Flow over an NACA Airfoil for different Angle of Attacks.

I. Aim: 2D CFD analysis of flow over an airfoil using Converge CFD.

II. Problem Statement: Perform 2D transient analysis of flow over an airfoil at different angle of attacks. The case setup is done using ConvergeCFD and simulation is run in the CYGWIN terminal. Further, post-processing is done using Converge CFD and ParaView. The main objective of this project is to check the effect of the turbulence model and different angle of attacks on the lift and drag coefficients using ConvergeCFD.

III Objectives:

Simulate flow over a 4 digit airfoil i.e NACA 2412 Airfoil. and calculate the following,

• Drag co-efficient Vs Angle of Attack
• Lift co-efficient vs Angle of Attack
• Compare the effect of turbulence models on the above two results.
• The inlet Reynolds number is should be 200,000
• Perform above calculations for the following angle of attacks,
  • Angle of attack = 1º
  • Angle of attack = 5º
  • Angle of attack = 10º
  • Angle of attack = 15º

IV: Introduction:

An airfoil or aerofoil is the cross-sectional shape of an object whose motion through a fluid is capable of generating significant lift, such as a wing, a sail, or the blades of a propeller, rotor, or turbine.

A solid body moving through a fluid produces an aerodynamic force. The component of this force perpendicular to the relative freestream velocity is called lift. The component parallel to the relative freestream velocity is called drag. An airfoil is a streamlined shape that is capable of generating significantly more lift than drag[1]. Airfoils designed for use at different speeds differ in their geometry: those for subsonic flight generally have a rounded leading edge, while those designed for supersonic flight tend to be slimmer with a sharp leading edge. All have a sharp trailing edge. Foils of similar function designed with water as the working fluid are called hydrofoils.

The lift on an airfoil is primarily the result of its angle of attack. When oriented at a suitable angle, the airfoil deflects the oncoming air (for fixed-wing aircraft, a downward force), resulting in a force on the airfoil in the direction opposite to the deflection. This force is known as aerodynamic force and can be resolved into two components: lift and drag. Most foil shapes require a positive angle of attack to generate lift, but cambered airfoils can generate lift at zero angle of attack[1]. This "turning" of the air in the vicinity of the airfoil creates curved streamlines, resulting in lower pressure on one side and higher pressure on the other. This pressure difference is accompanied by a velocity difference, via Bernoulli's principle, so the resulting flowfield about the airfoil has a higher average velocity on the upper surface than on the lower surface.

Airfoil design is a major facet of aerodynamics. Various airfoils serve different flight regimes. Asymmetric airfoils can generate lift at zero angle of attack, while symmetric airfoil may better suit frequent inverted flight as in an aerobatic airplane. In the region of the ailerons and near a wingtip a symmetric airfoil can be used to increase the range of angles of attack to avoid spin–stall. Thus a large range of angles can be used without boundary layer separation[1]. Subsonic airfoils have a round leading edge, which is naturally insensitive to the angle of attack. The cross-section is not strictly circular, however: the radius of curvature is increased before the wing achieves maximum thickness to minimize the chance of boundary layer separation. This elongates the wing and moves the point of maximum thickness back from the leading edge.

Supersonic airfoils are much more angular in shape and can have a very sharp leading edge, which is very sensitive to angle of attack. A supercritical airfoil has its maximum thickness close to the leading edge to have a lot of length to slowly shock the supersonic flow back to subsonic speeds. Generally such transonic airfoils and also the supersonic airfoils have a low camber to reduce drag divergence. Modern aircraft wings may have different airfoil sections along the wing span, each one optimized for the conditions in each section of the wing[1].

Airfoil terminology [1]:

The various terms related to airfoils are defined below:

Figure: Airfoil nomenclature [1]

• The suction surface (upper surface) is generally associated with higher velocity and lower static pressure.
• The pressure surface (lower surface) has a comparatively higher static pressure than the suction surface. The pressure gradient between these two surfaces contributes to the lift force generated for a given airfoil.

