## Flow Over NACA 2412 Airfoil Using Converge CFD

Airfoil: An airfoil is the term used to describe the cross-sectional shape of an object that, when moved through a fluid such as air, creates an aerodynamic force. Airfoils are employed on aircraft as wings to produce lift or as propeller blades to produce thrust. Both these forces are produce perpendicular to the air flow. Drag is a consequence of the production of lift/thrust and acts parallel to the airflow. By simulating flow over an airfoil, the drag and lift co-efficients can be calculated at different angle of attack. The angle of attack is the angle between the oncoming air and the relative line of reference known as the chord line.

Drag: Drag force acts parallel to the wind flow and opposes the relative motion of the object. A high drag force is an undesirable phenomenon that can stall an aircraft.The aerodynamic design of an aircraft or a car is a very big contributor to how much the drag force would oppose the motion of the object. Drag Co-efficient, which is normalized using the drag force gives an indication of how much aerodynamic a certain object is. Drag Co-efficient is calculated as:

Cd= 2Fd/(ρ*V²*A),

Cd is the drag coefficient,
Fd is the drag force
ρ= density of the fluid in which the object is moving
V= freestream velocity
A= Frontal Area of the object

Lift: Lift force acts perpendicular to the wind flow and is what helps to generate lift on an object. Aircraft are designed to generate as much lift as possible whereas cars, on the other hand, are designed in such a way that they produce a negative lift which is known as downforce. This negative lift force helps the car to maintain contact with ground surface even at very high speeds. The lift coefficient is normalized using the lift force formula:

Cl= 2L/(ρ*V²*A),

Cl is the lift co-efficient

L is the lift force

Expected Flow Trend over an Airfoil:  Flow over an airfoil follows the Bernoulli's Principle and the Coanda Effect. Bernoulli's Principle states that if a fluid flows around an object at different speeds, the fluid moving at a slower speed will exert a greater pressure on the object than the fluid moving at higher speeds. In the case of airfoils, this higher pressure acts at the bottom whereas the lower pressure acts at the to thus generating lift. However, using Bernoulli's principle alone does not account for why the flow at the top and bottom meet at the trailing edge if they are travelling at different speeds and it also does not explain why the flow follows the curved surface of the airfoil. The Bernoulli's equation is applied to a single streamline and not for two different streamlines. The Coanda Effect states that moving stream of fluid in contact with a curved surface will tend to follow the curvature of the surface rather than continue travelling in a straight line. Since the top of the airfoil is curved upwards, the pressure right above the airfoil surface is lower than the pressure far above it. This exerts a centrifugal force on the flow particle and keeps the flow particles attached to the curved surface. Towards the trailing edge, the bottom airfoil surface is curved downwards which according to the Coanda Effect suggests that the pressureds just above the surface would be higher than the pressure far below the airfoil. Since the pressure away from the airfoil is atmospheric this means the pressure at the top of the airfoil surface is lower than the atmospheric pressure whereas the pressure at the bottom surface of the airfoil is higher than the atmospheric pressure.

When the leading edge of the airfoil encounters the flow field at a particular angle of attack, a high-pressure region is created and the velocity of the flow reduces from freestream to nearly 0. This is the Stagnation Region of the airfoil. As the flow moves towards the top of the airfoil the fluid particles start to accelerate and since the upper surface is curved upwards a region of low-pressure occcurs. The point where the upper surface of the airfoil is curved the most, experiences a considerable drop in pressure and a subsequent increase in velocity. This region is known as the Suction Peak. At the bottom surface of the airfoil which is curved downwards, the higher pressure region created as a result of the Coanda Effect decreases the velocity of the fluid particle. Due to the decreasing pressure gradient towards the entire bottom surface of the airfoil, the velocity of the fluid particle keeps on decreasing until it reaches the trailing edge where a small region of high pressure increases the velocity of the fluid, though not significantly enough. At the top surface of the airfoil, as the flow moves downstream away from the suction peak region, it starts to decelerate due to an increasing pressure region. This difference in the pressure gradient between the top and bottom surface of the airfoil is what helps it to generate lift. In aircraft, the wings are designed to generate maximum lift whereas cars have spoilers, vortex generators, splitters etc to help create negative lift or downforce.

