It is widely accepted that a robust and efficient method to compute the linear spatial amplified rate ought to be developed in three-dimensional （3D） boundary layers to predict the transition with the e^N method, es...It is widely accepted that a robust and efficient method to compute the linear spatial amplified rate ought to be developed in three-dimensional （3D） boundary layers to predict the transition with the e^N method, especially when the boundary layer varies significantly in the spanwise direction. The 3D-linear parabolized stability equation （3D- LPSE） approach, a 3D extension of the two-dimensional LPSE （2D-LPSE）, is developed with a plane-marching procedure for investigating the instability of a 3D boundary layer with a significant spanwise variation. The method is suitable for a full Mach number region, and is validated by computing the unstable modes in 2D and 3D boundary layers, in both global and local instability problems. The predictions are in better agreement with the ones of the direct numerical simulation （DNS） rather than a 2D-eigenvalue problem （EVP） procedure. These results suggest that the plane-marching 3D-LPSE approach is a robust, efficient, and accurate choice for the local and global instability analysis in 2D and 3D boundary layers for all free-stream Mach numbers.展开更多
The evolution of Gortler vortices and its interaction with other instabilities are investigated in this paper. Both the Mack mode and the Gortler mode exist in hypersonic boundary-layer flows over concave surfaces, an...The evolution of Gortler vortices and its interaction with other instabilities are investigated in this paper. Both the Mack mode and the Gortler mode exist in hypersonic boundary-layer flows over concave surfaces, and their interactions are crucially important in boundary layer transition. We carry out a direct numerical simulation to explore the interaction between the GOrtler and the oblique Mack mode. The results indicate that the interaction between the forced Gortler mode and the oblique Mack mode promotes the onset of the transition. The forced oblique Mack mode is susceptible to nonlinear interaction. Because of the development of the GOrtler mode, the forced Mack mode and other harmonic modes are excited.展开更多
Gortler vortices are key issues in the design of gas turbine blades. The present study deals with flow visualization over concave surface for gas turbine applications. The aim is to comprehend qualitatively the flow t...Gortler vortices are key issues in the design of gas turbine blades. The present study deals with flow visualization over concave surface for gas turbine applications. The aim is to comprehend qualitatively the flow trends, particularly the Gortler vortices formation and development. Gortler vortices have the shape of mushroom-like vortices regularly spaced at 25 mm. These vortices grow and increase in strength more rapidly along the surface in the case of the same grid of turbulence applied to the measuring section. The curvature radius of the studied blade is 0.5 m and the stream turbulence intensity level is 2.6%. The velocity field is measured by hot wire anemometer in the streamwise direction. The velocity profile is found to be highly distorted by the momentum transfer associated with Gortler vortices. The results are compared to Blasius flow and to literature data for a blade with curvature radius equal to 2 m.展开更多
Competition of multiple Gortler modes in hypersonic boundary layer flows are investigated with the local and marching methods. The wall-layer mode （mode W） and the trapped-layer mode （mode T） both occur in the com...Competition of multiple Gortler modes in hypersonic boundary layer flows are investigated with the local and marching methods. The wall-layer mode （mode W） and the trapped-layer mode （mode T） both occur in the compressible boundary layer where there exists a temperature adjustment layer near the upper edge. The mode T has the largest growth rate at a lower Gortler number while the mode W dominates at larger G/Srtler numbers. These two modes are both responsible for the flow transition in the hypersonic flows especially when Gortler number is in the high value range in which the crossover of these two modes takes place. Such high Gortler numbers are virtually far beyond the neutral regime. The nonparallel base flows, therefore, cease to influence the stability behavior of the Gortler modes. The effects of the Mach number on the multiple Gortler modes are studied within a chosen Mach number of 0.95, 2, 4 and 6. When the flow Mach number is sufficiently large, e.g., Ma ≥4, the growth rate crossover of the mode T and mode W occurs both in the conventional G-β map as well as on the route downstream for a fixed wavelength disturbance. Four particular regions （Region T, T-W, W-T and W） around the crossover point are highlighted with the marching analysis and the result matches that of the local analysis. The initial disturbance of a normal mode maintains the shape in its corresponding dominating region while a shape-transformation occurs outside this region.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11272183,11572176,11402167,11202147,and 11332007)the National Program on Key Basic Research Project of China(No.2014CB744801)
