A Characteristics-based Implicit Finite- Difference Scheme for the Analysis of Instability in Water Cooled Reactors

Two-phase flow systems are prone to dynamic and static instabilities of many kinds. In the last few decades, a considerable amount of work on the two-phase flow instability has been carried out all over the world. Several numerical, experimental and analytical studies were conducted to understand two-phase flow instabilities and to derive the stability criteria. Theoretical modelling of density wave oscillation (DWO) stability analysis can be divided into two major groups: frequency-domain analysis and time-domain analysis. Frequency-domain analysis is based on the linearization of nonlinear equations by perturbing the governing equations around a steady-state point. Once this linear model has been converted from a time domain to a frequency domain, exact analytical solutions can be obtained. As a result, marginal stability boundaries (MSBs) in a parameter space can be determined and the space is divided into stable and unstable regions. The nonlinear time domain approach relies on a digital numerical simulation of nonlinear partial differential equations (PDEs) by means of finite-difference techniques. This approach is more accurate and suitable for limit cycle oscillations. The principal disadvantages of models based on this approach are tedious computations, numerical instabilities of algebraic equations and time-step constraints. Recent advances in high-speed computers and sophisticated finite-difference models have resulted in significant economic advantages and design confidence. Accuracy is no longer an expense or inconvenience. Consequently, the study of the nonlinear behavior of DWOs has attracted considerable interest. Hancox and Banerjee presented a benchmark solution procedure that is based on a method of characteristics analysis (MECA) and applicable to the Lagrangian coordinate system [1, 2]. They presented various numerical methodologies for the development of loss of coolant accident analysis, including two different finitedifference techniques: an explicit finite-difference The objective of the paper is to analyze the thermally induced density wave oscillations in water cooled boiling water reactors. A transient thermal hydraulic model is developed with a characteristics-based implicit finite-difference scheme to solve the nonlinear mass, momentum and energy conservation equations in a time-domain. A two-phase flow was simulated with a one-dimensional homogeneous equilibrium model. The model treats the boundary conditions naturally and takes into account the compressibility effect of the two-phase flow. The axial variation of the heat flux profile can also be handled with the model. Unlike the method of characteristics analysis, the present numerical model is computationally inexpensive in terms of time and works in a Eulerian coordinate system without the loss of accuracy. The model was validated against available benchmarks. The model was extended for the purpose of studying the flow-induced density wave oscillations in forced circulation and natural circulation boiling water reactors. Various parametric studies were undertaken to evaluate the model’s performance under different operating conditions. Marginal stability boundaries were drawn for type-I and type-II instabilities in a dimensionless parameter space. The significance of adiabatic riser sections in different boiling reactors was analyzed in detail. The effect of the axial heat flux profile was also investigated for different boiling reactors.