I have sajben nozzle encapsulating plasma. I have an inlet pressure at the upstream and atm. pressure at the downstream of the nozzle. I am currently simulating this phenomenon with flow and heat transfer module, The turbulence model is expensive from the computation - time perspective. What could I lose if I didn't include the turbulence model. Could anyone explain the physics from the perspective of cooling the plasma
The Reynolds number is a measure for the ratio of turbulent to molecular diffusion processes. When you have a problem with Re1000 you should suspect turbulent transport phenomena to be dominant. Typically when you pour milk in coffee without stirring it will taken a year before mixing is reasonable. By stirring you promote turbulent mixing and you reach perfect mixing within seconds.
Salaam!
I would like to point out colleagues to publications which I think are relevant in this regard.
https://www.researchgate.net/publication/234114374_THE_EFFECTS_OF_DISPERSAL_ALONG_ENVIRONMENTAL_GRADIENTS_ON_THE_DYNAMICS_OF_POPULATIONS_IN_HETEROGENEOUS_ENVIRONMENTS
https://www.researchgate.net/publication/260042030_Difffusion_and_Drift_Models_for_Population_Dispersal_from_Stochastic_and_Continuum_Views?ev=prf_pub
Kindest regards
FBMB.
Article The effect of dispersal along environmental gradients on the...
Article Difffusion and Drift Models for Population Dispersal from St...
Hi,
You should first build a Reynolds number with a clear characteristic length scale (the size of a eddy for instance if you observe some). Based on the value of this Reynolds number, you should be able to determine if turbulence has to be taken into account or not.
Basically, turbulence will accelerate your diffusion mechanism, but may not be relevant if the size of your simulation domain is rather small (then heat transfer in boundary layer may be considered).
Hope this will help.
Hello,
Indeed you should first estimate your Reynolds number. I don't know what plasma you are simulating but if it is fusion plasma you usually have turbulence also in the colder edge (the so-called SOL or Scrape-Off-Layer) so it should ideally be taken into account. The way to take it into account easily is just to add an heuristic turbulent flux of the form
q = v*p - chi*grad(p)
where p is the pressure and v and chi are a velocity and diffusion coefficients. In your heat equation the divergence of this flux would appear.
You can probably take the coefficients constant for your purpose. As to the question of their value, it is a rather difficult one, but you can be guided by your fellows experimentalists and by theories. For instance some model use a critical temperature gradient below which chi is constant to a small value and above which it increases with some power of grad T. It will depend on the kind of turbulence which you have. But for your purpose you can probably be satisfied with an order of magnitude estimate. For instance for my MHD core simulations, I just assume the diffusion coefficient to be somewhere around 1 m².s⁻¹, which is relevant to the experiment.
Hi,
It depends enormously on the velocity level (Reynolds number) and the kind of the study if it is qualitative or quantitative. In nozzle expansion problem, you can firstly try without turbulence model to get an abrupt idea about jet and reciculation zones.
see "Comparative Study of Numerical Simulations of the RESS Process: The Supercritical Pure Fluid Expansion" published in International Journal of Chemical Reactor Engineering
If you are simulating diffusion, you can ignore turbulence, However, if the diffusion may lead to convection, you may or may not include turbulence depending on your focus of study. For example, if you study convection caused by transient heat conduction, the scale of convection is low if the heat flux is small, say 100 W/m2. If the heat flux can cause very fast convection and boiling, then you will have to include turbulence. In each case, try to compute the Reynolds number with the relevant length scale and velocity of flow. You can read some of my papers for clues.
kk
Further, regarding the Reynolds number, you can estimate whether the simulation/model will actually 'resolve' the turbulence, by using the grid (mesh) spacing (or filter width) in your calculation of Re. Depending on how small that Re is, then you may need to effectively paramaterize more or less turbulence in the subgrid (subfilter) scales for your simulations.
Just a note of caution that in your cases Re may not be the best indicator. In low pressure cases, there are situations where the Re is low, but velocity is high. I would not ignore turbulence or do a simulation without turbulence. There was presentation by Dow who modified the turbulence model coefficients well to fit with measurements.
If the velocity of flow is faster than diffusion velocity, you better include turbulence model, as convection or advection velocity is several times that of diffusion velocity. There may be cross-flow typical of convection and turbulence.
What program are you using to perform the calculation? Something is odd - because the turbulence model should not be the expensive part of the solution (I would expect it to be 15% of the calculation time or much less for a plasma simulation). Typically it is two extra hyperbolic PDEs. Either your tolerances are far too tight for the turbulence solvers or far to loose for the rest of the flow calculations.
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