# Optimal number of boiler tubes.

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#### tenor

##### Active Member
Martin, you commented:
I also use the Stefan Boltzmann equation for radiation heat transfer. It needs modifying to account for emissivity as you state. Choosing those emissivity values for a given application is not easy. I assume a coal fire surface e = 1, but accept that may not be right. I would expect your ceramic burners to be near 1, otherwise they would not be widely used. But as for precise values?????
I think I must do some more work to get "the right answer" here.
I had to do "cooling" calculations on Power station electrical equipment being installed in Dubai, where the SUN heating could potentially heat the equipment above the maximum temperature where we wanted to run the plant. And at night, the air temperature could drop below freezing... So to stop the Sun we fitted sun-shades... but that meant we had a screen with sun (radiant) heating on one side, Hot air all around, and equipment trying to radiate heat as the air temperature was so high.... Emissivity factors were key to managing this problem.
So the table:
e.g. Emissivity

Material Emissivity:
• Aluminum (anodized) 0.77
• Aluminum (polished) 0.05
• Concrete 0.92
• Copper (polished) 0.05
• Copper(oxidized) 0.65
• Glass 0.92
• Gypsum 0.08
• Ice 0.97
• Sand 0.9
• Snow 0.8S
• oil (Dry) 0.92
• Soil (Saturated) 0.95
• Stainless Steel 0.59
• Water 0.95
• And from my memory...
• White painted (Aluminium) ~0.2,
• Grey painted ~0.5
• Matt black painted ~0.95
The "simple" analysis - as far as I can remember - is that a body cannot change its emissivity... -
SO (e.g.)
• a White ceramic emissivity of "0.2" - if considered as a "white" surface - could really act like concrete at "0.92" which is close to the "Matt black" 0.95.
• But Coal ash on the surface of coal (cheap household coal or charcoal, "coal substitutes", etc.) may act more like Gypsum at 0.08 than Matt black at 0.95!
And once agreed how the material is performing you can do proper sums, but I can only GUESS as I have no other information.
My GUESS of emissivity:
• For coal = Part hot matt black coals burning at e = 0.95 and part Ash-coated (like Gypsum) at e = 0.1, insulating the coals behind and at a much lower temperature because adjacent to the Cooler gases adjacent to the copper inner surfaces of the boiler where heat is being conducted from the gases to the copper at ~200~250C - so maybe really around e = 0.8 for a loco fire?
• I used e = 0.8 for emissivity of WHITE ceramic: The surface is made of small cones, with gas burning alongside heating the cones, therefore a part of the surface is white at the gas/air temperature at the fuel inlet holes, part is probably over 900C, and the rest of the cone is somewhere between the two? - Maybe averaging 900C? (book max. value... I assume measured as a mean temp. of a larger area?).
• Similarly, I considered the copper in a boiler to be tarnished, so used e = 0.8 (a guess! - poor memory) but should perhaps have used 0.65? - For the fire-hole door, the heat assumed to shine on the inside, 80% absorbed by the door (Lost outside), and 20% reflected "for absorption elsewhere" to become heated water...
• For "stainless steel mesh" I used e = 0.95... (a guess?) but considered inner and outer wires to be heated by burning gas so the whole surface area at ~1220C. - Even though in photos the corners, and odd places are not even red hot.
FOUND my fag-packet notes of my sums so I can do them properly for you if you need them? I have never actually verified any of these sums, but work simply on Gas power - with complete combustion - going "IN", and smoke-box gas temperature going "Out". Part radiant heating and part gas conduction (surface area) based to "text book" values...
Hope that clarifies my amateur ponderings?
K2

#### tenor

##### Active Member
Thanks Steamchick,
A useful table of starting values, but experience shows that real life throws all sorts of values into the mix. I had great fun trying to "measure" the temp of molten whitemetal with an IR thermometer. e was quite low, but I never did find a realistic value. Call me old and cynical if you like.
Martin

