Godunov’s Method for Simulatinons of Fluid-Structure Interaction in Piping Systems

Abstract

Constant coefficient one-dimensional linear hyperbolic systems of partial differential equations (PDEs) are often used for description of fluid-structure interaction (FSI) phenomena during transient conditions in piping systems. In the past, these systems of equations have been numerically solved with method of characteristics (MOCs). The MOC method is actually the most efficient and accurate method for description of the single-phase transient in the cold liquid where the constant coefficient mathematical model describes phenomenon with sufficient accuracy. In energy production systems where hot pressurized liquid is used for heat transfer between the heat source and the steam generator, more complex and nonlinear mathematical models are needed to describe transient flow and these models cannot be solved with MOC method because the models are not constant. In addition, the MOC method can be used for pipes having discontinuities like elbows, geometrical changes, material properties changes, etc., but only with some extra numerical modeling. An interesting alternative is explicit characteristic upwind numerical method, known as Godunov’s method that is frequently used for nonlinear systems or systems where properties change with position. In the present study, applicability of the Godunov’s method for the FSI analyses is tested with eight first order PDEs mathematical model. The conventional linear mathematical model is improved with convective term that makes the system nonlinear and additional terms that enable simulations of the FSI in arbitrarily shaped piping systems located in a plane. Two PDEs describe pressure waves in the single-phase fluid and six PDEs describe axial, lateral, and rotational stress waves in the pipe. The applied system of equations has stiff source terms. This numerical problem is solved introducing implicit iterations. The proposed model is verified with a rod impact experiment that is carried out on single-elbow pipe hanging on wires. Godunov’s method is found as a very promising numerical method for simulations of the FSI problems.