A basic feature of hyperbolic systems of conservation laws is that there are rich phenomena of wave interactions involving shock waves and contact discontinuities. In the classical inviscid gasdynamics framework, a wall boundary is modelled as a symmetry plane and the reflection of a shock wave thus. We also suppose that the diaphragm is completely removed from the. If the oblique shocks turn the flow 10 and 8, sequentially, determine. Shock w aves in gas dynamics 61 courantf riedrichs s book 19 gives the account of the e orts on the equations by many of the leading mathematicians before 1948. The material is presented in such a manner that beginners can follow the subject comfortably. With a strong emphasis on basic concepts and problemsolving skills, this text is suitable for a course on gas dynamicscompressible flowshighspeed aerodynamics at both undergraduate and postgraduate level in aerospace engineering, mechanical engineering, chemical engineering and applied physics. Let us consider the case where the physical domain. Unsteady interaction of shock and detonation waves in gases. For mach reflection in steady supersonic flow, the slipline and reflected shock. A common belief was that this impossibility is of thermodynamical nature. Solution of twodimensional riemann problems of gas dynamics. The course builds upon foundations laid in an earlier course where the emphasis was on subsonic ideal.
Because the shock has a very small thickness, changes in flow variables across the shock may be assumed to occur without change of crosssectional area. The triple shock pattern is pure if it is made only of the incident, re. Lecture notes compressible fluid dynamics mechanical. The content of this book is licensed under creative commons. Course held at the department of hydroand gasdynamics, july 1970. In this paper we establish the global existence of solutions for both configurations. In applied gas dynamics, professor ethirajan rathakrishnan introduces the hightech science of gas dynamics, from a definition of the subject to the three essential processes of this science, namely, the isentropic process, shock and expansion process, and fanno and rayleigh flows. Shock wave reflection phenomenaspringerverlag, new york. Compressible flow or gas dynamics is the branch of fluid mechanics that deals with flows having significant changes in fluid density. Size and shape of shock waves and slipline for mach reflection in. Aug 19, 2016 strength of a shock wave is defined as the ratio of increase in static pressure across the shock. A second series shows the effects of caloric imperfections on continuous onedimensional flow and on the flow through normal and oblique. Part of the modeling and simulation in science, engineering and technology book series msset.
Basic concepts of fluid mechanics astrophysical dynamics, vt 2010 gas dynamics. Shock waves in gas dynamics 61 courantfriedrichss book 19 gives the account of the e. Weak shock reflection in channel flows for dense gases. These are a set of class notes for a gas dynamics viscous. Since the flow in zone 1 is parallel to wedge a, it strikes the solid wall at angle a as shown by the white dashed line. Topics addressed include the thermodynamic and electrophysical parameters of gas flow behind shock waves, the effect of nonequilibrium physicochemical processes on the flow parameters behind a shock wave, shock tube investigations of unsteady swi, swi with a porous compressible medium, and the reflection of shock waves by a plane surface. Beginners will find thorough descriptions of these waves in c. Gas dynamics by james e a john intended for juniorseniorfirstyear graduate courses in gas dynamics or compressible flow, in departments of mechanical engineering. The solution of a simple wave type is obtained with the aid of the method of characteristics. Holographic interferometric animation of shock diffraction and reflection using a highly. The velocity just upstream of the shock is 500 ms, the static pressure is 50 kpa and the static temperature is 250 k. In this section the relationships between the two sides of normal shock are presented.
New the book makes exclusive use of spreadsheet computations a first in books on gas dynamics. The book broadly follows the two main categories of shock. A normal shock propagated into still air travels with a speed a equal to the speed of sound in the still air b larger than the speed of sound in the still air. Global solutions of shock reflection problem for the. This book was written as a graduate student courseshock dynamics. Global solutions of shock reflection by largeangle wedges. The dependences of magnitude of this shock change in reflected discontinuity s intensity on the intensity of the incident shock are plotted.
It makes use of spreadsheet programs, and contains unique procedures that have never appeared before in any gas dynamics book. Shock waves in real gases course held at the department of hydro and gas dynamics, july 1970. Shock is formed due to coalescence of various small pressure pulses. Analytic treatment of regular reflection for polytropic gases. Bendors book displays a lot of experimental results and describes, at least on a phenomenological basis. An investigation is presented of the numerical modeling of discontinuous flows of an ideal gas arising in the interaction of shock waves with barriers. Modeling of the interaction of shock waves with a barrier. Regular and mach reflection of shock waves researchgate. In gas dynamics, this means that with v the unit normal to the shock front pointing towards the plus region, then either u.