Another effect that can be observed from the flow pattern is that the airfoil boundary layer experiences a lot of shearing from the viscous stress and turbulent stress. Since at high Reynold's Number the viscous force is higher than the inertial force, so a drop in velocity is observed as we move towards the surface of the airfoil. The flow patterns that have been described above can be simulated using a CFD tool. In this project, the flow has been analysed using Converge CFD and Paraview Post-Processor. The airfoil selected for this purpose was a NACA-2412 type which has a chord length of 1m. The above image is of the same airfoil.

The geometry of the airfoil was constructed as per the co-ordinates mentioned in the following link: http://airfoiltools.com/airfoil/details?airfoil=naca2412-il

i) Plotting the points as per the co-ordinates ii) Extrusion of the geometry from the plotted points iii) Wind Tunnel Creation: The wind tunnel should be created in such a way that it should be atleast 25 times chord length away from the airfoil at one side and 12.5 times chord length  away perpendicularly. Case Setup: After the geometry was created, boundaries were flagged. The left edge of the geometry would be from where the flow takes place and the far right edge of the geometry would be the outflow boundary. Since the setup is 2-D the front and back surfaces were considered as Two-D boundaries with the top and bottom edges assigned symmetry boundary conditions. The airfoil was assigned the Wall boundary with 'Law of Wall' boundary type.

INFLOW BOUNDARY: The Reynold"s number was taken to be 200,000 and accordingly the freestream velocity was calculated using Reynold's Formula.

V∞= μ*Re/(ρ*c) ⇒ 31.367 m/s

V∞ is the free stream velocity

μ is the dynamic viscosity of air (1.846e-05 kg/ms)

Re is the Reynold's Number

ρ is the density of air (1.177 kg/m^3)

c is the chord length (0.1 m, the geometry was scaled down 10 times to save computational time)

OUTFLOW BOUNDARY: The flow conditions far outfield were taken as atmospheric.

The simulation was run for four different angles of attack: 1°, 5°, 10°, and 15°. Drag and Lift Coefficients were calculated for each value of the angle of attack and the results were also compared using different turbulence models. The first case was run for 1° degree angle of attack using the k-ω SST Turbulence Model and then using Realizable k-ε turbulence model. However. the former model is used for low reynold's number flows The airfoil was tilted by 1° about the z-axis.

Simulation End-Time: Since the length of the wind tunnel is 5.2m one flow through time would take 5.2/31.367 = 0.164 seconds. Ideally, the simulation end time must be atleast 5 times the flow through time. So the end time was taken as 1.7 seconds.

Grid: The base grid size chosen was 0.017 m with fixed embedding applied at the airfoil to get a finer mesh. The Scale of the embedding was 4 and the number of embed layers was 4. In order to monitor drag and lift forces 'Generate Wall Boundary averaged output' must be checked under 'Output Files'.

Flow at 1° Angle of Attack:

Fig: Airfoil tilted by 1° Fig: Velocity field at 1° angle of attack Velocity Field Animation:

