Page 246 - 48Fundamentals of Compressible Fluid Mechanics

208 CHAPTER 13. OBLIQUE-SHOCK
1
these models .

13.2 Introduction

13.2.1 Introduction to Oblique Shock

The normal shock occurs when there is a disturbance downstream which imposed
on the flow and in which the fluid/gas can react only by a sharp change to the
flow. As it might be recalled, the normal shock occurs when a wall is straight/flat
) as shown in Figure 13.1 which occurs when somewhere downstream a
2
disturbance appears. When the deflection angle is increased the shock must
match the boundary conditions. This matching can occur only when there is a
(c
discontinuity in the flow field. Thus, the direction of the flow is changed by a shock

wave with an angle. This shock communally is referred to as the oblique shock.
3
Alternatively, as discussed in Chapter 1 the flow behaves as it in hyperbolic field.
In such case, flow fluid is governed by hyperbolic equation which is where the
information (like boundary conditions) reaches from downstream only if they are
within the range of influence. For information such as the disturbance (boundary
condition) reaches deep into flow from the side requires time. During this time, the
flow moves ahead downstream which creates an angle.

13.2.2 Introduction to Prandtl–Meyer Function

Decreasing the defection angle results
0 ◦
in the same results as before: the ν ∞ (k) Prandtl θ max (k)
Meyer
Oblique
Function
boundary conditions must match the Shock
geometry. Yet, for a negative (in this
section notation) defection angle, the
No Shock
flow must be continuous. The anal- zone
ysis shows that velocity of the flow
Fig. 13.2: The regions where the oblique shock
must increased to achieve this re-
or Prandtl–Meyer function exist. No-
quirement. This velocity increase is tice that both a maximum point and
referred to as the expansion waves. “no solution” zone around zero. How-
As it will be shown in the next Chapter, ever, Prandtls-Meyer Function ap-
as oppose to oblique shock analysis, proaches to closer to zero.
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 is presented. This 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).
2 Zero velocity, pressure boundary condition are example of forcing shock. The zero velocity can be
found in a jet flowing into a still medium of gas.
3 This section is under construction and does not appear in the book yet.