[ZakBristol]

Hi,
I am trying to build a panel method using dirichlet boundary condition, combining source and doublets on lifting surfaces. And sources on non-lifting surfaces.

I am not sure how to calculate the pressure on none lifting surfaces, not sure that assuming that the sources are equal to -v_inf *n is correct when only sources is used.

Any help please?

[ZakBristol]

Hi,

Any good reference for panel method for thick blunt trailing edge, assuming two wakes are leaving the aerfoil.

Any help is appreciated.

[timea]

If you use the Dirichlet B.C. and set the inter potential to be equal to the free stream potential, then the strength of the sources are equal to the normal component of the free stream velocity at the collocation point, if there is no other(transpiration or mass flow rate BC).
I suggest the book, "Low Speed Aerodynamics by Katz and Plotkin"
At the end of the book, there is a program. You can use that program.
Sometimes, the program has small typos so it would be better to check the theory and the formula in the book.

[sbaffini]

Check this out http://www.3dpanelmethod.com/

[ZakBristol]

Hi Both,
I have checked the website and I am using Katz good.

However I am unable to combine non-lifting surfaces and lifting surfaces using Dirichlet boundary condition

[sbaffini]

Not sure if this is what puzzles you but:

1) you should use the sources for all the panels belonging to closed bodies, lifting or not, but not for wakes, of course

2) You shoud use doublets for all the panels, lifting or not, open or not, wake or not... ALL the panels

[ZakBristol]

Hi. Thanks for the reply. I have attached a photo with the derivation of the source for non lifting surfaces.

Which shows that using different BC will lead to different cp values.

[ZakBristol]

So, by using different BC we will get different pressure values.

[sbaffini]

I should give a look at Katz or my codes, but I'm pretty sure that your rendition of the Dirichlet condition is wrong because you need to add doublets or, in any case, you need to end up with a system of equations, which you don't.

[ZakBristol]

hi,

I did not include doublet barbecue I am calculating the pressure on a nonlifting surface only without including any lifting surface, so therefor there are no doublet.

Now, this method is in Katz book Using Neumann BC. But it is not using Dirichlet BC (sources only). And therefore I am really confused on how can we assume the following.

sigma = V_inf . normal vectors ----- in Dirichlet BC.
and, sigma = inv(AIC) * (- V_inf * normal vector) ----- in NeumannBC,

and then calculate the pressure using the same equation cp = 1- v_tan^2/v_inf

I hope i clarified my point.

[sbaffini]

Originally Posted by ZakBristol

hi,

I did not include doublet barbecue I am calculating the pressure on a nonlifting surface only without including any lifting surface, so therefor there are no doublet.

Now, this method is in Katz book Using Neumann BC. But it is not using Dirichlet BC (sources only). And therefore I am really confused on how can we assume the following.

sigma = V_inf . normal vectors ----- in Dirichlet BC.
and, sigma = inv(AIC) * (- V_inf * normal vector) ----- in NeumannBC,

and then calculate the pressure using the same equation cp = 1- v_tan^2/v_inf

I hope i clarified my point.

Indeed, what I get is that you can't use Dirichlet with sources only, because it makes no sense (if I recall correctly, sources actually fix the potential, doublets fix its gradient). Also, there is nothing wrong in using doublets with non lifting cases.

[ZakBristol]

Then in that case. Using dirichlet BC

if we have lifting and nonlifting surfaces, how can we calculate the source strength distribution and the pressure on nonlifting surfaces.

[sbaffini]

The fundamentals of the method are described in chapter 9 of Katz and Plotkin, especially 9.2 for the b.c., and the following chapters (11 and 12) for the examples.

Among the examples, the most presented one certainly is the source+doublet method, and it is made clear that when you have both you have to fix one of them. In all the cases they fix the sources (using arguments from 9.2) as you did in your picture and put them to the rhs, while a system for the doublets strengths remains to be solved.

Everything you need is explained, say, in 11.3.1 for the very common case of a constant source + constant doublet method in 2D. I coded my 2D code from that explanation and APAME (whose source code is available, that's why I posted a link to it) is based on its 3D counterpart.

