Numerical investigation of repeated mach reflection and amplification of shock waves coverging to the vertex of a cone

A. N. Sevchenko Scientific-Research Institute of Applied Physical Problems of the V. I. Lenin Belorussian State University, Minsk. Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 62, No. 2, pp. 220–227, February, 1992.     

State-of-the-art in research on Mach reflection of shock waves

Reflected shock transition from Mach to regular reflection over wedges and state-of-the-art of Mach reflection research are presented. Examples of shock wave reflection from multiple wedges and curved wedges are given in conjunction with the Mach reflection research.     

On reflection of shock waves and shock-wave configurations

A new approach to the problem of unsteady reflection of shock waves is proposed. It is shown that the type and parameters of the shock wave reflection configuration depend on the type of an object (single shock versus shock-wave configuration) incident on the reflecting surface. The concept of the reflection of a shockwave configuration is introduced, and data are presented to illustrate the fact that theoretically established boundaries of the existence of various types of configurations do not represent the transitions lines if shockwave configurations rather than single shocks interact with the surface.     

Boundaries of the ambiguity area upon reflection of compression shock waves

Oblique shock waves can be reflected from hard walls, the axis, or the plane of symmetry, as well as from other counterpropagating shock waves with the formation of regular and Mach shock wave configurations. The specific form of shock wave structures is determined by the parameters of the problem: Mach number and intensity of incident shock waves. On the plane of parameters, there exists an ambiguity area in which laws of conservation admit both the regular and Mach reflection of shock waves. The boundaries of this region have been determined.     

Experimental study of pressure behind reflected shock waves in argon at mach numbers of 10–35

The results are presented for a study of the pressure behind reflected shock waves for pressures of (1–10)·1.33 · 10² N/m² ahead of the incident shock wave. It is found that during the first 1.0–2.0 · 10^?5 sec after the reflection of the shock wave the pressure of an argon plasma behind it corresponds to that calculated from the conservation laws with allowance for ionization on the assumption that the plasma is ideal.     

The transonic integral equation method with curved shock waves

Summary In the existing solutions of the extended integral equation method for transonic flows the shock wave has been assumed normal to the freestream. In this paper the effect of removing this assumption is investigated and flows with curved shock waves are examined.

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Die transonische Integralgleichungsmethode bei gekrümmten Stoßwellen

Zusammenfassung In den bisher veröffentlichten Lösungen der erweiterten Integralgleichung für transonische Strömungen wurde ein gerader Stoß senkrecht zur Anströmung angenommen. In der vorliegenden Arbeit wird diese Annahme fallengelassen, und Strömungen mit gekrümmten Stößen werden betrachtet.

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With 2 Figures     

Focusing of shock waves on reflection from concave curvilinear surfaces

Results from a comparative analysis of experimental and numerical simulation of the processes of reflection of plane shock waves from concave axisymmetric and two-dimensional surfaces are presented.Academic Scientific Complex The A. V. Luikov Heat and Mass Transfer Institute, Academy of Sciences of Belarus, Minsk. Scientific-Industrial Company Prostor, Moscow Region, Krasnoarmeisk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 65, No. 5, pp. 548–552, November, 1993.     

Propagation of strong converging shock waves in a gas of variable density

The problem of a strong converging spherical (or cylindrical) shock collapsing at the centre (or axis) of symmetry is extended to take into account the inhomogeneity of a gaseous medium, the density of which is decreasing towards the centre (or axis) according to a power law. The perturbative approach used in this paper provides a global solution to the implosion problem yielding accurately the results of Guderley's similarity solution, which is valid only in the vicinity of the center/axis of implosion. The analysis yields refined values of the leading similarity parameter along with higher-order terms in Guderley's asymptotic solution near the center/axis of convergence. Computations of the flow field and shock trajectory in the region extending from the piston to the center/axis of collapse have been performed for different values of the adiabatic coefficient and the ambient density exponent.     

Internal density waves of shock type induced by chemoconvection in miscible reacting liquids

Technical Physics Letters - A theoretical explanation of the phenomenon of spontaneous emergence of density waves experimentally observed recently in bilayered systems of miscible liquids placed in...     

Spall in non-one-dimensional shock waves

Consideration is given to non-stationary shock wave on spallation. Spall strength can be written as (i) pressure — particle velocity diagram in a one-dimensional case, and (ii) pressure — angle of turn flow diagram in a two-dimensional case. Experimental procedure involves (i) loading of the explosive by sliding detonation and (ii) orthogonal flash X-raying. In this way, some metals in particular low-melting ones and plastics as well as liquids have been studied based on the present results and those of other researchers. The dependences of spall strength — deformation rate have been obtained for substances studied in the form of power or linear functions. Some aspects of spallation and of accompanying effects on the base relations obtained are discussed.     

Determining mean integral refractive indices in geodetic rangefinding

Translated from Izmeritel'naya Tekhnika, No. 10, pp. 17–18, October, 1990.     

Converging shock waves in porous media

We have numerically solved several problems related to converging shock waves, including (i) one-dimensional spherical and cylindrical waves with cumulation limited to a ball or cylinder of small radius and (ii) shock-wave flow in a cone-shaped solid target. The passage from a continuous loaded substance to a porous medium in these problems leads to a significant increase in both temperature and pressure in the sample. This character of pressure variation depending on the porosity qualitatively differs from the case of plane waves of constant intensity, for which an increase in the sample porosity under otherwise equal conditions of loading always leads to a decrease in the pressure.     

