Hi everyone,(adsbygoogle = window.adsbygoogle || []).push({});

I am working on a project for the development of a 2D Unsteady Panel Method for Airfoils. As often already suggested in this forum I have been using the book "Low Speed Aerodynamics" which has helped me a lot to produce the Steady State solver (I am writing the code in Matlab at the moment), which works very well.

However I am having great problems in validating my unsteady code.

I have followed the book, mainly the steps are:

1) compute the steady solution at first time step

2) move the airfoil via a prescribed motion path (in my case pitching A*sin(wt))

3) position a concentrated vortex at a certain distance from the T.E., which has unknown intensity GAMMA_W and which is therefore part of the solution

4) use the Kelvin theorem for completing the coefficients matrix A which will be N+2 times N+2 (N+1 gammas on the nodes of the panels) + 1 (latter) unknown shed concentrated vortex

5) compute the RHS (right-hand-side) term considering free stream velocity and wake induced velocity

6) solve the system

The problem seems that the Cp variations are not big enough. I am using a NACA report on wind tunnel experimental data (pitching motion 5 + 5sin(Wt) motion) to check the code. But also the comparison with results contained in the Katz and Plotkin (plot of CL-ALPHA of a 0012) isn't satisfactory.

I compute the Cp at each collocation point via the formula:

Cp_i = 1 - Vel_i^2

where Vel_i is the velocity at the i-th collocation point obtained from the different contributes: free stream (similar to steady state) + kinematic movement (sinusoidal motion) + induced velocities (by panels and by wake).

I consider the free stream V to be equal to 1.Honestly I am not quite sure that all of this is right (talking about Cp calculation).

Moreover I have great doubt about the Kutta condition: in the steady state case the last line of matrix A is set equal to: [1 0 0 0 . . . 0 1] so that vorticity at T.E. is 0:

gamma_1 + gamma_(N+1) = 0

I did not change this in the unsteady code only because I couldn't find any indication on how to modify it (the book says that for small oscillations the steady case condition should still work fine).

I would be really thankful if any of you could help me out, as it is more than a month that I am trying to solve the problem. I have also read many articles like Hancock and Mook's one, or similar, but they don't really say explicitly how to do things.

Thank you very much.

PS: do ask questions if you don't understand some of the procedures I have used, I will be happy to explain more thoroughly.

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# Linear-Strength Vortex Unsteady Panel Method (2D)

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