#### tenor

##### Active Member
Useful for straight forward type substances.
Now what about for bio-mass - - - and that would likely also depend upon the type of (I would bet!)?
TIA
Indeed, I found some quite useful values for emissivity and absorbtion from tests on forest fire propagation. I accept that those constants are probably not very constant across different fuels. My own interest is firmly on coal which is quite tricky as flue gas absorbs and emits depending on beam length. Then you have incidence angles to consider for all points in the firebox and you suddenly find the S-B equation starts to get very tricky indeed. Then add in that gas temperature might be increasing (as fuel burns above the bed) or drop (as heat transfer takes place) and life gets very complicated. At ameteur level, we just have to make some fairly crude approximations and carry on. I am under no illusions that my program is precise or exact, just better than guessing.
Martin

#### Steamchick

##### Well-Known Member
HMEM Supporting Member
A simple "principle of Design" that I was taught... and told to remember!
So have forgotten it, but put simply: "It is a starting point to build upon"...
Meaning you Design first, build second...
But also suggesting that the finished item often deviates from the original design - for whatever reason!
Another "gem" - If the design says "it won't work" - then the design is probably right!
But a Salesman told me: "If the design looks right he can sell it. If it looks wrong - he can't sell it or won't bother trying". Also- "if it fails because "the design was wrong" - he doesn't care. It's not his butt on the line!"
Martin, if you are "Old and cynical" - join the gang!
K2

#### Steamchick

##### Well-Known Member
HMEM Supporting Member
For Rayger's Boiler: I have re-worked the radiant heat calcs, using emissivities from Google.
• A ceramic burner (e = 0,92) could be rated: 5kW gas burner, 1.2kW radiant heat: remainder hot exhaust gas.
• Coal (e = 0.8): 8kW total fuel "Heat": 3.7kW radiant heat, remainder hot flue exhaust gases and smoke, and unburnt gases and ash.
• Wire mesh burner (e = 0.89): 5kW gas burner, 2.7kW radiant heat: remainder hot exhaust gas.
So the wire mesh burner does put around half of its heat into the boiler (water), but is still only about 75% of the radiant heat "power" of the coal fire. Assuming they all deliver a similar amount of burnt gas (heat) through conduction, And the coal fire potentially can produce more heat if forced, then the decision revolves around other factors:
• DO I want to bother with a coal fire?
• Do I want maximum performance of the boiler? - Or will "75% performance" run the engine adequately?
• Do I want the bother (and cost?) of developing a wire mesh burner?
• etc.
Martin, you may propose better simple sums/conclusions? - Please do...
Enjoy...
K2

#### ajoeiam

##### Well-Known Member
Indeed, I found some quite useful values for emissivity and absorbtion from tests on forest fire propagation. I accept that those constants are probably not very constant across different fuels. My own interest is firmly on coal which is quite tricky as flue gas absorbs and emits depending on beam length. Then you have incidence angles to consider for all points in the firebox and you suddenly find the S-B equation starts to get very tricky indeed. Then add in that gas temperature might be increasing (as fuel burns above the bed) or drop (as heat transfer takes place) and life gets very complicated. At ameteur level, we just have to make some fairly crude approximations and carry on. I am under no illusions that my program is precise or exact, just better than guessing.
Martin

Ye MAY be able to use coal there - - - - on this side of the water the present thinking is that coal is this hugely unsafe incredibly bad fuel and nuclear should replace it. Seems like the (what negative adjectives might be strong enough to express my disdain for the boffins in bureaucrat land)powers that be will no longer even the idea of thinking about using coal as a fuel - - - here it is now illegal!
So I've moved to bio-mass which is a real rats nest!

#### Steamchick

##### Well-Known Member
HMEM Supporting Member
Ajoeiam... It costs £65 for a bag (25kgs?) of good steam coal... albeit smokeless. It has to be imported from somewhere... They don't dig it in Wales anymore! But we use it in locos at the club...
We can still buy "smoke free" coal at upwards of £10 for 10kgs, I think? But we are not allowed to burn it in the North East of England, where we produced most of the coal burned in London for 200 ~ 1000 years or more! (depends on the records available). We were recorded as shipping coal from the Durham Coalfields recorded in the Domesday book 1000 years ago! But that stopped in 1984. They stopped us burning domestic coal soon afterwards. Propane is now around £6/litre, Butane just a tad cheaper. Diesel £170/L, Petrol £150/l.... So I am buying old petrol blow-lamps (£10~£20 each) and re-furbishing them for all my HOT work!
Crazy?
K2

