A new multi-phase model for low speed gas/liquid mixtures is presented; it does not require ad-hoc closure models for the variation of mixture density with pressure and yields thermodynamically correct acoustic propagation for multi-phase mixtures. The solution procedure has an interface-capturing scheme that incorporates an additional scalar transport equation for the gas void fraction. Cavitation is modeled via a finite rate source term that initiates phase change when liquid pressure drops below its saturation value. The numerical procedure has been implemented within a multi-element unstructured framework CRUNCH that permits the grid to be locally refined in the interface region. The solution technique incorporates a parallel, domain decomposition strategy for efficient 3D computations. Detailed results are presented for sheet cavitation over a cylindrical head form and a NACA 66 hydrofoil.

Numerical simulations of cavitation in liquid nitrogen and liquid hydrogen are presented; they represent a broader class of problems where the fluid is operating close to its critical temperature and thermal effects of cavitation are important. A compressible, multiphase formulation that accounts for the energy balance and variable thermodynamic properties of the fluid is described. Fundamental changes in the physical characteristics of the cavity when thermal effects become significant are identified; the cavity becomes more porous, the interface less distinct, and it shows increased spreading while getting shorter in length. The heat transfer model postulated in variants of the B-factor theory, where viscous thermal diffusion at the vapor-liquid interface governs the vaporization, is shown to be a poor approximation for cryogenic fluids. In contrast the results presented here indicate that the cavity is sustained by mass directly convecting into it and vaporization occurring as the liquid crosses the cavity interface. Parametric studies for flow over a hydrofoil are presented and compared with experimental data of Hord (1973, “Cavitation in Liquid Cryogens II—Hydrofoil,” NASA CR-2156); free-stream velocity is shown to be an independent parameter that affects the level of thermal depression.

Preconditioning techniques that are used to alleviate numerical stiffness due to low Mach numbers in steady flows have not performed well in unsteady environments since the preconditioning parameters that are optimal for efficiency are detrimental to the level of spatial dissipation necessary for accuracy. A unified flux formulation is presented where the optimal scaling required for spatial accuracy is independent of the preconditioning required for convergence thus providing a framework that is valid over a broad range of flow conditions. Both upwind flux-difference and AUSM-type schemes are investigated. In both cases, the use of unsteady preconditioning scaling in the flux formulation is shown to be critical for preserving unsteady accuracy. In the flux-difference case, the formulation is based on a generalized blending of the steady and unsteady preconditioning terms. In the AUSM case, the formulation introduces two modifications to the standard AUSM+up scheme, designated as AUSM+up' wherein the pressure dissipation is scaled using unsteady preconditioning and AUSM+u'p' wherein both the pressure and velocity dissipation terms are scaled by the unsteady preconditioning. Low Mach number vortex propagation and acoustic problems are used to demonstrate the strengths of the formulation. These studies show that the AUSM family generally performs better than the blended flux-difference schemes in terms of vortex shape preservation and control of odd-even splitting errors.

As an interim step towards the development of a hybrid upwind structured/unstructured solver for combusting/multiphase flowfields, the TRI3D unstructured code of Barth has been extended to analyze multicomponent combusting flows. The extensions mimic the Roe/total variation diminishing (TVD) based thermochemical extensions in the structured solver, CRAFT, and entail a strong coupling of chemical species equations and complete linearization of the chemical source term, treated hi a fully implicit manner. Issues regarding the quality of solutions obtained using locally one-dimensional Riemann flux procedures and TVD limiters are more pronounced in unstructured formulations and are dealt with in depth in this article. Comparative studies of structured and unstructured analyses of laminar premixed flames, ducted shock-induced combustion, and blunt-body shock-induced combustion serve to delineate these issues and the need for solution adaptive gridding and unproved flux limiters to capture flame zones properly.

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A method is presented for redesigning a centrifugal impeller and its inlet duct. The double-discharge volute casing is a structural constraint and is maintained for its shape. The redesign effort was geared towards meeting the design volute exit pressure while reducing the power required to operate the fan. Given the high performance of the baseline impeller, the redesign adopted a high-fidelity CFD-based computational approach capable of accounting for all aerodynamic losses. The present effort utilized a numerical optimization with experiential steering techniques to redesign the fan blades, inlet duct, and shroud of the impeller. The resulting flow path modifications not only met the pressure requirement, but also reduced the fan power by 8.8% over the baseline. A refined CFD assessment of the impeller/volute coupling and the gap between the stationary duct and the rotating shroud revealed a reduction in efficiency due to the volute and the gap. The calculations verified that the new impeller matches better with the original volute. Model-fan measured data was used to validate CFD predictions and impeller design goals. The CFD results further demonstrate a Reynolds-number effect between the model- and full-scale fans.

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