I have the following problems:

1) Do u know any paper with the numerical investigation of a vortex breakdown of a compressible swirling jet (be carfull, I need "compressible")

2) Do you know any simple test case for an axisymmetric flow but with all three components of velocity ? ( Vr,Vz,Vteta different than zero but all the derivatives respect to teta=0 ) Possibly I need a viscous test and inviscid test.

3) I'm trying to simulate a swirling jet of an incompressible flow...but I m using a compressible flow solver. In your opinion what should I do to achieve similar results? I mean....what needs to be done to make the density constant? ( plz, don't answer about Mach number!!!)

Thank You

In simulating chemcially reacting flow, if I do not want to resolve the chemical time scale, I use implict scheme, selecting the marching time step solely based on CFL number. My question is: Is there any restriction on the spatial grid size that is linked with chemical time scale similar to CFL? It seems that the chemical souce terms do not provide any spatial scale.

Daniel,

I am afraid I have only seen incompressible vortex breakdown solutions (especially of Turgut Sarpkaya and Juan M. Lopez), but maybe the latter author also published something for compressible flow. Have a look in his website (http://math.la.asu.edu/~lopez).

BTW, if you wish to to simulate a swirling jet of an incompressible flow, why are you looking for solution for compressible flow?

As to your last question: most of the codes defined as "compressible" solve the continuity equation with density as the solved-for variable. This approach is naturally problematic when density is constant. Even for nearly-constant density the set of transport equations are difficult to solve for Mach (oops, sorry for using this word...) No. less then about 0.3, and some special treatment is needed. However, there are also codes used for both compressible and incompressible flow, where variants of SIMPLE are typically used to allow you to overcome this difficulty. Therefore, the answer to your question depends on what approach is taken by your solver.

2) For an inviscid flow, you can try a free-vortex axial flow (Vtheta = constant/radius). You should obtain a constant Vx.

Excuse me, could u explain me again? For Re-->inf, a free vortex axial flow is a steady solution of the Euler equations if a radial pressure gradient can balance the centrifugal force. In this case...nothing hat to happen. If there' s not balance, well, what should happen is the growth of a radial component of velocity, so the flow is blowing to the center or from the center. Can U tell me why there is a Vx? Thank You

Many Thanks, RAmi...I think I ll Ask u something else later!

Hi Daniel,

Consider a straight axial annular duct (with inner radii different from zero).

At inlet, consider the following boundary conditions : Vr =0, Vth = const/r, total pressure and total temperature = const.

At outlet, impose the pressure, verifying the so-called "simple radial equilibrum" : dp/dr = rho* Vth**2/r.

In this case, the solution of the Euler equations should give you a constant axial velocity. You can check this by injecting the Vth law in the Euler equations and supposing Vr = 0. In the field of the turbomachine, this results is also given by the ISRE (Isentropic Simple Radial Equilibrium).

I hope this is more clear.

Also, if you find a viscous axisymmetric test case with swirl, please let me know (jf . simon @ ulg . ac . be).

JF

Hi, thanks for the answer. Starting from a completely 1d field (p gradient=centrif force) and a velocity profile Vx constant EVERYWHERE, not only at the inflow, I expect that for the effect of viscosity and for a mass balance at the inflow, I lose my 1dimensionality, and have a bubble just near the inflow.

Every thing is easy for incompressible flow.

II Derivative of Vteta <> 0 ===> there's a viscous force acting in tangential direction ===> the balance between pressure gradient and centrifugal force is broken ===> A Vr increase and blows from the center ===> Since the Vx at the inflow is fixed,

for the continuity it has to reduce along the axis achieving a stagnation point.

If the flow is compressible, as in my case, what happens is that at the center the density is reduced, but not the velocity, and this is my tragedy! Bye to everyone

Hi, thanks for the answer. I want to specify better my point

Starting from a completely 1d field (p gradient=centrif force) and a velocity profile Vx constant EVERYWHERE, not only at the inflow, I expect that for the effect of viscosity and for a mass balance at the inflow, I lose my 1dimensionality, and have a bubble just near the inflow.

Every thing is easy for incompressible flow.

II Derivative of Vteta <> 0 ===> there's a viscous force acting in tangential direction ===> the balance between pressure gradient and centrifugal force is broken ===> A Vr increase and blows from the center ===> Since the Vx at the inflow is fixed,

for the continuity it has to reduce along the axis achieving a stagnation point.

If the flow is compressible, as in my case, what happens is that at the center the density is reduced, but not the velocity, and this is my tragedy! Bye to everyone

My code is a density based solver... This is something that has never convinced me too much: The Low Mach number reduces the accuracy of a compressible (Density based) code or it just reduces the efficiency to get steady solutions? I m for the second option...but I don't know, maybe you are close to Eli Turkel, and could ask him. Ciao

In the early to mid 90s, there were some studies in the form of swirling flows issued from swirl vanes into a supersonic coflow streams. the result is a shock-vortex interaction, and vortex breakdown was studied along that context. otherwise, there were studies in the compressible flow region over delta wings which the axial flow is usually "jet-like". would those help?

Hi Daniel,

Of course, with a viscous flow you shoudn't obtain a constant Vx. May be I shoud have recall it, but the test case I propose you was an INVISCID (compressible) test case.

Good luck,

JF

Dear Jf, I know you were talking of an inviscid test, but what you have suggested to me is to impose a pressure at the outlet. Let me be honest.... if you introduce an axial pressure gradient, it's quite obvious that you have a Vx! This is not what I'm looking for, even if, you right, it may be used as test. Thanks a lot

Daniel,

Would you please elaborate on the problem you wish to solve (geometry, BC, properties, models and methods)? If you can simplify it to the extreme while still keeping the issues you have problems with, it would help the forum to assist you.

Rami

http://www.ts.wb.utwente.nl/TS/index.html

contact professor Hoeijmakers. He is an expert on the subject.