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 venkyr56 February 1, 2011 09:01

Generic Scalar Transport Equations

Hi All,
I would like to know few things about scalar transport equations

1. What are all the physical quantities or variables that can be written in scalar transport equations?... or in other way, what are the requirements to be met by any dependent variable, so as to be formulated by scalar transport equations and solved for that variable?

2. what is actually 'scalar' here?

Thanks,
Venkat

 venkyr56 February 2, 2011 08:40

Could anyone respond to this plz

 julien.decharentenay February 3, 2011 02:24

Hi Venkat,

Scalar transport equations would usually refer to the transport of a species, called a scalar.

However in more broad sense, a scalar can mean any quantity that can be put in the appropriate convection + diffusion + source term formulation. Examples are smoke, mixture fraction, age of air. The main common denominator here is that (a) you can express the variable into the appropriate formulation and (b) there is defined feedback mechanism (none for the age of air, PPDF function for a mixture fraction in combustion).

In short your question is very generic and difficult to answer due to the lack of context.

Hope this help. Julien

 venkyr56 February 5, 2011 01:59

venkat

Thanks Julien..,
To be more precise,
Recently we were analysing the eletromagnetic effect on plasma lamps.
In addition to the flow and energy equations, we needed to solve for electrostatic potential(phi). For this, we added one more scalar equation, with the help of UDS in Fluent and solved for 'phi'.

That is where I started thinking more about transport equations. So my question is , when i want to solve for a variable , how would i know or how can i decide if that variable can be written in tranport equations. Is it purely based on physics? Are there any simple tips to identify the cases? if possible, could you plz give me two cases...one for variable which can be written in the form of scalar transport equations.....and the second, for variable which cannot be written in the form of scalar transport equations

Could you plz throw some light on these equations.

Thank you once again
Venkat

 julien.decharentenay February 6, 2011 06:20

In my opinion, it is depends on whether you can write the equation you want to solve in the appropriate equation form (in finite volume form):
- unsteady(or under-relaxation) = convection + diffusion + source; or
- unsteady(or under-relaxation) = convection; or any combination of the above.

2 examples:
- A lagrangian multiphase model can not be solved using a UDS as it cannot be formulated in the appropriate finite volume form;
- An eulerian multiphase model could be solved using UDS (although one would need to solve several UDS and couple these together and to the flow field).

In summary, get the equations for the variable you want to solve. Try to make it fit in the UDS model. If it fits, great. If it does not, you can probably still hack through a user function to implement it:
- Get a pre or post-processing UDF (I would assume there will be one, but I can warrant for sure);
- Do a check on the iteration number to ensure that you run your model only once per iteration;
- Run your model at the beginning of each iteration using your own solver;
- Implement the feedback mechanism from your model onto the solver.

Note: if you have some spare cash, I am sure you can find a consultancy firm that can do the implementation for you. It would save you quite a few headaches.

Hope this help. Julien

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