Oblique shock reflection from an axis of symmetry

An exploratory computational study of the reflection of an inward-facing conical shock wave from its axis of symmetry is presented. This is related to more complex practical situations in both steady and unsteady flows. The absence of a length scale in the problem studied makes features grow linearly with time. The ensuing flow is related to the Guderley singularity in a cylindrical imploding shock. The problem is explored by making a large number of computations of the Euler equations. Distinct reflection congurations are identied, and the regions of parameter space in which they occur are delineated

Some aspects of hypersonic flow over power law bodies

This study concerns the hypersonic flow over blunt bodies in two specific cases. The first is the case when the Mach number is infinite and the ratio of the specific heats approaches one. This is sometimes referred to as the ‘Newtonian limit’. The second is the case of infinite Mach number and very large streamwise distance from the blunt nose with a strong shock wave, or the ‘blast wave limit’. In both cases attention is restricted to power law bodies. Experiments are described of such flows at M∞ = 7.55 in air. The Newtonian flow over bodies of the shape y ∝ x^m at zero incidence is shown to be divisible into three regions: the attached layer at small x, the free layer and the blast wave region. As m increases from zero, the free-layer region reduces in extent until it disappears at m = 1/(2+j) (j = 1 and 0 for axisymmetric and plane flow respectively). A difficulty arises in a transition solution of the type given by Freeman (1962b) connecting the free layer with the blast wave result. At m > 2/(3+j) the attached layer merges smoothly into the Lees-Kubota solution which replaces the blast-wave result in this range. In the blast wave limit, solutions were obtained for flow over axisymmetric power law shapes in the range [fraction one-half]γ < m < ½. Second-order results taking account of the body shape are given. These solutions are compared with experimental results obtained in air at a free stream Mach number of 7.55 and stagnation temperature of 630 °K, as well as with numerical solutions at Mach number of 100. The numerical method is tested by comparing solutions corresponding to the experimental conditions with experiment

Non-equilibrium dissociating nitrogen flow over spheres and circular cylinders

Theoretical results based on the methods of Freeman and Garr & Marrone show that the stand-off distance and flow pattern of non-equilibrium dissociating flow of nitrogen over the front part of a blunt body can be correlated in terms of a single reaction rate parameter ω taking account of parameters describing the speed, density, dissociation and temperature of the free stream. The density pattern, which is sensitive to the reaction rate, consists of two distinct regions dominated by the effects of reaction and pressure respectively. The shape and size of these regions depend on Q. Experimental results obtained by optical interferometry in a free-piston shock tunnel confirm the theoretical results. A scale effect consistent with the induction time phenomenon suggested by Shui, Appleton & Keck modifies the theoretical results considerably in the case of small models

Non-equilibrium dissociating nitrogen flow over a wedge

Experimental results for dissociating nitrogen flow over a wedge, obtained in a free-piston shock tunnel, are described. Interferograms of the flow show clearly the curvature of the shock wave and the rise in fringe shift after the shock associated with the dissociation. It is shown that the shock curvature at the tip of the wedge can be used to calculate the initial dissociation rate and that it is a more sensitive indication of the rate than can be obtained from fringe shift measurements under the prevailing experimental conditions. Because the freestream dissociation fraction can be adjusted in the shock tunnel, the dependence on atomic nitrogen concentration of the dissociation rate can be determined by the shock curvature method. A detailed calculation of the flow field by an inverse method, starting from the measured shock shape, shows good agreement with experiments

Oblique shock reflection from an axis of symmetry: shock dynamics and relation to the Guderley singularity

Oblique shock reflection from an axis of symmetry is studied using Whitham's theory of geometrical shock dynamics, and the results are compared with previous numerical simulations of the phenomenon by Hornung (2000). The shock shapes (for strong and weak shocks), and the location of the shock-shock (for strong shocks), are in good agreement with the numerical results, though the detail of the shock reflection structure is, of course, not resolved by shock dynamics. A guess at a mathematical form of the shock shape based on an analogy with the Guderley singularity in cylindrical shock implosion, in the form of a generalized hyperbola, fits the shock shape very well. The smooth variation of the exponent in this equation with initial shock angle from the Guderley value at zero to 0.5 at 90° supports the analogy. Finally, steady-flow shock reflection from a symmetry axis is related to the self-similar flow

