In this work, the mathematical implications of merging two different turbulence modeling approaches are addressed by deriving the exact hybrid RANS/LES Navier-Stokes equations. These equations are derived by introducing an additive-filter, which linearly combines the RANS and LES operators with a blending function. The equations derived predict additional hybrid terms, which represent the interactions between RANS and LES formulations. Theoretically, the prediction of the hybrid terms demonstrates that the hybridization of the two approaches cannot be accomplished only by the turbulence model equations, as it is claimed in current hybrid RANS/LES models. The importance of the exact hybrid RANS/LES equations is demonstrated by conducting numerical calculations on a turbulent flat-plate boundary layer. Results indicate that the hybrid terms help to maintain an equilibrated model transition when the hybrid formulation switches from RANS to LES. Results also indicate, that when the hybrid terms are not included, the accuracy of the calculations strongly relies on the blending function implemented in the additive-filter. On the other hand, if the exact equations are resolved, results are only weakly affected by the characteristics of the blending function. Unfortunately, for practical applications the hybrid terms cannot be exactly computed. Consequently, a reconstruction procedure is proposed to approximate these terms. Results show, that the model proposed is able to mimic the exact hybrid terms, enhancing the accuracy of current hybrid RANS/LES approaches. In a second effort, the Two Level Simulation (TLS) approach is proposed as a near-wall model for LES. Here, TLS is first extended to compressible flows by deriving the small-scale equations required by the model. The full compressible TLS formulation and the hybrid TLS/LES approach is validated simulating the flow over a flat-plate turbulent boundary layer. Overall, results are found in reasonable agreement with experimental data and LES calculations.

This report formulates the boundary conditions and discretization method for conducting a simulation of heat with liquids and solids through the finite element method. It introduces the reader to the movement that is due today with optimization of heat transport and mitigation generally described as the fourth generation of district heating. It presents the scope: calculating the heat release from pipes in hydronic underfloor heating, and presents the belonging question: how does heat release from different heating pipe patterns affect the body’s heat transfer? Simulation of the work is conducted with the delimitations of using a single boundary slip condition addressing friction and only using water as pipe flow medium. It focuses on the pattern’s ability to affect the heat to the body, of which characteristically manifests a square concrete slab in the running simulations. By using different cases, it analyses how patterns using the same length of pipes emit their average heat to the covering top surface differently, both as the heating level alternates, and duration for response changes. This meanwhile they are affected by analog boundary temperature conditions.    A sensitivity analysis is done answering how the various patterns tested are affected by change of propagation speed for the flowing medium, showing that a spiral formed pattern with evenly spread piping is the least affected. The results show that the pattern with alternating pipe spacing gives the best average heat emission in the simulated cases. It also concludes that minor changes in the pattern area will have profound effect on the average transferred heat from the body’s top surface.