3-D Axisymmetric Transonic Shock Solutions of the Full Euler System in Divergent Nozzles

We establish the stability of 3-D axisymmetric transonic shock solutions of the steady full Euler system in divergent nozzles under small perturbations of an incoming radial supersonic flow and a constant pressure at the exit of the nozzles. To study 3-D axisymmetric transonic shock solutions of the full Euler system, we use a stream function formulation of the full Euler system for a 3-D axisymmetric flow. We resolve the singularity issue arising in stream function formulations of the full Euler system for a 3-D axisymmetric flow. We develop a new scheme to determine a shock location of a transonic shock solution of the steady full Euler system based on the stream function formulation.

A Correction to the Barotropic Model of Gaseous Cavitation in Choked Converging-Diverging Nozzle Flows

The Barotropic Cavitation Model describes the behavior of a homogeneous mixture of liquid and gas bubbles (gaseous cavitation) as it traverses a converging-diverging (CD) nozzle. Its normal shock formulation makes reliable and accurate predictions of streamwise static pressure distribution from the nozzle inlet to just downstream of the throat and in the diverging section as the flow approaches the nozzle outlet. It fails in the intermediate portion of the divergence with maximum pressure prediction errors (as a fraction of nozzle inlet pressure) roughly equivalent to the back pressure ratio (as high as 0.46). A correction to the streamwise static pressure distributions predicted by the normal shock solution of the Barotropic Cavitation Model is proposed, applied and compared to experiments with aerated and non-aerated cavitation in several fluids. When used to simulate aerated cavitation of dodecane in a CD nozzle it predicts the location of first disagreement between the normal shock solution and experimental static pressure measurements within 4% of nozzle length. A polynomial curve fit between this predicted point (xcorr) and the normal shock location (xshock) then reduces maximum prediction error for static pressure in the correction region to no more than 0.11 (as a fraction of inlet pressure) for the aerated dodecane cases examined. For non-aerated gaseous cavitation in dodecane, water or JP8 jet fuel this error ratio does not exceed 0.13 and typical values are less than 0.07.

Expansion shock waves in regularized shallow-water theory

We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularized shallow-water equations that include the Benjamin–Bona–Mahony and Boussinesq equations. An expansion shock exhibits divergent characteristics, thereby contravening the classical Lax entropy condition. The persistence of the expansion shock in initial value problems is analysed and justified using matched asymptotic expansions and numerical simulations. The expansion shock's existence is traced to the presence of a non-local dispersive term in the governing equation. We establish the algebraic decay of the shock as it is gradually eroded by a simple wave on either side. More generally, we observe a robustness of the expansion shock in the presence of weak dissipation and in simulations of asymmetric initial conditions where a train of solitary waves is shed from one side of the shock.

The Research and Analysis on Lockpin Synchronizer

To improve the heavy-duty vehicles’ gear shock solution during shifting and improve shifting comfortable, a research direction is improve the performance of lockpin synchronizer. Through the analysis of the main technical parameters of lockpin synchronizer, got the main research direction to improve the performance of lockpin synchronizer. The synchronizer structure optimization design was discussed. And the synchronizer is simulated and analyzed using the virtual prototype technology, which give a way to improve the performance of synchronizer.

Godunov-type methods for two-component magnetohydrodynamic equations

This paper is concerned with a numerical solutions of two-component magnetohydrodynamic equations. While a hyperbolic system of wave equations admits a shock solution as a result of the selenoidality condition the MHD equations are not strictly hyperbolic. As a consequence of that these equations require special numerical treatment. An application of a resulting numerical code to a problem of solar wind interaction with the ionosphere of the planet Venus is presented.

Singular solutions of a fully nonlinear 2 × 2 system of conservation laws

Existence and admissibility of δ-shock solutions is discussed for the non-convex strictly hyperbolic system of equationsThe system is fully nonlinear, i.e. it is nonlinear with respect to both unknowns, and it does not admit the classical Lax-admissible solution for certain Riemann problems. By introducing complex-valued corrections in the framework of the weak asymptotic method, we show that a compressive δ-shock solution resolves such Riemann problems. By letting the approximation parameter tend to zero, the corrections become real valued, and the solutions can be seen to fit into the framework of weak singular solutions defined by Danilov and Shelkovich. Indeed, in this context, we can show that every 2 × 2 system of conservation laws admits δ-shock solutions.