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 Shuo October 8, 2008 23:37

underexpanded

I am trying to validate my results for a underexpanded supersonic impinging jet. But the literature doesn't give the nozzle chamber temperture. Should i assume that it is defined so that the temperature at the exit is greater than the ambient?

Shuo

 doki October 9, 2008 06:59

Re: underexpanded

since the flow is compressible, you can use isentropic relations between total and static pressure, temperature, etc. and obtain the required values. you do not need any further data.

 Shuo October 9, 2008 19:13

Re: underexpanded

But the paper only gives pressure ratio (nozzle exit/ambient) and nozzle throat/exit diameter. Assuming atmosphere pressure I can find P0 and also Mach at nozzle exit using the diameters. But i am not given information about temperature or density.

Shuo

 oe October 12, 2008 15:48

Re: underexpanded

Are you referring to the paper by Lamont and Hunt? I have seen papers by other authors where they compare their results based on the static ambient pressure 14.7 psia and ambient temperature like 520 degree Rankine. Knowing the ambient pressure and the pressure ratio, once can compute the total pressure and temperature using the isentropic flow relations.

 Shuo October 12, 2008 19:59

Re: underexpanded

Yes I am using Lamont's results. How can you find total temperature without making an assumption about the temperature at the nozzle exi?.

 oe October 14, 2008 21:57

Re: underexpanded

Yes you have to make an assumption about the temperature at the nozzle exit (ambient temperature). But, I think it should not matter as long as the simulation includes the nozzle geometry.

Also, In their experiments Lamont and Hunt produced "underexpanded, cold air jets".

 Oliver October 15, 2008 04:39

Re: underexpanded

In my opinion ambient temperature at the nozzle exit is a funny assumption.

If it is a cold experiment, maybe ambient temperature for the chamber is a reasonable assumption. So T0 of the jet is equal to T_ambient. The temperature has an effect on the viscosity and hence on the jet-mixing

 doki October 15, 2008 11:26

Re: underexpanded

I have not seen the paper though; but the fact remains that if you have the nozzle geometry, having the ratio of variables is equal to having themselves! I mean for the relation between the throat and exit area of the nozzle to other parameters. the unknowns can be taken out of isentropic Ideal gas tables and relations readily. also, usually the exit nozzle conditions is standard air conditions, i.e. p=101325pascal and t=300(or in some cases 298) k.

 Oliver October 15, 2008 11:41

Re: underexpanded

You are right on the isentropic relations!

The nozzle exit conditions are not the ambient conditions! As you, correctly, pointed out the nozzle exit conditions can be computed assuming isentropic flow; hence they only depend on the chamber conditions.

(This is not true if the ambient pressure would be significantly too high for the area ratio. In that case you will get a shock in the nozzle. Since here we have an under-expanded jet, this is not the case.)

The flow adapts to the ambient pressure by either an expansion around the lip or an oblique shock wave. Here we have an under-expanded jet and should therefore get an expansion around the lip. The temperature (in the jet), however, is determined by the up-stream conditions and not the ambient air. Of course it will mix with the ambient air downstream of the nozzle exit.

I don't know the paper either. But the questions was what could the temperature be. For a cold experiment I would simply assume that the chamber "sits" in a lab and has adapted itself to the room temperature -- that's it, just a guess... The jet temperature would then be significantly below of course.

 doki October 16, 2008 02:28

Re: underexpanded

you are right, the point just is usually the ambient conditions are considered to be sea level standard air conditions; which agrees with the Guess you mentioned. But there is a difference between nozzle exit conditions and ambient conditions; i.e. In the conditions which there is subsonic, or isentropic supersonic flow inside the nozzle, these two are the same; otherwise they differ each other a lot.

 oe October 19, 2008 15:53

Re: underexpanded

May be I confused people in the earlier post.Apologies for that. All meant to say was, the chamber temperature could be assumed to be equal to the ambient temperature. Here is my explanation please feel free to correct. The pressure ratio (PR)=1.2 =static pressure at nozzle lip(pe)

_____________________________

ambient pressure(pa) or pe = 1.2*pa assuming standard conditions, let pa = 14.7 psi (or 1 atm) so, pe=17.64 psi Its is a Mach 2.22 C-D nozzle. Now employing the isentropic relations the chamber total pressure can be obtained. I am not sure how if it is a good idea to assume the chamber total pressure to be same as ambient temperature.

The reference: "The impingement of underexpanded, axisymmetric jets on perpendicular and inclined flat plates"; J. Fluid Mech. (1980),v 100(3), 471-511

 Oliver October 20, 2008 01:55

Re: underexpanded

That makes sense to me, the only thing I objected was somebody's proposal to take the ambient temperature as condition for the nozzle exit (and then compute back to the chamber using isentropic relations).

 doki October 20, 2008 09:44

Re: underexpanded

well I could not understand the first line! you should have some information on the flow upstream to calculate the exit! because the flow is supersonic, and the condition at nozzle exit is not necessarily ambient conditions. I mentioned some notes in my previous reply!

 oe October 20, 2008 21:48

Re: underexpanded

Right, the condition at the nozzle exit is NOT same as ambient. It is an underexpanded jet with pressure ratio 1.2 (ratio of pressure at nozzle exit to ambient pressure).Therefore the pressure at the exit section of the nozzle can be calculated as 1.2*p_ambient. But I am still not convinced about assuming the chamber temperature to be ambient temperature.

 Oliver October 21, 2008 04:30

Re: underexpanded

It is a guess, that's all. Assume a simple experiment with a tank and a tube that connects it to the nozzle. You pressurise the tank, wait a bit, and then run your experiment. If it is a simple steel tank, the tank walls and the air inside "might" have adapted themselves to the temperature around the tank. They might not and maybe the tank is heated, or maybe ... and so on. Bottom line is: You need to know the temperature. The only halfway sensible guess, in my opinion, would be ambient temperature. BUT, there are loads of reasons that speak for a different chamber temperature.

Is there a velocity mentioned somewhere? If yes, maybe you can compute the speed of sound, since the Mach number is known at the nozzle exit. With that speed of sound and the assumption of perfect gas you'll get the temperature ...

 doki October 21, 2008 08:51

Re: underexpanded

com on. what are you talking about? thats a simple problem. just use the previously mentioned relations to get the temperature. no additional assumptions are needed. YOU CAN GET THE EXACT VALUE!

 Oliver October 21, 2008 09:17

Re: underexpanded

Ok, if it is so easy: Go ahead!

Assume that the ambient pressure is 101,325Pa, which gives you a nozzle exit pressure of 121,590Pa. The Mach number shall be 2.22, as mentioned before. That gives you a chamber pressure of 1,341,468Pa (all assuming gamma=1.4). The ambient temperature shall be 300K. Now, what is the chamber temperature ....??????

 oe October 21, 2008 22:36

Re: underexpanded

Yes that is exactly where I had the question, and made an assumption chamber temperature = ambient temperature. What do you think about using the sonic velocity at the throat?

Thanks

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