Gas Core Reactor Numerical Simulation Using a Coupled MHD-MCNP Model

Analysis is provided in this report of using two head-on magnetohydrodynamic (MHD) shocks to achieve supercritical nuclear fission in an axially elongated cylinder filled with UF4 gas as an energy source for deep space missions. The motivation for each aspect of the design is explained and supported by theory and numerical simulations. A subsequent report will provide detail on relevant experimental work to validate the concept. Here the focus is on the theory of and simulations for the proposed gas core reactor conceptual design from the onset of shock generations to the supercritical state achieved when the shocks collide. The MHD model is coupled to a standard nuclear code (MCNP) to observe the neutron flux and fission power attributed to the supercritical state brought about by the shock collisions. Throughout the modeling, realistic parameters are used for the initial ambient gaseous state and currents to ensure a resulting supercritical state upon shock collisions

Modeling of Bulk Evaporation and Condensation

This report describes the modeling and mathematical formulation of the bulk evaporation and condensation involved in liquid-vapor phase change processes. An internal energy formulation, for these phase change processes that occur under the constraint of constant volume, was studied. Compared to the enthalpy formulation, the internal energy formulation has a more concise and compact form. The velocity and time scales of the interface movement were obtained through scaling analysis and verified by performing detailed numerical experiments. The convection effect induced by the density change was analyzed and found to be negligible compared to the conduction effect. Two iterative methods for updating the value of the vapor phase fraction, the energy based (E-based) and temperature based (T-based) methods, were investigated. Numerical experiments revealed that for the evaporation and condensation problems the E-based method is superior to the T-based method in terms of computational efficiency. The internal energy formulation and the E-based method were used to compute the bulk evaporation and condensation processes under different conditions. The evolution of the phase change processes was investigated. This work provided a basis for the modeling of thermal performance of multi-phase nuclear fuel elements under variable gravity conditions, in which the buoyancy convection due to gravity effects and internal heating are involved

Modeling of Thermal Performance of Multiphase Nuclear Fuel Cell Under Variable Gravity Conditions

A unique numerical method has been developed to model the dynamic processes of bulk evaporation and condensation processes, associated with internal heat generation and natural convection under different gravity levels. The internal energy formulation, for the bulk liquid-vapor phase change problems in an encapsulated container, was employed. The equations, governing the conservation of mass, momentum and energy for both phases involved in phase change, were solved. The thermal performance of a multiphase uranium tetra-fluoride fuel element under zero gravity, micro-gravity and normal gravity conditions has been investigated. The modeling yielded results including the evolution of the bulk liquid-vapor phase change process, the evolution of the liquid-vapor interface, the formation and development of the liquid film covering the side wall surface, the temperature distribution and the convection flow field in the fuel element. The strong dependence of the thermal performance of such multiphase nuclear fuel cell on the gravity condition has been revealed. Under all three gravity conditions, 0-g, 10(exp -3)-g, and 1-g, the liquid film is formed and covers the entire side wall. The liquid film covering the side wall is more isothermalized at the wall surface, which can prevent the side wall from being over-heated. As the gravity increases, the liquid film is thinner, the temperature gradient is larger across the liquid film and smaller across the vapor phase. This investigation provides valuable information about the thermal performance of multi-phase nuclear fuel element for the potential space and ground applications

A Computational Fluid Dynamic and Heat Transfer Model for Gaseous Core and Gas Cooled Space Power and Propulsion Reactors

A computational model based on the axisymmetric, thin-layer Navier-Stokes equations is developed to predict the convective, radiation and conductive heat transfer in high temperature space nuclear reactors. An implicit-explicit, finite volume, MacCormack method in conjunction with the Gauss-Seidel line iteration procedure is utilized to solve the thermal and fluid governing equations. Simulation of coolant and propellant flows in these reactors involves the subsonic and supersonic flows of hydrogen, helium and uranium tetrafluoride under variable boundary conditions. An enthalpy-rebalancing scheme is developed and implemented to enhance and accelerate the rate of convergence when a wall heat flux boundary condition is used. The model also incorporated the Baldwin and Lomax two-layer algebraic turbulence scheme for the calculation of the turbulent kinetic energy and eddy diffusivity of energy. The Rosseland diffusion approximation is used to simulate the radiative energy transfer in the optically thick environment of gas core reactors. The computational model is benchmarked with experimental data on flow separation angle and drag force acting on a suspended sphere in a cylindrical tube. The heat transfer is validated by comparing the computed results with the standard heat transfer correlations predictions. The model is used to simulate flow and heat transfer under a variety of design conditions. The effect of internal heat generation on the heat transfer in the gas core reactors is examined for a variety of power densities, 100 W/cc, 500 W/cc and 1000 W/cc. The maximum temperature, corresponding with the heat generation rates, are 2150 K, 2750 K and 3550 K, respectively. This analysis shows that the maximum temperature is strongly dependent on the value of heat generation rate. It also indicates that a heat generation rate higher than 1000 W/cc is necessary to maintain the gas temperature at about 3500 K, which is typical design temperature required to achieve high efficiency in the gas core reactors. The model is also used to predict the convective and radiation heat fluxes for the gas core reactors. The maximum value of heat flux occurs at the exit of the reactor core. Radiation heat flux increases with higher wall temperature. This behavior is due to the fact that the radiative heat flux is strongly dependent on wall temperature. This study also found that at temperature close to 3500 K the radiative heat flux is comparable with the convective heat flux in a uranium fluoride failed gas core reactor

