Model boiler design information

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steamboatmodel

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xo18thfa said:
I think I need a copy of Part 3
I ordered a copy and received it very quickly. It is very well written and easy to understand a good buy.
Regards,
Gerald.
 

Nave

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Hi,

I'm just starting this myself and bought Harris and Parts 2&3 of the AMSC codes. Part 2 contains a lot of stuff I found useful when trying to work in the fitting locations, such as the sizes for various bushes and the min web in the tube plate. Given that harris is pretty thin on detail in his final design chapters, this was invaluable.

Dave.
 

Diversion900

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Just a quick question for the Aussies in the know....

My planned build of a inglis type Scotch boiler 100mm diam. but under 1 litre capacity, would this fall under code 3 regulations, or code 1 ?



Cheers, Neil
 

ianjkirby

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Hi Neil,
The codes are quite clear. In each of them, the "scope", or range of parameters allowable, is unambiguously stated.
Code part 3 has a maximum allowable diameter of 76mm, so your proposed 100mm dia boiler is clearly within the scope of code part 1. The fact that it is only 1 litre is of no consequence.
All parameters must be met simultaneously; barrel size, water volume, and pressure have stated limits. If any one of those limits is exceeded, then the next level applies. If any parameter of code part 1 is exceeded, then the boiler must be approved and inspected by commercial inspectors if insurance is required.
Above all, please discuss the matter with your local club boiler inspector.
Regards, Ian.
(ex-AMBSC chairman) ;)
 

Diversion900

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Thanks Ian, much appreciated. I've been wondering about this for a while now.

I have been given the name of a local club boiler man, so I will track him down and discuss the build further to get my head around the rules and regs before proceding too far.

Cheers, Neil
 

Dan Rowe

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The last chapter in Martin Evens "Model Locomotive Biolers" is about testing boilers for efficiency which is the work of Jim Ewins. The chapter describes the test set up and results obtained from the testing.

Now here is the good bit. I found a website that takes Jim Ewins research and placed it in excel so initial boiler design can be checked and compared to existing designs.
http://www.baggo.copperstream.co.uk/me/Loco%20design/design1.htm
http://www.modeng.johnbaguley.info/Loco design/design1.htm

A further page on this subject by Jim Ewins can be found here:
http://www.modeleng.org/articles/loco_research_je.pdf

Dan
 

xo18thfa

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Nice find Dan. That's handy info.

I finally ordered a Part III manual on sub-miniature boilers ans the steel boiler manual.
 

steamboatmodel

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Dan Rowe said:
The last chapter in Martin Evens "Model Locomotive Biolers" is about testing boilers for efficiency which is the work of Jim Ewins. The chapter describes the test set up and results obtained from the testing.

Now here is the good bit. I found a website that takes Jim Ewins research and placed it in excel so initial boiler design can be checked and compared to existing designs.
http://www.baggo.copperstream.co.uk/me/Loco design/design1.htm

A further page on this subject by Jim Ewins can be found here:
http://www.modeleng.org/articles/loco_research_je.pdf

Dan
Hi Dan,
The http://www.baggo.copperstream.co.uk/me/Loco design/design1.htm
Is no longer working.
Regards,
Gerald.
 

steamboatmodel

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Thanks Dan.
Its too bad that we can't get some of this information in a sticky.
Regards,
Gerald.
 

steamboatmodel

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Now that this is a sticky of some books;
Books
________________________________________
Here is a short list of Books.
(Maybe not so short ;<)

K.N Harris's book Model Boilers and Boilermaking.
(This one is almost considered the Bible among Boiler Makers)
Found online PDF copy:
http://www.fastonline.org/CD3WD_40/JF/424/19-422.pdf

"Model Stationary and Marine Steam Engines" by K.N.Harris
Found online PDF copy:
http://www.fastonline.org/CD3WD_40/JF/424/19-423.pdf

The next two have simple pot boilers in them;
Building Simple Model Steam Engines
Books 1 & 2
by Tubal Cain

Making Simple Model Steam Engines
Model Marine Steam
by Stan Bray

Another Article/book to add,
Safety of Copper Boilers by Kozo Hiraoka this nine page article was first in Live Steam & O.R. (Vol. 40 No. 6 Nov-Dec 2006) and is included in Building the New Shay.

