Bell Theory

[jgreen]

This is an off-shoot from the "rocket/bell project" thread. I started a new post because I didn't want to write a lengthy reply on an indirectly related topic, which could lead to a long divergence from the main focus of that thread. Please let me know if this should be relocated to a different part of the forum -- It's not strictly experimental results (more theoretical discussion) but I put it here because it comes from the other thread.

Specifically, I'm replying to part of an idea exchange with Donkey that started here: donkey32.proboards.com/index.cgi?action=display&board=experiment&thread=113&page=9#3320 and dealt with heat distribution in bells of various shapes, volumes and surface areas.

Here is the quote that I am responding to:

3. If the phenomenon you mentioned is correct--that a fluid flowing into a larger volume results in a high degree of contact (and therefore heat transfer) with the greater volume's surface area--then the above quote makes sense to me with this logic: placing a smaller bell first which opens into a larger bell, sets up the turbulence that allows for a great degree of contact with the larger surface area of the second bell. If you were to put the larger bell first, then the turbulence effect is not going to happen during the transition between the two bells (unless the phenomenon occurs when the volume is reduced as well, which I said before is more intuitive to my brain than how it was stated).

Yeah, I thought of that.. Except, the exhaust typically flows from the first bell into a pipe or channel to the second bell and so on. Each bell needs to be fed from the bottom and exhaust to the bottom and the flow will always pass through some connecting passageway. It's not like we have the one bell opening directly into the other. I do believe that the pipe or channel between the two bells tends to be what I've been calling (for lack of a better term) "system size".

I threw together some relatively crude diagrams that pose a few questions and propose a few general answers and help to visualize this phenomenon that Donkey mentioned. A link to the photo album containing these diagrams should appear below, and I add this disclaimer: these are meant to be conceptual diagrams and do not necessarily reflect realistic proportions. The shaded coloring is meant to abstractly represent a heat gradient, but certainly doesn't accurately describe the actual pattern of heat distribution.


picasaweb.google.com/seedballs/BellTheory?feat=directlink#5681755941480703634

picasaweb.google.com/seedballs/BellTheory?feat=directlink#5681755928639135298

picasaweb.google.com/seedballs/BellTheory#5681755933709094610

picasaweb.google.com/seedballs/BellTheory?feat=directlink#5681755926987061890

I think these should be mostly self-explanatory (if you can view them full-size and read the text), but I will quickly summarize my thinking. Heat absorption is roughly proportional to the exposed surface area inside a bell, and the phenomenon that Donkey described (which I refer to as a turbulence event or effect) reportedly increases the contact between gas particles and the exposed surface area, which would result in a greater rate of heat transfer. After making these drawings, I believe that this turbulence effect has a more pronounced influence on the order of two bells in a system (when they have significantly different volumes) if the bells are connected horizontally rather than stacked vertically.

In the case of two bells that are stacked vertically with columnar channels that bring the gases upwards (as Donkey describes in the quote above), I imagine that the flow through the vertical channels between bells accomplishes an affect similar to small bell opening into larger bell. The channels are "system sized" and thus significantly smaller in volume than the bell that they open into. So at the bottom of a bell, cooler more dense gases move into the opening at the bottom of a vertical channel and begin to rise upwards (due to total draft in the system and the fact that the channel itself has a heat gradient (it gets hotter as the height increases) due to the fact that it is embedded within the bell [not sure how this would change with an external channel]. As the gases emerge into the next bell, a great change in volume and pressure (inversely proportional) occurs and the turbulence effect is created. It seems to me that this can be repeated multiple times until the thermal energy of the gases at the terminal end drops below some "critical point" that negatively impacts the draft of the system. If this is the case, then it would seem to be a major advantage of going vertical.

I'd love to hear thoughts about this and also find out if my thought process is clear enough with the diagrams or needs a better explanation. Also, does anyone know anything about this stove: www.mha-net.org/docs/v8n2/wildac09f.htm I have a few questions about that might be answered by a written description of the stove and/or another set of pictures -- so just wondering if anyone has seen this stove from any other angle (or on another site).

-Jay

[peterberg]

Dec 2, 2011 23:22:17 GMT -8 jgreen said:

Also, does anyone know anything about this stove: www.mha-net.org/docs/v8n2/wildac09f.htm I have a few questions about that might be answered by a written description of the stove and/or another set of pictures -- so just wondering if anyone has seen this stove from any other angle (or on another site).

