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 同济大学学报(自然科学版)  2019, Vol. 47 Issue (1): 113-123.  DOI: 10.11908/j.issn.0253-374x.2019.01.015 0

### 引用本文

WANG Bingxin, YANG Zhigang, ZHU Hui. Transient Feature of Flow Field in Wake of Ahmed Body[J]. Journal of Tongji University (Natural Science), 2019, 47(1): 113-123. DOI: 10.11908/j.issn.0253-374x.2019.01.015

### 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. 北京民用飞机技术研究中心，北京 102211

Transient Feature of Flow Field in Wake of Ahmed Body
WANG Bingxin 1, YANG Zhigang 1,2, ZHU Hui 1
1. Shanghai Automotive Wind Tunnel Center, Tongji University, Shanghai 210804, China;
2. Beijing Aeronautical Science & Technology Research Institute, Beijing 102211, China
Abstract: Compared with the published data, the validity of the large eddy simulation method is verified. The large eddy simulation method is applied to the study of the flow field around slanted surface and rear vertical base of the Ahmed body with a slant angle of 25°at high Reynolds number. This work aims to gain a relatively thorough understanding of the transient features of the predominant coherent structures around the Ahmed body by sampling flow field information and spectrum analyses of a recirculation bubble over the slanted surface, one pair of counter-rotating longitudinal C-pillar vortices originating from the two side edges of the rear window, and a recirculation torus behind the vertical base. In different regions of flow field, the transient features of the wake are different. The flapping motion of the recirculation bubble over the slanted surface corresponds to an absolute unsteadiness while the activity of the coherent structures is convective. The pair of C-pillar vortices coupled with the spanwise vortices over the slanted surface are symmetric. However, they only mix with the recirculation torus behind the vertical base resulting in asymmetric characteristic. The rolling up and shedding of the recirculation torus behind the vertical base are similar to Karman vortex street. At high Reynolds numbers, the characteristic frequency of different regions tends to be consistent.
Key words: Ahmed body    large eddy simulation    transient feature

Thacker等[8-9]研究了不同雷诺数下背部斜面的主频，Str=0.18~0.21分别对应雷诺数ReH=(3.89~7.78)×105，相比其他研究其结果偏小，且指出马蹄涡对应的频率不是背部斜面的主导频率，而应为高频特性，与文献[7]相矛盾.Heft等[10]ReH =7.78×105时得出背部斜面主频Str=0.18；Pierric等[4]研究了不同雷诺数时背部斜面处与垂直面处流动的主频特性，Str=0.29~0.43与Stb=0.44~0.45对应ReH =(3.89~7.78)×105，指出主频会随雷诺数增大而增大，而高频特性对应由KH不稳定性造成的剪切层卷起频率.Zhang等[11]由主频特性与雷诺数关系的拟合曲线得出在ReH=7.78×105时，StrStb分别为0.52与0.46.由此可知，针对Ahmed类车体尾迹区非定常特性的研究结果存在明显差异.Jean-Francois等[12]定性地解释了背部斜面分离泡与“C柱”拖曳涡对存在竞争作用关系：较强较大的背部斜面分离泡会产生较低的背压，在使阻力增加的同时，导致从背部斜面侧“C柱”处卷起的拖曳涡对更强；另一方面，较强的“C柱”拖曳涡对在其涡核中心诱导出较大的低压区，从而延缓了背部斜面分离泡的分离，而且较强的“C柱”拖曳涡对诱导流体产生的下洗作用较强，减小了背部斜面分离泡尺度从而使阻力减小；但作者并未对此作进一步定量的论证.因此，有必要对Ahmed类车体尾迹区不同相干结构的相互作用进行深入研究.

1 数值仿真模型与计算方法 1.1 数值仿真模型

 图 1 类车体构造及尺寸(单位：mm) Fig.1 Structure and size of Ahmed body(Unit:mm)

 图 2 计算域分块结构 Fig.2 Blocks structure of computational domain
 图 3 体网格结构 Fig.3 Structure of volumetric mesh
1.2 数值模拟方法

 ${\mu _{\rm{t}}} = \rho L_{\rm{s}}^2\left| {\bar S} \right|$ (1)
 $\left| {\bar S} \right| = \sqrt {2{{\bar S}_{ij}}{{\bar S}_{ij}}}$ (2)
 ${\bar S_{ij}} = \frac{1}{2}\left( {\frac{{\partial {{\bar u}_i}}}{{{x_j}}} + \frac{{\partial {{\bar u}_j}}}{{{x_i}}}} \right)$ (3)
 ${L_{\rm{s}}} = {\rm{min}}(kd, {C_{\rm{s}}}{V^{1/3}})$ (4)

1.3 数值方法初步验证

 图 4 流向速度型曲线 Fig.4 Profile of longitudinal velocity
2 数值结果与分析

Ahmed类车体尾迹区展向流动结构如图 5所示.主要涡结构由尾迹区上、下展向涡对(涡核中心N1、N2)及斜面分离泡(涡核中心N3)构成.尾迹区上、下展向涡对中、上侧展向涡的尺度较大，下侧展向涡的尺度较小.上、下展向涡对形成鞍点S1.

