Calculating windage for rotating disks in fluid.
Calculating windage for rotating disks in fluid.
(OP)
Hello,
I am trying to calculate the power loss associated with windage for flat disks about 6 feet in diameter.
If I have disk speed, diameter and fluid properties; is there a generalized formula for calculating power loss?
I have found a document that calculates this value for a cylinder inside a cylinder (rotor inside stator) but not for the back and front of a short flat disk.
This is the NASA document
NASA TN D-4849
I tried looking for something online and was not able to find any information regarding this.
I am assuming this can be derived via integration across the disk radius, but I would rather not go through this process if there exists a general solution backed by experimental data.
Thank you,
- Dan
I am trying to calculate the power loss associated with windage for flat disks about 6 feet in diameter.
If I have disk speed, diameter and fluid properties; is there a generalized formula for calculating power loss?
I have found a document that calculates this value for a cylinder inside a cylinder (rotor inside stator) but not for the back and front of a short flat disk.
This is the NASA document
NASA TN D-4849
I tried looking for something online and was not able to find any information regarding this.
I am assuming this can be derived via integration across the disk radius, but I would rather not go through this process if there exists a general solution backed by experimental data.
Thank you,
- Dan





RE: Calculating windage for rotating disks in fluid.
derive with a changing velocity over the length of the plate (set V=diskspeed*radiusatpoint) to get dFdrag then.... W=F*D and dW=dFdrag*radius +Fdrag*dd(velocity integrated over the distance) ...integrate that and boom you have your amount of work lost per second (c=13/Re for a circular plate parallel to flow)
Could be done in less then 20 minutes.
RE: Calculating windage for rotating disks in fluid.
google: "NASA rotating disc drag"
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Of these papers, the Theodorsen & Regier, has a lot of good experimental data:
http://nt
Later papers explore more complex subjects regarding variations in the flow field of the disc shroud, which can have pretty big impacts on the drag forces. There's a gentleman over at the U. of Bath in England who has a lot of more recent papers on the subject, a google search should turn up his name.
By any chance, would your disc be turning at a tip speed over Mach 1?
RE: Calculating windage for rotating disks in fluid.
Disk tip is not passing mach 1. The integration is not that simple, Reynolds number for depends on radius as does tangential velocity so it becomes a very convoluted integration. I will try to make assumptions to simplify it.
RE: Calculating windage for rotating disks in fluid.
RE: Calculating windage for rotating disks in fluid.
dW=30.63*dynamicViscosity*DiskSpeed*Integral(From r1-r2)radius^2
integrate over the areas of the disk that are part of the flat disk, add the work from the shaft, and you have your total losses. (And the units work themselves out perfectly to a N*m!!)
RE: Calculating windage for rotating disks in fluid.
RE: Calculating windage for rotating disks in fluid.
"(c=13/Re for a circular plate parallel to flow)." check against the T&R paper posted, their term for the Cx coefficient is different. Note that the assumption of parallel (flat plate) flow is incorrect; the boundary layer is a true 3d layer, as the flow near the disc surface must include a radial outflow term. Even so, there is a closed form solution for the local Cx term, and allows development of the laminar theory.
Radial flow becomes significant as the far field flow gets restricted (i.e. if a shroud encloses the disc), and this "pumped" flow is inhibited. The T&R paper gives data and coefficients for a disc effectively without a boundary...though this is never clearly shown in the paper.
RE: Calculating windage for rotating disks in fluid.
Tell me if that sounds reasonable. It seems reasonable to me, tip speed for this disk is about 942 ft/s so nearing Mach 1, drag will be high. The data I am seeing in the document btrueblood gave me is extensive and I have yet to use it until I have a better understanding of the theory.
Thanks for the help.
RE: Calculating windage for rotating disks in fluid.
Ok, just did the calc. after getting back here to my PC - for your conditions I get a Reynolds no. of 1.65x10^7, which would give a free-air moment coefficient of ~.0053, which grinds down to about 109 HP of windage.
Where it gets tricky: to use pressurized air assumes some type of enclosure or shroud surrounding the disk, which affects the windage (usually increasing it). Bottom line, the Cm data from the T+R paper should probably be taken as a lower bound for the windage drag.
RE: Calculating windage for rotating disks in fluid.