Vortex Lattice Method: Calculating lift using circulation from vortex ring elements

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 June 24, 2011, 16:58 Vortex Lattice Method: Calculating lift using circulation from vortex ring elements #1 New Member   Ismail Hameduddin Join Date: Jun 2011 Posts: 6 Rep Power: 6 I am not an aerodynamics guy specifically but I need to do some aerodynamic modeling for my research and ran into some trouble: I am calculating the lift on a wing using the vortex lattice method (VLM) with vortex ring elements. I have 6 panels on my wing surface (2 chordwise, 3 spanwise) and wake panels up to approximately 20 wingspans downstream from the trailing edge. I calculated the lift on each panel using the Kutta-Joukowski theorem using the circulation I got from the VLM.To get the total lift I summed up the lift on all the panels (including the wake panels) as in Katz & Plotkin. Is this correct? Or should I ignore the wake panels when calculating total lift since they are supposed to be "force-free" and only concentrate on the panels actually on the surface of the wing? When doing the VLM, I only considered the upper surface of the airfoil -- thin airfoil/no thickness. Would also including the lower surface of the airfoil be more accurate (within the same calculations and using the same wake)? I am getting a suspiciously low lift/coefficient of lift from current calculations (without the suggestions above)...a couple of orders smaller than its supposed to be. Any help would be greatly appreciated! ~ IH Last edited by black&gold; June 24, 2011 at 16:59. Reason: added some info.

 June 24, 2011, 21:34 #2 Senior Member   Martin Hegedus Join Date: Feb 2011 Posts: 519 Rep Power: 9 For first order you should only use the bound legs (not the edges) and only for those panels which are on the wing. Do not include the trailing edge bound leg for the last chordwise wing panel since it will be canceled by the leading edge bound leg of the first wake panel. I do not recommend using the side edges to calculate effects of sideslip. If you need sideslip effects you will be better off going to a full panel method. I also recommend that the side edges be parallel to the x-z plane. Do not cant them in or out. Also, if you would like to get thickness effects you will probably be better off going to a full panel method. Pure vortex rings have controlability (i.e. the matrix is stiff) issues as the thickness decreases. You could use source/sink sheets to model thickness. Edit: the vortex ring panels should be placed on the camber line.

June 24, 2011, 22:15
#3
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Ismail Hameduddin
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Quote:
 Originally Posted by Martin Hegedus For first order you should only use the bound legs (not the edges) and only for those panels which are on the wing. Do not include the trailing edge bound leg for the last chordwise wing panel since it will be canceled by the leading edge bound leg of the first wake panel. I do not recommend using the side edges to calculate effects of sideslip. If you need sideslip effects you will be better off going to a full panel method. I also recommend that the side edges be parallel to the x-z plane. Do not cant them in or out. Also, if you would like to get thickness effects you will probably be better off going to a full panel method. Pure vortex rings have controlability (i.e. the matrix is stiff) issues as the thickness decreases. You could use source/sink sheets to model thickness. Edit: the vortex ring panels should be placed on the camber line.
Martin, thanks for the reply. I get a better (closer to the actually values) when I use only the panels as you suggested. I have not been placing the vortex rings panels on the camber line, however.

Also, what are the full panel methods?

June 25, 2011, 03:01
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Martin Hegedus
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Quote:
 Originally Posted by black&gold Martin, thanks for the reply. I get a better (closer to the actually values) when I use only the panels as you suggested. I have not been placing the vortex rings panels on the camber line, however. Also, what are the full panel methods?
Sorry, probably bad terminology on my part. Should have just said panel methods.

