Hi,

I'm trying to design an axisymmetric convergent-divergent nozzle for use in the calibration of supersonic probes. However, I'm having great difficulty in finding any program that will generate the contour of the nozzle using the method of characteristics. I have found code written in Fortran for the 2-D solution but not axisymmetric.

If anybody has such code or any helpful advice it would be greatly appreciated. Kind regards, Will James

If I am not mistaken, Fundamentals of Aerodynamics by John D., Jr. Anderson has it. But I am pretty sure that it has nice explaination about MOC used to design axisymmetric supersonic nozzle.

Danny

[Vivek Ahuja]

Based on some prior experience writing MOC software codes for a NASA short course material, I can vouch for thet fact that the design of 3D nozzles with MOC is a very different kettle of fish as compared to the 2D model from a computational and theoretical standpoint. The problem remains with the "undefined" region between the throat line and the first Mach line for axi-symmetric cases. This is of course not "undefined" in the case of 2D flows thanks to the Prandtl-Meyer equations and hence the initialization of flows is defined along the first sonic line characteristic for 2D flow and using reflection techniques for the centerline calculations.

For 3D flow, thanks to the undefined region, the computation must start from the centerline with a specified pressure distribution along that axis and must move radially outwards. The problem remains in the hit-and-trail methodology that must be used to get the proper characteristic solution for the 3D flow case with such a relatively intuitive and therefore probably unrealistic initial condition.

Also, Anderson's explanation for the axi-symmetric case in his book only describes the basic equation derivations. How to numerically integrate that equation (using finite difference schemes) and also to apply in the initial and necessary boundary conditions as well as the concept of the undefined region and its difference with the Prandtl-Meyer expansion system of 2D systems is not discussed. Frankly speaking, that left me thoroughly disappointed since we had to eventually develop that theory independently.

I would be very interested to be able to discuss our efforts with any members here who have worked on the 3D MOC problem as well.

Regards

[alikami]

I only worked on 2D MOC; recently started reading abt 3D...
Have you worked on contour design using MOC?
Regards
Alikami

[Vivek Ahuja]

Originally Posted by alikami

I only worked on 2D MOC; recently started reading abt 3D...
Have you worked on contour design using MOC?
Regards
Alikami

Part of our effort was to develop a series of GUI enveloped VISUAL FORTRAN codes for MOC as a tool in airframe design. The codes developed ranged from basic 2D internal and external flows to axi-symmetrical flows and currently to 3D versions that are completely generic (Internal/External). One aspect of this approach was contouring of airframe shapes and components for steady supersonic flight. So we also had to develop 3D grid generation subroutines for entire airframes in FORTRAN.

Is this something close to what you are looking for? If it is, let me know and I can discuss the details of our efforts...

Regards

[alikami]

What i mean is to contour an axi-symmetric using MOC , to maximize thrust.
any idea?
regards
alikami

[alikami]

sorry ...Axi-symmetric super sonic nozzle

[Vivek Ahuja]

Originally Posted by alikami

What i mean is to contour an axi-symmetric using MOC , to maximize thrust.
any idea?

I am guessing you mean contouring the shape of the required nozzle for maximum thrust? I believe you might want to take a look at this code that I had developed some time back. Let me know if we are talking about the same thing. I have put an image of the code output for the contour design of a supersonic nozzle contour design for given performance parameters.



I can send the code to you (via email etc) but the forum software wont allow me to upload it since it exceeds the size.

Regards

[ardent]

Hi guys,

I have designed a supersonic nozzle M = 2 using method of characteristics. Since then I have drawn the geometry and have attempted to conduct a simulation in fluent. However, my results have come out incorrect, the Mach number at the outlet of the nozzle is 2.8. I have only simulated flow through the divergent part. In fluent as the input conditions I simply calcuated them based on the pressure ratio. For the outlet it is possible that i may need to allow more of the straightening part to allow the flow to settle, however, i doubt that this is causing incorrect results. The discharge is straight to the atmosphere, so I expect a shock at the exit.

Does anybody have any codes for the generation of the contour to compare my own against?


Any advice would be appreciated.

R.C

[alikami]

From 1D theory of gas dynamics
mach is function o area ratio....
just check ur area ratio if it is ok or not?
regards
alikami

[ardent]

Hi thanks for your advice, I have since checked my area ratio, it is ok.

so I guess it must b my wall profile that is incorrect?

The Mach number at the exit is around Mach 2.3 and my design condition is meant to b M=2 which is quite a way out.

Do you think it could have anything to do with the fact i did not add a straightening part to the nozzle (as in where the wall is parallel) or that I have not drawn the converging part? Maybe Fluent cannot model the flow at the throat correctly hence an incorrect exit velocity?

I have been searching for codes for the Mach 2 or Mach 3 but I have come up empty handed.

regards

R. C

[alikami]

Well if your nozzle area ratio suggest mach number should be 2 , then some problem in your code, as 1D theory cannot be that incorrect.

can you send me your data, geometry and working fluid , to have a look.

Regards
Alikami

[ardent]

Right now i'm totally stuck for ideas why it is going wrong, so i may just start again if I come up empty.

I can send that through no problem just message me your email address and i'll send the case files unless i can send them through here. Do you use the fluent solver?

Many thanks,

R. C

[alikami]

Yep

a1k1s1@yahoo.com
regards
alikami

[ardent]

I do have one question which may solve everything before I send through the data so I dont waste your time:

If you use the method of characteristics to find a contour, does that mean once u define your throat height in the MOC calculations, that the exit height will be in the order of the area ratio necessary for design condition?

Or once you find the contour u then need to apply the area ratio?

Regards,

R. C

[alikami]

sometime ago i read RAO method for contouring.
if you know the throat diameter ( meaning you know mass flow rate)
so for the mass flow rate given , you give length of nozzle divergent as input.and maximize the thrust within that length.

Generally if u r desiging ideal nozzle (for gamma and moleculaer mass of gas) , for certain mach number ....
chk kernel region as the last charcteristic on initial expansion will be ur exit mach number. so the location is important .check tollerance on the location (x) .
but normally ideal nozzle is about L=50rt very long so not practicle. use TIC truncated ideal contoured nozzle, and in advance give length to be truncated , normally 15 to 20 percent less than 15deg conical nozzle.

[alikami]

one more thing the design criteria i think are
1. mach number and area ratio or
2. area ratio and length

[alikami]

Dear R.C
can you check the mass flow rate from last charateristic startinf from point A and intersecting at center line. .... compare with the reflected charateristic from axis to point E.

check chart 6
1. black line :: throat area decreases in initial stage , not sure how , it will increase area ratio

2. red line :: why the initial straight portion ? and exit radius decrease ? not sure why??
hope it helps

I think some problem in the code .

check chart 1

inflection point is far from throat even the angle is very small less less than 14, normally it is greater than 25 .... and arc length joing the bell and throat is equal to :: l = r*theta

one more point all characteristic start from point A normally last characteristic orignates from point of inflection and is the design mach number....

regards
alikami

[ardent]

Hi there

I have looked at it and I now have a new contour, however, I also have found a report that has solved for the profile using method of characteristics. I used this profile from the report and I am still getting Mach 3!

Do you have a code or know where i can find one to compare my steps against?

regards

R.C

A big thank you also for looking at what I have completed, much appreciated!

[alikami]

Can you mail me report?
May b some problem in FLUENT simulation....
I dont have a profile design code, one of my friend made some
3D MOC for analysis, presently he is out, i think he will be bac in 10 days.
I will ask him to check on his code....
If you have simulated the nozzle from report , send me the case file
Regards
Alikami