Supersonic expansions of a molecularly complex vapor occurring within the non-ideal thermodynamic region in the close proximity of liquid-vapor saturation curve were characterized experimentally for the first time. Results for two planar converging–diverging nozzles in the adapted regime and at different inlet conditions, from highly non-ideal to dilute gas state, are reported. Measurements of upstream total pressure and temperature are performed in the plenum ahead of the nozzle, while static pressure and supersonic Mach number measurements are carried out along the nozzle centerline. The investigated expansions are of interest for both fundamental research on non-ideal compressible flows and industrial applications, especially in the energy field. Siloxane MDM (octamethyltrisiloxane, $$\text {C}_8\text {H}_{24}\text {O}_2\text {Si}_3$$
 ), a high molecular complexity organic compound, is used. Local pressure ratio $$P/P_\mathrm{T}$$
 and Mach number M measurements display a dependence on the inlet total state, a typical non-ideal feature different from dilute gas conditions.

/pdf/experimental-evidence-of-non-ideal-compressible-effects-in-4lf3nqrwig.pdf

Experimental evidence of non-ideal compressible effects in expanding flow of a high molecular complexity vapor

14. On the Possibility of Rarefaction Shock Waves

Bethe-Zel'dovich-Thompson fluids are ordinary, single-phase fluids in which the fundamental derivative of gasdynamics is negative over a finite range of temperatures and pressures. We examine the steady transonic flow of these fluids over two-dimensional thin wings and turbine blades. The free-stream state is taken to be in the neighbourhood of one of the zeros of the fundamental derivative.

Transonic Flows of Bethe-Zel'dovich-Thompson Fluids

Assessing the feasibility of using the heat demand-outdoor temperature function for a long-term district heat demand forecast

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.

/pdf/non-ideal-compressible-flows-in-supersonic-turbine-cascades-40xyn2pu8w.pdf

Non-ideal compressible flows in supersonic turbine cascades

The non-monotone dependence of the speed of sound along adiabatic transformations is demonstrated to result in the admissibility of non-ideal increase of the flow Mach number across oblique shock waves, for pre-shock states in close proximity of the liquid-vapour saturation curve. This non-ideal behaviour is primarily associated with a less-than-unity value of the fundamental derivative of gasdynamics and, therefore, non-ideal shock waves are expected to be observed in flows of fluids with moderate molecular complexity. The simple yet qualitatively sound van der Waals model is used to confirm the present findings and to provide exemplary non-ideal shock waves.

https://iopscience.iop.org/article/10.1088/1742-6596/821/1/012003/pdf

Non-ideal compressible-fluid effects in oblique shock waves

From the analysis of the isentropic limit of weak compression shock waves, oblique shock waves in which the post-shock Mach number is larger than the pre-shock Mach number, named non-ideal oblique shocks, are admissible in substances characterized by moderate molecular complexity and in the close proximity to the liquid–vapour saturation curve. Non-ideal oblique shocks of finite amplitude are systematically analysed, clarifying the roles of the pre-shock thermodynamic state and Mach number. The necessary conditions for the occurrence of non-ideal oblique shocks of finite amplitude are singled out. In the parameter space of pre-shock thermodynamic states and Mach number, a new domain is defined which embeds the pre-shock states for which the Mach number increase can possibly take place. The present findings are confirmed by state-of-the-art thermodynamic models applied to selected commercially available fluids, including siloxanes and hydrocarbons currently used as working fluids in renewable energy systems.

/pdf/non-ideal-oblique-shock-waves-h3yiw0rw22.pdf

Non-ideal oblique shock waves

Non-ideal effects on the typical trailing edge shock pattern of ORC turbine blades

Steady self-similar solutions to the supersonic flow of Bethe–Zel’dovich–Thompson fluids past compressive and rarefactive ramps are derived Inviscid, non-heat-conducting, non-reacting and single-phase vapour flow is assumed For convex isentropes and shock adiabats in the pressure–specific volume plane (classical gas dynamic regime), the well-known oblique shock and centred Prandtl–Meyer fan occur at a compressive and rarefactive ramp, respectively For non-convex isentropes and shock adiabats (non-classical gas dynamic regime), four additional wave configurations may possibly occur; these are composite waves in which a Prandtl–Meyer fan is adjacent up to two oblique shock waves The steady two-dimensional counterparts of the wave curves defined for the one-dimensional Riemann problem are constructed In the present context, such curves consist of all the possible states connected to a given initial state (namely, the uniform state upstream of the ramp/wedge) by means of a steady self-similar solution In addition to the classical case, as many as six non-classical wave-curve configurations are singled out Moreover, the necessary conditions leading to each type of wave curves are analysed and a map of the upstream states leading to each configuration is determined

Oblique waves in steady supersonic flows of Bethe-Zel'dovich-Thompson fluids

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