The parabolized stability equation (PSE) was derived to study the linear stability of particle-laden flow in growing Blasius boundary layer. The stability characteristics for various Stokes numbers and particle concen...The parabolized stability equation (PSE) was derived to study the linear stability of particle-laden flow in growing Blasius boundary layer. The stability characteristics for various Stokes numbers and particle concentrations were analyzed after solving the equation numerically using the perturbation method and finite difference. The inclusion of the nonparallel terms produces a reduction in the values of the critical Reynolds number compared with the parallel flow. There is a critical value for the effect of Stokes number, and the critical Stokes number being about unit, and the most efficient instability suppression takes place when Stokes number is of order 10. But the presence of the nonparallel terms does not affect the role of the particles in gas. That is, the addition of fine particles (Stokes number is much smaller than 1) reduces the critical Reynolds number while the addition of coarse particles (Stokes number is much larger than 1) enhances it. Qualitatively the effect of nonparallel mean flow is the same as that for the case of plane parallel flows.展开更多
The nonlinear stability problem in nonparallel boundary layer flow fortwo-dimensional disturbances was studied by using a newly presented method called ParabolicStability Equations (PSE). A series of new modes generat...The nonlinear stability problem in nonparallel boundary layer flow fortwo-dimensional disturbances was studied by using a newly presented method called ParabolicStability Equations (PSE). A series of new modes generated by the nonlinear interaction ofdisturbance waves were tabu-lately analyzed, and the Mean Flow Distortion (MFD) was numericallygiven. The computational techniques developed, including the higher-order spectral method and themore effective algebraic mapping, increased greatly the numerical accuracy and the rate ofconvergence. With the predictor-corrector approach in the marching procedure, the normalizationcondition was satisfied, and the stability of numerical calculation could be ensured. With differentinitial amplitudes, the nonlinear stability of disturbance wave was studied. The results ofexamples show good agreement with the data given by the DNS using the full Navier-Stokes equations.展开更多
This article studies the nonlinear evolution of disturbance waves in supersonic nonparallel boundary layer flows by using nonlinear parabolic stability equations （NPSE）. An accurate numerical method is developed to ...This article studies the nonlinear evolution of disturbance waves in supersonic nonparallel boundary layer flows by using nonlinear parabolic stability equations （NPSE）. An accurate numerical method is developed to solve the equations and march the NPSE in a stable manner. Through computation,are obtained the curves of amplitude and disturbance shape function of harmonic waves. Especially are demonstrated the physical characteristics of nonlinear stability of various harmonic waves,including instantaneous stream wise vortices,spanwise vortices and Λ structure etc,and are used to study and analyze the mechanism of the transition process. The calculated results have evidenced the effectiveness of the proposed NPSE method to research the nonlinear stability of the supersonic boundary layers.展开更多
基金Project supported by the National Natural Science Foundation ofChina (No. 10372090) and the Doctoral Program of Higher Educationof China (No. 20030335001)
文摘The parabolized stability equation (PSE) was derived to study the linear stability of particle-laden flow in growing Blasius boundary layer. The stability characteristics for various Stokes numbers and particle concentrations were analyzed after solving the equation numerically using the perturbation method and finite difference. The inclusion of the nonparallel terms produces a reduction in the values of the critical Reynolds number compared with the parallel flow. There is a critical value for the effect of Stokes number, and the critical Stokes number being about unit, and the most efficient instability suppression takes place when Stokes number is of order 10. But the presence of the nonparallel terms does not affect the role of the particles in gas. That is, the addition of fine particles (Stokes number is much smaller than 1) reduces the critical Reynolds number while the addition of coarse particles (Stokes number is much larger than 1) enhances it. Qualitatively the effect of nonparallel mean flow is the same as that for the case of plane parallel flows.
文摘The nonlinear stability problem in nonparallel boundary layer flow fortwo-dimensional disturbances was studied by using a newly presented method called ParabolicStability Equations (PSE). A series of new modes generated by the nonlinear interaction ofdisturbance waves were tabu-lately analyzed, and the Mean Flow Distortion (MFD) was numericallygiven. The computational techniques developed, including the higher-order spectral method and themore effective algebraic mapping, increased greatly the numerical accuracy and the rate ofconvergence. With the predictor-corrector approach in the marching procedure, the normalizationcondition was satisfied, and the stability of numerical calculation could be ensured. With differentinitial amplitudes, the nonlinear stability of disturbance wave was studied. The results ofexamples show good agreement with the data given by the DNS using the full Navier-Stokes equations.
基金National Natural Science Foundation of China (10772082)Doctoral Foundation of Ministry of Education of China (20070287005)
文摘This article studies the nonlinear evolution of disturbance waves in supersonic nonparallel boundary layer flows by using nonlinear parabolic stability equations （NPSE）. An accurate numerical method is developed to solve the equations and march the NPSE in a stable manner. Through computation,are obtained the curves of amplitude and disturbance shape function of harmonic waves. Especially are demonstrated the physical characteristics of nonlinear stability of various harmonic waves,including instantaneous stream wise vortices,spanwise vortices and Λ structure etc,and are used to study and analyze the mechanism of the transition process. The calculated results have evidenced the effectiveness of the proposed NPSE method to research the nonlinear stability of the supersonic boundary layers.