Fig: Pressure Field at 1° The above two images show the pressure and velocity field across the airfoil at 1° angle of attack. The flow field conforms to the trends observed in the flow over an airfoil. At the leading edge, when the free-stream flow encounters the airfoil, the velocity significantly drops to near zero value because of the high pressure at the leading edge. As the fluid particle moves along the surface of the airfoil it starts to accelerate because of the low pressure field created as a result of the Coanda effect. And as the flow progresses downstream it starts to decelerate because of the gradual increase in pressure. At the bottom surface of the airfoil the pressure is significantly higher leading to a deceleration of the fluid particle as it flows along the bottom surface. It can also be observed that at the boundary layer the velocity of the particle is low due to shearing and as the particle moves away from the boundary layer the velocity goes up to a high value. According to Bernoulli's principle, velocity decreases as pressure increases. However, the velocity going from a low value to a high value as it progresses away from the boundary layer seems to have no effect over the pressure. The pressure does not follow the same trend here, indicating that the Bernoulli's principle cannot be applied at the boundary layer. The velocity also starts to decrease as it moves towards the trailing edge. This is because the pressure starts to increase downstream leading to thickening of the boundary layer which slows down the flow. The image below gives a visual explanation of the phenomenon explained above. A comparative study was also done by running the same setup for two different turbulence models as described above. The velocity and pressure fields were same for both the turbulence models. Y+ which is the non-dimensionalized wall distance tells us where the first cell is in the boundary layer. Typically for turbulence modelling involving high Reynolds Number flows, Y+ should be between 30 and 100 i.e in the log law region. If the mesh is refined too much, Y+ may reduce significantly putting it in the viscous sub-layer region. Y+ value is higher when k-w SST model is used. Y+ between 30-100 would also give a very good prediction of the drag co-efficient.  Drag and Lift Coefficients:Drag and Lift Co-efficients were calculated by taking the Pressure Force (X) and Pressure Force (Y) values respectively from the plots obtained by generating wall-boundary averaged output. The respective formulas for lift and drag co-efficients were used to come up with the following values: The difference between the values of the turbulence models used are very slight. At 1° angle of attack, both the drag and lift coefficient values are quite small. Generally, an airfoil at such a low angle of attack does not produce a very high lift force. The average Pressure Force (X) or drag force observed is nearly the same for both the turbulence models. The difference between Lift force for the two turbulence models is also very small.    Flow at 5° Angle of Attack: The second setup was run at 5° angle of attack, where the airfoil was tilted by 5° about the z-axis. The case setup was same as for the 1° setup. However the base grid size was increased to 0.018 m to save computational time.

Fig: Airfoil at 5° Angle of attack Fig: Velocity field at 5° Fig: Velocity Field Animation

Fig: Pressure Field at 5° The flow trends observed here were the same as for the 1° angle of attack. The clear difference that was observed is the free stream flow hitting the leading edge at a different angle. Another difference that was observed was the region of low pressure is relatively small over the top surface of the airfoil as compared to the 1° angle of attack case. The range of the velocity field was 1.1-45 m/s at 5° angle of attack whereas it was in the range of 1.1-39 m/s at the 1°. Apart from these differences, the flow pattern was exactly the same as it was expected.

The Y+ for the two turbulence models used was observed to be a lower using Realizable k-ε model.  During the case setup, the velocity was also specified in the regions under 'Regions and Initialisations' menu. However, since initial conditions are only used to specify the volume inside the flow field, in the initial runs the velocity wasn't being specified leading to erroneous flow patterns and plots that never seem to converge. A good sanity check that is done is the except near or at the airfoil surface, the velocity and pressure values are are the same as free-stream velocity and atmospheric pressure. However with the simulation not being converged to a steady state led to widely varying pressure and velocity fields across the entire geometry. This is also a result of the less simulation time used. If the flow is simulated for a much longer time, only then will it start to show the expected flow trends over an airfoil. The other reasoning is that since the velocity has only been specified at the inlet and not inside the regions, so when the simulation progresses the solver will take a longer time to run the simulation and compute the velocity and pressure at each cell. Thus it is adivsable that the velocity be specified inside the regions during initial condition setup.

Fig: Drag force at 5° using k-ω SST with velocity unspecified during the initial condition setup: Fig: Velocity field Drag and Lift Coefficients: Drag and lift co-efficients were calculated using the drag force and lift force values obtained from the wall-boundary average plots. The drag and lift coefficient obtained using k-ω SST model is higher than the realizable model. Compared to 1°, the drag and lift forces double as the angle of attack is increased. The lift force is significant enough to generate high lift on the airfoil. The difference observed between the drag force and lift force for the two turbulence models is very small. The plots below describe the same.    Flow at 10° Angle of Attack: The third setup was run at 10° angle of attack, where the airfoil was tilted by 10° about the z-axis. The case setup was the same as used previously.

