## Turbine calcs for dummies!

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Zippiot
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### Turbine calcs for dummies!

Hello all, I have amassed many formulas and calcs over the years. I wish to share a few with you, I'll be reading through my old notes and wont be able to post more than 1 or 2 a day! On a side note my handwriting is terrible...And if these are wrong take it up with my professor!

Well first off, the easiest one of all!

We will start with optimum rpm [rotations per minute] of the turbine. The turbine is "most efficient" when the tips of the compressor are spinning around mach 0.8*
While this is no where near the max rpm it is GENERALLY the most efficient speed unless the compressor is designed otherwise or adapted from a different application (such as vacume cleaners!).
Anything near or above mach causes shockwaves which interupt the combustion and cause a mess of problems :/

http://en.wikipedia.org/wiki/Speed_of_sound

We will estimate the speed of sound to be 760mph, no one really lives at sea level! Mach 0.8 is 608mph, or 642,048inch/min.
This is where it gets tricky for those [me] who are not so on top of that newfangled "mathematics". We need to find out at what rpm of the shaft is the tip of the comrpessor moving mach 0.8...

Well one rotation moves a distance of Pi*Diameter, so we super super simplify and skip a few lines of stoich to arrive at the formula:

642048/(Pi*D)

Does it work? Hell yes!

This is not max rpm but instead the rpm when the tips of the rotors are moving around mach 0.8, or 608 mph.
But what if we wanna know a different tipspeed?
X*1056/(Pi*D) where X is the mph you are looking for!

Now what if we want to find out how fast the tip of the blades are moving at a certain rpm? Well remember 1 rotation travels Pi*D, so if it is moving at Z rotations per minute multiply by (Pi*D) to see how far it has moved in one minute, then divide by 1056 to see your tipspeed in mph!

tipseed=(Z*(Pi*d))/1056 where Z is the rpm.

So lets take some numbers and plug in!

Info found on http://www.gtba.co.uk/engine_designs/wasp.htm

The Wasp's max rpm is 148,000rpm and has a 60mm compressor.

60mm=2.36in
So 608mph tipspeed is at the rpm of:
642048/(3.14*2.36)=86,641.5ish
so the tips of the 60mm compressor are moving at mach 0.8 at 86,641.5rpm

Now lets see how fast they r moving at max rpm:
(148000*(3.14*2.36))/1056=1,038.58mph! A bit past the speed of sound which is around 770mph at sealevel!

More to come, including design equations!
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racketmotorman
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Hi Zippiot

Ah ,............... but Mach numbers change with temperature , and things are going to be hotter at the comp tips

Also supersonic comp tips don't cause combustion problems , if they did , every commercial jet would be in big trouble .

Please get your facts correct , there are people new to turbines who might just believe your 'facts" are true .

Cheers
John

Zippiot
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Hi
I said the speed of sound "estimate" was 760
Commercial jets abide the mach 0.8 but military jets dont. The avg airliner cruises between 500 and 600, which allows them to stay near the mach 0.8 tipspeed.

Most turbojet aircraft cannot pass the speed of sound without an afterburner, and on planes like the f-14 there are special gates to make sure supersonic air never hits the engine. They say it causes the engine to stall, I consider that a combustuion problem!

And as I also stated, a jet can pass that number it just loses efficiency.
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Johansson
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A compressor tip speed of .8 Mach and an inlet air velocity of .8 Mach is two very different things...

//Anders

Zippiot
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Yes, no argument there.

If you look at the wiki site I believe there is a formula for determining what the speed of sound is for your conditions. You can plug that number into the formula (X*1056)/(Pi*D). Or 0.8 of that number etc...

These formulas and 98% of what I wrote is straight out of my textbook.
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racketmotorman
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Hi Zippiot

Unfortunately you're a classic case of "a little knowledge is a dangerous thing" , sorry , "just sayin' it as I sees it ", no offence meant :-))

Either you print the entire text you're quoting from so things aren't taken out of context or don't write/join "bits and pieces" unless you know what you're talking about , please .

An example of a very "supersonic'' compressor tip is that on the "larger" Allison 250 engines , the 500 hp ones , the compressor tip speed of the single stage centrifical compressor is >2100 ft/sec , and I don't see the helicopters they're powering falling out of the sky because of "combustion problems" .

The inlet ducts of supersonic aircraft use the shock waves at their "entrances" for compression and have subsonic air at the compressor wheel face , thought the relative air velocities between blades and air are another thing :-))

Supersonic inlets are complex "animals" and would require several thousand words to fully describe them , thankfully we don't need to worry about them

Commercial jets have cruise speeds of only ~M 0.8 because its economically sensible to do so , its all to do with dollars and cents.

I'll certainly agree with you that ~M 0.8 is a "sweet spot " number for lots of aerodynamic stuff , "not too fast and not too slow , just right " :-)

Please continue with your series of Formulii,m as it'll certainly create some lively discussion .

Cheers
John

Zippiot
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Ok, I'll try my best to copy paste the stuff....sorry if I got stuff wrong still lerning :)

Hard as hell to read those boks straight through....

Also I found some comparison things between tip speeds of centrifugal and axial, still tryin to decipher it.
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racketmotorman
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Hi Zippiot

LOL... those books can be very hard work , I'm still trying to decipher stuff in some of my texts that I've been reading for >15 years :-))

Theres enormous differences between axial and centrif. comps , completely different animals , axials are complicated , centrif pretty simple by comparison .

Cheers
John

Zippiot
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Well I spent about 30 mins typing up stuff directly from my shrecky book, when my comp went buzz...then the screen turned purple.
It works now, but I gotta go so expect many more turbine calcs later tonight!!!
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Zippiot
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Instead of attempting (and failing) to type these up, enjoy!
Attachments
Sailing Student- How do I know if my life jacket is tight enough?
Me- Can you breathe?
Sailing Student- Yes
Me- Then its too loose!