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Discretization of camberline

o Used 11 points to describe profile line

o The last point can vary its vertical position (parameter=angle of

deflection)

o Trailing edge deformable part = 10% of chord

o Cubic spline function used

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Relation between T.E. deflection and angle of zero lift shift

The following table applies to a flap deformation of 10% of the chord and 11points defining the camberline coordinates.

T.E deflectionangle

[]

Angle of Zero Lift[]

Ratio

-5 7.43 1.49-4 5.95 1.49-3 4.47 1.49-2 2.99 1.49-1 1.49 1.490 0 -1 -1.49 1.492 -2.99 1.493 -4.47 1.49

An angle of deflection of 1 shifts the lift curve 1.49 to the left.

The number of points that define the geometry of the camberline has a biginfluence on the results, because the spline that is being created dependsstrongly on that number.

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Relation between angle of attack and deflection angle to obtain same lift

angle of attack

[]

T.E. deflection

[]-5 -10.06

-4 8.04

-3 -6.03

-2 4.02

-1 2.01

0 0

1 2.01

2 4.02

3 6.03

4 8.04

5 10.066 12.07

7 14.09

8 16.12

9 18.14

10 20.16

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In solid >> flat plate at 3 with TE deflection=0 >> Cl=0.3288 , Cm=0.0

In dashed >> flat plate at 0 with TE def=6.03 >>Cl=0.3290 , Cm=-0.0757

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Testing of steady code

The following tests were made in order to validate the steady code.

1. Test of NACA23012 airfoil with fixed geometry

The analytic solution (not exact) given by Anderson, pag 279, has beencompared to the results obtained with the code.

Panel Code AndersonCl at 4 0.5569 0.559Cmc/4 -0.0134 -0.0127

2. Test of flat plate with trailing edge deflection (Katz & Plotkin, pag. 133)

Analytical solution , using small disturbance approximation of the boundarycondition, were analysed against the code. The results show agreementbetween both.

Flap length 10% of chordCamber line is straight from the L.E. until the hinge point, and then has aconstant slope until the T.E. 101 points have been used to define the profile.

Camber line for the flap analysis

Deflection of the T.E.[]

Cl Cmwith respect to leading edge

Panel Code AnalyticalSolution

Panel Code AnalyticalSolution

1 0.0424 0.0434 -0.0199 -0.02035 0.2124 0.2170 -0.0995 -0.1014

10 0.4266 0.4341 -0.1999 -0.202815 0.6443 0.6511 -0.3020 -0.3041

The differences seen might be attributable to the small disturbancesassumptions used in the analytical method.

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Unsteady Analysis

For a sinusoidal variation of deflection angle )tfreqamp *sin =

For a step change in deflection angle of 15=step

The steady Cl is 0.8145 at this deflection angle. And the unsteady looks likethe figure below, having an initial value after the step of 0.4264.

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The moment coefficient with respect to the leading edge has the followingbehaviour in time.

but the steady value for the moment is 0.3911.

The following figure shows the Cl, Cm and the deflection angle as function oftime in seconds.