Hi I am currently analyzing different wing designs using ANSYS Fluent. One of my designs has a straight leading edge but a swept trailing edge thus it is tapered with wing root chord at 50mm and wing tip chord at length 200mm. Wing span is 250mm. (See Picture) The airfoil shape used is the S1223 which has a CL max around 2.3. Therefore using the Lift formula which (i know is approximate), I calculate the wing can produce 58.5N of lift at 36.452m/s.

However using ANSYS Fluent I find the wing can only produce a maximum of 39N of lift which is a CL of 1.5.

I am fairly certain the simulations I'm running are accurate but need advice on what could be causing this difference. Assuming the results I've obtained are correct. What is the reason for the large difference in coefficient of lift ? Let me know if I need to provide any additional information! Any help greatly appreciated! EDIT : Forgot to add that the simulation used assumes the wind tunnel boundary is at wing tip and wing root. Thus the wing span takes up the full wind tunnel. Wing Design

Pressure contour at high AoA

Pressure contour at wing tip

XFLR5 2D Analysis Cl vs AoA

Fluent Tapered 3D CL vs AoA

  • $\begingroup$ the image seems to show the wing inverted -- are you measuring lift in the correct direction for the camber? $\endgroup$ – Zeiss Ikon Apr 10 at 15:45
  • $\begingroup$ Not sure what you mean by "wind tunnel boundary". You should set the plane corresponding to wing root to be symmetry boundary condition. There should be no boundary on the tip except the normal wall boundary for near field. The far field should be velocity inlet and the trefftz plane should be pressure outlet. $\endgroup$ – JZYL Apr 10 at 15:55
  • $\begingroup$ I'm actually measuring the downforce that the wing produces so yes I am measuring in the correct direction @ZeissIkon Thanks for your response. $\endgroup$ – James Green Apr 10 at 16:30
  • $\begingroup$ @JZYL I had set the boundaries to be at the tip and root for the time being, just to determine coefficient of lift neglecting any wing tip vortices. Both were set to be symmetry boundary condition. I have just corrected this according to your advice however there is no change in the lift value I am getting. However there is a small increase in drag. Thanks for your response $\endgroup$ – James Green Apr 10 at 16:36
  • $\begingroup$ what is your question? $\endgroup$ – Manu H Apr 10 at 19:42

By tapering the wing you have in effect a 3D case even if the wing is sitting between wind tunnel walls. Lift varies along span almost as if the wing would be in free flight with twice the span and the long chord at the root. Since tip chord is only a quarter of root chord, that full wing would have 0.075 m² area with 0.5 m span, giving it an aspect ratio of 3.33. Below is a figure from Sighard Hoerner's book Fluid Dynamic Lift (Chapter 3, Figure 4) which shows how the local lift coefficient varies over span for wings of different taper ratio. Your wing in free flight would be ¾ between the second and third from the left.

Hoerner Fluid Dynamic Lift, Chapter 3, Figure 4

A 2D case is only possible with constant chord as all of the wing would produce the same circulation (lift times chord). With the varying chord along span only the shorter end will reach the maximum lift coefficient of 2.3 locally, but at a lower angle of attack. You still get more lift with your wind tunnel walls than in free flight, but with a taper ratio of 0.25 not much of the 2D case is maintained.

The higher circulation of the long chord end produces extra circulation on the short chord end and lets it stall at a lower angle of attack when the root has only reached half of its full potential (see figure above where center lift coefficient is only half of the tip lift coefficient). The reduction in maximum angle of attack from -13° for the 2D case to -10° also shows how much potential lift is lost.

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  • $\begingroup$ thanks very much for your time and answer. Greatly appreciated. So as I understand only the shorter chord length reaches maximum lift coefficient? But the long chord end has higher circulation ? I though lift was directly proportional to circulation. Or are you saying that this is true however due to the large difference in circulation there is surplus circulation on the shorter chord length leading to loss of lift ? $\endgroup$ – James Green Apr 13 at 11:51
  • $\begingroup$ @JamesGreen Yes, only the shorter end reaches maximum lift and does so at a lower AoA. See the first kink in the lift curve slope: I expect that it is caused by separation onset on the short end. While the lift on the long end increases with increasing AoA, the short end stalls already. Did you try washout (different incidence between root and tip)? Regarding circulation: Yes, it is proportional to lift and high root circulation causes an AoA increase at the tip which lets it stall prematurely. $\endgroup$ – Peter Kämpf Apr 13 at 12:23

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