty. The results of Fg.9 present the mportant nformaton for sound nose source. The locaton of hgher SPL s located near the rear vehcle n vortex wake and the shape of t s hghly related to the volumetrc Vortcty values. Hgh to low Vortcty so-surfaces demonstrate the sound nose sources whch contan dfferent SPL. As the values of Vortcty are decreasng, the area of t and related SPL also ncrease, and explans the characterstcs of broadband dstrbuton of sound nose. The sound nose s dstrbuted on hgh frequency range. Thus, the Proudman BNS model can represent the upper bound of broadband sound nose quanttes. In order to get consstency, the BNS model must be less dependent to the grd qualty or resoluton. The frequency for unsteady pressure fluctuaton and SPL are hghly dependent to the sound or acoustcal wave length. To get accurate data of that n hgh frequency range, the more number of grds wth smaller unt grd length must be used. But these requrements for unsteady smulaton n enough tme perods may be not avalable or possble n many of engneerng and research capacty. In vehcle desgn process, the easy and quck soluton s acceptable. The results of approxmate Proudman show reasonable and acceptable nformaton for near to far-feld sound nose propagaton. The results of the BNS model must be reled on the RANS turbulent model whch the SST-turbulent model was used n ths study to predct the near-wall nstablty of separaton. The volumetrc hgher SPL s manly near the vehcle whch shows hgher Vortcty or velocty feld or turbulent flow from vehcle rear area. Fg.1 shows the comparatve overlapped mages for Vortcty and SPL. The properly choused Vortcty values are good agreement wth volumetrc SPL. The steady state CFD soluton can be sad as the averaged mean flow wthout tme varyng fluctuaton. The unsteady flow represents the tme dependent characterstcs. The flow vortex can be dfferent accordng to the adopted numercal scheme for LES, URANS, or DES. Fg.11 presents the Vortcty so-surface for steady and unsteady state respectvely. LES wth Smagornsky-Subgrd Scale (S-SGS) sub grd scales were used for tme dependent smulaton for pressure fluctuaton and acoustc. The bounded-central dfference scheme was selected for convecton term. The unsteady vortex sheddng s mpngng to the road Pont7 4dB 5(s -1 ) Pont8 3dB 4(s -1 ) Pont9 3(s -1 ) 2dB ground surface n far away from the vehcle whch can not be seen n steady state. Lower value of Vortcty so-surface s not dstngushable but smlar and combned very close. Thus, Vortcty so-surfaces of 3 to 5 n an unsteady case are smlar. But larger perodcally rotatng vortex sheddng s prevalng. Compared wth steady state, the sound energy can be largely dstrbuted over the wder area of bounded road ground surface. Due to the complex vortex sheddng phenomena n unsteady LES smulaton, there mght be wder SPL dstrbuton along the broadband frequency range. From the result of Fg.11, f the SPL of Proudman s theoretcally correct, the SPL of unsteady state can be predcted usng the steady state Proudman model. Approxmately, the steady SPL of 2-Vortcty value s 6dB from Fg.9 and Fg.1. Lkewse, 1Vortcty value s 5dB, and 3-Vortcty value s 2. As long as the assumpton s vald, smlar SPL can be obtaned from the unsteady smulaton. The unsteady pressure fluctuaton has sound nose source energy. Usually, the ntensty of acoustc fluctuaton s recognzed by SPL n frequency range. The Fourer transform s used to evaluate t from tme doman by usng recorded pont pressure tme hstory. The pressure fluctuaton at each ponts are llustrated n Fg.12(a). The defned ponts are descrbed n Fg.3. Fve of them are the front of vehcle and the