Sunday, June 07, 2009

Reynolds number

It looks like one of the problems with the fountain is that I'm pushing slightly too much water through the flow straightener.

At very low velocities, flow through a pipe is laminar.  I wanted laminar flow in the flow straightener because laminar flow has no turbulence which can then break up the output jet.  It turns out that the flow velocity in the pipe has to be incredibly slow, and it turns out that I managed to design my fountain to be right in the transition region between turbulent and laminar flow.

Here is the Engineering Toolbox link on Reynold's numbers.

At full flow, I'm pushing about 180 gallons/minute through 16 of those flow straighteners.  Each has an internal diameter of 15.3 cm, so that the flow rate is 3.85 cm/sec.  Plug that into the handy calculator (the one using kinematic viscosity) and you get a Reynold's number of 5213.  That's turbulent flow.

At the flow tested in January (which worked properly), I was going up about 33 inches instead of 65 inches, so my jet velocity was 71% of full flow now.  Also, the cross section of the jets was .41 inches instead of 0.5 inches as it is now, so that the velocity inside the flow straightener was 48% of what it is now.  Plug 1.84 cm/s into that Reynold's number calculator and I get... 2491.  That's transient flow, but quite close to the 2300 needed for laminar flow.

If this is really the only problem with the fountain, then I ought to be able to slow down the flow enough to get the Reynold's number down to something around 2300, and see laminar flow at the output.  How slow?  To get half as much flow, the jet velocity is halved, and the arc height goes to 1/4 of what it is now, or 16.5 inches.  In fact, at that velocity, I do indeed get laminar flow:


Note that the impact here is on the first step into the hot tub, which is a little lower than the nominal water surface, and the arc is about 20 inches above the nozzle rather than 16.

The jet is well behaved until it gets to the top of the arc, where the bottom of the jet interferes with the top of the jet, and the result is that is spreads out laterally. That lateral spread then turns into an oscillation in the flow until it hits the step.

Anya demonstrates that the jet is 18 inches above the bond beam, or about 20 inches above the nozzle.


At this point the default setting for the fountain is to throttle back to 40 inches throw height, which clears the occupants of the hot tub and isn't too noisy.


If we wanted to get the tall jets to behave properly, it appears we'd need to cut the flow rate approximately in half, which means we'd have to reduce the jet diameter to 0.350 inches instead of 0.500 as it is now (so the finished hole diameter would be 0.440 inches).  That means I'd have to pull the stainless steel nozzles (recall they are epoxied into the PVC heads right now), get new nozzle made (probably $300), and epoxy them back in.  That all sounds possible, and certainly cheap enough, and probably can be done fast enough given that it's going to take 5 weeks to get the tile delivered.

However, there's a good chance I'd just destroy the PVC heads in the process, and there is also a good chance I'd get the nozzles glued back in crooked.  I don't think we're going to try.

We're getting more comfortable with how it looks.