Allen3
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Hi, I'm attempting to estimate the windage losses in an axial motor design, and I'm having trouble with the formulas. It might be a math error, or a misunderstanding of the formulas, but I seem to be stuck.
An axial motor can be modeled as an annular disk spinning in an enclosure. The disk has outer radius R, inner radius r, the distance from each face of the disk to the wall of the enclosure is g, and it is spinning at rotational speed w.
This system was studied by Daily and Nece who came up with equations to describe the air friction on the disk. See the thesis papers at http://alexandria.tue.nl/extra2/200111643.pdf (page 133) and http://lib.tkk.fi/Diss/199X/isbn9512255766/isbn9512255766.pdf (page 17).
I'm trying to duplicate the computation in the first thesis. The basic parameters are:
Outer disk radius R = 190 mm
Inner disk radius r = 110 mm
Air gap g = 1.5 mm
Rotational speed w = 12000 rpm = 200 rev/sec = 1257 radians/sec
I'm also using the following values, which I looked up at http://www.mhtl.uwaterloo.ca/old/onlinetools/airprop/airprop.html :
Air density rho = 1.2 kg/m^3
Air dynamic viscosity u = 1.83E-5 kg-s/m
Air kinematic viscosity v = u/rho = 1.53E-5 m^2/s
From Eqn 6.23: Rotational Reynolds Number Rer = (w*r)*r/v = 1257*0.190^2/1.53E-5 = 2965000
From Figure 6.8: g/R = 0.008 which means the flow is in Regime III
From Eqn 6.28 for Regime III: Cf = 0.08/(g/R)^0.167/Rer^0.25 = 0.08/(1.5/190)^0.167/2965000^0.25 = 0.00433
From Eqn 6.26: Friction Torque T = 0.5*Cf*rho*pi*w^2*(R^5-r^5)
= 0.5*0.00433*1.2*pi*1257^2*(0.190^5-0.110^5)
= 3.0 N-m
From basic physics: Windage power P = T*w = 3*1257 = 3752 watts
The number I'm getting, 3752 watts, seems very high. The power loss shown in Figure 6.9 of the thesis is about 345 watts, which means my calculation differs by about a factor of 10.
Would anyone be able to tell me where I'm going wrong in this calculation? Any assistance you could provide would be greatly appreciated.
An axial motor can be modeled as an annular disk spinning in an enclosure. The disk has outer radius R, inner radius r, the distance from each face of the disk to the wall of the enclosure is g, and it is spinning at rotational speed w.
This system was studied by Daily and Nece who came up with equations to describe the air friction on the disk. See the thesis papers at http://alexandria.tue.nl/extra2/200111643.pdf (page 133) and http://lib.tkk.fi/Diss/199X/isbn9512255766/isbn9512255766.pdf (page 17).
I'm trying to duplicate the computation in the first thesis. The basic parameters are:
Outer disk radius R = 190 mm
Inner disk radius r = 110 mm
Air gap g = 1.5 mm
Rotational speed w = 12000 rpm = 200 rev/sec = 1257 radians/sec
I'm also using the following values, which I looked up at http://www.mhtl.uwaterloo.ca/old/onlinetools/airprop/airprop.html :
Air density rho = 1.2 kg/m^3
Air dynamic viscosity u = 1.83E-5 kg-s/m
Air kinematic viscosity v = u/rho = 1.53E-5 m^2/s
From Eqn 6.23: Rotational Reynolds Number Rer = (w*r)*r/v = 1257*0.190^2/1.53E-5 = 2965000
From Figure 6.8: g/R = 0.008 which means the flow is in Regime III
From Eqn 6.28 for Regime III: Cf = 0.08/(g/R)^0.167/Rer^0.25 = 0.08/(1.5/190)^0.167/2965000^0.25 = 0.00433
From Eqn 6.26: Friction Torque T = 0.5*Cf*rho*pi*w^2*(R^5-r^5)
= 0.5*0.00433*1.2*pi*1257^2*(0.190^5-0.110^5)
= 3.0 N-m
From basic physics: Windage power P = T*w = 3*1257 = 3752 watts
The number I'm getting, 3752 watts, seems very high. The power loss shown in Figure 6.9 of the thesis is about 345 watts, which means my calculation differs by about a factor of 10.
Would anyone be able to tell me where I'm going wrong in this calculation? Any assistance you could provide would be greatly appreciated.