Receptivity and transition to turbulence of supersonic boundary layers with surface roughness

Abstract

A deeper understanding of the different factors that influence the laminar-turbulent transition in supersonic boundary layers will help the design of efficient high-speed vehicles. In this work we study the effects of surface roughness on the stability and transition to turbulence of supersonic boundary layers. The investigation is carried out by direct numerical simulations (DNS) of the compressible Navier-Stokes equations and focuses on the modifications introduced in the transition process by localised roughness elements, for Mach numbers M? = 6.0 and M? = 2.5, and distributed slender pores at M? = 6.0. The first part of the investigation into the effects of localised roughness deals with the receptivity and initial exponential amplification of disturbances in boundary layers subjected to small external perturbations. Different transition scenarios are investigated by considering different free-stream disturbances and roughness elements with different heights. The results show that, for roughness heights approaching the local displacement thickness, transition is dominated by the growth of a number of instability modes in the roughness wake. These modes are damped by wall cooling and their receptivity is found to be more efficient in the case of free-stream disturbances dominated by sound. At M? = 6 the growth of Mack modes in the boundary layer is found to play a crucial role in the excitation of the most unstable wake modes. An investigation into the nonlinear stages of transition shows that the breakdown to turbulence starts with nonlinear interactions of the wake instability modes. This leads to the formation of a turbulent wedge behind the roughness element, which spreads laterally following mechanisms similar to those observed for the evolution of compressible turbulent spots. An oblique shock impinging on the transitional boundary layer significantly accelerates the breakdown process and leads to a wider turbulent wedge. The study ends with an analysis of porous walls as a passive method for transition control, which is carried out using a temporal DNS approach. The results show damping of both the primary, of second or Mack mode type, and secondary instabilities and indicate that, despite the high Mack number, first mode waves regain importance in this modified transition scenario.

More information

Identifiers

ORCID for N.D. Sandham: orcid.org/0000-0002-5107-0944

Catalogue record

Export record