**1. Introduction**

The issue of using energy more efficiently on ships seems urgent, and how to do this is greatly helped by the existence of CFD. In the last three decades, CFD as a numerical method, which is very sophisticated that can help humans to solve various problems in the fields of science and technology [1–6], but at a competitive cost, has played a very important role in advancing transportation technology [7], especially in naval architecture [8]. With this highly sophisticated method, the need for increased energy efficiency on ships is greatly helped. 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]. This number was predicted to increase 2–3 times in 2050 if there are no prevention efforts [10]. There are many ways to save on the use of energy on board [11, 12], such as improving hull and propeller design for more hydrodynamic performance. With the help of CFD, efforts to improve energy efficiency can be made more accessible.

Caring about the cleanliness of the hull due to biofouling is one of the efforts to maintain the hydrodynamic performance to prevent energy waste. Roughness can increase friction resistance, and then power requirements increase, resulting in losses, which have a significant impact on large vessels such as the VLCC (Very Large Crude Carrier) [13] or ships with low Fr (Froude number) [14]. A roughness, namely tubeworm fouling, can increase the friction resistance of ships by 23–34% [15], while a heavily fouled ship hull can increase the friction resistance by up to 80% [16]. Due to the growth of biofouling on ship hull, fuel consumption can increase over the operational time and can increase significantly just in a year [17]. The total economic losses from biofouling, including fuel additions, cleaning, and repainting, can reach \$ 15 million a year [18].

The phenomenon of the effect of roughness on fluid flow was first investigated by Nikuradse [19]. The mean velocity profile of the structure turbulence boundary layer of the smooth case (see Eq. (1)) is exposed to a downward shift in the log law region by a roughness to become a new velocity profile (see Eq. (2)) [20]. Thus, the concept of the roughness function (*ΔU*þ) as the downward shift and the roughness Reynold number (*ks* <sup>þ</sup>) were used (see Eqs. 3 and 4). Where: *U*<sup>þ</sup> is the nondimensional mean velocity profile equal to *U=Uτ*; *U* is the mean velocity at *y* (the normal from the wall); *U<sup>τ</sup>* is the friction velocity defined as ffiffiffiffiffiffiffiffiffiffi *τw=ρ* p ; *τ<sup>w</sup>* is the shear stress magnitude and *ρ* is the density of the fluid; *y*<sup>þ</sup> is the non-dimensional normal distance from the wall defined as *yUτ=ν*; *ν* is the kinematic viscosity; κ is the von Karman constant and *B* is the smooth wall log-law intercept; *ks* is equivalent sand roughness height. From the new velocity profile, there is an indication of an increased momentum deficit compared to the smooth case.

$$U^{+}\_{\;\;\;\;\;smooth} = \frac{1}{\kappa} \ln \; y^{+} + B \tag{1}$$

$$\text{LU}^{+}\_{\text{rough}} = \frac{1}{\kappa} \ln \text{y}^{+} + B - \Delta \text{U}^{+} \tag{2}$$

$$
\Delta U^{+} = f\left(\mathbf{k}\_{\circ}^{+}\right) \tag{3}
$$

$$k\_s^{+} = \frac{k\_s U\_\tau}{\nu} \tag{4}$$

The flow over surface roughness phenomenon can be simulated using CFD, which is generally solved by two different methods: modified wall function and

#### *The Phenomenon of Friction Resistance Due to Streamwise Heterogeneous Roughness with… DOI: http://dx.doi.org/10.5772/intechopen.99137*

geometrically resolved. 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 (*ΔU*þ) which will shift/modify the mean velocity profile. This method is only supported when using the RANSE (Reynolds-Averaged Navier–Stokes Equations). The modified wall function method is very effective for modeling large objects such as the hull of a ship, where the *ks* and *ΔU*<sup>þ</sup> values have been previously known and inputted, as was done by Demirel et al. [21], Song et al. [22], Andersson et al. [23], and also it can be used for propeller [24] and tidal turbine [25]. The modified wall function method prioritizes seeing results (impacts), such as increased drag, wake, and the like. Meanwhile, the geometrically resolved method used the real roughness geometry that formed from the mesh. These methods generally use to know how the *ks* value and the *ΔU*<sup>þ</sup> characteristic from a roughness. DNS (Direct Numerical Simulation) and LES (Large Eddy Simulation) are well known to be very good at doing this task. The geometrically resolved can also be done with RANSE as done by Atencio & Chernoray [26] with a difference of about 7% with their experimental results.

A reduction in hull performance due to roughness can be simulated using CFD with a modified wall function method with acceptable accuracy. 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]. Using the Kriso Container Ship model, Demirel et al. [21] continued the CFD simulation to predict the impact of marine coatings and biofouling. Song et al. [22] also looked at the effect of biofouling on the ship's hydrodynamic characteristics, using a different roughness function. Anderson et al. [23] performed a comprehensive review and comparative analysis of different methods to model hull roughness. The comparison of acceptable CFD and experimental results was carried out by Song et al. [29].

Much of the literature reported assumes that the roughness distribution is homogeneous, but in reality, it is much non-homogeneous. Hull roughness, mainly that arising from biofouling, rarely occurs homogeneously. From a personal review in the field, the authors found that the biofouling growth was thicker in the stern of the vessel than in the bow, which may be influenced by the distribution of shear stress and flow compressive forces, which are more favorable for biofouling to grow better at the stern [30].

Many studies are looking at the roughness problems at an inhomogeneous pattern. The smooth-to-rough and rough-to-smooth patterns in streamwise direction were studied by Antonia & Luxton [31, 32]. In a streamwise phenomenon, the flow of fluid through abruptly different roughness conditions produces an internal boundary layer, which limits the near-wall layer, which senses the new surface conditions, from the flow further away from the wall, which keeps a memory of the upstream surface conditions before the surface transition [33]. The internal boundary layer and the local wall shear stress, at the transition of the two difference roughness conditions, exceed the equilibrium value when the roughness is homogeneous and then change to relax according to the homogeneous roughness equilibrium value certain distance [34]. Experimental methods and numerical simulations carried out several studies related to this inhomogeneous roughness. However, the numerical simulations for solving this case are mostly DNS and LES. Few do that through the RANSE, as Suastika et al. [35] on a flat plate, and Song et al. [36] using the Wigley hull model.

The frictional resistance acting on the hull due to inhomogeneous roughness becomes important to be modeled and analyzed, considering that the hull roughness

#### *Applications of Computational Fluid Dynamics Simulation and Modeling*

due to biofouling is mostly inhomogeneous. In a simple method where the ship hull is represented by a flat plate, then an inhomogeneous roughness is applied by dividing the plate into three equal parts, namely the fore, middle, and after. The parts are given different roughness values in the form of *ks* and are arranged according to several combinations. From the simulation results on inhomogeneous roughness in the form of frictional resistance values will be compared with where if the condition is a smooth surface and some surfaces with homogeneous roughness. Then 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 then analyzed systematically, according to our knowledge is still a little done.
