[amin95]

Hi. I have written my own 3d panel method code in MATLAB using the famous book "Low Speed Aerodynamics".

My code could calculate correct pressure coefficients of a NACA0012 airfoil at zero AoA in a steady flow, but fails to get correct result at 5 degree of AOA, it seems pressure coefficients of lower and upper surface diverge near trailing point. I added figures of both results.

I think this may be caused by wrong calculation of source/doublet influence coefficients (problem with arc tangents functions). could anyone help me with this problem?

[amin95]

Here I upload a pdf file containing my influence coefficients calculation in MATLAB with description. could anyone tell me is it correct or not?

[apoorvs01]

http://www.3dpanelmethod.com/

[amin95]

Originally Posted by apoorvs01

http://www.3dpanelmethod.com/

Hi, thanks for your advice. i visited that site before and read the graduate work paper there also. I think it would be more helpful if you could tell me how to deal with problem at influence coefficients calculations.

[apoorvs01]

Hi Amin

I have never coded panel method; so cant be of much help. As per my knowledge "Vortex Element Method" by R.I Lewis would also be of good help.

https://www.staff.ncl.ac.uk/r.i.lewi...ementsBook.htm

Try to get it from your library.

Regards

Apoorv

[blackjack]

Which method did you use? What are dimensions of wing? I would suggest unswept rectangular wing of aspect ratio 20.

It looks like you have no wake. Run it without wake and with wake.

[blackjack]

Here is pressure on naca0012 at 5 degrees with no wake.

The small difference between your result and this is explainable by panel density.

[amin95]

Originally Posted by blackjack

Here is pressure on naca0012 at 5 degrees with no wake.

The small difference between your result and this is explainable by panel density.

Hi James ,thanks for your reply.

I used the Dirichlet boundary condition. The wing aspect ratio is about 6.5 and its unswept rectangular. I used 18 panels around airfoil section and 5 panels in each row, totally reaching to 90 panels. I ran the code both with and without wake but it seems that my results did not change with or without counting wake effect.

So if I'm not wrong, according to your posted pressure figure my panels influence coefficients calculation is correct, and the problem is caused by wrong wake modelling?

Here I upload pdf file of my wake influence coefficients calculation section in MATLAB for your notice. could you tell me where I did wrong?

By the way if you don't mind I'd like to know which software did you use to get that pressure figure of naca0012 airfoil without wake?

best regards

[blackjack]

Without a wake, a body will produce no lift. The lift coefficient of my wing without a wake is -.008, with a wake it's 0.51 (see attached Cp).

If your answer does not change when you add a wake: the wake influence coefficients are wrong, they are not added to the matrix correctly, or the matrix solver does not see them. Print the wake circulation for your wing.
Anyone writing computer programs must learn to recognize and debug errors.

To validate your body influence coefficients, run a sphere and cylinder with few/more/many panels. The exact answer can be found in many texts. Very close comparison should be obtained.

BTW you are solving an external Neumann problem. The work of PGL Dirichlet has nothing to do with it. I suggest you read the many papers by Luigi Morino (1970s).

Good Luck.

[blackjack]

The naca 0012 with wake.

[amin95]

Circulation over the airfoil section is zero. I used prescribed wake model that all its panels are parallel to the trailing point local velocity vector. Could this be cause of the problem?

[blackjack]

A picture is worth a thousand words: Plot your wake geometry. Does it extend at least 10 spans downstream? If the "local velocity vector" concept isn't working, just use a wake parallel to the chord.

Print your influence coefficient matrix. Are the wake terms non-zero?

[blackjack]

I'll get the hang of uploading files in a year or two.

[amin95]

Originally Posted by blackjack

A picture is worth a thousand words: Plot your wake geometry. Does it extend at least 10 spans downstream? If the "local velocity vector" concept isn't working, just use a wake parallel to the chord.

Print your influence coefficient matrix. Are the wake terms non-zero?

Here is my wing and its wake geometry figure at 5 degree AoA, as it could be seen the wake is parallel to the chord. Also I uploaded the wing panels doublet strengths figure too.

