Mathematical Modelling of the Entrainment Ratio of High Performance Supersonic Industrial Ejectors

For many years now, manufacturers have been producing supersonic ejectors with a high entrainment ratio for the chemical, oil, and food industries. In the present work, mathematical modelling of the entrainment ratio of such industrial ejectors is carried out, in which a variation of the diffuser efficiency is also assumed to be a function of the Mach number of the motive gas. To determine this unknown relationship, the mathematical modelling was overturned by inserting the entrainment ratios of ten different high-performance industrial ejectors, as identified through an experimental investigation. The mathematical modelling, completed through the use of the relationship between the diffuser efficiency and the Mach number of the motive gas, was applied to sixty-eight ejectors, built and tested experimentally over the last twenty years as part of research aimed at the development of thermal ejector refrigeration systems (ERSs), to obtain the entrainment ratios proposed by the manufacturers (industrial entrainment ratios). A comparison of the experimental entrainment ratios with respect to the industrial ones demonstrated that the former were always lower, ranging from a minimum of −17% to a maximum of −82%. These results indicate that the lab-built ejectors for ERS prototypes can be improved. Therefore, in the future, researchers should apply numerical analysis iteratively, starting from a given geometry of the ejector, and modifying it until the numerical analysis provides the industrial value of the entrainment ratio.