Strange Reynolds Number

[blckwtr]

I have a pipe flow through a 127mm pipe, velocity 0,658m/s, nu = 9,62E-06m^2/s giving a Reynolds number of 8685. This flow is passing an application inside the pipe where the flow passes four "ports" with cross section area 3637mm^2 and wetted perimeter 661,4mm. This gives a hydraulic radius 5,5mm, and hydraulic diameter of 22mm. With the velocity of 2,3 m/s given by the cross section area, I get a Reynolds number of 5239. This is actually lower than for the 127mm pipe. What is wrong?

 

[btrueblood]

Dunno that anything is wrong. There is no law of conservation of Reynold's number. The Re for the pipe is valid for computations of pipe friction, the Re for the "ports" is valid for...well, whatever you calculated it for.

 

[25362]

The difference is the result of the differing hydraulic diameters [Dh] taken to estimate the Re.

Take for example a circle and a square cross-section with the same area, equal velocities, and equal kinematic viscosities.

The Dh values for the circle is D (circle diameter).
The Dh for the square is L (square edge).

Therefore the Re for the circle is Re = v.D/[μ]
For the square, Re = v.L/[μ]

Now, the relation between both hydraulic diameters stemming from the equality: [π]D²/4 = L², results in D = 1.128 L.

Thus the Re for the pipe is 12.8% greater than for the square section, although all other parameters are equal.

 

[25362]

There is a natural tendency to link Re with velocity [v], for a given kinematic viscosity [μ], but we shouldn't forget that it actually depends on the product of [v] with D_H the hydraulic diameter.

 

[blckwtr]

Thanks for all your efforts, but I know how to calculate Dh and Re. The reason for asking is that I find it strange that the Reynolds number is so small for this given geometry. The velocity is 3,5 times higher, so if this was the "transition" area, the Moody diagram would be pointless.

I have to find the Reynolds number in order to get an idea of which turbulence model I have to use for a CFD software we are testing out...

 

[BigInch]

Glad you know how to calculate Re. Now think about what 25362 has already so kindly pointed out, Re is NOT just a function of VELOCITY! Re = f(V * D).

NOTE! Re will be CONSTANT for any V * D = k.

Twice the velocity in a diameter of D/2 = SAME REYNOLDS NUMBER.

A Moody diagram curve is valid only for 1 given D and roughness. You're jumping between curves!

How will you "validate" the CFD code if you don't get Re?



**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25% to 50% of the total electrical energy usage in certain industrial facilities." - DOE statistic (Note: Make that 99.99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[blckwtr]

Yes, I know, and the reason for asking this question is that I find it strange. I also know that 1/2 * 2 = 1.

There is no law in conservation of Reynolds number; fair enough. But is it then correct to use the very small hydraulic diameter pointed out in the starting post? This gives a very small Re compared to the velocity, as a result of the very small hydraulic diameter.

I will not validate the CFD code, that must be for the developers or NAFEMS, I will simply try to achieve a correct result. This is done as a combination of correct assumptions and manual calculations as far as possible.

-Tommy-

 

[BigInch]

If you agree, then why do you think its incorrect?

Seems like that's the whole point of the idea that Mssr. Reynolds wanted to convey when he made his number dependend on the product of the two. If not, he would have left D or V out of it.

I'd be more concerned with the losses in transitioning between one diameter to another.

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25% to 50% of the total electrical energy usage in certain industrial facilities." - DOE statistic (Note: Make that 99.99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[rcooper]

It is also worth highlighting 25362's comment and that the Reynold's number includes a characteristic length, but that length can be anything. With pipes it is often the diameter, for non-circular pipes and channels, it can be the hydraulic diameter or hydraulic radius. If you are looking at the boundary layer development, the length of a pipe is used as the characteristic length.

So just because the Reynolds number is a certain value, you then have to look at what it is telling you, and check the characteristic length used in the experimental data which you are relying on. You cannot be sure that the point at which laminar flow changes to transitional/turbulent is within a certain boundary unless you know the characteristic length you are dealing with.

There are even different Moody diagrams for use if you are using hydraulic diameter, hydraulic radius and pipe diameter, so look carefully at the defenitions of the axis on the one you are using.