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Contributions to pressure drag in rough-wall turbulent flows: Insights from force partitioning

Mostafa Aghaei-Jouybari1, Jung-Hee Seo1, Junlin Yuan2, Rajat Mittal1,*, and Charles Meneveau1,†

  • 1Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
  • 2Department of Mechanical Engineering, Michigan State University, East Lansing, Michigan 48824, USA

  • *mittal@jhu.edu
  • †meneveau@jhu.edu
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Phys. Rev. Fluids 7, 084602 – Published 8 August, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.084602

Abstract

The force partitioning method [Menon and Mittal, J. Fluid Mech. 918, R3 (2021)] is employed to decompose and analyze the pressure-induced drag for turbulent flow over rough walls. The pressure drag force imposed by the rotation-dominated vortical regions (Q>0, where Q is the second invariant of the velocity gradient tensor) and strain-dominated regions (Q<0) are quantified using a geometry dependent auxiliary potential field (denoted by ϕ). The analysis is performed on data from direct numerical simulations (DNSs) of turbulent channel flows, at frictional Reynolds number of Reτ=500, with cube and sand-grain roughened bottom walls. Results from both simulations indicate that the Q-induced pressure drag is the largest contributor (more than 50%) to the total drag on the rough walls. Data are further analyzed to quantify the effects of time-mean (coherent) and incoherent turbulent flow on the Q-induced drag force, and to discuss possible effects of roller and U-shaped structures expected to occur at the crest and midcrest locations of the roughness elements, respectively. Based on the observation that the ϕ field encodes information about the surface geometry that directly impacts the drag, we provide initial evidence that it can also be used to parametrize the surface drag. Specifically, we propose and test three norms based on the ϕ field (two of them related to the surface-induced potential flow), and explore the characterization of the Nikuradse equivalent sand-grain height ks based on these parameters for a number of channel flows with different roughness topologies. Data are provided from a suite of DNS cases by Aghaei-Jouybari et al. [J. Fluid Mech. 912, A8 (2021)]. An empirical correlation depending on these ϕ-based parameters, with five empirically tuned coefficients, is shown to predict ks with average and maximum errors of 10.5 and 26 percent, respectively. The results confirm that a purely geometric quantity, the ϕ field, provides useful additional information that can be used in drag law formulations.

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Phys. Rev. Fluids 7, 084602– Published 8 August, 2022
  • Received 7 February 2022
  • Accepted 15 July 2022
Article part of CHORUS
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