3D Solution of the Flow Field in a Boiling Water Reactor Annulus due to a Recirculation Outlet Line Break Using Heat Transfer Analogy

Abstract

During a Loss of Coolant Accident (LOCA) in a Boiling Water Reactor (BWR), subcooled water flows past jet pump assemblies located in the annular region between the Reactor Pressure Vessel (RPV) and the shroud as it moves toward the break location and is subsequently discharged from the RPV. Flow loads caused by such an event are required design basis loads that must be considered for BWR internal components. In previous works [1, 2], the three dimensional (3-D) flow field problem was simplified to be a 2-D problem by assuming the radial velocity variations to be negligible. The 2-D problem was solved using complex function techniques by assuming a potential flow. Further, the velocity field had to be suitably scaled up to account for the presence of components such as the jet pumps in the annulus. In order to solve the problem in the realistic environment of a populated annulus, this paper illustrates a methodology where Finite Element Analysis (FEA) is used to perform a 3-D potential fluid flow calculation utilizing the analogy that exists between steady state heat transfer and potential flow problems. For an ideal fluid, the potential flow and irrotational flow assumptions will result in the Laplace equation as the governing equation for the velocity field. This is the same equation that governs the steady state heat transfer in any domain of interest where the temperature field is determined by solving the Laplace equation and applying the appropriate boundary conditions. Once the analogy between steady state heat transfer problems and potential flow problems governed by Laplace equation can be established, any commercially available finite-element code may be employed to solve such fluid flow problems involving complicated regions of interest by employing elements meant to solve heat transfer problems. For illustration purposes, a LOCA flow problem will be solved using Finite Element Model (FEM) thermal elements and compared against 2-D flow field results.