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1994 | Buch

Interaction of Shock Waves

verfasst von: R. S. Srivastava

Verlag: Springer Netherlands

Buchreihe : Fluid Mechanics and Its Applications

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Über dieses Buch

One of the great twentieth-century achievements in the mechanics of fluids was the full elucidation of the physics of shock waves and the later comprehensive development of understanding of how shock waves propagate (i) through otherwise undisturbed fluid and (ii) in interaction either with solid bodies or with independently generated fluid flows. The interaction problems (ii) were soon found to raise some very special difficulties (beginning with the common formation of "Mach stems" in shock-wave reflection) yet they also turned out to possess enormous scientific interest as well as being highly important in practical applications. For all these reasons the appearance of this book on "Interaction of Shock Waves" by one of the world's major contributors to knowledge in that field is most particularly to be welcomed. It covers all those approaches to the subject which have been found fruitful, and most satisfactorily goes into comprehensive detail about each. At last the important achievements of the leading research workers, experimental as well as theoretical, on shockwave interaction problems are brought together in a single convenient and well written volume. I warmly congratulate the author and the publisher on having performed, for the benefit of everyone interested in the mechanics of fluids, this immensely valuable service.

Inhaltsverzeichnis

Frontmatter
Chapter - I. Introduction
Abstract
The problems relating to the behaviour of a shock wave encountering either another shock wave, or a rarefaction wave, or an interface separating two media (one of which may be rigid) are described as ‘Interaction of Shock Waves’. This subject, associated with almost all the real physical situations involving shocks, is one of the most important branches of modern mechanical science. This study is of great practical importance in connection with blast effect on supersonic aircrafts from the view point of weapon analysis and the vulnerability of either a missile or a re-entry vehicle to blast. This branch of science inspite of its manifold utility has not received the attention it warrants because of considerable difficulties involved in obtaining the solution of the problems.
R. S. Srivastava
Chapter - II. Reflection of Shock Waves
Abstract
The study of reflection of shock waves from rigid boundaries has been a subject of considerable interest. Reflection phenomenon can be divided into three sub-heads.
R. S. Srivastava
Chapter - III. Diffraction of Normal Shock Wave
Abstract
Investigations of the flow field produced by the interaction of a plane shock with an obstacle, stationary or moving, preclude an explicit theory because of the mathematical complications. The complication is primarily because of the fact that non uniform shock waves which occur imply variation in the entropy of the fluid and a loss of irrotational character of the motion. Two possible courses are open for attacking the problem from a theoretical stand point.
R. S. Srivastava
Chapter - IV. Diffraction of Oblique Shock Wave
Abstract
Lighthill (1949) has considered the diffraction of a plane shock travelling parallel to a wall and meeting an edge where the wall turns through a small angle. The analogous problem for a plane shock impinging on the wall at an incidence together with the reflected shock has been considered by Srivastava and Ballabh (1955), Srivastava (1968) and Srivastava and Chopra (1970). In Lighthill’s case the relative outflow from the normal shock is always subsonic but in the case of oblique shock wave, relative outflow from reflected shock can be subsonic, sonic or supersonic. In the oblique case therefore, three cases have to be considered. Before one considers the reflected diffracted shock, it would be necessary to consider the intermediate region between the incident and reflected shock waves.
R. S. Srivastava
Chapter - V. Diffraction of Normal Shock by Yawed Wedges
Abstract
Chester ( 1954 ) extended Lighthill’s ( 1949 ) theory by considering the interaction of a plane normal shock wave with an infinite thin wedge at small angle of incidence, and arbitrary angles of yaw up to a certain limiting value depending on the shock strength . If the velocity of the shock is U and the wedge is yawed through an angle ß, then the point of intersection of the shock front and leading wedge travelsalong the leading wedge with velocity \( {U \over {\sin \beta }}. \). If an equal and opposite velocity is superimposed on the whole field, the shock becomes stationary and we have the steady flow behind the shock . The flow in fact in many respects has similarity to Busemann’s cone field problem .
R. S. Srivastava
Chapter VI. Diffraction of Oblique Shock by Yawed Wedges
Abstract
Chester (1954) considered the problem of reflection and diffraction of plane shock wave interacted by yawed wedges which was the extension of the Lighthill’s (1949) problem of diffraction of a normal shock wave past a small bend. The results presented in this chapter are the generalisation of the results given in chapter IV to the case of yawed wedges (Chopra & Srivastava(1972), Chopra(1972)). More specifically this attempt is concerned with the study of interaction of an oblique shock configuration(consisting of incident and reflected shock) with a yawed wedge i.e. shock line (intersection of incident and reflected shock) makes some non zero angle with the leading edge of the wedge. The theoretical investigation of the flow field produced after the interaction is difficult not only because of the non- linear nature of the problem, but also because of the fact that the diffraction of the reflected shock will result in variations in entropy of the fluid and a loss of irrotational character of the motion. On the assumption that the wedge produces only small perturbations in the uniform flow, the entropy variations, though not negligible can, however, be suppressed from the equations governing the flow by basing the analysis on pressure perturbation; in any case the pressure is the most interesting variable.
R. S. Srivastava
Chapter - VII. Shock Interaction with Moving Aerofoil
Abstract
Lighthill (1949) investigated the diffraction of a normal shock wave past a small bend. Chester(1954) extended the work of Lighthill to include infinte wedges at yaw. The work presented in this chapter is that of Smyrl(1963) and is concerned with a plane shock wave meeting a thin two dimensional aerofoil moving in the opposite direction at supersonic speed. The effect of yaw has also been included in the analysis.
R. S. Srivastava
Chapter VIII. Diffraction of Shock by Flat Surfaces
Abstract
Ting and Ludloff (1952) have obtained the pressure and density fields that develop behind shocks advancing over arbitrary flat surfaces based on the linearized theory. The work presented here is more direct and the results obtained are more general than those of Lighthill (1949). Shocks passing over flat surfaces of arbitrary shape can be dealt with in such a manner that explicit expressions result for the pressure and density fields in the whole domain behind the advancing shock. In this way, comparison with shock tube experiments can be carried out, and interesting details about the nature of the “slip stream” occurring in Mach reflection can be determined.
R. S. Srivastava
Chapter IX. Approximate Theory on Diffraction of Shocks
Abstract
Whitham (1957,1959) proposed an approximate theory for a shock diffracting at a corner of any angle. This theory is not limited to the ease of a corner made up of plane walls but is applicable to wall of any shape. The shape of the shock may be obtained for all times, but no information about the flow field behind the shock is obtained.
R. S. Srivastava
Backmatter
Metadaten
Titel
Interaction of Shock Waves
verfasst von
R. S. Srivastava
Copyright-Jahr
1994
Verlag
Springer Netherlands
Electronic ISBN
978-94-011-1086-0
Print ISBN
978-94-010-4474-5
DOI
https://doi.org/10.1007/978-94-011-1086-0