Hydroelastic instability threshold in a turbulent boundary layer over a compliant coating

Abstract

In this paper we are concerned with a linear problem of hydroelastic instability in a turbulent boundary layer over a compliant coating of a ribbon-like material. A dispersion relation for hydroelastic waves is written in terms of complex stiffness coefficients that characterize the deformation of the compliant surface and the turbulent flow response to the wavy surface flexure. A membrane-type approximation is proposed for the stiffness coefficient of solid coating at sufficiently low frequencies. In order to evaluate the turbulent flow response, the eddy-viscosity model in a curvilinear coordinate system is employed. The quasipotential approximation for the description of flow stiffness is confirmed on the basis of the computations. The critical flow speed and the parameters of the hydroelastic waves at the instability threshold are determined both within general definitions for the stiffness coefficients and for their approximations. The computational results are compared with available experimental observations.

Turbulence over a compliant surface: numerical simulation and analysis

“…Results of numerical studies indicating benefits from compliant walls in the area of transition delay were reported by Carpenter & Morris (1990) and by Davies & Carpenter (1997). The case of transition manipulation is interesting, because in that case there is quite an extensive body of theoretical material on this problem, which is described by the linear stability theory and the asymptotic theory of transitional flows over compliant walls or in compliant channels (see Gajjar & Sibanda 1996;Larose & Grotberg 1996;Lucey & Carpenter 1995;Reutov & Rybushkina 1998;Riley, Gad-el-Hak & Metcalfe 1988;Yeo, Khoo & Zhao 1999). In fact, linear stability theory can provide satisfactory explanations for the failure of many experimental attempts aimed at delaying the onset of transition over compliant walls.…”

Nonlinear development of two-dimensional hydroelastic instability in a turbulent boundary layer on an elastic coating

“…The main term of expansion in the right part of (2) Y0 coincides with tile linear elasticity of the flow calculated in [7]; the coefficient Yl characterizes the nonlinear properties of the TBL resI)onse. According to [8] The deformation of the surface of the elastic coating under an external action may be characterized by the complex elasticity K0 = -/)/tb.…”

“…In tile quasi-linear approximation, the elasticity is a flmction of (ka) 2 and may be considered as a virtual el~tsticity [7]. For small ka, we obtain tim dimensionless ela.sticity of the flow…”

“…Reutov [8] proposed a immerical model, which allows one to calculate the nonlinear response of the TBL to a wavy flexure of the underlying surface. As in [9], where the interaction of waves on water with an atmospheric TBL was examined, Reutov [8] used a quasi-linear approximation, where the basic nonlinear effects are related to deformation of the profile of the mean (over the waviness period) flow.In tile present paper, which should be considered as a continuation of [7,8], we study the nonlinear stage of evolution of hydroelastic instability in the TBL on a single-layer coating. The main small parameter of the problem is tile slope of the wavy surface ka << 1 (k and a are the wavenumber and the amplitude of surface flexure).…”

“…Two 1)~usie regimes of generation of hydroeb~stic waves were ~bund: traveling-wave flutter (T~VF) and wave divergence. Reutov and Rybushkina [7] used an algebraic model of vortex viscosity to study linear hydroelastic instability in the TBL, and equations for two-(timensional wave perturbations in the boundary layer were written in curvilinear coordinates. The calculated vahles of the critical velocity of TWF and wave-divergence origimttion are in good agreement with the experimental data of [1,6].…”