Flow Over A NACA 2412 Airfoil For Different Angle Of Attack With Two Turbulence Models Using Converge Studio
FLOW OVER A NACA 2412 AIRFOIL USING CONVERGE STUDIO.
OBJECTIVE:
Simulate flow over a 4 digit airfoil i.e NACA 2412 Airfoil.
I have to calculate the following,
- Drag co-efficient Vs Angle of Attack
- Lift coefficient 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
NOTE:
In regions and initialization, the value of velocity should be the same as that of Inlet velocity.
AIRFOIL:
An airfoil is the cross-sectional shape of a wing, blade (of a propeller, rotor, or turbine), or sail. 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 the 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 asymmetric curvature of upper and lower surfaces. 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 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 angles 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 Bernouilli'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 and the Kutta joukowski theorem.
DRAG COEFFICIENT:
The drag coefficient (Cd) is defined as the aerodynamic drag coefficient is a measure of the effectiveness of streamlined aerodynamic body shape in reducing the air resistance to the forward motion of a vehicle. A low drag coefficient implies that the streamline shape of the vehicle's body is such as to enable it to move easily through the surrounding viscous air with the minimum of resistance; conversely a high drag coefficient is caused by poor streamlining of the body profile so that there is a high air resistance when the vehicle is in motion.
Cd= 2.D / ρ.A.V2
where:
d is the drag force,
ρ is the mass density of the fluid,
V is the flow speed of the object relative to the fluid,
A is the reference area.
LIFT COEFFICIENT:
The lift coefficient (CL) is a dimensionless coefficient that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area A lifting body is a foil or a complete foil-bearing body such as a fixed-wing aircraft. CL is a function of the angle of the body to the flow, its Reynolds number and its Mach number. The lift coefficient cl refers to the dynamic lift characteristics of a two-dimensional foil section, with the reference area replaced by the foil chord.
Cd= 2.L /ρ.A.V2
where:
L is the lift force,
ρ is the mass density of the fluid,
V is the flow speed of the object relative to the fluid,
A is the reference area.
GEOMETRY:
The NACA airfoils are airfoil shapes for aircraft wings developed by the National Advisory Committee of Aeronautics (NACA). The shape of the NACA airfoils is described using a series of digits following the word "NACA".
NACA 2412 AIRFOIL
The airfoil used for the simulation was NACA 2412 the coordinates were plotted using the vertex tool in converge studio to obtain the 3D model of the airfoil. Then the virtual wind tunnel was created around the airfoil to simulate the airflow. The wind tunnel inlet should be 25 times the chord length from the leading edge and outlet should be 50 times the chord length from the leading edge.
VIRTUAL WIND TUNNEL
BOUNDARY CONDITIONS:
|
BOUNDARY NAME |
TYPE |
OPERATING CONDITIONS |
|
INLET |
INFLOW |
PRESSURE – ZERO NORMAL GRADIENT, VELOCITY- 31.2357 m/s, TEMPERATURE: 300K |
|
OUTLET |
OUTFLOW |
PRESSURE-101325 PASCAL, TEMPERATURE: 300K, VELOCITY – ZERO NORMAL GRADIENT |
|
FRONT |
2 D |
2D |
|
BACK |
2D |
2D |
|
TOP |
SYMMETRY |
SYMMETRY |
|
BOTTOM WALL |
SYMMETRY |
SYMMETRY |
|
AIRFOIL |
WALL |
WALL |
MESH:
The base mesh and the embedding near the airfoil surface were decided based on the Y plus value. The Δ">Δs value is 0.00124. Then the simulation time was calculated using the flow-through time 5/31.2357= 0.1783 and the end time simulation value is 1.8 secs. Then the general averaged wall output was enabled at the output file to monitor lift and drag forces. The fixed embedding was applied to get the finer mesh around the airfoil surface. The base mesh chosen was 0.08.
Δ">Y plus calculator: http://www.pointwise.com/yplus/
Δ">Initially the turbulence K-ω">ω SST was used because it used for external flow simulation and in addition RNG K -ε">ε is used for comparing the two turbulence model performance.
