Moleculer viscosity? Eddy viscosity?

[hanson]

Hi all.
I am learning things about incompressible turbulent mena flow.
I am completely confused by these terms: moleculr viscosity and eddy viscosity.
What are they?
Is molecular viscosity the same as the visocosity of the fluid we often use?
And what exactly is eddy viscosity? I know it is used to characterize the momentum transfer for eddies, but I don't understand it.
Please kindly me or recommend some good references I can look into.
I am currently using Frank White's book on viscous fluid flow, which I don't really understand...

 

[stewartcs]

The turbulent transfer of momentum by eddies creates internal fluid friction. It is the fundamental idea of how we define viscosity in turbulent flow, i.e. internal fluid resistance. Eddy viscosity explains what causes the internal friction.

Is molecular viscosity the same as the viscosity of the fluid we often use?

Molecular viscosity is the same as viscosity. The Coefficient of Molecular Viscosity is the same value as dynamic viscosity.

Molecular viscosity is the transport of mass motion momentum solely by the random motions of individual molecules not moving together in coherent groups. Molecular viscosity is analogous in laminar flow to eddy viscosity in turbulent flow.

Check out this link for a little more info...

http://oceanworld.tamu.edu/resources/ocng_textbook/chapter08/chapter08_01.htm

 

[FredGarvin]

Good link there. Just a note that it looks like a type/font error in the viscosity section. They kept "n" as viscosity in the explanation of the stress equation instead of $${\nu}$$.

 

[Clausius2]

Eddie Viscosity is an imaginary concept (also termed 'The Ansatz' in turbulence). It does not exist as the molecular viscosity, which is a well defined transport coefficient as stated by the Kinetic Theory. The Eddie Viscosity hypothesis was posed for making the things simpler, in the sense that the turbulent Reynolds stresses (which are ugly and nonlinear in velocity perturbations) are simplified to be proportional to the gradients of the mean velocity, as happens in Newtonian laminar flows with the viscous stresses. The coefficient of proportionality is termed the Eddie Viscosity, which far from being a constant or fluid property, is a magnitude dependent on the flow field and its solution. The Eddie viscosity hypothesis is inherently wrong, in that the Reynold stresses are in general not co-linear with the mean velocity gradients, as has being discovered by DNS solutions. However, the numerical methods stemming from this simplification (such as RANS methods) are low-time consuming and can be used, sometimes massively, by computational fluid dynamicists to obtain approximate solutions of turbulent flows.

Hope everybody is doing fine over here, I don´t stop too much, I have too much work to do in my office.

 

[arildno]

Eddie Viscosity is an imaginary concept (also termed 'The Ansatz' in turbulence). It does not exist as the molecular viscosity, which is a well defined transport coefficient as stated by the Kinetic Theory. The Eddie Viscosity hypothesis was posed for making the things simpler, in the sense that the turbulent Reynolds stresses (which are ugly and nonlinear in velocity perturbations) are simplified to be proportional to the gradients of the mean velocity, as happens in Newtonian laminar flows with the viscous stresses. The coefficient of proportionality is termed the Eddie Viscosity, which far from being a constant or fluid property, is a magnitude dependent on the flow field and its solution. The Eddie viscosity hypothesis is inherently wrong, in that the Reynold stresses are in general not co-linear with the mean velocity gradients, as has being discovered by DNS solutions. However, the numerical methods stemming from this simplification (such as RANS methods) are low-time consuming and can be used, sometimes massively, by computational fluid dynamicists to obtain approximate solutions of turbulent flows.

Hope everybody is doing fine over here, I don´t stop too much, I have too much work to do in my office.

Of course, one might develop the idea of eddy viscosity into a general "eddy viscosity" matrix formulation, but that would hardly involve any simplifications at all..
Hope you're doing fine, Clausius2!