Aerodynamic Sound Radiated from Longitudinal and Transverse Vortex Systems Generated around the Leading Edge of Delta Wings

Transcription

1 Open Journal of Flud Dynamcs, 016, 6, Publshed Onlne June 016 n ScRes. Aerodynamc Sound Radated from Longtudnal and Transverse Vortex Systems Generated around the Leadng Edge of Delta Wngs Shgeru Ogawa, Jumpe Takeda, Tak Kawate, Keta Yano Department of Mechancal Engneerng, Natonal Insttute of Technology, Kure College, Hroshma, Japan Receved 14 May 016; accepted 18 June 016; publshed 1 June 016 Copyrght 016 by authors and Scentfc Research Publshng Inc. Ths work s lcensed under the Creatve Commons Attrbuton Internatonal Lcense (CC BY). Abstract Flow around the front pllar of an automoble s typcal of a flow feld wth separated and reattached flow by a vortex system. It s known that the vortex system causes the greatest aerodynamc sound around a vehcle. The obectve of the present study s to clarfy the relatonshp between vortcal structures and aerodynamc sound by the vortex system generated around the front pllar. The vortex system conssts of the longtudnal and the transverse system. The characterstcs of the longtudnal vortex system were nvestgated n comparson wth the transverse one. Two vortex systems were reproduced by three-dmensonal delta wngs. The flow vsualzaton experment and the computatonal flud dynamcs (CFD) captured well the characterstcs of the flow structure of the two vortex systems. These results showed that the longtudnal wth the rotatng axs along mean flow drecton had cone-shaped confguraton whereas the transverse wth the rotatng axs vertcal to mean flow drecton had ellptc one. Increasng the tp angles of the wngs from 40 to 140 degrees, there frst exsts the longtudnal vortex system less than 110 degrees, wth the transton regon rangng from 110 to 10 degrees, and fnally over 10 degrees the transverse appears. The characterstcs of aerodynamc sound radated from the two vortex systems were nvestgated n low Mach numbers, hgh Reynolds number turbulent flows n the lownose wnd tunnel. As a result, t was found that the aerodynamc sound radated from both the longtudnal and the transverse vortex system was proportonal to the ffth from sxth power of mean flow velocty, and that the longtudnal vortex generated the aerodynamc sound larger than the transverse. Keywords Aerodynamc Nose, Delta Wng, Longtudnal Vortex, Transverse Vortex, CFD How to cte ths paper: Ogawa, S., Takeda, J., Kawate, T. and Yano, K. (016) Aerodynamc Sound Radated from Longtudnal and Transverse Vortex Systems Generated around the Leadng Edge of Delta Wngs. Open Journal of Flud Dynamcs, 6,

