Independent Research Project : 

Comparative Study of Different Grid Shapes for Aerofoil Analysis.

• Objective :

1. Develop C-grid, O-grid and rectangular grid to simulate Aerofoil analysis.
2. Calculate the value of Cl and Cd at different angle of attacks for same Reynolds number.
3. Compare results for different grids.

• Introduction :

n airfoil is the cross-sectional shape of a wing, blade (of a propeller, rotor or turbine)or sail. Airfoils are also found in propellers, fans, compressors and turbines. Swimming and flying creatures and even many plants and sessile organism employ airfoils/hyrdrofoils. E.g. bird wings, bodies of fish. An airfoil that has the same shape on both sides of its centreline is called as symmetric airfoil. The movement of centre of  pressure is the least in this type of airfoil. This type of airfoil is used extensively in helicopters rotors. In aerodynamics, camber is the asymmetry between two acting surfaces of an airfoil, with the top surface of wing commonly being more convex (positive camber). Camber is  usually designed into an aerofoil to increase the maximum lift coefficient. This minimizes the stalling speed of aircraft using the aerofoil. An aircraft with wings based on a cambered aerofoil will have a lower stalling speed than an aircraft with a similar wing loading and wings based on a symmetric aerofoil.

The first patented airfoil shapes were developed by Horatio F. Phillips in 1884.Phillips was an Englishman who carried out the first serious wind-tunnel experiments on airfoils. In 1902, the Wright brothers conducted their own airfoil tests in a wind tunnel, developing relatively efficient shapes  which contributed to their successful first flight on December 17, 1903. Clearly, in the early days of powered flight, airfoil design was basically customized and personalized. However, in the early 1930s, NACA-the forerunner of NASA-embarked on a series of definitive airfoil experiments using airfoil shapes that were constructed rationally and systematically. Many of these NACA airfoils are  in common use today.

NACA - The National Advisory Committee for Aeronautics (NACA) was a U.S. federal agency founded on March 3, 1915, to undertake, promote, and institutionalize aeronautical research. On October 1, 1958, the agency was dissolved, and its assets and personnel transferred to the newly created National Aeronautics and Space Administration (NASA). NACA was initialism, i.e. it was pronounced as discrete letters, rather than as a whole word (as was NASA during the early years after being established).

NACA0012 - It is an symmetrical Airfoil.First digit describes maximum camber as percentage of the chord – 0%. Second digit describes the distance of maximum camber from the airfoil leading edge in tens of percents of the chord – 0%. Last two digits describing maximum thickness of the airfoil as percent of the chord – 12%.

Aerodynamic Force - 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.

Reynolds Number - The Reynolds number (Re) is an important dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations. The Reynolds number is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities, which is known as a boundary layer in the case of a bounding surface.

Coefficient of Drag (Cd) - The drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. 

Coefficient of Lift (Cl) - The lift coefficient 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 refers to the dynamic lift characteristics of a two-dimensional foil section, with the reference area replaced by the foil chord.

Spalart Allarmas Model - The Spalart–Allmaras model is a one-equation model that solves a modelled transport equation for the kinematic eddy turbulent viscosity. The Spalart–Allmaras model was designed specifically for aerospace applications involving wall-bounded flows and has been shown to give good results for boundary layers subjected to adverse pressure gradients. It is also gaining popularity in turbomachinery applications.

In its original form, the model is effectively a low-Reynolds Number model, requiring the viscosity-affected region of the boundary layer to be properly resolved ( y+ ~1 meshes). The Spalart–Allmaras model was developed for aerodynamic flows. It is not calibrated for general industrial flows, and does produce relatively larger errors for some free shear flows, especially plane and round jet flows. In addition, it cannot be relied on to predict the decay of homogeneous, isotropic turbulence.

It solves a transport equation for a viscosity-like variable . This may be referred to as the Spalart–Allmaras variable.

• Geometry :

1. The geometry generation for an Aerofoil requires creation of a aerofoil data file in .txt form.
2. Design modeller from Ansys is used for creation of geometry.
3. Using 3D curve feature for generating aerofoil geometry.
4. Since the analysis is 2D, the thickness in Z direction will be 0.
5. After generating 3D curve, 'surface from edges' feature is used.
6. A suitable grid around the aerofoil is generated and 'surface from sketches' feature is used to create a surface.
7. As the analysis is concerned around the edges of the aerofoil, the solid part is not required.
8. To remove the solid geometry, Boolean operation is done.
9. Projection feature is used to divide the grid into diffferent zones or faces.
10. The geometry is ready for meshing after this.

