Computational Fluid Dynamic for Performance Hydrofoil due to Angle of Attack

This study uses a 2-D computational fluid dynamic (CFD) with a hydrofoil object. The general parameters used are pressure-based with Reynold numbers (Re) 106. The Pressure velocity coupling method used is SIMPLE with Reynold k-? as the viscous model on ANSYS Fluent 2019R1. The angle of attack variations are used starting from 00, 20, 40, 60, 10, 120, 150, 200, 250, and 300. From the simulation shows the hydrofoil characters depicted in the Coefficient drag (CD), Coefficient Lift (CL) and Pressure graphs Coefficient (CP) approaches the experimental results.


Introduction
Hydrofoil was first introduced by Forlanini, who in 1906 demonstrated a ship that moved 1.65 tons reaching a speed of 38 knots with 75-hp, which compares favorably with the modern craft. To achieve better performance, hydrofoil with higher lift coefficients and higher lift-to-drag ratios are most desired [1]. The hydrofoil usually consists of a wing-like structure mounted on struts below the hull, or across the keels of a catamaran in a variety of boats. At present several hundred hydrofoil craft are in service throughout the world. Experiments have been carried out in wind tunnels show that as speed increases on water boats equipped with hydrofoil, the hydrofoil element under the hull develops enough lift to lift the hull out of the water, which greatly reduces the hull resistance. This provides an increase in speed and fuel efficiency accordingly. Experiments at the wind tunnel, computer mathematic, and simulation using computers have all played important roles in hydrofoil development.

Literature Review
Computer Fluid Dynamics (CFD) is like a virtual wind tunnel and while it offers much more than just a testing facility on the computer, it is mainly used is certainly in the analysis of flow around a given design and there are clear analogies [2]. CFD has indeed become a powerful tool to be employed either for applied research and industrial applications. Computational simulations and analyses are increasingly performed in many fluid engineering applications. However, several factors influence CFD simulation results, namely the experience and knowledge of the operator or user about CFD, adequate computer specifications, domain shape determination, meshing grid type and size, turbulent models, and others [2][3][4][5][6]. Hydrofoil studies with variations in the entry angle and form factor were also conducted [7] where the results showed there is a maximum point of CL to the variation of the angle of attack which is a stall phenomenon that occurred in the angle of 20 0 in each of NACA foil type. Besides, The maximum lift is increased by increasing the depth ratio from h/c = 1 to h/c = 4 [8]. The system drag coefficients and lift coefficient were found by using FLUENT [9][10]. The computations were based on the Reynolds-averaged Navier-Stokes equations, which were solved with the standard k-ε turbulence model. The standard wall function was adopted for the flow near the solid wall. The SIMPLE (semiimplicit method for the pressure linked equations) algorithm was employed for nonlinear iterations between the velocity and pressure fields [11]. The iterative formulations of the SIMPLE methods generally exhibit better behavior [12]. SIMPLE typically converges very fast and efficiently, but for industrial flows in complex geometries and with marginal flow stability, convergence may stall.

Computational Approach
Computational fluid dynamics (CFD) is based on three basic physical principles: conservation of mass, momentum, and energy. The governing equations in CFD are based on these conservation principles. The continuity equation 2-D is based on the conservation of mass for an incompressible fluid.
The turbulence model widely used in CFD is k-ε model. The transported turbulent quantities of the k-ε model have physical meaning. The first variable is the turbulent kinetic energy k The second variable is the viscous dissipation rate ε which governs the dissipation of turbulent kinetic energy due to the shearing of the smallest eddies For the k-ε model incoming turbulence was specified through turbulent intensity at 5% and turbulent viscosity ratio at a value of 10.

Lift and Drag Coefficient
Lift is generated on a foil in a flow, the force working in the normal direction on the flow. The magnitude of the angle of the lift will depend on the angle of attack, the thickness, hydrofoil, and the camber. In addition to the lift force, there will be a drag force that works in the flow direction, this is mostly due to viscous effects. Figure 1. 2D-foil geometry definition [13] Figure 2. 2D-foil with the angle of attack [13] A U where the characteristic area A corresponds to the hydrofoil planform area for a horizontally oriented, completely submerged hydrofoil. Value for pressure coefficient (CP) is, Where, P is the static pressure at the point at which the pressure coefficient is being evaluated,  P is the static pressure in the freestream, 0 P is the stagnation pressure in the freestream,   is the freestream fluid density, 2  V is the freestream velocity of the fluid, or the velocity of the body through the fluid [14][15].

Geometry and Mesh Generation
The geometry of the hydrofoil is shown in figure 3. Topologies of the domain are used C-meshes and structured grids. The mesh quality at the trailing edge in the C-mesh is quite good with nearly orthogonal cells.

Result and Analysis
The numerical method used here had been validated in the experimental study. The result is presented in Figures 26 and 27.

Contour Velocity and Pressure Coefficient
Hydrofoil performance obtained through the CFD approach with a fluid (water) velocity of 5.14 m/s or equivalent to 10 knots with variations angle of attack (AoA)-α, shows the boundary layer and wake increase in thickness with increasing angle of attack. The pressure coefficient of the hydrofoil's upper surface was positive and the lower surface was negative. The coefficient of pressure difference is much larger on the leading edge, while on the rear/trailing edge it was much lower.

Conclusion
From the result and analysis, 2D-hydrofoil simulation with the angle of attack variations are used starting from 0 0 , 2 0 , 4 0 , 6 0 , 1 0 , 12 0 , 15 0 , 20 0 , 25 0, and 30 0 with the constant Reynolds number 10 6 using realized k-ε turbulence model. The Pressure velocity coupling method used is SIMPLE. It is seen that with the help of CFD Ansys-Fluent software, successful analysis of the Hydrofoil performance has been carried at various angles of attack (AoA) -α (0 0 , 2 0 , 4 0 , 6 0 , 10 0 , 12 0 , 15 0 , 20 0 , 25 0 , 30 0 ) with constant Reynolds number 10 6 using the k-ε turbulence model. The boundary layer and wake increase in thickness with increasing angle of attack. In future works, more realistic environmental hydrodynamic conditions will be considered for practical investigation, including the shear flow with an exponential profile and the free-surface waves.