I am studying a round jet using a transient code, and have tried different turbulence models. The steady state solution I get at any particular z agrees pretty well with the text book, theoretical answer. But the time dependent solution at any given z (before that location reaches a steady state) seems to depend greatly on the choice of turbulence models.

I have two questions:

* Any reference for a the time dependent behaviour of a round jet?? Can someone point me to the "accepted" correct answer?

* Does anyone have experience using Reynolds Stress (RSM) for a 2D geometry; is it inappropriate to use RSM in 2D? (n.b. after all, 5 or the 7 equations are still meaningful)?

The time dependent results for a 2D (axisymmetric) jet using RSM are quite different from those using a modern version of k-e.

Thanks for any help

I neglected a qualifier or two:

* compressible; ~0.2 to 0.5* the sound speed

* Reynolds number: ~25,000

What you are saying is : 1) your code predicts steady state round jet solution independent of the turbulence models used. 2) your code predicts different transient solutions, depending on the turbulence model used. My feeling is: different turbulence models should produce different answers. Jet problem is a boundary layer type problem. Therefore, you need to have enough mesh points to cover both near field and the far field ( downstream ), say 41 points at jet exit to cover the jet port, and expand the mesh gradually in the downstream direction. In this way, you will have good enough resolution to cover the steady state part of the jet. Outside the jet, you still need mesh points to cover your computational domain. For the transient flow problem, assuming the jet is oscillating, it's somewhat difficult to define the jet boundary with fixed mesh. Since you did not mention how you run the code, real transient or accelerated for steady state mode, it's hard to tell why the transient solutions are different. Also you did not mention the transient nature of the problem. ( Initial flow field set equal to zero, and set the jet velocity then start the calculation ?) Try to improve your mesh first, then look at the jet near field. you should have a potential core region in your computed result. ( There is not much you can do when you are using a black box code. Mesh refinement is the first step.)

John, you brought up very good points regarding the solution dependence on mesh resolution and initial conditions.

The transient jet problem will require a solution methodology that uses adaptive gridding at each timestep - In order to resolve the jet flow correctly one has to resolve the vorticity field (or for the velocity-pressure people the velocity gradients) at the jet boundary.

However, having said that, since the same mesh is being used for all turbulence models (a wild guess since physical models are, hopefully, grid-independent) I doubt the difference can be attributed to meshing - we don't know how serious these differences are though! For example, you can use all the meshes in the world with the k-epsilon model and you will still not be able to capture the proper physics, because of the inherent problems of that model in capturing the important counter-gradients in this problem!

The problem is, IMO, in the turbulence models themselves. Most models start by _time averaging_ the statistics out of the Navier-Stokes equation, and for closure use empirical data based on _steady state_ experiments. Then they go back and write the transient equations using these constants. And when we don't get the correct results we wonder why Just because we can write transient k-epsilon equations doesn't mean that we are actually solving the transient problem!

Some models, because of including more correct fundamentals, will do better than others for the same grid distribution and the same time and space differencing order.

Again, we need to know what these differences in the results are. Are they in the frequency of "shedding"? are they in the rates of entrainment at different elevations? etc.

adrin

In the transient flow domain, a seemingly simple round jet problem becomes a very tough problem to handle. For round jet problem, sometimes I just estimete the turbulent Reynolds number first ( Reynolds number based on the eddy viscosity) , then used it in the constant viscosity Navier-Stokes equations. ( equivalent to a low Reynolds number laminar flow). I guess, it's all depend on what you are after in the calculation. Are you suggesting that there are steady-state turbulence models and un-steady-state turbulence models ?

All good questions and remarks. Let me elaborate.

I have run the simulations on a 100,000 element 2D grid that is ~60x500 jet diameters in extent. The grid is pretty well resolved in the region ~10x100 jet diameters nearest the jet origin, and well resolved in the inner most 5x50 jet diameters. The rest of the grid is more course and used to enforce BCs.

Since I proved to myself in earlier runs that the the jet's theoretical opening angle is reproduced in an orthogonal grid, I customize the current grid to be parallel to the jet's opening angle. This allows a more judicious use of grid cells. I do not do any time dependent grid refinement. The identical grid is used for both cases.

The inlet flow rate is constant.

The RSM version of the model does not show as much structure as the k-e version of the model. This is the opposite of my previous experiences with comparing results from RSM and k-e simulaitons. Usually RSM shows more separations (recirculations, etc) than K-e. This is why I was suspicious of the appropriateness of using RSM in 2D (any comments about this??).

The RSM jet propogates more quickly and has much less vortex shedding than the k-e results.

Reactions??

My experience with two-equation k-eps turbulence model is that it's more diffusive, and most of the time, I had to lower the Cmu coefficient from 0.09 to a lower value. I developed my own Navier-Stokes code, so it is easier to control these parameters and functions in the model. In early days, there was a problem in solving 2-D jet and round jet with the same set of parameters. And the radial velocity component was used in the turbulence model to bring the round jet calculation consistent with test data. I am not sure whether it has been resolved or not. So the general feeling is that the two-equation k-eps model is more diffusive. I am somewhat confused about the unit you mentioned, the jet diameters. I am concerned about the total number of mesh points ( or cells) between the jet axis and the jet boundary in the radial direction at any axial station.

I am using ~45 cells in the radial direction between the jet axis and the jet boundary. The aspect ratio is near 1.0.

I too am used to K-e being more diffusive. That is what motivated my question about the appropriateness of RSM in a 2D cylindrical (axisymmetric) mesh. This is also why I am curious about a reference to a lab result for a time dependent measurement that could be used to validate (or invalidate) my simulation results.

