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June 25, 2008, 07:50 
problem with highly underexpanded free jet

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I need to modelling an underexpanded transonic free jet. But my problem is that i couldn't obtain the correct shock structure! In fact, I have already read all the messages about the transonic jet, nozzle flow, etc. in this forum. However i didn't find the solution. In the paper: "Numerical Computations of steady transonic and supersonic flow fields, A.PALACIO, International journal of heat and mass transfer. Vol33. No6 pp11931204 1990" The author did some underexpaned free jets models with NPR = 1,88 ; 2,32 ; 3,56. Finally, he obtained the mach number distribution. In fact, i have obtained the same results. HOWEVER, when i increased the NPR, (=7,5 for example,), the shock structure (or the mach number distribution) remain the same with the NPR=3,56 suprisingly!! the only difference is the position of the "mach disk" (whose diameter was much less than the literrature). 

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June 25, 2008, 08:08 
Re: problem with highly underexpanded free jet

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My flow is transonic, so in the field, we could have supersonic and subsonic zones and also at least a mach disk
I use cylindrical polar coordinate. At the INLET of jet, i put in the velocity (Ma =1,01), and the inlet pressure (NPR =7.5) Kin et Ein. And then at the upside of that INLET2, i defined costream, ( W=17,3 m/s and P = 101325 Pa). then at the upside of the stream, i defined an OUTLET (external pressure 101325 Pa, coef:1000; Velocity Z 17,3m/s and KEext and EPext) I used the parabolic equation (transonic), and the turbulence model is KEmodel, i actived the energy equation (enthalpy static) The calculation schema, i used "upwind"( i wanna use VANL1, but it hardly converge!) What's more, i did a thin mesh( calculated nearly 6 hours). However, i did not obtain the right result. 

June 25, 2008, 08:41 
Re: problem with highly underexpanded free jet

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By the way, i have studied all the jet examples in the library of Phoencis. There is only one example who have obtained the Mach disk (N113, with Mach=1 NPR=3.56), but strangly, they used the elliptic equation!! (Shouldn't we use parabolic equation for the case of the underexpaned transonic free jet, non?) Anyway, i have also tried elliptic equation, but the calculation could not converge!
The parabolic examples with underexpanded jet like 159; the NPR is so small(1,85) that there was no mach disk in the field. In addition, i studied also several supersonic jets cases, like case160 (Mach=2;NPR=1,8 3D or 2D parabolic) case161(mach=2.39;NPR=3,8 parabolic) case911(same with case161, but elliptic). Comparing the result of case161 and case159, i found that appearently, the elliptic equation was more suitable for the calculation! So would you please give me same suggestion? Thanks a lot! 

June 29, 2008, 02:01 
Re: problem with highly underexpanded free jet

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I had struggled with a similar problem for several months (some 15 years ago), and was never satisfied with the results. I attempted to solve the inviscid flow of free underexpanded jets. I had many discussions with CHAM, and the best they offered was a turbulent solution, which also wasn't too close to the reference case. The shock smearing was very large, and occasionally nonphysical distributions (such as reversed flow, negative temperature etc) appeared behind the Mach disc. I haven't seen any advance in CHAM's announcements in this regard, so I assume the normal shock treatment was not significantly improved during these years.
As to the use of the parabolic solver, in principle, it may accelerate and enhance the efficiency of the solution if your equations are indeed parabolic, by neglecting some small terms. However, if this is not so (and in your case there are regions of low subsonic flow behind the Mach disc and also viscous effects that may invalidate omission of these terms), it is advisable to use the full NS equations, which in PHOENICS are only treated with the elliptic solver (and even there some terms are omitted, not always with proper general justification, as I had learned by numerous discussions with CHAM's support). 

June 29, 2008, 05:18 
Re: problem with highly underexpanded free jet

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Thanks a lot, Rami
In fact, recently, I have tried with the elliptic equation. Finally, i obtained the mach disk, however, the smearing was really large, a reverse flow appeared behind the mach disk, just like what you've mentioned. What a pity that CHAM did not improved the treatement of the shock during so many years! In fact, i have found some good results in the litterature, however they used Fluent, or some others special privite softwares. They obtained the mach disk. And compared with the litterature, their results were quite reasonable, particularly by using Fluent, they have modeled the whole field and finaly found a very impressed result which was very similar with the theory. however they used unstructured grid which was not supported by Phoenics. 

June 29, 2008, 05:42 
Re: problem with highly underexpanded free jet

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Raaf,
Would you please post the references you had found? I would be interested to see, although I am no longer working on such problems. I agree it is a pity this issue (better treatment of normal shocks) and many others (notably using unstructured grids) were not treated by CHAM. Over the years I was a PHOENICS user (since 1990) I did my best to convince them to do it  but failed. This may be a reason for many users (including our group and all other groups known to me in my country) to switch to other packages. In our case, we did it very unwillingly, since we had spent much effort to build a huge GROUND model fitted to our needs, but having too many unresolved issues made our progress impossibly slow till we gave up. Rami 

June 29, 2008, 06:09 
Re: problem with highly underexpanded free jet

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"Contribution Ã l'étude numérique des jets supersoniques sous détendus, Guillaume LEHNASCH" in french.
and the result of FLUENT is here: http://cfdchina.com/1st/007/007.html Which is in chinese However, some english papers also exist. It's not on me at present. I'll post it here as soon as i find it. 

June 29, 2008, 07:37 
Re: problem with highly underexpanded free jet

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Unfortunately, my Chinese is no better than my French, so I'll wait for the English references. Thanks a lot.


July 17, 2008, 15:02 
Re: problem with highly underexpanded free jet

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I have done similar things using the elliptic solver, and I believe the problem may be the pressurelinked scheme that SIMPLE uses. In looking around the web, I believe there's a consensus that SIMPLE can only be used up to about MACH 3.5 or so, then one has to switch to a momentumbased solver. YMMV. Patti


July 17, 2008, 15:04 
Re: problem with highly underexpanded free jet

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I obtained good results below MACH 4 with the elliptic solver (no reverse flows) but it is tricky to get good convergence, and the higherorder schemes introduce even more instability. I think the reverse flows you mentioned (if below MACH4) are due to not having optimal relaxations.


October 23, 2008, 21:06 
Re: problem with highly underexpanded free jet

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Did you take a look at the Case Library, case 911? It is a Mach 2.6 underexpanded jet.


April 8, 2009, 13:36 

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