The Influence of Boundary Conditions on Three-Dimensional Large Eddy Simulations of Calorically Perfect Gas Detonations

Abstract

In this work, we revisit the application of the compressible linear eddy model for large eddy simulation (CLEM-LES) of calorically perfect gas detonations in an attempt to clarify if the Kolmogorov number can be treated as a constant instead of a tuning parameter when no-slip boundary conditions are included in three-dimensional simulations. In its early development, the CLEM-LES with a one-step combustion chemistry model was used to simulate two-dimensional methane-oxygen detonations to gain insight on the roles and impact of turbulent mixing rates on the presence of unburned pockets of reactive gas and cellular structure. In these past simulations, special treatment of the boundary conditions was not considered, and therefore wave speeds always recovered the Chapman-Jouguet (CJ)-velocity. Moreover, tuning of the Kolmogorov number was required in order to qualitatively capture the experimentally observed flow fields. In this work we carefully perform three-dimensional simulations of detonation propagation using the CLEM-LES, and include no-slip walls as boundary conditions. Also, instead of tuning the Kolmogorov number to obtain the correct cell size, as was done in the past, we instead use a standard value of 1.5. We found that by carefully specifying the boundary conditions, and treating the Kolmogorov as a constant (thus no model calibration), both the expected propagation velocity deficit and cellular structure are recovered. Finally, upon constructing the resulting energy spectrum, we found that the kinetic energy cascade follows the well-known −5/3 power law description of incompressible turbulence in the inertial subrange, but was not symmetric nor isotropic.