Fig:Airfoil at 10° Angle of attack: Fig: Velocity field at 10° Velocity Field Animation:

Fig: Pressure Field at 10° For the 10° angle of attack case, the expected flow trends are nearly similar. However there are quite significant differences in the presure field and the velocity field at the trailing edge. A significant pressure increase is not observed as the flow hits the leading edge of the airfoil whereas the velocity does reduce significantly in the stagnation region. As the flow moves downstream, the velocity field thickens increasingly, even more than what was observed at 1° and 5° angles of attack suggesting a seperation of the boundary layer could occur if the angle of attack is increased even further. The velocity range also increases at 10° angle of attack (1.5-52 m/s).

The Y+ values differ significantly for the two turbulence models. For k-w SST model, the Y+ value was 38 whereas for Realizable k-e model, the value was 34.  Drag and Lift Coefficients: Drag and lift co-efficients were calculated using the drag force and lift force values obtained from the wall-boundary average plots. The drag coefficient obtained using k-ω SST model is higher than the realizable model, whereas, the lift coefficient obtained using the realizable k-e model was slightly higher. Compared to 1° and 5° where the lift forces nearly doubled, at 10° the lift force does not significantly increase in comparison to the lift force at 5 degrees. The drag force however doubles at 10° angle of attack indicating that the flow is being opposed greatly. The lift force is significant enough to generate high lift on the airfoil. The difference observed between the drag force and lift force for the two turbulence models is very small. The plots below describe the same.    Flow at 15° Angle of Attack: The fourth setup was run at 15° angle of attack, where the airfoil was tilted by 15° about the z-axis. The case setup was same used previously. However the base grid size was increased to 0.019 m to save computational time.

Fig: Airfoil  tilted at 15° Fig: Velocity field at 15°  Velocity Field Animation

Fig: Pressure Field at 15° The flow at 15° does not follow the expected trend over the airfoil. The velocity in the stagnation region does reduce to a very low value and then accelerates as it moves along the top surface of the airfoil. Due to the angle of attack being very high boundary layer seperation starts to take place as the flow moves downstream leading to a significant drop in velocity magnitude.The airfoil at the top surface while moving downstream does not follow the curve suggesting that the Coanda effect is losing power at such a high angle of attack. Instead, a vaccuum region known as cavitation is created at the trailing edge and the air starts to recirculate inorder to fill the vacuum leading to a condition known as stall which creates a lot of vibration on the wing thus decreasing its efficiency. The low pressure region also extends all the way back along the top surface of the airfoil. The velocity vector below shows the recirculation zone that is created as a result of the vacuum. The Y+ values differ significantly for the two turbulence models. For k-w SST model, the Y+ value was 38 whereas for Realizable k-e model, the value was 33.  Drag and Lift Coefficients: Drag and lift co-efficients were calculated using the drag force and lift force values obtained from the wall-boundary average plots. The drag coefficient obtained using k-ω SST model is higher than the realizable model, whereas, the lift coefficient obtained using the realizable k-e model was slightly higher. Compared to 1°, 5° and 10° where the lift and drag forces were increasing, at 15° the lift force does not increase, instead it reduces slightly in comparison to the lift force at 5 degrees. The drag force however increases by nearly 3 times at 15° angle of attack indicating that the flow is stalling. The lift force being generated at this angle of attack may not be significantly high to sustain lift.     Conclusion: After running the setup for four different cases it was observed that as the angle of attack increases so do the lift and drag forces. But beyond a certain point, if the angle of attack is increased the drag coefficient decreases significantly whereas the lift coefficient starts to decrease due to boundary layer seperation at the trailing edge which leads to a cavitation that gives rise to a phenomenon known as stall. The table below summarises the drag and lift coefficients that were calculated at different angles of attack for the two turbulence models used.   The plots above show the drag and lift coefficient at different angle of attack. Upto 10°, drag and lift coefficients increase almost linearly where it reaches the peak at 10°, but, beyond 10° the lift coefficient significantly reduces whereas the drag coefficient increase by nearly 3 times at 15 degrees. Aircraft designers take care of these factors when designing the wings.

The following link contains the excel sheet for the drag and lift coefficient calculations at different angles of attack: https://drive.google.com/file/d/1MXhtpuEAapvtdx_Xlyn4NBADSR0h40DN/view?usp=sharing

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