The vapor compression cycle is the idealized cycle for most modern air conditioning and refrigeration systems, i.e., isentropic compression; isobaric heat rejection; isobaric/isothermal heat rejection (condensation); isenthalpic expansion; isobaric/isothermal heat addition (evaporation).

The Rankine cycle is closely approximated in actual steam turbine plants. Its basic cycle is: isentropic compression; isobaric heat addition; isobaric/isothermal heat addition (evaporation); isentropic expansion; isobaric/isothermal heat rejection (condensation).

The Prof doesn't recall running across an idealized cycle described as "reversed Rankine", though no doubt it could be put on paper. Since it would seem the turbine would have to be reversed in such a cycle, it would seem an isentropic expansion process would be needed.

But if we have a vapor compressed by a centrifugal compressor, then condensed, then boosted by a pump, then the idealized cycle should read: isentropic compression; isobaric heat rejection; isobaric/isothermal heat rejection (condensation); isentropic compression...... with a few more steps to be added.

Your "multi-phase" fluid term is confusing. You mean a fluid at its triple point, i.e., solid, liquid and vapor coexist? Or a fluid that will change from vapor to two-phase to liquid states doing the cycle?