The compressor power is related to the mass flow rate through the compressor [m.sub.c], the

isentropic efficiency [[eta].sub.c] and the inlet and outlet temperatures and pressures.

b = 0.164 Btu/ (lb [degrees]F) - coefficient, universal for each

isentropic line in the most typical temperatures area: 32[degrees]F <[T.sub.e]< 45[degrees]F, 54[degrees]F < [T.sub.c] < 105[degrees]F (b= 0.688 kJ/kg/[degrees]C; 0[degrees]C < [T.sub.e] < 7.2[degrees]C, 12[degrees]C <[T.sub.c]< 41[degrees]C)

where M is, again, the measured torque around axis of cylinder liner, m is the measured mass flow through the inlet valve, [R.sub.cyl] is the radius of the cylinder, [U.sub.is] is the

isentropic valve velocity, [P.sub.R] is the absolute pressure ratio (static outlet pressure/total inlet pressure), R is the gas constant, [gamma] is the specific heat ratio and [T.sub.0] is the upstream stagnation temperature.

The ECMWF interim reanalysis of log(PV) along the 3S5-K

isentropic surface during the period of strong intensification for each of the major Atlantic hurricanes of 2017.

Similarly, an in situ compressor

isentropic efficiency can be defined as the ratio of the

isentropic enthalpy change of the refrigerant stream passing through the compressor to the power consumed by the compressor.

The nominal point corresponds to a maximum of 93.05% of total-to-total

isentropic efficiency and 85.63% of total-to-static

isentropic efficiency at the nominal speed and reduced mass flow rate of 1.638 x [10.sup.-3][kg x [s.sup.-1][K.sup.0,5][Pa.sup.-1]] which corresponds to a mass flow of 69.5 kg/s.

We mainly use the method of vanishing pressure limits which was introduced by Li [30] and Chen and Liu [31, 32] in which they studied the formation of delta shocks and vacuum states in the vanishing pressure limit of solutions to the

isentropic Euler equations and the concentration and cavitation in the vanishing pressure limit of solutions to the Euler equations for nonisentropic fluids.

The mass fraction of vapor, [x.sub.v], is determined as a function of local pressure p by the

isentropic relationship

At standard temperature and pressure conditions, the bulk modulus [B.sub.o] of air is 1.42 x [10.sup.5] Pa for an

isentropic process.

The iso-[[theta].sub.e] process is also called an

isentropic atmospheric process.

MC inlet pressure of 7.38Mpa and compressor

isentropic efficiency of 89% are selected.

Polytropic CAES with one, two, and three stages and an

isentropic CAES were considered.