Plug / Pellet Velocity
I've not studied the Konrad paper that you reference but I can comment on the plug / pellet velocity question that you raise.
As you know the dense-phase conveying of pellets is a discontinuous phenomenon, i.e. plugs are forming / moving / collapsing. This process is repeated on down the pipeline.
In horizontal conveying the plugs once formed tend to grow in length over time, which is consistent with Wf > Wb. As voidage within the plug increases a point is reached where the interstitial velocities are reduced, which in turn reduce the velocities of the individual pellets. Ultimately the moving plug collapses.
This manifests itself as follows 1) pellets in the stationary bed are picked up at the front of the moving plug 2) the pellets within the plug move forward but at the same time move from the front of the plug toward the back of the plug 3) pellets are lost from the back of the moving plug and are returned to the stationary bed. This is consistent with the expession Wf > Wb > Us.
I trust this will help your understanding of plug / pellet velocities.
Dennis Hauch, PE ■
Re: Plug / Pellet Velocity
If your description is right, then:
Originally posted by Dennis Hauch
1) pellets in the stationary bed are picked up at the front of the moving plug
This suggests Wf is positive, as pellets are moving ahead.
Originally posted by Dennis Hauch
2) the pellets within the plug move forward but at the same time move from the front of the plug toward the back of the plug
This suggest Us
Originally posted by Dennis Hauch
3) pellets are lost from the back of the moving plug and are returned to the stationary bed. This is consistent with the expession Wf > Wb > Us.
This suggest Wb=0, as pellets are droped from plug end and join in the stationary bed.
Therefore, I obtain: Wf>Us>Wb. This contradicts with your conclusion.
Maybe I am wrong, I'd like to see your opions.
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Reply
My conclusion is not contradicted. You overlook the fact that the expression Wf > Wb > Us deals with pellets in the moving plug, not in the bed.
Dennis Hauch, PE ■
Question on Konrad' paper: plug velocity, particle velocity difference
In Konrad's paper "The gas-liguid analogy in horizontal dense-phase pneumatic conveying" Power Technology, 39(1984) 191-198:
Konrad gave a equation Wb=Us/(1-Alpha),
where
Wb: velocity of the back of a plug
Us: particle veocity within a plug
Alpha: solids stationary bed fraction
Konrad claimed this equation is from continuity.
I'd like to know, how is this equation deducted? What is the difference between plug velocity and particle velocity in dense phase pneumatic conveying? Why Konrad didn't use Wf: velocity of the front of a plug in this equation? Bear in mind that, Konrad's data show that it is always Wf>Wb>Us.
Thanks in advance.
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