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Flows in liquid propellant rocket engines (LRE) are characterized by high pressures and extreme temperature ranges, resulting in complex fluid behavior that requires elaborate thermo-physical models. In particular, cubic equations of state and dedicated models for transport properties are firmly established for LRE simulations as a way to account f...

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... The heat will then flow from the hot side to the cold side, and a steady state will be reached once the heat flux across the domain is constant. The case was 1D, so the mesh used for the simulations was one cell tall, and there were 800 cells used in the length of the domain, sufficient to ensure that even the extreme transcritical fluid properties shown in Fig. 2 are reflected in the CFD solution [27]. ...

... While the volume translation methods [74,75] have been shown to increase the accuracy of PR estimations significantly, the associated complexity in obtaining analytical solutions of departure functions for thermodynamic properties has limited its applicability in CFD [22]. Both PR and SRK have also been found to significantly underestimate the specific heat capacity peaks at supercritical pressures [76]. Other non cubic, empirical EoS such as Younglove's [28,29] Modified Benedict Webb Rubin (MBWR) EoS have also been used but on a more limited basis (see for example [77]) due to the associated complexity. ...

Computational Fluid Dynamics (CFD) frameworks of supercritical cryogenic fluids need to employ Real Fluid models such as cubic Equations of State (EoS) to account for thermal and inertial driven mechanisms of fluid evolution and disintegration. Accurate estimation of the non-linear variation in density, thermodynamic and transport properties is required to computationally replicate the relevant thermo and fluid dynamics involved. This article reviews the availability, performance and the implementation of common Real Fluid EoS and data-based models in CFD studies of supercritical cryogenic fluids. A systematic analysis of supercritical cryogenic fluid (N2, O2 and CH4) thermophysical property predictions by cubic (PR and SRK) and non-cubic (SBWR) Real Fluid EoS, along with Chung’s model, reveal that: (a) SRK EoS is much more accurate than PR at low temperatures of liquid phase, whereas PR is more accurate at the pseudoboiling region and (b) SBWR EoS is more accurate than PR and SRK despite requiring the same input parameters; however, it is limited by the complexity in thermodynamic property estimation. Alternative data-based models, such as tabulation and polynomial methods, have also been shown to be reliably employed in CFD. At the end, a brief discussion on the thermophysical modelling of cryogenic fluids affected by quantum effects is included, in which the unsuitability of the common real fluid EoS models for the liquid phase of such fluids is presented.

... 29,30 Recently, also artificial neural networks, trained on tabulated data, have been employed for thermodynamic modeling for real gas CFD simulations. 31, 32 However, cubic EoS are still mostly used due to their simplicity and overall good accuracy. In addition to the EoS and the relations for thermodynamic properties, CFD simulations also require relations for the transport properties viscosity and thermal conductivity. ...

We further elaborate on the generalized formulation for cubic equation of state proposed by Cismondi and Mollerup [Fluid Phase Equilib. 232, 74–89 (2005)]. With this formulation, all well-known cubic equations of state can be described with a certain pair of values, which allow for a generic implementation of different equations of state. Based on this generalized formulation, we derive a complete thermodynamic model for computational fluid dynamics simulations by providing the resulting correlations for all required thermodynamic properties. For the transport properties, we employ the Chung correlations. Our generic implementation includes the often used equations of state Soave–Redlich–Kwong and Peng–Robinson and the Redlich–Kwong–Peng–Robinson equation of state. The first two assume a universal critical compressibility factor and are, therefore, only suitable for fluids with a matching critical compressibility. The Redlich–Kwong–Peng–Robinson overcomes this limitation by considering the equation of state parameter as a function of the critical compressibility. We compare the resulting thermodynamic modeling for the three equations of state for selected fluids with each other and CoolProp reference data. Additionally, we provide a Python tool called real gas thermodynamic python library (realtpl). This tool can be used to evaluate and compare the results for a wide range of different fluids. We also provide an implementation of the generalized form in OpenFOAM.