Keywords

Introduction

The cross section of an aeroplane’s wing that helps provide it the necessary lift for takeoff and during flight is known as an aerofoil. However, the same part of the wing also generates unwanted drag as a side effect. The purpose of a plane’s use determines how much lift it would require. Heavier planes require more lift and vice versa. An aerofoil-like body traveling through a fluid handles aerodynamic load. Lift is the perpendicular component of this load, whereas the parallel component is referred to as drag. Aerofoils built for subsonic flight have a characteristic design with adjustable heading edge, accompanied with a sharp trailing edge, usually with irregular camber [1]. In the past, extensive research works of countless two equation model forms of k–ε and k–ω have been explored flourishingly, and then after, it is quite admissible that the k–ε configuration is appeared to be inferior near the wall bounded regions of adverse pressure gradient flows [2].

A lot of research work has been done on through various studies of aerofoil design and its aerodynamic characteristics. For instance, the effect caused by boundary condition for computational fluid dynamics (CFD) software was assessed by Tan and Koay (2010) to produce the flow pattern for comparison with the visualized flow pattern generated due to custom conditions under a novel smoke technique. In the range 0° to 20° (with 4° steps) for the angle of attack, he also examined and correlated theoretical values of the lift and drag coefficients with the ones observed through CFD software [3]. The NACA 4412 aerofoil was analyzed by Kevadiya [4] where its role in the investigation of edge of wind turbines was emphasized, considering values between 0° and 12° for the angle of attack. Chakravarthy et al. [5] analyzed using computational fluid dynamics (CFD) of symmetric and asymmetric aerofoil element and found that CL was higher for asymmetric aerofoil than symmetric aerofoil for identical chord and maximum camber position on the same angle of attack. Asymmetric aerofoil of identical length and camber caused slightly more drag compared to symmetric aerofoil [5]. Dash [6] recommended CFD as a reliable alternative to experimental methods after studying the NACA 0012 aerofoil profile with realizable k–ε turbulence model, where a close agreement between theoretical and CFD simulated results was drawn successfully. Petinrin and Onoja [7] have studied the computational aerodynamic flow over NACA 4412 aerofoil. The continuity equation was solved through Ansys fluent. The Reynolds number ranged between 1.0 × 106 and 13.0 × 106 with a two-dimensional, incompressible, and steady flow, and the angle of attack was simulated between ‒10° and 18°. A balanced variation between the lift coefficient and the angle of attack was seen within the region of pre-existing stall. With the increase in Reynolds number, the stalling angle turned out to be a constant 14° with gradual increase in the maximum lift coefficient, at the same time, the drag polar remained consistently at 6°. These observations indicated the validity of numerical solution of flow problems to get the aerodynamic characteristics of an aerofoil as the data was correlated with outcome from wind tunnel experiments [7]. Fatahian et al. [8] have numerically investigated that the result of perpendicular suction (θjet =  − 90°) and tangential suction (θjet =  − 30°) was computationally studied over NACA 0012 flapped airfoil for five different hinge positions (H = 0.7c, 0.75c, 0.8c, 0.85c and 0.9c) and a flap deflection (δf) of 15° with a Reynolds number of 5 × 105 (Mach value = 0.021) and it was concluded that the effect of perpendicular suction was proved to be more significant in contrast to the tangential suction [8]. Menter [9] created the k–ω SST model to effectively mix together its accurate and sturdy formulation in the near-wall region with its free-stream independence in the far field. To make this possible, the k–ω model is converted into a k–ω formulation. Along with the features of the standard k–ω model, the k–ω SST model also includes some improvements. As a result, the k–ω SST model is more precise and reliable for a wider class of flows (e.g., adverse pressure gradient flows, airfoils, and transonic shock waves) compared to the standard k–ω model. Thus, he concluded that the k–ω SST turbulence model is a combined form of the k–ε and the k–ω models [9]. Krause and Schweitzer [10] presented the outcome of an experimental probe of the flow around a NACA 4412 profile in an fluctuate free stream. The experiment was performed in an Eiffel-type wind tunnel running at an average free stream velocity of u = 15 m/s, corresponding to an average chord Reynolds number of Re = 2 * 105. The probe of the pressure field ascertained that the reduced frequency of oscillation was not the only factor to affect the unsteady flow, but the relative amplitude of the freestream-velocity also affected it to a great extent. Distribution of pressure was found to deviate strongly both at an incidence of α = 8~ and α = 16~ in contrast with the steady one [10].

Although, numerous efforts have been made on various aerofoil designs, in the current study, the effect of lift and drag coefficients on the aerodynamic characteristics of three-dimensional NACA 4412 has been explored through the SST k–ω model, since Spalart–Allmaras and standard k–ε turbulence model had already strongly been tested for the prediction of flow across the various aerofoil shapes [4, 4]. Therefore, the SST with k–ω model was considered for this 3D aerofoil because SST with k–ω combines the advantages to study the flow region near the wall (automatic wall treatment of the standard k–ω model). It also accounts for the transport of turbulent shear stress and offers distinctly accurate predictions of the amount of flow separation. Thus, it became a good default choice. Moreover, the Reynold’s number with considered free stream velocity is 0.821 * 106, and efforts have been made to determine its drag coefficient, lift coefficient, and stalling angle with varying angles of attack (α).

Methodology

This study focusses on the computational simulation of the NACA 4412 solely. In real-time scenario, the aerofoil is in the influence of the three-dimensional airflow. Henceforth, the various variables can be computed likewise for more effective performance delivery by the aerofoil. Below mentioned in Table 86.1 are the assumptions and values under consideration for the simulation environment.