Yes, there's another picture here: mha-net.org/graphics/wild09/rocket/DSC_9804b.JPG
If memory's serving me well, they tried to build it with a normal door setup and a larger fire box. More or less along the lines of my own experiments minus the secondary (or tertiary) air ducts.
That didn't work at all so they changed it to a normal RS feed tube, the same size as the rest of the system.

[hpmer]

What about making the bell horizontal? For example a hollow bench, would that work or do you need more height for the effect to kick in?

[Deleted]

Bernoulli's principle is working in the bells.
In the tube to the first bell gas velocity and Brownian motion are high.
A relatively small change in volume will create enough turbulence for an effective heat transfer.
High Brownian motion together with sufficient turbulence allows even smaller surfaces to take away a lot of heat.
At a high energy level its relatively easy to capture energy efficiently.
Lower energy levels require more effort to capture a significant part.
If the first bell captures to much of the energy the second can not capture the remaining energy efficiently.
In the tube to the second bell the velocity will raise a bit again.
At lower velocity a bigger change in volume is needed to create sufficient turbulence,
Provided that there is still enough energy in the system to let it happen.

[peterberg]

Dec 3, 2011 5:01:36 GMT -8 hpmer said:

What about making the bell horizontal? For example a hollow bench, would that work or do you need more height for the effect to kick in?

Could be done, in theory the shape of the bell doesn't matter that much. Stratification will occur nevertheless.
In practise, on the other hand, the floor of the bell is coldest and won't count for much of the heat absorption. The ceiling is hotter and all the wall area above the exhaust opening will be quite good in transferring heat.

Keeping this in mind, the inner surface area of the bell which will absorb very well is limited. The floor is ruled out nearly entirely, the lower parts of the wall for most of it. Shaping the bell high and narrow could end up a lot better than a bench, volume-wise. The floor and lower parts of the walls will cover a smaller percentage of the surface area. So, in order to give a hollow bench the same capacity as a high and narrow cupboard-like construction, it'll need to be larger, and heavier as a result. Which in itself is a good thing.

[pinhead]

If I understand correctly, there are two predominant factors that effect the heat transfer of a bell: Surface area and convection. I believe convection is the "Brownian motion" that Karl mentioned. Inside the bell there will be both lsrge-scale convection and small scale convection that can very quickly move heat from the gasses to the relatively cool bell.

This Brownian motion is why fiber insulation is used to insulate the walls in your house; the insulation won't stop a draft, but will eliminate the convection that causes heat transfer.

[Deleted]

Brownian motion is the random movement of particles in a fluid.
Convection is the transfer of heat and mass taking place by both,
diffusion (mixing of particles and collisions caused by the random Brownian motion)
and advection (mass motion in a particular direction).
Brownian motion causes collisions of particles within the fluid and the fluid and any surface
Turbulences in the advection increase collisions of particles within the fluid and the fluid and any surface.
The third way of heat transfer is radiation.
Within solids diffusion cannot happen in a accountable way and radiation is limited too.
In solids heat travels mainly over the bonds of matter ( the harder the matter the better )
and by transfer of electrons ( mass ) in electrically conductive matter.
High heat usually weakens the bonds such restricting its own movement.
Mass transfer by electrons can play can usually rather small role in in fluids too.
Ionization by heat may temporally increase the role of electron transfers within fluids.

[mintcake]

Dec 6, 2011 4:21:09 GMT -8 @karl said:

...
Convection is the transfer of heat and mass taking place by both,
diffusion (mixing of particles and collisions caused by the random Brownian motion)
and advection (mass motion in a particular direction).
Brownian motion causes collisions of particles within the fluid and the fluid and any surface
Turbulences in the advection increase collisions of particles within the fluid and the fluid and any surface.
The third way of heat transfer is radiation.

Or, in summary, to get good heat transfer we need (a) turbulence or (b) surface area.
Since the heat capacity of a gas is pretty minimal, then for heat storage we want more mass,
and that mass should have surface area to get the heat into it fairly quickly. This is why masonary heaters have lots of complex channels to give turbulence plus surface area.

The bell solves a different problem - what happens when the fire goes out. This is the real beauty of the bell in that when the gases entering the bell are cold they stay low and don't steal heat from the stove to warm the chimney / environment.
We have a small tiled stove here - 0.5 x 0.75m base, 2m high. It heats up nicely on a couple of Kg of wood, but the wood burns out in 15-20 minutes and the tiles take about half an hour to start putting out any heat. If I forget to shut the ashbox door the instant the flames have stopped, then I never get much heat into the room. The heat goes into the first few millimetres of the tiles, and then once cold air starts entering then the nice hot inner side of the tiles gives up its heat into the air going up the chimney.

