Abstract
Surface roughness can reduce the performance of a system of fluid mechanics due to an increase in frictional resistance. The ship hull, which is overgrown by biofouling, experiences a drag penalty which causes energy wastage and increased emission levels. The phenomenon of fluid flow that passes over a rough surface still has many questions, one of which is the phenomenon of frictional resistance on heterogeneous roughness in the streamwise direction. In the ship hull, biofouling generally grows heterogeneous along the hull with many factors. RANSE-based Computational Fluid Dynamics was used to investigate the friction resistance for heterogeneous roughness phenomenon. The modified wall-function method represented equivalent sand grain roughness (ks) and a roughness function were applied together with k-epsilon turbulence model to simulate rough wall turbulent boundary layer flow. As the heterogeneous roughness, three different ks values were denoted as P (ks = 81.25 μm), Q (ks = 325.00 μm) and R (ks = 568.75 μm), and they are arranged by all possible combinations. The combined roughness, whether homogeneous (PPP, QQQ, or RRR) and inhomogeneous (PQR, PRQ, QPR, etc.), results in unique skin friction values. The step-change in the height of the heterogeneous roughness produced a sudden change in the local skin friction coefficient in the form of overshoot or undershoot, followed by a relaxation where the inhomogeneous local skin friction is slowly returning to the homogeneous local one, which was explained in more detail by plotting the distribution of the mean velocity profile near the step-up or step-down. The order of roughness arrangement in a streamwise heterogenous roughness pattern plays a key role in generating overall skin friction with values increasing in the following order: PQR < PRQ < QPR < QRP < RPQ < RQP. Those inhomogeneous cases with three different values of ks can be represented by a single value (being like homogeneous) by the calculations provided in this paper.
Highlights
In 2012, the International Maritime Organization (IMO) noted that the total emissions from the shipping sector worldwide were 2.2% compared to all human-made CO2 emissions [9]
The effects from the roughness height and the roughness sequence in the streamwise direction are studied by analyzing the plots of local skin friction coefficient as a function of the length and plotting the mean velocity profile for the step up and step-down phenomenon and by comparing its integral values (CF) for the different cases
Rough-wall turbulent boundary layer flow is a complex physical phenomenon that increases skin friction drag compared to the smooth wall case
Summary
The issue of using energy more efficiently on ships seems urgent, and how to do this is greatly helped by the existence of CFD. The modified wall function is a method in which the geometry model (mesh) remains smooth, and the roughness length scale represents the roughness, generally using ks (equivalent sand grain roughness height) as a variable for a roughness function (ΔUþ) which will shift/modify the mean velocity profile This method is only supported when using the RANSE (Reynolds-Averaged Navier–Stokes Equations). Reynolds-averaged Navier–Stokes Equations (RANSE) simulation to study the friction resistance of flat plates due to the antifouling coating performed by Demirel et al [27] They used the roughness function from the experimental result of Schultz [28]. How are the three roughness values in the inhomogeneous condition correlated to become one roughness value (homogenized) which is close to the inhomogeneous roughness value This CFD simulation uses the basis of Reynolds-averaged Navier–Stokes Equations (RANSE), where the roughness model uses a modified wall function. Research with variations in roughness that is streamwise inhomogeneous, which is analyzed systematically, according to our knowledge is still a little done
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