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Chapter 4: Modeling As shown in Eq. 14, the internal mass flow rate M ̇ i n is the difference between the mass flow rate M ̇ entering the expander and the leakage mass flow rate M ̇ leak . The internal mass flow rate is the volume flow rate V ̇ s ,exp divided by the specific volume of the fluid v su ,2 after entering cooling down and pressure drop. The volume flow rate is defined as the product of the swept volume Vs,exp and the expander rotational speed Nexp . The swept volume in expander mode is equal to that in compression mode divided by the built-in volume ratio ofthemachine rv,in. M ̇ in=M ̇ −M ̇ leak= V s,exp=Nexp⋅Vs ,cp= Nexp⋅V s ,exp (14) vr,su,2 60⋅vr ,su,2 60⋅vr,su,2⋅rv,in The leakage mass flow rate can be computed by reference to the flow through a simply convergent nozzle. The fictitious leakage area Aleak is assimilated to the nozzle throat area and must be experimentally identified. In the same manner as for the leakage mass flow rate, the pressure drop is computed as the flow through a simply convergent nozzle, whose throat diameter is the equivalent supply port diameter dsu . Figure 31: Conceptual scheme of the expander model The internal expansion power W ̇ i n is obtained by multiplying the internal work win by the internal mass flow rate. This internal work is the sum of the internal work w i n , s associated to the isentropic part of the expansion and the internal work win,v associated to the constant-volume evolution. In Eq 15, hin , vin and pin are respectively the specific enthalpy, the specific volume and the pressure of the fluid at the end of the isentropic part of the expansion. The specific volume v in is the product of the built-in volume ratio r v , in with the specific volume vsu,2 . 3PDF Image | Organic Rankine Cycles for Waste Heat Recovery and Solar Uses
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