Analysis of one-dimensional pressure pulse propagation in a closed fluid system

Abstract

Abstract This paper describes a unique numerical method for linear inviscid fluid hammer analysis based on the method of characteristics. The uniqueness lies in that it uses the analytical solutions of the wave equation in place of the compatibility relatins of the more conventional method of characteristics. The numerical solution is obtained by a simple superposition technique for tracing the waves traveling along each characteristic and extending the solution from one constant time line to the next. Using a predetermined finite difference net of grids with equal spacings, an elimination is made of the spatial interpolation, thereby maintaining the wave amplitudes in their full strength in the numerical procedure. This is in contrast to the case of a nonlinear problem in which the pressure peaks are always flattened to some degree in the interpolation procedure. The computer program NAHAMMER is a system analysis code adequate for short-term pressure transients of most engineering problems of significance involving a moderate pressure source. It considers the simplified one-dimensional, linear, inviscid set of governing equations with an isentropic flow assumption. A closed fluid-network system is considered to be composed of a multiple of one-dimensional pipe sections and components that are connected by various joints. An analytical solution is obtained under an acoustic approximation for a simple system and the result shows good agreement with the numerical solution. As examples of the application of the method, complex problems of engineering importance are calculated and the results are presented.