Pump-induced fluctuating pressure in a reactor coolant pipe

Abstract

An analytical model is proposed to describe the propagation of pressure pulsations originated at the pump outlet through the inlet pipe of a pressurised water reactor (PWR). Pressure pulsations data from a pre-critical vibration monitoring programme (PVMP) for a C-E reactor are presented and compared with those calculated by the analytical model. The propagation of pump-induced pressure pulsation is important because of the potential for vibration and resultant damage of reactor internals. The theory of pump-induced pressure pulsation distributions in the coolant annulus in a PWR has been developed by Penzes 1 and by Bowers and Horvoy 2 on the assumption that the pressure pulsations are due to excitations at the inlet nozzles. The pressures in the annulus are calculated based on prescribing the pressure at the inlet nozzles and on the concept of time dependent body force in the governing differential equations. The analytical model presented in the present paper and the theory given by Penzes 1 and Bowers and Horvoy 2 describe the propagation of pump-induced pressure pulsations in the critical regions (from the pump outlet through the inlet pipe and the coolant annulus in a PWR) for deterministic loads on PWR internals. In the present analytical model the pressure pulsations are assumed to travel in plane waves so that the governing equation is one-dimensional in nature. The boundary condition at the pump outlet end of the inlet pipe is a time-dependent harmonic function; amplitudes for pump related frequencies are established based on an existing theory for hydraulic noise in centrifugal pumps. 3 At the inlet nozzle end of the inlet pipe, due to the complexity of its acoustic characteristic, three types of boundary condition are considered—open, closed and piston-spring supported. Therefore, the analytical model essentially consists of a one-dimensional wave equation with time-dependent non-homogeneous boundary conditions. Closed-form solutions for the problem are derived using a linear transformation technique which reduces the problem to one involving a non-homogeneous differential equation with homogeneous boundary conditions. Numerical examples are given for a typical reactor. Pressure power spectral density data are presented for data taken at inlet nozzles during a C-E PVMP. Distinct peaks at various pump related frequencies such as rotor speed, twice rotor speed, blade passing frequency and twice blade passing frequency, are observed. RMS pressures predicted by the analytical model at pump related frequencies are compared with those from PVMPs. The spatial distributions of the pressure field along the length of the inlet pipe for the three typical boundary conditions are given. Finally, the effect of the pipe geometry on the pressure field and the acoustic frequencies is analysed.