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21`eme Congr`es Fran ̧cais de M ́ecanique Bordeaux, 26 au 30 aouˆt 2013 order of 80 bar (the inlet pressure being of about 150 bar in this case), which increases fabrication and installation costs. In addition, the high pressure drop per each stage, greater than 20 bar, could lead to significant leakage flows with respect to the organic fluid turbines. Table 1 – Summary of the considered turbine configurations; βi are stage pressure ratios, βtot the total one. Parameters SUBR134a SUBR245fa SUPR134a SUPR245fa SUPCO2 p0 (bar) 10.4 9.5 47.1 46.9 150.5 T0 (K) 315.51 370.15 396.57 450.43 416.21 Stages 3 3 4 4 4 β1 β2 β3 β4 βtot 1.832 1.840 1.819 1.823 1.836 1.838 - - 6.118 6.165 1.703 1.706 1.630 1.652 1.596 1.605 1.586 1.593 7.026 7.208 1.214 1.229 1.242 1.258 2.331 Table 2 – Adiabatic efficiencies for each stage. Stage SUBR134a SUBR245fa SUPR134a SUPR245fa SUPCO2 1 95.07 92.55 2 94.03 89.59 3 92.94 88.36 4 - - 4 Conclusions 94.63 91.12 95.80 91.99 95.87 92.45 98.41 93.62 98.72 98.27 99.86 99.11 In this work, dense gas flows through supercritical multistage axial ORC turbines were analyzed by means of a in-house dense gas numerical solver equipped with high-accurate multiparameter equations of state based on Helmholtz free energy and using a high-order finite volume scheme. Calculations were carried out for 3 different supercritical turbine configurations. Two subcritical ORC turbines were also studied for comparison. Steady, inviscid, two-dimensional numerical simulations were carried out in order to evaluate entropy losses associated to shock wave formation in the different cases. Different behaviors were observed according to the working fluid and turbine configuration considered. The Fundamental Derivative of Gas Dynamics Γ was studied to understand and explain differences in the computed results. Shock-wave formation has a crucial impact on the overall performance : carbon dioxide provides an optimal behavior since, because of the high values of the speed of sound in this fluid, the flow field is completely subsonic and no shocks are created. The use of R134a ensures satisfactory adiabatic efficiencies, both for the subcritical and the supercritical configuration, despite the presence of weak shocks at the suction sides of rotor blades, whereas R245fa develops, for the turbine configuration studied, stronger shocks leading to more significant losses. For both fluids, the use of supercritical inlet conditions tends to increase turbine isentropic efficiency for a given pressure ratio since, at high pressures, their thermodynamic behavior significantly deviates from that of a perfect gas, slowing down the increase of the Mach number during turbine expansion, and leading to weaker shocks. In the next future, we plan to take into account viscous and unsteady effects. Also, 3D calculations are planned as future work. R ́ef ́erences [1] Cinnella, P., Congedo, P.M. 2005 Numerical solver for dense gas flows. AIAA J. 43 pp. 2458-61 [2] Cinnella, P., Congedo, P.M. 2005 Aerodynamic performance of transonic Bethe-Zel’dovich- Thompson flows past an airfoil. AIAA J. 43 pp. 370-378 [3] Cramer, M.S., and Kluwick, A. 1984 On the propagation of waves exhibiting both positive and negative nonlinearity. Journal of Fluid Mechanics 142 pp. 9-37 4PDF Image | Numerical investigation of dense gas flows through transcritical multistage axial Organic Rankine Cycle turbines
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