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assumption of invisid flow

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Old   November 21, 2005, 11:10
Default assumption of invisid flow
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Lam
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i read an stament,

"the inviscid assumption is valid if the time scales for diffusion are much larger compared to the time scales for convection"

i didn't get what it say, anybody can give me an explaination? Thank you.
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Old   November 21, 2005, 12:36
Default Re: assumption of invisid flow
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ganesh
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Dear Lam,

No practical flow is inviscid, because all fluids possess some finite viscodity, however small. It would therfore be questionable as to why we focus so much on euler flows, which do not consider viscosity and are far from practice. It is here that the inviscid assumption must be looked at in the context described in your question. If the time scales for diffusion are larger than for convection, then this means that any quantity would be convected faster than it is diffused, so that the effect of diffusion can be neglected though it exists. Translated into non-dimensional terms it would imply that the Reynolds's number is huge. Truly, larger the Re, more valid the assumption, since Re is infinite for a truly inviscid flow. It must be noted that it is for this reason that Euler codes are handy, because if you are interested in the pressure distribution of a practical turbulent flow past a configuration, we could get this easily from an Euler code and the solution will be very close to what a turbulent code would have predicited. The utility of a turbulent solver would come in if the drag on the configuration is sought( The boundar layer effect is captured in the turbulent solver). It is also worth considering the fact that the inviscid Burger's equation( similar to Euler equation) can be seen to be the vanishing viscosity limit of the viscous Burgers equation( similar to the N/S equation).

The explanation to your question therefore is that larger time scales for diffusion would mean that the flow would not experience the diffusive action compared to the convection and it would be as if the flow did not experience any diffusion inspite of having viscosity. This assumption is one of the key-componenets in Prandtl-Batchelor theorem.

Hope this helps.

Regards,

Ganesh

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