Similarity Analysis and Invariant Difference Schemes for Hydrodynamics, Transient Heat Conduction Plasma Physics, and Multigroup Neutronics
R. A. Axford,* L. J. DeMers, B. A. Temple
Lawrence Livermore National Laboratory, B341494; University of Illinois

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 plasma physics. 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. Exact difference equations for transient heat conduction have been determined. 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.

A Study in Heat and Mass Transfer with Boiling in Porous Deposits
B. G. Jones,* C. Pan,* X. Li
University of Illinois (In conjunction with the Department of Mechanical and Industrial Engineering)

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 tube performance.

Axial Offset Anomaly in PWR Cores
B. G. Jones,* C. Pan,* X. Li
University of Illinois

A study of axial offset anomaly conditions in PWR cores, focusing on boron holdup and retention in porous layers on fuel pins, is underway. Computational models indicate sufficient boron accumulation in solution could account for the axial shift. Examination of potential mechanisms for crud deposition, including radiochemical processes, suggests that combined effects of electrolysis of water in the core may explain the controlling mechanisms. Research is focusing on clarifying which physical mechanisms dominate the processes. The nuclear power industry strongly desires to resolve this issue.

Effect of Boiling on Interfacial Behavior during Melt Quench Processes
B. G. Jones,* B. W. Spencer,* J. Schneider
U.S. Department of Energy, DE-FG07-89ER12900 (In conjunction with the Department of Mechanical and Industrial Engineering)

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 is found.

Hypervapotron Isothermal Flow Resistance Tests for Use in ITER Divertor Cooling
B. G. Jones,* D. Driemeyer* (McDonnell Douglas-St. Louis), X. Li
U.S. Department of Energy, DE-YBE233R-CO4A

Isothermal flow tests have been conducted to determine parametric flow resistance characteristics of hypervapotron (i.e., boiling in single-sided ribbed flow channels) configurations using low-pressure water systems, with prototypic dimensions and flow rates. Experimental data indicate friction factors significantly lower than previously published correlations and are only slightly higher than smooth wall values. For very small flow channel height, of the dimension of the tooth pitch or smaller, the tests show a modest friction factor increase, being very sensitive to accurate channel height determinations.

Stability Analysis of Boiling Water Reactor Nuclear-coupled Thermal Hydraulics
R. Uddin,* J. Dorning, A. A. Karve
University of Virginia

Nonlinear finite-amplitude flow and power oscillations are important safety concerns for BWR operations. Though many large-scale computational codes have been developed in recent years to study this problem, for efficient parametric analyses, simple and accurate models that can be studied using classical stability techniques and methods from modern bifurcation theory are needed. We are developing such a model that includes single- and two-phase thermal hydraulics and coupled point kinetics or modal reactor kinetics equations. Recent results obtained using modal reactor kinetics equations show that the low-flow/high-power region is even less stable than previously believed because of the important effect of the first harmonic.

Hopf-Bifurcation Analysis of a Natural Circulation Boiling Water Reactor
R. Uddin,* D. D. B. Van Bragt, T. H. J. J. Van der Hagen, R. Zboray
Nederlande Organisatie Voor Wetenschappelijk Onderzoek, Holland

Nonlinear dynamics of natural circulation BWRs is being analyzed. A low-dimensional boiling water reactor (BWR) model has been implemented in the Hopf-bifurcation code BifDD. This model describes the nonlinear dynamics of a BWR in the vicinity of the linear stability boundary. A bifurcation analysis and direct numerical simulations with and without nuclear feedback effects are being investigated. Preliminary results show both supercritical and subcritical bifurcations for an elementary thermohydraulic system. The elementary thermohydraulic system is being extended with an unheated riser on top of the heated section. Further bifurcation studies with the complete BWR model, including nuclear feedback effects, are being carried out.