Large-eddy simulation of nitrogen injection at trans- and supercritical conditions

Abstract

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.

Thermal Transport and Entropy Production Mechanisms in a Turbulent Round Jet at Supercritical Thermodynamic Conditions

“…Non-ideal correction of sensible enthalpy and isobaric heat capacity are expressed in terms of departure functions derived from the particular EoS, whereas quantities for the hypothetical, ideal gas state are calculated using seven-coefficient NASA polynomials [33] (National Aeronautics and Space Administration). Note, as pointed out by [20] and others, that it is not feasible to include the volume-translation method of [32] in the caloric equation of state. Therefore, no c p values are shown for the PRC-EoS.…”

“…Studies related to LES have been reported in [19,20]. Thereby, the subgrid scale (SGS) models applied have been developed for subcritical flow conditions.…”

Real-Gas Effects and Phase Separation in Underexpanded Jets at Engine-Relevant Conditions

“…In single phase systems the calculation of the speed of sound and the isenthalpic compressibility is almost straightforward, although it implies the calculation of some partial derivatives, which can be solved analytically for the cubic EoS used in this investigation, see, e.g., Müller et al [16] for the PR-EoS. In multi-phase systems this is not true anymore and the evaluation gets way more complicated.…”

“…4 c) and Eq. (16). In order to do a further evaluation of the numerical approach described above, we also show the different compressibilities (ψ s , ψ h and ψ T ) in Fig.…”

“…Recently, Kraposhin et al [14] extended the source code of the solver based on the work of Jarczyk and Pfitzner [15] and Müller et al [16] such that it consistently accounts for real-gas thermodynamics. Additionally, the multi-species transport equations were implemented by Banholzer et al [10].…”