Investigation of turbulent flow over irregular rough surfaces using direct numerical simulations

Abstract

Incompressible turbulent flow in irregular rough channels is investigated using a finite-difference direct numerical simulation code which includes an iterative embedded boundary treatment to resolve the roughness. Seventeen industrially relevant rough surfaces with a wide variation in surface topography are considered. Various studies are conducted to understand the flow physics and the relationship between key flow parameters and surface topography. Studies at low values of friction Reynolds number, Reτ, for a single surface, show that the flow is laminar up to Reτ = 89 and begins to develop quasi-periodic fluctuations at Reτ = 89.5. Fluctuations in the three velocity components continue to grow until Reτ = 91, and the flow is turbulent for Reτ ≥ 92. Transition depends on the surface topography as some roughness peaks trigger fluctuations before others. For all the surfaces, mean and turbulent flow statistics are computed at Reτ = 180, for which the flow is fully turbulent but transitionally rough. All surfaces are scaled to the same physical roughness height. Nevertheless, a wide range of roughness function, ∆U+, values is obtained, indicating that it depends not only on the roughness height but also on the detailed roughness topography. Other mean and turbulence flow statistics also vary considerably depending on the surface topography. Next, based on the simulation results database at Reτ = 180, a newly formulated method, that determines which surface topographical properties are important and how new properties can be added to an empirical model, is tested. Optimised models with several roughness parameters are systematically developed for ∆U+ and profile peak turbulent kinetic energy. In determining ∆U+, besides the known parameters of solidity and skewness, it is shown that the streamwise correlation length and rms roughness height are also significant. The peak turbulent kinetic energy is determined by the skewness and rms roughness height, along with the mean forward-facing surface angle and spanwise effective slope. A Reynolds number dependence study is conducted for a single surface, wherein the roughness height in viscous units, k+, is varied from the transitionally rough to the fully-rough regime in the range 3.75 ≤ k+ ≤ 120. Excellent agreement with the experimental data of Nikuradse (Laws of flow in rough pipes, NACA Technical Memorandum 1292, 1933) is observed. The value of equivalent sand-grain roughness height, k+s,eq, thus obtained is close to the mean peak-to-valley height.

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

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