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All about Gamma (or k if you want) - 5/31/2012 2:42 PM   
gaRCfield



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From: Mason, OH, USA
Status: online 		Hi All,
Unfortunately I'm not an aero engineer (yet), but that is where my passion is. I've been studying some notes I have from my Aero/Thermo class, and taking other classes related to aerodynamics. I am not one to 'just accept' the use of equations, so I've been spending some time to try to understand, in English, (gamma-1)/gamma.

I think this is the most interesting thing I've ever studied in 2+ degrees of college and a number of jobs. So I was driving home from work yesterday thinking about this, and thought of a pressure cooker. Here is what I came up with:

Gamma (ratio of specific heats) is basically showing the percentage of energy that goes to volumetric expansion of the gas when heated, so it takes more energy to heat a gas at constant pressure than at constant volume (hence the pressure cooker - if gamma=1.4, then it takes 40% more energy to heat the same air to the same temperature in an open pot).

(gamma-1)/gamma seems to me like a ratio of the (energy of expansion) to the (energy to raise temperature), or energy absorbed by the gas.

I think (gamma-1)/gamma comes up first as a way to equate total temperature to Mach number. I came up with the idea that Mach number is like the ratio of (kinetic energy of a moving gas) over something like the (expansion energy of the gas at that temperature), or the kinetic energy associated with pressure wave propagation. If the gas is moving with same kinetic energy associated with a pressure disturbance, M=1.

Got to run - would love to have a conversation about what is actually going on with these equations, rather than just moving numbers and letters around a page to find an answer.

Any links or book reference would be greatly appreciated too



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RE: All about Gamma (or k if you want) - 5/31/2012 7:38 PM   
Lnewqban



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Status: offline 		Check this link:

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

"Ganma is the adiabatic index also known as the isentropic expansion factor. It is the ratio of specific heats of a gas at a constant-pressure to a gas at a constant-volume(Cp/Cv), and arises because a classical sound wave induces an adiabatic compression, in which the heat of the compression does not have enough time to escape the pressure pulse, and thus contributes to the pressure induced by the compression."

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RE: All about Gamma (or k if you want) - 6/1/2012 8:12 PM   
Shoe



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From: Stuttgart, GERMANY
Status: offline 		I think your pressure cooker analogy for Cv is essentially correct, but the open pot analogy for Cp is not quite correct.

To determine Cp, you would need to heat air in a pot with a piston-like lid. If you kept the same amount of weight on the lid, allowing the lid to be displaced upward as the air is heated, you could measure the amount of energy required to raise the temperature of the air at constant pressure..

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RE: All about Gamma (or k if you want) - 6/2/2012 5:14 AM   
BFoote


 

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quote:

ORIGINAL: gaRCfield

Hi All,

Gamma (ratio of specific heats) is basically showing the percentage of energy that goes to volumetric expansion of the gas when heated, so it takes more energy to heat a gas at constant pressure than at constant volume (hence the pressure cooker - if gamma=1.4, then it takes 40% more energy to heat the same air to the same temperature in an open pot).

(gamma-1)/gamma seems to me like a ratio of the (energy of expansion) to the (energy to raise temperature), or energy absorbed by the gas.




Think of it this way. What requires more work done? Moving an object at slow speed, or accelerating said object to high speed over a shorter period of time. Same power inputted. One increases potential energy the other increases kinetic energy. That danged Velocity squared function gets you every time! A gas that has to be accelerated and moved requires more energy than a gas that is idle and essentially in stasis or free flowing.

Of course reality rears its ugly head and the quality and therefore useful efficiency curves derived from said quality of said stored energy when tied into mechanics of machines comes into play.

Not really much to discuss here. Aero/Thermo equations can generally be turned into pi equations where essentially they break down into constants with only 1-2 terms effecting the result as the rest cancel each other out.

Now if one can figure out how to broaden the compression wave at M1, now that could be quite useful as this could mean a gigantic leap forward in compressor design. So far, the math doesn't show this nor has it worked in reality. Many have attempted to do so. Needs another mechanism. So far we have no hope or inkling that such a hope exists.

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