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A well known idea is that for aerodynamic/streamlined bodies the friction drag is larger than pressure drag. Hence, a laminar boundary layer is preferable (only looking at minimal drag, no other design conditions).

Then, looking at the figure below it can be seen that the drag coefficient decreases with increasing Reynolds number, even at low angles of attack where one would not expect any significant flow separation. Also, up to Re 500000 one could expect laminar flow, but 'for sure' at Re 200000.

Is the XFOIL simulation realistic, or are there assumptions in the code which imply this behavior?

XFOIL prediction of a NACA 63-421 profile

lWindy
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  • Why do you expect a drag coefficient increase? Lower $c_{\textrm{d}}$ at higher Re-Numbers is the expected behavior (e.g., see the figures for a sphere https://aviation.stackexchange.com/a/24755/8749 or a flat plate https://aviation.stackexchange.com/a/71276/8749) – Gypaets May 12 '22 at 08:36
  • Well, I am talking about the ratio of friction drag and pressure drag (assuming XFOIL does not use induced drag). Also, I am not talking about a strict increase over all values for the angle of attack.

    But, given a low alpha where it is reasonable to assume that there is no flow separation (hence very little to no pressure drag) I expect the friction drag to be dominant. This is in turn lower for laminar flow i.e. Re < 5 * 10^5. I expect a cross between Re 200000 and Re2000000 at an angle where flow separation occurs.

     – lWindy May 12 '22 at 11:25
  • @Gypaets Also, case 2 in aviation.stackexchange.com/a/71276/8749 states that friction drag is dominant. Even more, at low Re i.e. laminar flow, the friction drag is lower. This is the reason for my question – lWindy May 12 '22 at 11:29
  • Are you graphing Clift/Cdrag vs alpha, or just Cd vs alpha? Assuming you are, as Velocity increases (more so than chord), your graphing would show these effects as Re increases. My guess is we are looking at the same airfoil, sped up. This would be a viscosity effect. – Robert DiGiovanni May 12 '22 at 13:00
  • @RobertDiGiovanni You are correct. The y-axis label should be C_d only. I have plotted a NACA 63 421 airfoil. – lWindy May 12 '22 at 15:18
  • @RobertDiGiovanni I still do not understand why the drag coefficient decreases? That is, assuming at low angle of attacks there is almost no pressure drag and friction drag is dominant. Therefore, low Re (laminar BL) should give lower Cd values – lWindy May 12 '22 at 15:20
  • Did you carry out those calculations/simulations with XFOIL yourself? If you did, please check where the laminar-turbulent transition takes place. I am assuming that XFOIL determines the flow to be laminar for all Reynolds numbers for a pretty large part of the chord, so the high Re = low c_d relation will be dominant over higher Re => earlier transition => more drag. – Raketenolli May 12 '22 at 16:44

1 Answers1

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Aerodynamic friction is caused by viscosity. The Reynolds number tells you how big viscosity is in relation to inertial forces. A bigger Reynolds number signifies lower viscosity. This means a higher Reynolds number almost always results in a lower friction coefficient. If you look at the plot below, the downward trend can be easily spotted.

Friction drag coefficient of a flat plate over Reynolds number
Friction drag coefficient of a flat plate over Reynolds number (picture source). Note the double logarithmic axes.

If your airfoil is not designed to keep the boundary laminar, a higher Reynolds number always means less friction. For laminar airfoils at low angle of attack that special spot between laminar and turbulent flow can indeed mean a drag increase with higher Reynolds number, but that occurs normally only at the edges of the laminar drag bucket.

Within the laminar drag bucket and outside of it the laminar-turbulent transition is very gradual with a small forward shift of the transition point for an increase in the Reynolds number of several hundred thousand counts.

Peter Kämpf
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    Excuse me for the (very) late reply; I disagree with your statement 'his means a higher Reynolds number almost always results in lower friction'. This is only true for the case where there is a turbulent boundary layer. My questions is aiming at why at low Re (assuming initial laminar BL) the Cd is higher using XFoil. See for example the difference in Cd at Re 5e5. Clearly, laminar is preferred over turbulent and is it in general not safe to assume that low Re have still laminar conditions? – lWindy Nov 21 '22 at 12:15
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    @lWindy Guess why I used the "almost" weasel word: This is to account for the transition when laminar runs get shorter with Re and the drag coefficient within the laminar drag bucket increases with Re. But that happens only in a small AoA range and for Reynolds numbers between 100,000 and a few million. Your polar at Re = 0.55 million suffers from large separation bubbles at the transition point and will become better with turbulators, so the boundary layer is tripped a bit sooner. – Peter Kämpf Nov 21 '22 at 16:03