Traditional Computational Fluid Dynamics (CFD) methods face accuracy and computing expense problems when dealing with aeroacoustic applications. A new formulation of the governing equations of inviscid compressible flow suitable for aeroacoustic simulations is presented. The flow variables of the Euler equations are split into a compressible unsteady flow part and an acoustics part making the assumption that the propagation of sound does not affect the flow field. Separate systems of equations, which allow for the unsteady interaction between the flow and acoustic fields, are obtained. These equations are solved using a simple, low order and low cost numerical scheme. The superior capability to resolve the sound field compared to a traditional CFD method is shown. For the evaluation of the method, an acoustic diffraction problem is solved and Flow/Acoustics Interaction Method results are compared to the linear analytical solution. The method captures the dynamic interaction between the flow and acoustic fields.
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References
1.
TamC. K. W. (2004), “Computational Aeroacoustics: An Overview of Computational Challenges and Applications”, Int. J. of Comp. Fluid Dyn., 18(6), pp. 547–567.
2.
MenounouP. and BlackstockD. T., “A new method to predict the evolution of the power spectral density for a finite-amplitude sound wave”, J. Acoust. Soc. Am.115 (2), pp. 567–580, 2004.
3.
HamiltonM. F., and BlackstockD. T., Nonlinear Acoustics, Academic Press, San Diego, 1998.
4.
LighthillM. J. (1952) “On sound generated aerodynamically, I: General theory”, Proc. R. Soc. London Ser: A211, pp. 564–587.
5.
LighthillM. J. (1954) “On sound generated aerodynamically, II: Turbulence as a source of sound”, Proc. R. Soc. London Ser: A222, pp. 1–32.
6.
CurleN. (1955), “The influence of solid boundaries upon aerodynamic sound”, Proc. R. Soc. London, Ser: A231, pp. 505–514.
7.
WilliamsFfowcs J. E. and HawkingsD. L. (1969), “Sound generation by turbulence and surfaces in arbitrary motion”, Philos. Trans. R. Soc. London, Ser. A: 264, pp. 321–342.
8.
LyrintzisA. S. (1994) “Review of the use of Kirchhoff's method in computational aero acoustics”, J. Fluids Eng.116, pp. 665–676.
9.
BrebbiaC. A. (ed.) (1994) Boundary Element Method XVI, Computational Mechanics.
10.
WellsV. L. and RenautR. A. (1997) “Computing aerodynamically generated noise”, Annu. Rev. Fluid. Mech.29, pp. 161–199.
11.
TamC. K. W.WebbJ. C. and DongZ. (1993) “A study of the short wave components in computational acoustics”, J. Comp. Acoust. 1, pp. 1–30.
12.
HardinJ. C.RistorcelliJ. R. and TamC. K. W. (eds.) (1995) ICASE/LaRC Workshop on Benchmark Problems in Computational Aeroacoustics (CAA), NASA CP 3300.
13.
ZinggD. W. (2000) “Comparison of high-accuracy finite-difference methods for linear wave propagation”, SIAM J. Sci. Comput. 22(2), pp. 476–502.
14.
ZinggD. W.LomaxH. and JurgensH. M. (1993) “An optimized finite difference scheme for wave propagation problems”, AIAA Paper 93–0459.
15.
ZinggD. W.LomaxH. and JurgensH. M. (1996) “High-accuracy finite difference schemes for linear wave propagation”, SIAM J. Sci. Comput. 17(2), pp. 328–346.
16.
DavisS. (1991) “Low-dispersion finite difference methods for acoustic waves in a pipe”, J. Acoust. Soc. Am.90(5), 2775–2781.
17.
DavisS. (1995) “Computational aeroacoustics using hyperbolic wave primitives”, ICASE / LaRC Workshop on Benchmark Problems in CAA, NASA CP 3300, pp. 27–33.
18.
LeleS. K. (1992) “Compact finite difference schemes with spectral-like resolution”, J. Comput. Phys.103, pp. 16–42.
19.
HarasZ. and Ta'asanS. (1994) “Finite-difference schemes for long-time integration”, J. Comput. Phys.114, pp. 265–279.
20.
FungK. Y.ManR. S. O. and DavisS. (1996) “Implicit high-order compact algorithm for computational acoustics”, AIAA J.35(10), pp. 2029–2037.
21.
KimJ. W. and LeeD. J. (1996) “Optimized compact finite difference schemes with maximum resolution”, AIAA J.34(5), pp. 887–893.
22.
HixonR. (1998) “A new class of compact schemes”, AIAA Paper 98–0367.
23.
LockardD. P.BrentnerK. S. and AtkinsH. L. (1995) “High-accuracy algorithms for computational aeroacoustics”, AIAA J.33(2), pp. 246–251.
24.
LiY. (1997) “Wavenumber-extended high-order upwind-biased finite difference schemes for convective scalar transport”, J. Comput. Phys.133, pp. 235–255.
25.
ZhuangM. and ChenR. F. (2002) “Applications of high-order optimized upwind schemes for computational aeroacoustics”, AIAA J.40(3), pp. 443–449.
