In this paper we provide insight into the thermophysical properties and the dynamics of cryogenic jets. The motivation of the work is to optimise the use of cryogenic fluids in novel ultra low emission engines. For demonstration, we use conditions relevant to an internal combustion engine currently being developed by Dolphin N2 and the University of Brighton, the CryoPower recuperated split cycle engine (RSCE). The principle of this engine is a split-cycle combustion concept which can use cryogenic injection in the compression cylinder to achieve isothermal compression and thus help maximise the efficiency of the engine. Combined experimental and numerical findings are presented and the effects of atomisation dynamics of the LN ${}_2$ are explored at both sub- and supercritical conditions in order to cover different pressure and temperature conditions representative of the engine compression cycle. For subcritical regimes, we observe that the appearance of the jet coincides with the predicted atomisation regimes based on the Weber, Ohnesorge and Reynolds numbers for other common fluids. For the modelling of supercritical jets, a new methodology within OpenFoam which accounts for Real Fluid Thermodynamics has been developed and the jet behaviour under various pressure and temperature conditions has been investigated. To our knowledge this is the first study where a cryogenic spray process evolution is examined for conditions relevant to the ones prevailing in a compression chamber accounting for both sub and supercritical conditions.

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.

Cryogenic supercritical fluids represent an intriguing category of fluids that combine mechanical and thermophysical properties of both ultralow temperature conditions and phenomena taking place well above the critical point. Recent research has demonstrated that it is a common misconception to consider the supercritical state as one homogeneous state. Instead, these fluids consist of two to four liquid and gas like phases, each with their own unique characteristics. In our work, we investigate numerically single-specie cryogenic fluid jets—initially at subcritical temperatures—which are injected into a supercritical environment (both the pressure and temperature exceed the thermodynamic critical state). For the investigation, a new solver, namely, “CoolFoam,” has been developed, which is designed for compressible non-isothermal two-fluid simulations where diffusive transport of heat and/or mass is accounted for. Real fluid thermodynamics are modeled using a polynomial fitting approach developed in our previous work. We introduce also a new phase characterization framework based on the association of phases with specific temperature ranges (rather than using a single line like the Widom line), which allowed us to better identify the similarity effects between the various conditions. We analyze the inter-dependence of the underlying phenomena: density gradient and diffusive mass transport [molecular and thermo(Soret)-diffusion] and turbulence. We also compared supercritical N₂ with subcritical liquid and gas jets to highlight potential differences with respect to how these jets behave. We find that the jet dynamics are largely dictated by the thermodynamic transition of the injected fluid and the associated variation in thermophysical properties.

The injection of cryogenic fluids into environments where the prevailing conditions are supercritical in comparison to the critical point of the injected cryogenic fluid is encountered in cryogenic rocket engines, and novel engine architectures such as the recuperated split cycle engine. The physical characteristics of cryogens injected into supercritical environment are rather unclear. While surface tension is usually assumed to be absent/negligible for supercritical fluids, recent experimental research has identified the existence of surface tension and its effects on liquid hydrocarbons in supercritical environment. This research work proposes an alternative computationally simple adaptive surface tension algorithm for the simulation of a liquid injected into supercritical environment. The numerical simulations presented here correspond to single- and binary-specie cases of iquid nitrogen and liquid methane respectively, undergoing phase transition post their injection into supercritical conditions. Following a critical review of related numerical works, this paper begins with a brief explanation of the physics behind the surface tension effect in a binary-fluid interface in which a supercritical fluid is involved and we present why this effect is of relevance to supercritical cryogenic jets? Then, the rationale and specifics of the the new modelling framework based on adaptive surface tension is discussed along with its implications. The results of the numerical simulations of low-temperature vs near-critical temperature iquid nitrogen and liquid methane injection dynamics revealed the drastically different fluid- and thermo-dynamics at play in these two cases. The role of surface tension at these conditions is also explored.

The injections of cryogenic and non-cryogenic fluids in a supercritical environment, respectively, liquid N2 into gaseous N2 and n-dodecane into gaseous N2, are investigated. The two systems are analyzed under dynamic and thermal similarity (same reduced temperatures, reduced pressures, and Reynolds numbers) using the same simplified two-dimensional configuration for the totality of the simulations. This work contributes to provide insight into the interpretation of numerical studies on single- and multicomponent systems under supercritical conditions. A comprehensive comparison of the results obtained from two numerical approaches, based on the volume of fluid and on the homogeneous mixture assumption, making use of two distinct thermophysical and mixing rule frameworks, is presented. Results show very similar and consistent fluid mechanics and mass diffusion processes predicted by the two approaches, but different thermal behaviors for binary-species configurations. The two different mixing models are found to have the greatest impact on the temperature predictions. Also, isobaric–adiabatic mixing, which is obtained with the mass-based homogeneous approach, leads eventually to a larger extension of the predicted two-phase region. Such findings have large implications in energy systems operating at high pressure, where accurate local temperature predictions are crucial.