RMH Chimney calcs

This all started because I have a new brick chimney with 8x8 square flue tile liners.  But the thimble going into the chimney is just slightly smaller.  And by manufacturers data, the interior CSA for an 8x8 flue liner is 49 square inches.  If I'm going to build a new RMH, I sure don't want to make any mistakes by having a restriction somewhere!

I have seen several posts, both in Permies and elsewhere, about the required size (practical and municipally defined) of chimneys being based on the size of the firebox, fireplace throat or RMH riser dimensions.  A number of threads have speculated that the chimney size does not need to be as large as the riser, and some even have built such units.

But I have yet to see any numbers to quantify the effect.  It makes sense, intuitively, that the riser exhaust will shrink as the heat is extracted, but just how much change is expected?

Please set me on the right path if I messed this up, but I recall some of "Ideal Gas Law" from science classes and I (silly me) went down the rabbit hole.

Assuming a 10 meter tall chimney with the base near sea level, air pressure difference between top and bottom is about 225 Pascals (per Google).

I made further assumptions that riser temp is 1300 degrees F and exhaust temp is 600 degrees F (these, I hope are conservative).

Ideal Gas Law says (P1xV1)/T1 = (P2xV2)/T2

  where P is pressure (Pascals)
              V is Volume (liters)
              T is temperature (degrees Kelvin)

               degrees K = (5/9)x( degrees F + 459.67)

   so, T1 = (5/9) x (1300+459.67) or 977 degrees K
         T2 =  (5/9) x (600+459.67) or 588 Degrees K

         P1 (sea level) = 101,325 Pa
         P2 (chimney top) = 101,325 - 225 = 101,100 Pa

         V1 (firebox volume for 8" system) = 3 Cubic Feet = 85 liters

 The formula (P1xV1)/T1 = (P2xV2)/T2
  when solved for V2 is (P1xV1xT2)/T1xP2
      (101,325 *  85 * 588) / 977 * 101,100
      (5064223500) / 98774700
      =51 liters

that's about a 40% reduction in volume between the riser gas and the chimney exhaust.

Seems like a pretty good safety margin for a slight reduction of chimney cross sectional area vs riser CSA.

Am I out in left field, or does this make sense - particularly to those who have actually build RMHs?

Thanks!
Randy

Hi Randy;
Well, most of your math went over my head... I helped by ducking down!

The numbers I do understand are a bit off.
Depending on your RMH design a J-Tube can have 1800F in the riser and a Batchbox can go over 2000F
Exit flue temps on either are ideally 150F-200F

In some cases, an 8" stove has been necked down to 6" just before the roof to avoid changing the roof jack out for an 8" one.
I know this has been done with J-Tubes but I do not recall any Batchboxes venting this way.
Each location has its own mini climate. What works at your neighbor's may not work for you.
In your case, I would say that an 8x8 clay liner will work just fine with either stove design.

Tell us what you were thinking of building.
Include pictures if you can.

Thomas - thanks for the reply.

And yes, I started with the 1300 and 600, knowing that they were very conservative numbers.

But what I am really hoping for is the input, discussions and questions that so often occur on Permies.  

If you think about the work that Peter vdb, et al have done to advance the knowledge and broader acceptance
of masonry heaters, that process started with someone's discussion on more efficient wood heat.  

We understand the mechanism so much better due to all the interactions of curious folks like you.
The information on design of an efficient and very scalable heater is now readily available.

But then you have a lot of folks like me - I know this works, but WHY?  
Now I can get around the big picture of burning hot and fast for cleaner combustion.
Just as the idea of extracting and storing the heat is sort of intuitive as well (the thermodynamic equations scare me).

But (I think) being able to go from the observable "this option has better Testo numbers" to
"changing your the air fuel mixture at the riser port to x/y improves the burn by some calculatable %"
will make the techies start to experiment more.

And more experiments are good.

So please (really, "this guy is nuts" won't offended me), if anyone in the Permies world has some input
or can help me understand this calculation better, I'd love to hear.

