Flow over an NACA 2412 AIRFOIL

• Given Problem:-

• Simulate flow over a 4 digit airfoil i.e NACA 2412 Airfoil.

• You will have to 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.
  • Make sure that the inlet Reynolds number is 200,000
  • Make sure you do above calculations for the following angle of attacks,
    • Angle of attack = 1º
    • Angle of attack = 5º
    • Angle of attack = 10º
    • Angle of attack = 15º

• Software used-

1. Converge CFD Software

2. Cgywin

3. Paraview

• Geometry -

Fig. 1, Virtual Wind Tunnel Structure

Fig.2 , Airfoil Structure created inside converge(NACA 2412)

Fig.3 , Airfoil Structure inside Virtual Wind tunnel

Fig.4 , Airfoil Structure inside Virtual Wind tunnel

• Steps Involved while solving this challenge-

1. The first challenge was to make the airfoil structure inside converge. The airfoil can eaisly made using any good CAD software but we choose converge to do the job just for sake of learning.

2. We get the airfoil data(Vertices points) from the irfoil library provided with challenge. We manually entered all the vertices points inside converge. The process had taken hours as there were lot of points to be entered.

3. After getting the desired airfoil shape, I created the airfoil design by copy and lofted command.

4. Now by using Vertices points option we created the virtual wing tunnel. The process was time consuming but we have created the wing tunnel for this challenge. The following dimensions have been used for wing tunnel-

Fig.5 , Wind tunnel Dimension

5. Now I have flagged the boundaries for the wing tunnel and airfoil.

6. Inflow and outflow boundaries are situated at left side and right side respectively. The air will come with velocity of 31.2357 m/s(derived from given reynolds number).

7. The case will run for 4 different angle of attack with 2 different turbulnce model i.e. K-w SST and reliazeble K-e.

8. We then complete the case setup and send it to cgywin for further simulation. 8 cases total were run.

9. Finally we will post process the result in converge and calculate the lift and drag coefficient for each cases.

• Case setup Important Parameters:-

1. Application- General Flow

2. Solver- Transient

3. Start Time- 0

4. End time- 1.6 sec

5. Initial time step and minimum time step- 1e-05 sec

6. Velocity in X direction- 31.2357 m/s

7. Region temperature- 300k

8. Region Pressure- 101325 Pa

8. Turbulence Model- 1. K-w SST

2. Reliazeble K-e

9. Base Grid- 0.017m

10. Fixed Embidding- Boundary- Airfoil

Type- Permanent

Scale- 3

Embedded Layers- 2

10. Boundary conditions- 1. Inflow- Inflow Type, Pressure(Zero Normal gradient), Velocity(Specifc value of 31.2357 m/s), Temperature(Specifid value of 300k).

2. Outflow- Outflow type, Pressure(Specifid value of 101325 Pa), Velocity boundary condition(Zero normal gradient: Backflow),Temperature(Specifid value of 300k).

3. Side 1- 2D

4. Side 2- 2D

5. Top- Symmetry

6. Airfoil- Wall(Default setting of Stationary wall)

• Airfoil Mechanism-

An airfoil-shaped body moving through a fluid produces an aerodynamic force. The component of this force perpendicular to the direction of motion is called lift. The component parallel to the direction of motion is called drag. Subsonic flight airfoils have a characteristic shape with a rounded leading edge, followed by a sharp trailing edge, often with a symmetric curvature of upper and lower surfaces.

The lift on an airfoil is primarily the result of its angle of attack and shape. 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. 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. The lift force can be related directly to the average top/bottom velocity difference without computing the pressure by using the concept of circulation.

• Airfoil Base Grid-

Fig.6 , Meshing with Fixed embedding

• 1 Degree Angle of Attack(AoA)-

Fig.7 , 1 Degree Angle of Attack

Fig.8, Pressure distribution over Airfoil(1 Degree AoA)

Fig.9, Velocity distribution over Airfoil(1 Degree AoA)

Explanation-

In Fig.8 we can see that low pressure region is developed above the airfoil compared to high pressure below the airfoil. Due to this high pressure region below airfoil, the wing get lift force which will provide lift to the wing.

At starting of airfoil, we can see red spot i.e. very high pressure region. It is obvious as air is attacking this part first and then gets divided between upper layer of airfoil and lower level of airfoil.

In fig.9, we can see that highest velocity is situated at upper layer of airfoil which is quite known as it have low pressure region upside.

The total lift generated is quite low as Angle of attack is mere 1 degree, which is very less. Such low Angle of attack cannot generate sufficient amount of lift.

