U.S. Department Of Energy's nuclear engineering education research: highlights of recent and current research-II. 6. A Flashing Simulator for Natural Circulation Heated Systems

By design, many of the next generation of nuclear reactors rely on 'natural circulation' either as the primary mode of heat removal or as a passive safety mechanism under off-normal conditions. Studies have shown that flashing-induced instabilities are of concern during startup of natural-circulation loops and small scale natural-circulation light water reactors. Flashing refers to the beginning of (adiabatic) boiling in the unheated riser when there is no boiling upstream. Flashing occurs because the saturation enthalpy at low pressures (under 20 bars, experienced during reactor startup conditions) decreases significantly with decreasing pressure. Hence, in systems with long risers and under low-power/low-pressure conditions (large pressure drop relative to the absolute pressure), even if there is no boiling in the heated core, it is possible that the saturation enthalpy somewhere in the riser might drop to the level of local enthalpy. This leads to local boiling in the unheated riser. (See Fig. 1.) Because of the nature of this instability -caused by a drop in saturation enthalpy with pressure- it cannot be analyzed using most current stability codes that, in general, assume constant saturation properties. Hence, experiments must be conducted and appropriate thermal-hydraulic models must be developed to analyze flashing and flashing-induced instabilities. A simulator with significantly enhanced modeling and simulation capabilities is being developed under a grant from the U.S. Department of Energy (DOE) Nuclear Engineering Education Research program to analyze flashing and flashing-induced instabilities. The model developed here allows an arbitrary number of nodes in both the heated section (allowing axially varying heat flux) and in the unheated riser section. Obviously, the saturation enthalpy in this model is a function of pressure. Pressure-dependent enthalpy leads to a modified energy equation and introduces a new dimensionless quantity, i.e., a flashing number, which is equal to zero when the saturation enthalpy is taken to be a constant. Currently, a linear dependence of saturation enthalpy on pressure is being used. (Later, this will be extended to quadratic dependence. The data for water show that a quadratic polynomial can very well capture the dependence over a wide range of pressures of interest.) A Galerkin-type approach is employed to reduce the partial differential equations (PDEs)-that arise during the modeling stage-to a dynamical system form. In this approach, after dividing the entire physical domain into physically meaningful sub-domains, trial functions with time-dependent coefficients are introduced to describe the spatial dependence of the dependent variables in each sub-domain. These trial functions are substituted into the relevant PDEs, which are then integrated over the respective sub-domains, leading to a set of ODEs for the (time-dependent) coefficients. Important parameters in the vector of all the parameters are the operating parameters such as inlet subcooling controlled via carry-under and bleed temperature and system pressure; geometric parameters such as core height and riser height; and modeling parameters such as number of nodes, order of the assumed spatial profiles, etc. The set of equations thus obtained is coded in the MATLAB environment. This allows an efficient capability to analyze the model. Specifically, the model developed is being used to perform the following: 1. steady-state (fixed point) calculations. This requires the solution of a set of nonlinear algebraic (transcendental) equations. 2. frequency domain (linear) calculations using classical stability analysis. This requires the evaluation of the eigenvalues of the Jacobian matrix, δF. This step is also carried out using MATLAB. 3. In addition, numerical simulation of the set of nonlinear ODEs can also be easily performed by MATLAB. This MATLAB environment hence provides an efficient approach to perform several steps in the comprehensive analysis of the flashing-related instabilities, which would otherwise require a separate user-developed code for each step. Preliminary simulations using the model show that it can capture the location of flashing in the experiments conducted on the Dodewaard reactor very well. As part of the international collaboration of this project, experiments are being conducted at the CIRCUS facility of the Kramers Laboratorium voor Fysische Technologie at the Delft University of Technology in the Netherlands (at no cost to DOE). Experiments are being performed covering a wide range of heat flux, flow rates, and subcooling. (authors)