Oblique shock

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

A numerical investigation of sound generation in supersonic jet screech

Abstract: : The noise of supersonic jet flows is due in part to the interaction between jet instability waves and the jet shock-cell structure. If no countermeasures are taken, the emitted shock-cell noise will re-excite certain instability wave modes at the nozzle lip and cause resonant feedback to occur. This feedback resonance, known as supersonic jet screech, causes the jet to flap violently at discrete frequencies and generate very strong, narrow banded tones. Jet screech has been shown to be a source of acoustic fatigue in the tail and nozzle structures of supersonic aircraft. It is important that methods for predicting the screech amplitude be developed. Screech sound generation is one such element. We isolate the interaction of an unsteady shear layer with a single oblique shock. To obtain an overall understanding of the phenomenon with fewest simplifications, we study this problem through the numerical solution of the Navier Stokes equations. We then consider idealizations which allow us to obtain a similar but wider range of results with specially linearized Euler equations. The findings of these r0sults motivate the use of geometric acoustics to describe the screech generation process. The Navier-Stokes and Euler simulations have revealed important details about the interaction process, how the acoustic field results, and why screech is so loud. The mechanism for sound production is found to be fundamentally different and more efficient when the instability waves are the large vortices typical of screech, than when they are small disturbances. Geometrical acoustics can be used to explain the leakage effect at high instability wave amplitude. We conclude that the mechanism for high amplitude screech generation is an unsteady modification to the velocity field by the instability waves that permits the incident shock to refract through the shear layer.

Electron Diffusion ahead of Shock Waves in Argon

Abstract: Experiments with electrostatic and magnetic probes were performed to investigate the electron diffusion ahead of shock waves of Ms = 8 to 12 in argon. Negative electrostatic signals of several volts were obtained with pronounced fronts propagating with velocities up to several times the shock velocity. The current produced by the diffusing electrons was determined from a measurement of the azimuthal magnetic field and found to be of the order of 10−5 amp for Ms = 12. By assuming that the electron flow velocity is approximately equal to the velocity of the electrostatic front, the measured current corresponds to an electron density of ne ≈ 107 cm−3 at about 1 m ahead of the shock front.

Existence and Stability of Multidimensional Transonic Flows through an Infinite Nozzle of Arbitrary Cross-Sections

Abstract: We establish the existence and stability of multidimensional steady transonic flows with transonic shocks through an infinite nozzle of arbitrary cross-sections, including a slowly varying de Laval nozzle. The transonic flow is governed by the inviscid potential flow equation with supersonic upstream flow at the entrance, uniform subsonic downstream flow at the exit at infinity, and the slip boundary condition on the nozzle boundary. Our results indicate that, if the supersonic upstream flow at the entrance is sufficiently close to a uniform flow, there exists a solution that consists of a C1,α subsonic flow in the unbounded downstream region, converging to a uniform velocity state at infinity, and a C1,α multidimensional transonic shock separating the subsonic flow from the supersonic upstream flow; the uniform velocity state at the exit at infinity in the downstream direction is uniquely determined by the supersonic upstream flow; and the shock is orthogonal to the nozzle boundary at every point of their intersection. In order to construct such a transonic flow, we reformulate the multidimensional transonic nozzle problem into a free boundary problem for the subsonic phase, in which the equation is elliptic and the free boundary is a transonic shock. The free boundary conditions are determined by the Rankine–Hugoniot conditions along the shock. We further develop a nonlinear iteration approach and employ its advantages to deal with such a free boundary problem in the unbounded domain. We also prove that the transonic flow with a transonic shock is unique and stable with respect to the nozzle boundary and the smooth supersonic upstream flow at the entrance.

Simulation of blast wave propagation over a cylinder

Abstract: A numerical study of the interaction of plane blast waves with a cylinder is presented. Computations are carried out for various blast-wave durations and comparisons are obtained with the corresponding results of planar shock-wave. Both inviscid and viscous results based on the solution of the Euler and Navier-Stokes equations are presented. The equations are solved by an adaptive-grid method and a second-order Godunov scheme. The shock wave diffraction over the cylinder is investigated by means of various contour plots, as well as, pressure and skin-friction histories. The study reveals that the blast-wave duration significantly influences the unsteady flow over the cylinder. The differences between the viscous and inviscid results are also discussed.

Transonic Shocks for the Full Compressible Euler System in a General Two-Dimensional De Laval Nozzle

Abstract: In this paper, we study the transonic shock problem for the full compressible Euler system in a general two-dimensional de Laval nozzle as proposed in Courant and Friedrichs (Supersonic flow and shock waves, Interscience, New York, 1948): given the appropriately large exit pressure p e(x), if the upstream flow is still supersonic behind the throat of the nozzle, then at a certain place in the diverging part of the nozzle, a shock front intervenes and the gas is compressed and slowed down to subsonic speed so that the position and the strength of the shock front are automatically adjusted such that the end pressure at the exit becomes p e(x). We solve this problem completely for a general class of de Laval nozzles whose divergent parts are small and arbitrary perturbations of divergent angular domains for the full steady compressible Euler system. The problem can be reduced to solve a nonlinear free boundary value problem for a mixed hyperbolic–elliptic system. One of the key ingredients in the analysis is to solve a nonlinear free boundary value problem in a weighted Holder space with low regularities for a second order quasilinear elliptic equation with a free parameter (the position of the shock curve at one wall of the nozzle) and non-local terms involving the trace on the shock of the first order derivatives of the unknown function.