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Effect of Geometry on Direct and Adjoint Linear Global Modes of Low Reynolds Number Laminar Flow over Body

Abstract

We study a two-dimensional flow over a cylinder and three ellipses with the aspect ratio \(a / b = 2.04\), \(3.65\), and \(5\) at a Reynolds number \(Re = 100\) based on the inflow velocity and hydraulic diameter using a direct numerical simulation (DNS) and linear stability analysis. The DNS shows that increase in \(a / b\) leads to stabilization of the flow due to decrease in the recirculation zone. The linear stability analysis based on the time-averaged velocity field shows that the modes of interest describe a Karman vortex street. The oscillation frequency reconstructed from the linear stability analysis is in excellent agreement with the DNS. Solving the linearized adjoint equations made it possible to identify the flow area where direct and adjoint modes overlap. These areas of the field \(S_w\), usually called “wavemaker,” change their shape with increase in \(a / b\). Non-zero values of \(S_w\) tend to approach the bottom part of the “tail” of the ellipse due to the asymmetry of the recirculation region, attached to the top side of the ellipse.

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Funding

The work was supported by RFBR, project nos. 18-38-20167 and 19-48-543036 (VR and RM for numerical simulations), and by RF Ministry of Education and Science, grant no. 075-15-2019-1923 (DS for global stability analysis). The development of numerical tools is performed under the state contract with IT SB RAS. The computational resources are provided by the Siberian Supercomputer Center SB RAS, Supercomputer Center of the Novosibirsk State University, and Joint Supercomputer Center RAS.

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Correspondence to V. O. Ryzhenkov.

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Ryzhenkov, V.O., Sozinov, D.A. & Mullyadzhanov, R.I. Effect of Geometry on Direct and Adjoint Linear Global Modes of Low Reynolds Number Laminar Flow over Body. J. Engin. Thermophys. 29, 576–581 (2020). https://doi.org/10.1134/S1810232820040050

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