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Thread: Scaled-Up Airfoils???

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    Registered User Aerowerx's Avatar
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    Scaled-Up Airfoils???

    I have learned the hard way about Reynolds numbers and scaling airfoils. Fortunately it was a virtual crash and burn.

    What I had done was create my full-size XFLR5 model using the PRANDTL-D airfoils, which I think are Horten-like in design. This did not work at all when dynamically scaled to 1/8th or even 1/5th scale.

    But then I changed to a Hepperle MH46, because it had the same 12% thickness and was made for lower Reynolds numbers (besides low pitch moment). After a it of tweaking, all the models worked fine.

    Since the MH46 was designed for the lower Reynolds numbers, my question is: Are there any problems with scaling an airfoil up in size to use at higher Reynolds numbers?
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    Re: Scaled-Up Airfoils???

    Do you have a drag polar at the lower and higher Re?
    ​simplify.

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    Re: Scaled-Up Airfoils???

    Quote Originally Posted by Aerowerx View Post
    I have learned the hard way about Reynolds numbers and scaling airfoils. Fortunately it was a virtual crash and burn.

    What I had done was create my full-size XFLR5 model using the PRANDTL-D airfoils, which I think are Horten-like in design. This did not work at all when dynamically scaled to 1/8th or even 1/5th scale.

    But then I changed to a Hepperle MH46, because it had the same 12% thickness and was made for lower Reynolds numbers (besides low pitch moment). After a it of tweaking, all the models worked fine.

    Since the MH46 was designed for the lower Reynolds numbers, my question is: Are there any problems with scaling an airfoil up in size to use at higher Reynolds numbers?
    Yes, there are. One way to look at Reynolds numbers is that they account for the fact that boundary layers don't (hardly) scale. This leads to all kinds of different effects. As an example, a very pointy section (i.e. small nose radius) can work perfectly in low Re enrvironment, while it will give you abysmal stall characteristics in high Re regimes.

    (In extremis have a look at "sections" deployed by insects. They fly fine, but only with very low re numbers ~10^2).

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    Re: Scaled-Up Airfoils???

    The only problem might be at higher Reynolds numbers the boundary layer might transition to turbulent on the upper surface sooner than at the lower Re giving a smaller maximum lift coefficient. You should be able to simulate this using an empirical method like XFLR5. If you increase the Re number and the boundary layer starts transitioning to turbulent on the upper surface sooner, you will be seeing this effect.
    Doug

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    Re: Scaled-Up Airfoils???

    And this is one of the issues with using even a dynamically-scaled model to "flight test" the full-size aircraft. You need to design the model for the flight environment in which it will operate and, as you've seen with Reynold's Number, that can mean the two aircraft are substantially different in many ways. Which begs the question as to how applicable the scale-model results will be to the full-size aircraft.

    The best use of a scale model - dynamic or otherwise - is to test your design methods. If you design the model to be grossly the same as the full-scale aircraft, but design the model as a model, and if the model performs as your methods predict it should perform, then you have one data point that validates your design methods. Which gives you confidence towards applying them to a full-scale aircraft.
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    Re: Scaled-Up Airfoils???

    Airfoils are designed for a particular Reynolds number range.
    An airfoil catalog, such as from Eppler, will have a chapter for each Reynolds range.

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    Re: Scaled-Up Airfoils???

    Quote Originally Posted by Aerowerx View Post
    Since the MH46 was designed for the lower Reynolds numbers, my question is: Are there any problems with scaling an airfoil up in size to use at higher Reynolds numbers?
    Yes. There's a region on the airfoil called a "transition ramp" where the pressure gradient changes from favorable to unfavorable. At high Re transition to turbulent flow happens over a very short distance so airfoils designed for high Re have very short transition ramps. At low Re the situation is a bit more complicated. The natural transition point moves forward with AoA, or at least it can if the transition ramp is long enough. Low Re flow can stay laminar pretty far aft into the unfavorable pressure gradient if the gradient isn't too steep. By making a long transition ramp the low Re flow can transition near the trailing edge at low AoA and move forward slowly as AoA is increased, resulting in a small bubble with low drag throughout the range of AoA. If you operate that low Re foil at high Re the long bubble ramp doesn't work so well because the high Re flow transitions at the point of minimum pressure (near the point of maximum thickness) resulting in high friction drag. On the other hand if you operate an airfoil designed for high Re (with a short transition ramp) at low Re the flow will separate at the minimum pressure point resulting in a big separation bubble and high pressure drag. By default graph 4 in XFLR5 shows the upper surface transition point (the one labeled "Xtr t" on the X axis). Notice that the curve for the Prandtl-D root airfoil on that graph has a long, nearly vertical, segment at about 55% of the chord but the curve for the MH-46 has a long sloping segment from about 75% at cl=0 to 5% at cl=0.88? That's the effect of a long bubble ramp in the MH-46's pressure distribution. However this is an efficiency issue and shouldn't have much affect on stability.

