Abstract
ABSTRACTRough surfaces are usually characterised by a single equivalent sand-grain roughness height scale that typically needs to be determined from laboratory experiments. Recently, this method has been complemented by a direct numerical simulation approach, whereby representative surfaces can be scanned and the roughness effects computed over a range of Reynolds number. This development raises the prospect over the coming years of having enough data for different types of rough surfaces to be able to relate surface characteristics to roughness effects, such as the roughness function that quantifies the downward displacement of the logarithmic law of the wall. In the present contribution, we use simulation data for 17 irregular surfaces at the same friction Reynolds number, for which they are in the transitionally rough regime. All surfaces are scaled to the same physical roughness height. Mean streamwise velocity profiles show a wide range of roughness function values, while the velocity defect profiles show a good collapse. Profile peaks of the turbulent kinetic energy also vary depending on the surface. We then consider which surface properties are important and how new properties can be incorporated into an empirical model, the accuracy of which can then be tested. Optimised models with several roughness parameters are systematically developed for the roughness function and profile peak turbulent kinetic energy. In determining the roughness function, besides the known parameters of solidity (or frontal area ratio) and skewness, it is shown that the streamwise correlation length and the root-mean-square roughness height are also significant. The peak turbulent kinetic energy is determined by the skewness and root-mean-square roughness height, along with the mean forward-facing surface angle and spanwise effective slope. The results suggest feasibility of relating rough-wall flow properties (throughout the range from hydrodynamically smooth to fully rough) to surface parameters.
Highlights
Rough surfaces are encountered in a large number of applications; from roughness in conjunction with industrial heat exchangers [1], turbomachinery [2,3], ship propellers and hulls [4,5,6] to roughness induced by plant canopies and vertical structures in an urban
The objective of the current study is to conduct direct numerical simulations (DNS) of a range of well-characterised, scanned irregular rough surfaces seen in practical applications and methodically relate their surface parameters to various flow properties
A wide range of the roughness function is obtained, from U+ = 1.28 to 5.02, despite all samples being scaled to the same roughness height of k = Sz, 5 × 5 = δ/6
Summary
Rough surfaces are encountered in a large number of applications; from roughness in conjunction with industrial heat exchangers [1], turbomachinery [2,3], ship propellers and hulls [4,5,6] to roughness induced by plant canopies and vertical structures in an urbanCONTACT Manan Thakkar mnt g @soton.ac.uk © The Author(s). According to [6], any solid surface exposed to the marine environment will be affected by fouling. Marine fouling, which is caused by the accumulation of organic molecules, microorganisms, plants and animals on a body submerged in the water [4], leads to an increase in roughness of the hull and its hydrodynamic drag. The drag penalty causes a decrease in ship speed and maneuverability and an increase in fuel consumption. A small part of the fouling on the marine vehicle, is important from the point of view of increased friction and fuel consumption which in turn hampers performance. Heat exchangers utilise roughness to improve their efficiency [1] as the increase in wall friction causes an increase in the wall shear stress which enhances the heat transfer rate
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