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An explicit algebraic Reynolds-stress and scalar-flux model for stably stratified flows
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.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: 0000-0001-8692-0956
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-2711-4687
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. Vol. 723, 91-125 p.
Keyword [en]
stratified turbulence, turbulence modelling, turbulent flows
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-122471DOI: 10.1017/jfm.2013.116ISI: 000317659400005Scopus ID: 2-s2.0-84876206588OAI: oai:DiVA.org:kth-122471DiVA: diva2:622615
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
In thesis
1. Explicit algebraic turbulence modelling in buoyancy-affected shear flows
Open this publication in new window or tab >>Explicit algebraic turbulence modelling in buoyancy-affected shear flows
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:nbn:se:kth:diva-122468 (URN)978-91-7501-797-6 (ISBN)
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
2. Turbulence modelling applied to the atmospheric boundary layer
Open this publication in new window or tab >>Turbulence modelling applied to the atmospheric boundary layer
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Turbulent flows affected by buoyancy lie at the basis of many applications, both within engineering and the atmospheric sciences. A prominent example of such an application is the atmospheric boundary layer, the lowest layer of the atmosphere, in which many physical processes are heavily influenced by both stably stratified and convective turbulent transport. Modelling these turbulent flows correctly, especially in the presence of stable stratification, has proven to be a great challenge and forms an important problem in the context of climate models. In this thesis, we address this issue considering an advanced class of turbulence models, the so-called explicit algebraic models.In the presence of buoyancy forces, a mutual coupling between the Reynolds stresses and the turbulent heat flux exists, which makes it difficult to derive a fully explicit turbulence model. A method to overcome this problem is presented based on earlier studies for cases without buoyancy. Fully explicit and robust models are derived for turbulence in two-dimensional mean flows with buoyancy and shown to give good predictions compared with various data from direct numerical simulations (DNS), most notably in the case of stably stratified turbulent channel flow. Special attention is given to the problem of determining the production-to-dissipation ratio of turbulent kinetic energy, for which the exact equation cannot be solved analytically. A robust approximative method is presented to calculate this quantity, which is important for obtaining a consistent formulation of the model.The turbulence model derived in this way is applied to the atmospheric boundary layer in the form of two idealized test cases. First, we consider a purely stably stratified boundary layer in the context of the well-known GABLS1 study. The model is shown to give good predictions in this case compared to data from large-eddy simulation (LES). The second test case represents a full diurnal cycle containing both stable stratification and convective motions. In this case, the current model yields interesting dynamical features that cannot be captured by simpler models. These results are meant as a first step towards a more thorough investigation of the pros and cons of explicit algebraic models in the context of the atmospheric boundary layer, for which additional LES data are required. 

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. xvi, 64 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2015.05
Keyword
turbulence; RANS models; explicit algebraic Reynolds-stress models; buoyancy; stable stratification; thermal convection; atmospheric boundary layer
National Category
Fluid Mechanics and Acoustics Meteorology and Atmospheric Sciences
Identifiers
urn:nbn:se:kth:diva-166806 (URN)978-91-7595-603-9 (ISBN)
Public defence
2015-06-12, Kollegiesalen, Brinellvägen 8, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20150522

Available from: 2015-05-22 Created: 2015-05-18 Last updated: 2015-05-22Bibliographically approved

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Brethouwer, GeertWallin, StefanJohansson, Arne

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