A two-phase method of characteristics for heat pump expander design

The greenhouse gases emissions due to the generation of energy through fossil fuels required for domestic heating could be reduced using electric heat pumps. Despite being well-known, heat pumps offer room for improvement, as it could be possible to recover energy from the expansion using a two-phase turboexpander. Since no robust design guidelines for two-phase turbines are available in the literature, the authors propose a methodology based on the method of characteristics (MOC). Despite its extension to real gases and fluid starting from two-phase condition, no method existed so far to handle fluid expanding from subcooled to fully two-phase conditions, as it usually occurs in heat pump expanders. The discontinuity in Mach number caused by the drop in speed of sound triggered by phase change prevented the application of usual series expansion methods. The proposed new general initialisation method holds for both single-phase, two-phase and subcooled liquid inlet conditions. A supersonic nozzle designed with the MOC is verified against a barotropic computational fluid dynamics (CFD) simulation considering different fluids (carbon dioxide, propane, R-1234ze(E)) and inlet conditions and the error is in all cases below 0.78%. Subsequently, the stator of a two-phase turbine is designed using the MOC and verified against both an inviscid and a viscous barotropic CFD simulation. The difference is below 1.18% when compared against the inviscid simulation and below 2.91% when compared against the viscous one. The promising results support the use of this new MOC as an initial design tool for this class of turboexpanders, for which no tried and tested guidelines are available.