Large eddy simulation of channel flows based on IPDG method and subgrid model estimation
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摘要:
在高精度改进内罚间断伽辽金（interior penalty discontinuous Galerkin，IPDG）有限元方法基础上，结合大涡模拟（large eddy simulation，LES）方法对槽道流进行数值模拟研究。研究采用4种亚格子模型（Smagorinsky模型、壁面修正Smagorinsky模型、壁面适应局部涡黏度（WALE）模型、动态模型）。体马赫数分别为0.2和0.7，分别对应不可压缩和弱可压缩流动。结果表明：在上述IPDG-LES框架内，Smagorinsky模型由于边界层内的过耗散特性精度较低；采用壁面衰减函数修正的Smagorinsky模型可以提升精度，但在近壁区黏度仍然过大；WALE模型和动态模型的结果总体上优于上述Smagorinsky模型，与参考文献较为接近。其中动态模型总体上精度最高。此外，不同模型在体马赫数0.2和0.7时表现近似，说明IPDG-LES方法对弱可压缩流动具有较好适应性。
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关键词:
- 内罚间断伽辽金（IPDG） /
- 大涡模拟 /
- 亚格子模型 /
- 槽道流 /
- 亚声速流
Abstract:Based on the method framework of the high-accuracy interior penalty discontinuous Galerkin (IPDG) finite element, combined with large eddy simulation (LES), a numerical simulation study was conducted on channel flows. Four different subgrid scale models (Smagorinsky model, Smagorinsky model with Van Driest damping function, wall-adapting local eddy-viscosity (WALE) model, and dynamic model) were employed, and the simulated Mach numbers were 0.2 and 0.7, corresponding to incompressible flow and weak compressible flow, respectively. The results indicated that, within the improved IPDG-LES framework, the Smagorinsky model exhibited lower accuracy due to its excessive dissipation characteristics within the boundary layer. The Smagorinsky model with a dumping function can improve the accuracy but still exhibited excessive viscosity near the wall. The results of WALE model and dynamic models generally outperformed the aforementioned Smagorinsky models and were closer to the reference data, with the dynamic model performing the best overall. Additionally, different models led to similar performances at Mach numbers of 0.2 and 0.7, indicating good adaptability of current IPDG-LES method to weak compressible flows.
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图 4 Van Driest变换后壁坐标系下的平均流向速度剖面（Mab=0.7）
Figure 4. Mean streamwise velocity profiles in wall coordinates with Van Driest transformation （Mab=0.7）
图 11 Dyn对应的瞬时流向速度云图，xz面为y+=10
Figure 11. Instantaneous streamwise velocity corresponding to Dyn, with the xz-plane at y+=10
图 12 Dyn对应的Q准则等值面，使用流向速度着色
Figure 12. Iso-surfaces of Q criteria corresponding to Dyn, colored based on the streamwise velocity
表 1 网格参数
Table 1. Mesh parameters
参数 Reτ mx my mz Δx+ $\dfrac{{\Delta y_{\min }^ + }}{{\Delta y_{\max }^ + }}$ Δz+ Ma02 180 23 80 23 98.2 0.98/8.4 49.1 Ma07 186 23 80 23 101.5 1.02/8.7 50.7 
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表 2 Mab=0.2时的平均参数
Table 2. Mean parameters at Mab=0.2
参数 τw Reτ uτ Cf/10−3 $\langle $uc$\rangle $ MKM（DNS） 11.21 178.0 0.0638 8.18 1.160 Sm_original 7.20 142.0 0.0507 5.14 1.234 Sm 10.37 170.4 0.0609 7.41 1.167 WALE 10.12 168.4 0.0602 7.23 1.155 Dyn 9.93 166.8 0.0595 7.09 1.160
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表 3 Mab=0.7时的平均参数
Table 3. Mean parameters at Mab=0.7
参数 τw Reτ uτ $\langle $ρw$\rangle $ $\langle $uc$\rangle $ $\langle $Tc$\rangle $ WP（DNS） 11.45 186.0 0.0615 1.0810 1.160 1.086 Sm 9.40 169.5 0.0555 1.0916 1.188 1.098 WALE 10.24 175.0 0.0585 1.0692 1.154 1.073 Dyn 10.52 177.5 0.0593 1.0688 1.160 1.072
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