Direct and large-eddy simulations of wall-bounded turbulent flows in complex geometries are presented in the thesis. To avoid the challenging resolution requirements of the near-wall region, we develop a virtual wall model in generalized curvilinear coordinates and incorporate the non-equilibrium effects via proper treatment of the momentum equations. The wall-modeled large-eddy simulation (WMLES) framework is formulated based on the wall model, accomplished via the stretched-vortex subgrid scale (SGS) model for the LES region. Based on this, we develop high-resolution in-house CFD codes, including direct numerical simulation (DNS), wall-resolved simulation (WRLES) and WMLES for wall-bounded turbulence simulations in complex geometries. First, we present LES of flow past different airfoils with Rec, based on the free-stream velocity and airfoil chord length, ranging from 104 to 2.1106. The numerical results are verified with DNS at low Rec, and validated with experimental data at higher Rec, including typical aerodynamic properties such as pressure coefficient distributions, velocity components, and also more challenging measurements such as skin-friction coefficient and Reynolds stresses. The unsteady separation behavior is investigated with skin friction portraits, which reveal a monotonic shrinking of the near wall structure scale. Second, we present LES of turbulent flow in a channel constricted by streamwise periodically distributed hill-shaped protrusions. Two Reynolds number cases, i.e. Reh=10595 and 33000 (based on the hill height and bulk mean velocity through the hill crest), are utilized to verify and validate our WMLES results. All comparisons show reasonable agreement, which enables us to further probe simulation results at higher Reynolds number (Reh=105). The Reynolds number effects are investigated, with emphasis on the mean skin-friction coefficients, separation bubble size and pressure fluctuations. The flow field at the top wall is evaluated with the empirical friction law and log-law as in planar channel flows. Finally, we present DNS of flow past the NACA0012 airfoil (Rec=104, AoA=10) with wavy roughness elements located near the leading edge. The effects of 2D surface roughness on the aerodynamic performance are investigated. For k8, massive separation occurs and almost covers the suction side of the airfoil dominating the airfoil aerodynamic performance.

A new hybrid approach to model high Reynolds number wall-bounded turbulent flows is developed based on coupling the two-level simulation (TLS) approach in the inner region with conventional large eddy simulation (LES) away from the wall. This new approach is significantly different from previous near-wall approaches for LES. In this hybrid TLS-LES approach, a very fine small-scale (SS) mesh is embedded inside the coarse LES mesh in the near-wall region. The SS equations capture fine-scale temporal and spatial variations in all three cartesian directions for all three velocity components near the wall. The TLS-LES equations are derived based on defining a new scale separation operator. The TLS-LES equations in the transition region are obtained by blending the TLS large-scale and LES equations. A new incompressible parallel flow solver is developed that accurately and reliably predicts turbulent flows using TLS-LES. The solver uses a primitive variable formulation based on an artificial compressibility approach and a dual time stepping method. The advective terms are discretized using fourth-order energy conservative finite differences. The SS equations are also integrated in parallel, which reduces the overall cost of the TLS-LES approach. The TLS-LES approach is validated and investigated for canonical channel flows, channel flow with adverse pressure gradient and asymmetric plane diffuser flow. The results suggest that the TLS-LES approach yields very reasonable predictions of most of the crucial flow features in spite of using relatively coarse grids.