26.
ThomasJ. P. and RoeP. L. (1993) “Development of non-dissipative numerical schemes for computational aeroacoustics”, AIAA Paper 93–3382.
27.
RoeP. (1998) “Linear bicharacteristic schemes without dissipation”, SIAM J. Sci. Comput. 19(5), pp. 1405–1427.
28.
CanutoC.HussainiM. Y.QuarteroniA. and ZangT. (1987) Spectral Methods in Fluid Dynamics (Springer-Verlag, New York).
29.
PateraA. (1984) “A spectral element method for fluid dynamics”, J. Comput. Phys.54, pp. 468–488.
30.
KoprivaD. A. (1986) “A spectral multidomain method for the solution of hyperbolic systems”, Appl. Num. Math.2, pp. 221–241.
31.
KoprivaD. A. and KoliasJ. H. (1996) “A conservative staggered-grid chebyshev multidomain method for compressible flows”, J. Comp. Phys.125(1), pp. 244–261.
32.
KurbatskiiK. A. and MankbadiR. R. (2004), “Review of Computational Aeroacoustics Algorithms”, Int. J. of Comp. Fluid Dyn.,. 18(6), pp. 533–546.
33.
HardinJ. C. and PopeD. S. (1994) “An acoustic/viscous splitting technique for computational aeroacoustics”, Theor. Comput. Fluid Dyn.6(5–6), pp. 334–340.
34.
EkaterinarisJ. A. (1999) “New formulation of Hardin-Pope equations for aeroacoustics”, AIAA J.37(9), 1033–1039.
35.
SlimonS. A.SoteriouM. C.DavisD. W. (1999) “Computational Aeroacoustics simulations using the expansion about incompressible flow approach.”AIAA Journal37(4), pp. 409–416.
36.
SlimonS. A.SoteriouM. C.DavisD. W. (2000) “Development of Computational Aeroacoustics Equations for Subsonic Flows using a Mach number expansion approach”J. of Comp. Phys., 159(2), pp. 377–406.
37.
ShenW. Z. and SorensenJ. N. (1999) “Comment on the Aeroacoustic Formulation of Hardin and Pope”, AIAA J.37(1), pp. 141–143.
38.
ShenW. Z. and SorensenJ. N. (2003) “Aeroacoustic Modeling for Turbulent Flows”15th Nordic Seminar on Computational Mechanics, Aalborg Denmark.
39.
ShenW. Z.MichelsenJ. A.SorensenJ. N. (2004) “A collocated grid finite volume method for aeroacoustic computations of low-speed flows”, J. of Comp. Phys., 196(1), pp. 348–366.
40.
FarshchiM.SiamakK. H.MohammadE., (2003) “Linearized and non-linear acoustic/viscous splitting techniques for low Mach number flows”, Int J. Num. Meth. in Fluids, 42(10), pp. 1059–1072.
41.
MorrisP. J.LongL. N.BangaloreA. and WangQ. Z. (1997) “A Parallel Three-Dimensional Computational Aeroacoustics Method Using Nonlinear Disturbance Equations”, J. of Comp. Phys., 133, pp. 56–74.
42.
HansenR. P.LongL. N. and MorrisP. J. (2000) “Unsteady, Laminar Flow Simulations Using the Nonlinear Disturbance Equations,”AIAA Paper 2000–1981.
43.
KozubskayaT. K.AbalakinI. V.BobkovV. G., (2001) “A half-stochastic model for noise in free turbulent flows”AIAA Paper 2001–2258.
44.
BecharaW.BaillyC.LafonP., & CandelS. (1994) “Stochastic approach to noise modeling for free turbulent flows.”AIAA J.32(3), 455–463.
45.
ViswanathanK. and SankarL. N. (1995) “Toward the direct calculation of noise: Fluid/acoustic coupled simulation”, AIAA J.33(12), 2271–2279.
46.
LongL.N. (2000) “A non conservative nonlinear flow field splitting method for 3-d unsteady fluid dynamics”, AIAA Paper 2000–1998.
47.
BogeyC.BaillyC. and JuveD. (2002) “Computation of flow noise using source terms in linearized Euler's equations”, AIAA J.40(2), 235–243.
48.
EwertR.SchröderW., (2003) “Acoustic perturbation equations based on flow decomposition via source filtering”, J. of Comp. Phys.188(2), pp. 365–398.
49.
GabardG.LefrancoisE., and TaharBen M., (2004) “Aeroacoustic Noise Source Simulations Based on Galbrun's Equation”, AIAA Paper 2004–2892.
50.
AhnH.T., and KallinderisY., “Strongly coupled flow structure interactions with a geometrically conservative ALE scheme on general hybrid meshes”, Journal of Computational Physics, Vol. 219, pp. 671–696, 2006.
51.
HirschC. (1990) Numerical computation of internal and external flows. Vol. 1 and 2, WileyNew York.
52.
BatchelorG. K., (1967) An Introduction to Fluid Dynamics, Cambridge University Press.
53.
FriedlanderF. G. (1958) Sound Pulses, Cambridge University Press.
