INLET SYNTHETIC TURBULENCE GENERATION METHOD FOR COMPRESSIBLE BOUNDARY LAYER
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摘要: 在壁湍流中开展RANS-LES方法混合模拟时, 入口处添加合理的湍流脉动能够缩短流场向完全湍流的发展距离, 提高数值模拟精度以及节省计算资源. 采用SA-IDDES方法对槽道湍流和可压缩湍流边界层开展了数值模拟研究, 对比了3种较为常用的合成湍流方法对流场发展的影响, 包括合成湍流生成器(STG)、数字滤波法(DFM)和合成涡方法(SEM); 研究了不同合成湍流入口条件下流场壁面摩阻、流场结构、雷诺应力的发展过程, 评估了各方法在壁湍流中的表现. 其中在不可压槽道湍流和可压缩湍流边界层的模拟中, STG方法展现了较短的摩阻恢复距离, 流场结构与雷诺应力发展相比DFM也有一定的优势. 在高马赫数湍流边界层的数值模拟中, 忽略热力学量脉动可能会降低合成边界层脉动恢复到物理真实脉动的速度. 因此, 文章进一步基于STG给出的速度脉动, 在入口处通过若干强雷诺比拟方法(SRA、GSRA和HSRA)添加热力学脉动量, 对比研究了对可压缩湍流边界层流场发展的影响, 结果显示是否添加热力学脉动对于流场摩阻和雷诺应力发展影响较小, 但对流场中的热力学量影响显著, 其中GSRA下流场热力学量恢复得最快.Abstract: In the RANS-LES hybrid simulation of turbulent boundary layers, adding reasonable turbulent fluctuations at the inlet can shorten the recovery distance of the flow field to fully developed turbulent flow, improve the simulation accuracy and efficiency. In this paper, the SA-IDDES method is used to the research on numerical simulation study of channel turbulence and compressible turbulent boundary layer. And three commonly turbulence synthetic methods are compared , including synthetic turbulence generator (STG), digital filter method (DFM) and synthetic eddy method (SEM). The development of wall friction, flow structure and Reynolds stress under different synthetic turbulence inflow conditions is studied, and the performance of each method is evaluated in wall turbulence. In the simulation of incompressible and compressible turbulent boundary layers, STG method shows the shorter recovery distance. The flow field structure and Reynolds stress development of STG also have advantages over DFM. In addition to velocity fluctuations, compressible turbulent boundary layer also includes fluctuations of thermodynamic variables such as temperature, density and pressure. Furthermore, in the numerical simulation of turbulent boundary layer in high Mach number, ignoring the thermodynamic fluctuations may reduce the speed at which the boundary layer return to fully-developed turbulence flow. The ST method can only provide velocity fluctuations, while the strong Reynolds analogy methods can obtain thermodynamic fluctuations based on velocity fluctuations. Therefore, based on the velocity fluctuations given by STG, thermodynamic fluctuation is added at the inlet by several strong Reynolds analogy methods (SRA, GSRA, HSRA), and the effects on the development of compressible turbulent boundary layer are evaluated. The results show that the addition of thermodynamic fluctuation has little effect on the development of friction and Reynolds stress, but has a significant effect on the development of thermodynamic quantities in the flow field. Among them, using GSRA generating thermodynamic fluctuation as inlet boundary condition has the fastest thermodynamic recovery.
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图 2 不同合成湍流入口下摩阻对比
Figure 2. Comparison of frictions of different inlet boundary conditions
图 3 流向速度着色的Q等值面(Q = 0.05)
Figure 3. Isosurfaces of the Q-criterion coloured by streamwise velocity(Q = 0.05)
图 4 槽道y/h = 0.2横截面涡量云图
Figure 4. Contours of Vorticity, over the x-z plane at y/h = 0.2 in channel flow
图 5 不同合成湍流入口下$ R_{12}^{} $随流向变化 (续)
Figure 5. $ R_{12}^{} $ development along streamwise using different inlet conditions (continued)
图 6 不同合成湍流入口下$ R_{11}^{} $随流向变化
Figure 6. $ R_{11}^{} $ development along streamwise using different inlet conditions
图 7 不同合成湍流入口下$ R_{22}^{} $随流向变化
Figure 7. $ R_{22}^{} $ development along streamwise using different inlet conditions
图 9 不同合成湍流入口摩阻对比
Figure 9. Comparison of frictions of different inlet boundary conditions
图 10 边界层内Q值等值面(Q = 0.2) (续)
Figure 10. Isosurfaces of the Q-criterion in boundary layer (Q = 0.2) (continued)
图 11 湍流边界层$ y/{\delta _0} = 0.2 $横截面涡量云图
Figure 11. Contours of Vorticity, over the x-z plane at $ y/{\delta _0} = 0.2 $ in turbulent boundary layer
图 12 不同合成湍流入口下$ R_{12}^* $随流向变化
Figure 12. $ R_{12}^* $ development along streamwise using different inlet conditions
图 13 不同合成湍流入口下$ R_{11}^* $随流向变化 (续)
Figure 13. $ R_{11}^* $development along streamwise using different inlet conditions (continued)
图 14 不同合成湍流入口下$ R_{22}^* $随流向变化
Figure 14. $ R_{22}^* $development along streamwise using different inlet conditions
图 15 不同入口条件下摩阻曲线
Figure 15. Comparison of frictions of different inlet boundary conditions
图 19 Ma = 2.5和5.0下不同流向位置$ f $
Figure 19. $ f $distribution in various streamwise position of Ma = 2.5, 5.0
表 1 来流条件
Table 1. Inlet conditions
来流速度 来流雷诺数${{Re} _\theta }$ 来流温度Tinf/K 壁面温度Tw/K Ma = 2.5 1200 228.0 300.0 
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表 2 来流条件
Table 2. Inlet conditions
来流速度 来流雷诺数${{Re} _\theta }$ 来流温度
Tinf/K壁面温度
Tw/KMa = 5.0 2300 228.1 433.4
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表 3 入口条件中强雷诺比拟系数表
Table 3. SRA’s coefficients
a c 强雷诺比拟
(SRA)0.0 1.0 Gaviglio’s强雷诺比拟
(GSRA)1.0 1.0 Huang’s强雷诺比拟
(HSRA)1.0 0.7
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