2 1. Introducton The sound nduced by turbulence n an unbounded flud s generally called aerodynamc sound. Wth respect to aerodynamc sound, Lghthll [1], Curle [] and Howe [3] [4] have made ther theoretcal contrbutons to clarfyng the relatonshp between turbulent flow and sound. Lghthll [1] transformed the Naver-Stokes and contnuty equatons to form an exact, nhomogeneous wave equaton whose source terms are mportant only wthn the turbulent regon. Ths equaton s called Lghthll s equaton. In most applcatons of Lghthll s theory t s necessary to generalze the soluton to account for the presence of sold bodes n the flow. Curle [] has made an extenson to Lghthll s general theory of aerodynamc sound so as to ncorporate the nfluence of sold boundares upon the sound feld. Howe [3] [4] recast Lghthll s equaton n a form that emphaszes the promnent role of vortcty n the producton of sound by takng the total enthalpy as the ndependent acoustc varable, whch leads to the vortex sound equaton. These theores have emphaszed that unsteady motons of the vortex play a crucal role n the generaton of aerodynamc sound. Regardng the vortex, emphass has been placed especally on longtudnal vortex whch rotates about the axs whose drecton concdes wth the flow drecton. In the automoble ndustry the reducton of aerodynamc nose becomes more and more mportant for the comfortable vehcle snce noses caused by engne, power tran, tres, and other nose sources have been steadly reduced n recent years. It s well known that the front pllar of an automoble s regarded as one of the most domnant area n generatng aerodynamc nose due to strong longtudnal vortces. Separated flows behnd the front pllar generate the longtudnal vortces. Based on the theores as mentoned above, many researchers have so far tred to reveal the generaton mechansm of aerodynamc sound. Haruna, Nouzawa, Kammoto and Sato [5] appled the Lghthll-Curle s theory of aerodynamc sound to automobles and expermentally estmated dpole nose emtted from the pressure fluctuatons on the body surface. Recently Nouzawa, L and Nakamura [6] have studed the mechansm of aerodynamc nose generated from front pllar and door mrror. Hamamoto, Okutsu and Yanagmoto [7] have nvestgated the effect of the external aerodynamc nose sources onto the nteror nose around the front pllar where longtudnal vortces exst. Numercal approaches have also been conducted wth delta wngs and actual vehcles (Haruna, Hashguch, Kammoto and Kuwahara [8], Takeda and Ogawa [9], Ogawa and L [10]). In addton to the aerodynamc engneerng feld, longtudnal vortex also has been focused n the heat transfer engneerng feld. Jacob and Shah [11] revewed enhancement of heat transfer through the use of longtudnal vortces. Recently Iwasak, Hara and Honda [1] used longtudnal vortces for EGR (exhaust gas recrculaton) system to cool down the temperature of exhaust gas from the engne. There have been so many studes to reveal the generaton mechansm of aerodynamc nose produced by longtudnal vortex. However, t has not yet been clarfed that how the longtudnal vortex system has been generated and how ths system produces the aerodynamc nose. The fnal obectve of our study, therefore, s to smplfy ths specfc aerodynamc nose problem to obtan a thorough understandng of how the longtudnal vortex s produced, and how the nose can be estmated quanttatvely. Ogawa and Takeda [15] have so far been nvestgatng mechansm of generaton and collapse of a longtudnal vortex system nduced around the leadng edge of a delta wng. As a second step, the present paper ams to clarfy the dfference between the longtudnal vortex system and the transverse vortex system n terms of ther confguratons, the dstrbuton of pressure coeffcents on the surface of the delta wngs, the magntude and the components of vortcty, and the characterstcs of aerodynamc sound radated from the longtudnal and the transverse vortex system. Theoretcal dscusson wll be developed to reveal the source of aerodynamc sound from the perspectve of Lghthll tensor, Reynolds stress, vortex sound, and Green s functon.. Vsualzaton of the Vortex Systems by Runnng Water Channel Fgure 1 shows one of the delta wngs employed for reproducton of the longtudnal and the transverse vortex system. The wng model has three dmensons wth 60 mm long, 160 mm wde and 3 mm thck. The models have 6 tp angles of 40, 90, 110, 10, 130, and 140 degrees as shown n Fgure. The models wth 15 degrees as attack of angles were mmersed n the runnng water channel shown n Fgure 3. The unform velocty of water flow s 0. m/s. The test secton s 1500 mm wde 800 mm hgh 4000 mm long, whch s large enough to vsualze the flow around the delta wngs. Fgure 4 depcts the longtudnal vortces and transverse vortces vsualzed by the hydrogen bubble method n the runnng water channel. The separated flows around the leadng edge were rotatng. Red lnes ndcate 10

3 Fgure 1. Three dmensonal delta wng used. Fgure. Sx delta wngs employed for flow vsualzaton and ther characterstc szes are almost the same as that shown n Fgure 1. Fgure 3. Runnng water channel (unt: mm). 103

4 Fgure 4. The longtudnal vortex system and the transverse system vsualzed by the hydrogen bubble method. rotatng mage of confguraton of the vortex system. Chan lne schematcally shows rotatng axes of the each vortex system. Two wngs wth the tp angles of 40 and 90 degrees show the longtudnal vortex system whose rotatng axs s located n the flow drecton has cone-shaped confguratons. However, wth the ncrease of tp angles, the cone-shaped confguratons began to collapse around 110 degrees and over 10 degrees the vortex system shfted to the transverse vortex system whose shapes are no longer cone-shaped but ellptc wth rotatng axes vertcal to the mean flow drecton. Ths vsualzaton method was able to clearly capture the change of vortex system from the longtudnal to the transverse vortex system. Although the spatal scale of the longtudnal vortex system s smaller than the transverse one, the rotatng speeds of hydrogen bubbles n the longtudnal qualtatvely seems to be faster than those n the transverse. 3. The Method of Numercal Smulaton As a next step, CFD wll be employed to analytcally nvestgate the structure of the longtudnal vortex. The study uses the software STAR-CCM+ wth software V In the smulaton, numercal delta wng model has sx tp angles of 40, 90, 110, 10, 130, and 140 degrees ust as n flow vsualzaton experment Numercal Method Ths study employed RANS (Reynolds Averaged Naver-Stokes Smulaton). Ths approach s vald when the maxmum Mach number n the doman s less than Eddy vscosty models use the concept of a turbulent vscosty to model the Reynolds stress tensor as a functon of mean flow quanttes. For the accurate smulaton, Menter SST k-ω model was used as the hybrd models n the form that k-ω model was used close to the 104