rest of them are behnd. Thus, the characterstcs of aerodynamc and resultng aero-acoustcs are obtaned, f the characterstcs of recorded data nvestgated. The steady state results, whch were llustrated n Fg.4 to Fg.11, can gve approxmate nformaton of the unsteady acoustc characterstcs. Far away from the vehcle, such as Pont1, does not have hgher value of Vortcty. Around Pont1, only weak vortex sheddng s emtted. And the ponts of the front vehcle are not surrounded by the vortex, but only free-stream ar flow s passng through. Thus, the lower SPL of the front of the vehcle s expected than behnd of t. When nvestgatng the ponts pressure fluctuaton n Fg.12(a), t s hard to classfy or predct the acoustc quanttes. The most of pont pressure fluctuatons are smlar to see. After transformng the data of tme to frequency range, those pont data can be classfed more clearly. Fg.13 represents the selected results for Pont5, Pont6 and Pont1. The SPL at each pont s smlar n low frequency range up to 2 Hz. After that, the SPL started to branch. At the hghest frequency of 5K Hz, the SPLs are 45dB, 25dB, 2dB for Pont6, Pont1 and Pont5 respectvely. These obtaned SPL for Pont6 and Pont1 are n approxmate agreement wth steady state results whch were obtaned from the Proudman BNS model, when nvestgatng the compactly overlapped mage of Fg.1. The steady state CFD soluton can not make unsteady acoustc fluctuaton exactly. But the overall SPL dstrbutons are smlar to the unsteady result n frequency range. 38

10 Volumetrc vortcty: 3 (/sec) Volumetrc vortcty: 3 (/sec), LES Volumetrc vortcty: 4 (/sec) Volumetrc vortcty: 4 (/sec), LES Volumetrc vortcty: 5 (/sec) Volumetrc vortcty: 5 (/sec), LES Volumetrc vortcty: 1 (/sec) Volumetrc vortcty: 1 (/sec), LES Volumetrc vortcty: 2 (/sec) Volumetrc vortcty: 2 (/sec), LES (a) Steady state (RANS) (b) Unsteady state (LES) Fg.11 Volumetrc Vortcty for steady and unsteady state 39

11 acoustc propagaton equatons. The represented sound nose s dealzed or maxmum acoustc values that can be obtaned n aero-acoustc feld. The grd model n ths study s not the dedcated model because of computng resource lmtaton. There are errors and msmatches between the SPL n steady and unsteady. But a fner qualty grd model wll ncrease the ntensty of SPL n hgher frequency range. (a) Pont pressure fluctuatons P6-P1 P1-P (b) Ponts sound pressure level (db) Fg.12 Pont pressure fluctuaton and correspondng sound pressure level (db) P5 P1 (a) Pont pressure fluctuatons: P5, P6, P1 (b) Ponts sound pressure level (db): P5, P6, P1 Fg.13 Selected pont pressure fluctuaton and correspondng sound pressure level (db) As explaned before, sound energy s contaned n broadband range of frequency n turbulent flow or aerodynamc flow. The Proudman model uses the concept of aero-acoustc analogy, whch conssts of replacng the actual flow feld responsble for generatng nose wth an equvalent system of volumetrc nose sources. The nose sources act on a unform stagnant flud that s governed usng standard P6 P1 P5 P6 VII. CONCLUSION In ths study, the Proudman approxmate broadband nose source model, whch s easy and effcent, was adopted wth the SST-turbulent model for steady state soluton. LES smulaton was performed for unsteady pressure fluctuaton nformaton. The Proudman SPL was concdent wth steady state vortex whch was dentfed by Vortcty rather than Q-crteron. It was expected that more numbers of grds for hgher qualty mesh can ncrease the Proudman result for SPL so-surface. But the Proudman model s for broadband nature for hgher frequency. It s rather hghly dependent to the vortex flow or steady state CFD results. The accuracy and