#### Steamchick

##### Well-Known Member
HMEM Supporting Member
Hi Raygers. There is another alternative burner: The combined radiant ceramic plus wire matrix. Essentially, a flat ceramic burner, with a wire mesh spaced 5 mm above the ceramic surface, that takes heat from the hot exhaust and heats the wires that glow a dull red... maybe 850~900C and increase the radiant heating at the sacrifice of the hot gas heating in a boiler like yours. And if the gas power is increased, the flames start to burn not just within the ceramic mini-coned surface, but above the surface as well, thus increasing the total "gas power", but losing some radiant heat from the ceramic surface. This extra heat, if used on a wire-mesh radiant situated above the ceramic surface, can still be partly radiant, because of the heated wire matrix. And overall, the power of the burner in increased... So the burner can be "turned-up" to the maximum that the flues can handle, before the burner becomes choked by back pressure and fails to induce sufficient air for the burner. I'll need to do some more work on this.... Maybe Martin can comment on how much "gas and air" can be achieved with the flue tubes planned?
K2

#### ajoeiam

##### Well-Known Member
Ajoeiam,
Fundamentally water tube boilers are similar in terms of calculation as for fire tube. Have a search around a website called Thermopedia.com (Thermopedia link) and you will find formulae for water tubes. They tend to be a bit less accurate than the simple firetube set up, but useable.
snip

I think we might have drifted away from the original post a bit!

Problem I have is I don't know how to 'use' the site - - - search term "water tube boiler formulas" basically gets me garbage.

Perhaps you might know a search term, or terms, that might get me closer to something useful?

(I understand that we have moved somewhat from the original ask but, at least imo, its related information.)

TIA

#### Steamchick

##### Well-Known Member
HMEM Supporting Member
Some stuff:

Raygers:
I have been amusing myself trying some numbers and a schematic ceramic pyramid burner. Basically, flat panel sloping inwards slightly so the bottom is a large as I can sensibly get inside a 12cm circle, the top inclined in to give 2cm clearance at minimum (the points of the shape) with a flat top to match at 3.5cm below the tube plate of the firebox.
Tried a hexagonal truncated pyramid, and an octagonal truncated pyramid....
Hexagonal ~22.1sq in of side panels,
Octagonal ~22.3 sq. in of side panels.
And similar slight difference for top panel.
As panels are 14mm thick, the holes for gas to pass through are defined by the inner surface area, not the outer...
A commercial paper defined the heating (real effect = possibly only the Radiant heating effect?) from a ceramic burner as based on 77W/sq. in. - Which means the ceramic is only "rated by industry standards" at 1.7kW. But I know burners that run with a higher "BTU" rating are sold ... maybe at up to 180w/sq.in? (total gas energy) - which would give a total (gas) power of about 4kW. But you must also consider the "lost power" of heat conducted and radiated from the outside of the boiler and fittings, and what goes up the chimney!
It may be possible to increase the power rating by pushing more gas and air into the burner, with a wire mesh cover situated 1/4" from the ceramic surface, so more post-ceramic combustion takes place and by heating the wire matrix gives off more radiant heat, as well as the extra gas heat going up the flue tubes... which may make possible up to 5kW of gas heating with this or similar burner.
But reasonable to assume a 4kW burner is practical in ceramic material. - Is this adequate for the steam you need/want?
The flues at 0.43in bore: CSA = 0.145sq.in. x 55 tubes = 8sq. in. of flue.... = 51.6sq.cm. Which converts to "gas exhaust limit" from a 89000BTU/hr burner... so flues will not limit the gas burner I suggest is possible in this boiler. Martin, I guess you have some calculation ideas better than my extrapolations from "other" boiler-burner combinations?
K2

#### tenor

##### Active Member
Problem I have is I don't know how to 'use' the site - - - search term "water tube boiler formulas" basically gets me garbage.

Perhaps you might know a search term, or terms, that might get me closer to something useful?

(I understand that we have moved somewhat from the original ask but, at least imo, its related information.)

TIA
Hi Ajoeiam,
I went into the A-Z index and searched for "tube banks". Cross flow over the tube bank is (I suspect) what you have in mind. It comes up with this:
There are further complications for boiling water side flow etc. etc.

You sounded a little frustrated that we can still get coal in UK. I think we are living on borrowed time, and we shall all be coming to Steamchick for radiant gas burners very soon!