    Reflexed airfoils have a similar problem on the bottom surface that does affect stability. There will be a very short run of adverse pressure near the trailing edge because of the reflex and this could cause a laminar separation bubble that will change the pitching moment of the airfoil. Graph 3 shows the Cm plot. Notice that in the smooth condition the Cm curves of both airfoils have a couple of kinks in them but the excursion is much bigger for the Prandtl-D than the MH-46. This will definitely affect stability. Forcing transition on the lower surface will smooth out those lines. How closely this reflects physical reality is hard to say but I do know that some full size sailplanes have a trip strip on the lower surface of the wing near the control surface hinge.
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    Re: Scaled-Up Airfoils???

    Wait, I thought that the Scale Effect was a possitive outcome from 1-9 10^6 Re, as the skin friction with a turbulent boundary layer decreases as Re increases? Is this not the same a high Re numbers... only subsonic flights and in the rage explained (need to check if that is the limits, but that's my mental note) I recall reading something in Chapter 5 of Theory of Wings to support this...

    The biggest problem is, using an airfoil designed Re 1<10^6 and scaling it below that Re... going the other way should prove positive... hence numerical theory predicts that higher Re yields higher Cl as the turbulent boundary layer is moved backwards on the airfoil... flattening out the parabola (slightly) as you increase Re...

    Maybe I'm having one of those brain farts today... but this is what I thought...

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    Re: Scaled-Up Airfoils???

    Quote Originally Posted by SpainCub View Post
    Maybe I'm having one of those brain farts today... but this is what I thought...
    Yes, farts can also transition from laminar to turbulent (depending on Reynolds Number, of course).

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    Re: Scaled-Up Airfoils???

    Quote Originally Posted by bmcj View Post
    Yes, farts can also transition from laminar to turbulent (depending on Reynolds Number, of course).
    Sometimes they break the sound barrier, I think.

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    Re: Scaled-Up Airfoils???

    The note on Hepperle's web site says the MH46 is good for Re above 100,000, but what does that mean?

    On my smartphone so am not sure but IIRC my scale model is at Re about 400,000 to 500,000. The full size one is about 8 to 10 times that.

    As I said, both look good in XFLR5, even with the self.trimming flaps at 60 degrees
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    Re: Scaled-Up Airfoils???

    Quote Originally Posted by Aerowerx View Post
    The note on Hepperle's web site says the MH46 is good for Re above 100,000, but what does that mean?

    On my smartphone so am not sure but IIRC my scale model is at Re about 400,000 to 500,000. The full size one is about 8 to 10 times that.

    As I said, both look good in XFLR5, even with the self.trimming flaps at 60 degrees
    A 2.5ft profile at 200mph is about Re 4.5M at 5k feet density. At least that is the one I was just doing so I know that is about correct.
    Jay K.

    VT USA

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    Re: Scaled-Up Airfoils???

    Easy way to guess at Reynolds number. Just remember:
    One foot wing and 100mph = 1 million RN (more or less)

    So a 6 inch wing and 100 mph = 1/2 million
    And a 4 foot wing at 100 mph = 4 million or a 4 foot at 50 mph = 2 million. And so on.

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    Re: Scaled-Up Airfoils???

    Quote Originally Posted by BBerson View Post
    Easy way to guess at Reynolds number. Just remember:
    One foot wing and 100mph = 1 million RN (more or less)

    So a 6 inch wing and 100 mph = 1/2 million
    And a 4 foot wing at 100 mph = 4 million or a 4 foot at 50 mph = 2 million. And so on.
    What? Your formula doesn't include distance from the center of the earth, the adiabatic laps rate, and temperature in degrees Rankin? I've been doing this all wrong!
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    Re: Scaled-Up Airfoils???

    Quote Originally Posted by BBerson View Post
    Easy way to guess at Reynolds number. Just remember:
    One foot wing and 100mph = 1 million RN (more or less)

    So a 6 inch wing and 100 mph = 1/2 million
    And a 4 foot wing at 100 mph = 4 million or a 4 foot at 50 mph = 2 million. And so on.
    Much closer if you use knots rather than mph.
    One foot & 100mph -> 0.93*10^6
    One foot & 100kt -> 1.07*10^6

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