For those who want to really move along.
"Experimental Flash Steam" by J.H.Benson and A.A.Rayman.

This link applies more to full size equipment than models, but does cover steam basics;
http://www.pipingnews.com/steam2.htm

Not really a book but usefull,I found this years back
The Truth about Steam Oil
by Harry Wade
http://www.southernsteamtrains.com/m...-oil-hwade.htm
Regards,
Gerald.
 

Bentwings

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One of the best sources of information on model boiler design is the Australian Miniature Boiler Safety Committee. (AMBSC) The four books (1) Copper (2) Steel (3) Sub-miniature and (4) Duplex Steel
http://www.smex.net.au/Store/Store_AALS-Codes.php

Model Boilers & Boilermaking by K. N. Harris has a wealth of good design information and construction methods. Topics covered include fuel and firing and accessories. (Copper boilers)

Model Locomotive Boilers by Martin Evans is also a good source of design information and methods. It covers welding equipment, workshop equipment, water, fuel and combustion, oil and gas firing, and testing. The testing is more than a simple hydro a full engineering test stand designed by J. Ewins is described with drawings of the boiler and test results. (Copper and steel boilers)

Safety of Copper Boilers by Kozo Hiraoka this nine page article was first in Live Steam & O.R. (Vol. 40 No. 6 Nov-Dec 2006) and is included in Building the New Shay. The design rules are presented in graph form for simplicity with the ASME formulas and code designation listed in the appendix. All graphs have a metric and an imperial version. The graphs are (1) Minimum thickness for a cylindrical shell under internal pressure (2) Maximum allowable pitch of symmetrically arranged staybolts (3) Maximum allowable diameter of a circle enclosing an unstayed surface area (4) Minimum staybolt diameter. This book like all of Kozos books is a treasure trove of useful information for the model engineer.

These are the four main sources of model boiler information in my stack. Several other model engineering books I own have boiler chapters but the information is not a complete design system. These include works by Greenly, LBSC, Tubal Cain, and Martin Evans.

Cheers Dan
I didn’t know this section was on here. I’ve posed some already about my new hobby,,,,steam engines an boilers.

Have. 4 cyl piston port mill stem engine ordered from chilertern in uk. They have been absolutely wonderful to deal with. I get overnight emails even though theeis 6 hours difference.
in my situation I simpl. Cannot have a fuel fired beer. I’ll have t use an ultra quivering compressor for initial start uwhhile I’m building the electrically heated boiler I write some about it already in the steam nine group. It’s 44” da meter 6062 aluminum 3/16 wall tube. I initially thought of makin it from a solid bar f aluminum, but between it being early wasteful even though I have a solid bar of 4” aluminum, it meant cutting threads internally on or ennd externally on a screw in end cap, it involved a lot of work I’m visually impaired ou will se spelling errors making some out of context things appear. I’m medically not even supposed to be in the shop. I have to use magnifying glass use to read micrometer. Lus the shop is 60 miles away so I have limited time there too. While I lit screw in cap would have been stronger I really wanted ssuprr high pressures. . I’m new to boilers so I had to do some self educating. I’m a life long mechanical ngineer anddtool. Maker welder. So I don’t have fabrication problems other an those I create myself. I hav access to solid works but limited. I hate manual drawing boards but have to give in to my med issues and make endless sketches and calculations. So enough.
I’ve determined my boiler is a heated water boiler not a fire tube boile like a locomotive. I hav a 50watt anda1200 watt electric immersion heaters. I was only going to use one ut I can plu theminto different circuits in my home.they should provide enough heat. The oiler has 10 1/2” ter tubes mounted in two aluminum ulheads . With heater going under them.the end caps have Teflon o rings it’s thee made by a retaining late oorming one side of the groove.that way th o ring does not have to be stretched over g of he groove. The engin pistons. Are made the same way.there will be a row of 8 NPT female fitting ports tapped in the upper or top of the tube for outlet boilerr I’ll pressure age tem gage plushe end cap will hav ports for levee and das well a ande port. May use a stainless steel center tie rod for extra safety. I’ve done hoop stress including the ring f button head end cap retaining screws. I think it is strong enough. I also have sketches for a simulation max pressure test. I’ve done this in industry. So I’m eelamiliarwith this. Test. We have a hyydaulic pump so I’ll be s
able to pressurize the test fixture t faailre when the time come it will be pressurized with water in a water tank so no explosions. It will fail by leaking first. Also the boiler wilhave two mounting legs on s solid aluminum plate. I may use a hot plate to keep intermittent if necessary the boiler will be wrapped with automotive exhaust header issuatingbwrap. Then a olished stainless steel decorative wrap. So Er is lots going on. My son and grand sn wi help with the machine work. Normally I’d TIG WELD IT BUT I JUST CANT SEE WELL ENOUGH TO MAKE ACCEPTABLE WELD. Did exactly this shortly after retirement but medically I can’t now. Ivory material and I jstfiised the boilerr tubes . I had not planned using both h easters but I have I ont know j ha fast the engine will run but I plan on abo 1,000 rpm cruising. I have a cool dynamo an at least half a dozen stepper moors and another half a dozen small gear motors so plenty of experiential stuff. I forgot I have two stem turbine too.the on thing I just ran into is the onmiser o. Condenser. I’m trying to lesrn a little about these but for models probably not necessary. I’ll have lubicated stem or air so my initial thought is to use the turbines as centrifugeto strain the remaining oil out of the exhaust steam air. I have an extra ir filter I can use too. them so in they go.
From my description aybe y’all could comment good o bad.I won’t have the engine for another couple weeks but I’ll start assembly right away As soon as it arrives. Take pictures as progress goes on the boiler.maybe a video E mounting board or floor is going to be 1/8” laminated oak oak strips in casting resin so it’s glass smooth. In other words a scale wood floor. I have a plastic mounting and assembly board now until eerthing is ready.everything is ready.
my kitty wants me to cne to bed so until later.

