An Immersed Boundary Method for RANS Simulation of Compressible Turbulent Flows

doi:10.19596/j.cnki.1001-246x.8563

Abstract

Abstract:

An immersed boundary method is proposed for RANS (Reynolds-Averaged Navier-Stokes) simulation of compressible turbulent flows. In the method reference points are no longer utilized in interpolation for solution reconstruction and flow variables at the mesh nodes in immediate vicinity of solid wall are determined with inverse distance weighting interpolation of those at surrounding computed nodes. To reduce the requirement of high near-wall mesh resolution in simulation of high-Reynolds-number turbulent flows, an explicit wall function is employed to transform the no-slip boundary condition into the no-penetration condition and a prescribed wall shear stress. The wall function does not need to be solved iteratively which improves computational efficiency. Numerical experiment for subsonic and transonic flows around RAE2822 airfoil verifies reliability of the method.

Key words: immersed boundary method, RANS simulation of turbulent flows, compressible turbulent flow, wall function

Wenhui HE, Tianmei PU, Chunhua ZHOU. An Immersed Boundary Method for RANS Simulation of Compressible Turbulent Flows[J]. Chinese Journal of Computational Physics, 2023, 40(3): 325-332.

Figures/Tables 13

Fig.1 Treatment of the immersed boundary (B: IB node;A and C: interior computed node; F: reference point; W: intersection between wall and normal line.)

Fig.2 A schematic for interpolation points

Fig.3 A schematic for IDW interpolation

Table 1 Corrected free-stream conditions for RAE2822 airfoil

	雷诺数	马赫数	攻角/°
Case 1	5.7 × 10⁶	0.676	2.04
Case 9	6.5 × 10⁶	0.730	2.80
Case 10	6.2 × 10⁶	0.750	2.72

Table 2 Node numbers of mesh with different near-wall intervals

	网格尺度h	节点数
粗网格	8.0 × 10^-4	78 850
中等网格	4.0 × 10^-4	98 086
细网格	2.0 × 10^-4	136 158
更细网格	1.0 × 10^-4	179 393

Fig.4 Case 1: CP on the surface

Fig.5 Case 1: Cf on the upper surface

Fig.6 Case 9: CP on the surface

Fig.7 Case 9: Cf on the upper surface

Fig.8 Case 10: CP on the surface, h = 2 × 10-4

Fig.9 Case 10: Cf on the upper surface, h = 2 × 10-4

Fig.10 Case 10: CP on the surface, h = 1 × 10-4

Fig.11 Case 10: Cf on the upper surface, h = 1 × 10-4

References 21

1	IACCARINO G , VERZICCO R . Immersed boundary technique for turbulent flow simulations[J]. Appl Mech Rev, 2003, 56(3): 331- 47. DOI
2	MITTAL R , IACCARINO G . Immersed boundary methods[J]. Annu Rev Fluid Mech, 2005, 37, 239- 261. DOI
3	SOTIROPOULOS F , YANG X . Immersed boundary methods for simulating fluid-structure interaction[J]. Progress in Aerospace Sciences, 2014, 65, 1- 21. DOI
4	WANG J , PAN Z , WU H . Numerical study of inertial focusing behavior of ellipsoidal particles in a microchannel[J]. Chinese Journal of Computational Physics, 2020, 37(6): 677- 686.
5	ZHAO X , YE Z . Numerical study of droplet splashing in a CIP-based model[J]. Chinese Journal of Computational Physics, 2016, 33(1): 39- 48. DOI
6	PESKIN C S . Numerical analysis of blood flow in the heart[J]. Journal of Computational Physics, 1977, 25(3): 220- 252. DOI
7	ZHU X , CHEN C , XIAO F . A multi-moment immersed-boundary finite-volume scheme[J]. Chinese Journal of Computational Physics, 2010, 27(3): 342- 352. DOI
8	PU T , ZHOU C . An immersed boundary/wall modeling method for RANS simulation of compressible turbulent flows[J]. International Journal for Numerical Methods in Fluids, 2018, 87(5): 217- 238. DOI
9	BERNARDINI M , MODESTI D , PIROZZOLI S . On the suitability of the immersed boundary method for the simulation of high-Reynolds-number separated turbulent flows[J]. Computers & Fluids, 2016, 130, 84- 93.
10	ZHOU C . RANS simulation of high-Re turbulent flows using an immersed boundary method in conjunction with wall modeling[J]. Computers & Fluids, 2017, 143, 73- 89.
11	TAMAKI Y , HARADA M , IMAMURA T . Near-wall modification of Spalart-Allmaras turbulence model for immersed boundary method[J]. AIAA Journal, 2017, 55(9): 3027- 3039. DOI
12	MAVRIPLIS D J , JAMESON A . Multigrid solution of the Navier-Stokes equations on triangular meshes[J]. AIAA Journal, 1990, 28(8): 1415- 1425. DOI
13	MELSON N D, SANETRIK M D, ATKINS H L. Time-accurate Navier-Stokes calculations with multigrid acceleration[C]. Proceedings of the The Sixth Copper Mountain Conference on Multigrid Methods, Copper Mountain USA, 1993.
14	Menter F R . Two-equation eddy-viscosity turbulence models for engineering applications[J]. AIAA Journal, 1994, 32(8): 1598- 1605. DOI
15	WILHELM S , JACOB J , SAGAUT P . An explicit power-law-based wall model for lattice Boltzmann method-Reynolds-averaged numerical simulations of the flow around airfoils[J]. Physics of Fluids, 2018, 30(6): 065111. DOI
16	WERNER H, WENGLE H. Large-eddy simulation of turbulent flow over and around a cube in a plate channel[M]//DURST F et al. (eds. ). Turbulent shear flows 8. Berlin Herdelberg: Springer-Verlag, 1993: 155-168.
17	CAI S G , DEGRIGNY J , BOUSSUGE J F , et al. Coupling of turbulence wall models and immersed boundaries on Cartesian grids[J]. Journal of Computational Physics, 2021, 429, 109995. DOI
18	FRANKE R . Scattered data interpolation: Tests of some methods[J]. Mathematics of Computation, 1982, 38(157): 181- 200.
19	KALITZIN G , MEDIC G , IACCARINO G , et al. Near-wall behavior of RANS turbulence models and implications for wall functions[J]. Journal of Computational Physics, 2005, 204(1): 265- 291.
20	VIESER W, ESCH T, MENTER FR. Heat transfer predictions using advanced two-equation turbulence models[R]. CFX Technical Memorandum CFX-VAL10/00602, 2002.
21	COOK P H, MCDONALD M A, FIRMIN M C P. Aerofoil RAE2822-pressure distributions, and boundary layer and wake measurements[R]. AGARD-AR-138, 1979: A6.1-A6.77.