Stability analysis of a single phase rectangular coupled natural circulation loop system employing a Fourier series based 1-D model

Abstract

A linear stability analysis of a single-phase Coupled Natural Circulation Loop (CNCL) is carried out, and the stability maps of the CNCL system are obtained. A Fourier series based 1-D model is used to develop the stability maps. A 3-D CFD study is undertaken to assess the ability of the 1-D model to capture the non-periodic oscillatory behaviour exhibited by the CNCL system. After the model verification, the method used to obtain the stability maps is verified, and finally, the stability maps of the system are obtained from the eigenvalues of the steady-state. The steady-state analysis of the 1-D model of the CNCL system indicates that the CNCL has multiple steady states and the stability of a few of the steady states are presented. A thorough parametric study is then conducted to observe the influence of non-dimensional numbers such as the Grashof number, the Stanton number, the Fourier number, flow resistance coefficient and aspect ratio. Increase in Fourier number and flow resistance coefficient lead to an increase in the domain of stability for the range of parameters considered. The linear stability map is then compared with the empirical stability map to demonstrate that the higher-order non-linear terms do not significantly affect the stability boundary.