Hamish Edgar on Tesla Disk Spacing 

April 29, 2002

Thanks to Hamish Edgar in New Zealand for sharing the following solutions. 

02/12/03 update: Hamish can be reached at h.edgar@irl.cri.nz 

Hi All,

First I'd like to say that I completely agree with your philosophy... Commercially driven research is just going to give us more of the same. I've been lucky enough to get my hands on two of the papers about Tesla's device and go through them. (W. Rice, multiple disc pumps and Hasinger, shear force pump). I had a couple of interesting results. First, the efficiencies of Tesla's device go up as the flowrate through each disc pair decreases.

Second was an analytical solution to how to determine disc spacing (this question seems to have been popping up a lot on this board). It's based on boundary layer theory and the Napier-Stokes equations for flow between two co-rotating discs. If the disc gap is too narrow, the flow will be choked. If the gap is too wide, the centre region will not have enough pressure and can even reverse flow. The solution they came up with was: 2P=(disc gap) x Square root of (angular velocity/kinematic viscosity). P was a dimensionless parameter, which under the best flow conditions would equal Pi/2. 

I had a look at this using charts of absolute viscosity, calculated values of density at various pressures and temperatures, and found that the disc gaps must be specifically matched to the fluid and working conditions (if all of this is right anyway).

So, if the designer was building a gas turbine intended to rotate at 27000 RPM, spacing for the inlet air would be 0.25mm. As pressure increased through the stage(s), the spacing would change, until at the last compressor (now at 10 atm outlet), the spacing would be 0.11mm. For the hot gas turbine, spacing would be 0.14mm if it was dealing with 10atm pressure at 400 degrees Celsius (OK this isn't likely in gas turbines _ I didn't have data for viscosity above these temperatures). The important thing is that if the density of the gas changes, then the optimum spacing also changes. Also, notice how much smaller this gap is than what is being used by most experimenters? The gaps get even smaller at high speed, 0.06mm for outlet of a 10atm compressor stage spinning at 81000RPM.

If the designer was building a hydro turbine, 20 degrees C, spacing would be 0.18mm for a turbine running at 3000RPM. If it was a feed pump handling water at 100 degrees C, spacing would be 0.08mm.

For a steam turbine, spacings would be on the order of 0.09mm for 400 degrees C, 3.5MPa steam, or 0.52mm for 400 degree atmospheric pressure steam.

Anyway, I hope that this is a help to people out there. Charts of viscosities, either absolute or kinematic, are in most good fluid mechanics textbooks.

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