The Research And Computation About The Rapid Distortion Theory

The Rapid distortion theory (RDT) is a method to analyze the linear distortion of rapid change turbulence (RCT). The mean velocity gradient was assumed to be constant and the transport equation is linearized. The development of the incompressible and compressible RDT method is introduced in the present study. Then the method is applied in the computation and analysis of several typical compressible and incompressible turbulent flows.In the first chapter the development of the incompressible and compressible RDT method is introduced. Since the development by Batchelor and Proudman in 1954, the RDT method was often used in the incompressible rapid distortion turbulence. And then the method is applied in the compressible flow. Compared to the incompressible case, the RDT method for compressible flow adds a parameter M_d= Sl /a and shows the difference in the time scale. The effect of compressibility on the RDT method is discussed based on the turbulence energy equation.In the second chapter the method of the RDT theory and corresponding numerical method for compressible and incompressible flow are introduced in details. The equation in the wave number space is derived through the DFT transform. Then we analyze the second-moment equations and their closure in the physics space. The control equations of velocity and pressure for compressible flow are deduced under the quasi-isentropic condition. The velocity fluctuation in the wave number space is decoupled into three modes and the interaction between the different modes can be investigated through the computational results.In the third chapter several typical incompressible flows are simulated and analyzed with the above-mentioned. The affection of the production and the diffusion is discussed. In the present study, the factors which affect the numerical results are also studied.In last chapter some typical compressible turbulent flows are simulated with the RDT method. The analytical solution to the spherical compression is afforded. And then the interaction of the several modes is analyzed. And the last, the affection of the distortion Mach is discussed.