In this paper,we study the transonic shock solutions to the steady Euler system in a quasi-one-dimensional divergent-convergent nozzle.For a given physical supersonic inflow at the entrance,we obtain exactly two non-i...In this paper,we study the transonic shock solutions to the steady Euler system in a quasi-one-dimensional divergent-convergent nozzle.For a given physical supersonic inflow at the entrance,we obtain exactly two non-isentropic transonic shock solutions for the exit pressure lying in a suitable range.In addition,we establish the monotonicity between the location of the transonic shock and the pressure downstream.展开更多
The flow in transonic diffusers as well as in supersonic air intakes becomes often unsteady due to shock wave boundary layer interaction. The oscillations may be induced by natural separation unsteadiness or may be fo...The flow in transonic diffusers as well as in supersonic air intakes becomes often unsteady due to shock wave boundary layer interaction. The oscillations may be induced by natural separation unsteadiness or may be forced by boundary conditions. Significant improvement of CFD tools, increase of computer resources as well as development of experimental methods have again.drawn the attention of researchers to this topic. To investigate the problem forced oscillations of transonic turbulent flow in asymmetric two-dimensional Laval nozzle were considered. A viscous, perfect gas flow, was numerically simulated using the Reynolds-averaged compressible Navier-Stokes solver SPARC, employing a two-equation, eddy viscosity, turbulence closure in the URANS approach.For time-dependent and stationary flow simulations, Mach numbers upstream of the shock between 1.2 and 1.4 were considered. Comparison of computed and experimental data for steady states generally gave acceptable agreement. In the case of forced oscillations, a harmonic pressure variation was prescribed at the exit plane resulting in shock wave motion. Excitation frequencies between 0 Hz and 1024 Hz were investigated at the same pressure amplitude.The main result of the work carried out is the relation between the amplitude of the shock wave motion and the excitation frequency in the investigated range. Increasing excitation frequency resulted in decreasing amplitude of the shock movement. At high frequencies a natural mode of shock oscillation (of small amplitude) was observed which is not sensitive to forced excitement.展开更多
In this paper, by use of the methods in [1-3], we establish the uniqueness of a 2-D transonic shock solution in a nozzle when the end pressure in the diverging part of the nozzle lies in an appropriate scope. Especial...In this paper, by use of the methods in [1-3], we establish the uniqueness of a 2-D transonic shock solution in a nozzle when the end pressure in the diverging part of the nozzle lies in an appropriate scope. Especially, we remove the crucial but unnatural assumption in recent references which the transonic shock must be assumed to go through a fixed point in advance.展开更多
A flow resonance accompanied by the emission of acoustic tones occurs in an over-expanded convergent-divergent(C-D) nozzle when operated at comparatively low pressure ratios. This phenomenon is distinguished from conv...A flow resonance accompanied by the emission of acoustic tones occurs in an over-expanded convergent-divergent(C-D) nozzle when operated at comparatively low pressure ratios. This phenomenon is distinguished from conventional screech tones and is referred to as "transonic tones". In contrast to screech tones, the peak resonant frequency for transonic tones increases with pressure ratio; the peak sound pressure level exceeds 110 d B. In this study, we investigated the basic characteristics of transonic resonance and tones using a circular C-D nozzle in an anechoic room. The effects of the boundary layer trip were also evaluated using a tripping wire for the suppressing transonic resonance and tones. The results of acoustic measurements show that several predominant peaks correspond to transonic tones. However, the boundary layer trip inside the nozzle effectively eliminated these tones and suppressed the unsteadiness of the flow inside the nozzle.展开更多
Classical transonic hodograph-based design methods are employed and revitalized using modern numerical tools to illustrate the design of a symmetrical accelerating-decelerating nozzle throat design. The concept of Ell...Classical transonic hodograph-based design methods are employed and revitalized using modern numerical tools to illustrate the design of a symmetrical accelerating-decelerating nozzle throat design. The concept of Elliptic Continuation is applied to solve transonic boundary value problems avoiding the inherently nonlinear nature of the basic equations and obtaining transonic flow examples using the Method of Characteristics in an inverse mode. Purpose of the present paper, besides describing a new special flow example, is to keep these classical methods alive for education of a new generation of creative engineers.展开更多
基金partially supported by NSFC(11871133,12171498)partially supported by NSFC(11971402,12171401)the NSF of Fujian province,China(2020J01029)。
文摘In this paper,we study the transonic shock solutions to the steady Euler system in a quasi-one-dimensional divergent-convergent nozzle.For a given physical supersonic inflow at the entrance,we obtain exactly two non-isentropic transonic shock solutions for the exit pressure lying in a suitable range.In addition,we establish the monotonicity between the location of the transonic shock and the pressure downstream.