The geometry of the airfoil is described with a variety of terms :

• The leading edge is the point at the front of the airfoil that has maximum curvature (minimum radius).
• The trailing edge is defined similarly as the point of maximum curvature at the rear of the airfoil.
• The chord line is the straight line connecting leading and trailing edges. The chord length, or simply chord, is the length of the chord line. This is the reference dimension of the airfoil section.

Other important concepts used to describe the airfoil's behavior when moving through a fluid are[1]:

• The aerodynamic center, which is the chord-wise length about which the pitching moment is independent of the lift coefficient and the angle of attack.
• The center of pressure, which is the chord-wise location about which the pitching moment is zero.

V: Solving & Modelling approach:

2D transient CFD analysis of flow over an airfoil for different angle of attacks case is set up in ConvergeCFD and then running the solution in CYGWIN terminal. Atmospheric air is used as the working fluid. Postprocessing is done using ConvergeCFD and ParaView. 

1. Geometry/Domain:

The point data of a standard NACA 2412 Airfoil in.dat format is downloaded from [2].  Based on the coordinate data vertices are created in Converge to create the airfoil cross-sectional point data. Further, the points are joined by edges to complete the airfoil curve. Then, using a triangle by open edges a surface geometry is created. Then, a flow domain is created around the airfoil. The 2d surface geometry is copied and offset to create a 3d domain. Further, the volume in the airfoil is deleted to have only a single flow domain the geometry. The whole geometry is scaled down by an order of 10. The airfoil and the flow domain are shown in the following figures.

Flow domain with a close-up view of airfoil cross section	Airfoil Geometry

2. Boundary Flagging:

The boundary zones in ConvergeCFD are created by flagging boundaries. This can be done by creating boundary flags in the boundary tab as shown below:

3. Case setup:

After assigning boundary zones as mentioned above, the solution case setup is to be done. ConvergeCFD has a dedicated menu to completely set up the solution. Details are as follows:

In the application type option, Time-based is selected.

- The materials option are selected as shown in the below images:

Air at atmospheric conditions is chosen as the working fluid. The following are properties of air used:

Density = 1.2 kg/m^3

Dynamic Viscosity = 1.86E-07 Pa-s.

- Simulation Parameters:

 The flow over the airfoil is simulated using transient analysis by selecting transient solver option and the respective setting for the solver are shown below:

- Boundary Conditions:

The boundary zones are applied with boundary conditions in this step. The inlet flow velocity is calculated based on Re=20000 and the air properties at the atmospheric condition of 1 Bar pressure and 300 K temperature.

The applied boundary conditions are as follows:

Since the flow is essentially 2D, the front and back faces of the domain are set to Two_D  boundary conditions. 

The above boundary conditions can be defined only after defining a region in the Initial conditions and Events section of the case setup as shown below:

The effect of the turbulence model is checked on the flow by comparing different turbulence models for the angle of attack 1 case.

The turbulence is modeled by selecting the appropriate model in the turbulence option of the physical model.

- Grid control:

The base mesh size for the domain is defined in this tab as shown below. Along with it, fixed embedding is used to accurately capture boundary layer physics on the airfoil wall by refining the mesh at its boundary.

- Output and post-processing:

The flow variables of interest, which are to be post-processed after the solution are selected in this option ad also at how many intervals these are written to the output file. Also, wall output (BOUNDARIES ONLY) is enabled for the airfoil boundary zone to post-process the wall physics.

After all the above setup is completed final validation option is selected to check for the case setup is correct. After validation, the case setup files are exported using the export option in the File menu to the working folder. These files will be used by the CGYWIN terminal to run the solution. The above process is repeated for all the turbulence models selected and the angle of attacks and the respective setup files are exported.

VI. Solution in CYGWIN :

The solution is run in the CYGWIN terminal. First, we have to navigate to the respective working folder in the CYGWIN terminal, where case setup files are present. Then by executing the following command, the solution can be run:

Navigating to folder:

Running the solution:

The solution will run-up to the total run time set in the run setup and the output files are saved to the respective folders.

VII. Post-Processing Results:

After the solution is complete, post-processing of the results is done using CONVERGE CFD and ParaView.

The plots are plotted in CONVERGE CFD, whereas to visualize the flow variables using contour plots the output files need to be converted to ParaView compatible files. This can be done in the CONVERGE CFD Post-Processing 3D tab as shown below:

Results Discussion:

I. Grid:

The above figure shows the sample grid for AOA=1 deg case with finer mesh around airfoil generated by fixed embedding.

