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Algebraic Reynolds stress modeling of turbulence subject to rapid homogeneous and non-homogeneous compression or expansion
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Swedish Defence Research Agency (FOI), Stockholm, Sweden.
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.
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2016 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 28, no 2, 026101- p.Article in journal (Refereed) Published
Abstract [en]

A recently developed explicit algebraic Reynolds stress model (EARSM) by Grigoriev et al. ["A realizable explicit algebraic Reynolds stress model for compressible turbulent flow with significant mean dilatation," Phys. Fluids 25(10), 105112 (2013)] and the related differential Reynolds stress model (DRSM) are used to investigate the influence of homogeneous shear and compression on the evolution of turbulence in the limit of rapid distortion theory (RDT). The DRSM predictions of the turbulence kinetic energy evolution are in reasonable agreement with RDT while the evolution of diagonal components of anisotropy correctly captures the essential features, which is not the case for standard compressible extensions of DRSMs. The EARSM is shown to give a realizable anisotropy tensor and a correct trend of the growth of turbulence kinetic energy K, which saturates at a power law growth versus compression ratio, as well as retaining a normalized strain in the RDT regime. In contrast, an eddy-viscosity model results in a rapid exponential growth of K and excludes both realizability and high magnitude of the strain rate. We illustrate the importance of using a proper algebraic treatment of EARSM in systems with high values of dilatation and vorticity but low shear. A homogeneously compressed and rotating gas cloud with cylindrical symmetry, related to astrophysical flows and swirling supercritical flows, was investigated too. We also outline the extension of DRSM and EARSM to include the effect of non-homogeneous density coupled with "local mean acceleration" which can be important for, e.g., stratified flows or flows with heat release. A fixed-point analysis of direct numerical simulation data of combustion in a wall-jet flow demonstrates that our model gives quantitatively correct predictions of both streamwise and cross-stream components of turbulent density flux as well as their influence on the anisotropies. In summary, we believe that our approach, based on a proper formulation of the rapid pressure-strain correlation and accounting for the coupling with turbulent density flux, can be an important element in CFD tools for compressible flows.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2016. Vol. 28, no 2, 026101- p.
Keyword [en]
Turbulence, compressible flow, EARSM, DRSM
National Category
Applied Mechanics
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-183447DOI: 10.1063/1.4941352ISI: 000371286500057Scopus ID: 2-s2.0-84958818780OAI: oai:DiVA.org:kth-183447DiVA: diva2:911360
Funder
Swedish Research Council, 621-2010-3938
Note

QC 20160314. QC 20160704

Available from: 2016-03-11 Created: 2016-03-11 Last updated: 2017-11-30Bibliographically 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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Brethouwer, GeertJohansson, Arne V.

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