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 Betty October 18, 2007 16:04

Supersonic nozzle exit conditions

If a study mentions that the jet exit mach number is 2.2 and the nozzle operates at a NOzzle Pressure Ratio = 1.2 (underexpanded) how does one compute the temperature , static as well as the total pressure at the nozzle exit(say for gamma=1.4)? assuming jet exits in to ambient air with static pressure 14.7 psi . any suggestions would help.

thanks

 Joe October 19, 2007 11:33

Re: Supersonic nozzle exit conditions

First of all, a NPR of 1.2 will give you a subsonic nozzle. NPR > 1.89 for supersonic flow.

I assume you are trying to avoid modeling the nozzle itself and want to specify the conditions at the jet exit as the inflow plane to your solution. For anything but and ideally expanded jet (where you can use simple 1-D gas dynamics to get the conditions) this is a bad idea. I always include the nozzle geometry as part of the simulation.

 Betty October 23, 2007 15:09

Re: Supersonic nozzle exit conditions

Thank you for the suggestion Joe. Just to begin with I wanted to keep things simple, and that's the reason I thought of specifying the Nozzle exit conditions. Is there a way of getting the flow properties at the exit plane given jet exit Mach number 2.2 and the nozzle pressure ratio 1.2?

Thanks again.

Betty

 Joe October 23, 2007 16:27

Re: Supersonic nozzle exit conditions

Nozzle Pressure Ratio is usually defined as the total pressure in the nozzle plenum divided by the ambient static pressure. You have a mismatch between Mach and NPR. For an NPR of 1.2, the Mach number should be ~0.5. For a Mach 2.2 nozzle the NPR should be 10.7.

 Betty October 24, 2007 14:43

Re: Supersonic nozzle exit conditions

Thanks again Joe. Here is something confusing me. Please take a look at the following website.

http://www.grc.nasa.gov/WWW/wind/val.../axinoz01.html

The study is about a supersonic jet flow (perfect expansion), from a C-D Mach 2.2 nozzle. The nozzle pressure ratio here is 0.09063 as per their definition and it would be 1/0.09063 = 11.0338 if we follow your definition. My question is how is this a perfect expansion ? wouldn't perfect expansion ratio be p/p0=1=po/p?

Other question is how is the nozzle exit velocity computed, it is given as 1770 ft/sec?

Also if this jet needs to be operated at any Mach number say 1 what would I need to change?

Betty

 ag October 24, 2007 15:41

Re: Supersonic nozzle exit conditions

A perfect expansion means there is no shock in the nozzle. All of the energy contained in the fluid at stagnation conditions is converted to kinetic energy at the nozzle exit. Since there is no shock in the nozzle, isentropic flow can be assumed throughout the flow and the conditions at any point in the flow can be computed easily using the isentropic flow relations that can be found in any first-year compressible flow text book. Alternately the NACA 1135 tables can be used.

If you wanted to run the nozzle at M=1, truncate the nozzle to retain only the convergent section and run a pressure ratio p/po <= 0.5283. Then you'll have M = 1 at the minimum area, which will be the nozzle exit. You can't do a converging-diverging M=1 nozzle (at least not isentropically).

 Betty October 24, 2007 16:51

Re: Supersonic nozzle exit conditions

Hi ag, Thank you for the prompt reply. If the flow is underexpanded(Nozzle Pressure ratio = 1.2)then how would I compute the nozzle exit mach number. It's a little confusing for me. I am just trying to get the nozzle exit conditions for a Mach 2.2 underexpanded nozzle flow. It's from an old paper :-"The impingement of underexpanded, axisymmetric jets on normal and inclined flat plates" by Lamont and Hunt .

One other question was what is meant by Mach 2.2 nozzle? Is this related to the area ratio? What is the maximum speed a Mach 2.2 nozzle can achieve??

Thank you very much in advance.

Betty

 shuo October 25, 2007 07:13

Re: Supersonic nozzle exit conditions

Hi Betty,

I am also simulating a superonic imping jet. What method are you using?

Shuo

 ag October 25, 2007 09:21

Re: Supersonic nozzle exit conditions

A CD nozzle has two design points where the flow is isentropic thorughout - one exit pressure yields a subsonic flow, and the second exit pressure yields a supersonic flow. The supersonic value is termed the design condition. Thus a Mach 2.2 nozzle is designed to operate at a pressure ratio that produces a M=2.2 flow at the exit with no shocks. This pressure ratio is dependent on the nozzle area ratio, and hence the design condition for the nozzle is dependent on the area ratio.

A nozzle that is underexpanded possesses an exit Mach number that will fall somewhere between the two isentropic conditions. You are applying an exit pressure (and hence pressure ratio) that is too low to give smooth subsonic flow in the diverging portion of the nozzle, and too high to allow the flow to expand to the supersonic design condition. Nature will seek to match the exit pressure of the flow to the imposed exit pressure and to do this a normal shock will form somewhere in the diverging section of the nozzle. In order to determine the exit conditions you have to determine where the shock forms - this problem is addressed in any first-year text on compressible flow.

An overexpanded nozzle is one where the exit pressure has been dropped below the design condition, in which case the flow can accelerate at the exit to the design condition, but then further expansion takes place outside the nozzle in a complex series of oblique shocks and expansions as the pressure in the jet adjusts to the surrounding pressure. In general, the highest useful speed a Mach 2.2 nozzle can generate is whatever velocity at the exit divided by the local speed of sound gives M = 2.2.

 Betty October 25, 2007 13:19

Re: Supersonic nozzle exit conditions

Thank you ag, that was helpful.

 Betty October 25, 2007 13:21

Re: Supersonic nozzle exit conditions

Hi Shuo, I am using wind-us and what about you?

Betty.

 shuo October 25, 2007 18:20

Re: Supersonic nozzle exit conditions

Right now I am using symmetric and upwind TVD schemes proposed by Yee, Klopfer & Montagne 1990 JCP 88. Is WIND the commercial code by Bush and Cain?

Shuo

 ag October 26, 2007 10:44

Re: Supersonic nozzle exit conditions

WIND is the offspring of the marriage of the NPARC code and Boeing's TLNS3D code, with a healthy dollop of an unstructured solver whose name currently escapes me. See

http://www.grc.nasa.gov/WWW/winddocs/

 upal_arif May 24, 2012 00:26

Looking for qualified freelancer to simulate supersonic flow through C-D nozzle using fluent 6.2.16