文摘The flow in transonic diffusers as well as in supersonic air intakes becomes often unsteady due to shock wave boundary layer interaction. The oscillations may be induced by natural separation unsteadiness or may be forced by boundary conditions. Significant improvement of CFD tools, increase of computer resources as well as development of experimental methods have again.drawn the attention of researchers to this topic. To investigate the problem forced oscillations of transonic turbulent flow in asymmetric two-dimensional Laval nozzle were considered. A viscous, perfect gas flow, was numerically simulated using the Reynolds-averaged compressible Navier-Stokes solver SPARC, employing a two-equation, eddy viscosity, turbulence closure in the URANS approach.For time-dependent and stationary flow simulations, Mach numbers upstream of the shock between 1.2 and 1.4 were considered. Comparison of computed and experimental data for steady states generally gave acceptable agreement. In the case of forced oscillations, a harmonic pressure variation was prescribed at the exit plane resulting in shock wave motion. Excitation frequencies between 0 Hz and 1024 Hz were investigated at the same pressure amplitude.The main result of the work carried out is the relation between the amplitude of the shock wave motion and the excitation frequency in the investigated range. Increasing excitation frequency resulted in decreasing amplitude of the shock movement. At high frequencies a natural mode of shock oscillation (of small amplitude) was observed which is not sensitive to forced excitement.
基金Cui Dacheng and Yin Huicheng are supported by the National Natural Science Foundation of China （No.10571082） and the National Basic Research Programm of China （No.2006CB805902）.
文摘In this paper, by use of the methods in [1-3], we establish the uniqueness of a 2-D transonic shock solution in a nozzle when the end pressure in the diverging part of the nozzle lies in an appropriate scope. Especially, we remove the crucial but unnatural assumption in recent references which the transonic shock must be assumed to go through a fixed point in advance.
文摘A flow resonance accompanied by the emission of acoustic tones occurs in an over-expanded convergent-divergent(C-D) nozzle when operated at comparatively low pressure ratios. This phenomenon is distinguished from conventional screech tones and is referred to as "transonic tones". In contrast to screech tones, the peak resonant frequency for transonic tones increases with pressure ratio; the peak sound pressure level exceeds 110 d B. In this study, we investigated the basic characteristics of transonic resonance and tones using a circular C-D nozzle in an anechoic room. The effects of the boundary layer trip were also evaluated using a tripping wire for the suppressing transonic resonance and tones. The results of acoustic measurements show that several predominant peaks correspond to transonic tones. However, the boundary layer trip inside the nozzle effectively eliminated these tones and suppressed the unsteadiness of the flow inside the nozzle.
基金supported by the Grant Agency of the Czech Technical University in Prague, grant no. SGS13/180/OHK2/3T/12Support from the project No. CZ.2.16/3.1.00/21569 Centre 3D Volumetric Anemometry
文摘Classical transonic hodograph-based design methods are employed and revitalized using modern numerical tools to illustrate the design of a symmetrical accelerating-decelerating nozzle throat design. The concept of Elliptic Continuation is applied to solve transonic boundary value problems avoiding the inherently nonlinear nature of the basic equations and obtaining transonic flow examples using the Method of Characteristics in an inverse mode. Purpose of the present paper, besides describing a new special flow example, is to keep these classical methods alive for education of a new generation of creative engineers.