5 wall whereas the standard k-ε n the completely turbulent regon was employed. The SST k-ω turbulence model s a two-equaton eddy-vscosty model whch has become very popular. The shear stress transport (SST) formulaton combnes the best of two worlds. The use of a k-ω formulaton n the nner parts of the boundary layer makes the model drectly usable all the way down to the wall through the vscous sub-layer, hence the SST k-ω model can be used as a Low-Re turbulence model wthout any extra dampng functons. The SST formulaton also swtches to a k-ε behavor n the free-stream and thereby avods the common k-ω problem that the model s too senstve to the nlet free-stream turbulence propertes. It therefore follows that SST k-ω model often mert t for ts good behavor n adverse pressure gradents and separatng flow. In the steady state analyss, the maxmum step number s Reynolds number s defned n Equaton (1), where mean ar flow velocty U = 10 m/s, representatve length L = 0.6 m, and knematc vscosty ν = m /s and results n Re = Ths mples that the flow s turbulent and Mach number s Mesh Generaton Method UL Re = (1) ν Fgure 5 shows the wng model n numercal wnd tunnel. The models employed n the smulaton have the tp angles of 40, 90, 110, 10, 130, and 140 degrees wth three dmensons as shown n Fgure 1. The characterstcs of the vortcty n the two vortex systems were nvestgated at three sectons, A, B, and C. The scale of the numercal wnd tunnel s 600 mm 600 mm 160 mm. The wnd scale was determned so that the unform (a) (b) Fgure 5. The delta wng model n the numercal wnd tunnel. (a) Sde vew; (b) Top vew. 105

6 flows can be mantaned around the delta wng model. The attack of angles for all the models are 15 degrees the same as that used n the runnng water channel. Total number of mesh ranges from 7.48 mllon to 8.11 mllon, dependng on the tp angles of the model. Mnmum mesh sze s 0.5 mm n closest vcnty to the leadng edge of the model. In generatng mesh, the prsm layer meshng method was adopted. Ths meshng method was used to optmze the mesh sze n the boundary layer as shown n Fgure 6. The prsm layer mesh model s used wth a core volume mesh to generate orthogonal prsmatc cells next to the surface of the delta wng. Ths layer of cells s necessary to mprove the accuracy of the flow soluton. The prsm layer mesh s defned n terms of ts thckness, the number of cell layers, and the sze dstrbuton of the layers. In ths study the total thckness of prsm layer s 3 mm wth fve cell layers and prsm layer closest to the model surface s 0.5 mm. To conduct the (a) (b) Fgure 6. Mesh condton around the delta wng surface. (a) Prsm layer close to the surface of the wng; (b) Dstrbuton of wall Y + on the wng surface. 106