byron
 

Steamchick

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Hi Byron,
You'll need all the heaters you can stuff into the boiler. You'll have to have at least 2kW just for the smallest engine using a little more than a whiff of steam. As the outside will not have flames lapping over it, you can do a serious job of lagging. On my 3" boilers, I have a "radiant" barrier - aluminium foil, insulation spacer and aluminium foil - surrounded by 1/2" of conductive barrier. Balsa wood is very good for that! I have held the outside of the wood to warm my hands when at full pressure, but it isn't hot like a coffee mug. And I always lag the steam pipework as well, as otherwise the losses from that can be huge!

Dan, and colleagues, I am glad Byron has introduced me to this site via his post...
I should like to let people know that the "Engineering" I do (crude calculations, and ideas) has caused me to "de-rate" some boilers that were "traditional" designs.
The simple reason is that copper in compression is really weak. (Compressive strength around 21% of the tensile strength at "boiler" temperatures). I haven't found ANY text book that covers this properly (I use properly in the sense that I have been a professional engineer all my career, and expect all the facets of a design to be covered). Typically, designs on tubes that are in compression, when larger than just flue tubes, are inadequate for the design pressure of boilers, and still have a factor of safety of 8.
So do your sums lads! And check compressive hoop stress against the compressive strength of copper at elevated temperature, before you even order the tubes form the supplier.
Anyone wanting more advice (or calculations) please ask. I do this for free, so all your boilers are safe.
Enjoy steaming!
K2
 

Bentwings

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Hi Byron,
You'll need all the heaters you can stuff into the boiler. You'll have to have at least 2kW just for the smallest engine using a little more than a whiff of steam. As the outside will not have flames lapping over it, you can do a serious job of lagging. On my 3" boilers, I have a "radiant" barrier - aluminium foil, insulation spacer and aluminium foil - surrounded by 1/2" of conductive barrier. Balsa wood is very good for that! I have held the outside of the wood to warm my hands when at full pressure, but it isn't hot like a coffee mug. And I always lag the steam pipework as well, as otherwise the losses from that can be huge!

Dan, and colleagues, I am glad Byron has introduced me to this site via his post...
I should like to let people know that the "Engineering" I do (crude calculations, and ideas) has caused me to "de-rate" some boilers that were "traditional" designs.
The simple reason is that copper in compression is really weak. (Compressive strength around 21% of the tensile strength at "boiler" temperatures). I haven't found ANY text book that covers this properly (I use properly in the sense that I have been a professional engineer all my career, and expect all the facets of a design to be covered). Typically, designs on tubes that are in compression, when larger than just flue tubes, are inadequate for the design pressure of boilers, and still have a factor of safety of 8.
So do your sums lads! And check compressive hoop stress against the compressive strength of copper at elevated temperature, before you even order the tubes form the supplier.
Anyone wanting more advice (or calculations) please ask. I do this for free, so all your boilers are safe.

