Dr Kamarul Arifin B. Ahmad PPK Aeroangkasa Gas Dynamics ESA 341 Bab 4 Dr Kamarul Arifin B. Ahmad PPK Aeroangkasa

Oblique shock wave Introduction Control volume and symbols Equation of motion Relation between mach number(M) and deflection and shock wave angles ( and ) Ratio of flow properties Mach number relations Relation of  and 

Introduction Definition A compression shock wave occurs that is inclined at an angle of the flow Still represent a sudden, almost discontinuous change in fluid properties We will be focused on the 2D straight oblique shock wave. A concave corner A symmetrical wedge

Control volume and symbols Vt1 Vn1 Vt2 Vn2 V1  y x 1  Upstream flow angle V2 Downstream flow angle   2 P2 P1 T2 T1 2 1 y x

Equations of motion Continuity equation Momentum Equation Energy equation

Relation between mach number(M) and deflection and shock wave angles ( and ) Vn1 Vt1  -   V1 Vn2 y

Ratio of flow properties y x 1  Upstream flow angle

Mach number relations Replacing M1sin for M1 and M2sin (-) for M2

Relation of  and  when: Mach Wave Vn1 Vt1  -   V1 Vn2 y Normal shock Mach wave Mach Wave

Physical phenomena associated with the oblique shock wave 1. For any given upstream Mach number M1, there is a maximum deflection angle, max. If the the physical geometry is such that > max, then the shock will be detached.

Physical phenomena associated with the oblique shock wave 2)For any given < max, there will be two straight oblique solutions for a given upstream Mach number. For example, for M1=2.0 and =150, then from the graph,  can be equal either 45.3 or 79.80. The smaller  is called the weak shock solution, and the larger is called the strong shock solution.  Strong shock Weak shock

Physical phenomena associated with the oblique shock wave This may sometimes be more conveniently plotted as:

Physical phenomena associated with the oblique shock wave 3) For attached shocks with a fixed deflection angle, as the upstream Mach number M1 increases, the wave angle  decreases, and the shock wave becomes stronger. Or, when M1 decreases, the wave angle increases, and the shock becomes weaker. =200 =53.30 M1=2.0 Mn1=1.60 P2/P1=2.82 =200 =29.90 M1=5.0 Mn1=2.49 P2/P1=7.07

Physical phenomena associated with the oblique shock wave 4)For attached shocks with fixed upstream Mach number, as the deflection angle increases, the wave angle  increases, and the shock becomes stronger. However, when > max, the shock wave will be detached. =530 M1=2.0 Mn1=1.6 P2/P1=2.8 =100 =39.20 M1=2.0 Mn1=1.26 P2/P1=1.69 =200

Oblique-shock reflections

Oblique-shock reflections cont. For a given M1 and d1, find 1. Find M2 and P2/P1. Since d2 = d1, use M2 to find 2. Find M3 and P3/P2. Finally: 1 2 1-  1

Oblique-shock Application

Application Oblique shocks desirable on supersonic intakes to reduce total pressure losses.

Group Exercises 5 1) Consider a supersonic flow with a Mach number M = 2, with a static pressure p = 105 Pa, and a static temperature T = 288K. The flow is deflected at a compression corner through 20o. Calculate the Mach number, the static pressure, the temperature, the stagnation pressure and the stagnation temperature behind the resulting oblique shock wave. 2) Consider a supersonic flow with M = 2, p = 1 atm, and T = 288K. The flow is deflected at a compression corner through 20o. Calculate M, p, T, po and To behind the resulting oblique shock wave.