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Capturing turbulent density flux effects in variable density flow by an explicit algebraic model
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Swedish Defence Research Agency (FOI), Sweden.ORCID iD: 0000-0001-8692-0956
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-9819-2906
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-2711-4687
2015 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 27, no 4, 1.4917278Article in journal (Refereed) Published
Abstract [en]

The explicit algebraic Reynolds stress model of Grigoriev et al. ["A realizable explicit algebraic Reynolds stress model for compressible turbulent flow with significant mean dilatation," Phys. Fluids 25, 105112 (2013)] is extended to account for the turbulent density flux in variable density flows. The influence of the mean dilatation and the variation of mean density on the rapid pressure-strain correlation are properly accounted for introducing terms balancing a so-called "baroclinic" production in the Reynolds stress tensor equation. Applying the weak-equilibrium assumption leads to a self-consistent formulation of the model. The model together with a K - ω model is applied to a quasi-one-dimensional plane nozzle flow transcending from subsonic to supersonic regimes. The model remains realizable with constraints put on the model parameters. When density fluxes are taken into account, the model is less likely to become unrealizable. The density variance coupled with a "local mean acceleration" also can influence the model acting to increase anisotropy. The general trends of the behaviour of the anisotropy and production components under the variation of model parameters are assessed. We show how the explicit model can be applied to two- and three-dimensional mean flows without previous knowledge of a tensor basis to obtain the general solution. Approaches are proposed in order to achieve an approximate solution to the consistency equation in cases when analytic solution is missing. In summary, the proposed model has the potential to significantly improve simulations of variable-density flows.

Place, publisher, year, edition, pages
2015. Vol. 27, no 4, 1.4917278
Keyword [en]
Algebra, Anisotropy, Cyclone separators, Pipe flow, Reynolds number, Tensors, Approximate solution, Explicit algebraic models, Explicit algebraic reynolds stress models, Production components, Quasi-one dimensional, Rapid pressure-strain correlation, Reynolds stress tensors, Variable-density flows
National Category
Other Physics Topics
Identifiers
URN: urn:nbn:se:kth:diva-166978DOI: 10.1063/1.4917278ISI: 000353835700030Scopus ID: 2-s2.0-84928130090OAI: oai:DiVA.org:kth-166978DiVA: diva2:814758
Funder
Swedish Research Council, 2010-3938 2013-5784 2014-5700
Note

QC 20150528

Available from: 2015-05-28 Created: 2015-05-21 Last updated: 2017-12-04Bibliographically approved
In thesis
1. Turbulence modeling of compressible flows with large density variation
Open this publication in new window or tab >>Turbulence modeling of compressible flows with large density variation
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this study we highlight the influence of mean dilatation and mean density gradient on the Reynolds stress modeling of compressible, heat-releasing and supercritical turbulent flows.Firstly, the modeling of the rapid pressure-strain correlation has been extended to self-consistently account for the influence of mean dilatation.Secondly, an algebraic model for the turbulent density flux has been developed and coupled to the tensor equationfor Reynolds stress anisotropy via a 'local mean acceleration',a generalization of the buoyancy force.

We applied the resulting differential Reynolds stress model (DRSM) and the corresponding explicit algebraic Reynolds stress model (EARSM) to homogeneously sheared and compressed or expanded two-dimensional mean flows. Both formulations have shown that our model preserves the realizability of the turbulence, meaning that the Reynolds stresses do not attain unphysical values, unlike earlier approaches. Comparison with rapid distortion theory (RDT) demonstrated that the DRSM captures the essentials of the transient behaviour of the diagonal anisotropies and gives good predictions of the turbulence kinetic energy.

A general three-dimensional solution to the coupled EARSM  has been formulated. In the case of turbulent flow in de Laval nozzle we investigated the influence of compressibility effects and demonstrated that the different calibrations lead to different turbulence regimes but with retained realizability. We calibrated our EARSM against a DNS of combustion in a wall-jet flow. Correct predictions of turbulent density fluxes have been achieved and essential features of the anisotropy behaviour have been captured.The proposed calibration keeps the model free of singularities for the cases studied. In addition,  we have applied the EARSM to the investigation of supercritical carbon dioxide flow in an annulus. The model correctly captured mean enthalpy, temperature and density as well as the turbulence shear stress. Hence, we consider the model as a useful tool for the analysis of a wide range of compressible flows with large density variation.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. xiv, 50 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2916:03
Keyword
Turbulence, DRSM, EARSM, active scalar, compressible flow, reacting flow, supercritical flow
National Category
Applied Mechanics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-183452 (URN)978-91-7595-887-3 (ISBN)
Public defence
2016-04-01, D3, Lindstedtsvägen 5, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Funder
Swedish Research Council, 621-2010-3938
Note

QC 20160314

Available from: 2016-03-14 Created: 2016-03-11 Last updated: 2016-04-05Bibliographically approved

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Wallin, StefanBrethouwer, GeertJohansson, Arne V.

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