Theory and application of a three-dimensional code SHAPS to complex piping systems

This paper describes the theory and application of a three-dimensional computer code SHAPS to complex piping systems. The code utilizes a two-dimensional implicit Eulerian method for the hydrodynamic analysis together with a three-dimensional elastic-plastic finite-element program for the structural calculation. A three-dimensional pipe element with eight degrees of freedom is employed to account for the hoop, flexural, axial, and the torsional mode of the piping system. In the SHAPS analysis the hydrodynamic equations are modified to include the global piping motion. Coupling between fluid and structure is achieved by enforcing the free-slip boundary conditions. Also, the response of the piping network generated by the seismic excitation can be included. A thermal transient capability is also provided in SHAPS. An energy equation is used to compute the coolant temperatures due mainly to the heat convection. This equation is linked together with a radial heat conduction equation to establish the temperature profile throughout the pipe-wall thickness. Thermal mechanical stresses are calculated by a thermo-viscoplasticity constitutive equation. The flow stress is then determined by an associated flow rule via Newton-Raphson procedure. To illustrate the methodology, many sample problems dealing with the hydrodynamic, structural, and thermal analyses of reactor-piping systems are given. Validation of the SHAPS code with experimental data is also presented