Non ideal compressible fluid dynamics

With the term dense vapors, we indicate all fluids in the gaseous state characterized by thermodynamic conditions close to saturation and the critical point.

The ideal-gas law can be employed in general as a reasonable approximation of the fluid thermodynamics for low pressures and high temperatures.

[4] This is extremely valid for gases made of complex and heavy molecules, which tend to deviate more from the ideal model.

This is particularly valid in supersonic conditions, namely for flow velocities larger than the speed of sound in the fluid considered.

All typical features of supersonic flows are affected by non-ideal thermodynamics, resulting in both quantitative and qualitative differences with respect to the ideal gas dynamics.

[6] On the other hand, when thermodynamic conditions approach condensation and the critical point or when high pressures are involved, real-gas models are needed in order to capture the real fluid behavior.

,[8] defined as where The compressibility factor is a dimensionless quantity which is equal to 1 for ideal gases and deviates from unity for increasing levels of non-ideality.

[12][13] State-of-the-art equations of state are easily accessible through thermodynamic libraries, such as FluidProp or the open-source software CoolProp.

[17] Typically, for single-phase fluids made of simple molecules, only the ideal gasdynamic regime can be reached, even for thermodynamic conditions very close to saturation.

It is for example the case of diatomic or triatomic molecules, such as nitrogen or carbon dioxide, which can only experience small departure from the ideal behavior.

in the single-phase region close to the saturation curve, where the speed of sound is largely sensitive to density variations along isentropes.

[18] Such fluids belong to different classes of chemical compounds, including hydrocarbons, siloxanes and refrigerants.

[19] Indeed, for an ideal gas expanding isentropically in a converging-diverging nozzle, the Mach number increases monotonically as the density decreases.

[21] Finally, fluids with an even higher molecular complexity can exhibit non-classical behavior in the single-phase vapor region near saturation.

In other words, the non-monotone Mach number evolution is also possible in the convergent section of an isentropic nozzle.

In the classical regime, expansions are smooth isentropic processes, while compressions occur through shock waves, which are discontinuities in the flow.

They are employed for example in Organic Rankine Cycles (ORC)[30] and supercritical carbon dioxide (sCO2) systems[31] for power production.

[32] Gases made of molecules of high molecular mass can be used in supersonic wind tunnels instead of air to obtain higher Reynolds numbers.

[33] Finally, non-ideal flows find application in fuels transportation at high-speed and in Rapid Expansion of Supercritical Solutions (RESS) of CO2 for particles generation or extraction of chemicals.

For the design of mechanical components, such as turbines, working in ORC plants, it is fundamental to take into account typical non-ideal gas-dynamic phenomena.

In fact, the single-phase vapor at the inlet of an ORC turbine stator usually evolves in the non-ideal thermodynamic region close to the liquid-vapor saturation curve and critical point.

Moreover, due to the high molecular mass of the complex organic compounds employed, the speed of sound in these fluids is low compared to that of air and other simple gases.

[38] High supersonic flows can produce large losses and mechanical stresses in the turbine blades due to the occurrence of shock waves, which cause a strong pressure raise.

[39] However, when working fluids of the BZT class are employed, expander performances could be improved by exploiting some non-classical phenomena.

Supercritical CO2 is chemically stable, very cheap, and non-flammable, making it suitable as a working fluid for transcritical cycles.

[44] By contrast, mechanical components within sCO2 Brayton cycles, especially turbomachinery and heat exchangers, suffer from corrosion.