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Modelling of subgrid-scale phenomena in supercritical transitional mixing layers: an a priori study

Selle, Laurant C. and Okong'o, Nora A. and Bellan, Josette and Harstad, Kenneth G. (2007) Modelling of subgrid-scale phenomena in supercritical transitional mixing layers: an a priori study. Journal of Fluid Mechanics, 593 . pp. 57-91. ISSN 0022-1120. doi:10.1017/S0022112007008075.

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A database of transitional direct numerical simulation (DNS) realizations of a supercritical mixing layer is analysed for understanding small-scale behaviour and examining subgrid-scale (SGS) models duplicating that behaviour. Initially, the mixing layer contains a single chemical species in each of the two streams, and a perturbation promotes roll-up and a double pairing of the four spanwise vortices initially present. The database encompasses three combinations of chemical species, several perturbation wavelengths and amplitudes, and several initial Reynolds numbers specifically chosen for the sole purpose of achieving transition. The DNS equations are the Navier-Stokes, total energy and species equations coupled to a real-gas equation of state; the fluxes of species and heat include the Soret and Dufour effects. The large-eddy simulation (LES) equations are derived from the DNS ones through filtering. Compared to the DNS equations, two types of additional terms are identified in the LES equations: SGS fluxes and other terms for which either assumptions or models are necessary. The magnitude of all terms in the LES conservation equations is analysed on the DNS database, with special attention to terms that could possibly be neglected. It is shown that in contrast to atmospheric-pressure gaseous flows, there are two new terms that must be modelled: one in each of the momentum and the energy equations. These new terms can be thought to result from the filtering of the nonlinear equation of state, and are associated with regions of high density-gradient magnitude both found in DNS and observed experimentally in fully turbulent high-pressure flows. A model is derived for the momentum-equation additional term that performs well at small filter size but deteriorates as the filter size increases, highlighting the necessity of ensuring appropriate grid resolution in LES. Modelling approaches for the energy-equation additional term are proposed, all of which may be too computationally intensive in LES. Several SGS flux models are tested on an a priori basis. The Smagorinsky (SM) model has a poor correlation with the data, while the gradient (GR) and scale-similarity (SS) models have high correlations. Calibrated model coefficients for the GR and SS models yield good agreement with the SGS fluxes, although statistically, the coefficients are not valid over all realizations. The GR model is also tested for the variances entering the calculation of the new terms in the momentum and energy equations; high correlations are obtained, although the calibrated coefficients are not statistically significant over the entire database at fixed filter size. As a manifestation of the small-scale supercritical mixing peculiarities, both scalar-dissipation visualizations and the scalar-dissipation probability density functions (PDF) are examined. The PDF is shown to exhibit minor peaks, with particular significance for those at larger scalar dissipation values than the mean, thus significantly departing from the Gaussian behaviour.

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Bellan, Josette0000-0001-9218-7017
Additional Information:Copyright © Cambridge University Press 2007. Reprinted with permission. (Received 27 October 2006 and in revised form 25 June 2007). Published online 23 November 2007. This work was conducted at the Jet Propulsion Laboratory (JPL), California Institute of Technology (Caltech) and sponsored by the Air Force Office of Scientific Research under the direction of Dr Julian Tishkoff, by the Army Research Office under the direction of Dr David Mann, both through interagency agreements with the National Aeronautics and Space Administration (NASA), by the group SAFRAN that provided Caltech funds (to J.B.) for a Post Doctoral Fellow (L.C.S.), and by the NASA Fluid Microgravity Program (in a collaborative effort with the Air Force Research Laboratory at Edwards Air Force Base led by Dr Douglas Talley) under the direction of Dr Walter Duval. The authors are grateful to Professor Corin Segal from the University of Florida and to Dr Michael Oschwald from the German Aerospace Center (DLR) for graciously providing their data. The computational resources were provided by the JPL Supercomputing Center.
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ID Code:9520
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Deposited On:29 Jan 2008
Last Modified:08 Nov 2021 20:59

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