Calculation of Lift and Drag coefficient of both turbulent model-

• Density(kg/m^3)= 1.2041
• Velocity(m/s)= 31.367
• Area(m^2)= 0.1

1. Kw sst- Drag force= 1.5 N

Drag Co-eff=0.025534

2. Kw sst- Lift force= 17.85 N

Lift Co-eff=0.30134202

3. Relizable K E- Drag force=1.40 N

Drag Co-eff=0.02383

4. Relizable K E- Lift force=17.65 N

Lift Co-eff=0.29796564

Fig.10, Drag Force acting over Airfoil(Kw SST)

Fig.11, Drag Force acting over Airfoil(Relizable K E)

Fig.12, Lift Force acting over Airfoil(Kw SST)

Fig.13, Lift Force acting over Airfoil(Relizable K E)

Fig.14, Y+ Value(Kw SST)

Fig.15, Y+ Value(Relizable K E)

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.

• 5 Degree Angle of Attack(AoA)-

Fig.15 , 5 Degree Angle of Attack

Fig.16, Pressure distribution over Airfoil(5 Degree AoA)

Fig.17, Velocity distribution over Airfoil(5 Degree AoA)

Explanation-

In Fig.16 the low pressure region over airfoil is low compared to 1 degree AoA conition. Furthermore the air is attacking the lower part of airfoil compared to AoA 1 degree.

The lift generated in this case is more compared to AoA 1 degree as more pressure is generated below airfoil.

Calculation of Lift and Drag coefficient of both turbulent model-

• Density(kg/m^3)= 1.2041
• Velocity(m/s)= 31.367
• Area(m^2)= 0.1

1. Kw SST- Drag force= 2.73 N

Drag Co-eff=0.04647

2. Kw SST- Lift force= 38.9 N

Lift Co-eff=0.65670613

3. Relizable K E- Drag force=2.68 N

Drag Co-eff=0.04562

4. Relizable K E- Lift force=39.2 N

Lift Co-eff=0.66177071

Fig.18, Drag Force acting over Airfoil(Kw SST)

Fig.19, Drag Force acting over Airfoil(Relizable K E)

Fig.20, Lift Force acting over Airfoil(Kw SST)

Fig.21, Lift Force acting over Airfoil(Relizable K E)

Fig.22, Y+ Value(Kw SST)

Fig.23 Y+ Value(Relizable K E)

• 10 Degree Angle of Attack(AoA)-

Fig.24 , 10 Degree Angle of Attack

Fig.25, Velocity distribution over Airfoil(10 Degree AoA)

Fig.26, Pressure distribution over Airfoil(10 Degree AoA)

Explanation-

In Fig.26 the low pressure region over airfoil is low compared to 1 and 5 degree AoA condition. At 10 degree AoA, high pressure region can be seen below airfoil. The High pressure region is quite strong at 10 Degree AoA. The lift is quite high in this case.

The lift generated in this case is more compared to AoA 1 and 5 degree as more pressure is generated below airfoil.

Calculation of Lift and Drag coefficient of both turbulent model-

• Density(kg/m^3)= 1.2041
• Velocity(m/s)= 31.367
• Area(m^2)= 0.1

1. Kw SST- Drag force= 5.77 N

Drag Co-eff=0.09822

2. Kw SST- Lift force= 62.40 N

Lift Co-eff=1.05343092

3. Relizable K E- Drag force= 5.73 N

Drag Co-eff=0.09754

4. Relizable K E- Lift force=62.5 N

Lift Co-eff=1.05511911

Fig.27, Drag Force acting over Airfoil(Kw SST)

Fig.28, Drag Force acting over Airfoil(Relizable K E)

Fig.29, Lift Force acting over Airfoil(Kw SST)

Fig.30, Lift Force acting over Airfoil(Relizable K E)

Fig.31, Y+ Value(Kw SST)

Fig.32, Y+ Value(Relizable K E)

• 15 Degree Angle of Attack(AoA)-

Fig.33 , 1 Degree Angle of Attack

Fig.34, Pressure distribution over Airfoil(15 Degree AoA)

Fig.35, Velocity distribution over Airfoil(15 Degree AoA)

Explanation-

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 rnagnitude.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 lift generated in this case is more compared to AoA 1 and 5 degree as more pressure is generated below airfoil.

This can be seen in Fig.34 where high pressure below wing is reduced significantly as compared to AoA 10 Degree.

Calculation of Lift and Drag coefficient of both turbulent model-

• Density(kg/m^3)= 1.2041
• Velocity(m/s)= 31.367
• Area(m^2)= 0.1

1. Kw SST- Drag force= 15.40 N

Drag Co-eff=0.26215

2. Kw SST- Lift force= 49.55 N

Lift Co-eff=0.83649843

3. Relizable K E- Drag force=14.95 N

Drag Co-eff=0.2545

4. Relizable K E- Lift force=46.82 N

Lift Co-eff=0.83649843

Fig.36, Drag Force acting over Airfoil(Kw SST)

Fig.37, Drag Force acting over Airfoil(Relizable K E)

Fig.38, Lift Force acting over Airfoil(Kw SST)

Fig.39, Lift Force acting over Airfoil(Relizable K E)

Fig.40, Y+ Value(Kw SST)

Fig.41, Y+ Value(Relizable K E)

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 separation at the trailing edge which leads to a cavitation that gives rise to a phenomenon known as stall.