Abstract
Flows in the close proximity of the vapour–liquid saturation curve and critical point are examined for supersonic turbine cascades, where an expansion occurs through a converging–diverging blade channel. The present study illustrates potential advantages and drawbacks if turbine blades are designed for operating conditions featuring a non-monotonic variation of the Mach number through the expansion process, and non-ideal oblique shocks and Prandtl–Meyer waves downstream of the trailing edge. In contrast to ideal-gas flows, for a given pressure ratio across the cascade, the flow field and the turbine performance are found to be highly dependent on the thermodynamic state at the turbine inlet, in both design and off-design conditions. A potentially advantageous design, featuring stationary points of the Mach number at the blade trailing edge, is proposed, which induces a nearly uniform outlet Mach number distribution in the stator–rotor gap with a low sensitivity to slight variations in the outlet pressure. These findings are relevant for turbomachines involved in high-temperature organic Rankine cycle power systems, in particular for supercritical applications.
Highlights
Flows of molecularly complex fluids in the neighbourhood of the vapour–liquid saturation curve and critical point depart significantly from the ideal-gas-like behaviour typical of dilute thermodynamic states
Fluid-dynamic effects associated with thermodynamic states featuring Γ < 1 include the non-monotonic variation of the Mach number along isentropic expansions (Cramer & Best 1991; Cramer & Crickenberger 1992), the discontinuous increase of the Mach number across oblique shocks (Gori, Vimercati & Guardone 2017; Vimercati, Gori & Guardone 2018) and non-classical phenomena in the regime Γ < 0 (Thompson 1971; Thompson & Lambrakis 1973; Cramer & Kluwick 1984; Menikoff & Plohr 1989; Kluwick 2001; Zamfirescu, Guardone & Colonna 2008; Guardone, Zamfirescu & Colonna 2010)
We have reported the performance of a supersonic converging– diverging cascade operating in the non-ideal gas-dynamic regime (Γ < 1) but qualitatively showing ideal-gas behaviour
Summary
Flows of molecularly complex fluids in the neighbourhood of the vapour–liquid saturation curve and critical point depart significantly from the ideal-gas-like behaviour typical of dilute thermodynamic states. The majority of ORC plants features cycles with relatively mild maximum pressures and temperatures (subcritical cycles) In these conditions, even if the expansion through the turbine may partly occur in the non-ideal gas-dynamic regime, non-ideal effects such as those mentioned above are, not observed (Hoffren et al 2002; Persico 2017). Depending on the upstream total conditions, two very different operating regimes can establish: one mirrors the ideal-gas scenario and is obtained with relatively dilute conditions at the cascade inlet; the other one, obtained for high-pressure inlet conditions, is characterized by non-ideal effects For both operating regimes, a parametric study, in which the boundary conditions of the turbine cascade are changed, is performed from the perspective of assessing the off-design behaviour.
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