Fig. 1 Schematic of a forward-facing step
Keywords
supersonic flow, shock wave, forward facing step, Mach 3
Purposes
• Validation of GASFLOW for highly compressible flow at Mach 3 .
Descriptions
• The wind tunnel is 1 unit length high and 3 units long (Fig. 1). The forward facing step is 0.2 units high and is located 0.6 units from the left inlet. Gas with γ = 1.4 is used, and the domain is initialized with p = 1, T = 1, and Mach = 3.
• The tunnel height was discretized into a regular mesh of 80 cells, with 240 along the length, which produces a mesh of square cells of side length 1/80.
• Second-order MUSCL Van Leer scheme in GASFLOW-MPI was used.
Fig. 1 Schematic of a forward-facing step
Results
• At 0.5 s, a detached bow shock develops ahead of the step (Fig. 2). It curves strongly toward the upper surface of the step.
• The figure at 1.0 s shows that the bow shock strikes the upper boundary and the curvature decreases rapidly.
• The shock is reflected downwards from the upper boundary and strikes the upper surface of the step, as the figure at 2.0 s shows. A Mach reflection starts to be formed when the incident angle to the upper boundary of the domain is large enough.
• From 2.0 s to 4.0 s, the triple point of incident, normal and reflected waves gradually moves upstream and to the lower surface. Even the Kelvin-Helmholtz instability starting from the triple point is well predicted.
Fig. 2 Comparisons of transient forward-facing step supersonic flow at various times
(left: GASFLOW-MPI, second-order Van Leer; right: Woodward, PPMLR)
Summary
• GASFLOW-MPI is able to accurately capture the principle features of this supersonic flow, including its unsteady characteristics and shock wave reflection.
Reference
B. Woodward, P. Colella, The numerical simulation of two-dimensional fluid flow with strong shocks, Journal of Computational Physics, p. 54:115–173, 1984.
J. Xiao, W. Breitung, M. Kuznetsov, H. Zhang, J. R. Travis, R. Redlinger, T. Jordan, “GASFLOW-MPI: A new 3-D parallel all-speed CFD code for turbulent dispersion and combustion simulations: Part I: Models, verification and validation”, International Journal of Hydrogen Energy, March 2017.