# How does Reynolds Number affect skin friction drag?

I'm an aerospace engineering student, and I'm worried about efficiency as it relates to high and low Reynolds numbers. I don't understand which is more helpful for a aircraft.

On a website I read this:

If the Reynolds Number is large, the viscosity effect is small. For the for us practical values the inertia or density forces dominate, and the parasite drag increases with the square of the velocity. However, although the viscosity is unimportant, it may still affect the very thin boundary layer, leading to the creation of turbulent flow. Thus the importance of the Reynolds Number is that it tells us the type of flow we can expect. It tells you whether you can hope for having laminar flow over the wing and other parts of your airplane. A low Reynolds Number gives laminar flow while a high Reynolds Number gives turbulent flow. For both a laminar and a turbulent boundary layer increasing Reynolds Number gives lower skin friction drag. However, because of the higher energy loss in the boundary layer, a turbulent layer always has higher skin friction drag.

In this, there is something like this: For both a laminar and a turbulent boundary layer, increasing Reynolds Number gives lower skin friction drag. I didn't understand the meaning of that statement.

Is there a rule like "Higher Reynolds number, higher drag force"?

And what exactly do parasite drag and boundary layer do? And what do their vastness or rarity contribute to?

Simply: how big should a Reynolds number be for an aircraft to be efficient?

First of all, friction is bad for efficiency. It slows moving things down and needs a constant energy supply to be overcome. The more friction, the more energy has to be supplied, and this energy is lost as heat.

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 lower friction. If you look at the plot below, the downward trend can be easily spotted.

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

Is there something like " higher Reynolds number, higher drag force " stuff ?

Yes, sometimes. Please look at the transition curve: Here a flow which is initially fully laminar slowly changes with increasing Reynolds number into one with a laminar start and a transition to turbulent flow somewhere downstream. This adds a section of turbulent boundary layer where at a lower Reynolds number the flow would had been laminar. You will notice that for the same Reynolds number, a fully laminar flow (lower line) is much less draggy than a fully turbulent one (upper line). Therefore, replacing some of the laminar flow with a turbulent one will result in more drag.

Now I need to explain why increasing the Reynolds number leads to more turbulent flow. For this, I turn to this answer:

Inside the laminar boundary layer, small disturbances become less and less damped the higher the local Reynolds number becomes, and at a Reynolds number of around 400,000 in unaccelerated flow some frequencies become unstable (see Tollmien-Schlichting waves) and will eventually create so much cross movement that the boundary layer becomes turbulent. Now parcels of air which flow at high speed in the outer part of the boundary layer will move close to the wall and kick the slow parcels there ahead, greatly reducing the deceleration of the flow close to the wall, at the price of slowing down and expanding the whole boundary layer.

Simply put: A laminar boundary layer cannot be sustained indefinitely but will change to a turbulent one if the Reynolds number is high enough. This will swap some of the previously laminar portion of the boundary layer to a turbulent one, increasing drag.

While all of the above is only strictly true for flow over a flat plate without a pressure gradient, real flow will complicate things again: Now turbulent flow is not all bad; the example of the dimpled golf ball shows that a turbulent boundary layer in flow with a pressure gradient can also lead to lower drag, given the right circumstances.

• Hi Peter: RE: greatly reducing the deceleration of the flow close to the wall, at the price of slowing down and expanding the whole boundary layer. -- I don't understand how (reducing the deceleration), (slows down) the whole boundary layer? Many thanks. – ymb1 Jan 30 '20 at 22:51
• @ymb1 Turbulent boundary layers "borrow" energy from their outer fringes and transport it to the wall. By kicking the laggards close to the wall forward, this mechanism decelerates the outer part of the BL, making it thicker in the process. While laminar BLs only exchange energy perpendicular to the flow by friction, turbulent BLs transport the moving air around the BL, so the energy exchange perpendicular to the flow direction is much higher. And there is no energy to be added – as Homer Simpson says: We obey the laws of thermodynamics! – Peter Kämpf Jan 31 '20 at 8:15