Pseudo-potential Model And Variational Method For Direct/Inverse Problems Of 3-D Compressible Rotational Flow In A Rotating System

The present dissertation consists of three parts: (1) The pseudo-potential function model for 3-D inviscid rotational rotor flow is systematically established , which is theoretically rigorous and generally applicable; (2) The Variational Principles for 2-D compressible rotational flow using pseudo-potential model encompassing pseudo-potential function and vorticity-potential function are established ,and the basic aerodynamic equations in terms of the pseudo-potential function are derived in image-plane; (3) Three kinds of quasi-variational formulation for 3-D vorticity-potential model are established.The main work of the thesis can be outlined as follow : The pseudo-potential function and vortex potential functions are derived by means of the term-condensing method ,this model not only remains the basic advantages of potential function model ,but also applies to the rotational flow. It is a physically self-consistent model and is a rational extension of the potential function to rotational flow. It removes the non-uniqueness of the potential function solutions at transonic speeds due to ignoring entropy gradient behind the shock.The general form of the fundamental equations of aerodynamics in terms of the pseudo-potential function, the vortex potential function and the enthalpy are derived in the general non-orthogonalcurvilinear coordinate system by means of both tensor calculus and Jacobians. To facilitate the numerical solution, an image-space based on a body-filled curvilinear coordinate system is introduced .Using the pseudo-potential function, Variational principles for direct and inverse problems of 2-D steady rotational compressible flow are developed rigorously.Three alternative formulations for the vortex-potential equations are provided.All these lay a firm theoretical basis for its application to computational fluid dynamics.