To achieve a detailed understanding of underexpanded supersonic jet structures influenced by afterburning and other flow conditions, the underexpanded turbulent supersonic jet with and without combustions are investig...To achieve a detailed understanding of underexpanded supersonic jet structures influenced by afterburning and other flow conditions, the underexpanded turbulent supersonic jet with and without combustions are investigated by computational fluid dynamics （CFD） method. A program based on a total variation diminishing （TVD） methodology capable of predicting complex shocks is created to solve the axisymmetric expanded Navie^Stokes equations containing transport equations of species. The finite-rate ratio model is employed to handle species sources in chemical reactions. CFD solutions indicate that the structure of underexpanded jet is typically influenced by the pressure ratio and afterburning. The shock reflection distance and maximum value of Mach number in the first shock cell increase with pressure ratio. Chemical reactions for the rocket exhaust mostly exist in the mixing layer of supersonic jet flows. This tends to reduce the intensity of shocks existing in the jet, responding to the variation of thermal parameters.展开更多
Central discontinuous Galerkin（CDG）method is used to solve the Navier-Stokes equations for viscous flow in this paper.The CDG method involves two pieces of approximate solutions defined on overlapping meshes.Taking ...Central discontinuous Galerkin（CDG）method is used to solve the Navier-Stokes equations for viscous flow in this paper.The CDG method involves two pieces of approximate solutions defined on overlapping meshes.Taking advantages of the redundant representation of the solution on the overlapping meshes,the cell interface of one computational mesh is right inside the staggered mesh,hence approximate Riemann solvers are not needed at cell interfaces.Third order total variation diminishing（TVD）Runge-Kutta（RK）methods are applied in time discretization.Numerical examples for 1D and2 D viscous flow simulations are presented to validate the accuracy and robustness of the CDG method.展开更多
In this paper, we use Daubechies scaling functions as test functions for the Galerkin method, and discuss Wavelet-Galerkin solutions for the Hamilton-Jacobi equations. It can be proved that the schemes are TVD schemes...In this paper, we use Daubechies scaling functions as test functions for the Galerkin method, and discuss Wavelet-Galerkin solutions for the Hamilton-Jacobi equations. It can be proved that the schemes are TVD schemes. Numerical tests indicate that the schemes are suitable for the Hamilton-Jacobi equations. Furthermore, they have high-order accuracy in smooth regions and good resolution of singularities.展开更多
When the high-pressure gas is exhausted to the vacuum chamber from the nozzle,the underexpanded supersonic jet contained with the Mach disk is generally formed.The eventual purpose of this study is to clarify the unst...When the high-pressure gas is exhausted to the vacuum chamber from the nozzle,the underexpanded supersonic jet contained with the Mach disk is generally formed.The eventual purpose of this study is to clarify the unsteady phenomenon of the underexpanded free jet when the back pressure continuously changes with time.The characteristic of the Mach disk has been clarified in consideration of the diameter and position of it by the numerical analysis in this paper.The sonic jet of the exit Mach number Me=1 is assumed and the axisymmetric conservational equation is solved by the TVD method in the numerical calculation.The diameter and position of the Mach disk differs with the results of a steady jet and the influence on the continuously changing of the back pressure is evidenced from the comparison with the case of steady supersonic jet.展开更多
In this paper,we developed a class of the fourth order accurate finite volume Hermite weighted essentially non-oscillatory(HWENO)schemes based on the work(Computers&Fluids,34:642-663(2005))by Qiu and Shu,with Tota...In this paper,we developed a class of the fourth order accurate finite volume Hermite weighted essentially non-oscillatory(HWENO)schemes based on the work(Computers&Fluids,34:642-663(2005))by Qiu and Shu,with Total Variation Diminishing Runge-Kutta time discretization method for the two-dimensional hyperbolic conservation laws.The key idea of HWENO is to evolve both with the solution and its derivative,which allows for using Hermite interpolation in the reconstruction phase,resulting in a more compact stencil at the expense of the additional work.The main difference between this work and the formal one is the procedure to reconstruct the derivative terms.Comparing with the original HWENO schemes of Qiu and Shu,one major advantage of new HWENOschemes is its robust in computation of problem with strong shocks.Extensive numerical experiments are performed to illustrate the capability of the method.展开更多
When the shock wave propagating in the straight circular tube reaches at the open end, the impulsive wave is generated by the emission of a shock wave from an open end, and unsteady pulse jet is formed near the open e...When the shock wave propagating in the straight circular tube reaches at the open end, the impulsive wave is generated by the emission of a shock wave from an open end, and unsteady pulse jet is formed near the open end behind the impulsive wave under the specific condition. The pulse jet transits to spherical shock wave with the increase in the strength of shock wave. The strength is dependent on the Mach number of shock wave, which attenuates by propagation distance from the open end. In this study, the mechanism of generating the unsteady pulse jet, the characteristics of the pressure distribution in the flow field and the emission of shock wave from straight circular tube which has the infinite flange at open end are analyzed numerically by the TVD method. Strength of spherical shock wave, relation of shock wave Mach number,distance decay of spherical shock wave and directional characteristics are clarified.展开更多
基金supported by the National Natural Science Foundation of China (No. 51306019)
文摘To achieve a detailed understanding of underexpanded supersonic jet structures influenced by afterburning and other flow conditions, the underexpanded turbulent supersonic jet with and without combustions are investigated by computational fluid dynamics （CFD） method. A program based on a total variation diminishing （TVD） methodology capable of predicting complex shocks is created to solve the axisymmetric expanded Navie^Stokes equations containing transport equations of species. The finite-rate ratio model is employed to handle species sources in chemical reactions. CFD solutions indicate that the structure of underexpanded jet is typically influenced by the pressure ratio and afterburning. The shock reflection distance and maximum value of Mach number in the first shock cell increase with pressure ratio. Chemical reactions for the rocket exhaust mostly exist in the mixing layer of supersonic jet flows. This tends to reduce the intensity of shocks existing in the jet, responding to the variation of thermal parameters.