文摘It is widely accepted that a robust and efficient method to compute the linear spatial amplified rate ought to be developed in three-dimensional （3D） boundary layers to predict the transition with the e^N method, especially when the boundary layer varies significantly in the spanwise direction. The 3D-linear parabolized stability equation （3D- LPSE） approach, a 3D extension of the two-dimensional LPSE （2D-LPSE）, is developed with a plane-marching procedure for investigating the instability of a 3D boundary layer with a significant spanwise variation. The method is suitable for a full Mach number region, and is validated by computing the unstable modes in 2D and 3D boundary layers, in both global and local instability problems. The predictions are in better agreement with the ones of the direct numerical simulation （DNS） rather than a 2D-eigenvalue problem （EVP） procedure. These results suggest that the plane-marching 3D-LPSE approach is a robust, efficient, and accurate choice for the local and global instability analysis in 2D and 3D boundary layers for all free-stream Mach numbers.
文摘The evolution of Gortler vortices and its interaction with other instabilities are investigated in this paper. Both the Mack mode and the Gortler mode exist in hypersonic boundary-layer flows over concave surfaces, and their interactions are crucially important in boundary layer transition. We carry out a direct numerical simulation to explore the interaction between the GOrtler and the oblique Mack mode. The results indicate that the interaction between the forced Gortler mode and the oblique Mack mode promotes the onset of the transition. The forced oblique Mack mode is susceptible to nonlinear interaction. Because of the development of the GOrtler mode, the forced Mack mode and other harmonic modes are excited.
文摘Gortler vortices are key issues in the design of gas turbine blades. The present study deals with flow visualization over concave surface for gas turbine applications. The aim is to comprehend qualitatively the flow trends, particularly the Gortler vortices formation and development. Gortler vortices have the shape of mushroom-like vortices regularly spaced at 25 mm. These vortices grow and increase in strength more rapidly along the surface in the case of the same grid of turbulence applied to the measuring section. The curvature radius of the studied blade is 0.5 m and the stream turbulence intensity level is 2.6%. The velocity field is measured by hot wire anemometer in the streamwise direction. The velocity profile is found to be highly distorted by the momentum transfer associated with Gortler vortices. The results are compared to Blasius flow and to literature data for a blade with curvature radius equal to 2 m.
基金supported by the National Natural Science Foundation of China(Grant Nos.10932005 and 11202115)
文摘Competition of multiple Gortler modes in hypersonic boundary layer flows are investigated with the local and marching methods. The wall-layer mode （mode W） and the trapped-layer mode （mode T） both occur in the compressible boundary layer where there exists a temperature adjustment layer near the upper edge. The mode T has the largest growth rate at a lower Gortler number while the mode W dominates at larger G/Srtler numbers. These two modes are both responsible for the flow transition in the hypersonic flows especially when Gortler number is in the high value range in which the crossover of these two modes takes place. Such high Gortler numbers are virtually far beyond the neutral regime. The nonparallel base flows, therefore, cease to influence the stability behavior of the Gortler modes. The effects of the Mach number on the multiple Gortler modes are studied within a chosen Mach number of 0.95, 2, 4 and 6. When the flow Mach number is sufficiently large, e.g., Ma ≥4, the growth rate crossover of the mode T and mode W occurs both in the conventional G-β map as well as on the route downstream for a fixed wavelength disturbance. Four particular regions （Region T, T-W, W-T and W） around the crossover point are highlighted with the marching analysis and the result matches that of the local analysis. The initial disturbance of a normal mode maintains the shape in its corresponding dominating region while a shape-transformation occurs outside this region.