[Deleted]

Posted by mintcake on Today at 11:25am

Or, in summary, to get good heat transfer we need (a) turbulence or (b) surface area.

There is not a lot of interaction between fluid and surface by a laminar stream.
There will always be a boundary layer of the fluid preventing interaction with the main stream.
Without turbulence the heat transfer to the surface will not be very effective,
regardless of the size of the surface area.
Thus both is needed.

[Donkey]

Dec 6, 2011 9:01:34 GMT -8 @karl said:

There is not a lot of interaction between fluid and surface by a laminar stream.
There will always be a boundary layer of the fluid preventing interaction with the main stream.
Without turbulence the heat transfer to the surface will not be very effective,
regardless of the size of the surface area.
Thus both is needed.

Which is how we can have such ridiculously long bench runs (50+ feet) and still expect the chimney to work. It's mainly laminar flow conditions in there.

[jgreen]

So I started this thread and haven't even had time to post any reply myself -- It's finals week for me and things are starting to get crazy. I am pleased to read what has been written. It's all fascinating to me.

Here is a quick question regarding:

Dec 6, 2011 9:01:34 GMT -8 @karl said:

There is not a lot of interaction between fluid and surface by a laminar stream.
There will always be a boundary layer of the fluid preventing interaction with the main stream.
Without turbulence the heat transfer to the surface will not be very effective,
regardless of the size of the surface area.
Thus both is needed.

Although a bell doesn't have the type of laminar flow conditions seen in a flue pipe (that being one of its advantages in terms of heat transfer), does the above quote suggest that a rougher surface on the inside of a bell would encourage more efficient heat transfer than a smooth surface? My thinking is two-fold: a rougher surface increases the overall surface area and might encourage further turbulence at the boundary where gases meet the mass of the bell (thinking trip-wire phenomenon discussed here: donkey32.proboards.com/index.cgi?action=display&board=experiment&thread=113&page=6#2522)

[Deleted]

Posted by jgreen on Yesterday at 7:11pm

does the above quote suggest that a rougher surface on the inside of a bell would encourage more efficient heat transfer than a smooth surface?

Unfortunately the answer is a sound NO.
The dynamics of fluids are more complicated as one may think.
In the hollows between the elevations very stable boundary layers will arise,
working like ball bearings.

For example sport balls do not have a smooth surface.
They have dents, hairs or big seams to create stable boundary layers,
ensuring laminar streams, which will allow the balls to fly fast and far.

Only grooves along a stream's direction could increase the surface without
the manifestation of extremely stable boundary layers.
However bells are turbulent by their very nature, thus there is no clear direction at a given point.

[peterberg]

Dec 6, 2011 16:11:35 GMT -8 jgreen said:

...does the above quote suggest that a rougher surface on the inside of a bell would encourage more efficient heat transfer than a smooth surface?

I'm afraid it won't. Trip wires do score best where there's a boundary layer and laminar flow. Once you've broken up the layer, it doesn't help at all to have more trip wires downstream. The effect of a trip wire isn't to cause a lot of turbulence, only to make the (thin) boundary layer turbulent.
In short, use only one trip wire exactly at the right spot. It will perturb the laminar flow and nothing else, it's not a medicine for every disease. Besides, there is no such thing as a laminar stream of gases inside the bell.

Dec 7, 2011 3:55:59 GMT -8 @karl said:

For example sport balls do not have a smooth surface. They have dents, hairs or big seams to create stable boundary layers, ensuring laminar streams, which will allow the balls to fly fast and far.

Maybe not everybody can agree with that statement.
See the crash course on aerodynamics, especially the part about Spheres and the one about Balls. According to this, sports balls are breaking up laminar flow.

[Deleted]

Posted by peterberg on Yesterday at 2:53pm

Yesterday at 6:55am, karl wrote:
For example sport balls do not have a smooth surface. They have dents, hairs or big seams to create stable boundary layers, ensuring laminar streams, which will allow the balls to fly fast and far.

Maybe not everybody can agree with that statement.
See the crash course on aerodynamics, especially the part about Spheres and the one about Balls. According to this, sports balls are breaking up laminar flow.

Depends on the point of view.
One can ensure laminar streams where it counts by creating goal-oriented low energy turbulences.

Maybe you should read it a second time.
Especially what is said about bluff bodies and wakes.

[peterberg]

Dec 8, 2011 3:00:51 GMT -8 @karl said:

One can ensure laminar streams where it counts by creating goal-oriented low energy turbulences.

Laminar flow and turbulence (albeit at low energy) at the same time?
Very interesting, but you've lost me now...