﻿ 类车体气动性能的大涡模拟
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 同济大学学报(自然科学版)  2018, Vol. 46 Issue (6): 811-818.  DOI: 10.11908/j.issn.0253-374x.2018.06.014 0

### 引用本文

ZHU Hui, ZHOU Yongxiang, YANG Zhigang, SHI Fanglin. Large Eddy Simulation of Aerodynamic Performance of MIRA Vehicle Body[J]. Journal of Tongji University (Natural Science), 2018, 46(6): 811-818. DOI: 10.11908/j.issn.0253-374x.2018.06.014.

### 文章历史

1. 同济大学 上海地面交通工具风洞中心，上海 201804;
2. 同济大学 上海市地面交通工具空气动力与热环境模拟重点实验室, 上海 201804;
3. 泛亚汽车技术中心有限公司，上海 201201

Large Eddy Simulation of Aerodynamic Performance of MIRA Vehicle Body
ZHU Hui1,2, ZHOU Yongxiang3, YANG Zhigang1,2, SHI Fanglin1,2
1. Shanghai Automotive Wind Tunnel Center, Tongji University, Shanghai 201804, China;
2. Shanghai Key Laboratory of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University, Shanghai 201804, China;
3. Pan Asia Technical Automotive Center, Shanghai 201201, China
Abstract: Based on the wind tunnel test data of aerodynamic performance of MIRA vehicle body, the iteration step, time step, and grid scheme were researched when large eddy simulation was adopt to solve the obviously transient flow field with large separation structure around bluff body near ground. Meanwhile, the simulation accuracy of three subgrid scale turbulence models was studied using the comparative analysis method. Finally, the solving strategy of large eddy simulation was proposed which is applicable for the simulation of aerodynamic performance of notchback vehicle.
Key words: large eddy simulation    aerodynamic performance    numerical simulation

1 大涡模拟

LES的基本思想：通过瞬时N-S方程求解大尺度涡，同时建立模型以量化小尺度涡对大尺度涡的影响，该模型即为亚格子模型(SGS).

 $\bar \varphi \left( x \right) = \int_D {\varphi \left( {x'} \right)G\left( {x,x'} \right){\rm{d}}x'}$ (1)

 $G\left( {x,x'} \right) = \left\{ \begin{array}{l} \frac{1}{V},\;\;\;x' \in V\\ 0,\;\;\;\;x' \notin V \end{array} \right.$ (2)

 $\bar \varphi \left( x \right) = \frac{1}{V}\int_V {\bar \varphi \left( {x'} \right){\rm{d}}x'} ,x' \in V$ (3)

 $\frac{{\partial \rho }}{{\partial t}} + \frac{\partial }{{\partial {x_i}}}\left( {\rho {{\bar u}_i}} \right) = 0$ (4)
 $\frac{\partial }{{\partial t}}\left( {\rho {{\bar u}_i}} \right) + \frac{\partial }{{\partial {x_j}}}\left( {\rho \overline {{u_i}{u_j}} } \right) = - \frac{{\partial \bar p}}{{\partial {x_i}}} + \frac{\partial }{{\partial {x_j}}}\left( {\mu \frac{{\partial {{\bar u}_i}}}{{\partial {x_j}}}} \right) - \frac{{\partial {\tau _{ij}}}}{{\partial {x_j}}}$ (5)

 ${\tau _{ij}} = \rho \overline {{u_i}{u_j}} - \rho {{\bar u}_i}{{\bar u}_j}$ (6)

 ${{\bar \tau }_{ij}} - \frac{1}{3}{\tau _{{\rm{kk}}}}{\delta _{ij}} = - 2{\mu _{\rm{t}}}{{\bar S}_{ij}}$ (7)

 ${{\bar S}_{ij}} = \frac{1}{2}\left( {\frac{{\partial {{\bar u}_i}}}{{\partial {x_j}}} + \frac{{\partial {{\bar u}_j}}}{{\partial {x_i}}}} \right)$ (8)

Smagorinsky给出了最基本的亚格子模型，经Lilly改进后形成Smagorinsky-Lilly模型.该模型对亚格子尺度涡黏系数μt的计算方法为

 ${\mu _{\rm{t}}} = \rho L_{\rm{s}}^2\left| {\bar S} \right|$ (9)

 ${L_{\rm{s}}} = \min \left( {kd,{C_{\rm{s}}}\Delta } \right)$ (10)

 ${\mu _{\rm{t}}} = \rho L_{\rm{s}}^2\frac{{{{\left( {S_{ij}^{\rm{d}}S_{ij}^{\rm{d}}} \right)}^{3/2}}}}{{{{\left( {{{\bar S}_{ij}}{{\bar S}_{ij}}} \right)}^{5/2}}{{\left( {S_{ij}^{\rm{d}}S_{ij}^{\rm{d}}} \right)}^{5/4}}}}$ (11)

