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Distributed Roughness Effects on Transitional and Turbulent Boundary Layers

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Abstract

A numerical investigation is carried out to study the transition of a subsonic boundary layer on a flat plate with roughness elements distributed over the entire surface. Post-transition, the effect of surface roughness on a spatially developing turbulent boundary layer (TBL) is explored. In the transitional regime, the onset of flow transition predicted by the current simulations is in agreement with the experimentally based correlations proposed in the literature. Transition mechanisms are shown to change significantly with the increasing roughness height. Roughness elements that are inside the boundary layer create an elevated shear layer and alternating high and low speed streaks near the wall. Secondary sinuous instabilities on the streaks destabilize the shear layer promoting transition to turbulence. For the roughness topology considered, it is observed that the instability wavelengths are governed by the streamwise and spanwise spacing between the roughness elements. In contrast, the roughness elements that are higher than the boundary layer create turbulent wakes in their lee. The scale of instability is much shorter and transition occurs due to the shedding from the obstacles. Post-transition, in the spatially developing TBL, the velocity defect profiles for both the smooth and rough walls collapsed when non dimensionalized in the outer units. However, when compared to the smooth wall, deviation in the Reynolds stresses are observable in the outer layer; the deviation being higher for the larger roughness elements.

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Notes

  1. Note that in some publications, (ξ 1,ξ 2,ξ 3) are represented as (ξ,η,ζ) and (x 1,x 2,x 3) as (x,y,z)

  2. We have also carried out additional simulations to explore the effects of free-stream turbulence (FST). However, this is beyond the scope of the current paper and will be published elsewhere.

  3. In the case of regularly distributed roughness, u ′ can also be defined by subtracting the instantaneous flow from the flow field averaged over multiple roughness elements at identical phase. However, this approach is not feasible for randomly distributed roughness.

  4. Note: The low-speed streak situated mid-way between the roughness peaks in Fig. 11a is due to the peaks of the roughness element at an upstream location (refer to the computational domain in Fig. 1)

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Funding

Author Nagabhushana Rao Vadlamani gratefully acknowledge the financial support from the St. Catharine’s college, Cambridge through the Bowring research fellowship. The simulations are performed on UK Supercomputer ARCHER, to which access was provided through the UK Turbulence Consortium Grant No. EP/L000261/1. Computational time from Hartree center (STFC) under Xeon Phi Access Programme is also acknowledged.

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  1. Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, UK

    Nagabhushana Rao Vadlamani & Paul G. Tucker

  2. Department of Aerospace Engineering, Iowa State University, Ames, IA, 50011, USA

    Paul Durbin

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Vadlamani, N.R., Tucker, P.G. & Durbin, P. Distributed Roughness Effects on Transitional and Turbulent Boundary Layers. Flow Turbulence Combust 100, 627–649 (2018). https://doi.org/10.1007/s10494-017-9864-4

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