applcablty of the Proudman BNS model mght be more dependent to the RANS turbulent model. Compared wth steady state, the unsteady state pressure fluctuaton for acoustc fluctuaton was complex and dffcult to classfy n tme doman. After transformng the pressure fluctuaton nto frequency range, the SPL was dstrbuted along the frequency range. The SPL of ponts was broadband nature n frequency spectra. The SPL of pont was converged to the smlar value of Proudman n hgh frequency range. As a result, the approxmate Proudman model adequately predcted the actual unsteady acoustc characterstcs. Even though dfferent pont locatons, the low frequency tonal SPL were smlar or equal n tonal sound. The hgher turbulent, whch s for hgher frequency range sound nose, was branched from 2 Hz n current grd model. Aero-acoustc characterstcs of the current study are hghly and drectly dependent to the CFD analyss n both of steady and unsteady soluton. It s well known the frequency of ar-flud doman s dependent to the grd sze. To get accurate aero-acoustc characterstc n hgh frequency range of broadband regon, more numbers of grds for hgh qualty flud doman should be used, but t s not easy n many cases. There are possbltes of convergng aero-acoustc SPL of unsteady state soluton whch was obtaned by usng LES to the steady state Proudman model. From the study, approxmate and acceptable dstrbuton of acoustc nformaton for unsteady pressure fluctuaton could be obtaned by performng the Proudman BNS model. In a future study, a hgher qualty grd model wll be used to valdate the Proudman's broadband characterstcs whch can predct the unsteady value. By usng the proper and adequate steady state RANS turbulent model, the results of the Proudman model wll gve accurate nformaton for unsteady SPL n broadband hgher frequency range. 4

12 ACKNOWLEDGMENT Ths research was supported by the Natonal Scence Foundaton (NSF) through the Center for Energy and Envronmental Sustanablty (CEES), a CREST Center (Award NO ). REFERENCES [1] U. Sandberg, "Road traffc nose The nfluence of the road surface and ts characterzaton", Appled Acoustcs, vol. 21, pp , [2] M. Brnkmeer, U. Nackenhorst, S. Petersen, and O. Estorff, "A fnte element approach for the smulaton of tre rollng nose", Journal of Sound and Vbraton, vol. 39, pp. 2 39, 28. [3] D. J. O Boy, and A. P. Dowlng, "Tyre/road nteracton nose Numercal nose predcton of a patterned tyre on a rough road surface", Journal of Sound and Vbraton, vol. 323, pp , 29. [4] G. Lao, M. S. Sakhaefar, M. Hetzman, Ra. West, B. Waller, S. Wang, and Y. Dng, "The effects of pavement surface characterstcs on tre/pavement nose", Appled Acoustcs, vol. 76, pp , 214. [5] N. Murad, J. Naser, F. Alam, and S. Watkns, Computatonal flud dynamcs study of vehcle A-pllar aero-acoustcs, Appled Acoustcs, vol. 74, pp , 213. [6] N. Murad, J. Naser, F. Alam, and S. Watkns, "COMPUTATIONAL AERO-ACOUSTICS OF VEHICLE A-PILLAR AT VARIOUS WINDSHIELD RADII", Ffth Internatonal Conference on CFD n the Process Industres CSIRO, Melbourne, Australa 13-15, December 26. [7] M. H. Shojaefard, K. Goudarz and H. Fotouh, "Numercal Study of Arflow around Vehcle A-pllar Regon and Wnd nose Generaton Predcton", Amercan Journal of Appled Scences, vol. 6(2), pp , 29. [8] Y. P. Wang, J. Chen, H. C. Lee, and K. M. L, "Accurate smulatons of surface pressure fluctuatons and flow-nduced nose near bluff body at low mach numbers", The Seventh Internatonal Colloquum on Bluff Body Aerodynamcs and Applcatons (BBAA7), Shangha, Chna, September 2-6, 212. [9] H. Dechpre, and M. Hartmann, "Aero acoustcs Smulaton of an Automotve A-Pllar Ran Gutter", EASC 29 4th European Automotve Smulaton Conference. 