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Modelling and simulation of turbulence subject to system rotation
KTH, School of Engineering Sciences (SCI), Mechanics.
2006 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Simulation and modelling of turbulent flows under influence of streamline curvature and system rotation have been considered. Direct numerical simulations have been performed for fully developed rotating turbulent channel flow using a pseudo-spectral code. The rotation numbers considered are larger than unity. For the range of rotation numbers studied, an increase in rotation number has a damping effect on the turbulence. DNS-data obtained from previous simulations are used to perform a priori tests of different pressure-strain and dissipation rate models. Furthermore, the ideal behaviour of the coefficients of different model formulations is investigated. The main part of the modelling is focused on explicit algebraic Reynolds stress models (EARSMs). An EARSM based on a pressure strain rate model including terms that are tensorially nonlinear in the mean velocity gradients is proposed. The new model is tested for a number of flows including a high-lift aeronautics application. The linear extensions are demonstrated to have a significant effect on the predictions. Representation techniques for EARSMs based on incomplete sets of basis tensors are also considered. It is shown that a least-squares approach is favourable compared to the Galerkin method. The corresponding optimality aspects are considered and it is deduced that Galerkin based EARSMs are not optimal in a more strict sense. EARSMs derived with the least-squares method are, on the other hand, optimal in the sense that the error of the underlying implicit relation is minimized. It is further demonstrated that the predictions of the least-squares EARSMs are in significantly better agreement with the corresponding complete EARSMs when tested for fully developed rotating turbulent pipe flow.

Place, publisher, year, edition, pages
Stockholm: KTH , 2006. , p. viii, 34
Series
Trita-MEK, ISSN 0348-467X ; 2006:04
Keywords [en]
Direct numerical simulations, least-squares method, turbulence model, nonlinear modelling, system rotation, streamline curvature, high-lift aerodynamics
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-3865OAI: oai:DiVA.org:kth-3865DiVA, id: diva2:9774
Public defence
2006-03-17, Sal F2, Lindstedtsvägen 26, Stockholm, 10:15
Opponent
Supervisors
Note
QC 20100825Available from: 2006-03-08 Created: 2006-03-08 Last updated: 2010-08-25Bibliographically approved
List of papers
1. Techniques for deriving explicit algebraic Reynolds stress models based on incomplete sets of basis tensors and predictions of fully developed rotating pipe flow
Open this publication in new window or tab >>Techniques for deriving explicit algebraic Reynolds stress models based on incomplete sets of basis tensors and predictions of fully developed rotating pipe flow
2005 (English)In: Physics of fluids, ISSN 1070-6631, Vol. 17, no 11, p. 115103-Article in journal (Refereed) Published
Abstract [en]

Different techniques for deriving explicit algebraic Reynolds stress models (EARSMs) using incomplete sets of basis tensors are discussed. The first is the Galerkin method which has been used by several authors. The second alternative technique, proposed here, is based on the least-squares method. The idea behind the latter method is to minimize the error induced in the implicit relation, i.e., the algebraic Reynolds stress model (ARSM) equation, due to the use of incomplete sets of basis tensors. It is argued that since the system matrix of the ARSM equation is not symmetric and positive definite, the Galerkin method does not give EARSMs that are optimal in the strict classical sense. The possible singular behavior depending on the choice of the basis tensors has also been investigated. It is demonstrated that many of the EARSMs based on incomplete tensor bases, expressed in general three-dimensional mean flows, have singularity problems in some flows, such as general two-dimensional (2D) mean flows or more specifically, strain- and/or rotation-free 2D mean flows. The different EARSMs emanating from the two derivation methods are investigated by computing fully developed rotating pipe flow. The results indicate that the EARSMs derived with the least-squares method capture the behavior of the complete EARSMs significantly better than those derived with the Galerkin method. Furthermore, by using mean flow data from the complete EARSMs to evaluate the square error of the incomplete EARSMs it is demonstrated that the least-squares based EARSMs have square errors significantly smaller than the Galerkin EARSMs, very close to minimum.

Keywords
Complex Turbulent Flows; Viscosity
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-5408 (URN)10.1063/1.2131921 (DOI)000233603000022 ()2-s2.0-30044441293 (Scopus ID)
Note
QC 20100824Available from: 2006-03-08 Created: 2006-03-08 Last updated: 2010-12-06Bibliographically approved
2. An explicit algebraic Reynolds stress model based on a nonlinear pressure strain rate model
Open this publication in new window or tab >>An explicit algebraic Reynolds stress model based on a nonlinear pressure strain rate model
2004 (English)In: International journal of heat fluid flow, ISSN 0142-727X, Vol. 26, no 5, p. 732-745Article in journal (Refereed) Published
Abstract [en]

