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4.2. Transonic dense gas flow through turbine cascade One of the major loss mechanisms in transonic and supersonic turbomachinery is related to the generation of shock waves. The use of a BZT fluid could avoid shock formation and, ideally, allow isentropic turbine expansion. However, simply utilizing a BZT working fluid is not sufficient to maximize the reduction in losses: it is also necessary to operate the turbine cascade at a pressure and temperature near the inversion zone. The inversion zone has a quite limited extent. Therefore, a reduction in the temperature jump between the heater and condenser stages is generally needed in order to operate the turbine cascade in the BZT regime. However, if the temperature jump is taken too small, the overall cycle efficiency and global power output tend to decrease. Then it’s necessary to find a trade-off between these two different needs. For this reason a parametric investigation of transonic BZT flows through linear transonic turbine cascades is computed. The von-Karman Institute LS-59 rotor blade cascade (VKI LS-59) is considered. Geometry and experimental data (for air flow) are available in [83]. The cascade has inlet angle equal 30°, and pressure ratio 1.82. The corresponding exit Mach number (for air) is about 1. All computations, concerning both perfect and real gas flows, have been performed at fixed inlet angle and pressure ratio. The computations are performed using C-grids of increasing density, composed by 86x8, 192x16 and 384x32 cells. The computed convergence order of the numerical solver, based on cascade efficiency, is in the range 2.2–2.5 for all the computed cases; grid convergence index (GCI) on the medium grid is less than 1%. Firstly, perfect diatomic gas flows have been computed. The perfect gas flow is characterized by a weak shock at mid-chord and a trailing edge shock (see Figure 14a). The computed efficiencies (real-to-ideal static enthalpy drop, η) is about 93.8%. Water vapor flows, with reduced inlet thermodynamic conditions p1/pc = 0.9, ρ1/ρc = 0.6, Γ1 = 1.26, are characterized by lower efficiency: η equals 87.7% for LS-59. Efficiency losses are related to the formation of strong shocks (upstream Mach number about 1.8) close to the trailing edge (Figure 14b). Then, computations are performed using the BZT fluorocarbon PP10 (pf- perhydrofluorene) as the working fluid. Several computations, corresponding to different thermodynamic inlet conditions are carried out. Figure 15 represents cascade efficiencies for different values of the inlet Fundamental Derivative. This one is changed at constant inlet entropy, and three different entropy values are considered. The first value corresponds to an isentropic line crossing the inversion zone, the second to a line almost tangent to the 65PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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