Martin

#### ajoeiam

##### Well-Known Member
Hi Ajoeiam,
I went into the A-Z index and searched for "tube banks". Cross flow over the tube bank is (I suspect) what you have in mind. It comes up with this:
There are further complications for boiling water side flow etc. etc.

You sounded a little frustrated that we can still get coal in UK. I think we are living on borrowed time, and we shall all be coming to Steamchick for radiant gas burners very soon!

Sign out
Martin

I had spent well over an hour looking for anything like what you just pointed out.
If one does not know the terms to use in a search - - - - well I was flailing around getting no where (ie drowning in information but even worse information that wasn't getting me even close to where I would like to go).
I just did a quick look so I still am quite uninformed (my fault - - - but working on it) - - is this where I find formulas on the heat transfer ie from the boiler into the water tubes?
(Sorta frustrating - - - I've worked on the real thing (full size coal boilers - - - ie circa 200 MW boiler so I sorta know how to build them but dunno how to figure out what I need to build - - - which is the present, or better, ongoing exercise.)

Ja frustrated - - - the less than informed persons (I'd much prefer a far more vulgar expression) don't seem to understand that a coil fired boiler can be constructed AND run and it CAN produce less Hg, less CO2, less soot, less S - - - - except its not quite so cheap to build. (80 MW version running in Japan for some over 35 years already!!)
Now reading about how we've past the 2 degree warmer than pre-industrialization - - with no mention that one underwater volcano increased the water vapor in the entire earth's atmosphere by some 10% (likely causing 1.5 to 2 C increase in temperature for at least 3 if not up to 5 years).
Sorry the science that's not really science (its all there to make rich people a LOT richer even faster) get real old.
I'll stop - - - post will likely be flagged as political.

Remember - - - the first casualty in a war is - - - - the truth!

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#### HMEL

##### Well-Known Member
Some stuff:

Raygers:
I have been amusing myself trying some numbers and a schematic ceramic pyramid burner. Basically, flat panel sloping inwards slightly so the bottom is a large as I can sensibly get inside a 12cm circle, the top inclined in to give 2cm clearance at minimum (the points of the shape) with a flat top to match at 3.5cm below the tube plate of the firebox.
Tried a hexagonal truncated pyramid, and an octagonal truncated pyramid....
Hexagonal ~22.1sq in of side panels,
Octagonal ~22.3 sq. in of side panels.
And similar slight difference for top panel.
As panels are 14mm thick, the holes for gas to pass through are defined by the inner surface area, not the outer...
A commercial paper defined the heating (real effect = possibly only the Radiant heating effect?) from a ceramic burner as based on 77W/sq. in. - Which means the ceramic is only "rated by industry standards" at 1.7kW. But I know burners that run with a higher "BTU" rating are sold ... maybe at up to 180w/sq.in? (total gas energy) - which would give a total (gas) power of about 4kW. But you must also consider the "lost power" of heat conducted and radiated from the outside of the boiler and fittings, and what goes up the chimney!
It may be possible to increase the power rating by pushing more gas and air into the burner, with a wire mesh cover situated 1/4" from the ceramic surface, so more post-ceramic combustion takes place and by heating the wire matrix gives off more radiant heat, as well as the extra gas heat going up the flue tubes... which may make possible up to 5kW of gas heating with this or similar burner.
But reasonable to assume a 4kW burner is practical in ceramic material. - Is this adequate for the steam you need/want?
The flues at 0.43in bore: CSA = 0.145sq.in. x 55 tubes = 8sq. in. of flue.... = 51.6sq.cm. Which converts to "gas exhaust limit" from a 89000BTU/hr burner... so flues will not limit the gas burner I suggest is possible in this boiler. Martin, I guess you have some calculation ideas better than my extrapolations from "other" boiler-burner combinations?
K2
I have been following this subject with an interest. It seems to me that if you are looking at heat transfer from a radiant aspect and given the assumption that a ceramic burner is about 950 degrees C it is lower than a conventional flame or coal fire by about 500 degrees C. As the radiant heat transfer is dependent on the temperature raised to a power you would have to proportionally increase the ceramic burner size by at least a factor of 25% to get equivalent heat transfer by radiation. Now I can see that the convection heat transfer in a boiler tubes might have a greater surface area to compensate for this heat transfer shift from radiant to convection. If I remember right the radiant heat transfer is temperature raised to the 4th power. The boiler might have to be designed slightly differently (more tube area) to compensate for this assumption.