 图 5 对称截面Y=0时均流线 Fig.5 Time-averaged streamlines of the symmetric plane

 图 6 Q准则等值面(Q=3.13×105 s-2) Fig.6 ISO-surface of vortices in the wake using Q-criterion when Q=3.13×105 s-2
2.1 背部斜面分离泡非定常特性

 图 7 A1~A4测点分布 Fig.7 Layout of sampling points from A1~A4

 图 8 A1~A4测点压力功率谱 Fig.8 PSD of the pressure at sampling points from A1 to A4

 $C{{\rm{o}}_{xy}}\left( f \right) = \frac{{{{\left| {{P_{xy}}\left( f \right)} \right|}^2}}}{{{P_{xx}}\left( f \right){P_{yy}}\left( f \right)}}$ (5)
 图 9 T1~T4测点分布 Fig.9 Layout of sampling points from T1 to T4
 图 10 T1与T2测点压力互谱与相谱 Fig.10 Coherence and phase functions from cross-spectra of the pressure between sampling points T1 and T2
 图 11 T1与T3测点压力互谱 Fig.11 Coherence function from cross-spectra of the pressure between sampling points T1 and T3
 图 12 T3与T4测点压力互谱与相谱 Fig.12 Coherence and phase functions from cross-spectra of the pressure between sampling points T3 and T4

 ${V_{\rm{c}}} = \frac{{2{\rm{ \mathsf{ π} }}\cdot\Delta L\cdot H}}{{{\rm{d}}\theta /{\rm{d}}St}}$ (6)

2.2 “C柱”拖曳涡对非定常特性

 图 13 B1~B4与C1~C4测点分布 Fig.13 Layout of sampling points from B1 to B4 and from C1 to C4
 图 14 B1~B4与C1~C4测点压力功率谱 Fig.14 PSD of the pressure at sampling points from B1 to B4 and from C1 to C4

 图 15 A列与C列测点压力互谱与相谱 Fig.15 Coherence and phase functions from cross-spectra of the pressure between sampling points A-series and C-series

 图 16 B列与C列测点压力互谱与相谱 Fig.16 Coherence and phase functions from cross-spectra of the pressure between sampling points B-series and C-series
 图 17 B列与C列测点X向速度互谱与相谱 Fig.17 Coherence and phase functions from cross-spectra of the X-velocity between sampling points B-series and C-series
 图 18 B列与C列测点Y向速度互谱与相谱 Fig.18 Coherence and phase functions from cross-spectra of the Y-velocity between sampling points B-series and C-series
 图 19 B列与C列测点Z向速度互谱与相谱 Fig.19 Coherence and phasefunctions from cross-spectra of the Z-velocity between sampling points B-series and C-series
2.3 回流区流动非定常特性

 图 20 D~O列测点分布 Fig.20 Layout of sampling points from D-series to O-series
 图 21 回流区内拖曳涡对测点压力功率谱 Fig.21 PSD of the pressure at sampling points within the C-pillar vortices shedding into the recirculation torus behind the vertical base

 图 22 D6~G6与H6~K6对应测点压力互谱与相谱 Fig.22 Coherence and phase functions from cross-spectra of the pressure between sampling points from D6 to G6 and their corresponding points from H6 to K6

 图 23 D6~G6与L6~O6对应测点压力互谱与相谱 Fig.23 Coherence and phase functions from cross-spectra of the pressure between sampling points from D6 to G6 and their corresponding points from L6 to O6
 图 24 D6~G6与L6~O6对应测点X向速度互谱与相谱 Fig.24 Coherence and phase functions from cross-spectra of the X-velocity between sampling points from D6 to G6 and their corresponding points from H6 to K6
 图 25 D6~G6与L6~O6对应测点Y向速度互谱与相谱 Fig.25 Coherence and phase functions from cross-spectra of the Y-velocity between sampling points from D6 to G6 and their corresponding points from H6 to K6
 图 26 D6~G6与L6~O6对应测点Z向速度互谱与相谱 Fig.26 Coherence and phase functions from cross-spectra of the Z-velocity between sampling points from D6 to G6 and their corresponding points from H6 to K6

H~K列测点压力功率谱分析结果如图 27所示.回流区上下剪切层卷起的展向涡特征频率Stb=0.49，上、下剪切层卷起的展向涡向下游发展，其能量在流向位置Ⅰ处达到最大，继续向下游发展能量逐渐耗散.根据上、下侧测点功率谱密度的曲线斜率可推断：上侧展向涡的耗散较快，下侧展向涡由于地面效应的存在，其在流场中的持续时间更长.

 图 27 H~K列测点压力功率谱 Fig.27 PSD of the pressure at sampling points from H-series to K-series

 图 28 H1~K1与H6~K6对应测点压力互谱与相谱 Fig.28 Coherence and phase functions from cross-spectra of the pressure between sampling points from H1 to K1 and their corresponding points from H6 to K6
3 讨论与结论

(1) 背部斜面上，分离泡的拍击振动具有绝对不稳定性特征，由KH不稳定性诱发的大尺度相干结构具有对流不稳定性特征.

(2) 两侧“C柱”拖曳涡对在背部斜面上与展向涡相互耦合，且具有较好的对称性；拖曳涡对在垂直面处回流区内与该区展向涡相互混掺，使得能量增加，但无耦合作用且不具有对称性.

(3) 垂直面处回流区内上、下侧剪切层卷起的展向涡以类似卡门涡街形式交替产生并脱落，上测展向涡耗散较快，下侧展向涡由于地面效应的存在，其在流场中的持续时间更长.

(4) 高雷诺数时，整个尾迹区流动的特征频率趋于一致，且与Zhang等[11]给出的不同区域主频特性与雷诺数关系的拟合曲线相符，此特征与钝体绕流的自适应现象相统一.

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