hello all. i am a little confused and wondered if someone can point me in the right direction.

1) firstly, is the following statement true.... image a turbulent jet flow. if we over predict the dissipation of turbulent kinetic energy, then there will be less enegy and motion in the eddies to mix the jet. therefore if we DO over predict the dissipation of turbulent kinetic energy the modelled jet will mix and spread less. are these statements true???

2) secondly, based on the first points, if in solving the navier stokes equations we use say an upwind scheme, i.e. a dissiaptive scheme, what effects does this have on the same jet simulation. i would have thought the dissipation would again damp fluctuations and therefore cause less mixing? but also the upwind scheme will 'smear' the solution on the mesh and therefore 'apparently show more mixing'. what are the effects of the upwind scheme on a spreading jet and how do these effects differ from the ones discussed in the first point i made.

any comments would be great as i am (as you may tell) a little confused.

The fundamental mechanism of upwinding is to take the nodal information from an upstream node (E) & to use it in place of the information at node P. Higher order upwind schemes just extend the process to further upstream nodes.

This process tends to 'smear' information across the simulation grid from the upstream side - hence the 'artifical diffusion' - it gives the appearance of what a fluid with greater viscosity would look like. This is upwind at its 'well known' level. In addition, which side should the upwinding be taken from? In many cases, the upwinding answers are just plain wrong. Look at the examples in most FVM text books. CD always seems to get close to the exact solution - before it reaches some magic limit, whereafter it blows up.

This 'nodal-strapping' process unfortunately eliminates certain underlying physics (a minute flow reversal mechanism). The problem is that folks have not understood the underlying mechanism for solution instability & have found the magic fix with upwinding. Golden rule - you may not strap out physics.

In CD flows, the flow-reversal mechanism is allowed to exert its rightful role. Unfortunately this is total disaster for a 'steady solver', unless it has enough inherent numerical viscosity to squash & suppress this flow-reversal phenomenon. The existing knowledge in the Engineering world is that flows become unstable at certain Reynolds numbers. I have found this to be only part of the story. Flows actually become unsteady at very, very, very low velocities. Reynolds observed a particular mode of unstable flow. Turbulence is deterministic.

This is why I avoid upwind & its friends. I do not use turbulence models - I find them of no use.

If you want to simulate the jet - instabilities, reversals & all - then I would use CD & a transient solver at small time-steps & very fine mesh. Take regular snapshots as the solution progresses & make a movie for yourself. View the movie & let your minds-eye absorb the finer details. Your minds-eye will then allow you to understand the real mechanisms at work.

A good FEM scheme will also showcase the physics better than FVM methods in terms of the details it will show.

Do not be in a hurry to stabilise the flow. Let transient analysis work for you - albeit a little slow. Any form of flow stabilisation is imposing existing understanding upon unknown physics phennomena.

I hope this helps your understanding a little.

diaw...

thankyou again diaw, you inslights are always very interesting.

however i would also like any other comments any readers may have on the comments made in the original post, in terms of the differences between over predicting the dissipation of turbulent energy and the use of a dissipative scheme in the momentum equation.

thankyou.

Hi Paul, I strongly recommand: never use upwind schemes for any field value in a CFD-simulation and never use a steady-state solver, when the problem is unsteady. Exception: You are interested in appropriate initial values for your final simulation. Best regards Marco

Marco, you are my hero... perfectly said...

Not many folks bold-enough in the CFD world to say that...

diaw...

Actually, high-resolution upwind-based schemes have been (and continue to be) used in countless CFD simulations and provide very good results - even with turbulence models. Unless you are purposefully running DNS (with all the associated work) and have a need to resolve all the scales of the flowfield, throwing extra points at a problem and simply reducing the time step is inefficient and can be counterproductive. Blanket statements to the effect that upwind schemes should never be used are at best hyperbolic and worst confuse CFD novices, unless you have some hard data to present to back up said statements.

Hi Ag,

Let me put it this way.

Upwinding (nodal-strapping) is useful as a convection-stabilisation mechanism because it prevents a certain oscillating velocity-component from forming. My research has shown that this reversal mechanism (a very small scale) is vital to understanding the turbulence mechanism.

I believe that higher-order upwinding schemes actually allow a little of this component to creep through because they are strapped across multiple nodes & this offers a little more flexibility than the 'hard-strap' of pure upwinding.

So, if you want to model the physics correctly - don't use upwinding. Pure & simple.

The reasons for the use of upwinding techniques is never adequately explained in most of the books I have read.