Enjoy steaming!
K2
Thanks for your response.I too am a life long mech eng as well as tool maker. We have a small shop so machining is not a big problem except my mobility is limited to have
Ing some one come and get me then spend the rest of the day in the shop not all bad but my vision limits me to being extremely careful and having my ever present magnifying glass. The boiler won’t have any closed copper tubes only the “ super heat” tubes I’m pretty sure the immersion heaters will be ok they are stainless steel and I’ve used them before in some plastic molds in industry. Since I’ve even intoning boats I’m well aware of using anodes so that was a natural. My tap water is terrible my humidifier needs weekly cleaning there is constant lime issues. I go through coffee pots once a year at best. I asked about bronze and brass as the question came up at our daily lunch debates brass is easy to the point of fun to machine bronze is harder and much more expensive and harder to Er. But I have some of each. There are store bought fittings that I can get as needed some times there is a choice of materials. I’d just like to not create issues I can avoide right from the start. My little engine is a 4 cyl double acting slide piston ported engine mill model from childrenmodelsteam in uk they have wonderful customer service I get email in less than half a day with 6 hour time difference . So after your note the question is what is the displacement of this engine 17mm bore 19 mm stroke ? 4 cyl I don’t know the piston thickness but I’d guess 1/8” based on design Vince it’s 4 cyl double acting it’s actually an 8 cyl engine three of us got different values. LOL ITS LESS THAN 1 cu in the object was to see if the air compressor can operate it for a while it has a small tank and about 2.2 cam at 90 psi.
I’m thinking that the boiler will run about 50 psi with 100 psi max . I’m working on a small gear pump for filling on the fly. There are a couple piston pumps available but converted to steam engine driven are horribly noise for small item plus overly expensive for what is purchased . Gear rod is readily available so I could change the size pretty easily I have at least half a dozen motors that th steamer could drive or I can dc power supply them so adding a check valve to the feed line should make filling the boiler easy .
Insulation the balsa wood idea is great I have just a great pile of every size you can imagine plus I’ve done balsa model airplane for over 65 years so bending cutting shaping is something I think I have a handle on
. I had planned on using automotive exhaust header wrap but the balsa will make this insulation much cleaner and easier. I also plan on a polished stainless decorative wrap. So it will now be much cleaner. Originally I was going to make the boiler one piece with a threaded end cap on one end then it evolved to threaded in both ends then to button headed screws to simulate riveted now there will be just polished end caps I backed away from the threaded end because the thermo expansion could cause leaking which I want to avoid. There will 8 8-32 stainless steel screws plus the tie rod holding it together. I have a max pressure test set up too no not air? Hydraulic . I’ve done this in industry so done this before
Anyway I really need all the help and comments I have thick skin so I can debate if necessary . I’ll keep politics out as I’m known to get on my invisible Podium

