Parametric investigation of hydrodynamic stability of a boundary layer on a flat plate over two-layer compliant coatings
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DOI: 10.1134/S086986432002002X
Parametric investigation of hydrodynamic stability of a boundary layer on a flat plate over two-layer compliant coatings * A.E. Darzhain1,2, A.V. Boiko3,4, V.M. Kulik5, and A.P. Chupakhin1,2 1
Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk, Russia
2
Novosibirsk State University, Novosibirsk, Russia
3
Khristianovich Institute of Theoretical and Applied Mechanics SB RAS, Novosibirsk, Russia
4
Tyumen State University, Tyumen, Russia
5
Kutateladze Institute of Thermophysics SB RAS, Novosibirsk, Russia
E-mail: [email protected] (Received June 5, 2019; revised July 27, 2019; accepted for publication November 6, 2019) The results of a parametric study of hydrodynamic stability in linear formulation of the Blasius boundary layer stability over two-layer compliant coatings are presented. In the calculations, experimental data for real silicon rubbers of several types on the elasticity modulus and the loss factor as functions of deformation frequency are used. Eight pairs of the coatings have been considered. The effect of coating layer thickness and external flow velocity on flow stability, in particular, on the behavior of the critical Reynolds number, has been studied parametrically. The regions of the critical Reynolds number of nonmonotonic nature, characteristic of most of coatings under consideration, have been found. A qualitative explanation of this effect is given. An analysis of the behavior of the critical Reynolds number allows determination of the optimal ratio of coating thicknesses for interaction with the flow. Keywords: compliant coatings, boundary layer, hydrodynamic instability, critical Reynolds number.
Introduction At present, there are a large number of studies on hydrodynamic stability of boundary layers over viscoelastic coatings (see, for example, [1–4] and reviews therein). The idea of using two-layer coatings, associated with practical applications, was put forward several decades ago (see, for example, [3]). It is known that hydrodynamic stability depends significantly on the coatings with a relatively small elasticity modulus, which are rather soft, i.e., their surfaces from the flow side are at substantial risk of defects. If it is necessary to use such a coating, *
The work was financially supported by the grant of the Russian Science Foundation No. 17-11-01156; experimental data have been obtained by V.M. Kulik in the framework of the grant of the Russian Foundation for Basic Research No. 18-08-00761.
A.E. Darzhain. A.V. Boiko, V.M. Kulik, and A.P. Chupakhin, 2020
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A.E. Darzhain, A.V. Boiko, V.M. Kulik, and A.P. Chupakhin
it seems quite natural to try to separate it from liquid by another, more rigid, but thin coating. At the same time, in most previous works on stability of the flows over compliant coatings, simulative coatings have been considered. This is due to the fact that the experimental data on the viscoelastic properties of promising coatings (mainly various silicon rubbers) in the range of vibration frequencies import
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