Pessu Behavior Analysis for Autologous Fluidations

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1 EXPERIENCE OF USING A CFD CODE FOR ESTIMATING THE NOISE GENERATED BY GUSTS ALONG THE SUN- ROOF OF A CAR Liang S. Lai* 1, Geogi S. Djambazov 1, Choi -H. Lai 1, Koulis A. Peicleous 1, and Fédéic Magoulès 2 1 School of Computing and Mathematical Sciences, Univesity of Geenwich Old Royal Naval College, London SE10 9LS, U.K. 2 Institut Elie Catan de Nancy, Univesite Heni Poincaé-Nancy 1 BP 239, F Vandoeuve les Nancy Cedex, Nancy, Fance L.S.Lai@ge.ac.uk Abstact The poblem to be examined hee is the fluctuating pessue distibution along the open cavity of the sun-oof at the top of a ca compatment due to gusts passing ove the sun-oof. The aim of this test is to investigate the capability of a typical commecial CFD package, PHOENICS, in ecognizing pessue fluctuations occuing in an impotant automotive industial poblem. In paticula to examine the accuacy of tanspoting pulsatoy gusts taveling along the main flow though the use of finite volume methods with highe ode schemes in the numeical solutions of the unsteady compessible Navie-Stokes equations. The Helmholtz equation is used to solve the sound distibution inside the ca compatment, esulting fom the extenally induced fluctuations. INTRODUCTION In the automotive industy cavities with diffeent geometical configuations occu in many instances such as; the ca doo gap, gea gap, open sun-oof and wheel wells. It has been obseved expeimentally [1-3] that the cavity flowfield is complex with intense pessue oscillation. Such cavity flows become one of the main aeodynamic noise souces. The intense fluctuating pessue distibution can cause discomfot to the dive s and passenges eas, and esult in an incease of dag. On the othe hand, the flow-induced aeodynamic noise contibutes to envionmental noise pollution. The flowfield chaacteistics ae stongly dependent on the length-to-depth atio (L/D) of the cavity, fee steam conditions, the upsteam bounday laye, etc. This pape examines a hypothetical ca configuation with an open sun-oof Eds.: L. S. Lai, G. S. Djambazov, C.-H. Lai, K. A. Peicleous, and F. Magoulès

2 L. S. Lai, G. S. Djambazov, C.-H. Lai, K. A. Peicleous, and F. Magoulès with pat of the compatment foming the esulting cavity. The ca is tavelling at a cuising speed with induced flow fluctuation due to the open sun-oof. The pessue along the sun-oof is computed by solving the unsteady compessible Navie-Stokes equations using a typical commecial finite-volume CFD package, PHOENICS, and the pessue fluctuation due to the sun-oof is extacted and analysed. Vaious numeical schemes ae used to povide a bette undestanding of thei advantages and disadvantages fo this application. In ode to study the acoustic esponse inside the ca compatment, the acoustic pessue distibution is calculated by solving the Helmholtz equation. THE PROBLEM DESCRIPTION Pevious expeience of an open cavity with a lip shows induced oscillatoy fluctuation of pessue [4] caused by shea laye sepaation at the upsteam end. This leads to futhe inteests in elated poblems such as a hypothetical ca with an open sun-oof as depicted in Figue 1. The length of the sun-oof is 0.6m and the effective depth of the opening lip is 0.05m. The fee steam velocity is 25 m/s (90 km/h). An atificial sinusoidal vetical-velocity distubance, as shown in Figue 1, is used to epesent a votex geneated by a vehicle tavelling at upsteam of this ca. The votex stength is given by W = W 0 sin(2π at), whee W 0 = -1.2 m/s and a is a paamete chosen as a constant independent of time. Diffeent fequencies of this upsteam vetical-velocity distubance ae applied to geneate diffeent the acoustic esponses at the top of the sun-oof. 25m/s 1.28m 0.52m 0.3m 0.6m 1.35m 0.35m 0.05m 0.52m 1.2m 0.85m Figue 1 A hypothetical ca with a sun-oof THE NUMERICAL PROCEDURE This section gives a bief desciption of the numeical algoithm fo the solution of unsteady flow poblems, the pessue fluctuations due to the cavity opening and the sinusoidal distubance, and the analysis of acoustic esponses. Solutions of unsteady Navie-Stokes Equations In the pesent pape, a stuctued finite-volume based softwae package, PHOENICS,

