Use of Vortex Lattice Method in Transonic Applications

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Discussion Overview

The discussion revolves around the use of the Vortex Lattice Method (VLM) for modeling transonic wings, specifically at a Mach number of around 0.8. Participants explore the applicability of the Prandtl-Glauert correction in this context, and its implications for span loading and drag estimates in preliminary design studies.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant, David, proposes using the Tornado VLM code with Prandtl-Glauert correction for preliminary design studies, questioning if span loading outputs and drag estimates would be acceptable despite the correction's limitations at transonic speeds.
  • David argues that span loading could be approximately uniform along the span, suggesting that differences in lift due to shock effects would not significantly alter the loading distribution.
  • Another participant counters that assuming uniform span load distribution is a poor approximation and highlights that shock effects are not uniform across the wing, complicating the analysis.
  • A third participant shares their experience with LamDes, noting that the Prandtl-Glauert correction was insignificant at high Mach numbers (M>0.8) and reports a relative error of about 15% in span loading when validated with Fluent.

Areas of Agreement / Disagreement

Participants express differing views on the validity of using the VLM code with Prandtl-Glauert correction for transonic applications. There is no consensus on whether the span loading outputs and drag estimates would be reliable for preliminary design studies.

Contextual Notes

Participants note limitations regarding the assumptions of uniform span loading and the effects of shocks, indicating that the governing potential flow equations become non-linear at transonic speeds. The discussion reflects a range of experiences with different modeling tools and their applicability to transonic flow.

Harmonic
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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
 
Last edited:
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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.
 
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.
 
Last edited:
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.
 

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