Hello Everyone:

I have a question for you all. Reynolds number tells us about the degree of turbulence, Grashof number about the degree of buoyancy forces, etc.

How about the Prandtl Number? What kind of physics it's telling us?

Thanks,

Thomas

The Prandtl number measures the relative diffusion rates nu/kappa, where nu is the kinematic viscosity and kappa is the thermal diffusivity. So it gives an estimate of the dominant diffusion process in the flow.

I saw a name "turbulence Prandtl Number". I wonder is the turbulence really can diffuse?

regards,

sheng

Pr=v/a => high Pr=momentum diffusion is dominant

low Pr=thermal diffusion is dominant

Regards Demselles

Is it true that Reynolds numbers tells about degree of turbulance? I think it only tells which one of the forces viz. momentum force and viscous force is dominant.

Can anybody explain?

Yogesh

The turbulent Prandtl number is the ratio between turbulent diffusivity of momentum and turbulent diffusivity of heat. The turbulent Prandtl number can in many cases be approximated as a constant, although it in reality varies. By assuming a constant turbulent Prandtl number you can estimate the turbulent transport of heat by using the eddy-viscosity computed with a common turbulence model. This is also what most people do, although there exists turbulence models which solve extra transport equations in order to account for the variation. Sometimes you also see models with algebraic formulas for the turbulent Prandtl number.

Not entirely true, but you can say that the higher Reynolds number you have the more likely it is that you will have a turbulent flow. A higher Re number also gives a larger range of turbulent scales.

I don't agree with this aspects. The reynolds-number is just the ratio of two forces. If it's larger than unity it says momentum forces are larger then viscous forces, if it's lower than unity it's vice versa -that's all nothing less and nothing more. Often -but not always- it allows conclusions about the "turbulence intensity" or the amount of energy needed to keep the fluid flowing in the way it does. Depending of the geometry and fluid conditions the change from laminar to turbulent flow may occure at Reynolds Numbers of 2000, or 3000, or even 100000. But this are only rules of the thumb.

Another important aspect of the Reynodls number is related to the boundary layer.

If you have a boundary where a boundary layer can form, then the Reynolds number gives you a first estimate of the size of the boundary layer that will form there.

e.g. if Re is very small (e.g. Re=10) then the boundary layer is relatively large, its size is a significant fraction of the size of the whole domain.

if Re is very large (Re=1000), then the size of the boundary layer is very small indeed, and you need to have a higher resolution close to the boundary.

IN general the size of the boundary layer L is related to the Reynolds number roughly as

L proportional to D/sqrt(Re)

where D is the size of the whole domain.

Yep, that's exactly what I said ... a larger Re makes it more *likely* to have a turbulent flow. Note the word likely.

[tayyab1986]

what is the range of prandtl number for viscoelastic fluids?
could it be near to 1 or 2??
i have seen that for viscoelastic polymer ethylene glycol its range is from 16 to 29.