Frequency domain analysis of density wave oscillations for two-phase flow in a vertical tube

Abstract

In order to investigate the boundary characteristics of density wave oscillations in nuclear reactor steam generators and boiler water-cooled wall tubes, a frequency domain method numerical calculation model applicable to different geometrical structures and operating parameters was developed. In order to make the results of the model more accurate, the state of the fluid at the outlet of the heated pipe and the time delay were fully considered on the basis of the traditional model. Depending on the physical properties of the fluid at the outlet of the heated pipe, the model calculation area was divided into single-phase, two-phase and superheated zones. Small-perturbation linearization and Laplace transform were performed on the conservation equations in the three regions. The Nyquist stability criterion was used in matlab software to judge the stability of the flow, and by varying the working parameters the flow instability boundary can be calculated. For a more in-depth study of density wave oscillations in heated pipes, the unstable boundary characteristics were analysed computationally for different influences such as pressure, mass flow rate, inlet subcooling degree and pipe geometry on the basis of model validation. In addition, the Nyquist function was used in Matlab to plot the Nyquist curve for different influencing factors and to analyse the stability margins for specific operating conditions. The unstable boundary characteristic diagram was obtained when the pressure was 5–10 MPa and the mass flux was 300–1300 kg·m−2·s−1. The calculated data was collated and mass flow rate and heat load boundary diagrams were plotted, which could visualise the boundary characteristics of the density wave oscillations under different operating conditions. In order to make the calculation results more applicable, Nsub and Npch were used to construct the dimensionless unstable boundary characteristic diagram. Results showed that the influence of inlet subcooling degree on flow stability is non-monotonic. In addition, the effects of factors such as pressure, mass flow rate and inlet throttling coefficient are monotonic.