System Dynamic Model and Design of a Stirling Pump

This paper presents the design and dynamic modeling of a second generation prototype combined Stirling engine pump. The Stirling pump is intended to fill the technological gap of a compact high energy density power supply for untethered fluid power applications in the 50W to 500W range. Specifically, this prototype is intended as a compact and quiet, untethered, hydraulic power supply for an ankle foot orthosis testbed associated with the Center for Compact and Efficient Fluid Power. The energy source for the unit is flexible and can include propane, butane, methane, natural gas, or other high energy density hydrocarbon source of heat. The target output pressure of 7 MPa (1000 psig) is obtained from a pumping stage that is driven by a sealed engine stage that utilizes high pressure helium as the working fluid. The separate pumping stage utilizes the differential pressure swing inside the engine section to pump hydraulic fluid to the desired output pressure. This paper presents the system dynamic model of the Stirling pump, and includes (1) heat transfer from the heat source to the working fluid in the hot space of the engine, (2) heat transfer from the working fluid in the cold space of the engine to the heat sink, (3) energetically derived pressure dynamics in the hot and cold spaces, (4) mass flow around the displacer piston in between the hot and cold sides, (5) work output to the pump driving section, (6) pumping piston inertial dynamics, (7) flow losses through the pump’s check valves, and (8) hydraulic power output. This dynamic model allows components of the Stirling pump to be sized. The paper includes results from the dynamic model.