I have a problem which might seem simple to most of you CFD specialists out there.

I have an airfoil mounted in an Inviscid Transonic Flow (Governed by Eulers Equations) performing a prescribed periodic motion in Pitch and Plunge. These periodic motions are described by a Fourier Series with a specified number of terms.

Ideally I would want to consider the motion of the airfoil over the duration of a single time period, and calculate the Lift and Pitch Moment Coefficient of the Airfoil.

What would be the best approach to tackle this problem, and are there any free aerodynamic codes out there that I could use to tackle this problem, since I'm incapable of developing these codes or grids myself.

You might try ins2d...what is the desired outcome of your simulation? Are you just interested in getting the integrated quantities or are you doing some sort of system identification? Also I wouldn't shortchange yourself..with a couple of months time you should be able to develop a 2D Euler code to your liking..also if you are just looking at harmonic motions you might want to try and code up a harmonic balance type solution which will save you some computational time since you won't have to integrate through any transients.

Hi Peter,

Thanks very much for the quick response, it is very much appreciated. Your response is very much in the direction I'm travelling.

Ideally I would like to know the values of the Lift and Moment Coefficients over the duration of the time period, at equally spaced time intervals. An unsteady Euler CFD code will give me this information, I am told.

With this information I'll be able to curve-fit the data into a trigonometric series function which describes the variation of the lift and moment co-efficients with time over the duration of this time period.

Initially, I'll be using this information for Harmonic Balance Analysis, and then build on that. I'd really like to try to develop a code but unfortunately time is not on my side. I'll check out the Ins2d you've recommended and keep you posted. Cheers

What Peter was referring to is a solution (not just post-processing) method based on harmonic balance, as opposed to a time-marching unsteady flow solver. Since the airfoil motion is periodic (and it seems that it's already given as a Fourier series) it could be a perfect application for a harmonic balance method. Simply speaking, the HB method is different from time-marching in applying the specified periodicity as a constraint to the problem by using Fourier modes to discretize the flow (derivatives) in time. As a result you'll get the whole period in one shot (or the Fourier coefficients, if done in the frequency domain).

I just don't know if there are any HB codes (either free or commercial) available. If you find one, let us know.

If you're unfamiliar with the HB concept, and you just want to get going quickly, stick with time-marching.

Cheers Mani, Thats exactly I am looking for, a 'time-marching unsteady flow solver'. I know it could done more efficiently in the frequency domain, rather than having to do the time marching for single period and then decompose time series data for Cl and Cm into Fourier coefficients. The truth is my knowledge on CFD is fundamental. So I intend to stick with the time-domain approach, after all its only for single period of the motion. I've tried the ins2d recommended by Peter, but it looks like an incompressible flow solver. So I need to find a 'time-marching unsteady transonic flow solver'. I've been informed that I need an Euler rather than a Navier-Stokes solver for the problem i'm solving. Any recommendations.

Duke and Stanford groups have spectral in time flow codes..not sure of the availablity though.

INS2D is an incompressible solver. He needs to capture shocks as they change during the pitch/plunge. A compressible flow code would be more appropriate.

Yeah I thought ins2d was compressible..sorry about that.

Would it be sensible for me to consider developing a 'time-marching unsteady Euler code' for this problem. I'm proficient in MATLAB, my knowledge of CFD is fundamental and limited to steady flows, and I only have 3 months to develop this code.

Good question..I don't know how much you know about CFD/fluid dynamics and numerical methods. Most free codes aren't going to be all that user friendly so it might take you a month just to figure out how to use the code. If you have a boss..I would talk to him about it. Let him know of the various scenarios..let him make the decision..: )

A free code might still be the way to go though. You have a lot on your plate doing this from scratch: coding up not just the unsteady Euler equations but also a grid motion scheme and the contributions to the fluxes from the grid motion.

If you need further infos about using a time-marching CFD code to build up generalized aerodynamic forces in the frequency domain I suggest having a look at my article on-line http://www.aero.polimi.it/%7Equaranta/Papers/IFASD-2005-1.pdf. Good luck. Luca

Thanks very much Peter, Mani, PC and Luca, I appreciate your help very much and your suggestions. I've reviewed the situation very carefully and I know that I need an 'unsteady time-marching Euler code' and if I am to use it in the very near future, I'll have to get a free code online or purchase it. Any suggestions as to where I can get one of these? What about the cost, if I indeed have to purchase a code? Is it astronomical?

If cant a free Euler code or a reasonably-priced one I'll buy the books and learn how to develop one myself. Although I'll have to wait for about a year I think before I'll have it done.

I've just thought about a more obvious approach, can I tackle this time-marching unsteady Euler problem in FLUENT?

Of course..if you have it. I've never used it so I don't know how well it handles moving grids,etc. I'm sure it can be done but you may have to code some user routines yourself. Also I don't think it has an Euler solver per se. but you can probably fudge around to get it behave like one.

BTW since my research is in aeroelasticity, may I ask where you got your degree and what type of research you are involved in at the moment?

I got my degree in the University of Manchester, in Aerospace Engineering and i'm now a research student in Non-Linear Aeroelasticity so I'm looking at things like LCO's in Aeroelastic Systems with Structural Non-Linearities. Some of the stuff I've done has been reasonably successful so I want to extend it to Aerodynamic Non-Linearities, i.e. Moving Transonic Shockwaves, and probably stall flutter.

So you work with Cooper I'm guessing?

The name rings a bell! Just kidding, he's my supervisor. He must be popular then. How about you, where do you do your research?

You would be better with a viscous solver. You should ask your supervisor whether he can get a copy of Ken Badcock's (Liverpool Uni) PMB solver for you to use (it will solve your problem and much more beside).