COMPUTATIONAL FLUID DYNAMICS ANALYSIS BASED ON THE FLUID FLOW SEPARATION POINT ON THE UPPER SIDE OF THE NACA 0015 AIRFOIL WITH THE COEFFICIENT OF FRICTION

A new method that is more practical, efficient and applicable is proposed to track the position of fluid flow separation on the upper side of NACA 0015. The proposed method is the coefficient of friction curve (C f ) method on the airfoil's upper side. The approach used is a computational fluid dynamics (CFD) approach. The governing equation used is the Reynolds Averaged Navier-Stokes (RANS) equation. k − is the turbulence model implemented in this study. The research is conducted on the low Reynolds number category. The low Reynolds number is in the range of values from 10 4 to 3  10 5 . C f can predict the location of fluid flow separation more practically, efficiently, and applicable than the fluid flow velocity profile method. Flow separation begins to form at 𝜶 =8° at position x/c=0.8. The location of the fluid flow separation continues to move closer to the leading edge as the 𝜶 airfoil increases. Through the C f curve, the location of the fluid flow separation is when the C f curve experiences a sudden decrease and approaches the x-axis. If the separation points are described in the form of velocity profiles and fluid flow velocity contours, it will form an extreme decrease.


INTRODUCTION
External fluid flow is an interesting topic for various research and development of fluid mechanics. In external fluid flow, various discussions can be explored. Among them is the ability of fluids to provide lift against an interacting body [1] [2]. One of the bodies that can generate lift when interacting with fluids is an airfoil [3] [4]. Because of their ability to generate lift, airfoils are used in aircraft, wind turbines, MAVs, and UAVs . The lift capacity of an airfoil is usually expressed in dimensionless units known as the lift coefficient (Cl) [5]. Cl data is usually presented in the curve of the change of Cl with the angle of attack ( ). One of the characteristics of Cl is the stall condition. The stall condition is defined as a decrease in the value of Cl [6]. Stall conditions are caused by fluid flow separation on the upper side of the airfoil or wing. On the plane, this stall condition can cause the plane to experience a significant loss of lift and can cause the plane to experience a free fall. Various flow control devices can overcome fluid flow separation [7] [8]. Optimization of the use of flow control devices is very dependent on the location of the fluid flow separation point [9] [10]. Thus, a method is needed to quickly, practically, and precisely determine the separation point of fluid flow. One way that can be done is to detect the coefficient of friction (Cf) of the fluid flow against the surface of the airfoil.
Research on fluid flow separation has been carried out in many previous studies. Sudhakar and Kartikheyan conducted an experimental study related to the visualization of fluid flow separation on the upper side of NACA 4415. At =18°, it is known that the fluid flow separation has been seen and covered 0.75 part of the upper side airfoil [11]. Dong et al. researched flow separation and transition on an airfoil at the low Reynolds number. The study was conducted experimentally and with CFD simulation. There are three variations of Reynolds number investigated, namely 200000, 300000 and 500000. Based on observations from the fluid flow velocity profile, at =4° a laminar separation bubble has formed in the FX63-137 airfoil. The increase in causes the location of the fluid flow separation to approach the leading edge of the airfoil. On the other hand, decreasing the Reynolds number causes the fluid flow separation location to approach the leading edge. Fluid flow separation is observed using a fluid flow velocity profile [12]. Another research is regarding the fluid flow separation point location on a symmetrical airfoil. The thicker the airfoil, the location of the flow separation will be closer to the leading edge. Meanwhile, an increase will make the fluid flow separation point on the upper side of the airfoil closer to the leading edge [13].
The above studies have summarized various things regarding the position of fluid flow separation at low Reynolds numbers. However, the method used to express the position of separation is not stated clearly and in-depth. Another study used the velocity profile method to find the position of the fluid flow separation. This method is quite complicated because it has to create many velocity profiles to determine the location of the fluid flow separation. Furthermore, this method will take much time and is inefficient because it requires at least two types of data, namely velocity contour data and velocity profile. Overall, a summary of what has been discussed in the studies above can be seen in Table 1. Thus, this study tries to provide an alternative way of tracking the location of fluid flow separation by determining the Cf value along the upper side of the airfoil. In this way, it is hoped that tracking fluid flow separation can be carried out quickly and precisely. This study aims to provide a new method for determining the location of fluid flow separation at a low Reynolds number. Low Reynolds number ranges from 10 4 to 310 5 . The proposed method is to plot the Cf curve along the upper side of NACA 0015. Through the results of this study, it is hoped that determining the separation location will be more practical, efficient and applicable. In addition, this study also aims to complete various data related to fluid flow separation.