RNG K-ε
Angle of attack:1º
Fig 1. Mesh(surface with edges)
VELOCITY CONTOUR:
Fig 2. Velocity profile
Video 1. Velocity animation
PRESSURE CONTOUR:
Fig 3. Pressure profile
Video 2. Pressure animation
Angle of attack:5º
Fig 1. Mesh(surface with edges)
VELOCITY CONTOUR:
Fig 2. Velocity profile
Video 1. Velocity mesh animation
PRESSURE CONTOUR:
Fig 3. Pressure profile
Video 2. Pressure animation
Angle of attack:10º
Fig 1. Mesh(surface with edges)
VELOCITY CONTOUR:
Fig 2. Velocity profile
Video 1. Velocity animation
PRESSURE CONTOUR:
Fig 3. Pressure profile
Video 2. Pressure animation
Angle of attack:15º
Fig 1. Mesh(surface with edges)
VELOCITY CONTOUR:
Fig 2. Velocity profile
Video 1. Velocity animation
PRESSURE CONTOUR:
Fig 3. Pressure profile
Video 2. Pressure animation
K-ω SST
Angle of attack:1º
Fig 1. Mesh(surface with edges)
VELOCITY CONTOUR:
Fig 2. Velocity profile
Video 1. Velocity mesh animation
PRESSURE CONTOUR:
Fig 3. Pressure profile
Video 2. Pressure animation
Angle of attack:5º
Fig 1. Mesh(surface with edges)
VELOCITY CONTOUR:
Fig 2. Velocity profile
Video 1. Velocity animation
PRESSURE CONTOUR:
Fig 3. Pressure profile
Video 2. Pressure animation
Angle of attack:10º
Fig 1. Mesh(surface with edges)
VELOCITY CONTOUR:
Fig 2. Velocity profile
Video 1. Velocity animation
PRESSURE CONTOUR:
Fig 3. Pressure profile
Video 2. Pressure animation
Angle of attack:15º
Fig 1. Mesh(surface with edges)
VELOCITY CONTOUR:
Fig 2. Velocity profile
Video 1. Velocity animation
PRESSURE CONTOUR:
Fig 3. Pressure profile
Video 2. Pressure animation
Y PLUS :
|
ANGLE OF ATTACK |
Y- PLUS ( RNG K -ε) |
Y- PLUS (K- ω SST) |
|
1 |
39.631 |
56.34 |
|
5 |
35.26 |
56.27 |
|
10 |
31.37 |
45.37 |
|
15 |
28.26 |
34.26 |
TURBULENCE MODEL (K- ω">ω SST):
COEFFICIENT OF LIFT AND DRAG TABLE :
| Angle of Attack | Lift Co-eff (k-w SST) | Lift Co-eff (RNG k-e) |
| 1 | 0.272 | 0.002 |
| 5 | 0.612 | 0.595 |
| 10 | 0.764 | 0.757 |
| 15 | 0.692 | 0.685 |
| Angle of Attack | Drag Co-eff (k-w SST) | Drag Co-eff RNG k-e |
| 1 | 0.002 | 0.020 |
| 5 | 0.003 | 0.004 |
| 10 | 0.008 | 0.007 |
| 15 | 0.024 | 0.025 |
LIFT AND DRAG TABLE :
| Angle of Attack | Lift (k-w SST) | Lift (RNG k-e) |
| 1 | 18.780 | 18.530 |
| 5 | 43.521 | 42.356 |
| 10 | 54.340 | 53.840 |
| 15 | 49.236 | 48.736 |
| Angle of Attack | Drag (k-w SST) | Drag (RNG k-e) |
| 1 | 0.953 | 1.130 |
| 5 | 1.893 | 2.190 |
| 10 | 4.791 | 4.180 |
| 15 | 14.359 | 14.734 |
CALCULATIONS:
1 degree:
| Drag and Lift Coefficient for 1° Angle of Attack using k-w SST | ||||
| Drag Force (X) in N | Density (kg/m^3) | Velocity (m/s) | Area (m) | Drag Co-eff |
| 0.953 | 1.177 | 31.2357 | 0.998 | 0.0017 |
| Lift Force (Y) in N | Density (kg/m^3) | Velocity (m/s) | Area (m) | Lift Co-eff |
| 18.78 | 1.177 | 31.2357 | 0.1201 | 0.2723 |
| Drag and Lift Coefficient for 1° Angle of Attack using RNG k-e | ||||
| Drag Force (X) in N | Density (kg/m^3) | Velocity (m/s) | Area (m) | Drag Co-eff |
| 1.13 | 1.177 | 31.2357 | 0.998 | 0.0020 |
| Lift Force (Y) in N | Density (kg/m^3) | Velocity (m/s) | Area (m) | Lift Co-eff |
| 18.53 | 1.177 | 31.2357 | 0.1201 | 0.2687 |
5 degree:
| Drag and Lift Coefficient for 5° Angle of Attack using k-w SST Turbulence Model | ||||
| Drag Force (X) in N | Density (kg/m^3) | Velocity (m/s) | Area (m) | Drag Co-eff |
| 1.893 | 1.2041 | 31.367 | 0.998 | 0.0032 |
| Lift Force (Y) in N | Density (kg/m^3) | Velocity (m/s) | Area (m) | Lift Co-eff |
