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Efficient treatment of the nonlinear features in algebraic Reynolds-stress and heat-flux models for stratified and convective flows
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Stockholm University, 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. 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: 0000-0002-2711-4687
2015 (English)In: International Journal of Heat and Fluid Flow, ISSN 0142-727X, E-ISSN 1879-2278, Vol. 53, 15-28 p.Article in journal (Refereed) Published
Abstract [en]

This work discusses a new and efficient method for treating the nonlinearity of algebraic turbulence models in the case of stratified and convective flows, for which the equations for the Reynolds stresses and turbulent heat flux are strongly coupled. In such cases, one finds a quasi-linear set of equations, which can be solved through an appropriate linear expansion in basis tensors and vectors, as discussed in earlier work. However, finding a consistent and truly explicit algebraic turbulence model requires solving an additional equation for the production-to-dissipation ratio (P+G)/ε of turbulent kinetic energy. Due to the nonlinear nature of the problem, the equation for (P+G)/ε is a higher-order polynomial equation for which no analytical solution can be found. Here we provide a new method to approximate the solution of this polynomial equation through an analysis of two special limits (shear-dominated and buoyancy-dominated), in which exact solutions are obtainable. The final result is a model that appropriately combines the two limits in more general cases. The method is tested for turbulent channel flow, both with stable and unstable stratification, and the atmospheric boundary layer with periodic and rapid changes between stable and unstable stratification. In all cases, the model is shown to give consistent results, close to the exact solution of (P+G)/ε. This new method greatly increases the range of applicability of explicit algebraic models, which otherwise would rely on the numerical solution of the polynomial equation.

Place, publisher, year, edition, pages
2015. Vol. 53, 15-28 p.
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-166800DOI: 10.1016/j.ijheatfluidflow.2015.01.005ISI: 000355367500002Scopus ID: 2-s2.0-84923270425OAI: oai:DiVA.org:kth-166800DiVA: diva2:812365
Funder
Swedish Research Council, 621-2013-5784
Note

QC 20150521

Available from: 2015-05-18 Created: 2015-05-18 Last updated: 2017-12-04Bibliographically approved
In thesis
1. 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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