A dynamic analysis of free piston Vuilleumier cycle heat pumps

A dynamic analysis of a free piston Vuilleumier cycle heat pump was perform ed by a time-stepping integration method. The nonlinear relationship betwee n displacement and force for pistons was taken into account for the motion of reciprocating components, in addition to the pressure change of working gas, nonlinear viscous dissipative force due to an oscillating flow and dis continuous damping force caused by solid friction. The displacement of pist ons and pressure changes in the Vuilleumier cycle heat pump were integrated by an ideal isothermal thermodynamic relationship. It was assumed that the flow friction was proportional to the kinematic pressure of working gas, a nd that the solid friction at the seals was due to the functions of the wor king gas pressure and the tension of seal springs. In order to investigate the dependence of the characteristics of a machine on various dynamical par ameters, some calculations were performed for a proposed case study machine and discussed. The roles of working gas pressure, the displacer piston rod and dissipative force due to flow and solid friction were clarified, and t he proposed method was found to be very effective in predicting dynamic beh avior of free piston Vuilleumier cycle heat pumps and in designing the mach ine components.