A deterministic model for the sublayer streaks in turbulent boundary layers for application to flow control

Abstract

We present a relatively simple, deterministic, theoretical model for the sublayer streaks in a turbulent boundary layer based on an analogy with Klebanoff modes. Our approach is to generate the streamwise vortices found in the buffer layer by means of a vorticity source in the form of a fictitious body force. It is found that the strongest streaks correspond to a spanwise wavelength that lies within the range of the experimentally observed values for the statistical mean streak spacing. We also present results showing the effect of streamwise pressure gradient, Reynolds number and wall compliance on the sublayer streaks. The theoretical predictions for the effects of wall compliance on the streak characteristics agree well with experimental data. Our proposed theoretical model for the quasi-periodic bursting cycle is also described, which places the streak modelling in context. The proposed bursting process is as follows: (i) streamwise vortices generate sublayer streaks and other vortical elements generate propagating plane waves, (ii) when the streaks reach a sufficient amplitude, they interact nonlinearly with the plane waves to produce oblique waves that exhibit transient growth, and (iii) the oblique waves interact nonlinearly with the plane wave to generate streamwise vortices; these in turn generate the sublayer streaks and so the cycle is renewed.

Introduction. Computational aerodynamics

“…As noted by Pope (2004), at cruise, a Boeing 777 wing has approximately 10 8 streaks (these estimates probably do not include the effects of pressure gradient and sweep) presenting a key LES resolution issue. Similar stark statistics relating to spatial and temporal scales, but this time for the fuselage of an Airbus A340-300, are brought out by Carpenter et al (2007). According to their estimates for the Airbus 340-300, there are 2000 streaks m K1 and approximately 20!10 8 for the whole fuselage.…”

“…Hence, the assessment of the future potential of such technologies through numerical modelling is important. A deeper understanding of near-wall behaviour and streak generation is also likely to be of importance in improving the theoretical foundations of RANS, hybrid LES-RANS and pure LES methods, thus adding to the importance of the work of Carpenter et al (2007). As noted by Pope (2004), at cruise, a Boeing 777 wing has approximately 10 8 streaks (these estimates probably do not include the effects of pressure gradient and sweep) presenting a key LES resolution issue.…”

“…Intricate, elongated near-wall structures (sublayer streaks) play a key role in the generation of skin friction. Hence, a novel numerical model for sublayer streak prediction is presented by Carpenter et al (2007). Also, practical aspects relating to the control of near-wall structures are discussed along with elements of flow Introduction control in general.…”

“…Carpenter et al (2007) outline the various drag sources and their relative importance. Aerodynamics design has improved so much that now over 50% of aircraft drag is due to skin friction, hence there is a pressing need to reduce it.…”

“…This theme issue has papers in the following areas: turbulence (Gatski et al 2007); flow/turbulence control (Carpenter et al 2007); propulsive jet dynamics and noise (Birch et al); aeroengine external air systems (Dawes 2007); aeroengine internal air systems (Chew & Hills 2007); aeroelasticity for aeroengines and external aerodynamics (Bartels & Sayma 2007); design optimization (Keane & Scanlan 2007); and unsteady flow modelling (Hassan et al 2007). …”