If I in a convergent-divergent nozzle have choked flow, and decrease the back pressure I will get a normal shock in the divergent section that moves downward as the back pressure decerases. It is also possible to overexpand the flow if the nozzle is "too long". But how do I know when I will get a normal shock in the divergent section and when I will overexpand the flow?

It depends on the ratio between the total pressure (before the shock) and the ambient pressure. As this ratio increases the shock moves towards the end of your nozzle extension. If you compute the flow properties, using isentropic flow relations, from the shock towards the exit plane you have to end up with the ambient pressure. At one point the shock reaches the exit, but the pressure is still slightly too low. A normal shock, however, would compress it too much (you have to reach ambient pressure after the shock). Hence the pressure is readjusted by an oblique shock. This is what you called overexpanded flow in your question. The jet forms a rather complex structure of alternating compression and expansion zones after the exit. Try to search the web for overexpanded jets, there should be some nice explanations somewhere.

Thanks. I am aware that in case of over/under expanded flow the pressure is adjusted by oblique shocks. My question is for the overexpanded case, how do I know when I will get a normal shock somewhere in the nozzle and when will I get a oblique shock emerging from the nozzle edge. It is related to the fact that if you make the nozzle "too long" the flow velocity keeps increasing and the pressure decreasing to below the ambient pressure = overexpanded. Another situation could be that a normal shock forms in the nozzle. I fail to see how I can predict which situation will be applied for a given nozzle. I have searched the internet, but have not found and guidelines to my question.

The keypoint is the pressure ratio. Try the following:

1. Assume a pressure ratio p_chamber/p_ambient
2. Compute the flow in the nozzle as isentropic flow (assume there is no shock at all)
3. Compare the nozzle exit pressure with the ambient pressure
4. Try to reach the ambient pressure by using the relations for a normal shock (between nozzle exit and ambient conditions)
5. If the pressure after the shock is below ambient pressure you have to move the shock towards the throat
6. If the pressure after the shock is above ambient pressure the nozzle is overexpanded. In this case you get an oblique shock plus cell structure downstream from the nozzle

I hope this helps.

- It does. Thanks.

[kabilan]

hey thank you guys.
i have seen your conversations it is very useful.
i have a problem, i do have only total pressure.
how can i give boundary condition value as pressure inlet condition in two spaces ie. total pressure and initial supersonic pressure condition.and operating condition.
i would like to see jet structure in under expansion and over expansion condition. thank you.