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Inviscid Simulation

This tutorial walks you through an external, inviscid simulation of a blunted cone at Mach 6 with angle of attack 12.5°. There are three outputs: a symmetry-plane slice, body-surface fields, and a pressure/Cp profile near the symmetry line.

For original test data and figures, see NASA TN D-1790 (Holloway & Dunavant, 1963).

Flowfield — symmetry-plane slice Flowfield (U-velocity) at Mach 6, α = 12.5°; symmetry-plane slice showing bow-shock stand-off and forebody structure.

Running the case​

Assuming the champs+ engine is on your path and you have a valid license file in the directory pointed to by CHAMPS_DATA, you can invoke the engine by simply typing champs+ on the command line. The engine will default to running the parameters in input.sdf, but if you want to run another input file you can simply run using champs+ other_input.sdf. See the command line reference for more information on command-line options.

Relevant input options​

1) Dictionary​

See dictionary.

  • Change angle of attack with aoa; change freestream Mach with mach.
  • dxmin sets the target minimum spacing.
  • Lscale = 1.0 defines the characteristic length; the characteristic time is tc = Lscale/umag.

2) Integration​

See integration.

  • Run for 5 characteristic times (stop time ≈ 5*tc). This is typically enough to settle a supersonic inviscid simulation.

3) IO​

  • output_directory = sim means that all data resulting from this simulation will be in the sim directory.

  • sym_plane (slice)

    • Plane normal direction = 2 at position = 0.001 (slight offset from symmetry).
    • output_interval = 1000 steps (output written every 1000 steps).
    • Use this to check bow-shock location and thickness.

  • surf_out (surface)

    • Writes body surface fields for stagnation pressure/Cp footprints.
    • Same cadence (output_interval = 1000).

  • press_out (profile)

    • A surface_slice on the body near the symmetry line: point = [0,0,0.001], normal = [0,0,1].
    • Exports: P, Cp = (P − Qinf::pinf)/(0.5*Qinf::rhoinf*umag^2), U, T: these expressions include flowfield values (P, T, U, V, W) and dictionary values.

What to expect​

Results from this case should approximately match the provided reference data. There is a python script included in the tutorial case called plot.py, which can be run using python3 plot.py.

Cp comparison: solver vs referenceCp comparison: solver vs reference

Example comparison of Cp along the symmetry meridian: solver (solid) vs. reference from TN D-1790 (dashed).