一种可压缩湍流RANS模拟的浸入边界方法

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

计算物理 ›› 2023, Vol. 40 ›› Issue (3): 325-332.DOI: 10.19596/j.cnki.1001-246x.8563

一种可压缩湍流RANS模拟的浸入边界方法

何文辉¹, 濮天梅², 周春华¹^,*()

1. 南京航空航天大学航空学院，江苏南京 210016
2. 南京航空航天大学通用航空与飞行学院，江苏南京 211106

收稿日期:2022-05-23 出版日期:2023-05-25 发布日期:2023-07-22
通讯作者: 周春华
作者简介:
何文辉(1997—)，男，硕士研究生，主要从计算流体力学研究
基金资助:
国家自然科学基金(11972191)

An Immersed Boundary Method for RANS Simulation of Compressible Turbulent Flows

Wenhui HE¹, Tianmei PU², Chunhua ZHOU¹^,*()

1. College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, China
2. College of General Aviation and Flight, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 211106, China

Received:2022-05-23 Online:2023-05-25 Published:2023-07-22
Contact: Chunhua ZHOU

摘要/Abstract

摘要：

提出一种可压缩湍流RANS(Reynolds-Averaged Navier-Stokes)模拟的浸入边界方法。该方法的解重构中，不再定义用于插值的参考点。利用其周围计算内点上已知的流动变量值，解域内紧靠壁面的网格节点上的流动变量通过距离倒数加权方法插值确定。为降低高雷诺数湍流模拟的近壁区域网格分辨率要求，采用一种显式壁面函数将无滑移边界条件转化为无穿透边界条件和当地剪切应力条件；该壁面函数无需迭代求解，提高了计算效率。RAE2822翼型亚、跨音速绕流的数值模拟验证了方法的可靠性。

关键词: 浸入边界法, 湍流RANS模拟, 可压湍流, 壁面函数

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

何文辉, 濮天梅, 周春华. 一种可压缩湍流RANS模拟的浸入边界方法[J]. 计算物理, 2023, 40(3): 325-332.

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.

图/表 13

图1 浸入边界处理(B：IB点； A、C：计算内点；F：参考点；W：物面与法线交点。)

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.)

图2 插值点处理示意图

Fig.2 A schematic for interpolation points

图3 IDW插值示意图

Fig.3 A schematic for IDW interpolation

表1 RAE2822翼型绕流修正的自由来流条件

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

表2 不同近壁尺度网格对应的网格节点数

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

图4 Case 1：表面CP分布

Fig.4 Case 1: CP on the surface

图5 Case 1：上表面Cf分布

Fig.5 Case 1: Cf on the upper surface

图6 Case 9：表面CP分布

Fig.6 Case 9: CP on the surface

图7 Case 9：上表面Cf分布

Fig.7 Case 9: Cf on the upper surface

图8 Case 10：表面CP分布，h=2 × 10-4

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

图9 Case 10：上表面Cf分布，h = 2 × 10-4

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

图10 Case 10：表面CP分布，h = 1 × 10-4

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

图11 Case 10：上表面Cf分布，h = 1 × 10-4

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

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一种可压缩湍流RANS模拟的浸入边界方法

An Immersed Boundary Method for RANS Simulation of Compressible Turbulent Flows

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