Validation of High Speed Reactive Flow Solver in OpenFOAM with Detailed Chemistry

Abstract

An OpenFOAM® based hybrid-central solver called reactingPimpleCentralFoam is validated to compute hydrogen-based detonations. This solver is a pressure-based semi-implicit compressible flow solver based on central-upwind schemes of Kurganov and Tadmor. This solver possesses the features of standard OpenFOAM® solvers namely, rhoCentralFoam, reactingFoam and pimpleFoam. The solver utilizes Kurganov & Tadmor schemes for flux splitting to solve the high-speed compressible regimes with/without hydrodynamic discontinuity. In this work, we present the validation results that were obtained from one-dimensional (1D) and two-dimensional (2D) simulations with detailed chemistry. We consider three different mixtures that fall into the categories of weakly unstable mixture (2H2 +O2 +3.76Ar and 2H2 +O2 +10Ar), and moderately unstable mixture (2H2 +O2 +3.76N2), based on their approximate effective activation energy. We performed the numerical simulations in both laboratory frame of reference (LFR) and shock-attached frame of reference (SFR) for the 1D cases. The 1D simulation results obtained using this solver agree well with the steady-state calculations of Zel’dovich von Neumann Döring (ZND) simulations with an average error below 1% in all cases. For the 2D simulations, circular hot-spots were used to perturb the initially-planar detonations to develop into spatio-temporally unstable detonation front. The convergence is declared when the front does not deviate much from the CJ speed (Chapman-Jouguet) and the regularity of cellular pattern on the numerical smoke foils reaches a steady state. We have verified from our preliminary studies that the SFR-based simulations are computationally cheaper in comparison to the LFR simulations and that the required grid resolution is always lesser in the former than the latter to reach the same level of accuracy (in terms of speed of the detonation front and cell sizes from the numerical smoke foil). We have also verified that at least 24 points per induction zone length (for weakly unstable mixture) and 40 points per induction zone length (for moderately unstable mixture) are required to sufficiently resolve the detonation structures that are independent of grids, boundary and initial conditions. Further reduction in computational cost of approximately 50% is achieved by using non-uniform grids, which converge effectively to the same solutions in comparison to the results from twice the number of grids with uniform resolution.