Low Reynolds Number Effects on the Aerodynamics of Unmanned Aerial Vehicles.

P. Lavoie

AER1215 Commercial Aviation vs UAV

Classical aerodynamics based on inviscid theory

Made sense since viscosity effects limited to a very small region near the surface

True because

inertial forces 2 1 Ul 6-8 Re = = ⇢U (µU/l) = 10 viscous forces ⌫ ⇠

AER1215 - Lavoie 2 Commercial Aviation vs UAV

Lissaman (1983)

AER1215 - Lavoie 3 Commercial Aviation vs UAV

For most UAV 103 Re 105  

As a result, one can expect the flow to remain laminar for a greater extent flow field. This has fundamental implications for the aerodynamics of the flow.

AER1215 - Lavoie 4 Low Reynolds Number Effects

Lissaman (1983)

AER1215 - Lavoie 5 Low Reynolds number effects

At high Re, the drag is fairly constant with lift

As low to moderate Re, large values of drag are obtained for moderate angles of attack

What is going on? How to explain all this?

Lissaman (1983)

AER1215 - Lavoie 6 The Boundary Layer

To understand what is going on, let us investigate the boundary layer a bit more closely. First, governing equations

@ (⇢u) @ (⇢v) Mass conservation + =0 @x @y x-momentum conservation @u @u @p @ 4 @u 2 @v @ @v @u ⇢u + ⇢v = + µ + µ + @x @y @x @x 3 @x 3 @y @y @x @y  ✓ ◆  ✓ ◆

AER1215 - Lavoie 7 Boundary Layer Equations

After some blackboard magic…

@ (⇢u) @ (⇢v) Mass conservation + =0 @x @y

x-momentum conservation @u @u dp @ @u ⇢u + ⇢v = e + µ @x @y dx @y @y ✓ ◆

AER1215 - Lavoie 8 Flow Separation

What is the momentum equation at the surface (assume constant viscosity)?

Blackboard magic…

Fluid is doing work against the adverse pressure gradient and loses momentum, until it comes to rest and is driven back by the pressure.

AER1215 - Lavoie 9 Laminar vs Turbulent Flow

At “high” Re, shear flows become unstable leading to velocity fluctuations - namely, turbulence.

Consider the case of the boundary layer.

Something happens that leads to higher shear at the wall and thicker boundary layer. But what?!

AER1215 - Lavoie 10 Average Effect of Fluctuating Velocities

Let us introduce Reynolds decomposition…

Blackboard Magic…

@u @ @ @ ⇢ + ⇢ u2 + u 2 + ⇢ u v + u v + ⇢ u w + u w @t @x 0 @y 0 0 @z 0 0 h i ⇥ ⇤ ⇥ ⇤ @p @⌧ @⌧ @⌧ = + xx + yx + zx @x @x @y @z

Extra terms, Reynolds stresses, imply an increase in momentum mixing - hence, fuller velocity profiles and viscous influences further away from the wall.

AER1215 - Lavoie 11 Transition

Ux Laminar boundary layer becomes more unstable as Re = increases. x ⌫ At some critical point, transition to turbulence occurs. Transition process affected by: 1. surface roughness, 2. freestream turbulence, 3. adverse pressure gradients. Re 4 105 cr ⇠ ⇥

AER1215 - Lavoie 12 Laminar Separation Bubbles

Laminar separation can often lead to “laminar separation bubbles”.

Häggmark et al. (2000)

AER1215 - Lavoie 13 Laminar Separation Bubbles

5 SD7003 for Re =6 10 at 4 ⇥

AER1215 - Lavoie 14 Laminar Separation Bubbles

The bubble can be short or long. Location is very dependent on conditions.

SD7003 Re =6 104 ⇥

Lian & Syhy (2007) AER1215 - Lavoie 15 Effect on lift (SD7003)

AER1215 - Lavoie 16 Effects on Lift/Drag Polar

Very high drag for moderate lift.

Non-linear changes.

AER1215 - Lavoie Lyon et al. (1983) 17 What else can go wrong!?

History matters!

Makes sense - easier to keep an attached boundary layer attached, than to reattach a separated shear layer.

AER1215 - Lavoie Mueller et al. (1983) 18 What else can go wrong!?

AER1215 - Lavoie Huber II & Mueller et al. (1987) 19 Improving Performance

Design for the purpose

Cause early transition • vortex generator • boundary layer trip • “turbulator” features

AER1215 - Lavoie 20 Summary

•UAVs are generally low Re number flying devices.

•Laminar separation has implications on performance •lower lift to drag ratio •more complex aerodynamic stability •non-linear lift slop •hysteresis

•Experimental study can be more tricky - more sensitive to boundary conditions (e.g., free stream turbulence, three-dimensional effects).

•Low flight speed also make them more susceptible to outside perturbation (e.g., wind gust)

AER1215 - Lavoie 21 References

- Haggmark, Bakchinov & Alfredsson (2000) Experiments on a two-dimensional laminar separation bubble. Phil. Trans. Math. Phys. Eng. Sci. 358:3193-3205. - Huber II & Mueller (1987) The effect of trip wire roughness on the performance of the Workman FX 63-137 airfoil at low Reynolds numbers. Exp. Fluids 5:263-272. - Lissaman (1983) Low-Reynolds-number airfoils. Ann. Rev. Fluid Mech. 15:223-239. - Lian & Shyy (2007) Laminar-turbulent transition of a low Reynolds number rigid or flexible airfoil. AIAA J. 45(7):1501-1513. - Lyon, Broeren, Giguère, Gopalarathnam & Selig (1997) Summary of Low- Speed Airfoil Data - Volume 3. Department of Aeronautical and Astronautical Engineering, University of Illinois at Urbana-Champaign. - Mueller, Polen, Conigliaro & Jansen (1983) The influence of free-stream disturbances on low Reynolds number airfoil experiments. Exp. Fluids 1: 3-14.

AER1215 - Lavoie 22