Water flow through a packed bed

[PenderJ]

Suppose you have a cylindrical column filled with packed, irregularly shaped particles. The bottom of the cylinder is flat and closed except for an array of small circular holes, regularly spaced except for a ring around the edge of the bottom where there are no holes. So, holes everywhere on the bottom except within some distance of the edge. If you force water through this bed would the flow through the outermost holes be faster than through the centermost holes?

 

[osilmag]

The profile of flow is usually a parabola with the center/vertex being faster than the outside.

 

[jrmichler]

The diagrams in Post #2 are for flow through a round tube with no obstructions. They show laminar flow on the left and fully developed turbulent flow on the right.

Flow through packed beds is different because it is controlled by the packing, and not (or barely) affected by the tube wall. If you search flow through packed bed, you will find a lot of good information. If the holes are evenly distributed, one would expect equal flow through each hole. If some holes are farther apart, one would expect more flow. But not a lot more.

 

[PenderJ]

I did a brief search prior to posting but concluded that I wouldn't be able to figure it out on my own easily. In the scenario I described the holes are all the same distance apart but there is an area with no holes. But it sounds like what you're suggesting is that the difference in flow between holes adjacent to the no-holes area and those surrounded by holes would be very small, perhaps insignificant. Am I understanding you correctly?

 

[Dullard]

If I understand what you're describing, the short answer is: Yes.

How much difference exists between flow through a perimeter hole depends on why you have to 'force' the water through the bed. If it's primarily because of head loss in the packed bed, the difference will be larger; if it's primarily because of restriction at the exit holes, smaller.

 

[PenderJ]

Thanks. What I'm actually interested in is an example of the former. Specifically, an espresso portafilter. The tamped coffee powder provides the vast majority of the pressure drop, typically 7-9 bar over a distance of a couple of centimeters. It's quite common to see the initial droplets of coffee emerge in a ring pattern from the outer holes. It's more difficult to know if the flow there is greater through the rest of the shot.

 

[Dullard]

Another semi-related consideration (assuming a simple cylinder):

Where the coffee meets the wall of the cylinder, the resistance to flow will be somewhat lower than in the middle of the bed - the wall is (presumably) flat - the shape/size of your grounds (whatever that is) won't allow the grounds to 'mate' with it very well. That effect will allow some 'sneak' flow around the perimeter of the bed - that will tend to 'over-supply' the outer holes.

 

[Lnewqban]

Thanks. What I'm actually interested in is an example of the former. Specifically, an espresso portafilter. The tamped coffee powder provides the vast majority of the pressure drop, typically 7-9 bar over a distance of a couple of centimeters. It's quite common to see the initial droplets of coffee emerge in a ring pattern from the outer holes. It's more difficult to know if the flow there is greater through the rest of the shot.

This video explains that, once the initial flow begins, some orifices get clogged, causing uneven extraction.
You can also see the ring formation that you mention.

 

[PenderJ]

Another semi-related consideration (assuming a simple cylinder):

Where the coffee meets the wall of the cylinder, the resistance to flow will be somewhat lower than in the middle of the bed - the wall is (presumably) flat - the shape/size of your grounds (whatever that is) won't allow the grounds to 'mate' with it very well. That effect will allow some 'sneak' flow around the perimeter of the bed - that will tend to 'over-supply' the outer holes.

If that gets out of hand it's referred to as "side channeling". Many of these cylinders also include some amount of taper. And the way the water is introduced to the top of the bed varies. I suppose it's complicated. People do all sorts of things to try to get the flow to appear as even as possible. Sometimes it's more voodoo than anything. But I wonder if the design actually means that one should expect a bias in the flow through the holes even when flow through the bed is as even as possible.

 

[PenderJ]

This video explains that, once the initial flow begins, some orifices get clogged, causing uneven extraction.
You can also see the ring formation that you mention.

While not really relevant to the question I asked, the guy, the "coffee expert", offered a hypothesis about why some holes get clogged. But he didn't actually offer any real evidence for his idea. What he did show was that a particular brand of precision basket, which they sell, worked better for their equipment and coffee than some no-name basket. That's not the same thing though. There are in fact divergent views about which basket works the best under which circumstances.

 

[Lnewqban]

While not really relevant to the question I asked, the guy, the "coffee expert", offered a hypothesis about why some holes get clogged. But he didn't actually offer any real evidence for his idea. What he did show was that a particular brand of precision basket, which they sell, worked better for their equipment and coffee than some no-name basket. That's not the same thing though. There are in fact divergent views about which basket works the best under which circumstances.

If you take a closer look, you could clearly see the pattern in which the flow reaches the filter at minutes 0:12 and 1:04.
Flow is consistently coming last from the central area for both filters, which means a YES to your OP's question.
Have you seen otherwise achieved by manufacturer's trying different techniques?

Another factor to consider is the possible uneven packing of the powder inside the porta-filter, which could be greater by the middle section of the powder volume than closer to the walls.
It is possible that manual packing of the granular material cannot fully compensate its natural critical angle of repose.

In addition to the above, when a pressure gradient forces molecules of water to flow through the many internal channels of a packed bed of powder, those molecules are forced to change directions many times while moving downwards.

Comparing to the peripheral flow (molecules flowing in between the flat metal wall and the packed bed), the more numerous changes of direction of the molecules of water by the central area of the cross section reduce their downwards velocity.

 

[PenderJ]

If you take a closer look, you could clearly see the pattern in which the flow reaches the filter at minutes 0:12 and 1:04.
Flow is consistently coming last from the central area for both filters, which means a YES to your OP's question.
Have you seen otherwise achieved by manufacturer's trying different techniques?

I don't know what you mean by "Manufacturer's". But the basic answer is yes. While a ring pattern is common it is also not uncommon to have an even pattern. With the same equipment. The ones in that video are actually fairly mild. Here's a more typical example. So this evidence doesn't answer the question I asked.

Another factor to consider is the possible uneven packing of the powder inside the porta-filter, which could be greater by the middle section of the powder volume than closer to the walls.

The primary strategy employed is to attempt to achieve as homogeneous a distribution of particles as possible through a variety of techniques and tools. It does make a difference. But again, it doesn't address the question I asked.

For the sake of argument, assume a perfectly even distribution of spherical particles.

 

[anorlunda]

It seems that you presume that an non-uniform distribution of flow results in inferior quality coffee. That's logical, but not necessarily true. It may also be possible that uneven hole flows is insignificant to product quality.

Rather that viewing videos of water distribution, I would have the coffee evaluated by professional coffee tasters. I'm familiar with one such company. They provided their clients with detailed reports.

 

[PenderJ]

It's not my presumption; it's a more standard belief. It stems from the notion that under/over-extracted coffee tends to be sour/bitter. So an uneven extraction, whether due to an uneven grind (bad grinder) or uneven percolation, is assumed to result in inferior coffee, one that can be both sour and bitter at the same time. Whether this is really the whole truth I do not pretend to know.

I'm not actually looking for taste evaluation. I was just curious about how this geometry might affect flow. The reason I didn't initially say the question pertained to coffee was because of the tendency, probably just human nature, to read things into what isn't there.

Anyway, I got an answer to my question: "Yes, but probably not that much."