Flow over an airfoil

Aim: Model the flow over a NACA0017 Airfoil with different angle of attacks.

Objective: To understand and determine following

1. NACA Airfoil Nomenclature
2. Calculation of drag and lift coefficients at different angle of attacks
3. Plot the graph of drag force v/s angle of attack
4. Plot the graph of lift force v/s angle of attack

Keywords: SOLIDWORKS, CFD, Flow over an Airfoil

Theory:

Fluid flow over solid bodies frequently occurs in practice, and it is responsible for numerous physical phenomena such as the drag force acting on auto mobiles, power lines, trees, and underwater pipelines; the lift developed by airplane wings; upward draft of rain, snow, hail, and dust particles in high winds; the transportation of red blood cells by blood flow, therefore, developing a good understanding of external flow is important in the design of many engineering systems such as air craft, automobiles, buildings, ships, submarines, and all kinds of turbines.

The flow fields and geometries for most external flow problems are too complicated to be solved analytically, and thus we have to rely on correlations based on experimental data. The availability of high-speed computers has made it possible to conduct series of “numerical experiments” quickly by solving the governing equations numerically, and to resort to the expensive and time-consuming testing and experimentation only in the final stages of design. This report also explains the numerical approach to a flow over an airfoil.

A fluid may exert forces and moments on a body in and about various directions. The force a flowing fluid exerts on a body in the flow direction is called drag. Drag is usually an undesirable effect, like friction, and we do our best to minimize it. Reduction of drag is closely associated with the reduction of fuel consumption in automobiles, submarines, and aircraft; improved safety and durability of structures subjected to high winds; and reduction of noise and vibration.

A stationary fluid exerts only normal pressure forces on the surface of a body immersed in it. A moving fluid, however, also exerts tangential shear forces on the surface because of the no-slip condition caused by viscous effects. Both of these forces, in general, have components in the direction of flow, and thus the drag force is due to the combined effects of pressure and wall shear forces in the flow direction. The components of the pressure and wall shear forces in the direction normal to the flow tend to move the body in that direction, and their sum is called lift. For two-dimensional flows, the resultant of the pressure and shear forces can be split into two components: one in the direction of flow, which is the drag force, and another in the direction normal to flow, which is the lift, as shown in below figure.

The drag and lift forces depend on the density `rho` of the fluid, the upstream velocity `V`, and the size, shape, and orientation of the body, among other things, and it is not practical to list these forces for a variety of situations. Instead, it is found convenient to work with appropriate dimensionless numbers that represent the drag and lift characteristics of the body. These numbers are the drag coefficient `C_D`, and the lift coefficient `C_L`, and they are defined as

`C_D=F_D/(1/2 ρAV^2 )` and `C_L=F_L/(1/2 ρAV^2 )`

where `A` is ordinarily the frontal area (the area projected on a plane normal to the direction of flow) of the body. In other words, `A` is the area that would be seen by a person looking at the body from the direction of the approaching fluid. The frontal area of a cylinder of diameter `D` and length `L`, for example, is `A=L×D` . In lift calculations of some thin bodies, such as airfoils, A is taken to be the planform area, which is the area seen by a person looking at the body from above in a direction normal to the body.

Airplane flight is based on lift, and thus developing a better understanding of lift as well as improving the lift characteristics of bodies have been the focus of numerous studies. For devices that are intended to generate lift such as airfoils, the contribution of viscous effects to lift is usually negligible since the bodies are streamlined, and wall shear is parallel to the surfaces of such devices and thus nearly normal to the direction of lift. Therefore, lift in practice can be taken to be due entirely to the pressure distribution on the surfaces of the body, and thus the shape of the body has the primary influence on lift. Then the primary consideration in the design of airfoils is minimizing the average pressure at the upper surface while maximizing it at the lower surface.

NACA Airfoils Nomenclature

The NACA airfoils are airfoil shapes for aircraft wings developed by the National Advisory Committee for Aeronautics (NACA). The shape of the NACA airfoils is described using a series of digits following the word "NACA". The parameters in the numerical code can be entered into equations to precisely generate the cross-section of the airfoil and calculate its properties.

The NACA four-digit wing sections define the profile by:[1]

• First digit describing maximum camber as percentage of the chord.
• Second digit describing the distance of maximum camber from the airfoil leading edge in tenths of the chord.
• Last two digits describing maximum thickness of the airfoil as percent of the chord.

