Study of startup transients and power ramping of natural circulation boiling systems

An Overview of the Numerical Approaches to Water Hammer Modelling: The Ongoing Quest for Practical and Accurate Numerical Approaches

Here, recent developments in the key numerical approaches to water hammer modelling are summarized and critiqued. This paper summarizes one-dimensional modelling using the finite difference method (FDM), the method of characteristics (MOC), and especially the more recent finite volume method (FVM). The discussion is briefly extended to two-dimensional modelling, as well as to computational fluid dynamics (CFD) approaches. Finite volume methods are of particular note, since they approximate the governing partial differential equations (PDEs) in a volume integral form, thus intrinsically conserving mass and momentum fluxes. Accuracy in transient modelling is particularly important in certain (typically more nuanced) applications, including fault (leakage and blockage) detection. The FVM, first advanced using Godunov’s scheme, is preferred in cases where wave celerity evolves over time (e.g., due to the release of air) or due to spatial changes (e.g., due to changes in wall thickness). Both numerical and experimental studies demonstrate that the first-order Godunov’s scheme compares favourably with the MOC in terms of accuracy and computational speed; with further advances in the FVM schemes, it progressively achieves faster and more accurate codes. The current range of numerical methods is discussed and illustrated, including highlighting both their limitations and their advantages.

Numerical Investigation of Startup Instabilities in Parallel-Channel Natural Circulation Boiling Systems

The behaviour of a parallel-channel natural circulation boiling water reactor under a low-pressure low-power startup condition has been studied numerically (using RELAP5) and compared with its scaled model. The parallel-channel RELAP5 model is an extension of a single-channel model developed and validated with experimental results. Existence of in-phase and out-of-phase flashing instabilities in the parallel-channel systems is investigated through simulations under equal and unequal power boundary conditions in the channels. The effect of flow resistance on Type-I oscillations is explored. For nonidentical condition in the channels, the flow fluctuations in the parallel-channel systems are found to be out-of-phase.