CONVERGENT nozzles contraction ratio and length

[jlchard1]

I am currently designing a convergent nozzle for use in experiments and wanted to check something:

Will the pressure and density of the flow always expand to ambient (following the isentropic relations) when it reaches the nozzle exit regardless of nozzle contraction ratio and length?

Any help / advice regarding just CONVERGENT nozzles will be much appreciated.

James

 

[boneh3ad]

I realize no one answered for first thread, but did you need to duplicate it rather than just bumping the original?
https://www.physicsforums.com/showthread.php?t=732087

At any rate, do you mean does the flow expand to those conditions after exiting the nozzle? Because it never will when it is still inside the nozzle.

 

[jlchard1]

No I am wondering if it will always correspond to ambient conditions directly at the nozzle exit? Will this always be the case irrespective of the nozzle geometry? (e.g. for a straight tube)

 

[boneh3ad]

That depends. Depending on the pressure ratio, you may also have a shock at the exit plane, in which case "at the exit plane" could correspond to two different values. Otherwise yes, the pressure is, in general, going to be ambient at the exit of a nozzle.

 

[jlchard1]

Ok thankyou. In that case, what is the point in the nozzle converging to smaller area when the speed at the exit plane is simply dictated by the nozzle pressure ratio? i.e. why not use just a straight pipe?

 

[cjl]

Otherwise yes, the pressure is, in general, going to be ambient at the exit of a nozzle.

I would tend to disagree with this statement, actually (for a supersonic nozzle). The pressure at the exit of a nozzle will be determined by the expansion ratio of the nozzle and the pressure feeding the nozzle. It will not tend to adjust itself to ambient, unless there is some mechanism to do so (such as the variable area nozzles found on many afterburning jet engines). Many rocket engines for example have exit pressures that are substantially different from ambient, either above or below (depending on the intended purpose of the motor), and this is what causes the "shock diamond" phenomenon visible in the exhaust.

 

[jlchard1]

But for a simple convergent subsonic nozzle the pressure will always be ambient at the exit plane?

 

[boneh3ad]

I would tend to disagree with this statement, actually (for a supersonic nozzle). The pressure at the exit of a nozzle will be determined by the expansion ratio of the nozzle and the pressure feeding the nozzle. It will not tend to adjust itself to ambient, unless there is some mechanism to do so (such as the variable area nozzles found on many afterburning jet engines). Many rocket engines for example have exit pressures that are substantially different from ambient, either above or below (depending on the intended purpose of the motor), and this is what causes the "shock diamond" phenomenon visible in the exhaust.

Yes, for a supersonic, converging-diverging nozzle I agree. The OP was asking about a strictly converging nozzle, in which case either the flow is going to end up at ambient pressure at the exit or else the nozzle will be choked and it will be too high and will have to equalize after leaving the exit.

Also note, I mentioned there could be a shock at the exit, but with that I, too, was thinking about converging-diverging nozzles. That doesn't make sense with a strictly converging nozzle because you either have an equalized pressure at the exit or higher pressure, never lower.

But again, that takes me back to the first part of my answer: it depends on your pressure ratio (back pressure over upstream total pressure, $p_b/p_{01}$). For air, if $p_b/p_{01}<0.528$, the flow will be choked and the exit pressure will be higher than ambient. If $p_b/p_{01}\geq 0.528$, the exit pressure equals the ambient pressure.

 

[cjl]

But for a simple convergent subsonic nozzle the pressure will always be ambient at the exit plane?

For a subsonic nozzle, yes, it will typically be ambient at the exit. I agree with bonh3ad's post above this one.