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∇∇∇∇∇∇∇∇∇∇∇∇∇∇∇∇∇∇∇∇∇∇ooooooooooooooooooooooooooooooooooooooFig. 12.4:The pressure ratio as a function of the dimensionless time
CHAPTER 13Oblique Shock13.1Preface to Oblique Shock= 0Fig. 13.1:A view of a straight normal shock asa limited case for oblique shockIn Chapter (5), discussion on a normalshock was presented. A normal shockis a special type of shock wave.Theother type of shock wave is the obliqueshock.In the literature oblique shock,normal shock, and Prandtl–Meyer func-tion are presented as three separateand different issues. However, one canview all these cases as three differentregions of a flow over a plate with a de-flection section. Clearly, variation of thedeflection angle from a zero (δ= 0) to apositive value results in oblique shock. Further changing the deflection angle to anegative value results in expansion waves. The common representation is doneby not showing the boundaries of these models. However, this section attempts toshow the boundaries and the limits or connections of these models1.1In this chapter, even the whole book, a very limited discussion about reflection shocks and collisionsof weak shock, Von Neumann paradox, triple shock intersection, etc are presented. The author believesthat these issues are not relevant to most engineering students and practices.Furthermore, theseissues should not be introduced in introductory textbook of compressible flow. Those who would liketo 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 VonNeuman paradox of oblique shock reflection,” Phys. Fluids 6, 1874 (1994).241
242CHAPTER 13. OBLIQUE SHOCK13.2Introduction13.2.1Introduction to Oblique ShockA normal shock occurs when there is a disturbance downstream which imposesa boundary condition on the flow in which the fluid/gas can react only by a sharpchange in the flow direction. As it may be recalled, normal shock occurs when awall is straight/flat (δ= 0) as shown in Figure (13.1) which occurs when somewheredownstream a disturbance2appears. When the deflection angle is increased, thegas flow must match the boundary conditions. This matching can occur only whenthere is a discontinuity in the flow field. Thus, the direction of the flow is changedby a shock wave with an angle to the flow. This shock is commonly referred toas the oblique shock. Alternatively, as discussed in Chapter (1)3the flow behavesas it does in a hyperbolic field. In such a case, the flow field is governed by ahyperbolic equation which deals with the case when information (like boundaryconditions) reaches from downstream only if they are within the range of influence.