Evaluation of the momentum integral method to determine the wall skin friction in separated flows
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RESEARCH ARTICLE
Evaluation of the momentum integral method to determine the wall skin friction in separated flows Meagan E. Wengrove1 · Alireza Ebadi2 · Christopher M. White2 · Diane L. Foster3 Received: 14 August 2020 / Revised: 17 September 2020 / Accepted: 22 September 2020 / Published online: 10 November 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The momentum integral-based method developed by Mehdi and White (Exp Fluids 50(1):43–51. https: //doi.org/10.1007/ s00348-010-0893-1, 2011) for determining wall skin friction in turbulent wall-bounded flow is evaluated in separated flows in which independent estimates of wall skin friction are known. Owing to flow complexities, a direct measurement of the wall skin friction in separated flow is experimentally challenging. In this pursuit, the momentum integral-based method is particularly attractive as the method is mathematically exact and determination of the wall skin friction only requires measurement of the wall-normal profile of mean velocity and Reynolds shear stress. The present analysis uses existing experimental particle image velocimetry and direct numerical simulation data of flow over a backward-facing step as well as DNS over a smooth hump to demonstrate that the method is viable. The method is also shown to be viable in estimating the wall skin friction in flows over non-flat geometries.
* Meagan E. Wengrove [email protected] Alireza Ebadi [email protected] Christopher M. White [email protected] Diane L. Foster [email protected] 1
School of Civil and Construction Engineering, Oregan State University, Corvallis, OR 97331, USA
2
Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, USA
3
School of Marine Science and Ocean Engineering, University of New Hampshire, Durham, NH 03824, USA
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Experiments in Fluids (2020) 61:250
Graphic abstract
1 Introduction The wall shear stress, 𝜏w = 𝜇(𝜕u∕𝜕y)||y=0 , is the local tangential surface force per area resulting from friction between a wall-bounded flow and its bounding surface, where 𝜇 is the dynamic viscosity, u is the velocity component tangent to the wall, y is the wall-normal direction and the wall is located at y = 0 . The ability to accurately estimate the wall shear stress is critically important in fluid dynamics and its related applications and technologies (Haritonidis 1989). It is indicative of turbulent boundary layer dynamics and serves as a primary √ scaling parameter (through the friction velocity u𝜏 = 𝜏w ∕𝜌 , where 𝜌 is the density) in wall-bounded turbulent flows (Prandtl and Tietjens 1934; Klewicki et al. 2007; Adrian 2007). Computational fluid dynamics (CFD) models are typically validated based on a comparison between the model computed wall skin friction, Cf = 𝜏w ∕0.5𝜌U02 , where U0 is a characteristic velocity, and a baseline standard (Pond et al. 2017). The wall shear stress is responsible for a large
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fraction of the total drag in interna
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