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Explicit algebraic turbulence modelling in buoyancy-affected shear flows
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence.
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Turbulent flows affected by buoyancy forces occur in a large amount of applica-tions, from heat transfer in industrial settings to the effects of stratification inEarth’s atmosphere. The two-way coupling between the Reynolds stresses andthe turbulent heat flux present in these flows poses a challenge in the searchfor an appropriate turbulence model. The present thesis addresses this issueusing the class of explicit algebraic models.     Starting from the transport equations for the Reynolds stresses and the tur-bulent heat flux, an explicit algebraic framework is derived for two-dimensionalmean flows under the influence of buoyancy forces. This framework consistsof a system of 18 linear equations, the solution of which leads to explicit ex-pressions for the Reynolds-stress anisotropy and a scaled heat flux. The modelis complemented by a sixth-order polynomial equation for a quantity relatedto the total production-to-dissipation ratio of turbulent kinetic energy. Sinceno exact solution to such an equation can be found, various approximationmethods are presented in order to obtain a fully explicit algebraic model.     Several test cases are considered in this work. Special attention is given tothe case of stably stratified parallel shear flows, which is also used to calibratethe model parameters. As a result of this calibration, we find a critical Richard-son number of 0.25 in the case of stably stratified homogeneous shear flow,which agrees with theoretical results. Furthermore, a comparison with directnumerical simulations (DNS) for stably stratified channel flow shows an excel-lent agreement between the DNS data and the model. Other test cases includeunstably stratified channel flow and vertical channel flow with either mixed con-vection or natural convection, and a reasonably good agreement between themodel and the scarcely available, low-Reynolds-number DNS is found. Com-pared to standard eddy-viscosity/eddy-diffusivity models, an improvement inthe predictions is observed in all cases.     For each of the aforementioned test cases, model coefficients and additionalcorrections are derived separately, and a general formulation has yet to be given.Nevertheless, the results presented in this thesis have the potential of improvingthe prediction of buoyancy-affected turbulence in various application areas.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. , viii, 27 p.
Series
Trita-MEK, ISSN 0348-467X ; 2013:13
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-122468ISBN: 978-91-7501-797-6 (print)OAI: oai:DiVA.org:kth-122468DiVA: diva2:622624
Presentation
2013-06-14, E3, Osquars Backe 14, KTH, Stockholm, 10:30 (English)
Opponent
Supervisors
Note

QC 20130530

Available from: 2013-05-30 Created: 2013-05-22 Last updated: 2013-05-30Bibliographically approved
List of papers
1. An explicit algebraic Reynolds-stress and scalar-flux model for stably stratified flows
Open this publication in new window or tab >>An explicit algebraic Reynolds-stress and scalar-flux model for stably stratified flows
2013 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 723, 91-125 p.Article in journal (Refereed) Published
Abstract [en]

This work describes the derivation of an algebraic model for the Reynolds stresses and turbulent heat flux in stably stratified turbulent flows, which are mutually coupled for this type of flow. For general two-dimensional mean flows, we present a correct way of expressing the Reynolds-stress anisotropy and the (normalized) turbulent heat flux as tensorial combinations of the mean strain rate, the mean rotation rate, the mean temperature gradient and gravity. A system of linear equations is derived for the coefficients in these expansions, which can easily be solved with computer algebra software for a specific choice of the model constants. The general model is simplified in the case of parallel mean shear flows where the temperature gradient is aligned with gravity. For this case, fully explicit and coupled expressions for the Reynolds-stress tensor and heat-flux vector are given. A self-consistent derivation of this model would, however, require finding a root of a polynomial equation of sixth-order, for which no simple analytical expression exists. Therefore, the nonlinear part of the algebraic equations is modelled through an approximation that is close to the consistent formulation. By using the framework of a K-omega model (where K is turbulent kinetic energy and omega an inverse time scale) and, where needed, near-wall corrections, the model is applied to homogeneous shear flow and turbulent channel flow, both with stable stratification. For the case of homogeneous shear flow, the model predicts a critical Richardson number of 0.25 above which the turbulent kinetic energy decays to zero. The channel-flow results agree well with DNS data. Furthermore, the model is shown to be robust and approximately self-consistent. It also fulfils the requirements of realizability.

Place, publisher, year, edition, pages
Cambridge University Press, 2013
Keyword
stratified turbulence, turbulence modelling, turbulent flows
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-122471 (URN)10.1017/jfm.2013.116 (DOI)000317659400005 ()2-s2.0-84876206588 (Scopus ID)
Funder
Swedish Research Council, 621-2010-4147Formas
Note

QC 20130523

Available from: 2013-05-22 Created: 2013-05-22 Last updated: 2017-12-06Bibliographically approved
2. Explicit algebraic models for turbulent flows with buoyancy effects
Open this publication in new window or tab >>Explicit algebraic models for turbulent flows with buoyancy effects
2013 (English)Report (Other academic)
Abstract [en]

An explicit algebraic model for the Reynolds stresses and turbulent heat fluxis presented for turbulent parallel shear flows in which buoyancy forces arepresent. The derivation is based on a model framework for two-dimensionalmean flows that was already presented in a previous work (Lazeroms et al.2013), and new test cases are investigated here. The model is formulated interms of the Reynolds-stress anisotropy and a normalized heat flux, which areexpanded as a linear combination of appropriate basis tensors. The coefficientsin this expansion can be found from a system of 18 linear equations. Thisformulation is complemented with a nonlinear equation for a quantity relatedto the total production-to-dissipation ratio, the solution of which is modelledwith an appropriate expression. Fully explicit model expressions are found fortwo fundamentally different flow geometries: a horizontal channel for whichthe temperature gradient is aligned with gravity, and a vertical channel wherethe temperature gradient and gravity are perpendicular. In the first case, weconsider both stable and unstable stratification, while in the second case, bothmixed and natural convection flows are investigated. Comparison with DNSdata shows that the model gives predictions that are substantially better thanstandard eddy-viscosity/eddy-diffusivity models.

National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-122473 (URN)
Note

QC 20150701

Available from: 2013-05-22 Created: 2013-05-22 Last updated: 2015-07-01Bibliographically approved

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