WENN Schemes Based On Piecewise Polynomial Mapping Functions And Corresponding Numerical Simulations On Detonation Combustion

In order to study the flow structures of different scales, high order schemes are more and more widely used in direct numerical simulation (DNS), large eddy simulation (LES). Aiming at enhancing the efficiency of thermodynamic cycle in aerial vehicle, more and more attention is paid to detonation combustion due to its advantages such as fast chem-ical react, short distance and high efficiency of thermodynamic cycle. It seems that the detonation combustion has a promising future. The flow structures of detonation com-bustion are very complex. It is needed to utilize high order schemes to capture the flow details.Aiming at the optimization of nonlinear weights based on WENO schemes, a new kind of mapping function has been proposed and the corresponding high order schemes have been constructed. The detonation combustion has been simulated using the new developed numerical method. The deflagration-to-detonation transition (DDT) in pulsed detonation engine (PDE) and the properties of rotating detonation engine (RDE) have been obtained. The flow instabilities in two dimensional RDE have been analyzed. The thesis is divided into six chapters, and the content of each chapter can be summarized as follows.The first chapter is introduction, which introduces the research progress in China and foreign countries of the work related to this thesis. The developments of high order difference schemes, especially the recent optimization of linear and nonlinear weights in WENO type schemes are introduced. The experiment and simulation studies of PDE and RDE are summarized. At last, the main works of this thesis are introduced.The second chapter is the study of high order finite difference schemes. In order to optimize the nonlinear weights of WENO scheme, a kind of Piecewise polynomial map-ping function (PPM) has been proposed to enhance the resolution with the premise of holding the computation stability. And the corresponding high order schemes WENN-PPMn have been constructed. Typical problems are computed using the newly developed numerical method to test its properties, and the comparisons with computational, experi-mental or theoretical solutions are carried out The reason of not suggesting single poly-nomials as mapping functions and the attempt in using PPM5 for symmetric WEN05 are also discussed. At last, PPM5 function is applied to symmetric third order scheme SYMNND, and compared with Henrick’s mapping function. The corresponding schemes SYMNND-PPM5 and SYMNND-M are constructed. Their properties have been tested through typical problems.In the third chapter, the DDT in PDE has been simulated using the new high or- der scheme WENN-PPM5. Firstly, the correctness of the computation codes is validated through the case of spherical shock-induced combustion experiment by Lehr. The verifi-cation of grid independence has been accomplished through one-dimensional detonation. At last, DDT processes with different ignition location, namely left wall,0.5D,1.0D, have been simulated and analyzed. The influence of ignition location on DDT distance and time has been discussed.In the fourth chapter, the two dimensional and three dimensional simulations of RDE have been accomplished using the new high order scheme WENN-PPM. In the two di-mensional simulation, typical structures in rotation detonation flow have been obtained. The self-sustained propagation, the distribution of parameters on inlet and outlet plane, the thermodynamic cycle and thrust performance are analyzed. The frequency and prop-agation velocity are calculated:In the three dimensional simulation, the effects of the chamber width are studied.The fifth chapter is the analysis of the instabilities in two dimensional RDE flow. The Kelvin-Helmholtz instability in the slip line between freshly detonated products and older products and the multi kinds of instabilities in the mixing region between fresh premixture and product gases are analyzed.Concluding remarks are given in the eighth chapter, in which the main work and conclusions of this thesis are summarized, and the future work is given.