Diffuse holographic interferometric observation of shock wave reflection from a skewed wedge

The pattern of shock wave reflection over a wedge is, in general, either a regular reflection or a Mach reflection, depending on wedge angles, shock wave Mach numbers, and specific heat ratios of gases. However, regular and Mach reflections can coexist, in particular, over a three-dimensional wedge surface, whose inclination angles locally vary normal to the direction of shock propagation. This paper reports a result of diffuse double exposure holographic interferometric observations of shock wave reflections over a skewed wedge surface placed in a 100 × 180 mm shock tube. The wedge consists of a straight generating line whose local inclination angle varies continuously from 30° to 60°. Painting its surface with fluorescent spray paint and irradiating its surface with a collimated object beam at a time interval of a few microseconds, we succeeded in visualizing three-dimensional shock reflection over the skewed wedge surface. Experiments were performed at shock Mach numbers, 1.55, 2.02, and 2.53 in air. From reconstructed holographic images, we estimated critical transition angles at these shock wave Mach numbers and found that these were very close to those over straight wedges. This is attributable to the flow three-dimensionality.      

Conical Mach reflection of moving shock waves

Conical Mach reflections differ from those of the equivalent plane, two-dimensional Mach reflection because in axisymmetry, the disturbances generated at the reflecting surface are modified by their more rapidly increasing or decreasing area as they move towards or away from the centerline. Equations for conical Mach reflection cases have now been developed using a simplified ray-shock theory formulation based on the initial assumption that the stem is straight and normal to the wall. These are in a form that applies generally. Their simple structure provides an easy conceptual understanding of self-similarity and non-self-similarity as well as a clear mathematical approach for the development of the curved triple-point locus of the latter by integration. They provide a quick and direct solution in all cases and can easily incorporate the Mach stem curvature by progressively calculating the new ray direction. A range of cases has been considered and results are presented for converging and diverging, self-similar and non-self-similar cases.     

A study of the interaction between two triple points

In the Mach reflection of plane shock on a concave double wedge, after two triple points collide with each other, the wave pattern is usually complicated. In this paper, firstly, a shock dynamic approach is used for studying this problem. In this approach, the method of shock-shock polar is used for better understanding the pattern of disturbance propagation. A downward-traveling shock-shock disturbance on the Mach stem is predicted theoretically. Secondly, based on the idea of shock dynamic approach, a gas dynamic model is built for studying the same problem. A similar result is obtained and the formation of the downward-traveling triple point is analyzed. This downward-traveling disturbance propagates and reflects between the upward-traveling shock-shock locus and the wall surface, causing the Mach number of Mach stem to increase and making the wave configuration approach to the one in the Mach reflection on a single wedge.Received: 19 April 2004, Accepted: 2 December 2004, Published online: 16 March 2005[/PUBLISHED]Correspondence to: P. Xie, Z.Y. Han     

Gradients at a curved shock in reacting flow

The inviscid equations of motion for the flow at the downstream side of a curved shock are solved for the shock–normal derivatives. Combining them with the shock–parallel derivatives yields gradients and substantial derivatives. In general these consist of two terms, one proportional to the rate of removal of specific enthalpy by the reaction, and one proportional to the shock curvature. Results about the streamline curvature show that, for sufficiently fast exothermic reaction, no Crocco point exists. This leads to a stability argument for sinusoidally perturbed normal shocks that relates to the formation of the structure of a detonation wave. Application to the deflection–pressure map of a streamline emerging from a triple shock point leads to the conclusion that, for non–reacting flow, the curvature of the Mach stem and reflected shock must be zero at the triple point, if the incident shock is straight. The direction and magnitude of the gradient at the shock of any flow quantity may be written down using the results. The sonic line slope in reacting flow serves as an example. Extension of the results – derived in the first place for plane flow – to three dimensions is straightforward. Received 12 February 1997 / Accepted 10 June 1997     

The Mach reflection triple-point locus for internal and external conical diffraction of a moving shock wave