For example, the NACA 2412 airfoil has a maximum camber of 2% located 40% (0.4 chords) from the leading edge with a maximum thickness of 12% of the chord.

For NACA 0017 airfoil, zero camber with maximum thickness of 17% of chord. All the terms stated can be well identified from the figure below along with NACA 0017 Airfoil. [2]

CAD Model

1. The airfoil curve was inserted in SolidWorks by importing a .dat file that contained x, y and z coordinates of the curve (the file was downloaded from the NACA website ref [2], also it was edited in notepad by adding Z coordinates to zero so as to get accepted by solid works) making sure that the unit systems were set to MKS system.
2. Then the sketch was converted into entities in front plane and was closed by connecting the curve using line command.
3. In order to vary the angles of attack, rotate entities command was used and the angle was changed to desired quantity. Finally, by exiting the sketch, it was extruded to 0.2 m and finally the part was saved for further flow simulation.
4. The cad model is shown below.

Some important things which needed to be followed before simulating the above airfoil are about the wind tunnel geometry and the flow simulation time, which are explained as follows:

For any external flow simulations in CFD, first an external domain has to be defined which in this case should be long enough to cover the pressure variations as airfoil is subjected to high velocities. For this problem, the analysis was set to 2D with the domain size as shown in the below figure.

Also, for calculating the end simulation time the formula followed is as follows

End flow time or simulation end time was calculated as follows, `"End Flow time"=2×"flow through time"`

where `"flow through time"= ("Length of Computational domain")/("Inlet Velocity")`

Flow Simulation

Using Solid works flow simulation add-In, external flow simulation was carried out using the following steps.

1. Clicking on flow wizard, and specifying the project title, then clicking next and setting SI units for calculations.
2. Analysis type was set to external with time dependent (Total analysis time = 0.105 sec and output time step to 0.01 sec).
3. Default Liquid was set to air and speed along X direction was set to 600 m/sec in Initial Boundary Conditions.
4. This made a default computational domain which was changed by right clicking Computational domain in feature manager to above set domain.
5. Local mesh was also set along the surface of the airfoil with mesh refinement control of 3.
6. Forces along X and Y direction along with frictional forces along X and Y directions were set as global goals.
7. Surface goals were also set in order to calculate the drag and lift forces.
8. Finally, the setup was allowed to run.
9. As the domain being so large, it would take a long time for the solver to finish the calculations, so close monitoring was done for the lift force while running the calculations and the solver was allowed to stop once there was no more change in the value of lift force (which could be seen in the figure below).
10. Cut plots of velocity and pressure were made after results were loaded in the setup.

Observations

1. The plots below show the pressure and velocity variations along the flow. As the domain is so large that the foil could not be seen, its magnified view is shown in the right side with their location of maximum and minimum parameters.
2. In each case, we can se that velocity is maximum where pressure is minimum and vice-versa.
3. Also, as the angle of attack is increased, there are variations is the velocity and pressure profiles.
4. Not much could be extracted from these velocity and pressure plots.
5. Drag and lift forces are also calculated.

Angle of Attack – 0 degree

Angle of attack – 2 degree

Angle of attack – 4 degree

Angle of attack – 6 degree

Angle of attack – 8 degree

Angle of attack – 10 degree

Angle of attack – 12 degree

Calculation of Drag and Lift coefficient

Area = 0.205 m²

density = 1.225 kg/m³

velocity = 600 m/s

Angle of Attack	Cd	Cl
0	0.030768	0.000256
2	0.031283	0.015087
4	0.032751	0.029535
6	0.034881	0.045201
8	0.038142	0.059738
10	0.04243	0.074239
12	0.047474	0.089034

Plots of drag force and Lift force at various angle of attacks

Conclusions

1. From the both graphs, it is clear that as the angle of attack increases, lift and drag forces also increase. However, the lift force is increase linearly as compared to the drag forces.
2. As the angle of attack is increased, lift and drag forces are also increased which may result in using more power to overcome these forces.
3. Flow separation takes place at minimum pressure which occurs soon as the attack angle is increased.

References

1. Airfoil - Wikipedia
2. NACA 0017 Airfoil Geometry
3. Fluid Mechanics Textbook by Cengel