Oblique shock

About: Oblique shock is a research topic. Over the lifetime, 6551 publications have been published within this topic receiving 119823 citations.

Numerical Simulation of a Real Shcramjet Flowfield

Abstract: A shock-induced combustion ramjet (shcramjet) geometry is considered wherein the fuel, gaseous hydrogen, is injected in a two-oblique shock external compression inlet via cantilevered ramp injectors and a wall slot. The combustible mixture formed at the exit of the inlet is then ignited through the shock generated by the cowl of the engine. The numerical simulation of the three-dimensional flowfield of a shcramjet flying at M = 11 and at an altitude of 35 km was performed using the WARP code, in which multispecies Favre-averaged Navier-Stokes equations are closed by the k-w turbulence model and the Wilcox dilational dissipation correction, to account for compressibility effects at high turbulence Mach numbers. The hydrogen/air chemical reactions are modeled by Jachimowsky's nine species, 20 reaction model. It has been found that the combustor length resulting from the shock-induced process is of the order of 25-30% of the inlet length. The relatively low value of the fuel specific impulse obtained, 573 s, is mainly due to incomplete mixing achieved in the adopted inlet model. To the authors' knowledge, the paper contains the first ever proof, in the open scientific literature, of the feasibility of this hypersonic propulsion concept in realistic flow situations, by numerical simulation.

One-dimensional model for microscale shock tube flow

Abstract: A one-dimensional model for the numerical simulation of transport effects in small-scale, i.e., low Reynolds number, shock tubes is presented. The conservation equations have been integrated in the lateral directions and three-dimensional effects have been introduced as carefully controlled sources of mass, momentum and energy, into the axial conservation equations. The unsteady flow of gas behind the shock wave is reduced to a quasi-steady flow by choosing a coordinate system attached to the shock. The boundary layer problem is thereby reduced to a laminar solution, similar to the Blasius solution, with the exception that the wall velocity can be nonzero. The resulting one-dimensional equations are then solved numerically using a two-step Lax-Wendroff/ MacCormack scheme with flux correction transport. For validation purposes, comparisons are performed against previously published shock structure and low Reynolds number shock tube experiments; good agreement is observed. The model has been used to predict the performance of a 10µm shock tube and the result of this simulation shows the possibility of shock wave disappearance at lower pressure ratios for a micro-scale shock tube.

Converging cylindrical shocks in ideal magnetohydrodynamics

Abstract: We consider a cylindrically symmetrical shock converging onto an axis within the framework of ideal, compressible-gas non-dissipative magnetohydrodynamics (MHD). In cylindrical polar co-ordinates we restrict attention to either constant axial magnetic field or to the azimuthal but singular magnetic field produced by a line current on the axis. Under the constraint of zero normal magnetic field and zero tangential fluid speed at the shock, a set of restricted shock-jump conditions are obtained as functions of the shock Mach number, defined as the ratio of the local shock speed to the unique magnetohydrodynamic wave speed ahead of the shock, and also of a parameter measuring the local strength of the magnetic field. For the line current case, two approaches are explored and the results compared in detail. The first is geometrical shock-dynamics where the restricted shock-jump conditions are applied directly to the equation on the characteristic entering the shock from behind. This gives an ordinary-differential equation for the shock Mach number as a function of radius which is integrated numerically to provide profiles of the shock implosion. Also, analytic, asymptotic results are obtained for the shock trajectory at small radius. The second approach is direct numerical solution of the radially symmetric MHD equations using a shock-capturing method. For the axial magnetic field case the shock implosion is of the Guderley power-law type with exponent that is not affected by the presence of a finite magnetic field. For the axial current case, however, the presence of a tangential magnetic field ahead of the shock with strength inversely proportional to radius introduces a length scale R = √μ_0/p_0I/(2π) where I is the current, μ_0 is the permeability, and p_0 is the pressure ahead of the shock. For shocks initiated at r ≫ R, shock convergence is first accompanied by shock strengthening as for the strictly gas-dynamic implosion. The diverging magnetic field then slows the shock Mach number growth producing a maximum followed by monotonic reduction towards magnetosonic conditions, even as the shock accelerates toward the axis. A parameter space of initial shock Mach number at a given radius is explored and the implications of the present results for inertial confinement fusion are discussed.

Relativistic Theory of Shock Waves

Abstract: The paper is concerned with the relativistic theory of shock phenomena in a simple, non-conducting fluid. Three conditions on the equation of state are exhibited which yield the result (demanded by the principle of causality) that the shock speed shall always be less than the fundamental velocity c. By a consideration of one-dimensional continuous flow, an additional condition, expressing the stability of compressive shocks, is derived. On the basis of these four conditions, it is then proved that, as in the classical theory, entropy rises across a compressive shock, and the transition in the fluid velocity relative to a normally incident shock is from supersonic to subsonic.