This paper examines the different behavior that occurs for the Mach reflection triple-point loci between the two fundamental axisymmetric cases, these being the external diffraction by a cone and the internal diffraction within a conically contracting channel. From equations derived in this paper using a shock dynamics approach, it has been shown that, for external diffraction over a cone, a possible solution is that the triple-point locus is a straight line which corresponds to the experimental results available, while for internal diffraction along a conically converging channel, it cannot be straight and is, in fact, a convex curve. In the latter case, a transition point is noted on the triple-point locus before which the locus is nearly straight but after which the curvature becomes marked. The second region diminishes as a proportion of the total locus with decreasing half cone angle.For the external case, a set of simple, axisymmetric equations are derived which allow a rapid estimation of the triple point locus angle and the Mach stem strength for any incident shock Mach number and cone angle combination. The equations for internal diffraction are similar and allow a quick computation of both the curved triple-point locus and the strength of the diffracting front of the shock wave. A comparison with experiment has been carried out and agreement is good.     

Unsteady interaction of a sphere with atmospheric temperature inhomogeneity at supersonic speed

The structure of the shock layer and the abrupt aerodynamic forces acting on a sphere moving in an atmosphere with inhomogeneous inclusions of various shapes are considered.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 174–183, May–June, 1993.     

Conical Mach reflection of moving shock waves, Part 2: Physical and CFD experimentation

Analytical consideration of Mach reflections over cones using the ray-shock theory showed that they differ from those of the two-dimensional Mach reflection over wedges. Conical configurations include both self-similar and non-self-similar cases. However, even when self-similar, the conical configurations exhibit triple-point locus trajectory angles with values which, for any given reflection angle, differ from those of self-similar, wedge cases. Additionally, within the range of possible conical configurations, different values of self-similar triple-point locus angles exist for any given reflection angle depending on the geometry of the particular reflection process. While the ray-shock theory, as discussed in a previous paper on this research, provides a useful guide and a means of readily identifying these variations, verification using both shock tube and numerical simulations is required and is now available. Results of experimentation for both self-similar and non-self-similar axisym metric cases using these techniques are reported here and comparisons are made with the previous analysis. These support the calculations of the ray-shock theory over much of the reflection angle, Mach number range as well as highlighting some limitations of the theory. Received 15 October 1996 / Accepted 14 April 1997     

Effect of boundary layer on Mach reflection over a wedge surface

Abstract. In this paper, we consider the phenomenon of unsteady Mach reflection generated by a plane shock wave advancing over a straight wedge surface, with particular attention to the deviation of the flow field from the self-similar nature. We examine the observed change in angle between incident and reflected shocks, which is in contrast to the fact that the angle should remain constant with time in a self-similar flow. The effect of the boundary layer behind the advancing shock wave over the surface of the wedge is considered to cause this, and boundary layer theory is utilized to estimate the thickness of the layer. It is found that the thickness increases as to the time t compared with t by the overall expansion in the self-similar flow. Assuming that the thicker boundary layer is effectively equivalent to a change in wedge angle, the effect of the boundary layer on the flow field should be less in later stages with larger t values in accordance with the observation above. Received 6 March 2000 / Accepted 23 April 2001     

Problem of the interaction of a wedge moving with supersonic velocity when it encounters an interface between two gases

A class of exact solutions is constructed for the problem of the interaction of a supersonic wedge when it encounters an interface between two gases. It is shown that the realization of these solutions requires the bow shock to be perpendicular to the interface between the gases. A numerical analysis is made of the exact solution as a function of the intensity of the bow shock and the specific-heat ratio of the oncoming gas.     