If one represents a surface with constant doublet panels then that is the same as a vortex ring. Technically what you mentioned above about representing the top and bottom surfaces with a vortex ring is a panel method. However, most people think of a panel which is represented by both a source/sink and doublet distribution as a true panel method. That is what I meant by a full panel method. PMARC and PANAIR would be true panel methods. PMARC in fact is not that much different than a vortex lattice method. The strengths of the individual source/sink panels are determined independently of all the others panels based on their slope and then their velocity contributions at the control points are moved to the RHS. The doublet panels, i.e. vortex rings, are then solved for with a matrix inversion. A true panel method and VLM differ on how the loads are calculated. The VLM method uses gamma cross V while a true panel method will calculate the pressure based on the tangental velocities at the control point, which includes the tangential velocity contribution due to the change in potential along the surface of the local panel and the edges. A lower order panel method, PMARC, will have potential jumps at the edges which need to be accounted for. Calculating the loads due to these jumps is analogous to gamma cross V. PMARC is based on VSAERO and the VSAERO theory is described here
http://ntrs.nasa.gov/archive/nasa/ca...1990004884.pdf

Glad to hear you're getting better results.

June 25, 2011, 16:23
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Ismail Hameduddin
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Quote:
 Originally Posted by Martin Hegedus Sorry, probably bad terminology on my part. Should have just said panel methods. If one represents a surface with constant doublet panels then that is the same as a vortex ring. Technically what you mentioned above about representing the top and bottom surfaces with a vortex ring is a panel method. However, most people think of a panel which is represented by both a source/sink and doublet distribution as a true panel method. That is what I meant by a full panel method. PMARC and PANAIR would be true panel methods. PMARC in fact is not that much different than a vortex lattice method. The strengths of the individual source/sink panels are determined independently of all the others panels based on their slope and then their velocity contributions at the control points are moved to the RHS. The doublet panels, i.e. vortex rings, are then solved for with a matrix inversion. A true panel method and VLM differ on how the loads are calculated. The VLM method uses gamma cross V while a true panel method will calculate the pressure based on the tangental velocities at the control point, which includes the tangential velocity contribution due to the change in potential along the surface of the local panel and the edges. A lower order panel method, PMARC, will have potential jumps at the edges which need to be accounted for. Calculating the loads due to these jumps is analogous to gamma cross V. PMARC is based on VSAERO and the VSAERO theory is described here http://ntrs.nasa.gov/archive/nasa/ca...1990004884.pdf Glad to hear you're getting better results.
Great...I thought I was doing something wrong. I'll go ahead and try to see if I can code this VSAERO; it seems like exactly what I've been looking for.

Thanks for the help.

June 25, 2011, 18:05
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Martin Hegedus
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 Originally Posted by black&gold Great...I thought I was doing something wrong. I'll go ahead and try to see if I can code this VSAERO; it seems like exactly what I've been looking for. Thanks for the help.
Depending on what your objective is, what you are proposing could take you a few (2-3) man months. If your intent is to do something like just a wing were the wake is easily conceptualized, then that is easier. If you would like to do something like a wing body, then that is more difficult and getting answers can be tricky. Doing a full generic geometry can be even more trickier. The reason is the wake. Some issue are 1) one doesn't really know how the wake connects to the body, 2) determining the loads (for a lower order method like PMARC/VSAERO) on the body panels next to the wake panels is difficult, 3) the wake edge that comes from the root of the wing should remain attached to the body (if it detaches than you'll get large velocities within the gap and this could bang on a control point nearby), and 4) if the wake cuts across another panel, such as those on a tail, it could bang on a control point.

Also, a vortex lattice method (or other methods which do not model thickness) might give you a better answers compared to experiment in regards to lift. The reason is that the real world airfoil/wing has a boundary layer and the VLM has compensating errors, i.e. thickness is not modeled. However, it you are looking for pressures on the top and bottom, and VLM won't help you out unless you make some assumptions.

Your probably on a budget, but you could get PANAIR from http://www.pdas.com/ for \$300. This is a higher order method. For the money you also get a bunch of other codes. I've got a geometry input code (Aero Troll, http://www.hegedusaero.com/software) which is free and you can create simplified geometries. It will not let you do a wing with thickness, but it should help you get an input deck up and running.

