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Temporal–Spatial Evolution of Kinetic and Thermal Energy Dissipation Rates in a Three-Dimensional Turbulent Rayleigh–Taylor Mixing Zone

1
Basic Courses Department, Shandong University of Science and Technology, Taian 271019, China
2
State-Province Joint Engineering Lab of Fluid Transmission System Technology, Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China
3
Department of Aeronautics, Imperial College London, London SW72AZ, UK
*
Authors to whom correspondence should be addressed.
Entropy 2020, 22(6), 652; https://doi.org/10.3390/e22060652
Received: 12 May 2020 / Revised: 7 June 2020 / Accepted: 10 June 2020 / Published: 12 June 2020
(This article belongs to the Special Issue Evolution and Thermodynamics)
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 t/τ ≥ 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. View Full-Text
Keywords: Rayleigh–Taylor; energy dissipation; heat transport; lattice Boltzmann method Rayleigh–Taylor; energy dissipation; heat transport; lattice Boltzmann method
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Guo, W.; Guo, X.; Wei, Y.; Zhang, Y. Temporal–Spatial Evolution of Kinetic and Thermal Energy Dissipation Rates in a Three-Dimensional Turbulent Rayleigh–Taylor Mixing Zone. Entropy 2020, 22, 652.

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