The process of evolution, especially that of nonlinear evolution, of C-type instability of laminar-turbulent flow transition in nonparallel boundary layers are studied by means of a newly developed method called parab...The process of evolution, especially that of nonlinear evolution, of C-type instability of laminar-turbulent flow transition in nonparallel boundary layers are studied by means of a newly developed method called parabolic stability equations （PSE）. Initial conditions, which are very important for the nonlinear problem, are investigated by computing initial solution of the harmonic waves, modifying the mean-flow-distortion, and giving initial value of TS wave and its subharmonic waves at initial station by solving linear PSE. A numerical method with high-order accuracy are developed in the text, the key normalization conditions in the PSE are satisfied, and nonlinear PSE are solved efficiently and implemented stably by the spatial marching. It has been shown that the computed process of nonlinear evolution of C-type instability in Blasius boundary layer is in good agreement with the experimental results.展开更多
An extended differential quadrature method is used to compute nonlinear partial differential equations for tbree-dimensional laminar boundary layer now in this paPer. The key technique to differential quadrature, whi...An extended differential quadrature method is used to compute nonlinear partial differential equations for tbree-dimensional laminar boundary layer now in this paPer. The key technique to differential quadrature, which is used in determining weighting coefficients for discretization of any order partial derivative, is investigated. The method of computing different weighting coefficients is presented. Three dimensional boundary layer equations are discretized by the differential quadrature method, and relative formula is obtained. The resulting scheme is applied to the computation of examples, which shows that the differential quadrature method can achieve rather high accurate solution using much less grid points than those of other methods, suck as finite difference and finite element methods.展开更多
The nonlinear evolution process of new vortex structures at the late-stage of the transition, including the 3-D spatial structure of barrel-shaped vortex and "dark spots" structure observed by experiment res...The nonlinear evolution process of new vortex structures at the late-stage of the transition, including the 3-D spatial structure of barrel-shaped vortex and "dark spots" structure observed by experiment research, has been confirmed by our computational results. The formation mechanisms of these structures have been explored. It is revealed that the new vortex structures, the ring-like vortex chain and induced disturbance velocities play a dominant role in the generation of turbulent spots.展开更多
文摘The process of evolution, especially that of nonlinear evolution, of C-type instability of laminar-turbulent flow transition in nonparallel boundary layers are studied by means of a newly developed method called parabolic stability equations （PSE）. Initial conditions, which are very important for the nonlinear problem, are investigated by computing initial solution of the harmonic waves, modifying the mean-flow-distortion, and giving initial value of TS wave and its subharmonic waves at initial station by solving linear PSE. A numerical method with high-order accuracy are developed in the text, the key normalization conditions in the PSE are satisfied, and nonlinear PSE are solved efficiently and implemented stably by the spatial marching. It has been shown that the computed process of nonlinear evolution of C-type instability in Blasius boundary layer is in good agreement with the experimental results.
文摘An extended differential quadrature method is used to compute nonlinear partial differential equations for tbree-dimensional laminar boundary layer now in this paPer. The key technique to differential quadrature, which is used in determining weighting coefficients for discretization of any order partial derivative, is investigated. The method of computing different weighting coefficients is presented. Three dimensional boundary layer equations are discretized by the differential quadrature method, and relative formula is obtained. The resulting scheme is applied to the computation of examples, which shows that the differential quadrature method can achieve rather high accurate solution using much less grid points than those of other methods, suck as finite difference and finite element methods.
基金supported by the National Natural Science Foundation of China (Grant No. 10772082)the Doctoral Foundation of Ministry of Education of China (Grant No. 20070287005)AFOSR (Grant No. FA9550-08-1-0201)
文摘The nonlinear evolution process of new vortex structures at the late-stage of the transition, including the 3-D spatial structure of barrel-shaped vortex and "dark spots" structure observed by experiment research, has been confirmed by our computational results. The formation mechanisms of these structures have been explored. It is revealed that the new vortex structures, the ring-like vortex chain and induced disturbance velocities play a dominant role in the generation of turbulent spots.