3 ICSV13, July 2-6, 2006, Vienna, Austia is used to compute time-accuate unsteady flow fields. The package may be used in the computations of compessible and incompessible flows. The Navie-Stokes equations and continuity equation fo a compessible fluid based on a Catesian coodinate system, ignoing body foces, may be witten as ρu + t ρ + t ( ρu) = 0, ( ρu u) = p( ρ) + ρν 2 u, whee ν is kinematic viscosity, velocity u = [ u ( t, x), u ( t, x), u ( t, x) ] T of the time, t ( 0,T ], and the spatial coodinate x Ω, whee exteio to the compact obstacle, ( ρ) (1) (2) ae functions 3 Ω R is a domain p is the pessue and ρ is the fluid density. In the pesent simulation, the computational domain is taken as 17.6m by 8.8m with 176 by 88 mesh points distibuted acoss it. Fine sub-gid egions with up to 16 times fine mesh ae applied in cetain pats of the computational domain, e.g. aound the sun-oof, to obtain an accuate solution. To satisfy both the mass and momentum consevation laws, the velocity and pessue field ae solved iteatively by using the SIMPLE pessue-coection algoithm poposed by Patanka and Spalding [5]. In using PHOENICS, standad bounday conditions ae used fo inflow, solid wall, symmety, and fa-field boundaies. Five diffeent discetisation schemes have been tested in this pape in ode to povide a bette undestanding of thei advantages and disadvantages fo the pesent study. In ode to esolve the acoustic distubance coectly a minimum of 20 tempoal integation steps wee chosen to epesent each oscillation cycle at the highest fequency of inteest. Fo this eason the time step length, δ t, chosen fo the tempoal integation is 1ms esulting in a maximum esolved fequency of 50Hz. Extacting Pessue Fluctuations Two factos contibuted to the pessue fluctuation above the sun-oof. Fist the incoming flow ove cetain vehicle. Second the atificial distubance intoduced upsteam of the configuation. Fo the pesent study the atificial distubance equies a time equal to 528 δ t to each downsteam of the sun-oof. It is possible to use the pessue obtained fom the CFD calculation to examine the fequency esponse inside the ca compatment. The pessue fluctuation along the uppe suface of the ca configuation and at the sun-oof opening is given by P f ( x, t) = P( x, t) P( x, t), whee P is the instantaneous pessue distibution along the uppe suface obtained by using the CFD calculation and P is the backgound pessue distibution along the uppe suface due to the upsteam velocity and the ca configuation.

