Handbook of Shock Waves

Shock waves have fascinated mankind from the dawn of history. Before the discovery of explosive materials the commonly encountered shock waves were thunders. Until the 17^th century such violent phenomena were enshrouded in mystery and they were related to evil powers. As mentioned in section 1.4.1 Earnshow (1851) was probably the first who related the thunder propagation to supersonic velocity. Now we know that shock waves result from a very sudden release of chemical, electrical, nuclear, or mechanical energy in a limited space. In nature the most frequently encountered shock wave is the thunder that follows the lightning. Shock waves are also associated with earthquakes and volcanic eruptions. A typical man-made shock wave results from the detonation of explosive materials. Also, complex shock wave structures appear in all supersonic flights. These all can range from weak shock waves associated with the use of any firearm up to shock waves resulting from nuclear explosions reaching enormous magnitudes. In descriptive terms, a shock wave is a very sharp, thin front through which there exists a sudden change in all flow properties, such as pressure, temperature, density, velocity and entropy. At standard atmospheric conditions the width of a shock wave front is about 2.5 Angstrom.

Shock waves appear in many forms and in various media. In the Handbook of Shock Waves we have tried to cover as many as possible of these forms. Firstly, in Chapter 1, a brief historical description indicating milestones of shock wave research and activities starting in the sixteen century and continuing up to the end of the Second World War is given. It was decided to end the historical survey at 1945 since many of the post-war investigations are presented in the various chapters of the Handbook.

General propagation laws governing shock wave transmission through matter is are outlined in Chapter 2, in which the basic equations governing shock wave propagation are presented. These equations are used in subsequent chapters.

In Chapter 3.1 a detailed description of shock wave propagation in gases is given; shock wave propagation in liquids follows in Chapter 3.2 and shock wave propagation in solids in Chapter 3.3. The rest of Chapter 3 is dedicated to special aspects of shock waves in gases. In Chapter 3.4 the unique case of rarefaction shocks is discussed; this is followed, in Chapter 3.5, by a discussion on shock wave stability. Although most of the Handbook deals with shock waves on earth and in the earth atmosphere, shock waves are not limited to our planet. One of the theories explaining the creation of the universe is via the 'big-bang', which is the ultimate shock wave. Shock waves are daily events in the sun's corona and a frequent occurrence in the solar wind in space. Chapter 3.6 is devoted to shock waves in space.

For experimental studies of shock waves one needs facilities that can generate flows in which shock waves appear in a laboratory environment. Furthermore, special diagnostics systems are required in order to detect, observe and provide records enabling the analysis of a laboratory-generated shock. In Chapter 4 various facilities suitable for the generation of shock waves are presented. The classical shock tube facility and the flow field it produces are outlined in Chapter 4.1. The extension of the shock tube concept to shock tunnels and piston driven shock and expansion tunnels is described in Chapters 4.2 and 4.3, respectively. The various shock tube facilities described in Chapters 4.1 to 4.3 are primarily designed to produce step like shock waves, i.e., shock waves associated with a sudden jump between two different, uniform states.

However, shocks generated in the atmosphere, i.e., blast waves, are usually different from those defined above. In such waves fast pressure decay follows the sudden jump in the pressure across the shock front. Chapter 4.4 describes blast tubes, which are facilities suitable for producing blast waves. A common feature to all facilities described in chapters 4.1 to 4.4 is the fact that they all produce very short duration flows, significantly less than a second. When longer flow durations are needed, for example if steady flow is studied, one resorts to supersonic and hypersonic wind tunnels. The flow duration in such facilities is measured in minutes. The construction and operation of supersonic and hypersonic wind tunnels is described in Chapter 4.5. Experimental investigation of shock wave phenomena requires, in addition to the facility for producing shock waves, appropriate measuring techniques. Such devices must have extremely short response times, should not disturb the investigated flow field and should produce unambiguous results. A survey of diagnostic techniques suitable for flow visualization is given in Chapter 5.1. A complementary diagnostic used for studying high temperature flows generated behind strong shock waves, is spectroscopy. This technique is presented in Chapter 5.2.

