D.I. Okhotnikov
Kazan Federal University, Kazan, 420008 Russia
E-mail: dmitry.okhotnikov@gmail.com
Received February 16, 2017
Abstract
This paper considers a method of building composite grids with local refinement for direct numerical simulation of flows in a channel with transverse cylindrical rib at moderate Reynolds numbers. The specific characteristic of the flows is LTT (laminar-turbulent transition) in a trace behind the rib. Grids characterized by resolution of the whole spectrum of vortices are needed for numerical simulation of LTT, thereby leading to significant computational costs and a need for supercomputers. The purpose of the study is to generate a cost-efficient computational grid based on the above-described method, as well as to test this grid for flows in a channel with the following two types of ribs: a semicircular ridge on the lower wall of the channel and cylinder near it. The grid has been built using the HybMesh generator, which is based on the composite approach, when the grid is built from a set of structured subdomains, in which grid generation and refinement is defined by several control parameters. As a result of superposition of the grids built in subdomains, a composite grid from structured parts superposed with unstructured inserts has been obtained. The results of the direct numerical simulation on a grid for the problem with a semicircular ridge have turned out to be in a good agreement with the results of the laboratory experiment, both along the profiles of average velocity and the profiles of pulsations. The results obtained on the grid for the problem with a circular cylinder have demonstrated good agreement with the results of the numerical simulation on high-definition grids, predicting in the right way the transition point to three-dimensionality in a trace behind the cylinder. The method of building composite grids with the use of the HybMesh generator allows to generate cost-efficient composite grids taking into account all flow peculiarities and allowing for calculations using medium-powered computers.
Keywords: flow in channel, transverse rib, laminar-turbulent transition, direct numerical simulation, composite grids, local refinement
Acknowledgments. We are grateful to A.B. Mazo, Professor and Doctor of Physics and Mathematics, and E.I. Kalinin, PhD in Physics and Mathematics, for valuable advice during the manuscript preparation.
The study was supported by the Russian Foundation for Basic Research (project no. 15-01-06172).
Figure Captions
Fig. 1. Computational domain geometry.
Fig. 2. The results of visualization (upwards) and calculation (downwards) of the instantaneous image of flow in plane parallel to side walls of the channel: a – Re = 270; b – Re = 480.
Fig. 3. Grid generation in the computational domain: a – division into subdomains; b – geometrical characteristics of the grid.
Fig. 4. Generation of the domain 1: a – circular domain; b – the result of cutting of the circular domain with the contour.
Fig. 5. Generation of the domain 2. The dotted line shows a part of the quadrilateral which is cut with the domain 1.
Fig. 6. Orthogonal grid built in the domain 1.
Fig. 7.The grid built in the domain 2: a – subdomain 2.2, b – subdomain 2.1.
Fig. 8. Division of the contour of the domain 3 into subcontours (a); the image of the grid generated near the contour c1 (b); the image of the grid generated near the contour c2 (c).
Fig. 9. The contour of the domain 5 (a) and the grid generated in it (b).
Fig. 10. A fragment of the resulting two-dimensional grid near the rib.
Fig. 11. A fragment of the three-dimensional grid near the rib (inside view).
Fig. 12. Epures of the longitudinal velocity, Re = 480: 1 – our data, 2 – experiment (SIV); a – along the straight line x = 2; b – along the straight line x = 4.
Fig. 13. Epures of the second moments u'v' and v'v' , Re = 480: 1 – our data, 2 – experiment (SIV), x = 4.
Fig. 14. The energy spectrum of flow velocity in a trace behind the rid in the point (10; 1; 0) : 1 – Re = 270; 2 – Re = 480.
Fig. 15. The dependence of the cylinder resistance coefficient (on the left) and the Strouhal
number (on the right) on Re: 1 – 2D-computation [7]; 2 – 3D-computation [7]; 3 – our 2D-
computation; 4 – our 3D-computation; 5 – 2D-computation [20].
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For citation: Okhotnikov D.I. Direct numerical simulation of laminar-turbulent transition on grids with local refinement. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2017, vol. 159, no. 2, pp. 216–230. (In Russian)
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