#### tenor

##### Active Member
Ajoeieam,
There are quite a few formulae on the page I linked, plus corrections for skewed flow patterns and calculations for pressure drop across the bank. It certainly becomes quite complicated sum, and you may need to spend time on more basic stuff on heat transfer first. Heat transfer is littered with a whole bunch of dimensionless numbers - Reynolds, Prandtl, Nusselt, Grashoff spring to mind - and you may well need to establish what they are before launching in. You obviously have a background in power engineering, so I am sure you will get there. I have a background in mechanical engineering design (including thermodynamics), which helps.
HMEL
I think we touched on the fact that gas firing with low radiant heat transfer is likely to need more tube area and less firebox way up in this thread. You are quite right and industrial boilers (typical 2 or 3 pass drum type) do exactly as you suggest if compared to a locomotive boiler, for example. You are also right that radiant transfer goes as the fourth power of temperature. Make sure the temperature is quoted as absolute, though. Having said all that, it is quite surprising that model locomotives can be made to run quite succesfully on gas with very little change to the boiler shell - possibly not as efficiently but that doesn't matter too much on a model.
Martin

#### Steamchick

##### Well-Known Member
HMEM Supporting Member
HMEL:You are right with your understanding about Stefan's law about the heat transmitted by radiation: t hot (4th) - t cold (4th power): in KELVIN. - remember the t cold is BOILER Temp. = 200C at 100psi... - so radiant heat transmitted is related to 1173K (4th power) - 473K (4th power)
Industrial suppliers of ceramic burners always set a limit around 900deg.C. for ceramics, because the mineral degrades with temperature and time, and when it gets "white hot" it cracks and blows back (failure within just a few minutes), but at a bright yellow-white it burns the "hottest tips" on the cones and they turn to powder within minutes. Also at a bright red, if there is too much air (lean burn) the conducted heat through the ceramic (12mm thick at each 0,5mm hole) heats through the ceramic thickness to the inner surface until it reaches ignition temperature of the gas-air inside the plenum, at which point it spontaneously ignites (flash-back) and burns back to the gas jet. This then produces huge amounts of TOXIC CO gas. And it can melt the burner and cause a fire as red-hot parts that should be cold, ignite adjacent materials.
However at "Red-to Orange", (~900deg.c. or 1173K) they last for many years. Fine mixture control, by adjusting the air at the required gas flow, can produce a burn where the small cones of combustion rise from the individual holes to just above the ceramic cones on the surface, when the cones do not get yellow hot at the tip, and will last a very long time.
e.g. this burner has lasted since the mid-1990s. used for about 5~10 hours per year for 15~20 years at shows, plus "other" time at home. FULL combustion in the boiler within ~1/in. of the burner holes. Tops of cones have "burnt and eroded" with time and usage. Fire door is normally closed in operation (opened here so I can see inside with the camera!)
But care must be taken to avoid "hot-spots". e.g.

N.B. I use a camera, and photograph without other light or flash in order for the camera to show the bright-patches and banding that is invisible to the naked eye.
The Orange is good, the brighter spots were NOT good, but the burner in a boiler had some back pressure which reduced the air-intake a small amount so the bright spots became more orange (not noticeable when viewed down the flue of the boiler using a mirror...). You can also see another factor about radiant ceramic burners, in that the 25% of "square black holes" are "lost surface area" when considering the area of actual radiant versus occupancy of the radiant.
When the mixture is too rich, this happens, which is not complete combustion - the free dark blue cone is CO combustion in secondary air (open space). a correctly designed radiant style boiler-burner will take all the air via the burner, and have no secondary air, but also have no "surplus cone" of burning CO - which is only visible in the dark, using a camera. Inside a boiler, with no secondary air, all the "blue cone CO" will pass through unburnt. - wasted fuel and poisonous CO. This one set-off the CO alarm.

