Large-eddy simulations (LESs) of cryogenic nitrogen injection into a warm environment at supercritical pressure are performed and real-gas thermodynamics models and subgrid-scale (SGS) turbulence models are evaluated. The comparison of different SGS models — the Smagorinsky model, the Vreman model, and the adaptive local deconvolution method — shows that the representation of turbulence on the resolved scales has a notable effect on the location of jet break-up, whereas the particular modeling of unresolved scales is less important for the overall mean flow field evolution. More important are the models for the fluid’s thermodynamic state. The injected fluid is either in a supercritical or in a transcritical state and undergoes a pseudo-boiling process during mixing. Such flows typically exhibit strong density gradients that delay the instability growth and can lead to a redistribution of turbulence kinetic energy from the radial to the axial flow direction. We evaluate novel volume-translation methods on the basis of the cubic Peng-Robinson equation of state in the framework of LES. At small extra computational cost, their application considerably improves the simulation results compared to the standard formulation. Furthermore, we found that the choice of inflow temperature is crucial for the reproduction of the experimental results and that heat addition within the injector can affect the mean flow field in comparison to results with an adiabatic injector.

Experiments and numerical simulations were carried out in order to contribute to a better understanding and prediction of high-pressure injection into a gaseous environment. Specifically, the focus was put on the phase separation processes of an initially supercritical fluid due to the interaction with its surrounding. N-hexane was injected into a chamber filled with pure nitrogen at 5 MPa and 293 K and three different test cases were selected such that they cover regimes in which the thermodynamic non-idealities, in particular the effects that stem from the potential phase separation, are significant. Simultaneous shadowgraphy and elastic light scattering experiments were conducted to capture both the flow structure as well as the phase separation. In addition, large-eddy simulations with a vaporliquid equilibrium model were performed. Both experimental and numerical results show phase formation for the cases, where the a-priori calculation predicts two-phase flow. Moreover, qualitative characteristics of the formation process agree well between experiments and numerical simulations and the transition behaviour from a dense-gas to a spray-like jet was captured by both.Keywords elastic light scattering, shadowgraphy, large-eddy simulation, Peng-Robinson, tangent plane distance IntroductionInjection into a high-pressure gaseous environment is a crucial process within energy conversion machines. Nowadays, many fluid flow devices are operated at pressures that exceed the critical pressure pc of the involved pure fluids. The increase in operating pressure in aircraft and car engines mainly stems from the demand for higher engine efficiency and reduced CO2 emissions. The main reason for rising the chamber pressure in liquid rocket engines (LREs) is the proportionality between operating pressure and specific impulse [1]. Typically, the operating pressure in LREs is supercritical with respect to both fuel and oxidizer (p > pc), whereas the injection temperature may be sub-or supercritical, corresponding to liquid-like or gas-like states. At supercritical pressure, the fluid properties, such as density, enthalpy and viscosity, are highly non-linear functions of temperature and pressure. Furthermore, phase separation due to non-linear interaction of the different components may occur. The phenomenon of phase separation due to mixing at high pressures is well-known in process engineering. Remarkably, up to now, high-pressure fuel injection into a gaseous environment is not completely understood and no commonly accepted theoretical approach exists. Within the past 20 years, many research groups have focused on understanding the behaviour of jets at high pressures using experimental and numerical methods. Chehroudi et al. [2] injected cryogenic nitrogen into gaseous nitrogen at sub-and supercritical pressures. Based on shadowgraphy visualizations, they observed classical twophase phenomena at subcritical pressure indicated by very fine ligaments and droplets being ejected from the jet. As the pressure exceeds the cr...

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a b s t r a c tThe paper describes the development of a compact, non-linear model for the turbulent heat fluxes, and its application to heated flow in a rotating channel. The model was formulated by expanding the tensorial functional of dependent variables, and by applying certain simplifications to obtain an algebraic and explicit model that contains direct dependence on the rotational body forces, and on the gradients of mean velocity. The model was implemented into OpenFOAM, the open-source flow solver, and its performance was assessed in stationary wall-bounded and free heated flows, and in a heated channel with spanwise rotation. Comparisons with experimental data and with results from Direct Numerical Simulations show that the new model performs better than alternative closures.