The use of a pressure strain rate model including terms nonlinear in the mean strain and rotation rate tensors in an explicit algebraic Reynolds stress model (EARSM) is considered. For 2D mean flows the nonlinear contributions can be fully accounted for in the EARSM formulation. This is not the case for 3D mean flows and a suggestion of how to modify the nonlinear terms to make the EARSM formulation in 3D mean flows consistent with its 2D counterpart is given. The corresponding EARSM is derived in conjunction with the use of streamline curvature corrections emanating from the advection of the Reynolds stress anisotropy, The proposed model is tested for rotating homogeneous shear flow. rotating channel flow and rotating pipe flow and the nonlinear contributions are shown to have a significant effect on the predicted flow characteristics. In cases where the 3D effects are strong, the approximations of the production to dissipation ratio made in the EARSM formulation for 3D mean flows must be made carefully and a 3D mean flow correction is considered. For the rotating pipe flow at the highest rotation rate investigated. the standard formulation even prevented convergence, while inclusion of the 3D correction gives reasonable results

Keywords
turbulence modelling; earsm; nonlinear modelling; rotating flow; projection method
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-5409 (URN)10.1016/j.ijheatfluidflow.2005.04.004 (DOI)000231888500005 ()2-s2.0-23944451347 (Scopus ID)
Note
QC 20100824Available from: 2006-03-08 Created: 2006-03-08 Last updated: 2010-12-06Bibliographically approved
3. Observations on the predictions of fully developed rotating pipe flow using differential and explicit algebraic Reynolds stress models
Open this publication in new window or tab >>Observations on the predictions of fully developed rotating pipe flow using differential and explicit algebraic Reynolds stress models
2006 (English)In: European jounal of mechanics. B, ISSN 0997-7546, Vol. 25, no 1, p. 95-112Article in journal (Refereed) Published
Abstract [en]

The differences between two differential Reynolds stress models (DRSM) and their corresponding explicit algebraic Reynolds stress models (EARSM) are investigated by studying fully developed axially rotating turbulent pipe flow. The mean flow and the turbulence quantities are strongly influenced by the imposed rotation, and is well captured by the differential models as well as their algebraic truncations. All the tested models give mean velocity profiles that are in good qualitative agreement with the experimental data. It is demonstrated that the predicted turbulence kinetic energy levels vary dramatically depending on the diffusion model used, and that this is closely related to the model for the evolution of the length-scale determining quantity. Furthermore, the effect of the weak equilibrium assumption, underlying the EARSMs, and the approximation imposed for 3D mean flows on the turbulence levels are investigated. In general the predictions obtained with the EARSMs rather closely follow those of the corresponding DRSMs

Keywords
rotating pipe flow; swirling flow; Reynolds stress turbulence model
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-5410 (URN)10.1016/j.euromechflu.2005.03.004 (DOI)000233196200007 ()2-s2.0-27144456785 (Scopus ID)
Note
QC 20100824Available from: 2006-03-08 Created: 2006-03-08 Last updated: 2010-12-06Bibliographically approved
4. Application of EARSM turbulence models to high-lift aerodynamics applications
Open this publication in new window or tab >>Application of EARSM turbulence models to high-lift aerodynamics applications
2005 (English)In: Proc. of Engineering turbulence modelling and measurements 6 (ETMM-6), 2005Conference paper, Published paper (Refereed)
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-5411 (URN)978-0-08-044544-1 (ISBN)
Conference
ETMM6, Sardinia, Italy, 23–25 May, 2005
Note

QC 20100824

Available from: 2006-03-08 Created: 2006-03-08 Last updated: 2017-04-18Bibliographically approved
5. Direct numerical simulations of rotating channel flow
Open this publication in new window or tab >>Direct numerical simulations of rotating channel flow
(English)Article in journal (Other academic) Submitted
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-5412 (URN)
Note
QS 2011 QS 20120326Available from: 2006-03-08 Created: 2006-03-08 Last updated: 2012-03-26Bibliographically approved
6. A priori evaluations and least-squares optimizations of turbulence models for fully developed rotating turbulent channel flow
Open this publication in new window or tab >>A priori evaluations and least-squares optimizations of turbulence models for fully developed rotating turbulent channel flow
2008 (English)In: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390, Vol. 27, no 2, p. 75-95Article in journal (Refereed) Published
Abstract [en]

The present study involves a priori tests of pressure-strain and dissipation rate tensor models using data from direct numerical simulations (DNS) of fully developed turbulent channel flow with and without spanwise system rotation. Three different pressure-strain rate models are tested ranging from a simple quasi-linear model to a realizable fourth order model. The evaluations demonstrate the difficulties of developing RANS-models that accurately describe the flow for a wide range of rotation numbers. Furthermore, least-squares based tensor representations of the exact pressure-strain and dissipation rate tensors are derived point-wise in space. The relation obtained for the rapid pressure-strain rate is exact for general 2D mean flows. Hence, the corresponding distribution of the optimized coefficients show the ideal behaviour. The corresponding representations for the slow pressure-strain and dissipation rate tensors are incomplete but still optimal in a least-squares sense. On basis of the least-squares analysis it is argued that the part of the representation that is tensorially linear in the Reynolds stress anisotropy is the most important for these parts.

Keywords
a priori testing, turbulence model, least-squares method, channel flow
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-5413 (URN)10.1016/j.euromechflu.2007.03.001 (DOI)000254116800001 ()2-s2.0-38849191249 (Scopus ID)
Note
QC 20100825Available from: 2006-03-08 Created: 2006-03-08 Last updated: 2017-11-21Bibliographically approved

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