[AR] Re: Turbopump prime mover
- From: "Ed LeBouthillier" <codemonky@xxxxxxxxxxxxx>
- To: <arocket@xxxxxxxxxxxxx>
- Date: Wed, 2 Dec 2015 07:09:34 -0700
Monroe L. King Jr. said
If Ve is Volumetric efficiency the turbochargers original VE is around
76% That will change I expect as this design is perhaps more impulse in
nature.
No, Ve is the exhaust velocity of the gases impinging on the turbine.
In point of fact, Ve is the delta gas velocity between what is impinging
into the turbine versus what is exiting the turbine (which represents
the percentage of energy that is transferred to the turbine). Therefore,
the force transferred to the turbine is m_dot * delta_Ve. Again, the
triangles
representing the angles of impingement are important, but if you
just presume perfect impingement it'll at least give you a ballpark
figure for HP.
So (very approximately):
HP = torque * RPM / 5252 (for customary units of ft-lbs and RPM)
HP = force * radius * RPM / 5252
HP = mdot * Ve * radius * RPM / 5252
HP = mdot * Ve * .15 feet (?) * 50000 / 5252
So, you can either fix mdot and determine Ve or you can fix Ve and get mdot
knowing the horsepower. Again, all of this is just order of magnitude
estimates
at this point; the real calculation has to account for impingement velocity
at
input minus exit velocity to determine how much of the energy was actually
transferred to the turbine (but again, a ballpark perfect estimate is at
least a
place to start).
If you're driving it with a monoprop peroxide without a nozzle, you might
presume
that the Isp is about 100 seconds. Thus, Ve will be on the order 3220 feet
per second.
Again, all of the above is ballpark figures and off the top of my head. The
likelihood for errors is high.
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