Use of Vortex Lattice Method in Transonic Applications

[Harmonic]

Hi,

I'm looking for an aerodynamic code to model a transonic (say around M=0.8) wing for some basic structural sizing and performance estimation. I'm hoping to use the MATLAB based VLM code Tornado. It has an inbuilt Prandtl-Glauert correction option. I realize that this is technically applicable only below transonic speeds (say M<0.7) but I was wondering if:

1. The span loading outputs would be acceptable for some preliminary design studies and spar/cover sizing?
2. The drag estimates would be useful in any way?

My initial thoughts are that the span loading could be used for preliminary sizing as although the model will not include the effect of shocks, my thinking is that this will be approximately uniform along the span. Therefore a difference in lift (between the P-G correction and a model including shocks) will be the same along the span and so the loading will be the same. How does that sound?

As far as performance estimate goes... Given my above argument I also believed the induced drag values will be usable. I could then tack on viscous and wave drag data and bob's your mother's brother!

I'd really appreciate any thoughts on my reasoning here, if it's good/bad/needs modification, other points to consider that I've missed or suggested relevant reading (as I'm struggling to find anything specifically on this topic). Thanks for reading!

David

 

[RandomGuy88]

I do not think that will work. First, assuming a uniform span load distribution is probably not a great approximation. More importantly though the effects of shocks are not uniform across the span. The shock will not necessarily form everywhere on the wing at once. Even at a sufficient speed to generate a shock along the entire span the shock will not be at the chord wise location and will therefore not affect each part of the wing in the same way.

Transonic flow is harder because the governing potential flow equation is no longer linear.

I do not work in transonic flow so perhaps someone else can provide more insight than me.

 

[Harmonic]

Thanks for your reply random guy.

Just to clarify, I wasn't suggesting that I'd use a uniform span load distribution, because then why use a VLM code at all!

I understand that the effect of the shock will not be the same everywhere on the wing, but I was thinking this might not be too bad a first order model of it to get a span loading, and I suppose that's what I was looking for comments on.

 

[granbycools]

Hi,

I´ve been using LamDes (also some VLM, for modelling lifting surfaces as thin plates)
and the used Prandtl-Glauert correction was insignifcant for high Mach numbers (M>0,8).
The span loading from the planforms calculated with LamDes had an relative error about 15% (validated with Fluent).
Unfortunately I have no experience with tornado.

 

[alphy]

Hi David,

The use of Vortex Lattice Method (VLM) in transonic applications can be a useful tool for preliminary design studies and performance estimation. However, it is important to note that VLM is best suited for subsonic flow and may not accurately capture the effects of shocks in transonic flow.

Regarding the span loading outputs, it is possible to use them for preliminary design studies as you have suggested. However, the results may not be as accurate as using a more advanced method that accounts for shocks. It is important to keep in mind that the lift distribution may change significantly in transonic flow, and therefore the loading along the span may not be uniform.

As for drag estimates, the induced drag values from VLM can be used as a starting point, but again, they may not be as accurate as using a method that accounts for shocks. It would be beneficial to include other sources of drag, such as viscous and wave drag, to get a more comprehensive estimate.

In terms of your reasoning, it is important to consider the limitations of VLM in transonic flow and to use the results with caution. It may also be helpful to compare the results with those from other methods to validate the accuracy.

I hope this helps and provides some insight into using VLM in transonic applications. As for further reading, I would suggest looking into literature on VLM and its limitations in transonic flow, as well as comparing it with other methods such as panel methods or CFD. Good luck with your research!