7 smulaton wth hgher accuracy, the thckness of prsm layer was decded so that wall Y + can be less than 5 across the wng surface as shown n Fgure 6. Wall Y + ndcates the dmensonless dstance from the wall surface of the wng as defned n Equaton (), where u * s frctonal velocty, y dstance from the surface, and ν knematc vscosty. 4. Numercal Results and Dscusson Y uy ν = * () Quanttatve Characterstcs of the Longtudnal and the Transverse Vortex System Fgure 7(a) shows the streamlnes of the longtudnal vortex system and the transverse one generated behnd the leadng edge of the each delta wng wth the tp angles of 40, 90, 110, 10, 130, and 140 degrees. In order to exactly grasp the streamlnes whch go through the regon of the vortex systems, the streamlnes was extracted so that total pressure coeffcents Cp t could be less than 1.0 n the secton C. The confguraton of the vortex stll remans cone-shaped untl 100 degrees. Around 110 degrees the vortex system becomes unstable. Over 10 degrees, the rotatonal radus of the vortex ncreases and the confguraton of the vortex begns to shft from cone-shaped to ellptcal. That s, the vortex generated behnd the leadng edge changed from the longtudnal vortex system to the transverse vortex system whose rotatng axs s vertcal to the mean flow drecton. It follows, therefore, that the longtudnal vortex can reman untl the tp angle of 100 degrees, and gong through the transent regon around 110 degrees, the longtudnal vortex has been changed to the transverse vortex over 10 degrees. Fgure 7(b) shows equ-contour lnes of pressure coeffcents. The defnton of the pressure coeffcent C p s descrbed n Equaton (3) where P m s the pressure on the wng surface and P s the statc pressure n the unform flow speed U. C P P m p = (3) ( 1) ρu C p coeffcents show how the pressure on the wng behaves, compared wth the pressure n the unform flud flow. It, therefore, follows that f C p has negatve value, the pressure on the wng surface s lower than that n the unform flows. The characterstcs of the longtudnal vortex are well reflected by pressure coeffcents on the wng surface. The fast flows close to the wng tp are rapdly separated, but the rotatonal radus s small. Snce the centrfugal force has the property that t s proportonal to the square of the velocty and s n nverse proporton to the rotatonal radus, ths causes the tp of the longtudnal vortex to nduce the largest negatve pressure. As a result, the wng tp has the lowest pressure coeffcents n dark green color for θ = 90 and 110 degrees as shown n Fgure 7(b). The pressures n the longtudnal vortex gradually tend to recover due to the dffuson of the vortcty and convecton of flows. The characterstcs of equ-contour lnes of pressure coeffcents agree well wth the expermental results of actual vehcle by Ogawa [13] [14] especally for θ = 90 degrees. Durng the state of the longtudnal vortex system, the partcles n the system wll be accelerated untl the veloctes of the partcles are faster than mean flow velocty. Ths makes pressure on the wng surface lower than that n the mean flow, and much lower than that n the mean flow partcularly for θ = 90 degrees. On the other hand, although the transverse vortex system s larger n spatal scale, the veloctes of the partcles are much slower than those of the partcles n the longtudnal system. The numercal results agree well wth the expermental ones obtaned by flow vsualzaton wth the hydrogen bubble method n the runnng water channel. Due to the slow velocty of the flud partcles, the transverse vortex system causes smaller negatve pressure on the wng surface, compared wth the longtudnal system. 4.. Vortcty Dfferences between the Longtudnal and the Transverse Vortex System Although t s of great mportance to nvestgate the relatonshps between the vortcty and the unsteady movement of the vortex systems n terms of aerodynamc sound generaton, the characterstcs of the longtudnal and the transverse vortex system were, as our frst step, nvestgated to clarfy the relatonshps between the typcal vortex systems and the vortcty n detal. The vortcty of the longtudnal and the transverse vortex system were calculated for tp angles of the wng model wth 40, 90, 110, 10, 130, and 140 degrees ust as nvestgated n streamlnes and C p dstrbutons. The vortcty wll be descrbed n Equaton (4) to Equaton (8) wth respect to 107

8 (a) Fgure 7. Streamlnes and C p dstrbutons. (a) Streamlnes around the leadng edge of the wngs; (b) C p dstrbutons on the delta wng surface. (b) 108

9 the X, Y, Z coordnate axes and velocty vector ( uvw,, ) U. Three components ω, ω, and ω k express the vortcty n the X, Y, Z axal drectons respectvely, and ω expresses the magntude of the vortcty. ( ω, ω, ω ) k rot m ω = = U = U (4) w v ω = Y Z u w ω = Z X v u ωk = X Y ω = ω + ω + ω (8) m k Fgure 8 shows the relatonshp between vortcty and tp angles n each secton of A, B, and C for the tp angles of the wngs 40, 90, 110, 10, 130, and 140 degrees. Of the three sectons, the secton A near the tp angle has by far the strongest vortcty n terms of magntude of vortcty ω m. In each secton three quanttes ( ω, ω, ω m ) fluctuate sharply whereas ω k remans almost constant. In partcular, the component ω whch rotates on the X axs n the mean flow drecton decreases rapdly between 110 degrees and 10 degrees n secton A. On the other hand the ω rotatng on the Y axs ncrease untl 110 degrees at whch the ω becomes almost equvalent to the ω n both secton A and B. Over 10 degrees, however, the ω becomes much greater than the ω, and ncrease n all the sectons. The ω m greatly decrease at 10 degrees due to the large decrease of the ω. Over 10 degrees, ω m begns to ncrease agan due to ncrease of the ω. The longtudnal vortex can stll reman untl the tp angle of 110 degrees. However, between 110 degrees and 10 degrees the longtudnal characterstcs become unstable. Over 10 degrees the characterstcs of the vortex are consdered to have been converted from the longtudnal to the transverse one. It s, therefore, found that the vortcty of the longtudnal vortex tends to be stronger than that of transverse vortex n terms of magntude of the vortcty ω m, although the governed component of the vortcty shfts from ω to ω. 5. Expermental Measurement of Aerodynamc Nose 5.1. Low-Nose Wnd Tunnel Test The measurements of aerodynamc sound radated from the delta wngs wth tp angles of 40, 90, 110, 10, 130, and 140 degrees were conducted at the wnd flow velocty of 10, 0, 30, and 40 m/s n the low-nose wnd tunnel of Kyushu Unversty. Fgure 9 shows the measurements of aerodynamc sound radated from the delta wngs and background nose wthout delta wngs. Aerodynamc sound was measured at the poston where a mcrophone was set at the same heght as the delta wngs 1.5 m away n the drecton vertcal to the delta wng as shown n Fgure 10. The delta wngs were set wth 15 degrees of angles of attack ust as n the flow vsualzaton experment and the numercal smulaton for streamlnes and vortcty. 5.. Measurng Technques The mcrophone used s NL-5 of RIONCo., whch can measure the sound wth the frequency rangng 0 to 0,000 Hz. The measured aerodynamc sound was sent to the personal computer by means of a data-logger; NR-500 and a measurng unt; NR-HV04 of KEYENCE Co. All the data of aerodynamc sound were measured n the form of Z characterstcs wthout any flter. Samplng frequency s 0 khz and number of data are 400,000. To avod frequency alasng, dgtal samplng of the sgnal must be performed at least twce as rapdly as the hghest frequency expected. Ths crtcal samplng rate s known as the Nyqust frequency. Therefore Nyqust frequency s 10 khz n ths test. 6. Expermental Results and Dscusson Aerodynamc sound measured n the far feld s defned as Sound Pressure Level; SPL (db) n Equaton (9), where p s RMS of sound pressure measured 1.5 m away from the delta wng by the mcrophone, and p 0 s (5) (6) (7) 109

