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Annual Review of Fluid Mechanics

Volume 56, 2024

Nonideal Compressible Fluid Dynamics of Dense Vapors and Supercritical Fluids

Abstract

The gas dynamics of single-phase nonreacting fluids whose thermodynamic states are close to vapor-liquid saturation, close to the vapor-liquid critical point, or in supercritical conditions differs quantitatively and qualitatively from the textbook gas dynamics of dilute, ideal gases. Due to nonideal fluid thermodynamic properties, unconventional gas dynamic effects are possible, including nonclassical rarefaction shock waves and the nonmonotonic variation of the Mach number along steady isentropic expansions. This review provides a comprehensive theoretical framework of the fundamentals of nonideal compressible fluid dynamics (NICFD). The relation between nonideal gas dynamics and the complexity of the fluid molecules is clarified. The theoretical, numerical, and experimental tools currently employed to investigate NICFD flows and related applications are reviewed, followed by an overview of industrial processes involving NICFD, ranging from organic Rankine and supercritical CO cycle power systems to supercritical processes. The future challenges facing researchers in the field are briefly outlined.

Keyword(s): fundamental derivative of gas dynamics, nonideal compressible fluid dynamics, nonideal thermodynamics, organic Rankine cycle power systems, supercritical carbon dioxide flows and power systems, supercritical injection
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2024-01-19
2025-04-28
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Nonideal Compressible Fluid Dynamics of Dense Vapors and Supercritical Fluids
Annual Review of Fluid Mechanics 56, 241 (2024); https://doi.org/10.1146/annurev-fluid-120720-033342
/content/journals/10.1146/annurev-fluid-120720-033342
/content/journals/10.1146/annurev-fluid-120720-033342
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Supplementary Data

  • Download the Supplemental Material (PDF).

    Supplemental Video 1A: Schilieren visualization of the flow evolution around a diamond-shaped airfoil. The video shows the first 60 seconds of the experiment performed with the TROVA blow-down wind tunnel, therefore total conditions change due to the emptying of the high-pressure reservoir.

    Supplemental Video 1B: Schilieren visualization of the flow evolution around a diamond-shaped airfoil together with the time evolution of the pre-shock state value of the fundamental derivative of gasdynamics ΓA, the static-to-reservoir pressure ratio PA/PR, the value of the pre-shock Mach number MA, and of the post-shock to pre shock states pressure ratio PA/PR. The experiment was performed with the blow-down TROVA wind tunnel therefore quantities vary in time.

    Supplemental Video 1C: Schlieren video of the dense vapor flow of siloxane MM through a linear supersonic blade cascade installed in the test section of the TROVA facility. The blade row is representative of an ORC (organic Rankine cycle) turbine stage stator. Blade channels are converging-diverging, since the design outlet Mach number is Mout,des=1.6. The stagnation pressure at the inlet of the test section is Pt,in=12.6 bar, the stagnation temperature is Tt,in=232 °C; moreover Zt,in=0.67 (compressibility factor) and Γt,in=0.62 (fundamental derivative of gas dynamics), therefore the compressible flow is highly nonideal. At these conditions the Mach number is Mout=1.8 at the beginning of the test and it increases during the run due to the reduction of flow nonideality. The Mach number decrease is made evident by the reduction of the slope of both Mach lines in the diverging portion of the blade channel and of fish-tail shock arising from the blade trailing edge. Further details are documented in

    Manfredi M, Persico G, Spinelli A, Gaetani P, Dossena V. 2023. Design and commissioning of experiments for supersonic ORC nozzles in linear cascade configuration. Appl. Therm. Eng. 224:119996.

    Supplemental Video 1D: Schlieren video of the nonideal vapor flow of siloxane MDM through the planar converging-diverging nozzle mounted in the test section of the TROVA facility. The design outlet Mach number is Mout,des=1.5, which increases along the test due to reduction of flow nonideality (a nonideal effect). The increase of Mach number is related to the reduction of the angle of the Mach lines which can be observed within the diverging portion of the nozzle. The stagnation pressure at the inlet of the test section is Pt,in=4.59 bar, the stagnation temperature is Tt,in=239 °C. In addition, Zt,in=0.81 (compressibility factor) and Γt,in=0.78 (fundamental derivative of gas dynamics), therefore the compressible flow is appreciably nonideal.

    Downstream of the nozzle, expansion fans are visible as well as slip lines due to underexpansion which lasts for most part of the test run.

    Further details can be found in

    Spinelli A, Cammi G, Gallarini S, Zocca M, Cozzi F, et al. 2018. Experimental evidence of non ideal compressible effects in expanding flow of a high molecular complexity vapor. Exp. in Fluids 59:126.

    Supplemental Video 2A: Timelapse of the realization of the ORCHID (organic Rankine cycle hybrid integrated device) facility in the Propulsion and Power laboratory at Delft University of Technology.

    Supplemental Video 2B: Schlieren video of the startup phase of the nozzle test section of the ORCHID facility. It can be observed that, at the opening of the control valve upstream of the nozzle, the vapor flow passing through the nozzle condenses on the walls. At a certain instant, the amount of condensate formed in the nozzle test section completely blocks off the light. The liquid then gradually disappears due to temperature increase and the flow of siloxane MM reaches steady-state supersonic conditions. The steady state flow conditions become visible starting from the third minute: weak compression waves originate from the walls of the diverging section due to roughness, and two oblique shock waves depart from the leading edge of the slender pin installed at the outlet of the nozzle. The nominal thermodynamic state of the working fluid at the inlet of the nozzle, defined in terms of total pressure and temperature, is Pt,in = 11.1 bar, Tt,in = 525 K. The compressibility factor at the inlet of the nozzle is Zt,in = 0.8.

    Supplemental Video 2C: Simulation of the unsteady flow within the high-speed (100 krpm) supersonic ORC turbine to be tested using the ORCHID facility. Contour plot of the specific entropy associated with points lying on the blade to blade plane at mid-span. The working fluid is siloxane MM. The results have been obtained with a URANS simulation with a stator/rotor sliding mesh interface. The largest share of entropy generation leading to fluid dynamic losses occurs when the flow passes through the rotor, and the flow is highly nonuniform when passes through the turbine outlet section.

    Supplemental Video 3: Background oriented schlieren (BOS) video of the nonideal vapor flow of NOVEC 649 past a circular cylinder (5 mm diameter) placed in the test section of the CLOWT facility. The inlet flow properties are Mach number Min=0.67, turbulence intensity TU=0.3%, stagnation pressure Pt,in=2.6 bar, stagnation temperature Tt,in=103 °C. The inlet state therefore features a compressibility factor Zt,in equal to 0.91 and a fundamental derivative of gas dynamics Γt,in equal to 0.92 (mild nonideal conditions). The video shows the apparent horizontal displacement of the background pattern, related to density gradients in the same direction. Further details can be found in

    Sundermeier SC, Matar C, Aus der Wiesche S, Cinnella P, Hake L, Gloerfelt X. 2023. Experimentaland numerical study of transonic flow of an organic vapor past a circular cylinder. In Proceedings of NICFD 2022, eds. M White, et al., vol. 29 of ERCOFTAC Series. Springer, 209–216.

  • Article Type: Review Article

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