Investigation of shock waves interference and associated hysteresis effect at variable-Mach-number upstream flow

Experimental investigations and numerical simulations have been performed to study the transition between steady regular and Mach reflections induced by flow Mach number variation. The experiments have been carried out in the supersonic wind tunnel SIGMA 4B, at the Institut Aérotechnique (IAT) in St Cyr L'Ecole, France. Symmetric and asymmetric arrangements of wedges have been tested. No significant hysteresis phenomenon has been detected experimentally. However, this phenomenon has been revealed by numerical computations obtained by solving the Navier-Stokes equations.Received: 9 October 2001, Accepted: 11 October 2002, Published online: 21 February 2003     

Interferometric measurement of density in nonstationary shock wave reflection flow and comparison with CFD

We present density measurements from the application of interferometry and Fourier transform fringe analysis to the problem of nonstationary shock wave reflection over a semicircular cylinder and compare our experimental measurements to theoretical results from a CFD simulation of the same problem. The experimental results demonstrate our ability to resolve detailed structure in this complex shock wave reflection problem, allowing visualization of multiple shocks in the vicinity of the triple point, plus visualization of the shear layer and an associated vortical structure. Comparison between CFD and experiment show significant discrepancies with experiment producing a double Mach Reflection when CFD predicts a transitional Mach reflection.Received: 12 November 2003, Accepted: 21 October 2004, Published online: 31 March 2005[/PUBLISHED]PACS: 47.40.-x, 42.40.Kw     

Numerical and analytical study of transverse supersonic flow over a flat cone

Quasisteady supersonic flow over a flat cone on a plane surface is studied. A formula is derived for the angle through which the flow lines turn at the cone. The results are used to justify the use of two-dimensional simulations of the flow. Peak pressures and total impulses are obtained numerically for various cone angles.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Mach reflection of a plane shock wave passing a mountain of 45° inclination

The transition from regular reflection (RR) to Mach reflection (MR) as a plane shock wave diffracts around a triangular mountain of 45° inclination is analysed in this paper, both by optical measurement in a shock tube and by numerical simulation the numerical method developed by Li Yingfan^[1] is of the FLIC type with triangular mesh. The dependence of the critical transition point Lk ofRR→MR on shock Mach numberM _i is analyzed and the variations of the incidence angle ω _i of the impinging shock and the reflection angle ω _r with the distanceL ^* are investigated. Our experimental and numerical results agree well with the theoretical results of Iton and Italya.     

The reflection of a shock wave over a cone

An investigation was made of the reflection of planar shock waves from cones. 86 cones, the half apex angle of which varied from 10° to 52° at every 0.5°, were installed in a 60 mm×150 mm diaphragmless shock tube equipped with holographic interferometry. The diaphragmless shock tube had a high degree of reproducibility with which the scatter of shock wave Mach number was within ±0.25% for shock wave Mach number ranging from 1.16 to approximately 2.0. The reflection of shock waves over cones was visualized using double exposure holographic interferometry. Whitham's geometrical shock wave dynamics was used to analyse the motion of Mach stems over cones. It is found that for relatively smaller apex angles of cones trajectory angles of resulting irregular reflections coincide with the so-called glancing incidence angles and their Mach stems appear to be continuously curved from its intersection point with the incident shock wave, which shows the chractericstic of von Neumann reflection. The domain of the existence of the von Neumann reflection was analytically obtained and was found to be broadened much more widely than that of two-dimensional reflections of shock waves over wedges.     

Nonstationary shock reflection over nonstraight surfaces: an approach with a method of multiple steps

Shock reflection phenomena over nonstraight surfaces have been investigated. The models used in this experiment are ordinary circular cylindrical concave and convex wedges and step-like wedges which simulate the former. The step-like wedges were used to investigate the process of reflected-wave formation over circular cylindrical wedges (method of multiple steps). The reflected-wave structure has been photographed with a schlieren apparatus. The formation of the reflected wave over circular cylindrical wedges is physically well understood by comparing it with shock reflection over step-like wedges. In particular, the reason why the reflected wave over a concave circular cylindrical wedge is very weak away from the reflection point is elucidated. Moreover, the structure and the formation mechanism of the so-called transitioned regular reflection (TRR) are illustrated in detail. As a by-product, based on acoustic theory, analytical formulae for the transition wedge angle are found. They are in good agreement with experiments. Received Received 28 February 1996 / Accepted 7 August 1996