The parabolized stability equations （PSEs） for high speed flows, especially supersonic and hypersonic flows, are derived and used to analyze the nonparallel boundary layer stability. The proposed numerical technique...The parabolized stability equations （PSEs） for high speed flows, especially supersonic and hypersonic flows, are derived and used to analyze the nonparallel boundary layer stability. The proposed numerical techniques for solving PSE include the following contents： introducing the efficiently normal transformation of the boundary layer, improving the computational accuracy by using a high-order differential scheme near the wall, employing the predictor-corrector and iterative approach to satisfy the important normalization condition, and implementing the stable spatial marching. Since the second mode dominates the growth of the disturbance in high Mach number flows, it is used in the computation. The evolution and characteristics of the boundary layer stability in the high speed flow are demonstrated in the examples. The effects of the nonparallelizm, the compressibility and the cooling wall on the stability are analyzed. And computational results are in good agreement with the relevant data.展开更多
Linear and nonlinear evolutions of TS wave and high-order harmonic waves in boundary layers are studied based on the parabolic stability equation （PSE）. Initial conditions are derived by the local method with the La...Linear and nonlinear evolutions of TS wave and high-order harmonic waves in boundary layers are studied based on the parabolic stability equation （PSE）. Initial conditions are derived by the local method with the Landau expansion. The evolution process and characteristics of the disturbance amplitude and the velocity profile, etc. , especially stronger nonlinear effects, are computed by an efficient numerical method. Effects and regulations of different initial amplitudes, frequencies and pressure gradients on the evolution of disturbances are explored, which are directly relative to the stability and the transition in boundary layers. Simulation results are in good agreement with the data of the accuracy direct numerical simulation （DNS） using full Navier-Stokes equations.展开更多
The transition criterion in the improved eN method is that transition would occur whenever the velocity amplitude of disturbance reaches 1%-2% of the free stream velocity,while in the conventional eN method,the N fact...The transition criterion in the improved eN method is that transition would occur whenever the velocity amplitude of disturbance reaches 1%-2% of the free stream velocity,while in the conventional eN method,the N factor is an empirical factor.In this paper the reliability of this key assumption in the improved eN method is checked by results of transition prediction by using the Parabolized Stability Equations(PSE).Transition locations of an incompressible boundary layer and a hypersonic boundary layer at Mach number 6 on a flat plate are predicted by both the improved eN method and the PSE method.Results from both methods agree fairly well with each other,implying that the transition criterion proposed in the improved eN method is reliable.展开更多
Nonlinear parabolized stability equations are employed in this work to investigate the nonlinear development of the G6rtler insta- bility up to the saturation stage. The perturbed boundary layer is highly inflectional...Nonlinear parabolized stability equations are employed in this work to investigate the nonlinear development of the G6rtler insta- bility up to the saturation stage. The perturbed boundary layer is highly inflectional both in the normalwise and spanwise directions and receptive to the secondary instabilities. The Floquet theory is applied to solve the fundamental, subharmonic and detuned secondary instabilities. With the Gortler-vortices-distorted base flow, two classes of secondary disturbances, i.e. odd modes and even modes, are identified according to the eigenfunctions of the disturbances. These modes may result in different patterns in the late stages of the transition process. Li and Malik [ 1 ] have shown the sinuous and varicose types of breakdown originating from the odd and even modes. The current study focuses on the four most amplified modes termed the even modes I ＆ Ⅱ and odd modes I ＆ lI. Odd mode II was missing in the work of Li and Malik [1] probably due to their inviscid simplifeation. The detuned modes are confirmed to be less amplifed than the fundamental （for the odd mode I） and subharmonic modes （for even modes I ＆ II and the odd mode II）.展开更多
文摘The parabolized stability equations （PSEs） for high speed flows, especially supersonic and hypersonic flows, are derived and used to analyze the nonparallel boundary layer stability. The proposed numerical techniques for solving PSE include the following contents： introducing the efficiently normal transformation of the boundary layer, improving the computational accuracy by using a high-order differential scheme near the wall, employing the predictor-corrector and iterative approach to satisfy the important normalization condition, and implementing the stable spatial marching. Since the second mode dominates the growth of the disturbance in high Mach number flows, it is used in the computation. The evolution and characteristics of the boundary layer stability in the high speed flow are demonstrated in the examples. The effects of the nonparallelizm, the compressibility and the cooling wall on the stability are analyzed. And computational results are in good agreement with the relevant data.
文摘Linear and nonlinear evolutions of TS wave and high-order harmonic waves in boundary layers are studied based on the parabolic stability equation （PSE）. Initial conditions are derived by the local method with the Landau expansion. The evolution process and characteristics of the disturbance amplitude and the velocity profile, etc. , especially stronger nonlinear effects, are computed by an efficient numerical method. Effects and regulations of different initial amplitudes, frequencies and pressure gradients on the evolution of disturbances are explored, which are directly relative to the stability and the transition in boundary layers. Simulation results are in good agreement with the data of the accuracy direct numerical simulation （DNS） using full Navier-Stokes equations.
基金supported by the National Natural Science Foundation of China (Grant No.11002098)the National Basic Research Program of China (Grant No.2009CB724103)the Specialized Research Fund for the Doctoral Program of Higher Education
文摘The transition criterion in the improved eN method is that transition would occur whenever the velocity amplitude of disturbance reaches 1%-2% of the free stream velocity,while in the conventional eN method,the N factor is an empirical factor.In this paper the reliability of this key assumption in the improved eN method is checked by results of transition prediction by using the Parabolized Stability Equations(PSE).Transition locations of an incompressible boundary layer and a hypersonic boundary layer at Mach number 6 on a flat plate are predicted by both the improved eN method and the PSE method.Results from both methods agree fairly well with each other,implying that the transition criterion proposed in the improved eN method is reliable.
基金supported by the National Natural Science Foundation of China(Grant Nos.10932005 and 11202115)
文摘Nonlinear parabolized stability equations are employed in this work to investigate the nonlinear development of the G6rtler insta- bility up to the saturation stage. The perturbed boundary layer is highly inflectional both in the normalwise and spanwise directions and receptive to the secondary instabilities. The Floquet theory is applied to solve the fundamental, subharmonic and detuned secondary instabilities. With the Gortler-vortices-distorted base flow, two classes of secondary disturbances, i.e. odd modes and even modes, are identified according to the eigenfunctions of the disturbances. These modes may result in different patterns in the late stages of the transition process. Li and Malik [ 1 ] have shown the sinuous and varicose types of breakdown originating from the odd and even modes. The current study focuses on the four most amplified modes termed the even modes I ＆ Ⅱ and odd modes I ＆ lI. Odd mode II was missing in the work of Li and Malik [1] probably due to their inviscid simplifeation. The detuned modes are confirmed to be less amplifed than the fundamental （for the odd mode I） and subharmonic modes （for even modes I ＆ II and the odd mode II）.
