[Roule]

hi,

is there any particular value of Reynolds number, where the viscosity of water can be ignored.

Like i know that in turbulent flow, viscosity effect is less, and this is what distinguishes turbulent flow from laminar flow; but someone told me that for Re > 10k, viscosity can be ignored.

However, i cannot find any source.

So can anyone confirm this, or cite some published paper, or anything like that.

I am considering open channel flow here.

Thanks a lot.

[FMDenaro]

Originally Posted by Roule

hi,

is there any particular value of Reynolds number, where the viscosity of water can be ignored.

Like i know that in turbulent flow, viscosity effect is less, and this is what distinguishes turbulent flow from laminar flow; but someone told me that for Re > 10k, viscosity can be ignored.

However, i cannot find any source.

So can anyone confirm this, or cite some published paper, or anything like that.

I am considering open channel flow here.

Thanks a lot.

Using the Euler equations (zero viscosity assumption) in channel flows is actually a very bad assumption...what do you want to simulate?

[Roule]

i am not particularly looking into any simulation.

i was just doing some dimensional analysis (buckingham's pi theorem and all), and had the dynamic viscosity term. i want to get rid of this viscous term, and someone told me that it can be ignored if reynolds number is > 10k.

so i want to confirm this thing if this is indeed true, and if there is any published paper saying the same.

[FMDenaro]

Originally Posted by Roule

i am not particularly looking into any simulation.

i was just doing some dimensional analysis (buckingham's pi theorem and all), and had the dynamic viscosity term. i want to get rid of this viscous term, and someone told me that it can be ignored if reynolds number is > 10k.

so i want to confirm this thing if this is indeed true, and if there is any published paper saying the same.

It is well known from the old Prandtl theory that very low viscous flows can be treated as inviscid everywhere except from a small bounday layer near to a wall where viscous forces are always relevant.

[Roule]

ya, i guess i will look into the prandtl theory then, to get a definitive value of such a limiting reynolds number, if any such thing exists. thanks :-)

[FMDenaro]

Originally Posted by Roule

ya, i guess i will look into the prandtl theory then, to get a definitive value of such a limiting reynolds number, if any such thing exists. thanks :-)

No, for flow over a wall, the boundary layer thickness diminuishes as the viscosity diminuishes but it still exist. Using the inviscid hypothesis (Euler equation) leads to unphysical stress analysis on the wall.
A classical field is the aerodynamics where wing section studied with potential flows leads to acceptable solution for the pressure distribution but the viscous corrections are then necessary

[Roule]

okay, so i guess there will be viscous effects close to the wall even when turbulence is high and viscosity is low (in case of air) but away from the wall, i can ignore the viscous term, right?

edit: i guess i can ignore the viscous term outside the viscous sub-layer..which is generally thin in case of high reynolds number.

[FMDenaro]

Originally Posted by Roule

okay, so i guess there will be viscous effects close to the wall even when turbulence is high and viscosity is low (in case of air) but away from the wall, i can ignore the viscous term, right?

edit: i guess i can ignore the viscous term outside the viscous sub-layer..which is generally thin in case of high reynolds number.

be carefull, in confined flow is somehow arbitrary a subdivision in internal (viscous) and external (inviscid) flow conditions...It strongly depends on what you are looking for...

[Roule]

oh i see, will look into that..

thanks for all your replies :-) :-)

[LuckyTran]

Viscosity can be ignored, which gives you an Euler equation, when you want to examine far-field effects. If you have a wall-bounded flow and specifically want to look at the near-field region then viscosity can never be ignored.

As Reynolds number increases, the influence of viscosity decreases, however the velocity gradients increases. In the case of infinite Reynolds number where viscosity influence tends to 0 the gradients tends towards infinity so that the dissipation rate tends towards a constant. Actually this is analogous to criticality phenomenon and viscosity is only ever zero at the critical point, which mathematically happens to be infinite Reynolds number.

[Roule]

Originally Posted by LuckyTran

As Reynolds number increases, the influence of viscosity decreases, however the velocity gradients decreases. In the case of infinite Reynolds number where viscosity influence tends to 0 the gradients tends towards infinity so that the dissipation rate tends towards a constant.

hi, thanks for replying.

can u check the words in bold and confirm if u mean that:
when Re tends to infinity, velocity gradient tends to infinity or zero?

i didnt get it completely..

[FMDenaro]

the Re number can be written as (U/L) * L^2/ni, U/L is homogeneous to the gradient of the velocity.
Re-> inf can be due to ni->0 for finite U/L, or U/L-> inf for finite value of ni.

[Roule]

oh i see, thanks for the answer :-)

[LuckyTran]

sorry velocity gradient increases with Reynolds number. I fixed it now.