Table 86.1 Specification of the aerofoil and details about methodology parameters [4, 6, 11]
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Modelling and Meshing of an Aerofoil Naca 4412

The effort has been made to collect the associated aerofoil database of coordinates with closed trailing edge to procure three-dimensional geometry followed by the fine refining of the aerofoil and its computational domain to get accurate result.

Figure 86.1 displays the three-dimensional geometry of NACA 4412 aerofoil created using its coordinates in the Ansys design modeler.

Fig. 86.1
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Geometry of the NACA 4412 aerofoil

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Figure 86.2 shows the computational domain sketched in design and an unstructured mesh with tetrahedral elements generated over the aerofoil after inflation having a total number of nodes and elements to be 144,483 and 511,793, respectively.

Fig. 86.2
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Mesh is performed around the aerofoil and its surface adeptly

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Figure 86.3 depicts a refined structured mesh around the aerofoil achieved at 0.005 mm which is pretty good result, as Y +  <0.028 mm

Fig. 86.3
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Close view of the mesh around the aerofoil walls

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CFD Simulation of NACA 4412 Aerofoil

The generated mesh data was then solved in FLUENT for further computation and simulation of pressure and velocity distribution to determine the coefficient of lift and drag values with inlet velocity 12 m/s at 0°.

Figures 86.4 and 86.5 show the tetrahedral mesh elements generated in the meshing being converted into polyhedral elements in FLUENT setup. In case of non-symmetrical aerofoil alike given, a bigger low-pressure zone has been observed on top of the aerofoil even at 0°.

Fig. 86.4
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Pressure contours around the aerofoil and symmetry at 0°

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Fig. 86.5
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Pressure contours on the aerofoil at 0° with polyhedral mesh elements

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Figure 86.6 shows a head-on collision between particles of free stream velocity and the aerofoil at 0° angle of attack. Due to its non-symmetric nature, upper layer of the aerofoil has a high-velocity flow, while there is low velocity in the lower area of the aerofoil.

Fig. 86.6
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Distribution of magnitude of velocity (m/s) at 0°

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The same methods have been applied to determine the values for the angle of attack continue from 0° to 24°. However, the stall angle emerges out to be at 20° for the aerofoil, and the pressure and velocity contours are illustrated below:

Figures 86.7 and 86.8 show the maximum pressure zone on the lower nose of the aerofoil while the minimum pressure on the upper surface of 3D aerofoil at α = 20°

Fig. 86.7
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Pressure contours for the aerofoil surface at 20°

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Fig. 86.8
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Pressure contours around the aerofoil at 20° stall angle with polyhedral mesh elements

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Figure 86.9 displays the distribution of velocity for the flow around the aerofoil at stall angle. The flow does not appear to be attached to the surface of the aerofoil in contrast to the behavior in Fig. 86.6 at 0° angle of attack.

Fig. 86.9
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Distribution of velocity magnitude (m/s) for stall angle 20°

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Result and Discussion

The behavior of aerodynamic parameters (α, CL, and CD) is shown below, which are later used to draw further conclusions.

The stalling angle was remarked at 20° because the flow on the upper surface of the aerofoil gets separated and generation of the maximum lift coefficient has been witnessed. Above the stalling angle, as the α increases, the value of lift coefficient falls from its peak value due to flow separation. The air commences to flow slightly smoothly over the upper surface of the aerofoil and set about to separate from the upper surface causing turbulence. Upon majority aerofoil designs, as the angle of attack increases, the flow separation point of the upper surface shifts toward the leading edge from the trailing edge.

Thus, the fluid flow deviates from its boundary layer (upper surface of the aerofoil) due to the formation of eddies and vortices (a region in a fluid in which the flow revolves around an axis line) on the upper layer of the aerofoil resulting in significant reduction in lift and increase in drag coefficient at stall angle 20°.

Table 86.2 can be used to observe the change in lift coefficient with α for the given Reynolds number. Graph 1 shows a stable increase in the lift coefficient for angles through 0°–24°. The coefficient of lift reaches the greatest value (CL = 0.68328) at 20° and decreases gradually after this angle. This angle is recognized as the stalling angle for the aerofoil. Negative value for lift coefficient is noted at negative angle of attack.

Table 86.2 Change in coefficients of lift and drag with varying α
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Figure 86.10 also displays the drag feature of the aerofoil to one order of magnitude. The curve continues to increase gradually in the positive direction. Differentiating the lift and drag characteristics, it is promptly seen that within the positive angles of attack, drag accompanies the generation of lift within the given range. Also, as the angle of stall is approached, the coefficient of drag increases rapidly with a drop in lift coefficient.

Fig. 86.10
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Shows the change in coefficients of lift and drag with varying α

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Conclusion

From the results and analysis, the following conclusions are drawn and summarized as follows:

  • The lift coefficient (CL) escalates linearly with rise in angle of attack up to 20° (stall angle).

  • The drag coefficient (CD) increases gradually with angle of attack, but after 20° angle of attack, the CD increases rapidly with the decrease in CL due to the flow separation from the boundary layer of the aerofoil.

  • The computational simulation of an aerodynamic flow over 3D NACA 4412 aerofoil with pointed trailing edge was analyzed through SST k–ω turbulent model with Re = 0.8214 * 106 found that the model can be attributed for effective solutions of flow problems in addition to adverse pressure gradient.