Admittedly, among the several possibilities, there are few missing cases in the K&P presentation, but they are not excluded as not working. In your case, however, you need to follow the general recipe. If you have only sources, you don't just fix them, they are the solution of your problem. That is, say, in eq. 11.6 of K&P you set the doublets to 0 and you end up with a system for the sources. This is different from the combined case, where you instead fixed them upfront.

I'm not sure if I was clear enough but, really, your best chance is to read the book page to page and use one of the combinations shown in the examples. Then, from that, you can move into your own direction if you want.

[timea]

in the Neumann B.C., the strength of the source means the total velocity component normal to the surface. Thus, after obtaining the strengths of the sources by satisfying no penetration B.C., you can calculate the total velocity(free stream + perturbation vel.) component on the surface by just using the inverse matrix.

In the Dirichlet B.C., the strength of the source represents the free stream component normal to the surface and fixes the value of free stream components normal to the surface so that the doublet has the role of determining the perturbation velocity. In the Dirichlet B.C., it changes by how you put the inner potential equal to something, many people put the inner potential equal to the free stream potential.

[ZakBristol]

Hi both,

I am still not sure how the pressure is calculated on non-lifting surfaces, where we have sources only, using Dirichlet BC.

In your reply you mentioned "In the Dirichlet B.C., the strength of the source represents the free stream component normal to the surface and fixes the value of free stream components normal to the surface so that the doublet has the role of determining the perturbation velocity.". By which I understood that the sources do not perpetuate the flow. So, for non-lifting surfaces if we have sources only what effects they have ?

[ZakBristol]

Originally Posted by sbaffini

The fundamentals of the method are described in chapter 9 of Katz and Plotkin, especially 9.2 for the b.c., and the following chapters (11 and 12) for the examples.

Among the examples, the most presented one certainly is the source+doublet method, and it is made clear that when you have both you have to fix one of them. In all the cases they fix the sources (using arguments from 9.2) as you did in your picture and put them to the rhs, while a system for the doublets strengths remains to be solved.

Everything you need is explained, say, in 11.3.1 for the very common case of a constant source + constant doublet method in 2D. I coded my 2D code from that explanation and APAME (whose source code is available, that's why I posted a link to it) is based on its 3D counterpart.

Admittedly, among the several possibilities, there are few missing cases in the K&P presentation, but they are not excluded as not working. In your case, however, you need to follow the general recipe. If you have only sources, you don't just fix them, they are the solution of your problem. That is, say, in eq. 11.6 of K&P you set the doublets to 0 and you end up with a system for the sources. This is different from the combined case, where you instead fixed them upfront.

I'm not sure if I was clear enough but, really, your best chance is to read the book page to page and use one of the combinations shown in the examples. Then, from that, you can move into your own direction if you want.

Hi,

I have coded, constant doublet using N BC and D BC , and constant sources using N BC. all from Katz book,

What I could not do,
1. is combining sources and doublet using newmann condition.
2. A combination of lifting and non-lifting surfaces using Dirchelt BC, where:
a. lifting surfaces includes doublet and sources
b. non-lifting surfaces using sources only.

[sbaffini]

You actually have to use doublets also on non lifting bodies, even if there are no lifting bodies at all in your problem. Only sources cannot be used on wakes

[timea]

In the formulation, there are two things:1)Total potential formulation, and 2)Perturbation potential formulation. In case of the Dirichlet B.C., as you can see at Katz and Plotkin's book, you can set the inner potential as various things such as free stream potential or zero...by doing so, the potential you represent using the singularities will represent the total potential or perturbation potential.

In the combination of the sources/doublets(or vortices), you can choose several combinations if it is sure that the solution exists and is unique depending on the boundary conditions. If you look at the 2D problems in the Katz and Plotkin's book, you can find the possible combinations.

In the case of Dirichlet B.C., as 'sbaffini' said, you have to use both source and doublet(or vortex) even for the non-lifting body. If you'd like to use source only for the Dirichlet B.C., I am not sure if the solution is unique.

The most important thing for the combination of singularities for the given B.C. is the existence and uniqueness of the solution. If it exists and is unique, then you can build the AIC and solve the linear equations, and find the velocities or surface pressures using many numerical schemes or techniques.

[Eli_]

thank you for your response.