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Betty November 6, 2007 11:42

supersonic nozzle
 
For a nozzle with design lip Mach number of 2.2, if we are given the pressure ratio = pstatic/pambient = 1.2 , then if the isentropic relations were used to calculate the exit Mach number(using po/pstatic = 1.2) it gives a really small value Mexit=0.103.

I know something is wrong here. How do I get the stagantion pressure just from the pressure ratio? Or what would be the right way to compute the exit mach number given the above pressure ratio??

I would appreciate any help.

Thanks


ag November 6, 2007 14:46

Re: supersonic nozzle
 
First, you don't get the stagnation pressure just from the pressure ratio pstatic/pambient. The parameter that defines the operating condition for a converging/diverging nozzle is the ratio pstag/pexit. For a shock-free flow, pstag is uniform through the nozzle, so pstag represents the stagnation condition upstream at the inlet as well. Since the inlet flow is typically at very low velocity, pinlet ~ pstag, and thus you can see the physical relevance of defining the operating condition based on the pstag/pexit ratio. Second, if you are given an exit Mach number, and the flow is shock-free (meaning the nozzle is operating as designed) then you can compute the pressure ratio pstag/pexit using the exit Mach number. In fact, you can always compute pstag/pstatic based on the local Mach number, where pstag and pstatic are both local quantities. However, as mentioned above, if the flow is shock-free (and inviscid) then pstag is constant over the flowfield and the ratio is equal to pstag(inlet)/pstatic(exit). If you do this, you will find that for M=2.2, the pressure ratio is 10.695. Now if you have the exit static pressure you can compute the exit stagnation pressure as 10.695*pstatic(exit), which then also gives you the inlet stagnation pressure under the aforementioned shock-free operation. Finally, if the pressure ratio really is pstag/pexit = 1.2, then the exit Mach number would be roughly 0.52 using the isentropic relationships - not sure where your error is (all of the above assuming gamma = 1.4).

Have you checked out any resources like

http://www.grc.nasa.gov/WWW/K-12/Und...rogs/index.htm


shuo November 6, 2007 16:36

Re: supersonic nozzle
 
Hi Betty

I have a paper that models the same conditions used by Lamont. Basically if you use nondimensional variables the exit Mach, rho, P are 2.2, 1/gamma, 1.

The remaining quiescent field is defined as Ma = 0, P = 1/(gamma*P_r), rho = 1/rho_r. P_r is given as 1.2 (Lamont) while rho_r = P_r/T_r. T_r is calculated from isentropic conditions assuming the stagnation temperature inside the nozzle is equal to the ambient temperature: 1/(1 + (Gamma - 1)/2*pow(Ma, 2)).

I can forward you a pdf of the paper if you like.

Shuo

Betty November 6, 2007 17:24

Re: supersonic nozzle
 
Thank you ag, The pressure ratio given in the study is pstatic/pambient = 1.2 which isn't same as pstag/pexit = 1.2 but it can be considered the same due to low inlet velocity. Am I right?

I am really confused, the other thing is the stagnation temperature of the jet isn't given so I need a way to figure it out, any suggestions?

Thanks again

Betty

Betty November 6, 2007 17:26

Re: supersonic nozzle
 
Shuo I would really appreciate it if you could please forward the paper to me.

Thanks a lot.

Betty finsea@yahoo.com

ag November 6, 2007 18:18

Re: supersonic nozzle
 
It can if pstatic refers to the inlet and pambient refers to the exit. The stagnation temperature can be computed if you know the static temp. somewhere in the flow, like the exit. Or you can assume an exit temperature and key other calculations off that, i.e. stagnation temp., fluid density, etc.

Betty November 7, 2007 15:33

Re: supersonic nozzle
 
Shuo, Could you please send the paper to me.

Thanks a lot


shuo November 8, 2007 02:51

Re: supersonic nozzle
 
Hi Betty

I'll try to forward you the paper to tommorrow.

Shuo

Betty November 20, 2007 13:46

Re: supersonic nozzle
 
Thanks a lot Shuo. I recieved the paper.


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Quote:

Originally Posted by ag
;52633
First, you don't get the stagnation pressure just from the pressure ratio pstatic/pambient. The parameter that defines the operating condition for a converging/diverging nozzle is the ratio pstag/pexit. For a shock-free flow, pstag is uniform through the nozzle, so pstag represents the stagnation condition upstream at the inlet as well. Since the inlet flow is typically at very low velocity, pinlet ~ pstag, and thus you can see the physical relevance of defining the operating condition based on the pstag/pexit ratio. Second, if you are given an exit Mach number, and the flow is shock-free (meaning the nozzle is operating as designed) then you can compute the pressure ratio pstag/pexit using the exit Mach number. In fact, you can always compute pstag/pstatic based on the local Mach number, where pstag and pstatic are both local quantities. However, as mentioned above, if the flow is shock-free (and inviscid) then pstag is constant over the flowfield and the ratio is equal to pstag(inlet)/pstatic(exit). If you do this, you will find that for M=2.2, the pressure ratio is 10.695. Now if you have the exit static pressure you can compute the exit stagnation pressure as 10.695*pstatic(exit), which then also gives you the inlet stagnation pressure under the aforementioned shock-free operation. Finally, if the pressure ratio really is pstag/pexit = 1.2, then the exit Mach number would be roughly 0.52 using the isentropic relationships - not sure where your error is (all of the above assuming gamma = 1.4).

Have you checked out any resources like

http://www.grc.nasa.gov/WWW/K-12/Und...rogs/index.htm



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