Theoretical and Computational Fluid Dynamics Large-eddy Simulation of the Temporal Mixing Layer Using the Clark Model
Theoretical and Computational Fluid Dynamics Large-eddy Simulation of the Temporal Mixing Layer Using the Clark Model
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通讯作者：
Bert Vreman;B. Geurts;H. Kuerten;M. Y. Hussaini
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作者：
Bert Vreman;B. Geurts;H. Kuerten;M. Y. Hussaini
从理论和计算的角度研究了大涡模拟中湍流应力张量的Clark模型。为了适用于可压缩湍流，克拉克模型已被重新制定。实际的大涡模拟弱可压缩，湍流，时间混合层表明，原来的克拉克模型的涡粘性部分引起过度耗散的能量在过渡制度。另一方面，如果忽略涡粘性部分而只保留“梯度”部分，则模型会产生不稳定性。Burgers方程的线性稳定性分析的补充克拉克模型进行，以澄清不稳定的性质。结果表明，不稳定性的增长率是无限的无粘极限和足够的（涡）粘性可以稳定的模型。将动力学过程应用于Clark模型，得到了一个既避免了原Clark模型的过度耗散又避免了“梯度”部分不稳定的模型。大涡模拟使用这个新的动态克拉克模型相比，过滤直接数值模拟时，发现产生令人满意的结果。与标准的动态涡粘性模型相比，动态克拉克模型产生更准确的预测，而与动态混合模型相比，新的模型提供了相同的精度在较低的计算工作量。
The Clark model for the turbulent stress tensor in large-eddy simulation is investigated from a theoretical and computational point of view. In order to be applicable to compressible turbulent flows, the Clark model has been reformulated. Actual large-eddy simulation of a weakly compressible, turbulent, temporal mixing layer shows that the eddy-viscosity part of the original Clark model gives rise to an excessive dissipation of energy in the transitional regime. On the other hand, the model gives rise to instabilities if the eddy-viscosity part is omitted and only the "gradient" part is retained. A linear stability analysis of the Burgers equation supplemented with the Clark model is performed in order to clarify the nature of the instability. It is shown that the growth-rate of the instability is infinite in the inviscid limit and that sufficient (eddy-)viscosity can stabilize the model. A model which avoids both the excessive dissipation of the original Clark model as well as the instability of the "gradient" part, is obtained when the dynamic procedure is applied to the Clark model. Large-eddy simulation using this new dynamic Clark model is found to yield satisfactory results when compared with a filtered direct numerical simulation. Compared with the standard dynamic eddy-viscosity model, the dynamic Clark model yields more accurate predictions, whereas compared with the dynamic mixed model the new model provides equal accuracy at a lower computational effort.