Indian Institute of TechnologyHyderabad

SUPERSONIC FLOW OVER NACA4412

Sunil kumar Reddy(ME12B1003) Haardik Garg(ME12B1018)

INTRODUCTION

An airfoil is the shape of a wing, blade(of a propeller, rotor or turbine) or sail.

An airfoil-shaped body moved 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.

GeometryThe NACA airfoils are airfoil shapes for aircraft wings developed by

the National Advisory Committee for Aeronautics(NACA).

The shape of the NACA airfoils is described using a series of digits following the word "NACA".

The parameters in the numerical code can be entered into equations to precisely generate the cross-section of the airfoil and calculate its properties.

Blue-chord, green- camber mean line

NACA 4412:chamber is 0.04 or 4% of chord(first digit).maximum chamber is at 0.4 or 40% of chord(second digit).Thickness is 0.12 or 12% of the chord(last two digits).

NACA 4 digit airfoil calculation:

The NACA airfoil section is created from a camber line and a thickness distribution plotted perpendicular to the camber lineThe equations are:

P-maximum chamber positionThe thickness distribution is given by the equation:

The position of the upper and lower surface can then be calculated perpendicular to the camber line.

This is the shape of NACA 4412 obtained from points generated through the equations

Analytical Equations[Linearized Supersonic Flow on Airfoil Lift & Drag]

Geometry

Mesh

Nodes-11772 Elements-11522

Analysis for different Mach numbersInputs Analysis is done for different Mach numbers Angle of attack – 60

At sea level Ambient pressure at outlet Second order upwind scheme is used

Static Pressure for mach-0.8

Static Pressure for mach-1

Static Pressure for mach-1.2

Static Pressure for mach-2

Mach number Minimum static pressure(gauge pressure)(pa)

0.8 -5.56e4

1 -8.67e4

1.2 -1.25e5

2 -3.47e5

Velocity for mach-0.8

Velocity for mach-1

Velocity for mach-1.2

Velocity for mach-2

Mach number Maximum velocity magnitude(m/s)0.8 4.09e2

1 5.11e2

1.2 6.13e2

2 1.02e3

Analysis at different altitudesInputs Analysis is done at different altitudes Angle of attack – 60

Mach number - 2 Second order upwind scheme is used

Static Pressure at sea level

Static Pressure at 4000m high

Static Pressure at 6000m high

Static Pressure at 8000m high

Static Pressure at 10000m high

Altitude(m) Minimum static pressure(gauge pressure)(pa)

0 -3.47e5

4000 -2.06e5

6000 -1.6e5

8000 -1.24e5

10000 -9.45e4

velocity at sea level

velocity at 4000m high

velocity at 6000m high

velocity at 8000m high

velocity at 10000m high

Altitude(m) Maximum velocity magnitude(m/s)0 1.02e3

4000 9.55e2

6000 9.31e2

8000 9.06e2

10000 8.81e2

Analysis for different angle of attackInputs Analysis is done for different angle of attack At sea level Mach number - 2 Ambient pressure at outlet Second order upwind scheme is used

Static Pressure at 20 angle of attack

Static Pressure at 40 angle of attack

Static Pressure at 60 angle of attack

Static Pressure at 100 angle of attack

Angle of attack(degree) Minimum static pressure(gauge pressure)(pa)

2 -2.64e5

6 -3.47e5

10 -4.78e5

20 -9.32e5

velocity at 20 angle of attack

velocity at 60 angle of attack

velocity at 100 angle of attack

velocity at 200 angle of attack

Angle of attack(degree) Maximum velocity magnitude(m/s)2 9.58e2

6 1.02e3

10 1.09e3

20 1.26e3

Lift Coefficient & Drag Coefficient

Lift coefficient vs angle of attack Drag coefficient vs angle of attack

Analysis for different Mach numbers with viscous effectsInputs Analysis is done for different Mach numbers Angle of attack – 60

At sea level Ambient pressure at outlet Second order upwind scheme is used K-Ԑ model is used

Static Pressure for mach-0.8

Static Pressure for mach-1

Static Pressure for mach-1.2

Static Pressure for mach-2

Mach number Minimum static pressure(gauge pressure)(pa) with viscous effects

Minimum static pressure(gauge pressure)(pa) without viscous effects

0.8 -5.01e4 -5.56e41 -7.86e4 -8.67e41.2 -1.14e5 -1.25e52 -3.19e5 -3.47e5

Velocity for mach-0.8

Velocity for mach-1

Velocity for mach-1.2

Velocity for mach-2

Mach number Maximum velocity magnitude(m/s)With viscous effects

Maximum velocity magnitude(m/s)Without viscous effects

0.8 3.81e2 4.09e2

1 4.77e2 5.11e2

1.2 5.73e2 6.13e2

2 9.58e2 1.02e3

References https://en.wikipedia.org/wiki/Airfoil http://airfoiltools.com/airfoil/details?airfoil=naca4412-il http://www.edforall.net/index.php/engineering-a-technology/aeronautical-engineeri

ng/100-aerodynamics/1951-implications-of-linearized-supersonic-flow-on-airfoil-lift-and-drag