A posteriori study using a DNS database describing fluid disintegration and binary-species mixing under supercritical pressure: heptane and nitrogen

Abstract

A large eddy simulation (LES) a posteriori study is conducted for a temporal mixing layer which initially contains different species in the lower and upper streams and in which the initial pressure is larger than the critical pressure of either species. A vorticity perturbation, initially imposed, promotes roll-up and a double pairing of four initial spanwise vortices to reach a transitional state. The LES equations consist of the differential conservation equations coupled with a real-gas equation of state, and the equations utilize transport properties depending on the thermodynamic variables. Unlike all LES models to date, the differential equations contain, additional to the subgrid-scale (SGS) fluxes, a new SGS term denoted a 'pressure correction' (p correction) in the momentum equation. This additional term results from filtering the Navier-Stokes equations and represents the gradient of the difference between the filtered p and p computed from the filtered flow field. A previous a priori analysis, using a direct numerical simulation (DNS) database for the same configuration, found this term to be of leading order in the momentum equation, a fact traced to the existence of regions of high density-gradient magnitude that populated the entire flow; in that study, the appropriateness of several SGS-flux models was assessed, and a model for the p-correction term was proposed.In the present study, the constant-coefficient SGS-flux models of the a priori investigation are tested a posteriori in LES devoid of, or including, the SGS pcorrection term. A new p-correction model, different from that of the a priori study, is used, and the results of the two p-correction models are compared. The results reveal that the former is less computationally intensive and more accurate than the latter in reproducing global and structural features of the flow. The constantcoefficient SGS-flux models encompass the Smagorinsky (SMC) model, in conjunction with the Yoshizawa (YO) model for the trace, the gradient (GRC) model and the scale similarity (SSC) models, all exercised with the a priori study constant-coefficient values calibrated at the transitional state. Further, dynamic SGS-flux model LESs are performed with the p correction included in all cases. The dynamic models are the Smagorinsky (SMD) model, in conjunction with the YO model, the gradient (GRD) model and 'mixed' models using SMD in combination with GRC or SSC utilized with their theoretical coefficient values. The LES comparison is performed with the filtered-and-coarsened DNS (FC-DNS) which represents an ideal LES solution. The constant-coefficient models including the p correction (SMCP, GRCP and SSCP) † Email address for correspondence: josette.bellan@jpl.nasa.gov 212 E. S. Taskinoglu and J. Bellan are substantially superior to those devoid of it; the SSCP model produces the best agreement with the FC-DNS template. For duplicating the local flow structure, the predictive superiority of the dynamic mixed models is demonstrated over the SMD model; however, even be...

A priori and a posteriori investigations for developing large eddy simulations of multi-species turbulent mixing under high-pressure conditions

“…compared to employing the standard LES assumptions. These conclusions are different from those obtained for binary-species high-p mixing 13,14 and indicate that care should be taken not to infer properties of multi-species mixing from binary-species experiments.…”

“…IV B; unclosed terms with significant activity are identified and modeled. Modeling of the conventional SGS fluxes is not addressed since previous studies have already evaluated, both in the a priori 12 and a posteriori 13,14 contexts, the accuracy of these SGS flux models (e.g., Smagorinsky model, gradient model, and self-similarity model) in the supercritical-p realm. Finally, the potential of the newly proposed models for the unconventional terms to increase the accuracy of LES for supercritical-p flows is determined through an a posteriori assessment.…”

“…13,43 For the purpose of performing a posteriori computations using the DMG model, we consider the filter width  ∆ corresponding to the double convolution of the two filters having filter widths ∆ and  ∆, and following Vreman et al, 44 we compute…”

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

“…Within this study, it is shown that entropy production rates in cryogenic injection are dominated by heat transport effects and not by viscous dissipation. Other researchers applied direct numerical simulations (DNS) [16] and large eddy simulations (LES) [17] to examine entropy generation rates in supercritical transitional mixing layers. The authors provided entropy production rates arising from viscous stress, species mass fluxes and heat fluxes and showed that the entropy production rates are fundamentally different from their subcritical counterpart.…”

The subgrid-scale scalar variance under supercritical pressure conditions

“…According to the scalar equation under supercritical conditions, [8][9][10][11][12] the transport equation of the SGS scalar variance is…”