﻿ 低速修正的可压缩求解器对湍流模拟精度的影响<sup>*</sup>
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1. 北京机电工程研究所, 北京 100074;
2. 北京航空航天大学 航空科学与工程学院, 北京 100083

Effect of low-speed modification of compressible solver on turbulence simulation accuracy
LI Yansu1,2, ZHANG Kun1, HE Chengjun1, YAN Chao2
1. Beijing Electro-Mechanical Engineering Institute, Beijing 100074, China;
2. School of Aeronautic Science and Engineering, Beihang University, Beijing 100083, China
Received: 2019-03-27; Accepted: 2019-06-21; Published online: 2019-07-11 09:36
Corresponding author. LI Yansu.E-mail:yansu_li@126.com
Abstract: The calculation accuracy of low-speed region in high speed turbulence can be improved by modifying the compressible solver. However, it is difficult to evaluate the contribution of such modification, because simulation accuracy results from complex factors including solver type, accuracy of schemes, grid number, etc. This paper focuses on the influence of the compressible solver with and without low-speed modification on complex turbulence simulation when using different order or resolution of the schemes and different amount of grid. With the calculation example of Taylor-Green vortex, the differences of the results are evaluated quantitatively. The results show that the influence of the low-speed modification is different with different scheme-grid combinations. The low-speed modification method can effectively improve the calculation accuracy with coarse grids and low-accuracy reconstruction schemes.
Keywords: compressible turbulence     low-speed modification     high-accuracy schemes     all-speed schemes     Taylor-Green vortex

1 控制方程及计算方法 1.1 三维可压缩Navier-Stokes方程及离散方法

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1.2 通量格式

Roe格式[11]是Godunov类方法，是目前经典的通量格式，通过求解线化Riemann问题获得全场的数值近似解, 其具有间断分辨率高、稳定性强、计算效率高等优点，广泛使用于可压缩流动求解中。以x方向为例，Roe格式可以写成

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1.3 重构格式

2m-1阶WENO格式的表达式可写为

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 图 1 不同重构格式的分辨率特性曲线 Fig. 1 Resolution properties of different reconstruction schemes
2 泰勒-格林涡算例 2.1 算例设置

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EkεEk能够反映流动发展过程中流场动能变化的情况，从而衡量模拟结果的精度。

2.2 计算结果与讨论

 图 2 体平均动能随时间变化曲线(网格间距2π/64) Fig. 2 Variation of volume-averaged kinetic energy with time under grid space 2π/64
 图 3 动能耗散率随时间变化曲线(网格间距2π/64) Fig. 3 Variation of energy dissipation rate with time under grid space 2π/64

 图 4 体平均动能随时间变化曲线(网格间距2π/64和2π/128) Fig. 4 Variation of volume-averaged kinetic energy with time (grid space 2π/64 and 2π/128)
 图 5 动能耗散率随时间变化曲线(网格间距2π/64和2π/128) Fig. 5 Variation of energy dissipation rate with time (grid space 2π/64 and 2π/128)

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 图 6 不同格式和网格量下体平均动能误差柱状图 Fig. 6 Histogram of volume-averaged kinetic energy error for different schemes with different grids
 图 7 不同格式和网格量下动能耗散率误差柱状图 Fig. 7 Histogram of energy dissipation rate error for different schemes with different grids
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 图 8 不同网格量下Roe和LMRoe通量格式的计算差异(体平均动能) Fig. 8 Calculation difference of Roe and LMRoe flux schemes with different amounts of grid (volume-averaged kinetic energy)
 图 9 不同网格量下Roe和LMRoe通量格式的计算差异(动能耗散率) Fig. 9 Calculation difference of Roe and LMRoe flux schemes with different amounts of grid (energy dissipation rate)

 重构格式 体平均动能 动能耗散率 WENO3 0.36 0.57 WENO5 0.63 0.61 WENO7 0.69 0.75 compact5 1.04 1.00

 重构格式 体平均动能 动能耗散率 WENO5 0.56 0.57 compact5 1.85 0.76

3 结论

1) 当流场中存在低速流动时，使用低速修正的通量格式能够一定程度上改进计算结果。

2) 通量格式对模拟结果的影响是与重构格式耦合的。当重构格式的精度较低时，通量格式对结果的影响显著，但当重构格式的精度足够高后，通量格式对结果的影响不明显。

3) 随着网格加密，有无低速修正的通量格式计算结果都呈现出向精确解收敛的特征。使用较粗网格时，低速修正的通量格式对计算结果的改进更明显。

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文章信息

LI Yansu, ZHANG Kun, HE Chengjun, YAN Chao

Effect of low-speed modification of compressible solver on turbulence simulation accuracy

Journal of Beijing University of Aeronautics and Astronsutics, 2019, 45(11): 2199-2206
http://dx.doi.org/10.13700/j.bh.1001-5965.2019.0129