Rotating diaphragm deflection

[Bokke]

I'm designing a hollow rotating disc of around 0.5m dia. The disc rotates in the horizontal plane attached to a hollow drive shaft fixed by a flange to the centre of the lower disc. Water is to be fed up the centre of the hollow driveshaft and into the disc which will impart a centrifugal pressure inside the disc of zero at the centre of the disc, rising to a maximum at the edge of the disc.

I'm interested in calculating the deflection and stresses of the disc surface due to the centrifugal pressure as I need to keep this as thin as possible for heat transfer.

I've treated the diaphragm surface as a fixed beam, however the calcs I've come accross cater for either a UDL or point loading. I would appreciate any help in locating a formula for this particular application.

 

[jte]

Bokke-

A curious question...

I'm confused on a few issues. You describe how the water gets in, but not how it gets out. Or is this somehow a batch process - the water gets put in, heat is transferred, then the water is drained. If the water is flowing out through an axial outlet on top, then I'd say that you'll have very little heat exchange, as the water will fill the cavity and then the flow will simply go from the inlet to the outlet and leave the water at the periphery stagnant.

Another issue I'd suggest you verify is the effect of the metal (presumably) thickness on the heat transfer. In my experience the metal is essentially at a uniform temperature while convection governs (is the bottleneck) in the heat transfer.

As for structure, it sounds like you are envisioning two flat disks with a short shell section at their periphery. To optimize thickness you might consider using two semi-elliptical (with a higher ratio than 2:1) or torispherical heads end to end. Section VIII-1 provides some guidance in Appendix 1-4(c) for SE heads and (d) for torispherical.

As to the variable pressure... I think you're into an axisymmetric FEA on that. The easy way out is to assume that the pressure is uniform at the max pressure.

jt

 

[Bokke]

Thanks jte, I was under the impression that FEA work would be required in view of the variable pressure. I've also been pointed in the direction of Roark's book (chapt 11, where the recommendation is made to divide the disc into annular sections and perform discrete calculations on each of the areas.

Wrt the flow of the water inside the disc, there is a spiral mechanism that effects this - I ommited the details to avoid confusing the issue.

Thanks,
jj

 

[prex]

If you look in the site below, under Plates -> Simple bending -> Annular pl. -> 2 supports (or any other end condition, 2 supports is of course on safe side) , there are loading conditions with linearly and parabolically increasing load over the radius that should avoid to you lengthy calculations. You can of course add the results of two different loading conditions to have, for example, a constant base pressure added to a parabolic increase over radius.

prex

http://www.xcalcs.com

Online tools for structural design

 

[Bokke]

Thanks prex, the xcalcs site was great as a check for the manual calcs, and a lot quicker - much appreciated.

jj