Verification and validation of numerical solutions of two-dimensional reactive flow in rocket engine nozzles

Two-dimensional mathematical models for gaseous H₂/O₂ reactive flows are solved for two geometries: a conical and a parabolic one. Five different physical models are studied: two one-species and three multi-species models (frozen, equilibrium and non-equilibrium flows). In the mathematical model, temperature is used as unknown in the energy equation and velocity is obtained for all speed flows. For all analyses, a non-orthogonal finite volume code was implemented, taking into account first (UDS) and second (CDS) order interpolation schemes and co-located grid arrangement. Model predictions of the pressure distribution and Mach number in the nozzle with a conical geometry, calculated using a CDS scheme, were found to agree well with experimental results. For both geometries, numerical results for apparent orders of convergence agreed well with the asymptotic (expected) ones for one-species flows. Some other analyses were provided for mixture of gases flows; in this case, for frozen flow, the apparent order values tend to the asymptotic ones in all cases; for local equilibrium flow, the use of CDS degenerated the apparent order to unity; this fact can be associated to the use of UDS interpolation scheme in the source term of the energy equation. Numerical solutions, including their error estimates, are provided for UDS and CDS schemes. Their analysis shows that global variables of interest (such as thrust and specific impulse) are less affected by the chosen physical model than are local variables of interest (such as the temperature at the symmetry line).