Randy, I am not good at all with math at that level. What I do know however: in practise the chimney size need to be about the same as the riser. In some cases people used the same idea as you stipulated and installed an undersized chimney, but such combinations are rarely succesful. What I love about physics is their reliability, one could really build on. So there might be some flaw in the reasoning above, otherwise more unequal instances would be working right out of the box but apparently they don't.

I'd think there should be one more parameter in the equasion, namely gas velocity. Volume is much larger in the riser, about four times, but so is speed. Moreover, chimney temperature is much lower than with normal wood stoves so the chimney draw would be lower as well. In order to persuade the afterburner function to work, there should be a minimal underpressure in the chimney. Most of the time, the start underpressure is between 5 and 10 Pascal, depending on wheather conditions and left-over temperature in the mass heater.

Does this sound plausible?

Dear Peter (the guru)

I was hoping someone would provide insight into my incomplete understanding of the equation - and here it is!
The velocity factor never crossed my mind.  Not that I know what to do with it, formula-wise.  
But at least now I see why the numbers SEEMED like they should work.

I knew the existing 8" square flue would be a limiting factor, so I planned on an 8" RMH (batch box) system.
But my thimble into the masonry chimney  is about 7.5" (mostly square), so I was deliberating if that would force me to a smaller riser.
I'm guessing, given a 30' chimney and the restriction being roughly 46 square inch, I should still be okay with 8".

It would be really nice if we could find someone that understands fluid dynamics enough to expand on the formula and
augment what you instigated as the scalable basis for constructing these heaters.

Thank you so much for the input!
Randy

The chimney to riser diameter question very much depends on the type of core you have. Peter has determined through many experiments that a batch box requires the same size chimney as riser. I have found that in my 8" J-tube/bell build, a 6" metal chimney with a jog to outside the wall and up works excellently.

8" flue tiles that I have measured have inside dimensions about 6 3/4" square with rounded corners, so 49 square inch cross section seems a bit generous. What are you basing your 8" batch box plan on? Is your house especially large, drafty, or poorly insulated for the Maine climate? An 8" batch box is a beast, and a typical house system size is 6". I would expect a 7" batch box would have no real restriction from a good 8" flue tile chimney.

I'd think Glenn is right here, a 6.75" square chimney would likely drive a 7" batchrocket quite well. Officially I should say something like "within reasonable tolerances" but "close enough" will do as well.
And yes, the whole of the batchrocket system scales up very fast. So a seven-incher is already a very capable heater.

The site for the heater is an old cottage, 1.5 story, very little insulation, about 1200sf and open to cathedral ceiling.
I have no plans for winter usage (pipes are drained and the place is unoccupied during the cold spell), but I
do want to extend from mere summer use to three seasons.

The design has the firebox in the cellar with the bell extending through the floor and up into the center of the open space living area.
It allows me to have the actual firebox at a very comfortable loading level, and keep the bark and wood chips mess out of the travelled path.
I will be burning 80 to 90% red spruce - that's what grows all around us, so I figured that an 8 (which seems to have anecdotal evidence to be
the best behaved and most forgiving) would be my best bet.

Since the dual flue chimney is the only thing that is built so far, I'm happy to take suggestions!

Among batch boxes, I don't think there is much difference in ease of use and reliability. A smaller J-tube than 6" has been generally found to be finicky, while 8" may be the most common size and is easy to use in my experience.

It is true that softwood like spruce is generally less dense than hardwood and will give less heat per volume load; I still think using your current chimney with a 7" batch box will work fine for you. I understand Peter burns largely softwood in his 6" batch box.

Randy Butler wrote:The site for the heater is an old cottage, 1.5 story, very little insulation, about 1200sf and open to cathedral ceiling.
I have no plans for winter usage (pipes are drained and the place is unoccupied during the cold spell), but I
do want to extend from mere summer use to three seasons.

