[JMDag2004]

Hello fellow Foamers! I hope everyone is having a good day. I have simulated one pulse from a pulsed detonation engine cycle, H2-Air fuel/oxidizer.

Geometric set up: Structured mesh and the PDE is enveloped within a duct. Is a conceptual design for a propulsion system capable for providing thrust from static to hypersonic conditions with multi-mode operational settings. Search "multi-mode ejector augmented pulsed detonation rocket" if you wish to see a full description on the subject.

Case set up: Mode one operation is intended to provide thrust from runway conditions to roughly Mach 4, the limit to maintaining subsonic flow within the ejector duct and mixing chamber. Think of mode one as a thrust augmented ramjet. Not simulated is the inlet as this component has not been part of my research. Consequently, Military Spec 5008B along with 1D equations have been used to determine the ram recovery pressure, velocity, and temperature that would exist at the exit of the inlet compression system. These figures were then used as the inlet boundary conditions for my domain. As a result I ran simulations for freestream Mach numbers of 0,2, and 4.

Problem: I have run simulations for each scenario on three successive grid refinements. As far as the combustion is concerned, specie mass fraction histories look good, von-Neumann spike is accurately captured, while pressures and temperatures are a little off but pretty close. I've compared the data to NASA CEA and shock-tube experiments. Mixing of the flow streams, inlet (secondary flow) and combustion products (primary flow) seems to have been captured pretty well also. Unfortunately there isn't much experimental data available to compare results. So my line of thought is...because the combustion seems to be accurate, the other flow physics should be fairly accurate so I was going to move forward with quantifying my error and working on a grid independent solution. I'm trying to use Richardson Extrapolation but I'm running into some issues. My grid refinement ratios are not integer ratios, thus complicating the process of picking values from each mesh at the same location. In paraView I plotted variables over a line and in some instances there is monotonic convergence where in other instances there seems to be oscillatory convergence. I'm not sure if I should choose an average value over the outlet patch, I've noticed the same issue with monotonic and osc convergence when I averaged pressure and temperature over the outlet. Should I pick values where the gradients are high? My question here is I used limitedLinear and I am concerned the order of convergence was reduced to one in these areas because of the flux limiter and I need values determined with an order of convergence of two. This would be values far removed from high gradients. What values should I even pick? Never used Richardson Extrapolation so any help would be greatly appreciated! Please let me know if you have questions about other set up specifics, I wasn't sure what I should include in the post.

[JMDag2004]

Sorry I did forget to include the simulation is transient, if that wasn't clear. This also poses another question about using RE, which time step should I use or should I do the analysis for several time-steps? Again, any help would be greatly appreciated. Also, please feel free to suggest other validation methods as I am open to anything at this point, trying to wrap up thesis work and I am getting run down.