5.1 Thermodynamic analysis of MCI-ORC combine power unit
5.1.2 The ORC simple cycle
5.1.2.1 The optimal pressure of vaporization
In this section some preliminary evaluations are reported in order to assess the preferable turbine inlet pressure that should be considered for the cycles based on the three fluids under study.
In Fig. 5.4 the cycle efficiency is plotted for the reference fluids in the range of turbine inlet pressures between pcond and pcrit (where pcrit is the critical pressure of the fluid). As expected benzene displays the highest achievable efficiency. The curves are monotonical for all fluids (solid lines): this is a consequence of the hypothesis of introducing a little degree of superheating when the isentropic expansion is not completely dry. For higher pressures the superheating introduced becomes more significant and this
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slightly increases the cycle efficiency. The corresponding dotted curves are plotted for the saturated Rankine cycle (with no superheating) and in this case the curves show a maximum for pressures not far from the critical: particularly a maximum value of ηT=0.247 is achieved by benzene at a pressure of 4470kPa.
Fig. 5.4. Simple cycle efficiencies for evaporation pressures between pcond and pcrit.
The curves in Fig. 5.5 refer to the net power (PORC=m hf
(
3'−h4)
, see Fig. 5.2) achievable from the cycles at different pressures of vaporization. The curves again are monotonical as a consequence of pattern of the efficiency curves. In the analysis it will be chosen a optimal value of p2 as the one that maximizes the efficiency curves referred to saturated Rankine cycles (dotted lines of Fig. 5.4) and the optimal condition is indicated by the symbol * in the figures reported in this section. Therefore the optimum pressure is chosen to be 4470kPa for benzene which gives a net power output of 327kW, 3303kPa for R123 with 231kW, and 3723kPa for R134a with 133kW.In Fig. 5.6 the cycle power output is plotted in non-dimensional form in the assumed range of pressure with reference to the cycle power output determined at the optimal pressure for each fluid (* of Fig. 5.4).
It is possible to note that not only benzene is the fluid that displays the highest value of power output in the range of accepted pressure but also it shows small variations with respect to optimal power over a wide range of pressures. For example at pressures of 1700kPa a Rankine cycle based on benzene still provides about 90% of the optimal power output. This characteristic would allow considering cycles with lower pressure ratios between condenser and evaporator simplifying the compression and expansion phases and still providing good performances from the point of view of the total power provided.
Fluids with bell shaped vapour lines display instead higher variability in the power output with respect to vaporization pressure and a small decrease from the optimal pressure causes a significant reduction in the cycle power output especially for R134a. This means that the Rankine cycles for these fluids must be operated at a pressure as close as possible to the critical pressure.
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179 Fig. 5.5. Simple cycle power output at different
evaporation pressures.
Fig. 5.6. Variation of net cycle power output for simple Rankine cycles at different evaporation
pressures.
In Fig. 5.7 the estimated value of working fluid mass flow rate is plotted again with respect to the pressure at turbine inlet. It is possible to observe that benzene requires the lowest fluid mass flow rate as consequence of the highest enthalpy increase between state 3’ and 1 in steady state operation (Tab. 5.2).
The energy balance at the evaporator determines higher masses of fluid for R123 and R134a in order to match the total energy of the transfer fluid.
Fig. 5.7. Simple cycle working fluid mass flow rate required at different evaporation pressures.
Fig. 5.8. Simple cycle turbine enthalpy drop at different evaporation pressures.
In Fig. 5.8 the enthalpy drop through the turbine (∆h3’-4) is displayed for the different fluids. A relatively small enthalpy drop for R123 and R134a per unit mass requires relatively high fluid mass flow rates in order to achieve reasonable power at the turbine output, as displayed in Fig. 5.7. Benzene on the other hand shows quite high values of the enthalpy drop over a wide range of evaporating pressures. As a consequence it is reasonable to use a multiple stages turbine while a single stage turbine can be considered for wet fluids. This is further supported by the analysis of Fig. 5.9 where, for each fluid, curves referring to actual volumetric flow rate at the expander inlet (V ) and the turbine outlet/inlet 3 volume flow ratio (v4/v3) are reported. The ratio v4/v3 indicates the increase in fluid volume through the expansion and consequently how much the outlet section of the expander must be wider than the inlet.
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From Fig. 5.9 (a) (that refers to benzene) it is possible to note that high turbine outlet/inlet volume flow ratio are reached when the evaporation pressure is chosen to provide maximum power. In these conditions v4/v3 =374 and the volume flow rate
V
3 =0.015m3/s. The turbine outlet/inlet volume flow ratio could be too high for a single stage solution and a more complicated expander would be required, regardless if dynamic or volumetric.Considerations regarding the power output for benzene (Fig. 5.5 and Fig. 5.6) however suggest that a lower evaporating pressure would allow lower turbine outlet/inlet volume flow ratios still providing net power outputs close to the maximum. Therefore if a lower pressure is chosen probably a simpler expander could be employed. As a reference for this analysis a new optimal value of turbine inlet pressure for benzene is chosen at about 2000kPa (this new condition is indicated by the symbol in Fig. 5.9 (a), even if further and more precise considerations would require the matching with an actual commercial expander. For this value of evaporating pressure the net power output from the cycle becomes 302kW, the ratio v4/v3 decreases to 103 and the volumetric flow rate at the expander inlet increases to 0.04 m3/s (Tab.
5.2).
On the other hand R123 and R134 allow for a lower turbine outlet/inlet volume flow ratio even at the optimal evaporating pressure. A simple single stage expander can be used with these fluids.
As observed the parameter v4/v3 changes significantly depending on the working fluid used for the cycle. Some fluids can achieve values up to 550 and usually, when v4/v3 is smaller than 50, expansion efficiencies higher than 0.8 can be achieved via a single stage axial turbine [15]. Therefore, according to Fig. 5.9, it can be assumed that cycles based on R123 and R134a can be based on relatively simple expanders with good expansion efficiencies.
Main parameters of the thermodynamic cycles based on the three fluids are reported in Tab. 5.2 where the values for benzene are evaluated at the pressure of 2000kPa. Among the fluids it can be observed that benzene allows for higher efficiencies in converting into work the thermal energy available from the heat source, followed by R123 and R134a. This result is consistent with what found in [7]
Tab. 5.2.Comparison of ORC cycles for benzene, R123 and R134a. Simple cycle.
(a) (b) (c)
Fig. 5.9. Volume flow rate at turbine inlet (V3) and turbine outlet/inlet volume flow ratio (v4/v3) for different fluids at different evaporation pressures.
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