These photos were taken during "tuning" of the burner, and using various gas jets and pressures, as well as tuning the baffles in the sub-ceramic plenum.
There are difficulties of making the gas-air column (at high velocity and lower pressure) slow down to change the high velocity into low velocity and higher pressure in the plenum, and obtain a near uniform gas-air mix and pressure beneath the ceramic... as shown by the colour banding of the bright spots on the burner in the second photo. This is at regions where there is too much gas-air beneath the ceramic, and also how the column of gas-air is forming a standing wave beneath the ceramic.... (the spot and curved line of brightness) Gas-"dymanics" are simply crazy!
Guys who do not make good burners produce these things, (e.g. long burner photo) where the burner is actually drawing-in air at the low pressure (high velocity) zone where there is no combustion... or are simply over fuelled and poorly mix the gas and air so the mixture changes along the length of the burner. e.g. as in this one from e&@y where the flame height varies with length, and combustion goes from "Almost OK to NO GOOD" (yellow flames) along the length. Things like this should be banned from the Sales websites, as simply dangerous (from CO production) in a boiler.

This photo was on the sales blurb for the burner being sold on the internet. Another photo of one of his burners had no flames for the first 2 or 3 rows of holes... where it was drawing-IN more air...

Disclaimer: I have deliberately shown some burners that are not safe, so you can see what you MUST avoid when making your own burners. ALWAYS operate "burning fuel" Boilers etc. in the OPEN AIR, NOT a garage with an open door, etc., and well away from any other combustible material. Correct use of gas appliances must be followed at all times. USE a CO detector mounted above and near the exhaust flue. (CO is invisible and toxic. It causes permanent lung and brain damage - or worse). (Here-endeth the lesson!).

Enjoy!
K2

#### Steamchick

##### Well-Known Member
HMEM Supporting Member
Hi Raygers. I am unsure of the design of the fire-hole assembly....
While this looks to be something like the foundation ring - a 1/4in square section (or some-such) silver soldered to inner and outer tubes.... I am musing here, so please bear with me and (anyone?) reply where my musings are incorrect... please?
On a Foundation ring the forces of internal pressure on foundation ring and tubes are as follows (I reckon?):
The pressure is trying to force the foundation out by putting the 2 large surface areas of silver solder in shear.
The (Internal) pressure on the outer tube is causing the hoop stress - up to the point of silver soldering to the foundation ring - to try and expand the tube, and where it reaches the silver solder, is trying to peel the outer tube away from the foundation ring with a large stress concentration at the corner where the silver solder - overlap to foundation ring - starts.
From my calculations, and current knowledge, the ASME limiting (hoop) stress shall not exceed 3142psi in tension. You have a design with a hoop stress of 2608psi. BUT ASME also require a boiler tube per the outer shell to have a stress concentration factor of 3.3 applied to any tube with penetrations. - And your design has many penetrations - so the resulting limiting "developed" tensile stress shall be calculated as 3.3 x 2608 = 8608psi... which means this stress is 2.7 times higher than the ASME limiting tensile stress. Or to put it another way, the tube ONLY has a Factor Of Safety of 3, not 8 as required by ASME. This isn't good, but you probably would not see a failure at the hydraulic test of 2 x Normal working pressure.... even if the calculations are based on "worst case" for the annealed copper, etc.
But when it comes to the foundation ring inner, or more particularly the inner (5" dia) firebox tube local to the fire-hole door, the pressure of water/steam is trying to peel the copper tube away from the foundation ring or fire-hole ring. What seriously bothers me is that the stress concentration of this "peeling effect" - stress in the tube being high but meeting a corner that is "well supported" but being silver-soldered to the adjacent ring section. In addition there is the stress concentration of the tube at the fire-hole (at fire-hole horizontal centre line) being incomplete, so the normal tube stress cannot form a hoop but stress lines must deviate off to the corners of the fire-hole and concentrate there. The combination of these 2 stress concentrations further increases the stress above the failure stress of copper in compression (Tube collapsing inwards from steam/water pressure). I suggest the hydraulic test at 2 x NWP would fail the joint at the corners of the fire-hole door.
Curiously, I have had an "old boiler" - unknown provenance - and repaired and de-rated it for low pressure use only, because it had failed at the silver soldering at the corners of the fire-hole aperture. I think I now understand "why?"
Any experts able to offer advice/criticism of my musings?
K2

#### Steamchick

##### Well-Known Member
HMEM Supporting Member
Ajoeiam:
I simply went onto the Thermopedia contents page, then went to W - and found "water tube boilers =>

