Concepts from the transformation theory of ordinary and partial differential equations have been applied to determine self-similar solutions of the nonlinear partial differential equations of nonlinear and linear diffusion phenomena, hydrodynamics, and radiation hydrodynamics. Equations of state for which self-similar solutions for shock waves in solids exist have been found. Invariance properties of turbulence models have been calculated together with the corresponding solutions. An invariant source iteration method for one- and two-dimensional multigroup neutronics calculations has been developed. The theory of Lie group extensions in discretized jet spaces needed to construct invariant difference schemes has been worked out in terms of grid point values of dependent variables.

Isothermal flow tests to determine parametric flow resistance characteristics of hypervapotron (i.e., single sided ribbed flow channels) configurations are being conducted in low-pressure water with prototypic dimensions and flow rates. Initial data compare well with previous measurements and good friction correlation of the data is achieved.

A numerical model of boiling heat transfer in heterogeneous porous layers with and without chimneys has been conducted. Experimental observations have provided qualitative modeling information and model refinements. 1-D and 2-D models have been evaluated numerically with nonlinear coupling between mass, momentum, energy, capillary pressure, and evaporation rate. Good agreement with published data has been obtained. Examination of artificially created layer performance suggests broad potential application for controlled boiling heat transfer, such as computer chip cooling via freon or other CFCs, with heat fluxes in excess of 100 W/cm², and in steam generator performance.

The effects of interfacial mixing and contact area between two liquids of differing densities and temperatures have been studied, which result from a high-density, high-temperature liquid passing through a lower density, low-temperature liquid. Heat transfer effects, including the effects of vapor generation as well as break-up and solidification, are modeled. Analytical modeling was carried out at UIUC while simulant experimental studies of both single and multiple injected columns were conducted at Argonne National Laboratory. Good agreement between model predictions and experimental data has been found.

Heat transfer in random porous media is usually dominated by conduction. However, in the situation of coal ash deposits, granular nuclear fuel, and debris beds in nuclear reactor accidents, conduction is coexisting with radiation and even convection. The multimode situation increases the mathematical nonlinearity of the problem and suggests the use of the Monte Carlo method for such simulations. An iterative process is envisioned with coupling between the different heat transfer mode through an energy balance equation. Variance reduction methods are being investigated for the conduct of the simulations.

* Denotes principal investigator.