Open AccessScaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations
Author(s) -
Ali Ercan,
M. L. Kavvas
Publication year - 2017
Publication title -
scientific reports
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.24
H-Index - 213
ISSN - 2045-2322
DOI - 10.1038/s41598-017-06669-z
Subject(s) - scaling , similarity (geometry) , self similarity , reynolds number , solver , flow (mathematics) , boundary value problem , mathematics , navier–stokes equations , similarity solution , dynamic similarity , non dimensionalization and scaling of the navier–stokes equations , space (punctuation) , computational fluid dynamics , mathematical analysis , reynolds averaged navier–stokes equations , computer science , physics , boundary layer , mathematical optimization , mechanics , geometry , turbulence , artificial intelligence , compressibility , image (mathematics) , operating system
Scaling conditions to achieve self-similar solutions of 3-Dimensional (3D) Reynolds-Averaged Navier-Stokes Equations, as an initial and boundary value problem, are obtained by utilizing Lie Group of Point Scaling Transformations. By means of an open-source Navier-Stokes solver and the derived self-similarity conditions, we demonstrated self-similarity within the time variation of flow dynamics for a rigid-lid cavity problem under both up-scaled and down-scaled domains. The strength of the proposed approach lies in its ability to consider the underlying flow dynamics through not only from the governing equations under consideration but also from the initial and boundary conditions, hence allowing to obtain perfect self-similarity in different time and space scales. The proposed methodology can be a valuable tool in obtaining self-similar flow dynamics under preferred level of detail, which can be represented by initial and boundary value problems under specific assumptions.