Influence of Spatial Distribution of Roughness Elements on Turbulent Flow Past a Biofouled Surface

In most fundamental studies on the effect of roughness elements on wall-bounded turbulence regular arrangements of roughness elements are investigated. In this study, direct numerical simulations are used to study the flow past irregular rough surfaces composed of barnacle-type roughness elements. The aim is to assess the influence of clustering, i.e. non-uniform distribution, of the roughness-elements on near-wall turbulence. Three surfaces covered with random arrangements of a population of barnacles with the same planform and frontal solidities, but differing degrees of clustering, have been investigated using direct numerical simulations of turbulent channel flow at Reτ = 395. For comparison, a simulation over a classical staggered arrangement of barnacle elements of uniform size with matching planform and frontal solidity has been conducted. Surfaces with a high degree of clustering yield a lower roughness function ∆U+ compared to surfaces that are more homogeneously covered by roughness elements. The staggered arrangement yields a value for the roughness function that is comparable to a homogeneous random distribution of barnacles with a low degree of clustering. Clustering also affects the levels of the Reynolds and dispersive stresses in the near-wall region, with strongly clustered arrangements leading to elevated spanwise and wall-normal Reynolds stresses and the highest levels of dispersive normal stresses above the rough surface. Visualisations of the time-averaged streamwise velocity field show a clear interaction between barnacles within a closely packed cluster, leading to strong shielding effects for barnacles with upstream neighbours, and a merging of wakes. Overall, closely clustered barnacles form a ‘super-obstacle’ and thus interact differently with the near-wall flow compared to surfaces where roughness elements are clearly segregated from each other and interact with the flow on an individual basis. On the other hand, a classical, regular staggered arrangement of roughness elements serves as good proxy of non-clustered random arrangements of roughness elements when considering mean-flow statistics. INTRODUCTION Marine biofouling has affected seafaring since ancient times by decreasing the maximum speed and range of ships (Schultz et al., 2011). When marine organisms start to accumulate on a ship hull, the skin friction drag of the hull rises rapidly, increasing the fuel burn and associated emissions such as carbon dioxide and noxious or sulphurous gases. Calcareous macrofouling, caused by organisms protected by a calcareous outer shell, is considered the form of marine biofouling with the most severe consequences for the shipping industry. Barnacles are one of the most common forms of calcareous macrofouling. Barnacles start their life-cycle as swimming larvae. When maturing, the larvae search for a surface to settle on permanently. Once settled on a surface, they build a calcareous protective shell around their body that is securely fixed to the supporting surface. Barnacles tend to settle next to other barnacles to gain good feeding grounds and conditions for reproduction by forming colonies (Knight-Jones & Crisp, 1953). Previous research on barnacle-type macrofouling has mainly been based on experiments on plates that were exposed for longer periods of time to biofouling conditions (see e.g. Schultz (2004)). Furthermore, flow over surfaces covered by ordered arrays of barnacle-like shapes has been investigated both numerically (Sadique et al., 2015) and experimentally (Barros et al., 2016). However, a regular arrangement of barnacles does not closely match realistic barnacle fouled surfaces as barnacles tend to form clusters when they colonise a surface. In the current work, a range of irregular barnacle-type rough surfaces are investigated focusing on the effect of increasing clustering of roughness elements on the roughness function and near-wall turbulence levels. METHODOLOGY Three different rough surfaces with irregular barnacle roughness have been investigated using direct numerical simulations of turbulent channel flow. An additional rough