Fluid Mechanics and Flight Mechanics

A sharp-interface immersed boundary method combined with wall model to simulate turbulent flow

  • Shizhao ZHANG ,
  • Jie WU ,
  • Dewu YANG ,
  • Xinyu CONG
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  • College of Aerodynamics,College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China
E-mail: wuj@nuaa.edu.cn

Received date: 2022-06-23

  Revised date: 2022-09-26

  Accepted date: 2022-10-11

  Online published: 2022-10-14

Supported by

National Natural Science Foundation of China(12072158);Natural Science Foundation of Jiangsu Province(BK20191271)

Abstract

A robust sharp-interface immersed boundary method is proposed to simulate the incompressible turbulence flow over a solid obstacle. Based on the OpenFOAM, the solver combines the implicit split operator algorithm with the kω Shear Stress Transfer turbulence model to solve the velocity⁃pressure coupling in Navier⁃Stokes equations and the turbulent flow near the obstacle surface. The wall model is used to reduce the number of girds near the wall. The wall shear stress is obtained from the mirror point away from the wall, and the flow variables at image points are obtained using the surrounding flow field by Inverse Distance Weight (IDW). To validate the efficiency and accuracy of this method for simulation of incompressible turbulence flow, five turbulent flow cases are considered as follows: flow over a flat plate, flow pass a NACA0012 airfoil, Buice 2D diffuser, flow around a circular cylinder, and flow around a square cylinder. The simulation results show good agreement with literature, validating the efficiency and accuracy of the method proposed.

Cite this article

Shizhao ZHANG , Jie WU , Dewu YANG , Xinyu CONG . A sharp-interface immersed boundary method combined with wall model to simulate turbulent flow[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023 , 44(11) : 127673 -127673 . DOI: 10.7527/S1000-6893.2022.27673