基金Supported by the National Natural Science Foundation of China(11602262)
文摘Central discontinuous Galerkin（CDG）method is used to solve the Navier-Stokes equations for viscous flow in this paper.The CDG method involves two pieces of approximate solutions defined on overlapping meshes.Taking advantages of the redundant representation of the solution on the overlapping meshes,the cell interface of one computational mesh is right inside the staggered mesh,hence approximate Riemann solvers are not needed at cell interfaces.Third order total variation diminishing（TVD）Runge-Kutta（RK）methods are applied in time discretization.Numerical examples for 1D and2 D viscous flow simulations are presented to validate the accuracy and robustness of the CDG method.
基金the National Natural Science Foundation of China(No.10571178)
文摘In this paper, we use Daubechies scaling functions as test functions for the Galerkin method, and discuss Wavelet-Galerkin solutions for the Hamilton-Jacobi equations. It can be proved that the schemes are TVD schemes. Numerical tests indicate that the schemes are suitable for the Hamilton-Jacobi equations. Furthermore, they have high-order accuracy in smooth regions and good resolution of singularities.
文摘When the high-pressure gas is exhausted to the vacuum chamber from the nozzle,the underexpanded supersonic jet contained with the Mach disk is generally formed.The eventual purpose of this study is to clarify the unsteady phenomenon of the underexpanded free jet when the back pressure continuously changes with time.The characteristic of the Mach disk has been clarified in consideration of the diameter and position of it by the numerical analysis in this paper.The sonic jet of the exit Mach number Me=1 is assumed and the axisymmetric conservational equation is solved by the TVD method in the numerical calculation.The diameter and position of the Mach disk differs with the results of a steady jet and the influence on the continuously changing of the back pressure is evidenced from the comparison with the case of steady supersonic jet.
基金the National Natural Science Foundation of China(Grant No.10671097)the European project ADIGMA on the development of innovative solution algorithms for aerodynamic simu-lations+1 种基金Scientific Research Foundation for the Returned Overseas Chinese ScholarsState Education Ministry and the Natural Science Foundation of Jiangsu Province(Grant No.BK2006511)
文摘In this paper,we developed a class of the fourth order accurate finite volume Hermite weighted essentially non-oscillatory(HWENO)schemes based on the work(Computers&Fluids,34:642-663(2005))by Qiu and Shu,with Total Variation Diminishing Runge-Kutta time discretization method for the two-dimensional hyperbolic conservation laws.The key idea of HWENO is to evolve both with the solution and its derivative,which allows for using Hermite interpolation in the reconstruction phase,resulting in a more compact stencil at the expense of the additional work.The main difference between this work and the formal one is the procedure to reconstruct the derivative terms.Comparing with the original HWENO schemes of Qiu and Shu,one major advantage of new HWENOschemes is its robust in computation of problem with strong shocks.Extensive numerical experiments are performed to illustrate the capability of the method.
文摘When the shock wave propagating in the straight circular tube reaches at the open end, the impulsive wave is generated by the emission of a shock wave from an open end, and unsteady pulse jet is formed near the open end behind the impulsive wave under the specific condition. The pulse jet transits to spherical shock wave with the increase in the strength of shock wave. The strength is dependent on the Mach number of shock wave, which attenuates by propagation distance from the open end. In this study, the mechanism of generating the unsteady pulse jet, the characteristics of the pressure distribution in the flow field and the emission of shock wave from straight circular tube which has the infinite flange at open end are analyzed numerically by the TVD method. Strength of spherical shock wave, relation of shock wave Mach number,distance decay of spherical shock wave and directional characteristics are clarified.
