The motivation for this research is to overcome the costs of using the current wind tunnels which replicate the high speed, temperatures and Reynolds numbers of new concept vehicles such as Hyper-Sonic passenger jets. The idea is that by employing accurate computational methods, costs can be reduced and more scenarios can be investigated. It will be argued that the characteristic based split scheme is a modified central difference temporal scheme, and can be utilized to capture the flow regimes of interest to the European Space Agency (ESA). The hypothesis of this thesis is that it is possible to model Hyper-Sonic applications with shock capturing reliably in a collocated, unstructured polyhedral, Finite Volume (FV) software framework. The reason for this hypothesis is a desire to develop an alternative approach for accurate, non-oscillatory solutions to the conservation laws for high speed flows that does away with calculating the upwind flow direction, donor nodes, Riemann solvers and can avoid Jacobian evaluations. The finite volume method is generally preferred for industrial Computational Fluid Dynamics (CFD) because it is relatively inexpensive and lends itself well to the solution of large sets of equations associated with complex flows according to Greenshields et al. Usually physical variables such as velocity, temperature, density and pressure are co-located, which means that the values at the centroid of a control volume are chosen to represent these physical variables in the enclosed control volume. Co-location is popular in industrial CFD, because it allows greater freedom in mesh structure for complex 3D geometries and for refinement of boundary layers as mentioned in Greenshields et al. It is no coincidence that collocated, polyhedral, FV numerical methods are adopted by several of the best known industrial CFD software packages, including FLUENT, STAR CCM+ and CFD-ACE+. There is a current preference for unstructured meshes o f polyhedral cells with six faces (hexahedra) or more, rather than tetrahedral cells that are prone to numerical inaccuracy and other problems. For example, Ferguson and Peric mention that they are unsuitable for features such as boundary layers. Discontinuities, such as shocks, in Hyper-Sonic compressible computations require numerical schemes that can accurately capture these features while avoiding spurious numerical oscillations. Current methods that are effective in producing accurate non-oscillating solutions are first of all monotone upstreamcentred schemes for conservation laws- by Van Leer; secondly the nonoscillatory (ENO) schemes by Harten A, Engquist B, Osher S, and lastly the weighted ENO schemes known as WENO schemes by Liu, X. D., Osher, and Chan. Unfortunately these methods typically involve Riemann solvers and Jacobian evaluation, making them complex and difficult to implement in a collocated, 3D unstructured framework. This work seeks to find a method which overcomes these disadvantages.

The thesis focuses on the prediction of solvation thermodynamics using integral equation theories. Our main goal is to improve the approach using a rational correction. We achieve it by extending recently introduced pressure correction, and rationalizing it in the context of solvation entropy. The improved model (to which we refer as advanced pressure correction) is rather universal. It can accurately predict solvation free energies in water at both ambient and non-ambient temperatures, is capable of addressing ionic solutes and salt solutions, and can be extended to non-aqueous systems. The developed approach can be used to model processes in biological systems, as well as to extend related theoretical models further.

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The boiling of distilled water in a 9 ft long 2 in. I.D. copper single tube natural circulation evaporator was investigated with particular reference to entrance effects. Heat transfer coefficients and pressure drops were compared for with and without an entrance. The tube was divided into six sections and the heat transferred to each measured separately. Measurements included inlet velocities, heat fluxes, pressure drops and stream and wall temperatures. The heat transfer results from all the six sections were correlated by the following non-dimensional equations. With an entrance, hTFd/Kl = 0.38(Pr)0.6L (Re)0.35L (L/D) 0.06 (Q/GA)0.3 (/PD)-0.54 and without an entrance hTFd/Kl = 0.12 (Pr)0.6L (Re)0.28L (L/D)0.14 (Q/GA)0.27 (/PD)-0.65. The pressure drop results were correlated by the following equations. With an entrance, (PTP/L / PSPL/L) -- 1 = 1890 (Xo)0.81 and without an entrance, (PTP/L / PSPL/L) -1 = 649(Xo)0.45 by using a resistance probe technique, flow regimes during boiling were also investigated and graphs were produced for predicting the flow regimes. Throughout this work the terms "With and Without an entrance" refer to entrance effects.

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