References

1 L?HNER R, CEBRAL J R, CAMELLI F F, et al. Adaptive embedded/immersed unstructured grid techniques[J]. Archives of Computational Methods in Engineering200714(3): 279-301.
2 L?HNER R, BAUM J D, MESTREAU E, et al. Adaptive embedded unstructured grid methods[J]. International Journal for Numerical Methods in Engineering200460(3): 641-660.
3 PESKIN C S. Numerical analysis of blood flow in the heart[J]. Journal of Computational Physics197725(3): 220-252.
4 HUANG W X, TIAN F B. Recent trends and progress in the immersed boundary method[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science2019233(23-24): 7617-7636.
5 CUI Z, YANG Z X, JIANG H Z, et al. A sharp-interface immersed boundary method for simulating incompressible flows with arbitrarily deforming smooth boundaries[J]. International Journal of Computational Methods201815(1): 1750080.
6 SCHNEIDERS L, GüNTHER C, MEINKE M, et al. An efficient conservative cut-cell method for rigid bodies interacting with viscous compressible flows[J]. Journal of Computational Physics2016311: 62-86.
7 MURALIDHARAN B, MENON S. Simulation of moving boundaries interacting with compressible reacting flows using a second-order adaptive Cartesian cut-cell method[J]. Journal of Computational Physics2018357: 230-262.
8 EHSAN KHALILI M, LARSSON M, MüLLER B. Immersed boundary method for viscous compressible flows around moving bodies[J]. Computers & Fluids2018170: 77-92.
9 BRAHMACHARY S, NATARAJAN G, KULKARNI V, et al. A sharp-interface immersed boundary method for high-speed compressible flows[J] Immersed Boundary Method Development and Applications2020: 251-275.
10 BLAZEK J. Principles of grid generation[M]∥Computational Fluid Dynamics: Principles and Applications. Amsterdam: Elsevier, 2001: 353-392.
11 PU T, ZHOU C. An immersed boundary/wall modeling method for RANS simulation of compressible turbulent flows[J]. International Journal for Numerical Methods in Fluids201887(5): 217-238.
12 CABOT W, MOIN P. Approximate wall boundary conditions in the large-eddy simulation of high Reynolds number flow[J]. Flow, Turbulence and Combustion200063(1): 269-291.
13 杜银杰, 舒昌, 杨鲤铭, 等. 扩散界面浸入边界法结合壁面模型在湍流模拟中的应用[J]. 航空学报202142(): 54-64.
  DU Y J, SHU C, YANG L M, et al. Wall model based diffuse-interface immersed boundary method and its application in turbulent flows[J]. Acta Aeronautica et Astronautica Sinica202142(Sup 1): 54-64 (in Chinese).
14 李旭, 周洲, 薛臣. 一种适合迭代求解的反馈力浸入边界法[J]. 航空学报202041(9): 123712.
  LI X, ZHOU Z, XUE C. Feedback forcing immersed boundary method for iterative calculations[J]. Acta Aeronautica et Astronautica Sinica202041(9): 123712 (in Chinese).
15 胡国暾, 杜林, 孙晓峰. 基于浸入式边界法的振荡转子叶片数值模拟[J]. 航空学报201435(8): 2112-2125.
  HU G, DU L, SUN X F. An immersed boundary method for simulating oscillating rotor blades[J]. Acta Aeronautica et Astronautica Sinica201435(8): 2112-2125 (in Chinese).
16 陈浩, 华如豪, 袁先旭, 等. 基于自适应笛卡尔网格的飞翼布局流动模拟[J]. 航空学报202243(8): 125674.
  CHEN H, HUA R H, YUAN X X, et al. Simulation of flow around fly-wing configuration based on adaptive Cartesian grid[J]. Acta Aeronautica et Astronautica Sinica202243(8): 125674 (in Chinese).
17 唐志共, 陈浩, 毕林, 等. 自适应笛卡尔网格超声速黏性流动数值模拟[J]. 航空学报201839(5): 121697.
  TANG Z G, CHEN H, BI L, et al. Numerical simulation of supersonic viscous flow based on adaptive Cartesian grid[J]. Acta Aeronautica et Astronautica Sinica201839(5): 121697 (in Chinese).
18 XU Y C, LIU X F. An immersed boundary method with y +-adaptive wall function for smooth wall shear[J]. International Journal for Numerical Methods in Fluids202193(6): 1929-1946.
19 KNOPP T, ALRUTZ T, SCHWAMBORN D. A grid and flow adaptive wall-function method for RANS turbulence modelling[J]. Journal of Computational Physics2006220(1): 19-40.
20 MENTER F R. Two-equation eddy-viscosity turbulence models for engineering applications[J]. AIAA Journal199432(8): 1598-1605.
21 SPALDING D B. A single formula for the “law of the wall”[J]. Journal of Applied Mechanics196128(3): 455-458.
22 HOLZMANN T. Mathematics, numerics, derivations and OpenFOAM[D]. Loeben: Holzmann CFD, 2016.
23 KALITZIN G, MEDIC G, IACCARINO G, et al. Near-wall behavior of RANS turbulence models and implications for wall functions[J]. Journal of Computational Physics2005204(1): 265-291.
24 KALITZIN G, IACCARINO G. Toward immersed boundary simulation of high Reynolds number flows[R]. 2003.
25 LEE J D, RUFFIN S. Development of a turbulent wall-function based viscous Cartesian-grid methodology[C]∥45th AIAA Aerospace Sciences Meeting and Exhibit. Reston: AIAA, 2007: 1326.
26 Buice 2D diffuser[EB/OL]. (2021-02-10). .
27 OBI S, AOKI K, MASUDA S. Experimental and computational study of turbulent separating flow in an asymmetric plane diffuser[C]∥9th International Symposium on Turbulent Shear Flows. Kyoto: Shinnosuki Obi, 1993: 305-312.
28 YE H X, WAN D C. Benchmark computations for flows around a stationary cylinder with high Reynolds numbers by RANS-overset grid approach[J]. Applied Ocean Research201765: 315-326.
29 YEON S M, YANG J M, STERN F. Large-eddy simulation of the flow past a circular cylinder at sub- to super-critical Reynolds numbers[J]. Applied Ocean Research201659: 663-675.
30 NGUYEN V B, DO Q V, PHAM V S. An OpenFOAM solver for multiphase and turbulent flow[J]. Physics of Fluids202032(4): 043303.
31 SCHEWE G. On the force fluctuations acting on a circular cylinder in crossflow from subcritical up to transcritical Reynolds numbers[J]. Journal of Fluid Mechanics1983133: 265-285.
32 TRIAS F X, GOROBETS A, OLIVA A. Turbulent flow around a square cylinder at Reynolds number 22, 000: A DNS study[J]. Computers & Fluids2015123: 87-98.
33 SOHANKAR A, DAVIDSON L, NORBERG C. Large eddy simulation of flow past a square cylinder: Comparison of different subgrid scale models[J]. Journal of Fluids Engineering2000122(1): 39-47.
34 NORBERG C. Flow around rectangular cylinders: Pressure forces and wake frequencies[J]. Journal of Wind Engineering and Industrial Aerodynamics199349(1-3): 187-196.
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