Parameter-free symmetry-preserving regularization modeling of a turbulent differentially heated cavity
Parameter-free symmetry-preserving regularization modeling of a turbulent differentially heated cavity
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DOI：
10.1016/j.compfluid.2010.06.016
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发表时间：
2010-12
影响因子：
2.8
通讯作者：
F. Trias;R. Verstappen;A. Gorobets;M. Soria;A. Oliva
中科院分区：
文献类型：
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作者：
F. Trias;R. Verstappen;A. Gorobets;M. Soria;A. Oliva
由于浮力驱动流动的直接数值模拟无法在高瑞利数下进行计算，因此需要寻找一种动态上不那么复杂的数学公式。在寻求这样一个公式的过程中，我们考虑非线性的正则化（光滑近似）：通过涡旋拉伸来改变对流项以减少小尺度运动的产生。在此过程中，我们建议精确地保持对流项的对称性和守恒性质。这一要求产生了一类新的正则化[computer Fluids 2008；[07:88 . 87]以一种无条件稳定的方式限制越来越小的运动尺度的对流产生，这意味着速度在能量范数（在二维中也是：熵范数）中不会爆炸。用于求解控制方程的数值算法也保持了对称性和守恒性。本文提出了一种动态确定正则化参数（局部滤波长度）的判据：该判据是基于涡流的拉伸必须在网格设定的尺度上停止的要求。因此，所提出的方法构成了一个无参数湍流模型。对高宽比为4的空气填充（Pr=0.71）差热腔内的三维自然对流流进行了正则化测试。与瑞利数6.4×108 < Ra > 1011的DNS结果直接比较，即使对于非常粗糙的网格，也显示出相当好的一致性。最后，在Ra为1017的情况下进行仿真，验证了该方法的鲁棒性。在Ra的研究范围内，得到了Nusselt数的2/7标度定律。
Since direct numerical simulations of buoyancy driven flows cannot be computed at high Rayleigh numbers, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider regularizations (smooth approximations) of the non-linearity: the convective term is altered to reduce the production of small scales of motion by means of vortex stretching. In doing so, we propose to preserve the symmetry and conservation properties of the convective terms exactly. This requirement yielded a novel class of regularizations [Comput Fluids 2008;37:887] that restrain the convective production of smaller and smaller scales of motion in an unconditionally stable manner, meaning that the velocity cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. In the present work, a criterion to determine dynamically the regularization parameter (local filter length) is proposed: it is based on the requirement that the vortex stretching must stop at the scale set by the grid. Therefore, the proposed method constitutes a parameter-free turbulence model. The resulting regularization method is tested for a 3D natural convection flow in an air-filled (Pr=0.71) differentially heated cavity of height aspect ratio 4. Direct comparison with DNS results at Rayleigh number 6.4×108⩽Ra⩽1011shows fairly good agreement even for very coarse grids. Finally, the robustness of the method is tested by performing simulations with Ra up to 1017. A 2/7 scaling law of Nusselt number has been obtained for the investigated range of Ra.