The 7-incher would be perfectly adequate, you won't be there in the depth of winter anyway. The cathedral ceiling won't hinder at all, most heat is emitted as radiation which leaves the heater's walls at right angles. Only hot air will rise to the ceiling, people tend to forget that.

Randy Butler wrote:The design has the firebox in the cellar with the bell extending through the floor and up into the center of the open space living area.
It allows me to have the actual firebox at a very comfortable loading level, and keep the bark and wood chips mess out of the travelled path.
I will be burning 80 to 90% red spruce - that's what grows all around us, so I figured that an 8 (which seems to have anecdotal evidence to be
the best behaved and most forgiving) would be my best bet.

Please, don't build the firebox in the cellar. The firebox will get hot as well, that part of the bell would emit heat in an unoccupied space. The heater being in the center of the licing space is almost ideal, though.

I'd strongly recommend to build a footing in the cellar, ending just level with the floor above. This way, the entire bell will be in the living quarters and the fire is also visable there. Have the core elevated from the floor, about 2 feet would be very nice. You said there's a cathedral ceiling, so in practrice, there won't be height restrictions.

Red spruce will be a very potent fuel in a batchrocket. Good to know: every wood species has got more or less the same energy content, by unit of weight, that is. Coniferous species contains resins which has a higher heating value than the wood itself. Which means species with a high resin content have about 5% higher heating value as compared to oak, again per unit of weight, of course.

And last but not least: the batchrocket development has been done exclusively using soft wood. You will be surprised how much heat is generated with such humble fuel in a batchrocket.

More questions, and perhaps reasonings.

First and foremost gentlemen - Thank you!
Please understand my comments below are not dispelling your wisdom, merely explaining why I am where I am.
And perhaps you can suggest ways around my limitations.

For the last two summers, we have been living with a small (Little Moe All Nighter) woodstove - in the cellar.
No where near big enough to heat the upstairs, but with 13" thick ICF cellar walls, nearly all the heat hangs under the wooden floor.
Not exactly a "radiant heat" floor, but it did make the place very livable. So heating the unoccupied area is not a "make or break" deal.

The open space in the main living space is largely kitchen and living room.  And the bell will emerge between the two.
BUT - I need to keep the height below 4 feet, or the brickwork will eliminate the line of sight between the areas (wife says "no").
So while I can make a wider bell, or add a bench seat for more radiant exposure, I am limited on elevation.

On the 7 vs 8 inch device, can I not run an RMH at less than full load capacity?
Is it less efficient, or just more costly to build the larger size?
I have plenty of K26 Insulating Fire Brick, and so far, nearly all the red brick has been free for the taking.
What is the disadvantage of having a larger heater?

And here I thought I had a pretty good handle on this project!  So much to learn.
Darn good things there are folks like you willing to educate us newbies.

Randy Butler wrote:For the last two summers, we have been living with a small (Little Moe All Nighter) woodstove - in the cellar.
No where near big enough to heat the upstairs, but with 13" thick ICF cellar walls, nearly all the heat hangs under the wooden floor.
Not exactly a "radiant heat" floor, but it did make the place very livable. So heating the unoccupied area is not a "make or break" deal.

OK, understood.

Randy Butler wrote:The open space in the main living space is largely kitchen and living room.  And the bell will emerge between the two.
BUT - I need to keep the height below 4 feet, or the brickwork will eliminate the line of sight between the areas (wife says "no").
So while I can make a wider bell, or add a bench seat for more radiant exposure, I am limited on elevation.

OK, the WAF (Wife Acceptance Factor) is a very important one, in some cases The Most Important One.

Randy Butler wrote:On the 7 vs 8 inch device, can I not run an RMH at less than full load capacity?
Is it less efficient, or just more costly to build the larger size?
I have plenty of K26 Insulating Fire Brick, and so far, nearly all the red brick has been free for the taking.
What is the disadvantage of having a larger heater?