Direct energy conversion in fission reactors: A U.S. NERI project

In principle, the energy released by a fission can be converted directly into electricity by using the charged fission fragments. The first theoretical treatment of direct energy conversion (DEC) appeared in the literature in 1957. Experiments were conducted over the next ten years, which identified a number of problem areas. Research declined by the late 1960's due to technical challenges that limited performance. Under the Nuclear Energy Research Initiative the authors are determining if these technical challenges can be overcome with todays technology. The authors present the basic principles of DEC reactors, review previous research, discuss problem areas in detail, and identify technological developments of the last 30 years that can overcome these obstacles. As an example, the fission electric cell must be insulated to avoid electrons crossing the cell. This insulation could be provided by a magnetic field as attempted in the early experiments. However, from work on magnetically insulated ion diodes they know how to significantly improve the field geometry. Finally, a prognosis for future development of DEC reactors will be presented

Performance of molybdenum with UF4 at high temperatures as a wall material for space reactors

Thin 99.99 pet purity molybdenum (Mo) foils for use in gas core reactors have been tested in both liquid and gaseous uranium tetrafluoride (UF4) at temperature ranges of 1500 to 2000 K under argon pressures approaching 600 torr for exposure times of 15 to 75 minutes. Weight change measurements have been performed before and after the experiments. Surface and cross-sectional analyses of the samples have been done using scanning electron microscopy (SEM), electron microprobe (EMP), and energy dispersive spectroscopy (EDS). The Mo container, which was exposed for nearly 9 hours to both liquid and gas phase UF4, was also examined. No reaction or diffusion of uranium or fluorine has been found on the cross sections of the samples under the experimental conditions. These results indicate that molybdenum can be a candidate wall material in contact with UF4 as used as a circulating fuel at ultrahigh temperatures

Conceptual design analysis of an MHD power conversion system for droplet-vapor core reactors. Final report

A nuclear driven magnetohydrodynamic (MHD) generator system is proposed for the space nuclear applications of few hundreds of megawatts. The MHD generator is coupled to a vapor-droplet core reactor that delivers partially ionized fissioning plasma at temperatures in range of 3,000 to 4,000 K. A detailed MHD model is developed to analyze the basic electrodynamics phenomena and to perform the design analysis of the nuclear driven MHD generator. An incompressible quasi one dimensional model is also developed to perform parametric analyses

Computation of high-temperature near-wall heat transfer using an enthalpy balancing scheme

The objective of this work is to analyze high-temperature, high heat-flux hydrogen flows under a variety of boundary conditions, in particular wall-heat flux boundary conditions. Both laminar and turbulent flows are investigated. An enthalpy balancing scheme is formulated and implemented allowing accurate, fast converging solutions of turbulent flows with high wall-heat flux boundary conditions. The solutions obtained are assessed along with several correlations proposed in the literature. © 1994

Comparative Performance of the Conjugate Gradient and SOR (Successive Over Relaxation) Methods for Computational Thermal Hydraulics

Finite difference approximations to the continuity, momentum, and energy equations in thermal hydraulics codes result in a system of N by N equations for a problem having N field points. In a three dimensional problem, N increases as the problem becomes larger or more complex, and more rapidly as the computational mesh size is reduced. As a consequence, the execution time required to solve the problem increases, which may lead to placing limits on the problem resolution or accuracy. A conventinal method of solution of these systems of equations is the Successive Over Relaxation (SOR) technique. However, for a wide range of problems the execution time may be reduced by using a more efficient linear equation solver. One such method is the conjugate gradient method which was implemented in COMMIX-1B thermal hydraulics code. It was found that the execution time required to solve the resulting system of equations was reduced by a factor of about 2 for some problems. This paper summarizes the characteristics of these iterative solution procedures and compares their performance in modeling of a variety of reactor thermal hydraulic problems, using the COMMIX-1B computer code