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I'm used to see images of the boundary layer over a wing like this:

enter image description here
Transition from laminar to turbulent flow over the wing. Left: source, right: source

As many others, these pictures indicate the airflow is laminar over the first portion of the wing. But I was told (in a comment) this cannot happen in a full-scale aircraft, as the Reynolds number involved are not compatible with laminar flow. Would these pictures be misleading?

After some research, I understand the flow in the boundary layer remains laminar until some "quantity" is reached and then it becomes turbulent. The quantity is indeed expressed by the Reynolds number (Re) which is "the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities". Re takes scale effects into account.

At some critical Re, the flow in the boundary layer stops being laminar to become turbulent:

enter image description here
Source

I believe the change happens because of the thickness of the boundary layer increases with Re, but I'm not sure.

Questions:

  1. Can someone clarify the conditions that make a flow transition from laminar to turbulent?

  2. How does this transition relate to the separation of the boundary layer occurring over a wing?

  3. In conclusion, is the flow laminar or not before the boundary layer is separated?

If that matters, let's take two aircraft for velocity values: a C172 and/or a commercial airliner.

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    $\begingroup$ Look here for details on how transition works. $\endgroup$ – Peter Kämpf Apr 7 '17 at 16:27
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In still air every boundary layer starts laminar. How soon it transitions to a turbulent boundary layer depends on:

Flat plate flow (without pressure changes) normally transitions at a Reynolds number of around 400,000. If the flow is accelerated, all speeds in flow direction increase while cross flow will not be affected, so a laminar boundary layer in accelerating flow is stabilized. On modern gliders the lower surface is laminar in excess of 80% chord at higher angles of attack, which can correspond to a Reynolds number of 5,000,000 or more when transition eventually occurs.

On the other hand, a pressure rise in flow direction corresponds to a deceleration in flow direction, so any movements perpendicular to the flow direction will grow relative to the flow speed, and as a consequence the turbulent transition occurs rather quickly. Upper side flow past the suction peak near the leading edge is a prime candidate for transition, and that is what causes flow around the "traditional airfoil" to become turbulent earlier. The graph in your question is misleading because the lower side flow of the traditional airfoil should be as laminar as that of the P-51 airfoil if the surface smoothness of both is comparable.

How laminar was the P-51 wing?

At the flight speed of the P-51 very little laminar flow was left; the full effect of laminar airfoils can only be exploited at Reynolds numbers below 5,000,000. At higher Reynolds numbers it needs progressively steeper gradients to keep the boundary layer laminar, such that the range of angles of attack where a long laminar boundary layer is possible on both sides of an airfoil (the laminar bucket) gets smaller and smaller.

The "rooftop" distribution of the 6-digit NACA airfoils did help, though, because it gives them a higher critical Mach number than the "peaky" distributions of earlier airfoils. The suction peak near the nose of older airfoils will lead to local supersonic flow at a lower flight Mach number, and increased drag from the shocks which would follow. Most important for its low drag, however, was the very smooth wing surface of the P-51 with no gaps ahead of the spar. See this article for details.

Influence of Sweep

Wing sweep will also make it hard to maintain laminar flow. As explained here, on a swept wing only the speed component perpendicular to the wing will be affected by it, so the accelerating flow past the stagnation point will curve inwards on a sweptback wing. At the same time, viscosity will slow down the flow near the wing skin. The consequence is a twist in the speed distribution over the boundary layer, which destabilizes the laminar flow and leads to early transition.

A C-172 with its four-digit NACA airfoil has the peaky upper surface which will trip the boundary layer very early on the upper surface. On the lower surface laminar flow will last a little longer but will be destabilised by gaps in the surface, so most of the flow on the C-172 is turbulent. On an airliner the Reynolds number is in the tens of millions, so transition will be very early and very little laminar fraction remains. This is mostly found near unswept leading edges like the engine nacelles. Only with advanced technologies like boundary layer suction will it be conceivable that a larger part of an airliner wing can be kept laminar.

Transition and Separation

Laminar separation sometimes happens when the flow separates shortly after negotiating the nose, like on a five-digit NACA airfoil or an undimpled golf ball. This leads to an abrupt stall and should best be avoided. Normally, the boundary layer transitions into the turbulent state and stays attached until the turbulent boundary layer separates, either at the trailing edge, or progressively further ahead of it when the airfoil stalls.

Sometimes, transition happens in a laminar separation bubble. The decelerating flow past the suction peak is slowed down by friction near the surface, and both effects combine to bring the flow to a standstill at some point. The boundary layer thickens, such that the pressure rise is momentarily suspended, and speed oscillations in the boundary layer get amplified such that cross flows become more intense, mixing outer and inner parts of the boundary layer. The speed profile becomes fuller and the flow near the wall picks up speed again, such that the separation disappears and pressure rise resumes.

Below I plotted the XFOIL results for the pressure distribution around the HQ-17 at Re = 1 Mio (the HQ-17 is used on the ASW-22 Open Class glider, for example). The dashed, black lines show the inviscid pressure while the colored lines show the viscous flow results. On both sides you will see a kink in the colored lines - this is where the laminar separation bubble is.

Pressure distribution around the HQ-17 at Re = 1 Mio.

When the flow separates, the pressure line becomes horizontal. After transition it jumps back down near the inviscid line, which shows how much steeper the pressure gradient is that a turbulent boundary layer will tolerate. Reattachment is complete when the steep pressure rise has brought the local pressure back near the inviscid level. Note in the airfoil plot at the bottom that the boundary layer thickness peaks where the separation bubbles are.

Yes, the boundary layer is laminar before and into the separation here. This phenomenon occurs at the scale of model aircraft, gliders and small GA aircraft (100,000 < Re < 5,000,000) but is absent at higher Reynolds numbers because then the transition happens before the laminar flow separates.

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Reynolds number is basically the ratio between the viscous and inertial forces acting on the system. At low Reynolds numbers, the viscous force is dominant compared to the inertial force and it is the other way at higher Reynolds numbers.

The effect of the viscosity can be considered analogous to the dampers in a car suspension. If the damping is good, the suspension eats up any bumps on the road and the ride is smooth. In case of fluid flow, if the viscous term is dominant (i.e. if the Reynolds number is low), small disturbances in the velocity field, caused by perhaps surface roughness or vibrations, are not allowed to grow and the flow is smooth; however, as the Reynolds number increases, the viscous damping reduces and the small disturbances in the fluid field can grow and the flow becomes erratic i.e. turbulent. The flow can also become unstable due to resonance.

It's important to note that the turbulent flow (which is found over most of the commercial aircraft wings) is different from separated flow. Flow over most of the wing is turbulent, but attached. The Reynolds number of large commercial aircraft increases over the wing at the rate of over a million per foot. In these cases, the flow is rarely, if ever, laminar. In fact, Boeing admits:

Current Boeing commercial airplanes are not expected to have significant regions of laminar flow, with the exception of the 787 nacelles near the inlet lip, as expressly designed. There may be very limited regions of laminar flow near the leading edges of wings, especially lesser swept wings such as used on the 737 and 757, and blended winglets.

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