| 43.521 | 1.2041 | 31.367 | 0.1201 | 0.6118 |
| Drag and LiftCoefficient for 5° Angle of Attack using RNG k-e Model | ||||
| Drag Force (X) in N | Density (kg/m^3) | Velocity (m/s) | Area (m) | Drag Co-eff |
| 2.19 | 1.2041 | 31.367 | 0.998 | 0.0037 |
| Lift Force (Y) in N | Density (kg/m^3) | Velocity (m/s) | Area (m) | Lift Co-eff |
| 42.356 | 1.2041 | 31.367 | 0.1201 | 0.5954 |
10 degree:
| Drag and Lift Coefficient for 10° Angle of Attack using k-w SST | ||||
| Drag Force (X) in N | Density (kg/m^3) | Velocity (m/s) | Area (m) | Drag Co-eff |
| 4.791 | 1.2041 | 31.367 | 0.998 | 0.0081 |
| Lift Force (Y) in N | Density (kg/m^3) | Velocity (m/s) | Area (m) | Lift Co-eff |
| 54.34 | 1.2041 | 31.367 | 0.1201 | 0.7638 |
| Drag and LiftCoefficient for 10° Angle of Attack using RNG k-e Model | ||||
| Drag Force (X) in N | Density (kg/m^3) | Velocity (m/s) | Area (m) | Drag Co-eff |
| 4.18 | 1.2041 | 31.367 | 0.998 | 0.0071 |
| Lift Force (Y) in N | Density (kg/m^3) | Velocity (m/s) | Area (m) | Lift Co-eff |
| 53.84 | 1.2041 | 31.367 | 0.1201 | 0.7568 |
15 degree:
| Drag and Lift Coefficient for 15° Angle of Attack using k-w SST | ||||
| Drag Force (X) in N | Density (kg/m^3) | Velocity (m/s) | Area (m) | Drag Co-eff |
| 14.359 | 1.2041 | 31.367 | 0.998 | 0.0243 |
| Lift Force (Y) in N | Density (kg/m^3) | Velocity (m/s) | Area (m) | Lift Co-eff |
| 49.236 | 1.2041 | 31.367 | 0.1201 | 0.6921 |
| Drag and LiftCoefficient for 15° Angle of Attack using RNG k-e Model | ||||
| Drag Force (X) in N | Density (kg/m^3) | Velocity (m/s) | Area (m) | Drag Co-eff |
| 14.734 | 1.2041 | 31.367 | 0.998 | 0.0249 |
| Lift Force (Y) in N | Density (kg/m^3) | Velocity (m/s) | Area (m) | Lift Co-eff |
| 48.736 | 1.2041 | 31.367 | 0.1201 | 0.6851 |
Graphs:
RESULTS:
At the top surface of the airfoil when flow strikes the leading edge if it curved upwards the velocity increases and pressure decreases. This happens because of Bernoulli's principle. This point is also known as the stagnation point. In the bottom of the airfoil if it curved down the velocity decreases and the pressure increases then the lift force is generated.
When the angle of attack increases the lift also increases up to 10 degrees after that it decreases and the drag increases as the angle of attack increases.
A comparative study was done for the same setup case with different turbulence models. The only difference is Y plus value is higher when we use the K- ω SST turbulence model. If we use the higher y plus value we can find drag coefficients easily.
Drag and lift coefficients were calculated by taking the pressure force values. The drag and lift coefficients are both quite small at the 1-degree angle of attack. The lift and drag force both are relatively small for both turbulence model.
At 15 degree angle of attack, the region of circulation is created this happens when the angle of attack exceeds the limit of the angle of an airfoil. It results in the reduced amount of lift ad the increased drag it makes the airfoil to be reduced efficiency.
The plots above for drag and lift coefficients for a different angle of attack. Up to 10 degrees the value of lift coefficients increases but after that the value decreases and the drag coefficient increases as the angle of attack increases. So for this NACA 2412 airfoil, it is advised to keep the angle of attack below 15 degrees.