VM-EXD-MECH-001

VM-EXD-MECH-001
Flow of Gas Past an Infinite 2-D Wedge

Overview

Reference: Harlow, Francis H. et al., Fluid Dynamics – A LASL Monograph, LA-4700, June 1971.
Analysis Type(s): Explicit Dynamics 2-D
Elements: Multi-material Euler Quad
Boundary Conditions: Euler Outflow, Default Wall
Structural Interactions: No
Fluid-Structure Interactions: Yes, fully coupled
Bonds: No
Materials: Ideal Gas

Test Case

Perform a dynamic flow analysis of a Mach 2 gas flowing past a 2-D wedge until a steady-state configuration is obtained. An attached shock is formed, the angle of which is determined by the flow conditions.

Because the appearance of the configuration is independent of magnification, there is no significant length to the system.

Calculation Description

The scenario is modeled as a rigid piston pushing a column of ideal gas over the wedge. The top boundary is set to rigid to prevent the gas from flowing out from there. At the bottom, the gas is contained by the geometry. At the right is a Euler outflow boundary.

Figure 224: Model Setup

Model Setup

The initial conditions for the Ideal Gas in both parts are:

γ = 1.4
ρ = 0.001 gm/cc
p+ = 100 MPa
I0 = 2.5E5 J/Kg
ux = 1000 m/s

The calculation is run for 3000 cycles, by which time a steady-state condition is achieved.

Results Comparison

The sound speed of the gas is given by m/s. The inflow Mach number is therefore . The angle of the detached shock is approximately 49 degrees, in agreement with the reference result:

Figure 225: Pressure of the Gas in a Steady-State Condition

Pressure of the Gas in a Steady-State Condition