byron
 

Bentwings

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Thanks for your response.I too am a life long mech eng as well as tool maker. We have a small shop so machining is not a big problem except my mobility is limited to have
Ing some one come and get me then spend the rest of the day in the shop not all bad but my vision limits me to being extremely careful and having my ever present magnifying glass. The boiler won’t have any closed copper tubes only the “ super heat” tubes I’m pretty sure the immersion heaters will be ok they are stainless steel and I’ve used them before in some plastic molds in industry. Since I’ve even intoning boats I’m well aware of using anodes so that was a natural. My tap water is terrible my humidifier needs weekly cleaning there is constant lime issues. I go through coffee pots once a year at best. I asked about bronze and brass as the question came up at our daily lunch debates brass is easy to the point of fun to machine bronze is harder and much more expensive and harder to Er. But I have some of each. There are store bought fittings that I can get as needed some times there is a choice of materials. I’d just like to not create issues I can avoide right from the start. My little engine is a 4 cyl double acting slide piston ported engine mill model from childrenmodelsteam in uk they have wonderful customer service I get email in less than half a day with 6 hour time difference . So after your note the question is what is the displacement of this engine 17mm bore 19 mm stroke ? 4 cyl I don’t know the piston thickness but I’d guess 1/8” based on design Vince it’s 4 cyl double acting it’s actually an 8 cyl engine three of us got different values. LOL ITS LESS THAN 1 cu in the object was to see if the air compressor can operate it for a while it has a small tank and about 2.2 cam at 90 psi.
I’m thinking that the boiler will run about 50 psi with 100 psi max . I’m working on a small gear pump for filling on the fly. There are a couple piston pumps available but converted to steam engine driven are horribly noise for small item plus overly expensive for what is purchased . Gear rod is readily available so I could change the size pretty easily I have at least half a dozen motors that th steamer could drive or I can dc power supply them so adding a check valve to the feed line should make filling the boiler easy .
Insulation the balsa wood idea is great I have just a great pile of every size you can imagine plus I’ve done balsa model airplane for over 65 years so bending cutting shaping is something I think I have a handle on
. I had planned on using automotive exhaust header wrap but the balsa will make this insulation much cleaner and easier. I also plan on a polished stainless decorative wrap. So it will now be much cleaner. Originally I was going to make the boiler one piece with a threaded end cap on one end then it evolved to threaded in both ends then to button headed screws to simulate riveted now there will be just polished end caps I backed away from the threaded end because the thermo expansion could cause leaking which I want to avoid. There will 8 8-32 stainless steel screws plus the tie rod holding it together. I have a max pressure test set up too no not air? Hydraulic . I’ve done this in industry so done this before
Anyway I really need all the help and comments I have thick skin so I can debate if necessary . I’ll keep politics out as I’m known to get on my invisible Podium

byron
I just got a piece of 4” aluminum tube to serve as the mold for the stack of balsa I have waiting . The ammonia I won’t get until Sunday then I’ll start the boiler wrap insulation . I may still add the automotive exhaust wrap maybe even mold it right into the balsa. I have 1/4 40 ME tap and die ordered also found 1/16” NPT TAP AND DIE actually found 1/116 pipe. I didn’t know it existed . I just got the pressure relief valve and spring set. I’m going to try and get to the shop over the week end. Also got s tooth belt an handful of pulleys. Snd a self aligning bearing for the engine outer crankshaft support. I haven’t modeled it yet but I have some ideas. It will be aluminum , maybe polished. I still have some others parts coming. I have to make a choice shortly on gages and fittings. I’m thinking 1/8 NPT at present as a compromise size cost and space. The engine is supposed to arrive tomorrow. It’s might cold out now probably -15 F by morning . It time to start thawing my test oils out both are frozen solid. I’m going to lay them flat and see when they start running or pouring . Then I’ll go from there.
Byron
 

chrsbrbnk

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Do I have this correct ,your planning on building a boiler out of 3/16 wall aluminum tube 4 inches in dia. . the end caps are held on with 8-32 screws and sealed with rubber o rings . your planning on running this at 50-100psi?
 

abby

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Nah it's 44" dia and 3/16 thick wall ! he was going to machine it from a solid bar but it was a bit wasteful .
 

Bentwings

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Do I have this correct ,your planning on building a boiler out of 3/16 wall aluminum tube 4 inches in dia. . the end caps are held on with 8-32 screws and sealed with rubber o rings . your planning on running this at 50-100psi?
Yes I’m planning on 50!psior less. They said 20 would run the engine but I don’t think there will be much torque. I’ll have an air compressor to start with I think we’ll see hot the heat works. I spilled a full glass of water on my notes and sketches so I’ll have to te do things agin. I have a couple nice gears so I’ll make a gear boiler fill pump out of them . My son and I talked a both this to day . I got a tooth belt and pulley drive today. Now I need to make this into a gear down to make sure the engine can run the generator to drive the water pump . I think there is a 3:1 reduction plus enough to double that if necessary. I would like to keep engine around 1,000 rpm I think it will go faster but I done want to break anything right away. The stepper motor generators may take more power than I thought the turbine needs a gear reduction too so I need to do some thinking on it. I don’t have any idea how it will work out already heard of one wrecked. The little one will be more noise maker than very productive it will go about a jillion rpm but I don’t have hopes of any torque.
Byron
 