Sigh...
The batchrocket is burning as fast as it can, even with half a load.
It's not about money or efficiency, it's about the existent chimney.
The larger heater is as good as the slightly smaller one. The larger heater won't run well on a 6.75" chimney, as I told you before. 'Nuf said.

All that said, here's the proposal. A large column in the basement/cellar, containing the batchrocket core of whatever size. All hot gases rising up to the main floor, nothing down to the cellar's floor. The walls of the column heavily insulated, in order to minimize heat dissipation downstairs. A wide bell in the living, partly not higher than the WAF allows, partly bench, but large enough to have sufficient Internal Surface Area together, according to the bell sizing table. Exhaust gases are to be extracted from the living floor level.

How to build it is quite another story, though.

Phew!!
I was looking for the correct term and you nailed it (WAF) perfectly.

That long tall insulated column was in my brain, but clearly not well conveyed.  

As far as installation, the intent is still to build a complete mockup of the core outdoors to ensure I have everything in place.
Dry fit K26 IFB with thin Superwool gaskets between each layer.  Angle iron frame to keep everything aligned.
I'll label, de-construct and re-assemble in its new home (on a pedestal) next to the chimney.

Support is not something to worry about - the concrete slab is poured over about 4" of packed crushed ledge.
Below that is granite bedrock. Since the contractor broke his 50 ton hydraulic jackhammer trying to remove it, I call it stable enough.

So a 7" it will be - and the intent is to have a buddy (professional videographer) help setup the gear to record the whole construction process.
And about 80cf ISA should be no problem.

Good Morning.

Peter - I re-read your response a few times before I figured out where I wasn't clear on some of my questions.

I accept that the 7" system is the right answer for my chimney.  Now I can layout the monolithic base.

Inadvertently, I asked the "what about smaller fires in a larger system" in the same discussion.  

That query, was meant in regards to any RMH.  

There are mornings that I'd like to just take off the chill, not toast the entire house.  So less than full loads are the way to go.

Apologies for the mis-communication!

Thanks again,
Randy

I don't have any sort of heating stove and haven't for many years, but I was recently reading about exhaust stacks for another reason. Earlier in this thread there was brief mention of friction, and exhaust velocity - so let me talk about that a little. When you are burning biomass, there are three origins of gas MASS: There is the chemical conversion of fuel to combustion products - pound for pound each unit of biomass consumed generates about 3.6 units of combustion gas (by combining with 2.6 units of oxygen), then there is atmospheric nitrogen which is associated with that consumed oxygen but not burned - about 10 units of nitrogen, and finally there is "excess air" which in an efficient burner is about 20% additional over what is needed to provide just enough oxygen - so that is about 2.5 units more. All up, that is a little over 16 units of gas to the chimney per unit of fuel. 16 pounds of exhaust per pound of wood.

The density of cold air is about 1.2 kg/cubic meter, but it is only about 1/5 as great at combustion temperatures - so that density difference is creating the buoyant force that makes a chimney draw. A pound of wood burning is going to make about 1000 cubic feet of exhaust gas from about 215 cubic feet of inlet air - mostly due to expansion from heating.  Opposing the flow is the friction due to the gas moving past the chimney walls, and decreasing buoyancy if the exhaust gas is cooling significantly as it rises. The larger the chimney, the lower the velocity and therefore the less friction - but I don't have any numbers for that except that industrial boiler houses often used to use a stack velocity of about 150 feet/second - and that was for forced draft, not really apples-and-apples. Anyway, it has become common in industrial stacks to have a nozzle at the top. This restriction really doesn't create much friction - the flow increases in speed, but the interval is short so there is little friction. The jet-effect of the nozzle causes the gas from the stack to shoot higher into the air - sort of a virtual chimney effect.

If you know the rate you burn fuel in different stoves, this would give you a way to estimate chimney gas rate for different stoves - and therefore chimney velocity. You should expect that when the chimney velocity gets too high, problems with poor draft ensue. I think it would be interesting to compare some peoples' results on that basis (well, it would be interesting if I had a wood burner).