Boundary Layer Thickness

Hi guys.

I have been reading a bunch of techy stuff and there is a lot of discussion about the Boundary Layer in fluid dynamics.

Here is the question: For a typical sailboat at typical sailboat speed, how thick is the boundary layer? Is it thousandths of an inch thick? Inches thick? Feet thick?

 

It increases in thickness as you move lengthwise along the hull but it is of the order of inches toward the stern for small sailing craft. It is a function of the pressure distribution along the hull but a flat plate calculator will give you some indication.

There are some calculators and explanation on the link that will give you an idea:
http://www.engapplets.vt.edu/fluids/bls2/index.html

Rick W

 

Well, a typical speed of a typical boat is typically not worth worrying about. One very rarely designs a boat with this in mind, normal boats have many design issues to over come, not one. But as a student is is important to know and how to calculate the boundary layer thickness and its relationships with skin friction and Reynolds number.

However, as Rick noted it does get thicker as you go aft, but how much and where is not so easy to calculate, as it all depends upon the shape of the boat (since all studies have in general, been on flat plates). It is worth learning a bit more from aeronautics if you wish to go deeper in the subject. Since as one goes aft on a boat, the gradients are constantly changing hence, the "outer edge" of the layer (which is affected by the shape ie the velocity gradient) no longer remains streamline. The extent of this may become so large towards to aft end that the concept of a 'thin' boundary layer is no longer tenable. But again how much and where??.... under these conditions any simplification of the complex equations describing the flow in such a region leads to misleading results. The major important factor in this is the estimation of the local shear stress to calculate the local skin friction force.

 

Rick, that is exactly the answer I needed.

I didn't know if the references were talking about the thickness of a sheet of paper or a zone that was so deep that the rudder was operating completely within the boundary layer.

Thanks Rick!

 

It varies a great deal, but small fractions of an inch to inches would be the order of magnitude. This figure shows the computed BL displacement thickness on a large wingmast+sail section, along with many of the boundary layer features.

The red and blue lines in the cross section show the boundary layer displacement thickness to scale.

The boundary layer doesn't have a definite edge, so defining just what the thickness is, is problematic. The typical definition is based on integrating some quantity from the surface to very far away. As the boundary layer peters out, the integral stops changing so it's not really necessary to accurately define where the boundary layer stops. There are many different "thicknesses" defined in this way. The boundary layer thickness itself is sometimes defined as where the flow velocity is 99% of the freestream velocity.

The displacement thickness integrates the velocity deficit with respect to distance, and the displacement thickness is the distance that has the same mass-flow at the freestream velocity. It's called the displacement thickness because this is how much the outer streamlines are shoved aside by the boundary layer - it is the equivalent shape of the body or sail.

The momentum in the boundary layer and the energy in the boundary layer can also be integrated in a similar manner to get the thickness that has the same momentum or energy if all the thickness were moving at the freestream velocity. These thicknesses are each different from the displacement thickness and from each other. There are actually ratios of the thicknesses that are used, called shape factors, to indicate the quality of what is going on in the boundary layer. The shape factors are very important for predicting the point of separation.

That's probably more than you ever wanted to know about boundary layer thickness. The key things are that the thickness is thinner when the velocity is higher. When the flow is slowing down, the thickness increases rapidly.