Exam ii november 8 autumn 20, questions and answers studocu. When a plane shock hits a wedge head on, it experiences a reflection diffraction process and then a selfsimilar reflected shock moves outward as the original shock moves forward in time. Theory of shock waves and introduction to gas dynamics ya. Normal shock wave equations, shock wave,normal shock tables,normal shocks,chapter five normal shock waves,normal. These are a set of class notes for a gas dynamicsviscous.
Experimental, computational, and asymptotic analysis has shown that various patterns of shock reflection may occur, including regular and mach reflection. We are concerned with the shock reflection in gas dynamics for the pressure gradient system. This edition of a very successful and widely adopted book has been brought uptodate with computer methods and applications throughout. The riemann problem and interaction of waves in gas dynamics.
With a strong emphasis on basic concepts and problemsolving skills, this text is suitable for a course on gas dynamics compressible flowshighspeed aerodynamics at both undergraduate and postgraduate level in aerospace engineering, mechanical engineering, chemical engineering and applied physics. Attention is given to the reflection of a plane shock wave from a concave cylindrical surface. Since shock reflection in presence of walls imposes a direction to the velocity in the diffracted flow. A normal shock wave occurs in a nozzle in which air is steadily flowing. The book begins with a quantitative description of the fundamental laws of gas dynamics and goes on to explain such phenomena. More specifically, it is a flow whose mach number exceeds 1.
Bird, molecular gas dynamics and the direct simulation of gas flows. Beginners will find thorough descriptions of these waves in. The flow downstream of the reflected shock is denoted as zone 2. The article also provides dependences of reflected discontinuity s intensity on the intensity of incident shock falling on the wall for all types of reflections. Up to now, the first author has taught this course to the graduate students in the field of fluid mechanics, department of modern mechanics, university of science and technology of china for seven times. Numerical modeling of chemistry and gas dynamics during shockinduced ethylene combustion. These are a set of class notes for a gas dynamicsviscous flow course taught to juniors in. Shock wave,normal shock wave equations,strength of characteristics at a curved shock wave, shock.
This paper discusses the refraction of plane shock waves in media with arbitrary equations of state. This book was written as a graduate student course shock dynamics. The richer complexity of flows scenarios possible beyond classical shock reflection is demonstrated. This book introduces the shock dynamic method and explains the underlying concepts, then progresses to a systematic description of the methods, equations and applications of shock dynamics. Apr 06, 2018 the shock wave then strikes a solid wall and reflects from the wall generating a new shock. One series of charts presents the characteristics of the flow of air considered a perfect gas for oblique shock waves and for cones in a supersonic air stream. Beyond constant flows, we consider piecewise constant flows. The onset of a gradient catastrophe as well as discontinuous solutions in continuous flows is shown. It analyzes the evolution of the gas jet from the continuum to the regime of almost free collisions between molecules, and includes numerous figures, illustrations, tables and references. Shock wave reflection phenomena request pdf researchgate. Due to the complexities of gasdynamic shock reflection phenomena, the reflected and incident waves merge into a new wave front called the mach stem 18.
Aug 19, 2016 compression wave front being normal to the direction of compressible fluid flow. These effects are caused by the nonlinear terms in the gas dynamics. Supersonic flow and shock waves by richard courant, 9780387902326, available at. The latter take place either between two shocks or between a shock and a boundary. When a plane shock hits a wedge head on, it experiences a reflectiondiffraction process and then a selfsimilar reflected shock moves outward as the original shock moves forward in time. Emanuel covers all the important aspects of gasdynamics, with particular emphasis. Shock is an abrupt discontinuity in the flow field and it occurs in flows when the local flow speed exceeds the local sound speed. Part of the international centre for mechanical sciences book series cism, volume 37. While all flows are compressible, flows are usually treated as being incompressible when the mach number the ratio of the speed of the flow to the speed of sound is less than 0. Shock waves in real gases course held at the department of. Numerical methods of calculation of reflection of shock waves in real gases. Selfsimilar solutions for weak shock reflection siam.
The theories for the laval nozzle and normal and oblique shock waves. These effects are caused by the nonlinear terms in the gas dynamics equations. On the refraction of shock waves journal of fluid mechanics. In this discussion, the flow is assumed to be in a steady state, and the thickness of the shock is assumed to be very small. Experimental and computational analysis has shown that two patterns of regular reflection may occur. Find materials for this course in the pages linked along the left.
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