Hope that helps you?
K2

#### Steamchick

##### Well-Known Member
HMEM Supporting Member
Not knowing exactly what you want to calculate, I found a couple of pages:

Hope there is something of use to you?
K2

#### Raygers

##### Member
HMEM Supporting Member
Hi Raygers. I am unsure of the design of the fire-hole assembly....
While this looks to be something like the foundation ring - a 1/4in square section (or some-such) silver soldered to inner and outer tubes.... I am musing here, so please bear with me and (anyone?) reply where my musings are incorrect... please?
On a Foundation ring the forces of internal pressure on foundation ring and tubes are as follows (I reckon?):
The pressure is trying to force the foundation out by putting the 2 large surface areas of silver solder in shear.
The (Internal) pressure on the outer tube is causing the hoop stress - up to the point of silver soldering to the foundation ring - to try and expand the tube, and where it reaches the silver solder, is trying to peel the outer tube away from the foundation ring with a large stress concentration at the corner where the silver solder - overlap to foundation ring - starts.
From my calculations, and current knowledge, the ASME limiting (hoop) stress shall not exceed 3142psi in tension. You have a design with a hoop stress of 2608psi. BUT ASME also require a boiler tube per the outer shell to have a stress concentration factor of 3.3 applied to any tube with penetrations. - And your design has many penetrations - so the resulting limiting "developed" tensile stress shall be calculated as 3.3 x 2608 = 8608psi... which means this stress is 2.7 times higher than the ASME limiting tensile stress. Or to put it another way, the tube ONLY has a Factor Of Safety of 3, not 8 as required by ASME. This isn't good, but you probably would not see a failure at the hydraulic test of 2 x Normal working pressure.... even if the calculations are based on "worst case" for the annealed copper, etc.
But when it comes to the foundation ring inner, or more particularly the inner (5" dia) firebox tube local to the fire-hole door, the pressure of water/steam is trying to peel the copper tube away from the foundation ring or fire-hole ring. What seriously bothers me is that the stress concentration of this "peeling effect" - stress in the tube being high but meeting a corner that is "well supported" but being silver-soldered to the adjacent ring section. In addition there is the stress concentration of the tube at the fire-hole (at fire-hole horizontal centre line) being incomplete, so the normal tube stress cannot form a hoop but stress lines must deviate off to the corners of the fire-hole and concentrate there. The combination of these 2 stress concentrations further increases the stress above the failure stress of copper in compression (Tube collapsing inwards from steam/water pressure). I suggest the hydraulic test at 2 x NWP would fail the joint at the corners of the fire-hole door.
Curiously, I have had an "old boiler" - unknown provenance - and repaired and de-rated it for low pressure use only, because it had failed at the silver soldering at the corners of the fire-hole aperture. I think I now understand "why?"
Any experts able to offer advice/criticism of my musings?
K2
Steamchick you make an interesting, if not terrifying, observation there. There is a ring around the base of the boiler shell that should/maybe resist any outward pressure. But the inner firebox is simply relying on a silver solder joint. I wonder if an inner ring were placed inside the firebox at the base would work. Silver soldered and riveted, would the heat from coal fire melt the solder due to less conduction to the water?
The fire-hole door would probably be riveted as well as silver soldered.
Ray

Edit, looking at the drawing again there's no need to solder the proposed lower ring, just a very good fit and riveted.

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#### Steamchick

##### Well-Known Member
HMEM Supporting Member
Hi Raygers.
For the foundation ring, it does not need rivets. It should be silver soldered. ASME do not permit riveted boilers any longer. The problem is the copper tubes. Too thin at 3mm. While the foundation ring at the bottom is unlikely to fail, the outer (6") tube has too little Safety Factor to meet Regulation certification to ASME standard.
But the inner (5") tube, is in compression from steam-water pressure and is overstressed at the corners of the fire-door hole, because it is way too thin. This is likely to split the silver soldered joint on hydraulic test, or split the copper tube.... because of the stress concentrated at the corners of the fire-hole.
My calculations may not be perfect, but if they say the copper tubing is too thin, I feel duty bound to tell you. It would be a shame if you made a boiler and it failed to hold the pressure you want it to hold, safely. Or if the finished boiler was failed by the boiler inspector. I have seen the dissappointment when that happens.
A second opinion from your local club boiler inspector is a good idea.
Cheers,
K2

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