10 Fgure 8. Relatonshp between vortces and tp angles. (a) Secton A; (b) Secton B; (c) Secton C. 110

11 (a) Fgure 9. Measurement of aerodynamc sound radated from the delta wngs n low-nose wnd tunnel. (a) Measurements of aerodynamc sound; (b) Measurements of background nose wthout delta wngs. (b) Fgure 10. Setup of measurement of aerodynamc sound. 5 reference sound pressure; ( ) 10 Pa. SPL p = 10log10 p0 Fast Fourer Transform (FFT) analyses were conducted under the condton that Hann wndow was used as wndow functon wth 50 blocks for data numbers of 400,000, overlappng coeffcents 50%, numbers of arthmetc mean 99, and frequency resoluton.5 Hz. Fgure 11 shows sound pressure level radated from the delta wngs for 4 arflow veloctes wth 6 tp angles of the wngs. Aerodynamc sound s assocated wth frequency obtaned by FFT analyss under the condton mentoned above. The study focuses on the frequency range from 00 to 5000 Hz where typcal aerodynamc sound s captured, takng Nyqust frequency 10 khz nto consderaton. The FFT results are processed by hghpass flter of 00 Hz and low-pass flter of 5000 Hz. In Fgure 11 there exsts a promnent frequency regon wth sound pressures whch are larger than the background nose wthout wngs shown n black color for each arflow (9) 111

12 (a) (b) (c) 11

13 (d) Fgure 11. FFT analyses of measured aerodynamc sound radated from the delta wngs wth varous tp angles. (a) FFT analyss for 10 m/s; (b) FFT analyss for 0 m/s; (c) FFT analyss for 30 m/s; (d) FFT analyss for 40 m/s. velocty. Ths promnent frequency regon s consdered to be aerodynamc sound radated from the vortex systems behnd the leadng edge of the delta wngs. Focuses are, therefore, put on the sound pressure level of the promnent frequency regon. Snce t s well known that human ear s the most senstve n frequency band between 000 to 4000 Hz, attenton s pad to the promnent frequency band f from 900 to 4000 Hz for the arflow velocty of 40 m/s. Generally speakng, the frequency f of sheddng vortces from a bluff body s proportonal to flow velocty U and nversely proportonal to representatve length of the body L, usng Strouhal number St. The relatonshp s descrbed as follows. U f = St (10) L In the study, frequency band f was chosen as standard values of f = Hz at U = 40 m/s. Snce the frequency of sheddng vortces s proportonal to the arflow velocty n accordance wth Equaton (10), frequency bands are set as 0.5f = Hz at 0.5U = 10 m/s, 0.5f = Hz at 0.5U = 0 m/s, and 0.75f = Hz at 075U = 30 m/s. These chosen frequency bands are depcted n red-colored zone n Fgure 11. Snce the red-colored zone covers the promnent frequency band at the respectve arflow velocty, t follows that measurements of aerodynamc sound are qute reasonable. Wth respect to aerodynamc sound obtaned by FFT analyses, t s found that aerodynamc sound for the longtudnal vortex system wth both redcolored lne of θ = 40 degrees and green-colored lne of θ = 90 degrees are larger than that for the transverse vortex system wth other four colored lnes. Next step s to nvestgate the dependence of both aerodynamc sound produced by the longtudnal and the transverse vortex system on the arflow velocty. Aerodynamc sound s evaluated n the form of overall values SPL OA gven by summng up sound pressure level L of the frequency band n the red-colored zone for the respectve arflow velocty, based on Equaton (11). SPL ( L 10) 10log10 10 OA = (11) The purpose of our research s to clarfy not only the characterstcs of aerodynamc sound but also generaton mechansm of aerodynamc sound produced by the longtudnal and the transverse vortex system. As our frst step, the characterstcs of aerodynamc sound wll be studed n the present paper. Accordng to Equaton (11), sound pressure levels were calculated for sx delta wngs and for mean arflow speeds as shown n Fgure 1. It s found that the characterstcs of aerodynamc nose radated from the longtudnal and the transverse vortex 113

