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o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o Fig. 12.4: The pressure ratio as a function of the dimensionless time
CHAPTER 13 Oblique Shock 13.1 Preface to Oblique Shock = 0 Fig. 13.1: A view of a straight normal shock as a limited case for oblique shock In Chapter ( 5 ), discussion on a normal shock was presented. A normal shock is a special type of shock wave. The other type of shock wave is the oblique shock. In the literature oblique shock, normal shock, and Prandtl–Meyer func- tion are presented as three separate and different issues. However, one can view all these cases as three different regions of a flow over a plate with a de- flection section. Clearly, variation of the deflection angle from a zero ( δ = 0 ) to a positive value results in oblique shock. Further changing the deflection angle to a negative value results in expansion waves. The common representation is done by not showing the boundaries of these models. However, this section attempts to show the boundaries and the limits or connections of these models 1 . 1 In this chapter, even the whole book, a very limited discussion about reflection shocks and collisions of weak shock, Von Neumann paradox, triple shock intersection, etc are presented. The author believes that these issues are not relevant to most engineering students and practices. Furthermore, these issues should not be introduced in introductory textbook of compressible flow. Those who would like to obtain more information, should refer to J.B. Keller, “Rays, waves and asymptotics,” Bull. Am. Math. Soc. 84, 727 (1978), and E.G. Tabak and R.R. Rosales, “Focusing of weak shock waves and the Von Neuman paradox of oblique shock reflection,” Phys. Fluids 6, 1874 (1994). 241
242 CHAPTER 13. OBLIQUE SHOCK 13.2 Introduction 13.2.1 Introduction to Oblique Shock A normal shock occurs when there is a disturbance downstream which imposes a boundary condition on the flow in which the fluid/gas can react only by a sharp change in the flow direction. As it may be recalled, normal shock occurs when a wall is straight/flat ( δ = 0 ) as shown in Figure ( 13.1 ) which occurs when somewhere downstream a disturbance 2 appears. When the deflection angle is increased, the gas flow must match the boundary conditions. This matching can occur only when there is a discontinuity in the flow field. Thus, the direction of the flow is changed by a shock wave with an angle to the flow. This shock is commonly referred to as the oblique shock. Alternatively, as discussed in Chapter ( 1 ) 3 the flow behaves as it does in a hyperbolic field. In such a case, the flow field is governed by a hyperbolic equation which deals with the case when information (like boundary conditions) reaches from downstream only if they are within the range of influence.

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