| A model for calculating the interaction between shock waves and a reacting aluminum droplet was developed. The model accounts for acoustic impedance mismatch at the liquid surface, droplet deformation, wave propagation in the liquid, and cavitation. To solve this problem, a low-dissipation method for computing reacting gas dynamic flows was developed. This method combines features from the double-flux multi-component model, nonlinear error-controlled WENO, adaptive TVD slope limiters, rotated Riemann solvers, and adaptive mesh refinement to obtain a method that is both robust and accurate. Success of the technique is demonstrated using an extensive series of numerical experiments including premixed deflagrations, Chapman-Jouget detonations, re-shocked Richtmyer-Meshkov instability, shock-wave and hydrogen gas column interaction, and multi-dimensional detonations. An extended Riemann problem accounting for phase change and surface tension was developed to couple a reacting gas to a vaporizing compressible liquid. The numerical method compares well with empirically measured separation locations over spheres, heat transfer correlations, and droplet deformation criterion. The numerical algorithms developed in this work are fairly robust and applicable to a wide variety of compressible chemically reacting flows with or without interface capturing and phase change. Computed results for shock waves interacting with liquid droplets indicate that shock waves reduce evaporation rate for non-reacting Al droplets, while increasing the burning rate when chemical reactions are considered; suggesting that the combustion of aluminum droplets may be kinetically-controlled mechanisms. To the author's knowledge, this work represents the first time that a compressible reacting gas-dynamic flow has been coupled to a compressible liquid with vaporization and surface tension. |
