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 (C_d)  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.      

C_d=  2.D / $\mathrm{\rho .A.V2}$

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 (C_L) 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. C_L is a function of the angle of the body to the flow, its Reynolds number and its  Mach number. The lift coefficient c_l refers to the dynamic lift characteristics of a two-dimensional foil section, with the reference area replaced by the foil chord.

C_d=  2.L /$\mathrm{\rho .A.V2}$

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-

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-$\omega$ 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- $\omega$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.