ISO 4391:1984 gives the common efficiency definition for positive displacement machines. ISO 4409:2019 uses this efficiency definition to specify the procedure for efficiency measurements. If the machine conditions do not correspond with an incompressible flow due to operation at high pressure levels, the compressibility of the fluid and the dead volume of a pump must be taken into account. On this point, ISO 4391:1984 is physically inconsistent.
Achten et. al. address this issue in their paper at FPMC 2019 presenting a critical review of ISO 4409:2007. They introduce new definitions of the overall efficiency as well as the mechanical-hydraulic efficiency. At the same time, they question the validity of the volumetric efficiency definition. Li and Barkei continue on this issue in their paper at FPMC 2020 and give a new efficiency definition based on the introduction of a new quantity Φ which describes the volume specific enthalpy of the conveyed fluid.
The motivation of this paper is to contribute to the ongoing and fruitful discussion. Our approach starts with the most general efficiency definition, namely the isentropic efficiency. Subsequently, we make assumptions concerning the fluid properties with respect to the compressibility of the conveyed fluid. On the basis of the ideal cycle of a positive displacement pump and the p-v diagram, we derive physically consistent and more meaningful representations of the overall, the mechanical-hydraulic and the volumetric efficiency that address the inconsistency of ISO 4391:1984. Furthermore, we compare our findings with the existing results of Achten et. al. and Li and Barkei.