Flow Over an Airfoil
Abstract:
In this project, we are going to calculate the drag and lift coefficients for the NACA 2412 airfoil on four different angles of attacks i.e. 10, 50, 100, 150.
Introduction:
Airfoil is the cross-sectional shape of a wing, blade of a propeller, rotor, or turbine, or sail as seen in cross-section. 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. 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, 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. Airfoil design is a major facet of aerodynamics. Various airfoils serve different flight regimes.
The angle of attack of an airfoil is the angle between the direction of the apparent or relative wind and the chord line of the airfoil. At very low angles of attack, the airflow over the airfoil is essentially smooth and laminar with perhaps a small amount of turbulence occurring at the trailing edge of the airfoil. The point at which laminar flow ceases and turbulence begins is known as the separation point. Increasing the angle of attack increases the area of the airfoil facing directly into the wind. This increases the lift but it also moves the separation point of laminar flow of the air above the airfoil part way up towards the leading edge and the result of the increased turbulent flow above the airfoil is an increase in the drag.
Maximum lift typically occurs when the angle of attack is around 15 degrees but this could be higher for specially designed airfoils.
Above 15 degrees, the separation point moves right up to the leading edge of the airfoil and laminar flow above the airfoil is destroyed. The increased turbulence causes the rapid deterioration of the lift force while at the same time it dramatically increases the drag, resulting in a stall.
The drag coefficient `Cd` is defined as
`Cd=(2Fd)/(rhou^2A)`
where:
`Fd`=is the drag force, which is by definition the force component in the direction of the flow velocity,
`rho=`is the mass density of the fluid,
`u=`is the flow speed of the object relative to the fluid,
`A=`is the reference area.
The lift coefficient `CundersetL` is defined as:
`undersetL C= (2L)/(rhou^2S)`
L= lift force
`rho=`is the mass density of the fluid,
`u=`is the flow speed of the object relative to the fluid,
S= relevant surface area.
Method:
A CFD simulation of the airfoil was carried in CONVERGE STUDIO software by a virtual wind tunnel. The profile of NACA 2412 was carved out of the virtual wind tunnel behaving as a solid object in it. The dimensions of wind tunnel are 5m X 3m X 0.25m.
Simulation Setup:
A 2D transient simulation was carried out for 0.5 seconds. Simulation run time was set to 0.5 sec by calculating the flow-through time of air from a wind tunnel.
`Time=( Dista nce)/ (Speed.)`
`Time= (5 metre)/ (40m/s)`
Time= 0.31 sec ~ 0.5sec.
The inlet flow was set to Re= 200000. The velocity being calculated is,
`Re= (rhoVL)/mu`
where,
`rho`= density of free stream air 1.225 kg/m3,
`mu`= dynamic viscosity of air 1.85e-5 kg/m3,
L= length of the airfoil,
Therefore the velocity calculated was 30.56 m/s.
The front and back face of a virtual wind tunnel where assigned TWO_D boundary condition. Top and bottom face where assigned Symmetry boundary. The airfoil walls were assigned as Walls.
Inlet condition :
Neumann Boundary condition for pressure and Dirichlet Boundary Condition for velocity.
Outlet Condition:
Neumann Boundary condition for velocity and Dirichlet Boundary Condition for pressure.
Turbulence Model:
K-`omega`SST model is used as it helps to resolve the viscous sublayer near to the wall and it is extremely preferable for external aerodynamics flow simulations.
Mesh:
The base mesh of 0.02m was set. A fixed boundary embedding of scale 4 and layer of 2 is set to capture the turbulence near the walls. A fixed Box embedding of scale 2 is set around the airfoil. The mesh corresponds to obtain a Y+=30.
Results:
- ANGLE OF ATTACK `1^0`:
Pressure:
Velocity:
A high-pressure low-velocity profile is seen at the bottom face of the airfoil and low-pressure high-velocity is seen at the upper face of the airfoil. At the leading edge of the airfoil highest pressure and low velocity is seen creating it a stagnation point. The velocity is high near the leading edge and falls at the trailing edge due to boundary layer effects. Also, the flow is uniform and mostly attached due to streamline body of the airfoil.
ANIMATION:
- ANGLE OF ATTACK `5^0`:
Pressure:
Velocity:
The pressure at the leading edge is high as more area of the airfoil comes into direct contact with the air developing a high-pressure region with low velocity below the airfoil. The velocity near the leading edge is high which decreases to the trailing edge. An adverse pressure gradient helps the boundary layer to separate near the middle of the airfoil. The boundary layer separation point is shifted towards the leading edge. i.e. in the middle of the airfoil.
ANIMATION:
- ANGLE OF ATTACK `10^0`:
Pressure:
Velocity:
At the `10^0`angle of attack, the pressure is highest slightly lower to the leading edge due to the fact that more area of the airfoil is in contact with the air increasing the drag force. Thus creating a high-pressure region below and low-pressure region on the upper side of the airfoil. This creates lift for the airfoil. A low-pressure region on the upper side near to the leading edge is developed creating a stagnant pressure region. The velocity at the leading edge is highest which quickly diminish down to the trailing edge and even zeroing itself at the trailing edge due to boundary separation effect. Separation point moves furthermore towards the leading edge.
ANIMATION:
- ANGLE OF ATTACK `15^0`
Pressure:
Velocity:
At the `15^0` angle of attack, the airfoil acts as an obstruction to the airflow causing a turbulent wake at the back of it. The separation point is nearly at the leading edge or could be assumed to be at some point as of leading edge. As stated earlier in the introduction, the angle of attack of 15 is considered to be a critical angle in which the turbulence increases and the increased turbulence causes the rapid deterioration of the lift force while at the same time it dramatically increases the drag, resulting in a stall. This separation creates vortices at the back of the airfoil.
ANIMATION:
- DRAG:
|
PARAMETERS |
10 |
50 |
100 |
150 |
|
DRAG force |
0.96 N |
1.76 N |
4.82 N |
11.17 N |
|
PARAMETERS |
10 |
50 |
100 |
150 |
|
DRAG Coefficient |
0.067 |
0.12 |
0.33 |
0.766 |
- From the above graph, it is clear that the drag force and coefficient of air are proportional to the angle of attack.
- LIFT:
|
PARAMETERS |
10 |
50 |
100 |
150 |
|
LIFT force |
17.48 N |
39.83 N |
54.81 N |
36.52 N |
|
PARAMETERS |
10 |
50 |
100 |
150 |
|
LIFT Coefficient |
0.294 |
0.671 |
0.92 |
0.62 |
As seen in the graph, the coefficient of lift increase up to the `10^0` angle of attack which also the highest and after which there is decrease due the aerodynamic stall obtained at `15^0`angle of attack.
Conclusion:
The highest Lift force and coefficient of Lift, 54.81 N and 0.92 respectively are obtained at an angle of attack `10^0`, while the highest drag force and coefficient of drag, 11.17 N and 0.766 respectively are obtained at an angle of `15^0`. For better accuracy of the drag and lift forces, the Y+ should be set below Y+< 5 i.e. in viscous sub-layer. In all the above cases the Y+ is set at 30 i.e. in the log-law region considering the computational limit and time for simulation.
REFERENCE: