The influence of compliant surfaces on bypass transition

Abstract

The objective of the work was to investigate the effect of compliant surfaces on the receptivity and bypass transition of a boundary layer. Hot wire measurements in the pre-transitional and transitional boundary layers on nine different compliant and one rigid surface with identical geometries were made. The experiments were conducted in air and the compliant surfaces were manufactured from gelatine covered by a 10 μm protective PVC film. The laminar boundary layer profiles and growth rate results were the same for all the surfaces. However, the receptivity of the laminar boundary layer to freestream disturbances increased close to the leading edge of each compliant surface. Further downstream the majority of the compliant surfaces were successful in reducing the receptivity to a value below that for the rigid surface. The transition onset position on the compliant surfaces ranged from 3% downstream to 20% upstream of the rigid surface position. It was concluded that compliant surfaces with optimum properties can reduce receptivity and delay transition.

Appendix: dimensional analysis

The transition process for a boundary layer is governed by the receptivity. For bypass transition the receptivity can be characterised by the near wall gain. For a zero pressure gradient boundary layer on a rigid surface, this will depend on the fluid density ρ, the fluid viscosity μ, the flow velocity U, the length scale of the freestream turbulence λ _s and the boundary layer thickness δ. This leads to the dimensionless equation

$$ {\text{Gain}}_{{{\text{NW}}}} = f{\left( {Re_{\delta } ,\frac{{\lambda _{{\text{s}}} }} {\delta }} \right)} $$

(A1)

When the rigid surface is replaced by a compliant one, the properties of the compliant surface must also be included. These are the density ρ _cs, the Young’s modulus E, the damping coefficient ζ and the thickness of the layer L. A further four dimensionless quantities are then formed such that

$$ {\text{Gain}}_{{{\text{NW}}}} = f{\left( {Re_{\delta } ,\frac{{\lambda _{{\text{s}}} }} {\delta },\frac{{\zeta ^{2} }} {{E\rho _{{{\text{cs}}}} L^{2} }},\frac{\rho } {{\rho _{{{\text{cs}}}} }},\frac{L} {\delta },\frac{E} {{\rho U^{2} }}} \right)} $$

(A2)

where $\frac{{\zeta ^{2} }} {{E\rho _{{{\text{cs}}}} L^{2} }}$ characterises the density, elastic and damping properties of the compliant surface and is used for this purpose in the current paper. The remaining three quantities compare the density, characteristic lengths and stresses, respectively for the compliant surface and fluid.