Compressibility effects in supercritical mixing layers

My research focuses on CO₂ mixing layers, where a lower-temperature, higher-speed stream interacts with a higher-temperature, lower-speed stream. The code simulates these flows, capturing shear layer growth, turbulence anisotropy, turbulent kinetic energy (TKE) budgets, and vorticity. As of now, I am studying non-reacting ideal gas cases. In time, we will move onto multicomponent cases such as CH₄/O₂, with the possibility of extending to reacting flows for comparison. The goal is to generate high-fidelity datasets at multiple grid resolutions, comparing and investigating supercritical compressibility and thermal inhomogeneity effects on turbulence. 

The research conducted will be the subject of my master's thesis. I am working alongside my advisor Doctor Joseph Oefelein and his Research Engineer Dhruv Purushotham. I will be presenting my findings at the AIAA SciTech 2025 conference. 

Thanks to this research opportunity I'm learning key CFD skills: 

  • Linux command line
  • Python coding
  • Field Visualization Software: ParaView, tecplot
  • Methods of solving Partial Differential Equations
  • Fluid dynamics
  • Grid creation

Characteristic Boundary conditions

I implemented characteristic boundary conditions on the inflow and outflow boundaries of the domain following the paper by Poinsot and Lele on "Boundary Conditions for Direct Simulations of Compressible Viscous Flows". 

Outflow

At the downstream plane I treat the flow locally as one-dimensional and inviscid in the normal direction. I compute two wave amplitudes that are leaving the domain and one that is entering. The two outgoing waves come entirely from interior gradients of pressure, density, and the normal velocity; the incoming wave is modeled with a mild pressure-relaxation law that nudges the mean exit pressure toward a target far-field value. From those three wave amplitudes I recover the normal derivatives of pressure, normal velocity, density, and temperature using the standard local one-dimensional inviscid relations. Finally, I advance the halo values one cell outside the domain by adding those normal derivatives times the local grid spacing to the last interior values; the transverse velocities are simply copied.

 

Inflow

On the inflow plane I impose the time-dependent velocity vector from the SEM inflow generator and, I set a fixed temperature. I then estimate the wave that leaves the domain from the interior gradients and obtain the single incoming acoustic wave by combining that estimate with the measured time rate of change of the imposed normal velocity (this is the standard “LODI with target velocity” relation). With those two waves I reconstruct only the pressure gradient in the normal direction and update the halo pressure by one grid spacing; I do not overwrite the SEM velocities or the imposed temperature. This keeps the pressure compatible with the incoming velocity waveform while preventing reflections.

Understanding Boundary Condition Equat

Equations for Outflow:

Equations for Inflow: