Microstructures of the localized shear bands generated during explosion with a thick-walled cylinder specimen in Ti-6AI-4V alloy, were characterized by TEM and SEM. The results show that the twinning is a major mode o...Microstructures of the localized shear bands generated during explosion with a thick-walled cylinder specimen in Ti-6AI-4V alloy, were characterized by TEM and SEM. The results show that the twinning is a major mode of deformation, and the distortion-free grains in the bands with the size of 10μm in diameter were proposed to be the re-crystallization during dynamic explosion. The further observations show that the α→α2 phase transformation may occur in the bands, and this kind of transformation could be confirmed by its dark field image and electron diffraction analysis. Analysis shows that there is specified orientation between the α and α2 Phases.展开更多
This paper presents an efficient numerical method for solving the Euler equations on rectilinear grids. Wall boundary conditions on the surface of an airfoil are implemented by using their first order expansions on th...This paper presents an efficient numerical method for solving the Euler equations on rectilinear grids. Wall boundary conditions on the surface of an airfoil are implemented by using their first order expansions on the airfoil chord line, which is placed along a grid line. However, the method is not restricted to flows with small disturbances since there are no restrictions on the magnitude of the velocity or pressure perturbations. The mathematical formulation and the numerical implementation of the wall boundary conditions in a finite volume Euler code are described. Steady transonic flows are calculated about the NACA 0006, NACA 0012 and NACA 0015 airfoils, corresponding to thickness ratios of 6%, 12%, and 15%, respectively. The computed results, including surface pressure distributions, the lift coefficient, the wave drag coefficient, and the pitching moment coefficient, at angles of attack from 0° to 8° are compared with solutions at the same conditions by FLO52, a well established Euler code using body fitted curvilinear grids. Results demonstrate that the method yields acceptable accuracies even for the relatively thick NACA 0015 airfoil and at high angles of attack. This study establishes the potential of extending the method to computing unsteady fluid structure interaction problems, where the use of a stationary rectilinear grid offers substantial advantages in both computer time and human work since it would not require the generation of time dependent body fitted grids.展开更多
This paper presents an efficient numerical method for solving the unsteady Euler equations on stationary Cartesian grids. Wall boundary conditions are implemented on non moving mean wall positions by assuming the airf...This paper presents an efficient numerical method for solving the unsteady Euler equations on stationary Cartesian grids. Wall boundary conditions are implemented on non moving mean wall positions by assuming the airfoil being thin and undergoing small deformation, but the mean angle of attack of the body can still be large and we use the full nonlinear Euler equation in the field for accurate resolution of shock waves and vorticity. The method does not require the generation of moving body fitted grids and thus can be easily deployed in any fluid structure interaction problem involving relatively small deformation of a thin body. We use the first order wall boundary conditions in solving the full Euler equation. Unsteady transonic flow is calculated about an oscillating NACA 0012 airfoil at free stream Mach number M ∞ =0.755, mean angle of attack α m =0.016, amplitude of pitching oscillation α 0 =2.51, reduced frequency κ = 0.081 4. The computed results, including surface pressure distribution, instantaneous lift and moment coefficients are compared with known experimental data. It is shown that the first order boundary conditions are satisfactory for airfoils of typical thicknesses with small deformation for unsteady calculations.展开更多
基金supported by the National Natural Science Foundation of China(No.50071064 and 19891180-2)the US Army Research Office MURI Program under Contract DAAH04-96-1-0376the Department of Energy Grant DEFG0300SF2202.
文摘Microstructures of the localized shear bands generated during explosion with a thick-walled cylinder specimen in Ti-6AI-4V alloy, were characterized by TEM and SEM. The results show that the twinning is a major mode of deformation, and the distortion-free grains in the bands with the size of 10μm in diameter were proposed to be the re-crystallization during dynamic explosion. The further observations show that the α→α2 phase transformation may occur in the bands, and this kind of transformation could be confirmed by its dark field image and electron diffraction analysis. Analysis shows that there is specified orientation between the α and α2 Phases.
文摘This paper presents an efficient numerical method for solving the Euler equations on rectilinear grids. Wall boundary conditions on the surface of an airfoil are implemented by using their first order expansions on the airfoil chord line, which is placed along a grid line. However, the method is not restricted to flows with small disturbances since there are no restrictions on the magnitude of the velocity or pressure perturbations. The mathematical formulation and the numerical implementation of the wall boundary conditions in a finite volume Euler code are described. Steady transonic flows are calculated about the NACA 0006, NACA 0012 and NACA 0015 airfoils, corresponding to thickness ratios of 6%, 12%, and 15%, respectively. The computed results, including surface pressure distributions, the lift coefficient, the wave drag coefficient, and the pitching moment coefficient, at angles of attack from 0° to 8° are compared with solutions at the same conditions by FLO52, a well established Euler code using body fitted curvilinear grids. Results demonstrate that the method yields acceptable accuracies even for the relatively thick NACA 0015 airfoil and at high angles of attack. This study establishes the potential of extending the method to computing unsteady fluid structure interaction problems, where the use of a stationary rectilinear grid offers substantial advantages in both computer time and human work since it would not require the generation of time dependent body fitted grids.
文摘This paper presents an efficient numerical method for solving the unsteady Euler equations on stationary Cartesian grids. Wall boundary conditions are implemented on non moving mean wall positions by assuming the airfoil being thin and undergoing small deformation, but the mean angle of attack of the body can still be large and we use the full nonlinear Euler equation in the field for accurate resolution of shock waves and vorticity. The method does not require the generation of moving body fitted grids and thus can be easily deployed in any fluid structure interaction problem involving relatively small deformation of a thin body. We use the first order wall boundary conditions in solving the full Euler equation. Unsteady transonic flow is calculated about an oscillating NACA 0012 airfoil at free stream Mach number M ∞ =0.755, mean angle of attack α m =0.016, amplitude of pitching oscillation α 0 =2.51, reduced frequency κ = 0.081 4. The computed results, including surface pressure distribution, instantaneous lift and moment coefficients are compared with known experimental data. It is shown that the first order boundary conditions are satisfactory for airfoils of typical thicknesses with small deformation for unsteady calculations.