14 Fgure 1. Relatonshps between aerodynamc sound and mean arflow veloctes. system ncreases n proporton to the 5th to the 6th power of mean arflow speeds, and that aerodynamc nose radated from the longtudnal vortex system s greater than that from the transverse vortex system. So far the two vortex systems have been nvestgated n terms of the confguratons, vortcty, pressure coeffcents on the wng surface, and aerodynamc nose expermentally and numercally. From now on, focuses are put on the generaton mechansm of the aerodynamc nose from standponts of the theoretcal phase. As t s well known, Lghthll s equaton s descrbed as Equaton (1), 1 T c 0 ( ρ ρ0), c0 t = xx (( ) ( )) T = ρvv + p p c ρ ρ δ σ (13) 0 0 0, where T s Lghthll stress tensor, ρv v : Reynolds stress. The problem of calculatng the turbulence generated sound s therefore equvalent to solvng ths equaton for the radaton nto a statonary, deal flud produced by a dstrbuton of quadrupole sources whose strength per unt volume s the Lghthll stress tensor T. The formal soluton of Lghthll s equaton s gven as ( y, x y 0 ) 1 T t c c, t d y. 3 0 ( ρ ρ0)( x ) = 4π x x x y In the study, the mean densty and sound speed are consdered to be unform throughout the flud and the varatons n the densty ρ wthn a low Mach number, hgh Reynolds number source flow are then of order ρ 0 M. ρvv ρ 1 O M vv ρ vv c x, t s the local speed of sound n the source Therefore, 0( ( )) 0 regon, t may also be shown that ( c ) ( 0 c 1 O M ) = +. Smlarly, f ( ) = +, so that (1) (14) 114

15 c 0 p p0 c0 ( ρ ρ0) ( p p0) 1 O ( ρ 0v M ). c Thus, f vscous dsspaton s neglected we make the approxmaton, provded that The far-feld acoustc pressure p(, t) stress s known. p ( x t) T ρ0 vv. M 1 (15) (16) x n the far feld s gven by Equatons (17) and (18), f Reynolds (, t c ) ρ0vv y x y 0 3, d x x y 4π x y xx ρ 3 ( ) 4πc t y x y y x x 0 3 0vv, t c0 d,. Accordng to Howe [3] [4], ths equaton s expressed n the form of the vortcty ω as follows n terms of dpole source of the vortcty. Ths means that ths equaton s gven by neglectng the retarded tme caused by the dfference of the place of the source n the source regon due to the effects of the dpole from the quadrupole sound source ρ0xx 3 p( x, t) y 3 ( ) (, 0 ) d. t c 4πc t ω v y x y (19) x 0 It therefore follows that snce aerodynamc sound n the far feld can be expressed as a functon of the vortcty nstead of the Reynolds stress, the vortcty plays a crucal role n generatng aerodynamc sound. Equaton (19) nvolves a double tme rate of change. Ths mples that the vortces whch change rapdly n tme gve great contrbutons to generatng aerodynamc sound. Curle [3] has derved a formal soluton of Lghthll s equaton for the sound produced by turbulence n the vcnty of a sold body. The contrbuton to the dpole sound pressure p d from a surface element of dameter wthn whch the turbulence pressure fluctuatons are correlated s evdently of order 1 v ( ρ0v ) = ρ0vm, (0) c x x 0 whch exceeds by an order of magntude (1 M 1) the sound pressure produced by a quadrupole n V of length scale. If A s the total surface area wetted by the turbulent flow, there are A ndependently radatng surface elements, and the total power Π d radated by the dpole s proportonal to the sxth power of arflow velocty. p d 3 3 Πd 4π x Aρ0vM. (1) ρ0c0 Ths equaton ndcates that total power radated by the dpole sound source ncrease n proporton to the sxth power of the mean arflow velocty. The drect power Π q radated by quadrupole occupyng a volume V 0 n the absence of the body s gven as n Equaton (). Ths s Lghthll s eghth power law. 3 5 ( ) ρ (17) (18) Πq V0 A 0 vm. () The sound produced by the turbulence near sold body S s therefore domnated by the dpole snce M s nearly equvalent to 0.01 n ths study, and as M approaches zero the acoustc power exceeds the quadrupole by a factor ~ 1 M 1. That s, rato of the dpole to the quadrupole s descrbed as Equaton (3) Πd 1 ~. (3) Π M q Precsely how small M should be for ths to be true depends on the detals of the flow, whch determne the approxmate values of A and V0. Curle s theoretcal results support, followng Equaton (1), the expermental 115