4 L. S. Lai, G. S. Djambazov, C.-H. Lai, K. A. Peicleous, and F. Magoulès Numeical Schemes fo convection discetisation In all finite-volume CFD codes fo which cell-cente values of vaiables ae stoed, as in the schematic diagam below, values of the vaiable φ ae known fo the cell centes W, P and E; but the values of φ at face w, which tavels fom cell W to cell P, o fom P to W, may be calculated by using a numbe of numeical schemes W w P E > The numeical scheme influences the balance equations fo both cell W and cell P. To ensue faily good solution one can choose φw = φw when the flow is fom W to P, but φw = φp when the flow is fom P to W. This, o athe the so-called "hybid" vaiant of it, is used as the default numeical scheme, togethe with othe schemes, in PHOENICS. In this pape, five diffeent numeical schemes, thee linea and two non-linea schemes as listed below, ae being tested and each of them has a diffeent appoach to calculate the cell face value φ w. UDS Upwind-diffeencing scheme: φw = φw φp + φw CDS Cental-diffeencing scheme: φw = QUICK Quadatic upwind scheme: φw = φp + φw φww SMART Bounded QUICK: φw = φw + 0.5B ( φw φww ) if 0, φw = φw HQUICK Hamonic QUICK: 2( φp φw )( φw φww ) if > 0, φw = φw + φp + 2φW 3φWW Hee B= max 0,min 2,,4 4, φp φw =, and φ WW is the cell-cente φw φww futhe upsteam. Figue 2 shows nine obsevation points maked with thei node numbes, along y = 1.6m, i.e. just one-cell above the sun oof. The time histoy of the pessue fluctuations at these obsevation points ae shown in column 2 of Table 1. A zoom-in to the neighbouhood of the sun-oof with seven othe obsevation points and thei pessue fluctuations ae shown in column 3 of Table 1. It can easily be seen that fist ode accuate Hybid / Upwind and HQUICK schemes ae too dissipative and theefoe not suitable fo this type of example. As a esult, the magnitude of pessue fluctuations obseved on top of the sun-oof is vey small. CDS even failed to convege because the cell Peclet numbe is not guaanteed to be less than 2. Howeve, SMART and QUICK scheme show inteesting esults. The pessue fluctuations on top of the sun-oof gadually gow in magnitude in a sinusoidal fom. The

5 ICSV13, July 2-6, 2006, Vienna, Austia Figue 2 Nine obsevation points in the computational domain Table 1 Compaison of pessue fluctuations using diffeent numeical schemes Numeical Scheme Pessue Fluctuation at nine obseving points Pessue Fluctuation at all seven points on top of sun-oof Hybid / Upwind HQUICK SMART QUICK fluctuations obtained by using QUICK scheme lead to a moe stable and egula sinusoidal shape. At this stage, this seems to be the best schemes to use in this application.

6 L. S. Lai, G. S. Djambazov, C.-H. Lai, K. A. Peicleous, and F. Magoulès Analysis of Acoustic Response Fequency components of the pessue fluctuations ae then examined by poducing an acoustic powe spectum of the time histoy at all seven points on the sun-oof via sampling a 512-point Fast Fouie Tansfom. The spectum is depicted in Figue 3 and shows the dominant fequency at all obsevation points on the sun-oof occus oughly at aound 13Hz. Powe Spectum Density cm Sunoof Fequency Figue 3 powe spectum density of the time histoy via a 512-point FFT To study the acoustic esponse along the sun-oof, diffeent fequencies of the upsteam distubance ae applied. Numeical tests as a function of input distubance ae pefomed to veify the hypothesis that the lowe the fequency of distubance, the lowe the fequency of acoustic esponse obtained. In this study, 25Hz and 10Hz distubance fequencies ae compaed with the maximum esolvable fequency of 50Hz (see Table 2). The powe specta show that fo incoming distubance at a fequency highe than 25Hz the dominant mode of the noise geneated due to the sunoof occus at oughly 13 Hz which is the esonant fequency. On the othe hand fo incoming distubance at lowe fequency, say 10 Hz, seems to excite a half hamonic at aound 6Hz while maintaining the hamonic of 13Hz at a weake stength. Sound distibution inside the ca component To compute the sound distibution inside the ca compatment, one needs to solve the Helmholtz equation, i.e. i65 i66 i67 i68 i69 i70 i ωψ c ψ = 0, whee ψ i t = pe ω dt (4) In applying this equation, it is assumed that the flow inside the ca compatment is negligible. Fo the pesent study the analysis of sound distibution fo the dominant fequency of f = 13Hz due to an incoming distubance of 50 Hz is examined. The powe spectum density along the sun-oof is used as Diichlet bounday conditions fo the Helmholtz equation, which gives the acoustic pessue distibution inside the

