Conditional moment closure for LES of compressible turbulent reactive flows

While the Conditional Moment Closure (CMC) method has been de- veloped with reference to low Mach number flows, the formulations considered in this thesis work avoid taking any simplification on the acoustics, so as to pursue a fully compressible formulation. Two cou- pling strategies for a LES formulation of fully compressible reactive flows adopting the CMC method are presented. Similarly to standard CMC approaches, both strategies rely on re- casting the full Navier-Stokes system into two sub-systems, the first filtered and solved by means of LES in the physical space, the other conditionally filtered and solved in the CMC space. The two approaches differ by the way the two sub-systems are cou- pled. In the first coupling strategy, referred to as ”Vector Field Up- date” (VFU), the CMC interacts with the LES sub-system by actually modifying the density and sensible energy LES fields. In the second coupling strategy, referred to as ”Energy Source Update” (ESU), the source term in the LES energy equation is computed on the basis of the species source terms obtained by the time integration of the CMC system. This way, the CMC interaction with the LES sub-system re- lies on the modification of the LES energy source term, while any LES state variable is directly modified. The numerical implementation of the LES/CMC equations for both coupling strategies has been carried out and explained in detail. The LES flow solver relies on central two-to-six order discretization of the convective terms of the Navier-Stokes equations cast in fully split form, leading to a locally conservative formulation which guarantees discrete conservation of the total kinetic (mechanical) energy. This approach allows a stable and accurate spatial discretization of the convective terms without the addition of numerical dissipation.The conditionally filtered CMC subsystem is discretized on a Carte- sian mesh in the CMC space, and the time advance is based on a further splitting in time between an explicit treatment of the convec- tive operator and an implicit treatment (using BDF, as in CVODE) of the fully coupled reactive-diffusive operators. The predictive capabilities of a zero-dimensional version of the CMC code are presented. The solution sensitivity to scalar dissipations is tested varying its strength and shape. An a-priori prediction of the SANDIA-D flame has been performed, and the comparison with ex- perimental results is presented. The VFU and ESU CMC-LES cou- pling strategies are compared by means of 2D test case, and the differ- ences are discussed. The scalability performance, and the preliminary results of a 3D version of the code are presented.