 ${L_{\rm{s}}} = \min \left( {kd,{C_{\rm{w}}}{V^{1/3}}} \right)$ (12)
 $S_{ij}^{\rm{d}} = \frac{1}{2}\left( {\bar g_{ij}^2 + \bar g_{ji}^2} \right) - \frac{1}{3}{\delta _{ij}}\bar g_{{\rm{kk}}}^2$ (13)

DKE模型计入了亚格子尺度湍动能的输运，其亚格子尺度湍动能定义为

 ${k_{{\rm{sgs}}}} = \frac{1}{2}\left( {\overline {u_{\rm{k}}^2} + \bar u_{\rm{k}}^2} \right)$ (14)

 ${\mu _{\rm{t}}} = {C_{\rm{k}}}\rho \sqrt {{k_{{\rm{sgs}}}}} \Delta$ (15)

2 流场仿真相关信息

 图 1 仿真模型构造 Fig.1 Structure of simulation model

 图 2 仿真计算区域 Fig.2 Domain of simulation

 图 3 体网格布局 Fig.3 Arrangement of mesh

xyz 3个方向速度记为uvw，计算域入口边界设为速度入口，速度均匀分布：u＝30 m·s-1vw＝0 m·s-1.出口边界设为压力出口，表压为0 Pa.车体及地面皆采用无滑移壁面边界条件，计算域左、右两侧及顶部采用对称边界条件.按车长计算的雷诺数为Re≈2.81×106.

LES属于非稳态计算方法，在时间积分方案上保证二阶精度; 同时，采用二阶精度的空间离散格式.根据文献[22]的研究成果，以低雷诺数模型计算所得定常解作为LES计算的初始场.

MIRA车体外部绕流为充分发展的湍流流动，脉动特征显著，具有很强的时间相关性，任一点的流动参数皆为时间的函数.因此引入物理量的时均值，以便将计算值与试验值进行对比

 $\bar \varphi = \sum\limits_{i = 1}^n {{\varphi _i}/n}$ (16)

 $\sigma \left( {\varphi '} \right) = \sqrt {\frac{{\sum\limits_{i = 1}^n {{{\left( {{\varphi _i} - \bar \varphi } \right)}^2}} }}{{n - 1}}}$ (17)

3 仿真参数的确定

3.1 时间步长内最大迭代步数

 图 4 监测点位置 Fig.4 Location of monitoring points

 图 5 压力系数变化曲线 Fig.5 Variation of Cp

 图 6 速度变化曲线 Fig.6 Variation of velocity
3.2 时间步长

 图 7 监测点位置 Fig.7 Location of monitoring points
 图 8 压力系数平均值及标准差 Fig.8 Average value and standard deviation of Cp
3.3 网格数量及初始场

 图 9 不同部位压力系数分布 Fig.9 CP distribution on each particular location

 图 10 压力系数误差统计 Fig.10 Error statistics of CP

4 湍流模型的对比

 图 11 3种模型气动阻力系数对比 Fig.11 Comparison of CD
 图 12 3种模型气动升力系数对比 Fig.12 Comparison of CL

 图 13 对称面压力系数分布 Fig.13 Cp distribution on symmetry plane

 图 14 后风窗压力系数分布 Fig.14 Cp distribution on rear window

 图 15 行李箱压力系数分布 Fig.15 Cp distribution on trunk

 图 16 尾部端面压力系数分布 Fig.16 Cp distribution on tail end

 图 17 上翘面压力系数分布 Fig.17 Cp distribution on upswept surface

 图 18 压力系数误差统计 Fig.18 Error statistics of Cp
5 结论

(1) 应用大涡模拟法计算MIRA三厢车体的气动性能过程中，时间步长推荐值为5×10-4s，时间步长内最大迭代步数推荐值为25步，1:3缩尺比模型的面网格推荐尺寸为1.5 mm，推荐采用低雷诺数湍流模型获得定常初始场，定常初始场应具备明显的左右对称特征.

(2) 对三维性较弱的车体头部及顶部区域流动，3种亚格子模型的时均结果预测能力相当，均与试验值符合较好; 对存在地面效应和局部分离的底部区域流动，DSL模型的预测能力最强.

(3) 对三维性较强、存在大分离结构且非定常特征显著的车体后风窗、行李箱及尾部区域流动，DKE模型时均结果的计算准确性最高，WALE模型的计算准确性最低.

(4) DKE模型对CD值的计算结果最接近试验值，DSL模型对CL值的计算结果误差最小; 以车身表面254个测点处压力系数时均值为准，DKE模型的计算准确性略优于DSL模型，WALE模型的计算准确性最低.

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