7 ICSV13, July 2-6, 2006, Vienna, Austia ca compatment. Figue 4 shows the acoustic pessue distibution along seveal hoizontal lines and vetical lines below the sun-oof inside the ca compatment. It shows that the highest acoustic pessue is expeienced at x = 7.1m. On the othe hand along the hoizontal line just below the sun-oof the pessue shows an oscillatoy behaviou esulting fom the pessue fluctuation above the sun-oof. This oscillatoy behaviou gadually becomes weaken as one moves deepe into the ca compatment. The acoustic pessue distibution along all vetical lines seems to show the coesponding behaviou in such a way that oscillatoy effects deep inside the ca compatment disappea. This shows that the solution obtained is eliable. The acoustic pessue tends to be moe stable at the bottom of the ca compatment. Powe Spectum Density Table 2 Compaison of peak fequencies obtained via a 512-point FFT due to diffeent incoming distubances of 50, 25 and 10Hz 50Hz 25Hz 10Hz 60cm Sunoof Fequency i65 i66 i67 i68 i69 i70 i71 Powe Spectal Density Hz inlet distubence Fequency i65 i66 i67 i68 i69 i70 i71 10Hz inlet distubence i i i i i i i Fequency Obtained f = 13Hz Obtained f = 12Hz Obtained f = 6Hz Powe Spectam Density CONCLUSION Sound distibution inside a ca compatment due to incoming distubance ove the sun-oof is studied. The ca compatment excites a paticula fequency of oscillation at 13 Hz. Input distubance has an influence on the paticula hamonic excites. Lowe fequency input excites a half hamonic at oughly 6 Hz. Highe ode schemes ae necessay to extact such pessue fluctuations. The Helmholtz equation has been used to descibe the acoustic pessue distibution inside the ca cavity. ACKNOWLEDGEMENT This wok is patially suppoted by the Fanco-Bitish Alliance Patneship Pogamme PN The Helmholtz equation pogam used in this study was coded by D. Fédéic Magoulès 2. The authos ae gateful to CHAM Ltd fo allowing the use of thei code PHOENICS in this eseach. REFERENCES [1] K. Kishnamuty, Acoustic Radiation fom Two-Dimensional Rectangula Cutouts in Aeodynamic Sufaces, NACA TN 3487 (1955) [2] J. E. Rossite, Wind Tunnel Expeiments on the Flow Ove Rectangula Cavities at Subsonic and Tansonic Speeds, Royal Aicaft Establishment, TR No (1964)

8 L. S. Lai, G. S. Djambazov, C.-H. Lai, K. A. Peicleous, and F. Magoulès [3] B. M. Spee, Wind Tunnel Expeiments on Unsteady Cavity Flow at High Subsonic Speeds, AGARD CP No. 4 (1966) [4] Z. K. Wang, G. S. Djambazov, C.-H. Lai, K. A. Peicleous, Numeical expeiments of a souce extaction technique based on an acoustic coection method, Computes and Mathematics with Applications, to appea. [5] S. V. Patanka, Numeical Heat Tansfe and Fluid Flow, (Hemisphee, 1980) [6] B. P. Leonad, A Stable and Accuate Convective Modelling Pocedue Based on Quadatic Upsteam Intepolation, Compute Methods in Applied Mechanics and Engineeing, 19, (1979) [7] L. Kinsle, A. Fey, A. Coppens, and J. Sandes, Fundamentals of Acoustics. (John Wiley & Sons, New Yok, 1982) [8] Z. K. Wang, A Souce-extaction Based Coupling Method fo Computational Aeoacoustics, PhD Thesis, Univesity of Geenwich (2004) [9] G. S. Djambazov, Numeical Techniques fo Computational Aeoacoustics, PhD Thesis, Univesity of Geenwich (1998) Acoustic Pessue X diection Y diection Figue 4 Acoustic pessue inside the ca component along seveal hoizontal and vetical lines

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