Axisymmetric nozzle design using the MOC
Hi,
I'm trying to design an axisymmetric convergentdivergent 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 2D solution but not axisymmetric. If anybody has such code or any helpful advice it would be greatly appreciated. Kind regards, Will James 
Re: Axisymmetric nozzle design using the MOC
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 
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 axisymmetric cases. This is of course not "undefined" in the case of 2D flows thanks to the PrandtlMeyer 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 hitandtrail 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 axisymmetric 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 PrandtlMeyer 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 
Moc
I only worked on 2D MOC; recently started reading abt 3D...
Have you worked on contour design using MOC? Regards Alikami 
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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 
Moc
What i mean is to contour an axisymmetric using MOC , to maximize thrust.
any idea? regards alikami 
Moc
sorry ...Axisymmetric super sonic nozzle

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http://img838.imageshack.us/img838/7605/54287876.jpg 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 
Mach 2 Nozzle
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 
Moc
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 
Nozzle
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 
Moc
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 
Nozzle
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 
Moc

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