Dear Francesco,

The given information is rather incomplete.

Densities are not mentioned and the way of injecting the products into the mainstream is not explained. Also the relative amounts of gas flow and material flow are not given.(SLR)

From the size distributions it can be concluded that one product ranges from 2 to 26 micron and the other ranges from 10 to 50 micron or larger.

If the velocity is chosen based on the weight weighed average particle size and suspension velocity of the material combination, then the pneumatic conveying system should work. (the faster moving smaller particles transfer impulse to the slower moving bigger particles)

Electrostatic build-up should be no problem in earthed steel pipes.

Sedimentation of particles is velocity dependant and the velocity profile is depending on the Reynolds number (turbulence)

success

Teus ■

Dear Francesco,

From your data, I calculate the following.

Velocity in 100 mm pipe = 600/3600 / (3.14/4*0.1^2) = 21.2 m/sec

Velocity in 3000 mm pipe = 600000/3600 / (3.14/4*9^2) = 23.6 m/sec

For the 3 m flue gas pipe this results in a ReynoldsNumber of 3.72*10^6

The wall velocity is then approx. 12.8 m/sec

The respective suspension velocities are:

26 micron and 1000 kg/m3 = 0.74 m/sec

50 micron and 400 kg/m3 = 0.65 m/sec

V-wall = 17.3 times and 19.7 times the suspension velocities.

Sedimentation will occur below a wall velocity of approx 1.5 times the suspension velocity.

I would say that there will be no possibility for the formation of a sediment material bed

Success

Teus ■

Dear Francesco,

The ReynoldsNumber is calculated for the 3000 mm pipe according:

Re = airdensity * velocity * Diameter / eta

In this formulae ,D is a for the flow characteristic length-dimension.

For a channel with a circular circumference the diameter D is chosen.

eta = dynamic viscosity in Nsec/m^2 (including temperature correction)

Re = 1.1 * 23.6 * 3 / (2.09 * 10^-5) = 3.72*10^6

(Temperature 100 degrC)

The wall velocity is derived from a set of velocity profiles at different ReynoldsNumbers, which I found in a book.

I made a regression formal : v-wall = (-0.0165 + 0.0369*lnRe) * v-mean

have a nice day

Teus ■

Check your 4 ton/m3 density again it sounds wrong!

High velocities you mentioned are normally requested in dust extraction systems. ■

Dear Francesco,

The new calculated suspension velocity for 50 microns and 4000 kg/m3 is 2.04 m/sec.

If the density should be lower, it does not change anything on the conclusions.

The minimum pneumatic conveying gas velocity is firstly related to the suspension velocity.

Conveying will take place when the drag force on the particle is able to accelerate the particle and keep the particle in suspension.

This requires gas velocities above the suspension velocity.

F.i. If the gas velocity in a vertical pipe is less than the suspension velocity, the particle will fall.

As I had the opportunity to experiment with many pneumatic unloaders and many products, ranging from grains to powders, I was able to find the velocity limits of pneumatic conveying.

I just had to lower down the rpm of the diesel driven floating unloaders and monitor when the pneumatic conveying became unstable or sedimentation took place or even stopped.

From those field experiments (done with the very much appreciated assistance of the operating officers on board) and the calculated velocity profiles based on the existence of turbulence (ReynoldsNumber), it was found that:

- Horizontal conveying requires higher gas velocities than vertical conveying

- Bigger particle require relatively higher gas velocities then smaller particles.

- If the local wall velocity becomes lower than a factor times the local suspension velocity, then sedimentation started.

As the very small particles are smaller than the boundary layer of the gas flow, where the gas velocity is below the suspension velocity, a boundary bed of particles is formed along the pipewall, in which particles with a radial velocity are absorbed, thereby preventing to hit the wall.

This is the reason that abrasive products like cement and alumina can be conveyed pneumatically without significant wear on the pipelines.

Powdery particles can be conveyed with local wall velocities of approx 1.5 times the local suspension velocity.

The mean velocity of the gas is then higher, depending on the turbulence.

Are the values for mean gas velocity, you found in the various books, also motivated and if so, how?

Sometimes, I also encounter high recommended gas velocities, of which I know that in reality it is no problem at all to convey at much lower velocities.

I am sure that a lot of big pneumatic conveying installations are operating at too high velocities and at too low pressures than designed for, causing high energy costs.

It would be interesting to recalculate all those installations though.

Have a nice day

Teus ■

MSDS composition list is not an indicator of bulk density. Few years ago I did an EAF dust system and in my experience with this dust the bulk density ranged between 1800-2200 kg/m3 but then it can be highly variable due to variable ingredient range. If you have big lumps in it then the density can go up further and lumps will also cause other problems.

