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Logesh June 18, 2003 02:39

High mach number flow
I have a flow problem statement as follows,

There is a big cylinder connected to a small cylinder, which in turn connected to a big cylinder. That is small cylinder in between two big cylinders. One side of the cylinder is open to atmosphere and another side is connected to low pressure (Pressure is not known but less than atmospheric pressure, but velocity is known)

This is simulated in CFD by applying atmospheric pressure at the inlet condition and applying negative velocity at the outlet. Whether this boundary condition is appropriate?

The second issue at the small cylinder region, the velocity is substantially higher than sound velocity. It is in supersonic flow (Shock and sound waves are formed). What model to use in this regard?

Currently, I am using segregated solver+implicit formulation with standard k-E turbulence model with ideal gas relation for material property in order to account for the compressibility effects around the small cylinder region.

Whether coupled solver is preferred than segregated solver?

Looking forward for the suggestions/comments.


Jim Park June 18, 2003 13:29

Re: High mach number flow
Are you talking about flow through these cylinders (an internal flow problem) or flow across the cylinders (an external flow problem)?

logesh June 18, 2003 22:55

Re: High mach number flow
It is an internal flow problem with maximum mach number of the order of 3.


logesh June 19, 2003 07:27

Re: High mach number flow

In the manuals it is mentioned that coupled solver is preferred than segrgated solver high velocity compressibility flows.

I have to play with courant number in coupled solver in order to get convergence.

The other query, I have in this regard whether the mass flow rate wouldn't change beyond mach number>1.

I tried different boundary condition values(negative velocity) at the outlet, which resulted in, change in pressure drop.But the mass flow rate remained the same.Whether this is expected behaviour or something unusual?

Regards, Logesh

Danny Tandra June 19, 2003 11:36

geometry ???
I tried to understand the geometry of your problem here.

If the diameter of the cylinder is fixed (constant) then I don't think you can get supersonic velocity at the small cylinder.

For compressible flow in a pipe with constant cross section area: 1. if you start from subsonic flow, the maximum velocity that you can get is sonic velocity M=1 2. If you start from supersonic flow, the velocity will decrease to M=1.


Apurva June 19, 2003 13:31

Re: High mach number flow
I guess you are using Fluent for this problem.

Best solution is go for Coupled solver with 2nd order discretization, use explicit solver, intially start with low CFL .., also do adaptation of grid on regular intervals based on Mach number i.e. around mach no 1. You will get better solution.



logesh June 20, 2003 00:21

Re: High Mach flow geometry ???

Tandra:- I explain the geometry once again.

The big cylinder is connected to inlet of small cylinder.The outlet of small cylinder is connected to big cylinder.It is similar to converging,diverging nozzle.The only difference is big cylinder aren't tapered.Therefore changes are stepped fashion from big cylinder to small cylinder diameter.

Apurva:- Thanks for your suggestions. I will try the same. Suggestions from fluent manual also in similar lines for high velocity compressible flows.

Have a nice weekend.


Nicola June 20, 2003 06:18

Re: High mach number flow
As in a converging-diverging nozzle, mass flow rate gets its maximum value when back-pressure is lower enough to have a sonic region in the pipe. Once you have a sonic flow (if the flow were frictionless and adiabatic, this condition should be reached at the point of the minimum of the cross area) the mass flow rate doesn't increase even if you lower the back pressure. Of course, you will have a complex interaction of shocks and expansion waves after the sonic region. You can see by yourself that this shock system will change with the outlet pressure.

In my opinion, a velocity boundary condition at outlet plane is not the best choice because when Mach number goes to infinity then velocity reaches asymptotically its maximum value (k*R*Ttot)^0.5. I would use a pressure condition at outlet.

Hope it helps

logesh June 20, 2003 09:51

Re: High mach number flow

Thanks for your valuable comments.

I will try to get pressure outlet condition.

"Once you have a sonic flow (if the flow were frictionless and adiabatic, this condition should be reached at the point of the minimum of the cross area) the mass flow rate doesn't increase even if you lower the back pressure".

Do you have any reference for the above statement.Some text book or web-site reference.I already searched in google,once again I will do it.

logesh June 23, 2003 02:03

Re: High mach number flow

Whether increasing the small cylinder diameter will be of any help in achieving least pressure drop and the same mass flow rate.May be it is better to achieve mach number 1 or sligthly less than that in achieving maximum mass flow rate.

Regards, Logesh.E

Nicola June 30, 2003 08:30

Re: High mach number flow
Hodge, Koenig, Compressible Fluid Dynamics, Prentice Hall is the book I used during my studies, but I think you can look in many books concerning compressible flows.

I have found this link:, I hope it will be useful.


Nicola June 30, 2003 09:03

Re: High mach number flow
If you increase the small cilinder diameter then the mass flow rate at sonic condition will be higher. If your goal is the mass flow rate, raise the back pressure and increase the 'throat' area to avoid supersonic flow while keeping constant the mfr. If you want to have the same exit Mach number to study the shock interaction, then you have to use the same pressure ratio Pexit/Ptot_inlet: increasing the cross area of the small tube, while keeping the same pressure ratio, will reduce the shock intensity until the shock will disappear.


logesh June 30, 2003 09:43

Re: High mach number flow
Hai Nicola,

Great and very useful reply.

The web-site mentioned is excellent and useful for my application.

Thanks for spending time in sharing your knowldege.

Regards, Logesh.E

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