The purpose of this work is to implement four additional inviscid flux methods in the U2NCLE solver being developed at Mississippi State University. The goal is that some or all of these methods may provide benefits over the current options with respect to accuracy or robustness. These four methods include both the Harten, Lax, Van Leer, Einfeldt (HLLE) and Harten, Lax, Van Leer ? Contact (HLLC) methods as well as the Advection Upstream Splitting Method (AUSM) and its successor AUSM+. The HLL family, which includes both HLLE and HLLC are based on the Riemann problem, which is divided into a number of states. The AUSM family attempts to combine the effects of both flux vector and flux difference splittings to create better schemes. Several simple and complex cases were run with each new method and compared to the methods currently available as well as experimental and analytical results when available. The results of the simple tests showed that all the methods were similarly suited for delivering accurate results on simple cases. In more complex cases, however, the AUSM family proved to be less robust and failed to converge for the final case. The HLLE method showed excellent robustness qualities but seemed to over predict the viscous values in several cases. The HLLC method proved equally as accurate and robust as Roe's Method.

Of the surface capturing schemes, the levelset and multi-phase models are implemented and extensively examined. First, the levelset method is shown, and its weaknesses are identified; a mis- appropriation of changes in momentum, a strong dependence on the density by the eigenvalues of the inviscid flux Jacobian, and a prescribed density transition. These weaknesses are specifically addressed and overcome by the formulation of the multi-phase model. Consequently, the multi-phase model is chosen for this work. Previous surface fitting techniques simply absorb the gravitational source term into the pressure. It must be noted that this absorbtion is valid only for single density flows; since the surface fitting approach is solving only one side of the interface, there is no significant change in the density througout the domain. Consequently, absorbing the gravitational source into the pressure term is not possible in a surface capturing scheme in which both sides of the interface are solved. Thus, a new treatment of the gravitational source term is required and is presented in this work. A multi-phase model is implemented into a parallel, three-dimensional, unsteady, incompressible Navier-Stokes flow solver for the purpose of examining free surface flows on unstructured meshes. The reasons for choosing this model above others are presented, and the multi-phase model is discussed. The base algorithm is briefly examined with emphasis given to the areas which require additional care. The construction of the gravity source term which drives the formation of the waves is explained in detail, and its effects on the rest of the algorithm are identified. Finally, the method is carefully compared with available data on a submerged NACA 0012 airfoil, the Wigley Hull, the Series 60 Cb=0.6 ship, and the DTMB 5415 ship.

A precise prediction of the heat loads in metal materials in contact with the hot gas is an increasingly demanding problem in the design phase of the complex cooling schemes in the modern turbine engines. The coupled calculation of the fluid flow and the heat transfer is a promising approach as heat transfer coefficients are not necessary in the calculation and the heat transfer itself is part of the calculation and can be derived from local heat fluxes. Therefore, it is useful to incorporate an appropriate scheme for directly coupled heat transfer computations (conjugate heat transfer), capable of handling complex geometries into the existing Computational fluid dynamics (CFD) codes. The intent of the present work is to add the conjugate heat transfer solving capability to an existing flow solver. The coupled approach is achieved by maintaining a continuous local heat flux and a common temperature at the points along the fluid-solid interface. At every iteration, the temperature which is directly calculated via the equality of the local heat fluxes passing the fluid-solid contacting cell faces serves as the thermal boundary condition on the interfaces, instead of traditional isothermal/adiabatic thermal boundary conditions. In the solid domain, simplified energy equation is solved using the discretization and computational methods which have been used in the flow by introducing an effective equation of state. The connectivity is built for the points at the fluid-solid interfaces in order to communicate the thermal conditions with each other. Validation of the developed conjugate capability has been investigated. Computed results have been compared with theoretical or experimental results for laminar flat plate, high pressure guide vane, cooled plate, and effusion-cooled plate. All results obtained thus far compare rather favorably with theoretical or experimental results.

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