29. [1] N. Hamamoto, M. Yoshda, Y. Goto, A. Hashmoto, and Y. Nakamura, "Drect Smulaton for Aerodynamc Nose from Vehcle Parts", SAE Internatonal, , 27. [11] M. J. LIGHTHILL, "On Sound Generated Aerodynamcally. I. General theory / II. Turbulence as a source of sound, Proc. Roy. Soc. London, vol. A 222, [12] N. Curle, The Influence of Sold Boundares upon Aerodynamc Sound, Proceedngs of the Royal Socety of London, seres A, Mathematcal and Physcal Scences, vol. 231, pp , [13] I. Proudman, The Generaton of Nose by Isotropc Turbulence, Proc. R. Soc. Lond. vol. 214, pp , [14] G. M. Llley, The radated nose from sotropc turbulence revsted, NASA Contract Report No , NASA Langley Research Center, [15] S. Sarkar, and M. Y. Hussan, Computaton of the Sound Generated by Isotropc Turbulence, NASA Report , ICASE Report No , [16] J. E. Ffowcs Wllams, and D. L. Hawkngs, "Sound generaton by turbulence and surfaces n arbtrary moton," Phlos Transact A Math Phys Eng Sc, vol. 264(1151), pp , [17] K. S. Brentner, and F. Farassat, "An Analytcal Comparson of the Acoustc Analogy and Krchhoff Formulatons for Movng Surfaces," AIAA Journal, vol. 36(8), pp , [18] K. S. Brentner, and F. Farassat, "Modelng aerodynamcally generated sound of helcopter rotors," Progress n Aerospace Scences, vol. 39, pp , 23. AUTHOR BIOGRAPHY Kyoungsoo Lee receved hs BS, MS, Ph.D n Depart. of Archtectural Engneerng from Inha Unversty, Incheon, South Korea. He s workng for the CEES, Prare Vew A&M Unversty, Prare Vew, Texas, USA as a post doc. Researcher. He was a research professor n department of Cvl & Envronmental Engneerng, KAIST n South Korea. Hs professonal areas are the structural engneerng and desgn, CFD, FSI and Impact & Blast smulaton. Currently, he s focusng on the developng the sound nose smulaton for the wnd blade. Dr. Lee s the member of AIK, KSSC n South Korea. Zaul Huque receved hs BS degree n mechancal engneerng from Bangladesh Unversty of Engneerng and Technology, Bangladesh, MS n mechancal engneerng from Clemson Unversty, USA and Ph.D. degree n mechancal engneerng from Oregon State Unversty, USA. He s currently a professor n the department of mechancal engneerng and the drector of Computatonal Flud Dynamcs Insttute at Prare Vew A&M Unversty. Professor Huque publshed over 5 journal and conference papers. Hs current research nterests are wnd turbne nose reducton, flud-structure nteracton, propulson, nlet-ejector system of rocket based combned cycle engnes, clean coal technology, self-propagatng hgh-temperature synthess. He receved Wellver Summer Faculty Fellowshp from Boeng n 22 and NASA Summer Faculty Fellowshp n 23. Raghava Kommalapat receved hs B.Tech degree n cvl engneerng and M.Tech degree n engneerng structures from Inda. He receved MS and PhD degrees n cvl engneerng (envronmental engneerng) form Lousana State Unversty, Baton rouge, LA, USA. Dr. Kommalapat s the Drector of 41

13 Center for Energy and Envronmental Sustanablty, a NSF funded center. He s a professor n Cvl & Envronmental engneerng department where he served as Interm Department head between January 21 and August 213. He s a regstered Professonal Engneerng (PE) n the State of Texas and a Board Certfed Envronmental Engneer (BCEE). He s elected as Fellow of Amercan Socety of Cvl Engneers (ASCE) n 215. Hs major feld of study s envronmental engneerng wth partcular focus on energy and envronmental sustanablty and ar qualty. He s author/edtor of on book, and have publshed more than 35 peer-revewed journal artcles and more than 9 proceedngs and presentatons at regonal, natonal and nternatonal conferences. 42