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, 115103- p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2005. Vol. 17, no 11, 115103- p.
Complex Turbulent Flows; Viscosity
Fluid Mechanics and Acoustics
IdentifiersURN: urn:nbn:se:kth:diva-5408DOI: 10.1063/1.2131921ISI: 000233603000022ScopusID: 2-s2.0-30044441293OAI: oai:DiVA.org:kth-5408DiVA: diva2:9768
QC 201008242006-03-082006-03-082010-12-06Bibliographically approved