Growth of shocked gaseous interfaces in a conical geometry

The results of experiments on Richtmyer-Meshkov instability growth of multimode initial perturbations on an air-sulfur hexafluoride (SF6) interface in a conical geometry are presented. The experiments are done in a relatively larger shock tube. A nominally planar interface is formed by sandwiching a polymeric membrane between wire-mesh frames. A single incident shock wave ruptures the membrane resulting in multimode perturbations. The instability develops from the action of baroclinically deposited vorticity at the interface. The visual thickness delta of the interface is measured from schlieren photographs obtained in each run. Data are presented for delta at times when the interface has become turbulent. The data are compared with the experiments of Vetter [Shock Waves 4, 247 (1995)] which were done in a straight test section geometry, to illustrate the effects of area convergence. It is found from schlieren images that the interface thickness grows about 40% to 50% more rapidly than in Vetter's experiments. Laser induced scattering is used to capture the air-helium interface at late times. Image processing of pictures is also used to determine the interface thickness in cases where it was not clear from the pictures and to obtain the dominant eddy-blob sizes in the mixing zone. Some computational studies are also presented to show the global geometry changes of the interface when it implodes into a conical geometry in both light-heavy and heavy-light cases

Aspects of planar, oblique and interacting shock waves in an ideal dissociating gas

We develop a compact dimensionless framework for the analysis of canonical thermo-chemical nonequilibrium flow fields involving normal, oblique and interacting shock waves. Discontinuous solutions of the conservation equations are coupled with thermodynamic and kinetic models for an ideal dissociating gas. Convenient forms are provided for the variation of the relevant dimensionless parameters across shock waves in dissociating gases. The treatment is carried through in a consistent manner for the pressure–flow deflection angle plane representation of shock wave interaction problems. The contribution of the current paper is a careful nondimensionalization of the problem that yields a tractable formulation and allows results with considerable generality to be obtained

The influence of non-equilibrium dissociation on the flow produced by shock impingement on a blunt body

We describe an investigation of the effects of non-equilibrium thermochemistry on the interaction between a weak oblique shock and the strong bow shock formed by a blunt body in hypersonic flow. This type of shock-on-shock interaction, also known as an Edney type IV interaction, causes locally intense enhancement of the surface heat transfer rate. A supersonic jet is formed by the nonlinear interaction that occurs between the two shock waves and elevated heat transfer rates and surface pressures are produced by the impingement of the supersonic jet on the body. The current paper is motivated by previous studies suggesting that real gas effects would significantly increase the severity of the phenomenon. Experiments are described in which a free-piston shock tunnel is used to produce shock interaction flows with significant gas dissociation. Surprisingly, the data that are obtained show no significant stagnation enthalpy dependence of the ratio of the peak heat transfer rates with and without shock interaction, in contrast to existing belief. The geometry investigated is the nominally two-dimensional flow about a cylinder with coplanar impinging shock wave. Holographic interferometry is used to visualize the flow field and to quantify increases in the stagnation density caused by shock interaction. Time-resolved heat transfer measurements are obtained from surface junction thermocouples about the model forebody. An improved model is developed to elucidate the finite-rate thermochemical processes occurring in the interaction region. It is shown that severe heat transfer intensification is a result of a jet shock structure that minimizes the entropy rise of the supersonic jet fluid whereas strong thermochemical effects are promoted by conditions that maximize the entropy rise (and hence temperature). This dichotomy underlies the smaller than anticipated influence of real gas effects on the heat transfer intensification. The model accurately predicts the measured heat transfer rates. Improved understanding of the influence of real gas effects on the shock interaction phenomenon reduces a significant element of risk in the design of hypersonic vehicles. The peak heat transfer rate for the Edney type IV interaction is shown to be well-correlated, in the weak impinging shock regime, by an expression of the form [equation] for use in practical design calculations