Resonance reflection of acoustic waves in piezoelectric bi-crystalline structures

The paper studies the bulk wave reflection from internal interfaces in piezoelectric media. The interfaces of two types have been considered. Infinitesimally thin metallic layer inserted into homogeneous piezoelectric crystal of arbitrary symmetry. Rigidly bonded crystals whose piezoelectric coefficients differ by sign but the other material constants are identical. Analytic expressions for the coefficients of mode conversion have been derived. An analysis has been carried out of specific singularities arising when the angle of incidence is such that the resonance excitation of leaky interface acoustic waves occurs. The conditions for the resonance total reflection have been established. The computations performed for lithium niobate (LiNbO3) illustrate general conclusions.     

Propagation of spherical shock waves in water

The propagation and attenuation of spherical shock waves in water, produced by the explosion of spherical charge, is studied. Our results compare favourably with experimental data.     

Formation of shock waves in hyperelastic solids

Summary This paper studies the mechanism of shock formation from generalised simple waves in the case of an isotropic incompressible hyperelastic material. Fast and slow waves are identified and it is established that slow simple waves cannot tend to shocks on the wavefront. The time and position of occurrence of shocks when they do form is investigated with the aid of generalised Riemann invariants and a circularly polarised slow wave is identified. The special case of plane shear waves is commented upon.

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Ausbildung von Stoßwellen in hyperelastischen Festkörpern

Zusammenfassung Diese Arbeit beschäftigt sich mit dem Mechanismus der Ausbildung von Stoßfronten aus verallgemeinerten einfachen Wellen im Fall eines isotropen inkompressiblen hyperelastischen Werkstoffes. Schnelle und langsame Wellen werden identifiziert und es wird festgestellt, daß langsame einfache Wellen nicht zur Ausbildung von Stoßfronten an der Wellenfront führen können. Zeit und Ort des Auftretens von Stoßfronten, sofern sie sich bilden, werden mit Hilfe von verallgemeinerten Riemannschen Invarianten untersucht und eine zirkular-polarisierte langsame Welle wird identifiziert. Der Spezialfall ebener Scherwellen wird diskutiert.

     

Attenuation of laser-generated shock waves in Plexiglas

A simple analytic model is derived for describing the attenuation of a shock wave in a Plexiglas plate. At the same time, experimental measurements are presented with a well-designed optical-fiber sensor based on detection-beam deflection. The amplitude of the shock-wave pressure is measured experimentally and calculated numerically for analytic expressions at different distances from the region of the surface breakdown by the radiation of a single-pulse Nd:YAG laser. Good agreement between the experimental and the calculated values of the shock-wave pressure is established.     

Approximate solutions for the structure of shock waves

Summary Approximate solutions of the B-G-K model equation are obtained for the structure of a plane shock, using various moment methods and a least squares technique. Comparison with available exact solution shows that while none of the methods is uniformly satisfactory, some of them can provide accurate values for the density slope shock thickness _n . A detailed error analysis provides explanations for this result. An asymptotic analysis of _n for largeMach numbers shows that it scales with theMaxwell mean free path on the hot side of the shock, and that their ratio is relatively insensitive to the viscosity law for the gas.

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Näherungsweise Lösungen für die Struktur von Stoßwellen

Zusammenfassung Unter Verwendung verschiedener Momentenmethoden und der Methode der kleinsten Quadrate werden Näherungslösungen der Gleichung des B-G-K-Modells für die Struktur eines ebenen Stoßes erhalten. Der Vergleich mit der verfügbaren exakten Lösung zeigt, daß zwar keine der Methoden durchwegs befriedigend ist, einige von ihnen aber genaue Werte für die Dichteanstiegs-Dicke _n des Stoßes liefern. Eine genaue Fehleruntersuchung gibt Erklärungen für dieses Ergebnis. Die asymptotische Analyse der Dicke _n für großeMachzahlen zeigt, daß sie mit derMaxwellschen mittleren freien Weglänge auf der heißen Seite des Stoßes vergleichbar ist und daß der Quotient aus beiden verhältnismäßig unempfindlich gegen das Viskositätsgesetz des Gases ist.

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With 7 Figures     

The reflection of nonlinear irregular surface water waves

This paper concerns the reflection of irregular surface water waves from an impermeable vertical wall and investigates the similarities between this case and the direct, head-on collision of two identical wave groups travelling in opposite directions. A new set of experimental measurements is presented and compared with fully nonlinear numerical predictions based upon a multiple-flux boundary element method (BEM). Comparisons concern both the spatial and the temporal water surface elevations in the vicinity of the focused wave event; the latter occurring at the location of the wall. Linear and second-order irregular wave theories, commonly adopted as the basis for design solutions, are shown to significantly under-predict both the wave steepness and the maximum crest elevation in the vicinity of the wall. In contrast, the fully nonlinear numerical predictions are shown to be in very good agreement with the experimental measurements; the present results having been achieved without the need for smoothing, filtering or regridding.