Theoretical analysis of the flow stability of HTGR supercritical steam generators using dimensionless numbers

Abstract

High Temperature Gas-cooled Reactors (HTGR) have the advantages of inherent safety and high temperature. Due to the high temperature, adoption of supercritical steam generator will further increase the power generation efficiency of HTGR. Flow instability may happen in supercritical steam generators due to acute changes in physical properties near the critical region. A theoretical model is established, verified and adopted to analyze the flow stability of HTGR supercritical steam generators. Secondary side supercritical water is divided into three regions. Partial differential governing equations describing supercritical systems are simplified to linear ordinary differential equations using integral and small disturbance linearization. The variables of differential equations are inlet velocity, the length of region 1 and the total length of region 1 and region 2. Routh stability criterion is adopted to determine supercritical system stability. Algebraic criterion is obtained from the coefficient matrix using Routh stability criterion. Similar to subcritical system, supercritical system stability is determined by algebraic criterion expressed by six dimensionless numbers. They are the inlet resistance coefficient, outlet resistance coefficient, sub-pseudo-critical number (similar to subcooling number in subcritical system), true trans-pseudo-critical number (similar to phase change number in subcritical system), friction number and Froude number. The actual supercritical steam generators of HTGR belong to the system with high inlet resistance coefficients and high friction numbers. Supercritical steam generators of HTGR (with high inlet resistance coefficients) can operate stably and have enough safety margin at full power level and partial power levels. Supercritical steam generators (with high inlet resistance coefficients and high friction numbers) become stable when system pressure, the inverse of Froude number (or angle inclination) and tube inner diameter increase. They become unstable when friction number (or friction factor) and tube length increase. The reasonable application range of the figure expressed by true trans-pseudo-critical number (NTPC) and sub-pseudo-critical number (NSUBPC) is discussed when analyzing parameters’ effects. The conclusions about parameters’ effect in supercritical systems are the same as that in subcritical systems. Previous contradictory conclusions about some parameters’ effects (friction number, tube length and tube inner diameter) are explained. The main reason is that the effect of friction numbers on supercritical systems is different at different inlet resistance coefficients.