Boundary layer

I was wondering exactly how thick the boundary layer on an IOM hull or fin was. One millimetre? Ten millimetres? Is this when it is laminar, or when it's turbulent? So I dipped into Hoerner's classic "Fluid Dynamic Drag" (insofar as one could ever be said to "dip" into such an extraordinary collection of engineering data) and came up with a spreadsheet, which does three things (now four; see the update below).

First, the boundary layer thickness depends upon the local Reynolds number. That is, it depends upon where along the hull or fin you are looking. Given a flow, such as a hull speed of 1 m/sec, and a position that is, say, 50 mm aft of the bows, the local Rn is about 44,000. Further back, perhaps amidships 500 mm from the bows, local Rn is about 440,000. So the spreadsheet calculates a local Rn, given your input about the points along the hull (or whatever) where you want the calculation made.

Then there is the question of whether the boundary layer has experienced transition from laminar flow to turbulent flow. A turbulent boundary layer is thicker, but there is no hard and fast rule about the transition point. The best that can be said in a very general way, without actually putting the hull of interest into a towing tank and taking some measurements, is that transition probably takes place somewhere between a Rn of 100,000 and 1,000,000. The spreadsheet applies one of two formulas, depending upon whether the local Rn has reached the critical transition value you specify. Assuming transition at Rn = 300,000, for the hull data we've developed so far, the spreadsheet says the boundary layer is laminar 50 mm from the bows, and is about 1.3 mm thick, while it is said to be turbulent 500 mm from the bows, and about 12 mm thick (with a hull speed of 1 m/sec).

Finally, there is more than one definition of "boundary layer thickness". A second definition is called the "displacement" distance, and I have to say immediately that I can't see the difference between this "displacement" thickness, and the earlier "total" thickness. Never mind, displacement thickness is somewhere between 12% (if turbulent) and 31% (if laminar) of the "total" thickness. Choose whichever number you like best!

Update

I went back to school to try and do something about my ignorance here, and came away with two new understandings. Before I discuss these, I realise I have not emphasised enough that the spreadsheet calculations strictly apply only to a flat plate, and not to an aerofoil with any degree of camber.

I discovered that the "displacement" thickness is a rather neat idea. It is a measure of how much the free flow has been "displaced" away from the surface, due to the boundary layer. It isn't equal to the "total" thickness, because it allows that some surface friction will slow the fluid next to the surface, so it is measuring the "effective" boundary layer thickness by only starting to count this after a "significant" drop in the speed of the flow.

The second thing I found out is that there is a rule of thumb for whether separation of the flow from the surface is likely to occur, and hence whether a bubble will develop under the separated flow and above the surface. The rule of thumb is that, if the Reynolds number of the displacement thickness is less than around 400, separation is probable, and if it is greater than around 550, separation is unlikely. I have updated the spreadsheet to show predicted separation of the flow. It shows that, in low wind speed of 1 m/sec (light winds in No.1 rig), a separation bubble is likely for most of the leeward side of the main and jib, if we accept the extrapolation from the "flat plate" to which this rule of thumb strictly only applies. When wind speed is 10 m/sec (middle of No.3 rig), a separation bubble is only likely for the forward 50 mm or so of each sail.

The usefulness of this is that while it makes sense to hang tell-tales some way from the luff of the jib in No.1 suit, it makes no such sense for No.3 jib -- there just will not be a separation bubble there to detect, and the tell-tales will therefore not be reading properly.

2005-12-18