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κ pκ−1 w=ηis( )RT11−( 2)κ κ−1 p1 (5.3.1) For increasing pressure ratios, an increase in isentropic efficiency of the turbine can be seen. A physical explanation is that the increase in temperature due to friction in one part of the expansion can be recovered as work on the turbine in the next part, Cohen (1996). The produced power from the turbine is then: (5.3.2) The turbine is mounted on the same shaft as the compressor, producing enough torque to power the compressor and the generator. Similar to the compressor, the turbine has a mechanical efficiency, depending on design and construction. The relation between the mechanical torque and the power produced can be written as: (5.3.3) 5.4 The turbine model in Modelica The turbine is like the compressor modelled as a flow model, thus neglecting its small volume. The equations presented earlier describe the power produced by the turbine as a function of mass flow, the pressure ratio and temperature. To know what pressure and temperature we have at the equilibrium state, we need information about the correlation between the mass flow, rotational speed and pressure ratio. Like the compressor all this information is contained in a turbine map produced by Volvo Aero Corporation AB, see figure 19 below. κ pκ−1 P = m& ⋅ η ( ) R T 1 − ( 2 ) κ turbine isκ−11p1 P ⋅η =τ ⋅ω turbine mec turbine Turbine map for various speeds pressure ratio pin/pout 40 50 60 70 000 rpm 000 rpm 000 rpm 000 rpm Pressure ratio pin/pout Figure 19: Turbine map generated by Volvo Aero Corporation AB 31 Corrected mass flow Isentropic efficiencyPDF Image | Modelling of Microturbine Systems
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