[amin95]

Originally Posted by blackjack

A picture is worth a thousand words: Plot your wake geometry. Does it extend at least 10 spans downstream? If the "local velocity vector" concept isn't working, just use a wake parallel to the chord.

Print your influence coefficient matrix. Are the wake terms non-zero?

And at the end as you requested I uploaded wing panels doublet\source influence coefficient matrix plus the wake's first and lateral row panels doublet influence coefficient matrix in Excel file.

The lateral wake terms term are between magnitude of e-03 and e-07, and the first wake terms are between e-02 and e-07.

Best regards

[blackjack]

Is your panel method steady-state or time-dependent? The results I have provided are from a steady-state calculation.

What does the color of the wake panels signify? The circulation (doublet)?

The circulation of the wake panel attached to the trailing edge of the wing is determined from what equation? Zero circulation in the wake would give the same result as no wake.

In 30 years, I have not heard the phrase "lateral wake terms". Please define or provide a reference that describes this terminology.

[amin95]

Originally Posted by blackjack

Is your panel method steady-state or time-dependent? The results I have provided are from a steady-state calculation.

What does the color of the wake panels signify? The circulation (doublet)?

The circulation of the wake panel attached to the trailing edge of the wing is determined from what equation? Zero circulation in the wake would give the same result as no wake.

In 30 years, I have not heard the phrase "lateral wake terms". Please define or provide a reference that describes this terminology.

I'm just following instructions from Katz & Plotkin Low Speed Aerodynamics Book chapter 13. My panel method is time dependent but the wake model for now is not free. It develops over each time step and only moved back parallel to the chord line by free stream velocity. Doublet strength of each new wake panel in every time step is determined by upper and lower trailing edge panels doublet strengths.

The color of the wake panels does not signify any value and by "lateral wake panels" I mean the wake panels that has already been shed by trailing edge panels with known doublet values in previous time steps.

[amin95]

Originally Posted by blackjack

Is your panel method steady-state or time-dependent? The results I have provided are from a steady-state calculation.

What does the color of the wake panels signify? The circulation (doublet)?

The circulation of the wake panel attached to the trailing edge of the wing is determined from what equation? Zero circulation in the wake would give the same result as no wake.

In 30 years, I have not heard the phrase "lateral wake terms". Please define or provide a reference that describes this terminology.

This figure may help. The wake panels doublet strengths are non zero.

[blackjack]

On July 10, you said "Circulation over the airfoil section is zero". Indeed, the "wing panels doublet strength" shown on 15 July corroborates this statement.

Yesterday, you say "The wake panels doublet strengths are nonzero." and "Doublet strength of each new wake panel in every time step is determined by upper and lower trailing edge panels doublet strengths"

The circulation of the airfoil section must equal the circulation of the wake panel attached to the trailing edge. Are the wake panel circulations non-zero, but very small?

You should plot the strength of the trailing-edge wake panel (at the wing center) vs. time. And you should run 50-100 timesteps. Have you run enough time steps that the wake strength becomes asymptotic?

[amin95]

Originally Posted by blackjack

On July 10, you said "Circulation over the airfoil section is zero". Indeed, the "wing panels doublet strength" shown on 15 July corroborates this statement.

Yesterday, you say "The wake panels doublet strengths are nonzero." and "Doublet strength of each new wake panel in every time step is determined by upper and lower trailing edge panels doublet strengths"

The circulation of the airfoil section must equal the circulation of the wake panel attached to the trailing edge. Are the wake panel circulations non-zero, but very small?

You should plot the strength of the trailing-edge wake panel (at the wing center) vs. time. And you should run 50-100 timesteps. Have you run enough time steps that the wake strength becomes asymptotic?

This is the figure of strength of the trailing-edge wake panels over 100 timesteps. they became asymptotic after 6 timesteps and their values are about between 1.45 and 1.65.

I don't know why circulation of airfoil section is zero but trailing edge wake's is not.