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

Mach Stem Height and Growth Rate Predictions

A new, more accurate prediction of Mach stem height in steady flow is presented. In addition, starting with a regular reflection in the dual-solution domain, the growth rate of the Mach stem from the time it is first formed till it reaches its steady-state height is presented. Comparisons between theory, experiments, and computations are presented for the Mach stem height. The theory for the Mach stem growth rate in both two and three dimensions is compared to computational results. The Mach stem growth theory provides an explanation for why, once formed, a Mach stem is relatively persistent

The flow field downstream of a hydraulic jump

A control-volume analysis of a hydraulic jump is used to obtain the mean vorticity downstream of the jump as a function of the Froude number. To do this it is necessary to include the conservation of angular momentum. The mean vorticity increases from zero as the cube of Froude number minus one, and, in dimensionless form, approaches a constant at large Froude number. Digital particle imaging velocimetry was applied to travelling hydraulic jumps giving centre-plane velocity field images at a frequency of 15 Hz over a Froude number range of 2–6. The mean vorticity determined from these images confirms the control-volume prediction to within the accuracy of the experiment. The flow field measurements show that a strong shear layer is formed at the toe of the wave, and extends almost horizontally downstream, separating from the free surface at the toe. Various vorticity generation mechanisms are discussed

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