16 results that aerodynamc nose radated from the longtudnal and the transverse vortex system ncreases n proporton to the 5th to the 6th power of mean arflow speeds as shown n Fgure 1. The surface dpole represents the producton of sound by the unsteady surface force that the body exerts on the exteror flud. Ths ncrease n acoustc effcent brought about by surface dpoles on acoustcally compact body occurs also for arbtrary, noncompact bodes when turbulence nteracts wth compact structural elements, such as edges, corners, and protuberances. How [3] [4] derves the followng vortex sound equaton for the small Mach number 1 B dv = ( ω v ). (4) c0 t In the far feld the acoustc pressure s gven by the lnearzed approxmaton p x, t ρ B x, t, (5) where B(, t) ( ) ( ) 0 x s the total enthalpy. The contrbuton to the sound from surface frcton f normally of order v 1 Re 1, Re =, (6) υ relatve to the contrbuton from the volume vortcty, where s the characterstc length scale of the turbulence or body and v s a typcal velocty. At hgh Reynolds numbers the surface term can therefore be dscarded, and n the present case n whch the body does not vbrate, the acoustc far feld s then gven wth the Green s G x, y, t τ by functon ( ) G p( x, t) = ρ ( )( ) ( ) 3 0 ω v y, τ x, y, t τ d yd τ, V y The next step of our study s, by means of the above vortex sound equaton, to smplfy ths specfc aerodynamc nose problem to obtan a thorough understandng of how the longtudnal and the transverse vortex system s produced, and how the nose can be estmated quanttatvely. 7. Conclusons Flows around the front pllar of an automoble are typcal of a flow feld wth separated and reattached flow by a vortex system. It s known that the vortex system causes the greatest aerodynamc sound around a vehcle. The obectve of the present study s to clarfy the relatonshp between vortcal structures and aerodynamc sound by the vortex system generated around the front pllar. The effects of the slant angles of the front pllars on the generaton of the vortex systems were nvestgated by changng tp angles of the wngs. The separaton vortces behnd the pllars generate the organzed vortex systems, dependng on the slant angles of the front pllars. The typcal flows are reproduced by the three dmensonal delta wngs under the condton of low Mach numbers and hgh Reynolds numbers. The vortex systems were essentally reproduced by three-dmensonal delta wngs whch consst of the longtudnal and the transverse system. The characterstcs of the longtudnal vortex system were nvestgated n comparson wth the transverse system. The results obtaned are as follows. 1) The flow vsualzaton experment and the computatonal flud dynamcs (CFD) captured well the characterstcs of the flow structure of the two vortex systems. These results showed that the longtudnal wth the rotatng axs along mean flow drecton had cone-shaped confguraton whereas the transverse wth the rotatng axs vertcal to mean flow drecton had ellptc one. Increasng the tp angles of the wngs from 40 to 140 degrees, there frst exsts the longtudnal vortex system less than 110 degrees, wth the transton regon rangng from 110 to 10 degrees, and fnally over 10 degrees the transverse vortex system appears. ) The longtudnal vortex system wth small tp angles of the wngs less than 90 degrees has much faster streamlnes due to the shape of the delta wng than those of the transverse one. The fast arflows cause the pressure on the wng surface to be much larger negatve pressures, compared wth those of the mean flow speeds. In the magntude of the vortcty, the longtudnal vortex has much greater than the transverse vortex. The rotatonal velocty and vortcty have ther largest values at the tp of the vortex and reduce downstream along the vortcal axs. Ths resulted n nducng the largest negatve pressure at the tp of the delta wng surface. Due to the (7) 116