Bentwings

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Yes I’m planning on 50 psi or less. They said 20 would run the engine but I don’t think there will be much torque. I’ll have an air compressor to start with I think we’ll see how that heat works. I spilled a full glass of water on my notes and sketches so I’ll have to te do things agin. I have a couple nice gears so I’ll make a gear boiler fill pump out of them . My son and I talked a about this to day . I got a tooth belt and pulley drive today. Now I need to make this into a gear down to make sure the engine can run the generator to drive the water pump . I think there is a 3:1 reduction plus enough to double that if necessary. I would like to keep engine around 1,000 rpm I think it will go faster but I done want to break anything right away. The stepper motor generators may take more power than I thought the turbine needs a gear reduction too so I need to do some thinking on it. I don’t have any idea how it will work out already heard of one wrecked. The little one will be more noise maker than very productive it will go about a jillion rpm but I don’t have hopes of any torque.
Byron
Yes that’s correct the 8-32 button head screws will go in from the out side like a RR boiler there is also a 3/8” dia stainless steel tie rod from one end cap to the other with 2/4 28 unf gr 8 bolt through the end caps to provide extra end cap anti blow out . The o rings will be Teflon rather than rubber I think final assembly will have high temp silicone sealer around the perimeter of the end cap. Due to thermo expansion it’s possible the o rings might leak but it’s the same material as the pistons have for piston rings.
My hunt and peck targeting was not good on my first post. Spell check does unusual things some times and I miss letters some times as I see two of each which one to poke at sometimes is a dead miss good thing I’m not a sniper. LOL I don’t THINK THE END CAPS WILL FLEX MUCH As they WILL BE 1/2” thick aluminum dome shape I may use an end gasket or o ring there is not much land area so I may create a groove with an internal groove seal if if 1/4 wall tube was available I’d have used it and there would have been room for an end face o ring seal I know this sounds complicated and I have not finished re drawing my ruined sketches. Fortunately my son understands what I’m planning actually I think the 8-32 screws are the weak point due to thermal expansion. They may be subject to loosening so I’ll be sure to check them as things progress. I’ll know more over the week end as things progress. I just wish I could be there making chips myself instead of being here watching the thermometer fall -10 F now going down to -15 by morning . Hopefully engine will arrive on schedule

Byron
 
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Steamchick

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Hi Byron, You sound to be very productive with your ideas. Just a couple I want to debate:
  1. If you are planning on just balsa wood for insulation, that will be all you need for conductive losses, if around 1/2" or more. So I can't see any reason for the car exhaust stuff? But your choice. However, you should consider radiation losses (the radiant heat shines straight through the balsa or other until it hits the stainless steel). So if you polish the aluminium tube that will be excellent, or wrap in aluminium foil. Either will reduce radiant losses significantly compared to doing nothing with the surface of the tube.
  2. My biggest issue is the use of aluminium with steam. I thought this was always a "NO! NO!" because water doesn't corrode aluminium rapidly, yet STEAM does, especially at elevated temperature. And when it does it gives off hydrogen, which has the potential of being very explosive... So although domestic pressure cookers with steam at up to 15psi exist and are safe to use, please check what higher temperature steam will do to your boiler.
  3. A quick check suggests you need >5.2kW of steam to extract if the engine needs 50psi at1000rpm (and a generator to load the engine). Of course, at 20psi you'll only need 3kW... of steam power. Allowing for losses (maybe a couple of hundred W if well lagged?) you'll need more than those figures from the heaters. Unless I have screwed-up the calculations? (I had to correct some glitches in my spreadsheet). What did you calculate?
  4. What "penetrations" will you make in the outer shell cylinder? (If any?) I can see a design where all the safety valves, water gauge connections, steam extraction, water-feed, etc. is done via the end plates, so the boiler shell is "without penetrations". but that is unusual. Mostly there is a steam dome (to collect steam high above the spraying surface of water), water feed, connection for safety valve, etc. so that affects the hoop stress calculations and comparison of the design with permissible safety limits. ASME uses a "Standard" value of 3.3 for the SCF if ANY penetrations exist in a boiler shell or tube. With this SCF (assuming at least 1 penetration) for your boiler at 50psi, I get a hoop stress of 1902psi and I think the permissible stress will only be 1141psi for aluminium..? which I reckon is a FOS of less than 5. But the regulations normally require a FOS of 8? But I may be wrong? If there are no penetrations in the shell tube, then the FOS is over 15 - which is good. - What have you calculated? - I am keen to be sure my calcs are sensible, and if you have close results I'll be happy.
Thanks,
K2
 

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