II. Comparison of different turbulence models:

In order to check the effect of the turbulence model on the lift and drag coefficient on the airfoil, the following turbulence models are used keeping the angle of attack at 1 degree. The angle of attack is modified by rotating the airfoil geometry in Converge.

Since Law of wall approach is used, the Turbulence models applicable in the log-law region are used as follows:

1.`Standard k-epsilon`

2. `RNG k-epsilon`

3. Realizable `k-epsilon`

All the above models are used with converge default settings.

Y-Plus:

The Y-plus should be between 30-300 for the log-law region turbulence models. From the above plot it can be seen that all the models have Y-Plus above 30. Hence the mesh density near the airfoil boundary is sufficient to accurately capture the wall physics. Also, the `RNG k-epsilon` model has Y-plus (46) closer to the Y-plus lower limit range (30) of the log-law turbulence range.

Drag:

The above plot compares the drag force on the airfoil for different turbulence models. The generated drag is least with `RNG k-epsilon` and `Standard k-epsilon` models and higher with Realizable `k-epsilon`model.

Lift:

The lift forces almost identical for all the three turbulence models compared as shown in the above figure.

Turbulence model comparison 

From the above-discussed plots and the comparison of lift and drag coefficients, it can be seen that the `RNG k-epsilon` turbulence model captures the wall physics with a Y-plus value (46) closer to the lower limit of the log-law range (30), lesser drag value and higher lift value when compared to the other two models. Hence, the `RNG k-epsilon` turbulence model is appropriate for the current flow physics and will be used further for analyzing the effect of angle of attack variation on the lift and drag coefficients.

III. Results at various angle of attacks:

The effect of angle of attack on the lift and drag is studied for the following angle of attacks using the `RNG k-epsilon` model.

• Angle of attack = 1º
• Angle of attack = 5º
• Angle of attack = 10º
• Angle of attack = 15º

Y-Plus:

The Y-plus should be between 30-300 for the log-law region turbulence models. From the above plot, it can be seen that all the models have Y-Plus above 30. Hence the mesh density near the airfoil boundary is sufficient to accurately capture the wall physics and using `RNG k-epsilon`is appropriate. It can also be seen that the Y-plus decreases as the angle of attack increases. 

Drag:

The above plot compares the drag force on the airfoil for the angle of attacks. The generated drag increases with an increase in the angle of attack. This is expected because, as the angle of attack increases the frontal area of the airfoil facing the flow increases, and hence the drag increases.

Lift:

The above plot compares the lift force on the airfoil for the angle of attacks. The generated lift increases with an increase in the angle of attack up to AOA=10 deg and reduces for AOA=15 deg. This is because, as the angle of attack increases the top and bottom streams of air behind the airfoil doesn't meet at  higher angle of attacks, and flow separation occurs. Further increase in the angle of attack may lead to much lesser lift and finally, stalling occurs.

Pressure and Velocity Contours:

1. AOA = 1º

Pressure	Velocity

2. AOA = 5º

Pressure	Velocity

3. AOA = 10º

Pressure	Velocity

4. AOA = 15º

Pressure	Velocity

The below plot compares the lift and drag force variation with respect to the angle of attack. It can be seen that the drag increases as the angle of attack increases. But lift increases up to AOA=10 and reduces for AOA=15. This is because flow separation occurring behind the airfoil as shown in the above velocity contour of AOA=15 deg.

The below plot compares the coefficient of lift and drag with respect to AOA.

Summary of Results:

Conclusion:

In this project, the flow over an airfoil is simulated for different angles of attacks in converge for a Re=200000. Comparison is made between different turbulence models and the `RNG k-epsilon` model showed good results. Further, the effect of the angle of attack on lift and drag coefficients is studied. it is observed that the drag coefficient increases as AOA is increased. The lift coefficient increases up to AOA=5 deg and thereafter starts reducing. This is due to flow separation occurring behind airfoil for higher angle of attacks.

References:

1. Airfoil

2. http://airfoiltools.com/airfoil/naca4digit%20