METHODOLOGY
This research uses numerical methods to simulate fluid flow, known as computational fluid dynamics (CFD). The CFD computation process is carried out by varying the of the airfoil to collect aerodynamic data. In order to make the computation process more efficient, the variation is done by changing the velocity vector of the fluid flow on the x-axis and y-axis, so there is no need to change the geometry and mesh to vary of the airfoil. The data from this research are Cl, Cd, Cf and fluid flow contours. The data for Cl and Cd are grouped and sorted by to get Cl and Cd curves for changes in . Various aerodynamic information of NACA 0015 can be known through this curve, such as curve's trend, stall and Cl max. The Cl and Cd are validated by the previous study by Kekina and Suvanjumrat. The Cf curve of each was proposed as a new method for tracking the location of fluid flow separation. It was used as the primary data in this study. The results of tracking the location of the fluid flow separation from the Cf curve are then compared with the commonly used method, namely by looking at the velocity profile of the fluid flow contour.

NACA 0015
The NACA 0015 airfoil is a type of airfoil created by the National Advisory Committee for Aeronautics (NACA) [16]. NACA 0015 is a symmetrical airfoil. The digit 0015 has its meaning; the number 0 in the first digit represents the maximum airfoil chamber. The second digit is the maximum position of the chamber. The airfoil's maximum thickness can be seen in the third and fourth digits, which is 15% of the chord length. The chord length of the airfoil used in this study is 1m. Overall, NACA 0015 can be seen in Figure 1.
The turbulence model chosen in this study is standard k  − . The turbulence model was chosen

Domain, mesh and boundary condition
The mesh made for this research is a structured mesh. The mesh element used is a mesh with a quadrilateral element shape. The main advantage of quadrilateral mesh is that it can be applied well to curved objects. So this mesh is very suitable for the NACA 0015 airfoil, which has a curvature on the upper and lower sides. Furthermore, the quadrilateral mesh can provide better quality with fewer elements than triangles mesh. The shape of the domain and the mesh in this study can be seen in Figure 2. The tail of the airfoil is placed right at the center of the circle of the domain [20]. This side of the domain is divided into two boundary conditions, namely velocity-inlet and pressureoutlet. Meanwhile, the boundary condition for the airfoil surface is the wall (no-slip). Overall, the boundary conditions in this study can be seen in Figure 2 (b). Furthermore, the boundary condition parameters can be seen in Table 2

Mesh independence test
The mesh independence test in this paper is carried out using the Richardson extrapolation generalized by Roache. In this mesh independence test, there are several equations used. The first step is to determine the ratio of the grid variations with equation 5. The mesh independence test in this paper uses an order whose value is determined by equation 6. The Grid Convergence Index (GCI) is used to determine the error of the grid. There are two GCIs utilized in this paper. The first GCI is used to measure the error value between the fine and medium mesh, known as GCIfine. The second GCI is the error value between the medium and coarse mesh known as GCIcoarse. The GCIfine and GCIcoarse equations can be found in equations 7 and 8. There are two objectives in the mesh independence test. The first objective is to determine whether the mesh variation is within the convergence range; the equation used is equation 9. The second objective is to determine the number of meshes used for further computation; the selected mesh is the mesh that can give the smallest relative error to the parameter values. Parameter values can be determined by equation 10 [21].
There are three types of mesh proposed for the mesh independence test. The highest number of elements is a fine mesh with 50000 elements. Meanwhile, the medium mesh is 25000 elements and the coarse mesh is 12500. The variation of the mesh can be seen in Figure 3. The selected mesh is the mesh with the smallest number of errors. Based on table 3, it can be concluded that the mesh with 50000 elements is the most ideal for use in the next computational process.  76 gradient so that if a velocity profile is made, it will show the direction of the velocity profile, which is reversed towards the upstream velocity [22]. Overall, the separated fluid flow and various related matters can be seen in Figure 4.

