基于格子Boltzmann方程的大涡模拟对湍流时空关联性的研究

Time-Space Correlations of Isotropic Turbulence by Lattice-Boltzmann-Based Large Eddy Simulation

将格子Boltzmann方程和大涡模拟(LBE-LES)相结合,提出适应于格子Boltzmann方法(LBM)的涡黏性亚格子尺度模型,开展均匀各向同性湍流时空关联性的研究.采用D3Q19格式计算湍流的三维能谱、湍动能耗散率和其它高阶统计量,与实验和直接数值模拟结果的比较表明,该模型比传统涡黏模型有明显改进.考察了不同亚格子模型预测湍流频率波数能量谱的能力,结果表明,尺度涡产生的横扫作用是造成小尺度涡时间去关联的主要因素,不同波数的频率能量谱之间有一定的相似性,横扫速度是描述湍流频率波数能量谱的特征量.

Using combined method of large-eddy simulations with lattice Boltzmann （LES-LBM）, an eddy-viscosity sub-grid scale （SGS） model has been developed, which is suitable for the LES- LBM framework to study space-time correlation of homogeneous isotropic turbulence. The lattice Boltzmann algorithm of 19-velocity D3Q19 lattice mode was implemented to calculate time evolution of the kinetic energy, the decay exponents of the dissipation rate, the instantaneous energy spectra and the high-order statistical quantities. Comparing with the evaluations of the model coefficients as a function of sub-grid activity obtained from direct numerical simulation （DNS） and other experiments, the obtained results from LES-LBM based new SGS model exhibit more satisfactory behavior than that of the classical one. Further, the abilities of several SGS models to predict the frequency-wave number energy spectra in turbulent flows were examined. It is found that the temporal de-correlation of smaller scales is determined by random sweeping motion of larger scales, the normalized frequency energy spectra of different wave number exhibit a common similarity to a certain extent and the sweeping velocity dominates the frequency-wave number energy spectra.