So I’ve been reading some texts from the 40s to early 50s, and they all mention the importance of firebox volume to the evaporative capacity of the locomotive, but there doesn’t seem to be any concrete relationship or formula that I’ve found in any of these texts.
‘The Steam Locomotive in America’ declares that it was around 1932-33 that evaporative calculations started taking into account firebox volume, but I want to see what that means quantitatively.
The book also shows that if you only use surface area to calculate evaporative capacity, you end up with amounts that are only a fraction of actual results for later steam (notably the Niagara). What exactly are they doing when taking firebox volume into account? Is it a constant added proportional to cubic feet, or was there an entirely new set of equations?
I’m not an expert at steam locomotives but I’m sure that there is indeed an equation to calculate the surface area for the evaporative capacity, I do think that firebox volume will account into the equation.
It isn’t firebox volume per se; it’s a combination of long luminous combustion plume and radiant uptake. “Combustion chambers” are not so much there for more complete combustion before the plume enters the tubes – they provide more radiant uptake surface.
The great realization was that the firebox is surrounded by water not to prevent the inner wrapper from softening or melting, but to provide a large mass of water in close contact with transferred radiant heat, for steam generation. Very late in the big-steam era, the Cunningham circulator increased vertical circulation flow in the water legs, to stave off DNB there, and the result could be over 10% improvement in fuel consumption for the same mass flow of throttle steam. A good waterwall forced-circulation arrangement, as in the LaMont system described on the SACA ‘phorum’, can do dramatically better still, and avoid the crown-sheet and fusible-plug efficacy issues doing it.
More should have been described about the Lima double-Belpaire boiler, which carefully maximized the available area of a good combustion chamber (even if it restricted driver diameter underneath to about 76" for contemporary loading gage).
I suppose my question is how did they calculate (within a reasonable error bar) the evaporative capacity of the Niagara before it was even built, because the older 20s calculations using only surface areas clearly weren’t going to give accurate results.
Clearly something else was added theoretically between the late 20s and early 40s and I want to know what it was.
The ‘classic’ analysis in the United State’s was Lawford Fry’s (circa 1923) and this is well worth reading for the analytical technique and assumptions (e.g. to my knowledge he was the first to note that heat transfer in tubes and flues should be treated as a lolog function). The problem is that the actual formulae rely on so many empirical factors scaled to the ‘state of the art’ in that pre-SuperPower era as to be unusable in modern design.
I presume you have read LeMassena’s article about Niagara design in Trains Magazine in the early '80s. While in my opinion at least some of his boiler-analysis method is peculiar, it takes some cognizance of the different, sometimes recursive elements used to design the steam-generation system in good modern practice.
That Kiefer had a good fundamental grasp of more than just high-speed efficiency can be seen in a story related by Tuplin (in part supporting Tuplin’s belief in lower operating pressures) about a Niagara doing the work of an H-class 2-8-0 with the fuel consumption and water rate of an H-class engine – which was astounding to me when I read it. This was done by the fireman using sliding-pressure firing with a little anticipation of when the locomotive would need acceleration. The combustion path was so well determined that ‘automatic action’ (proportioning draft to evaporation) was effective even so far out of normal operating envelope for a high-delivered 4-8-4.
I don’t remember exactly, and it may take me a few hours to check.
In the meantime, he had an article in 1968 about general big-steam design, and one about optimized 4-8-4 design in February 1975. Trains ran a number of interesting articles about steam design in the intervening years which found me at an ‘impressionable age’.
DNB = Departure from Nucleate Boiling - Nucleate boiling is where a small bubble forms on a heated wetted surface, detaches and in much of the time collapses from the steam inside condensing due to the water temperature being lower than the boiling point for the given pressure. This is a very efficient way of transferring heat to the bulk of the water. When the heat flux is high enough to dry out the surface facing the water, the radiant heat transfer in what is now film boiling requires orders of magnitude higher temperature difference which lead to failure of the metal to hold up to boiler pressure.