Guo Wenjing, Guo Xiurong, Wei Yikun, Zhang Yan
Basic Courses Department, Shandong University of Science and Technology, Taian 271019, China.
State-Province Joint Engineering Lab of Fluid Transmission System Technology, Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China.
Entropy (Basel). 2020 Jun 12;22(6):652. doi: 10.3390/e22060652.
In this work, the temporal-spatial evolution of kinetic and thermal energy dissipation rates in three-dimensional (3D) turbulent Rayleigh-Taylor (RT) mixing are investigated numerically by the lattice Boltzmann method. The temperature fields, kinetic and thermal energy dissipation rates with temporal-spatial evolution, the probability density functions, the fractal dimension of mixing interface, spatial scaling law of structure function for the kinetic and the thermal energy dissipation rates in 3D space are analysed in detail to provide an improved physical understanding of the temporal-spatial dissipation-rate characteristic in the 3D turbulent Rayleigh-Taylor mixing zone. Our numerical results indicate that the kinetic and thermal energy dissipation rates are concentrated in areas with large gradients of velocity and temperature with temporal evolution, respectively, which is consistent with the theoretical assumption. However, small scale thermal plumes initially at the section of half vertical height increasingly develop large scale plumes with time evolution. The probability density function tail of thermal energy dissipation gradually rises and approaches the stretched exponent function with temporal evolution. The slope of fractal dimension increases at an early time, however, the fractal dimension for the fluid interfaces is 2.4 at times / ≥ 2, which demonstrates the self-similarity of the turbulent RT mixing zone in 3D space. It is further demonstrated that the second, fourth and sixth-order structure functions for velocity and temperature structure functions have a linear scaling within the inertial range.
在这项工作中，通过格子玻尔兹曼方法对三维（3D）湍流瑞利 - 泰勒（RT）混合中动能和热能耗散率的时空演化进行了数值研究。详细分析了温度场、动能和热能耗散率的时空演化、概率密度函数、混合界面的分形维数以及三维空间中动能和热能耗散率结构函数的空间标度律，以增进对三维湍流瑞利 - 泰勒混合区时空耗散率特性的物理理解。我们的数值结果表明，动能和热能耗散率分别随着时间演化集中在速度和温度梯度较大的区域，这与理论假设一致。然而，最初位于半垂直高度截面处的小尺度热羽流随着时间演化逐渐发展为大尺度羽流。热能耗散的概率密度函数尾部随着时间演化逐渐上升并趋近于拉伸指数函数。分形维数的斜率在早期增加，不过在时间(t\geq2)时流体界面的分形维数为2.4，这表明三维空间中湍流RT混合区的自相似性。进一步证明，速度和温度结构函数的二阶、四阶和六阶结构函数在惯性范围内具有线性标度。