• Meshing :

1. After importing the geometry, named selections feature is used to specify inlet, outlet and aerofoil wall.
2. Edge sizing and face meshing is used in all cases to achieve quadrilateral mesh.
3. As the mesh needs to be dense towards the airfoil, bias feature is used.
4. The edge sizing is given by using number of divisions options.
5. The number of divisions can vary for each grid style.
6. To compute the the answers correctly, y+ value should be calculated beforehand.
7. Number of divisions and bias value helps in achieving right y+ value.

C-Grid :

O-Grid 

Rectangular Grid :

• Case Setup :

Turbulence Model :- Spalart Allarmas (Strain Vorticity based) with curvature correction enabled.

Algorithm Scheme :- Coupled.

Fluid :- Air.

Inlet Velocity :- 88.65 m/s.

Outlet Pressure :- 0 Pa.

Turbulence viscosity ratio :- 1

Initialization :- Hybrid.

X-direction velocity :- cos 10 = 0.98480775301; cos 15 = 0.96592582628

Y-direction velocity :- sin 10 = 0.17364817766; sin 15 = 0.2588190451

Plots - Drag Coefficient and Lift Coefficient at airfoil wall.

• Plots :

C-Grid : 

Angle of Attack 0 :

Velocity Contour

Pressure Contour

Velocity Streamlines

Angle of Attack 10 :

Velocity Contour 

Pressure Contour

Velocity Streamlines

Angle of Attack 15 :

Velocity Contour 

Pressure Contour

Velocity Streamlines

O-Grid : 

Angle of Attack 0 :

Velocity Contour

Pressure Contour

Velocity Streamlines

Angle of Attack 10 :

Velocity Contour 

Pressure Contour

Velocity Streamlines

Angle of Attack 15 :

Velocity Contour 

Pressure Contour

Velocity Streamlines

Rectangular - Grid :

Angle of Attack 0 :

Velocity Contour

Pressure Contour

Velocity Streamlines

Angle of Attack 10 :

Velocity Contour 

Pressure Contour

Velocity Streamlines

Angle of Attack 15 :

Velocity Contour 

Pressure Contour

Velocity Streamlines

• Results :

Observation Table

Grid	Angle of Attack = 0		Angle of Attack = 10		Angle of Attack = 15
	Cl	Cd	Cl	Cd	Cl	Cd
O-grid	-2.29E-05	0.008032	0.94435	0.023815	1.27421	0.04344
C-grid	-1.35E-06	0.008114	0.99796	0.01545	1.3236	0.026727
Rectangular	-4.36E-05	0.00795	1.02983	0.012342	1.367303	0.021268

Experimental Data (NACA Turbulence Modelling Resource)

CODE	CL (alpha=0)	CL (alpha=10)	CL (alpha=15)	CD (alpha=0)	CD (alpha=10)	CD (alpha=15)
CFL3D	approx 0	1.0909	1.5461	0.00819	0.01231	0.02124
FUN3D	approx 0	1.0983	1.5547	0.00812	0.01242	0.02159
NTS	approx 0	1.0891	1.5461	0.00813	0.01243	0.02105
JOE	approx 0	1.0918	1.5490	0.00812	0.01245	0.02148
SUMB	approx 0	1.0904	1.5446	0.00813	0.01233	0.02141
GGNS	approx 0	1.0941	1.5576	0.00817	0.01225	0.02073

Error %

Grid	Angle of Attack = 0		Angle of Attack = 10		Angle of Attack = 15
	Cl	Cd	Cl	Cd	Cl	Cd
O-grid	Can't say	1.35%	13.50%	92.63	17.77	104.4
C-grid	Can't say	0.36%	8.65	25	14.58	25.74
Rectangular	Can't say	2.33%	5.73%	0.16	11.76	0.04

• Conclusion :

1. The values of Cl an Cd match well for angle of attack = 0 for all types of grids.
2. Circular grid or O-grid has the lowest accuracy of all. A back flow is detected while computing for angle of attack more than 0.
3. C-grid has the highest accuracy for Cd at AoA = 0. But accuracy is lower in other cases.
4. Rectangular grid has the good accuracy for Cd for all angle of attacks. It is highest for all Cl values. 
5. In conclusion it can be said that Rectangular grid is most suitable for this case.
6. The same cases can be run using other turbulence models like K-Epsilon SST.