I believe that there is no need for a 'turbulence model' if the physics is allowed to exert itself correctly. It appears that we are constantly trying to tell nature what is can, or can't do - to suit our need for a solution. I have learned to live with the physical phenomena that manifest themselves & for my research work do not use convection-stabilisation in any shape, or form.

The main issue in the N-S is that the choice of certain input parameters can drive the solution into a different mode to the 'bulk flow mode' we want to simulate. So upwinding has been found to help prevent this departure from a 'bulk flow' solution - but, it comes at a price - generally, incorrect answer.

diaw...

Well, there is another aspect. The engineering aspect that is. Usually a moderately good answer (i.e. slightly incorrect) can be deemed ok. Without the time-advantages associated with robust schemes and turbulence models, much engieneering work would be impossible. DNS is not an option (today).

However your input is really interresting diaw. Do you have any papers regarding your research in the field, that might be downloaded?

Best Regards

Diaw,

How do you solve a turbulent flow without a turbulence model?

Isn't that DNS?

Are you saying that Bousinessq and Reynolds were both wrong?

I'm getting good agreement with experimental data by RANS models and second order upwinding.

Is this pure fluke? Ar

I'm a novice so I'd like to be enlightened

'Ford Perfect' wrote: However your input is really interresting diaw. Do you have any papers regarding your research in the field, that might be downloaded?

diaw's reply: Hi, Ford... I am in the middle of a major research 'rush' at the moment with 3 computers running simultaneously round-the-clock, & am planning to set much of what I have been working with formally down in papers within the next few months.

It has been an amazing experience that began as a 'search for a singularity in the N-S' & for the reason why solutions tend to diverge when a 'magic threshold' is crossed. The insights gained have been somewhat like opening Pandora's box... a true 'paradigm shift'.

The N-S equations have so many interesting facets, that even with the new ground I've broken, it will take many years to uncover all its secrets.

diaw...

Hi Joe,

My research has shown that Reynolds was not wrong, but only halfway to the answer. The scaling he applied does work in some situations eg. for similar pipe lengths, but different diameters. The Reynolds number applied to diameter, scales linearly in that case. Beware when the pipe length changes, or end boundary-condition alters slightly.

Take a careful look at pictures of similar flow experiments & you will see sinuous phenomena beginning at almost the tube entrance. Take a look at Bejan's work on the onset of instability. He works with a sinusoidal shape. These phenomena indicate a flow field that is already unstable. I believe that the Reynolds phenomena is one form of unsteady flow phenomena - we call it turbulence.

I tend to adopt a 'brute force approach' & model the flow domains with tiny elements - I guess DNS would be the correct terminology.

I must stress that most of my theoretical development has been directly with the N-S themselves - reworking them & gaining a physical perspective on how all the terms fit. This predicted certain phenomena, which I have been 'proof simulating'. The turbulence effects are clear in the simulation - no need for a mathematic model to conjure them up - N-S does that already.

The issues with turbulence are that, in general the mechanisms are not understood. Science has proclaimed that turbulence is chaotic & can only be understood statistically. My work has shown that turbulence is 'deterministic' & reproducable.

Do not forget the effects of geometry when you scale - they change the game completely.

diaw...

Okey A couple of thoughts... Turbulence is deterministic ??? Too strong to say that, it is impossible to know the "exact" initial conditions of a "real" problem. Your simulations will be always conditioned on the initial and boundary condition. I do not know any Science statement saying that turbulence is "chaotic", moreover the only thing it can be say is that turbulent flows have some chaotic behaviour where small changes in the initial conditions produce solutions which are far away (bifurcation). So, What you mean by "reproducible" Brute-force approach? Whats the size of the domain? what problem are you simulating? If you keep reducing the domain you also have to include other effects, angle of contact of the fluid to the wall which change depending the material of the wall. Are you therefore away form the wall? Periodic BC ?

Regarding Numerics.

Central Difference (CD) schemes have higher formal accuracy than first order or upwind schemes so obviously they are better if they are using within stability limits. However in hyperbolic systems (Euler equations, sclar advection, Burgess..) the Godunov theorem states that ther is no better LINEAR scheme than first order. This simple rule is true, you can just check-it solving the 1D linear advection equation with the step function as initial conditions trying as many linear schemes as you want. To cirunvent this people use non-linear schems like TVD, ENO and so on. All this schemes introduce a numerical diffusion which of-course is non physycal but it is bounded.

If turbulent flows if you solve the flow field u,v,w with a TVD or upwind your solution will be too dissipative and you will destroy turbulence. However when you solve the N-S equations there is one equation which is hyperbolic in nature (the continuity equation). If you are using constant density then must of the problems are gone and the choices generally are DNS (spectral), LES (CD,compact schemes) and RANS (CD). In variable density, some form of TVD or upwind will be used either for the density or the passive scalar, ortherwise you could end up with negative density specially when large gradients are present.

