Subgrid-scale models and large-eddy simulation of oxygen stream disintegration and mixing with a hydrogen or helium stream at supercritical pressure

Abstract

For flows at supercritical pressure, p, the large-eddy simulation (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. Compared to previous LES models, the differential equations contain not only the subgrid-scale (SGS) fluxes but also new SGS terms, each denoted as a 'correction'. These additional terms, typically assumed null for atmospheric pressure flows, stem from filtering the differential governing equations and represent differences, other than contributed by the convection terms, between a filtered term and the same term computed as a function of the filtered flow field. In particular, the energy equation contains a heat-flux correction (q-correction) which is the difference between the filtered divergence of the molecular heat flux and the divergence of the molecular heat flux computed as a function of the filtered flow field. We revisit here a previous a priori study where we only had partial success in modelling the q-correction term and show that success can be achieved using a different modelling approach. This a priori analysis, based on a temporal mixing-layer direct numerical simulation database, shows that the focus in modelling the q-correction should be on reconstructing the primitive variable gradients rather than their coefficients, and proposes the approximate deconvolution model (ADM) as an effective means of flow field reconstruction for LES molecular heat-flux calculation. Furthermore, an a posteriori study is conducted for temporal mixing layers initially containing oxygen (O) in the lower stream and hydrogen (H) or helium (He) in the upper stream to examine the benefit of the new model. Results show that for any LES including SGS-flux models (constant-coefficient gradient or scale-similarity models; dynamic-coefficient Smagorinsky/Yoshizawa or mixed Smagorinsky/Yoshizawa/gradient models), the inclusion of the q-correction in LES leads to the theoretical maximum reduction of the SGS molecular heat-flux difference; the remaining error in modelling this new subgrid term is thus irreducible. The impact of the q-correction model first on the molecular heat flux and then on the mean, fluctuations, second-order correlations and spatial distribution of dependent variables is also demonstrated. Discussions on the utilization of the models in general LES are presented.

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.…”

Extension of the subgrid-scale gradient model for compressible magnetohydrodynamics turbulent instabilities

“…We stress that the functional forms of the terms related to the pressure (τ pres , τ k adv ) depend on the equation of state and, like τ k adv , had been neglected or only partially considered before. The pressure term τ pres has been studied for the nonmagnetized fluid in a few scenarios [44][45][46][47] , for instance with a Peng-Robinson equation of state 48 , considering the performances of the gradient model 49 . Here we consistently include all the terms at play.…”

Germano identity-based subgrid-scale modeling: A brief survey of variations on a fertile theme

“…Other applications of the Germano identity related to combustion can be found for the case of modeling the scalar variance, 44 in multiphase flows including real-gas equations of state and associated terms requiring closure, 45 or in the context of filtering in the presence of discontinuities. 46…”