The dissertation explores a framework for numerically simulating the deformation of the liquid metal wall's free surface in Z-pinch fusion devices. This research is conducted in the context of utilizing liquid metals as plasma-facing components in fusion reactors. In the Z-pinch fusion process, electric current travels through a plasma column and enters into a pool of liquid metal. The current flowing through the liquid metal generates Lorentz force, which deforms the free surface of the liquid metal. Modeling this phenomenon is essential as it offers insights into the feasibility of using liquid metal as an electrode wall in such fusion devices. The conventional magneto-hydrodynamic (MHD) formulation aims at modeling the situation where an external magnetic field is applied to flows involving electrically conducting liquids, with the initial magnetic field is known and then evolved over time through magnetic induction equation. However, in Z-pinch fusion devices, the electric current is directly injected into a conducting liquid. In these situations, an analytical expression for the magnetic field generated by the applied current is not readily available, necessitating numerical calculations. Moreover, the deformation of the liquid metal surface changes the geometry of the current path over time and the resulting magnetic field. By directly solving the Maxwell equations in combination with Navier-Stokes equations, it becomes possible to predict the magnetic field even when the fluid is in motion. In this dissertation, a numerical framework utilizing the Maxwell-Navier-Stokes system is explored to successfully capture the deformation of the liquid metal's free surface due to applied electric current. / Doctor of Philosophy / In this dissertation, a method is described that uses a computer to simulate how the initially stable, flat surface of liquid metal deforms when subjected to electrical currents in Z-pinch fusion devices, a specific type of nuclear fusion technology. Z-pinch fusion devices generate plasma, a hot fluid-like substance, through the nuclear fusion process, triggered and maintained by strong pulsated current. There's a growing interest in using liquid metal as the first layer of material to isolate the hot plasma from the rest of the nuclear fusion reactor body, rather than solid materials, due to its unique benefits. However, the Z-pinch fusion process, by introducing electric currents through the liquid metal layer, induces a Lorentz force that consequently deforms the surface of the liquid metal. Developing a tool to predict this deformation is vital as it aids in evaluating the potential of using liquid metal as a plasma-facing layer over solid materials in these fusion devices. The simulation tools presented in this dissertation are able to successfully captures the dynamics of how the liquid metal surface deforms under the impact of electrical currents.

Lors du développement d’un nouvel avion, l’estimation des échanges d’énergie entre l’air ambiant et les parois est une donnée cruciale pour la conception aérothermique. Cette conception repose de plus en plus sur des simulations numériques mais certains phénomènes d’aérothermique externe, comme le jet débouchant du système de dégivrage des nacelles moteur, montrent les limites des modèles RANS classiques. La simulation des grandes échelles (LES) se révèle bien adaptée à ce type de phénomène mais se heurte à un coût de calcul extrêmement élevé pour ces écoulements pariétaux à très grand nombre de Reynolds. Pour lever cette limitation, cette thèse propose l’étude de deux briques fondamentales : la LES avec loi de paroi (WMLES) conjuguée à l’injection d’une couche limite turbulente à l’entrée du domaine. Pour une meilleure compréhension et une utilisation fiable de l’approche loi de paroi, on se concentre tout d’abord sur les sources d’erreur qui lui sont associées. Après les avoir identifiées, on propose une correction de l’erreur de sous-maille ainsi qu’une loi de paroi adaptée aux écoulements compressibles. Grâce à ces deux éléments, on obtient une estimation correcte du flux de chaleur pariétal sur des simulations WMLES de canal plan supersonique sur parois froides. Puis, pour préparer la transition vers des applications plus industrielles, on introduit un schéma numérique plus dissipatif ce qui nous permet d’étudier l’influence de la méthode numérique sur l’approche loi de paroi. Dans une seconde partie dédiée à l’injection de couche limite pour la WMLES, on sélectionne une méthode basée sur l’injection de perturbations combinée à un terme de contrôle volumique. On montre que des simulations WMLES utilisant cette méthode d’injection permettent d’établir une couche limite turbulente réaliste à une courte distance en aval du plan d’entrée, à la fois sur une plaque plane mais également sur un écoulement de jet débouchant à la géométrie plus complexe, représentative d’un cas avion. / During the design of a new aircraft, the prediction of energy exchanged between the ambient air and the aircraft walls is crucial regarding aerothermal design. Numerical simulations plays a role of increasing importance in this design. However classical RANS models reach their limits on some external aerothermal flows, like the jet-in-cross-flow from the anti-icing system oh the engine nacelles. The large eddy simulation (LES) is well suited to this kind of flow but faces an extremely large computational cost for such high Reynolds number wall-bounded flows. To remove this limitation, we propose two building blocks: the Wall Modeled LES (WMLES) combined with a turbulent inflow generation. For a better understanding and a reliable use of the WMLES, we first focus on the sources of error related to this approach. We propose a correction to the subgrid-scale error as well as a wall model suitable for compressible and anisothermal flows. Thanks to these two elements, we correctly predict the wall heat flux in WMLES computations of a supersonic isothermal-wall channel flow. Then, to allow the computation of more industrial flows, we introduce some numerical dissipation and study its effect on the wall modeling approach. The last part is dedicated to turbulent inflow generation for WMLES. We select a method based on synthetic perturbation combined with a dynamic control term. We validate this method on WMLES computations of a flat plate turbulent boundary layer and a hot jet-in-cross-flow representative of an industrial configuration. In both cases, we show that a realistic turbulent boundary layer is generated at a small distance downstream from the inlet plane.