June 25, 2011, 22:20
#7
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Ismail Hameduddin
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Quote:
 Originally Posted by Martin Hegedus Depending on what your objective is, what you are proposing could take you a few (2-3) man months. If your intent is to do something like just a wing were the wake is easily conceptualized, then that is easier. If you would like to do something like a wing body, then that is more difficult and getting answers can be tricky. Doing a full generic geometry can be even more trickier. The reason is the wake. Some issue are 1) one doesn't really know how the wake connects to the body, 2) determining the loads (for a lower order method like PMARC/VSAERO) on the body panels next to the wake panels is difficult, 3) the wake edge that comes from the root of the wing should remain attached to the body (if it detaches than you'll get large velocities within the gap and this could bang on a control point nearby), and 4) if the wake cuts across another panel, such as those on a tail, it could bang on a control point. Also, a vortex lattice method (or other methods which do not model thickness) might give you a better answers compared to experiment in regards to lift. The reason is that the real world airfoil/wing has a boundary layer and the VLM has compensating errors, i.e. thickness is not modeled. However, it you are looking for pressures on the top and bottom, and VLM won't help you out unless you make some assumptions. Your probably on a budget, but you could get PANAIR from http://www.pdas.com/ for \$300. This is a higher order method. For the money you also get a bunch of other codes. I've got a geometry input code (Aero Troll, http://www.hegedusaero.com/software) which is free and you can create simplified geometries. It will not let you do a wing with thickness, but it should help you get an input deck up and running.
I am developing the code for use in a larger project. I will only be considering a specific wing (with airfoil, wingspan, etc. specified). I went through the VSAERO manual and it seems quite doable for this particular application. I was taken aback when you said 2-3 man months...is that your experience with it? I have about a 2 week time budget for this part of the project.

The larger project is to incorporate aeroelastic effects into a dynamic simulation of an aircraft. I have a rigid body model of an aircraft with C_L, C_M, functions specified. The plan is to match my panel code results to the given C_L,etc. functions assuming that the majority of lift comes from the wings (since it is a high-aspect ratio design...this seems a reasonable assumption). For this, I cannot ignore the thickness effect of airfoil, etc. Some fudging of parameters may be required to get an exact match.

Once this is done, I incorporate the panel code within the dynamic simulation in lieu of the C_L, etc. functions. The aeroelastic effects can then be handled by simply changing the shape of the wing in the panel code within the simulation. The shape change is determined via the Rayleigh-Ritz method (assumed shapes approach, etc.) with the loads on the wing calculated using the results from the panel code. Yes, I realize this will take a gigantic amount of computing resources (each time step, 0.01-0.02 times the time interval...up to 60 seconds) but I have access to some powerful servers for overnight use.

This is the reason I am developing the code myself and not using something like Tornado or the numerous other packages available out there. I could reasonably reverse engineer these codes to fit my application but I hate to get into a wild goose chase trying to decipher someone else's code especially since I'm not an aerodynamics guy (and they use some advanced methods in these packages) and also the packages are going to be for very general geometries (whereas I only care about the wing).

Since my application is not precisely to be accurate...I think I can get away without needing to do alot of coding. What do you think?

 June 25, 2011, 22:25 #8 New Member   Ismail Hameduddin Join Date: Jun 2011 Posts: 6 Rep Power: 6 Also, I couldn't find any detailed references for coding panel methods apart from the NASA reports; thats one of the reasons I am looking into VSAERO. I have been using Katz & Plotkin, Bertin, Houghton, and some Springer books on computational fluid dynamics but most of these are just gloss overs without much specific information about the codes. It seems they were written so that someone can use and understand commercially available code rather than develop something by themselves.