So upwind and CD,both have their use

Salvador wrote: Turbulence is deterministic ??? Too strong to say that, it is impossible to know the "exact" initial conditions of a "real" problem. Your simulations will be always conditioned on the initial and boundary condition. I do not know any Science statement saying that turbulence is "chaotic", moreover the only thing it can be say is that turbulent flows have some chaotic behaviour where small changes in the initial conditions produce solutions which are far away (bifurcation). So, What you mean by "reproducible" Brute-force approach? Whats the size of the domain? what problem are you simulating? If you keep reducing the domain you also have to include other effects, angle of contact of the fluid to the wall which change depending the material of the wall. Are you therefore away form the wall? Periodic BC ?

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diaw's reply:

Hi Salvador, "Deterministic" in the sense that for a given set of I/C's & B/C's, the computed result will be the same - no need for a reliance on statistical methods. Many fluids books refer to the 'turbulence phenomenon' as chaotic in nature - thus requiring a statistical approach - since the 'mechanism' behind turbulence is not yet completely understood.

My concept of "deterministic" - as in having developed a reasonably clear insight into the mechanisms behind the turbulence phenomenon - thus allowing computation of these mechanisms from first principles, rather than reliance on either statisitics, or various 'turbulence' models. In essence, perhaps you could call this yet another 'turbulence model' - but it is based on a firm theoretical basis.

The N-S could definititely be understood as a 'chaotic' system, since very small changes in either B/C's or I/C's can produce some rather unexpected results. It all depends on whether the physics of each term in the N-S can be clearly explained. Then the so-called 'chaotic' concepts tend to merge with 'deterministic' concepts - it depends on the point of view - but, there are many, many cross-links in the N-S which can lead to unexpected results.

If you begin to understand fluids as a system of non-linear springs & then look deeper into non-linear springs & chaos theory, then you will soon realise the beast you are dealing with. The main issue is that the N-S can change 'mode' depending on more than just the I/C's & B/C's - the spatial & temporal discretisation affects scaling in a remarkable way.

Enjoy...

diaw...

A simple question:

What is the reason of turbulence? viscosity? or Nonlinearity? or IC/BC? If you can answer this, that will help me a lot,

Wen

Wen wrote:

A simple question:

What is the reason of turbulence? viscosity? or Nonlinearity? or IC/BC? If you can answer this, that will help me a lot,

-------------

diaw replies:

A 'simple question'...

In my view, the reason for the 'turbulence' phenomenon is a combination of all of the above.

Kinematic viscosity: affects dispersive/damping effect of a particular fluid ie. how much elastic/shear characteristic.

IC/BC's : Will demand certain physical solutions from N-S.

Non-linearity: This is a fact of the N-S equations - in particular the 'substantial derivative'. This is managed in different ways, depending on the type of solution looked for.

I hope that my comment answers your questions, but, I'm sure it really doesn't give you much to go on... I have my own views, which are certain to be contrary to those of most readers. Such is the nature of physics.

diaw...

Thanks,, I enjoy thinking (most of time in vain) and talking (which reminds me I'm alive)

What confuses me a lot is people always say that viscosity has the effect of dissipation, damping, blah blah to the flow. And now mostly, people use eddy-viscosity kind of concept to model turbulence. If that can be a good method, doesn't mean that the "simulated" turbulence will be more damped (dissipated) then the true problem? If there is no viscosity, then should there be no turbulence? I think turbulence concept it self is the problem, it's not well defined at all.

Also, about the nonlinearity, does god know about this? I bet it's more a man-created stuff. When we say nonlinear problem, nonlinear physics, blah, blah again, we really mean the equations we humans use to describe the nature are nonlinear. And sometimes I wonder why can't we just creat a better math tool? If that tool exists and then we don't have nonlinearity, then should there be no turbulence at all?

Wen

Hi Wen,

I think that we often try to prescribe to the physics what it should be doing, instead of adjusting our simulations & understanding to fit in with what the physics wants.

I prefer to let the N-S dictate to me during a simulation, rather than the other way round.

Non-linearities are a fact-of-nature, to be sure.

Turbulence seems to be a particular form of unsteady flow. I have been able to simulate various modes of fluid flow & am pretty confident of the underlying mechanism behind the phenomenon that we call 'turbulence'. Its no rocket science really. Again, just look at nature more closely.

A thought: At low speeds we have wave activity in water (sea waves etc). At high speed we have wave activity (mach >= 1, shock waves ). What exists inbetween?

diaw...