Different values on gamma and k?

[HattoriHanzo]

I was doing some simulations on rocket propellants when I noticed something peculiar.
The program shows different values for γ(gamma) versus k. Why is that?
Is this an error in the program or am I missing something important in thermodynamics?

In all my literature k can be a substitute symbol for γ.
And the same literatures also states that γ=cp/cv, k=cp/cv

[HattoriHanzo]

Maybe this was a really stupid question :wink:

One more try.
Here is two examples that shows different values.

LOX/LH

Cp (kJ/(kg)(K)): 5.92161
Cv (kJ/(kg)(K)): 4.96321
Cp/Cv: 1.19310
Gamma: 1.18857



LOX/HTPB

Cp (kJ/(kg)(K)): 4.81622
Cv (kJ/(kg)(K)) : 4.06339
Cp/Cv: 1.18527
Gamma: 1.15696

[skyfrog]

I left this question to be answered by yourself, the trick is to find a correct thermodynamics textbook which involves combustion.

Not meant to be offensive but howcome I got this feeling that you're a student ?

[HattoriHanzo]

I left this question to be answered by yourself, the trick is to find a correct thermodynamics textbook which involves combustion.

Not meant to be offensive but howcome I got this feeling that you're a student ?

Do you think I am a student beacuse I am inquisitive and ask much question on this site? No, I finished my school several years ago, and I regret not to choosed an engineering program...
I am still just a happy amatuer.


Can you recommend such a textbook that explain the difference?

To me it often seems to be a very small difference when all comes around and can be ignored, but sometimes its fairly big difference and can affect the results.
I am surprised that literature in propulsion do not discuss this difference. Sometimes the writer use k when others use γ in the same equation and operations.

[HattoriHanzo]

I have ordered the book Thermodynamics and mechanics of propulsio from my local library. Maybe I found answers in this book.

[HattoriHanzo]

I have not found a explanation of the difference yet. But I got a clue using the speed of sound:D


If we start with the expression of speed of sound:

a = (γ*R*T)^1/2

and continue with the expression of throat velocity in a convergent section, because the nozzle is choked M=1 is the maximum velocity. So again:

vt= (γ*R*T)^1/2

it is also possible to write the speed of sound or throat velocity as:

vt=(2k/(k+1)*R*T)^1/2

then

γ=2k/(k+1)

Am I wrong here?


Even if this should be correct it do not answer my question, why the difference?

[mk]

What do a, v, and t stand for?

Acceleration, velocity, and time?
It just confuses me to read vt, which, most likely, does not seem to equal a velocity. Hmmm.

To explain myself a bit:
Having some arbitrary, dimensionless factor f, as e.g. k = c(p) / c(V), the temperature in question T in Kelvin, and the universal gas constant R with R = (M)^(-1) 8314 J/kg/K, where M is the dimensionless(!) relative molecular mass of a certain (gaseous) medium (-- it is equal to the magnitude of the molar mass of the latter --), it would be expected to get a dimension representing a velocity.

Okay, I'm not an expert here, but I'd be glad if you could clarify the abbrevations you employed.

[HattoriHanzo]

Thanks for reply.

a=acoustic velocity
vt=throat velocity

[mk]

Oh, it represented an index.

Well, some kind of a trivial problem.

It seems like I cannot help you in this case.
However, wouldn't the 2k/(k+1) expression -- wherever it came from -- yield for values γ>k?

Your above posts do show the oposite. Hmmm.

[HattoriHanzo]

However, wouldn't the 2k/(k+1) expression -- wherever it came from -- yield for values γ>k?

No, it wouldn't. It would yield γ<k
This expression can be found in Sutton 7Ed on page 57 and also in most literature dealing with thermodynamics and fluid mechanics. Nothing unique for Sutton.

[mk]

However, wouldn't the 2k/(k+1) expression -- wherever it came from -- yield for values γ>k?

No, it wouldn't. It would yield γ<k
This expression can be found in Sutton 7Ed on page 57 and also in most literature dealing with thermodynamics and fluid mechanics. Nothing unique for Sutton.

EDIT:

Ouch! Damnit!

Yes, you're correct Hattori.

I should have had looked at it more concentrated before. Not besides doing other stuff.

Sorry for confusing you all then.

[leo]

similar problem?
http://www.eutech.com/helpdesk/ees00570 ... enDocument

[skyfrog]

For ideal gas, gamma is constant, so is k, but you are dealing with real gas. In general, for real gases over normal working ranges of pressure and temperature, gamma (and Cp, Cv etc) is a function of temperature alone.

Furthermore, if dissociation is taken into account, in which case when temperature > 1500K the effect will be significant, you will find that pressure also influences the value of gamma.

Real gas is real gas, ideal gas is ideal gas, they are different, do not mess them up.