Laminar-turbulent transition induced by a discrete roughness element in a supersonic boundary layer

Abstract

The linear instability and breakdown to turbulence induced by an isolated roughness
element in a boundary layer at Mach 2:5, over an isothermal flat plate with
laminar adiabatic wall temperature, have been analysed by means of direct numerical
simulations, aided by spatial BiGlobal and three-dimensional parabolized (PSE-3D)
stability analyses. It is important to understand transition in this flow regime since
the process can be slower than in incompressible flow and is crucial to prediction
of local heat loads on next-generation flight vehicles. The results show that the
roughness element, with a height of the order of the boundary layer displacement
thickness, generates a highly unstable wake, which is composed of a low-velocity
streak surrounded by a three-dimensional high-shear layer and is able to sustain the
rapid growth of a number of instability modes. The most unstable of these modes are
associated with varicose or sinuous deformations of the low-velocity streak; they are
a consequence of the instability developing in the three-dimensional shear layer as a
whole (the varicose mode) or in the lateral shear layers (the sinuous mode). The most
unstable wake mode is of the varicose type and grows on average ?17% faster than
the most unstable sinuous mode and ?30 times faster than the most unstable boundary
layer mode occurring in the absence of a roughness element. Due to the high growthrates
registered in the presence of the roughness element, an amplification factor of
N D 9 is reached within ?50 roughness heights from the roughness trailing edge. The
independently performed Navier–Stokes, spatial BiGlobal and PSE-3D stability results
are in excellent agreement with each other, validating the use of simplified theories for
roughness-induced transition involving wake instabilities. Following the linear stages
of the laminar–turbulent transition process, the roll-up of the three-dimensional shear
layer leads to the formation of a wedge of turbulence, which spreads laterally at a rate
similar to that observed in the case of compressible turbulent spots for the same Mach
number.

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Identifiers

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

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