Coefficient of friction
The friction coefficient is a dimensionless value associated with the friction between the airfoil skin and the fluid. The mathematical equation Cf can be found in equation 11 [23]. When a fluid passes through a surface, there will be a friction effect. The skin friction effect is caused by the viscosity of the fluid. This friction effect proves that no actual fluid is inviscid. Friction between the body's surface and the fluid predominantly occurs in the boundary layer. When the boundary layer is separated from the body's surface, the friction between the surface of the body and the fluid will decrease drastically [24]. In general, in the form of a Cf curve along the surface of the airfoil (x/c), as shown in Figure 5. The point of fluid flow separation can be detected when Cf approaches the value of 0 [25]. After passing the separation point, friction will occur again but at a number of the smaller ones. Friction on the airfoil surface when the fluid has undergone separation is caused by a change in the velocity profile towards the upstream velocity.

a) Validation
Before discussing the primary data of the CFD analysis, validation is needed to ensure that all models made can meet various actual fluid flow conditions. Validation was carried out with aerodynamic data such as Cl and Cd NACA 0015 at Reynolds number 160000. Comparative data for the validation process were experimental data from research conducted by Kekina and Suvanjumrat [26]. Figure 6 (a) shows the Cl data from the computational and experimental results. The Cl curve pattern from the experimental results and CFD generally shows a similar trend. At ≤10°, the Cl curve shows conditions that tend to approach a linear form. At the =11°, there was a sudden decrease in the value of Cl in the CFD and experimental data. This sudden decrease in Cl condition is known as a stall. This sudden decrease in Cl value was caused by the eruption of the laminar separation bubble on the upper side of the airfoil. Thus, the Cl curve shown in this study can be classified as a "drop curve". This stall condition also affects the value of Cd, where the experimental results and CFD show a very extreme increase, as shown in Figure 6(b). However, at ≤10°, the Cd curve shows results that correspond to the experimental results and CFD.
In order to see the accuracy of CFD data specifically, it can be determined by looking at the error value. The error value is only calculated at ≤10°. When >10°, the error value is not calculated because the resulting aerodynamic data has become unstable and unpredictable. Overall the distribution of error values can be seen in table 4. The average error value for Cl is 4.900%, while the average error value for Cd is 30.51%. Thus, it can be concluded that the data obtained from the CFD results are quite valid and can be continued in the following discussion. .       Figure 10 shows the velocity profile on the upper side airfoil at =11. There are three stages of the velocity profile displayed. The first fluid flow velocity profile is the fluid velocity profile under normal conditions without fluid flow separation. The velocity profile of the fluid decreases as the airfoil approaches the surface. However, the velocity profile near the airfoil surface can still be seen. The second velocity profile is the fluid velocity profile for flow at the separation point. Through this velocity profile, it can be seen that the fluid flow velocity profile decreases when approaching the airfoil surface. This drastic decrease in velocity profile is caused by the presence of a fluid flow separation point so that the velocity value is close to zero. The position of the separation point is at the position x/c=0.22. These results follow the results obtained in Figure  8. Meanwhile, the third velocity profile is the velocity profile of the separated fluid. This separated fluid flow profile is seen in the form of a velocity profile that is reversed or negative velocity.

CONCLUSION
Tracking fluid flow separation with the Cf curve method is proven to provide satisfactory results where the position of fluid flow separation is not much different when compared to the fluid flow velocity profile method. The Cf curve method is very efficient and easy to apply because it only requires Cf data without the need for fluid flow contours and fluid flow velocity profiles. Fluid flow separation begins to appear at =8° at position x/c=0.8. If the of the airfoil increases, the location of the fluid flow separation is getting closer to the leading edge. The separation on the Cf curve can be seen by the sudden decrease in the Cf value and the Cf value close to zero. The velocity profile method also shows the same results in terms of the initial separation and its position after the increases. Overall, it can be concluded that the Cf curve method can track the fluid flow separation position more practically, applicable and efficiently compared to the fluid flow velocity profile method.