Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations

Date

2017-07-01

Author

Ercan, Ali
Kavvas, M. Levent

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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.

URI

https://hdl.handle.net/11511/100387

Journal

SCIENTIFIC REPORTS

DOI

https://doi.org/10.1038/s41598-017-06669-z

Collections

Department of Civil Engineering, Article

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Citation Formats

A. Ercan and M. L. Kavvas, “Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations,” SCIENTIFIC REPORTS, vol. 7, pp. 0–0, 2017, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/100387.