Thanks for your time in reading and responding to these questions.

> Are you suggesting that there are steady-state turbulence
> models and un-steady-state turbulence models ?

No. I'm suggesting that all turbulence models (that I am aware of) are steady-state models; i.e., the empirical constants are independent of time! There _are_ no transient turbulence models that are commonly used.

adrin

Maybe the problem is: we really don't know too much about the round jet at all. It could be 3-D all the time, it's not 2-d axisymmetrical at all. I mean, the unsteady round jet flow may not be 2-D axisymmetrical .

> Maybe the problem is: we really don't know too much about
> the round jet at all. It could be 3-D all the time, it's
> not 2-d axisymmetrical at all. I mean, the >unsteady round
> jet flow may not be 2-D axisymmetrical .

For high Reynolds number flows, there is no doubt that the jet will not stay axisymmetric downstream of the jet inlet. However, close to the inlet, where most of the interesting/important time-dependent jet dynamics occur it is quite safe to assume that the jet will remain axi-symmetric. Since the jet is inherently unstable, a small perturbation will eventually lead to the development of streawise vortices, which itself causes the flow to change from 2D/axisymmetric to 3D.

It is easier to understand the jet dynamics if one looks at it in terms of the interaction of toroidal vortices that develop due to jet/surrounding interaction. In the simplest case - when the jet is just developing - one can view the jet as one toroidal vortex (or vortex ring). Now, it becomes clear - backed up by theory, experiment, computations - that a small perturbation around the azimuth of the ring (or the jet boundary) will eventually lead to the development of streamwise vortices - the 3D regime. But for this to happen, you need perturbation, time and distance, so near the jet the flow is most probably _not_ 3D.

adrin

I agree with you that in the near-field where the jet potential core still exists, the round jet flow field is axi-symmetrical. Downstream of that point, the 3-D nature of the jet will force the centerline velocity decay behave differently. So the important issue is whether you can capture the shear-layer development from the jet exit or not. ( that is to provide accurate initial profile at the end of the potential core station so that the jet decay can be handled accurately further downstream.)

>I agree with you that in the near-field
>where the jet potential core still
>exists, the round jet flow field is
>axi-symmetrical. Downstream of that
>point, the 3-D nature of the jet will
>force the centerline velocity decay
>behave differently. So the important
>issue is whether you can capture the
>shear-layer development from the jet
>exit or not. ( that is to provide
>accurate initial profile at the end of
>the potential core station so that the
>jet decay can be handled accurately
>further downstream.)

I have to take exception to this assessment of axisymmetry. I have to be careful about Re and Mach numbers in what I'm saying, but for a very wide range of flows, experiments and flow visualization shows the jet to be significantly 3-D long before the end of the potential core. If this were not the case the concept of coherent structures would have been much more useful than it is today. Even in very clean, quiet facilities, such as the one pictured in Van Dyke's "An Album of Fluid Motion" Fig 118, there is significant three-dimensionality before the end of the potential core.

Now there may be some regimes, especially low Re, high M, where this is not true, but these jets are more the exception rather than the rule in the real world.

So, there is a strong interaction between the inner edge of the shear layer. The disapperance of the core region tends to couple the inner edge of the shear layer more closely. Maybe the inner edge of the shear layer must diffuse inward more quickly in this region to account for the 3-D effect ?

Actually, my impression from flow vis is that longitudinal vorticity develops quite early in the shear layer, long before the two sides of the shear layer "feel" one another. Due to the strong strain rates in the shear layer, any azimuthal disturbance is highly amplified, be it from small imperfections in the nozzle or feedback from downstream azimuthal disturbances. The scale of this azimuthal instability is of interest to me. One estimate would have it related to the core of the ring-like vortices in the jet, e.g. an instability of the vortex rings. However I have also seen low order azimuthal modes at low Re, effectively causing the shear layer rings to tilt. When this occurs, the interaction between two rings at the point where they touch produces a very sudden cascade into small scale turbulence. Again, I'm not sure about the scaling of this behavior at high Re and Mach numbers, but these 3-D dynamics take place in the first few diameters of the jet, and generally higher Reynolds numbers simply accelerate the cascade process, making this happen closer to the nozzle.

Back to the point at hand, that of calculating time-dependent jet flow fields, I have seen many axisymmetric calculations of round jets, and none that I can think of had the right spread rate or potential core length as data. I've always believed that this was due to ignoring the azimuthal component of motion which strongly contributes to the growth of the shear layer. The few 3-D calculations I've seen do much better and show strong axial vorticity in the initial shear layer. I'll try to look up some URL's to illustrate.

James

The geometry at the jet exit probably affect the shear layer development to some extend, whether there is a round lip, or a sharp lip, or simply a hole in a flat wall, not mentioning the boundary layer thickness ahead of the jet exit. If you look at the wide range of possible flow patterns behind a circular cylinder in terms of the Reynolds numbers, then the mixing layer of the jet is simply an unsteady wake. So the lip thickness ratio ( relative to the diameter of the jet ) may also control the circumferential stability ( symmetry ). In the turbine flow passage calculations, I am having problems with the accurate definition of the trailing edge geometry. Bcause of the relative thickness the mesh code is unable to see the trailing edge geometry. As a result, the wake solution is un-predictable . The computational trailing edge definition actually changes from mesh to mesh. I think, it also applies to the real flow situations where the experimental data is also linked to the lip geometry in the tests. It's amazing to see that the loss is a function of the mesh used because the wake loss is not negligible. I think the jet exit case is similar to the blade trailing edge problem, we may have to define the geometry accurately also in order to nail down the solutions.