17 slow velocty of the flud partcles, the transverse vortex system causes smaller negatve pressure on the wng surface, compared wth the longtudnal system. 3) The characterstcs of aerodynamc sound radated from the two vortex systems were nvestgated n low Mach number flows at hgh Reynolds numbers n the low-nose wnd tunnel. As a result, t was found that the aerodynamc sound radated from both the longtudnal and the transverse vortex system was proportonal to the ffth from sxth power of mean flow velocty. The results almost agree wth Curle s dpole predcton. 4) The longtudnal vortex generates the aerodynamc sound larger than the transverse vortex system. Ths mght be due to the fact that the vortex sound generaton source dv(ω v) n the longtudnal vortex probably s larger than that n the transverse vortex system, as s the case wth the comparson of steady vortcty for two vortex systems. References [1] Lghthll, M.J. (195) On Sound Generated Aerodynamcally I. General Theory. Proceedngs of the Royal Socety of London A, 11, [] Curle, N. (1955) The Influence of Sold Boundares upon Aerodynamc Sound. Proceedngs of the Royal Socety of London A, 31, [3] Howe, M.S. (003) Theory of Vortex Sound: Cambrdge Texts n Appled Mathematcs. Cambrdge Unversty Press, Cambrdge. [4] Howe, M.S. (014) Acoustcs and Aerodynamc Sound. Cambrdge Unversty Press, Cambrdge. [5] Haruna, S., Nouzawa, T., Kammoto, I. and Sato, H. (1990) An Expermental Analyss and Estmaton of Aerodynamc Nose Usng a Producton Vehcle. SAE Transactons: Journal of Passenger Cars, 99, SAE Techncal Paper [6] Nouzawa, T., L, Y. and Nakamura, T. (011) Mechansm of Aerodynamc Nose Generated from Front-Pllar and Door Mrror of Automoble. Journal of Envronment and Engneerng, 6, [7] Hamamoto, N., Okutsu, Y. and Yanagmoto, K. (013) Investgaton for the Effect of the External Nose Sources onto the Interor Aerodynamc Nose. Proceedngs of SAE 013 World Congress & Exhbton, Detrot, Aprl 013, SAE Techncal Paper [8] Haruna, S., Hashguch, M., Kammoto, I. and Kuwahara, K. (199) Numercal Study of Aerodynamc Nose Radated from a Three-Dmensonal Wng. SAE Transactons: Journal of Passenger Cars, 101, SAE Techncal Paper [9] Takeda, J. and Ogawa, S. (014) Predcton of Aerodynamc Nose Radated from a Delta Wng. Proceedngs of the 4th Internatonal Symposum on Technology for Sustanablty, Tape, 19-1 November 014. [10] Ogawa, S. and L, Y. (014) Control of Longtudnal Vortex Generated around Front Pllar of Vehcles, Based on Clarfcaton of the Vortex Generaton Mechansm Usng a Delta-Wng. Proceedngs of the 1th Internatonal Conference on Moton and Vbraton Control, Hokkado, 3-7 August 014. [11] Jacob, A.M. and Shah, R.K. (1995) Heat Transfer Surface Enhancement through the Use of Longtudnal Vortces: A Revew of Recent Progress. Expermental Thermal and Flud Scence, 11, [1] Iwasak, M., Hara, J. and Honda, I. (014) Development of Vortex Generator for EGR Cooler. Proceedngs of FISITA 014 World Automotve Congress, Maastrcht, -6 June 014. [13] Ogawa, S. (1995) Aerodynamc Nose of a Body wth Separated and Reattached Flow by Longtudnal Vortces. Ph.D. Thess, Unversty of Tokyo, Tokyo. [14] Ogawa, S. (1995) Generaton Mechansm of Aerodynamc Nose by Interference between Longtudnal Vortex and Body. Proceedngs of the 44th Japan Natonal Congress for Appled Mechancs, 44, [15] Ogawa, S. and Takeda, J. (015) Mechansm of Generaton and Collapse of a Longtudnal Vortex System Induced around the Leadng Edge of a Delta Wng. Open Journal of Flud Dynamcs, 5,

18 Nomenclature Re: Reynolds Number U: Flow Velocty (m/s) L: Representatve Length (m) ν: Knematc Vscosty (m /s) ω: Vortcty (1/s) θ: Tp Angle of the Delta Wng (degree) Cp t : Total Pressure Coeffcent C p : Pressure Coeffcent P m : Pressure of Measurng Pont on the Wng (Pa) P : Pressure n the Unform Flow (Pa) ρ: Densty of Flud (kg/m 3 ) SPL: Sound Pressure Level (db) f: Frequency T : Lghthll Stress Tensor ρv v : Reynolds Stress M: Mach Number Π d : Total PowerRadated by the Dpole Π q : Total Power Radated by the Quadrupole G(x,y, t-τ): Green s Functon Submt your manuscrpt at: 118