Until the late 1960's most of the shock wave investigations were experimental. This was an unavoidable consequence of the fact that the equations of motion governing shock wave generated flows are non-linear. Only for special flow conditions do such equations have analytical solutions. Otherwise, a numerical solution is the only available option. This option became feasible only after the rapid development in computer software and hardware that started in the 1970's. Today, numerical analysis is replacing experimental investigation as a primary tool in studying shock wave phenomena. Many different codes have been developed especially for studying shock wave phenomena. The major ones are described in Chapter 6 where numerical methods suitable for investigating shock wave phenomena are discussed.

The rest of the Handbook deals with some specific types and aspects of shock wave phenomena. In Chapter 7 the simplest shock wave generated flow and wave interactions, the one-dimensional flow case, is discussed. The natural second step, described in Chapter 8, is the two-dimensional wave interaction. In Chapter 8.1 reflections of oblique shock waves from rigid surfaces are discussed. Shock wave refraction is presented in Chapter 8.2, followed, in Chapter 8.3, by a description of shock waves interactions with boundary layers. This complex process is of major importance because it appears in real supersonic flows over bodies. A special case of two-dimensional flow is that resulting from shock wave reflection from axi-symmetric bodies; such cases are the topic of Chapter 9.

Propagation of shock waves in straight tunnels was described while discussing shock tube facilities (Chapter 4.1) and one-dimensional interactions (Chapter 7). In practice one encounters tunnels in which there are bends, curvatures, splittings and other obstacles. Obviously, such additions spoil the one-dimensional nature of the flow and thereby increase the complexity of the prevailing flow field. Chapter 10 treats, theoretically, experimentally and numerically shock wave propagation in channels of different geometry.

A special case of one-dimensional shock wave flow is the case in which the flow has a spherical symmetry. Spherical shock waves result from detonation of spherical explosives. These shocks decay as they expand until they reduce to sound waves. Their fast decay is a direct result of the fact that a given amount of energy is spread out over an ever-increasing volume of fluid. The opposite is true for spherical shock waves that propagate towards the center namely, imploding shocks. In such cases the shock strength increases as it approaches the center. The physical background of imploding shock waves is outline in Chapter 11 where shock wave focusing is discussed. Shock wave focusing is the cornerstone of lithotripsy, a technique employed for shattering kidney stones. Recently it was extended for usage in ophthalmology, gene therapy, thrombus ablation and food preservation. Details regarding these recent applications are given in Chapter 12 where the application of shock waves in medicine is discussed. A survey of expanding spherical shock waves (blast waves) is given in Chapter 13.1. The last chapter discussing spherical shocks, Chapter 13.2, provides a general attenuation law for spherical expanding shock waves.

An important topic that has drawn attention in recent years is shock-induced instabilities of interfaces separating different gases or phases. This is the topic of Chapter 14. Chapter 15 deals with various aspects of shock wave propagation in multi-phase media. In Chapter 15.1 shock wave propagation in porous media is presented. The considered media are composed of deformable or rigid skeletons whose voids are filled with gas. A special case of porous media is a granular medium. In such a case the skeleton is composed of small solid particles packed on together. Propagation of shock waves in granular media is the topic of Chapter 15.2. Cases of two-phase flow are discussed in Chapters 15.3 and 15.4. The former deals with shock wave in inert and reactive bubbly liquids and the latter with shock wave propagation in liquid-gas suspensions.

The last part of the Handbook, Volume 3 whose editing was done by Professor Assa Lifshitz of the Hebrew University in Jerusalem, is dedicated to chemical reactions taking place in the hot post-shock flow. These topics are considered in Chapter 16. A special case of chemical reactions induced by strong shock waves propagating in a combustible gas mixture is the case of combustion, detonation and deflagration. This topic is covered in Chapter 17.

The present Handbook is the result of a cooperative effort of 47 scientists from 15 countries, each knowledgeable in his own field. We hope it will serve as a useful source of information for scientists, engineers and students active in shock wave research. Although we have tried to cover as many aspects of shock wave phenomena as we could, we are fully aware that this is a target one may approach but not necessarily reach. It is hoped that in future editions additional topics will be added.

Many scientists, engineers and students around the world are engaged in shock wave studies. Each has his reason for being attracted to investigating these phenomena. For two of us (Gabi Ben-Dor and Ozer Igra) it was the late Professor Irvine I. Glass who opened the door to the world of shock waves and was our guide through this fascinating subject while we took our early steps in the field of shock wave phenomena. We are grateful to him for introducing us to the path along which we continue to walk with ever increasing interest.