 June 26, 2011, 03:01 #9 Senior Member   Martin Hegedus Join Date: Feb 2011 Posts: 519 Rep Power: 9 For your purpose is sounds like VSAERO/PMARC would be the way to go, since they would give you results similar to a higher order panel method such as PANAIR. Higher order methods are nice if you want to get off body velocities, for example velocities which are close to a panel edge. Higher order methods are also necessary for supersonic analysis, but I gather that is not your concern. The 2-3 month time frame was for the generic geometry and includes debugging. Rest assured debugging can take a lot of time. Sometimes it is not straight forward to find the bug due to the fact that coefficients influence one another. I've got experience with it. It's painful. The coding part is relatively straight forward. If you are good at coding, and debugging is included in the two weeks, two weeks is cutting it close. You'll need to finish the coding in under a week. Make sure you are alert when coding. Don't pull all nighters. Avoid bugs at all cost. When you are done coding, walk through a print out of the code line by line. Don't assume the code works. To increase your analysis speed, and your deformations are small, you can modify the right hand side to account for the deformations. The LHS matrix only needs to change when there is more than a small geometry change. This will save you the cost of an inversion. Or you can recalculate the inversion at large times steps and change the RHS at small time steps. For example, invert every 1 second and recalculate RHS every 0.01 seconds. Good Luck!

June 26, 2011, 05:55
#10
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Ismail Hameduddin
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Quote:
 Originally Posted by Martin Hegedus For your purpose is sounds like VSAERO/PMARC would be the way to go, since they would give you results similar to a higher order panel method such as PANAIR. Higher order methods are nice if you want to get off body velocities, for example velocities which are close to a panel edge. Higher order methods are also necessary for supersonic analysis, but I gather that is not your concern. The 2-3 month time frame was for the generic geometry and includes debugging. Rest assured debugging can take a lot of time. Sometimes it is not straight forward to find the bug due to the fact that coefficients influence one another. I've got experience with it. It's painful. The coding part is relatively straight forward. If you are good at coding, and debugging is included in the two weeks, two weeks is cutting it close. You'll need to finish the coding in under a week. Make sure you are alert when coding. Don't pull all nighters. Avoid bugs at all cost. When you are done coding, walk through a print out of the code line by line. Don't assume the code works. To increase your analysis speed, and your deformations are small, you can modify the right hand side to account for the deformations. The LHS matrix only needs to change when there is more than a small geometry change. This will save you the cost of an inversion. Or you can recalculate the inversion at large times steps and change the RHS at small time steps. For example, invert every 1 second and recalculate RHS every 0.01 seconds. Good Luck!
Thanks for the tips :-)...even though all-nighters seem inevitable at some point during this project. I realized the complexities of this type of coding (nonlinear panel generation, etc.) while doing my simple VLM program. Even though I commented everything very well and tried to distribute the functions in different files in a structured manner, I still found it very difficult to locate errors and also modify the program structure.

The NASA report actually mentions the higher order methods. It seems a poor choice of singularity elements (in the surface distribution) could cause very large internal cross flow between the upper and lower surfaces of the wings requiring high panel densities to get good accuracies. This problem with low order methods lead to the development of higher order methods, which according to document proved to be unnecessary for subsonic flow. The VSAERO method overcomes this challenge by inverting the problem: specifying the desired internal flow and using this boundary condition to find a source/doublet distribution.

By the way, I saw your website. Best of luck, I hope your company takes off!

 June 26, 2011, 21:17 #11 Member   Tobino Join Date: Jan 2011 Location: Osaka,Japan Posts: 33 Rep Power: 6 Hi, Please teach me what is this and how to know clearly about them: Fluent reporting/ force: pressure resistance; viscous resistance and total resistance. Total resistance = Viscous resistance + Pressure resistance. How I can calculate Frictional resistance in Fluent. Would you help me, thank you so much!

June 26, 2011, 23:51
#12
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Martin Hegedus
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 Originally Posted by tobino Hi, Please teach me what is this and how to know clearly about them: Fluent reporting/ force: pressure resistance; viscous resistance and total resistance. Total resistance = Viscous resistance + Pressure resistance. How I can calculate Frictional resistance in Fluent. Would you help me, thank you so much!
I think you posted on the wrong thread. You'll need to post your question in the Fluent section.

 Tags lift calculation, vlm, vortex lattice method

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