Maximum Conveying Capacity.
Dear Mr. Teus,
So nice to see you again. Thank you one more time for your valuable comments and sharings.
With your permission, I want just to point out some considerations:
- should be mention that this is more precise valid for the critical points of the line, for example just after the bends or imemdiately after the pipe loading point. If the condition is fulfilled in these critical points, than the rest of the route will be ok.
- should be mentioned also that the approximation #suspension velocity is valid for perfect spherical particles, otherwise there should be a domain and the condition to be satisfied is for the particles with the most deviation from the spherical form, having the
higher suspension velocity from the given mixture (particles of the same density).
The limit point is given by the curve of particle floating speed (that depends on the mixture ratio, clogging constant, Fr^2, pipe cross section and pressure ratio) and the maximum available pressure.
Wish you all a happy new year 2021, with health, peace and prosperity !
Sincerely yours,
Tanase TANASE ■
Re: Pipe Diameter Maximum Conveying Capacity Limit, Explained B…
Dear Dr. Tanase,
Thank you for your interest and comments. These are important to increase the understanding of the pneumatic conveying technology.
- should be mention that this is more precise valid for the critical points of the line, for example just after the bends or immediately after the pipe loading point. If the condition is fulfilled in these critical points, then the rest of the route will be ok.
Here the question arises what the Zenz diagram represents.
In general, the Zenz diagram represents the pressure drop of a complete pneumatic conveying installation, plotted against the gas velocity at a constant conveying rate.
In this definition it is unclear, whether the velocity is the starting velocity, end velocity, or average velocity.
All these velocities are depending on the pressure and the pipe diameter, which is not necessarily always the same.
Therefore, it makes more sense to use the air volume flow or air mass flow as the variable to plot against.
That is normally the way, I calculate the Zenz diagram.
The critical points in the installation, which you mention (plus an increase in diameter) automatically are calculated as increased pressure drops at low air flows, causing (with the increasing SLR) the increasing pressure left of the lowest point in the Zenz diagram.
You are correct, that the rest of the installation does not cause any significant increase in pressure drop to become a problem.
But then we are suddenly discussing the Zenz diagram of a part of the pneumatic conveying system.
I made a lot of calculations for a coal injection system, where the issue of dilute or dense phase for different parts of the installation had to be assessed (main conveying line and split line to the injection lances) and the conclusion was that different parts of the system have different Zenz diagrams.
- should be mentioned also that the approximation #suspension velocity is valid for perfect spherical particles, otherwise there should be a domain and the condition to be satisfied is for the particles with the most deviation from the spherical form, having the higher suspension velocity from the given mixture (particles of the same density).
The suspension velocity is not necessarily for spherical particles of the same size.
The suspension velocity can also be for non-spherical particles of the same size (measured)
When a material consists of a range of sizes (particle size distribution), an average particle size can be calculated with a corresponding Solid Loss Factor to calculate the pressure drop and the common particle velocity.
All particles are namely traveling at the same velocity through the pipe.
The small particles undergo higher accelerations, resulting in higher velocities (impulse), but because of the interparticle collisions, all particles end up with same velocity.
(Otherwise, there would be particle segregation in the pipeline, which is not the case in the real world)
To make it even more complex, the “average particle size” for keeping the particles in suspension differs from the “average particle size” for acceleration.
The limit point is given by the curve of particle floating speed (that depends on the mixture ratio, clogging constant, Fr^2, pipe cross section and pressure ratio) and the maximum available pressure.
This remark is not completely clear to me:
-The floating speed (= suspension velocity) is depending on the local pressure and temperature (= air density)
-I do not see how the
mixture ratio, clogging constant, Fr^2, pipe cross section and pressure ratio) and the maximum available pressure
are influencing the local particle floating speed
I am not familiar with the term “clogging constant” and the use of the Froude number is in my opinion not necessary in a gas or liquid submerged particle flow.
Only the Reynold’s number must be used.
Using your words: Wish you all a happy new year 2021, with health, peace and prosperity ! ■
Teus
Re: Pipe Diameter Maximum Conveying Capacity Limit, Explained B…
Dear Mr. Teus,
Thank you for your answer.
When i checked the forum in this morning, i found out, as always from you, this new/older topic.
I'm a flour milling engineer dealing with flour mill technology design as for diagrams, machines, pneumatic conveying, aspiration plants, and so on.
I did never considered the pneumatic conveying such complex. Until some years ago, when i felt very uncomfortable about missing of good literature for to design correct pneumatic conveying system.
And i made some industrial scale research on it for to determine this clogging constant of intermediate stock from the flour mill.