These dusts are very cohesive and if you can feed them into the system conveying is rather easy. 15 m/s pick up velocity will work fine. Since they are highly abrasive all wear bits need to be ceramic. ■

As a generalised rule particle density is twice the bulk density. ■

If all the particles are in suspension why do you worry about the velocity profile? Design your system for the coarse / higher density particles and then fine particles will get conveyed. If the pick up velocity is high enough to pick the material in the start that is good enough as the velocity will keep on increasing as the particles moves down the line. Since there is no accumulation in the conveying pipe all the particles will exit on the other end particle velocity profile becomes meaningless.

I don’t think it matters what is the velocity difference between coarse and fine particles since the velocity is constantly increasing. Particle size is not the only factor influencing this profile, if you really want an academic calculation on velocity profile then you should account for the position for the particles in the pipe as the particles closer to pipe wall will be slower than the ones in the middle. Particle shape will have influence on the drag produced. Then there are particle- particle collisions and lets not forget few weaker forces i.e. electrostatic, Magnus forces and the list goes on!!! ■

Dear Francesco, Mantoo

A particle with a lower suspension velocity is accelerated more in an airstream then a particle with a higher suspension velocity.

Small, light particles have the lower suspension velocity.

In an airstream, the small particles are accelerated to a higher velocity than the bigger particles,

The smaller particles will collide with the bigger particles in the direction of the flow, exchanging impulse.

The small particles will decelerate and the bigger particle will accelerate. In this way a more uniform particle velocity is reached.

In my calculations, I always use the weighted average particle size, assuming that that particle reaches that uniform velocity.

These collisions are not 100% elastic, and therefore some impulse will be lost in the collision and converted into other energies (heat or breaking the particle)

This loss of impulse causes the velocity slip of the particle relative to the gas velocity.

It is actually not of any importance, whether the particles are of a different material. The only thing that counts is the difference in suspension velocity.

The product loss factor is depending on the “collision” properties of the respective products.

By relating the suspension velocity to the wall velocity of the gas flow, we are, in fact, considering the velocity profile of the flow. The wall velocity is a function of the turbulence, which is related to the velocity profile.

If a system is designed for the higher suspension particles, it will also convey the lower suspension particles, because the velocities are sufficient to keep both in suspension.

The coarser particles will “benefit” from the presence of the finer particles, because the coarse particles will consume a part of the impulse from the fine particles through the collisions.

All for now

Teus ■

Originally Posted by Teus Tuinenburg

Dear Francesco,

From your data, I calculate the following.

Velocity in 100 mm pipe = 600/3600 / (3.14/4*0.1^2) = 21.2 m/sec

Velocity in 3000 mm pipe = 600000/3600 / (3.14/4*9^2) = 23.6 m/sec

For the 3 m flue gas pipe this results in a ReynoldsNumber of 3.72*10^6

The wall velocity is then approx. 12.8 m/sec

The respective suspension velocities are:

26 micron and 1000 kg/m3 = 0.74 m/sec

50 micron and 400 kg/m3 = 0.65 m/sec

V-wall = 17.3 times and 19.7 times the suspension velocities.

Sedimentation will occur below a wall velocity of approx 1.5 times the suspension velocity.

I would say that there will be no possibility for the formation of a sediment material bed

Success

Teus

Dear Tues,

I have tried calculating 26 micron, density of particle 1000 kg/m3 using stoke equation but the value turns out to be 0.074 instead of 0.74. Would it be a typo in this case ?

Thanks, Best Regards ■

Dear SeventhEro,

Probably, you used the particle diameter instead of the particle radius in your calculation.

The suspension velocity is calculated from:

v-susp = SQRT((4*particle dens * particle diam)/(3*drag coeff.*gas dens.))

For a material, the suspension velocity can be measured and the drag coefficient calculated.

The calculated drag coefficient is size and shape related.

Using the calculated drag coefficient for comparable shaped materials gives a good estimate of the suspension velocity.

At approx. 300 micron, both calculation ways give the same calculated suspension velocity, while the particle Reynolds number is still laminar.

It is true that the drag coefficient increases at lower Reynolds numbers.

Which is accounted for in the acceleration and suspension pressure drop calculations, because the particle velocities, relative to the gas velocities are higher than the suspension velocity.

Solving the suspension velocity must be an iterative process:

-drag coefficient is function of Reynolds number

-Reynolds number is a function of suspension velocity

-suspension velocity is a function of drag coefficient

-etc.

The best way is to measure the suspension velocity of a material and calculate back the drag factor.

In the calculations, only the (measured) suspension velocity is relevant.

This is a complicated subject to get the theory matched with practical applications.

Take care ■