I succeeded it, but i was astonished to discover the beautiful uncomprehensive complexity of this phenomenon.
Just one point for it: the people are asking about the limit of the SLR. According to my experience, the beauty here is that there is no limit !
As you already mentioned in your first comment in this topic, everything stays in the balance mixing ratio-pipe-pressure.
I have seen your post in this morning. And i couldn't resist to comment on your very detailed explanation.
I left all the other tasks, just to answer to it. I have to recognize that, beside smoking, i'm afraid that pneumatic conveying is my first addiction !
And this is the reason i'm somehow avoiding entering this forum too often.
I would like to have to the opportunity to meet you and discuss on this subject.
To be your apprentice, but the geography and this new "fashion" of pandemic is not allowing me to do that. At least for the moment.
However, i'm enjoying a lot having you as mentor here. Thank you warmly for it.
And have you consider to write some book about it ? At the end, only the information is forever in this univers. And education.
Or maybe, again in the fashion of the times, have you considered in organizing some webinars ?
About your last comment: nothing to say, just a big thank you.
On the floating speed: just a remark in my opinion. It is known that for the same particles we have different floating speed in different pipe diameters, it is the our older discussion about the ratio of particle diameter/pipe diameter.
Thank you very much Sir !
Sincerely yours,
Tanase TANASE ■
Re: Pipe Diameter Maximum Conveying Capacity Limit, Explained B…
Dear Dr. Tanase,
the limit of the SLR. According to my experience, the beauty here is that there is no limit!
Well, thinking about the limit for the SLR.
Consider 1 m3 of material + air.
Then the mass of material and the volume of air are:
Mass of material = bulk density
Volume of gas = (1 - bulk density/material density). m3
Mass of gas is = ((1 - bulk density/material density) * gas density)
Maximum material SLR = bulk density / ((1 - bulk density/material density) * gas density)
When the bulk density = 0 (no material present) then SLR =0
At the same time, there is no material conveyed.
When the gas density = 0 (absolute vacuum) then SLR =infinite
At the same time, there is no material conveyed, as there is no driving gas.
Between these 2 extremes there must be a maximum SLR for each installation design.
This maximum SLR for each installation design whereby conveying is possible is always < Maximum material SLR.
everything stays in the balance mixing ratio-pipe-pressure.
Also, velocity is to consider as shown from the Zenz diagram.
pneumatic conveying is my first addiction
Give up your second addiction.
I have, of course, documented the theory, physics, and formulas of pneumatic conveying, otherwise it is not possible to overview all pneumatic conveying phenomena and interactions.
No, I never considered webinars.
On the floating speed: just a remark in my opinion. It is known that for the same particles we have different floating speed in different pipe diameters, it is our older discussion about the ratio of particle diameter/pipe diameter.
Floating speed is a particle property in which the pipe diameter plays no role.
The presence of particles in the pipe influences the air velocity though.
The ratio of particle diameter/pipe diameter requires attention when this ratio becomes too small.
Think of the situation, where a particle diameter equals the pipe diameter (the ratio is then 1). Then the particle becomes a piston. ■
Teus
Pipe diameter maximum conveying capacity limit, explained by the Zenz diagram
The maximum possible conveying capacity of a defined conveying system is depending on:
-Conveying velocity (# suspension velocity)
-Maximum compressor pressure
-Pipe diameter
-Length
-Air only pressure drop
When the air only pressure drop equals the maximum compressor drop, there is no energy (pressure drop) available for material conveying,
To design an installation for the same product and the same pipe routing, the only changeable variable is the pipe diameter, requiring a bigger compressor to maintain the minimum required conveying velocity.
The solution is to increase the pipe diameter and to increase the compressor volume, which decreases the air only pressure drop, leaving more pressure drop for material related pressure drops.
The air only pressure drop decreases with the pipe diameter.
Where the air only pressure drop equals the maximum compressor drop, can be considered as a point of the Zenz diagram for the capacity = 0.
Left of this point in the Zenz diagram, the pipeline will choke and the compressor pressure rises above the allowable compressor pressure.
To the right side of this point, the air only pressure rises above the allowable compressor pressure and if there was some material conveyed, that would have generated an extra pressure drop.
The conclusion from this evaluation is:
-The Zenz curve always lays above the air only pressure curve.
-High velocity pneumatic conveying (high suspension velocities) require bigger pipes and compressors.
Pneumatic conveying software must in case of the just described situation result in capacity = 0 or result in some sort of “Not Solvable”.
Attachments
zenzdiagrampipediameter (PNG)
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Teus