Steam Radiator Math

HowardLong

I'm making a little calculator for steam systems for my own enjoyment and business. I'd like to bounce some of my understanding of things off other people.

Right now I'm looking into radiators. I have estimates on the internal volume of radiators, if I use that estimate, a 50sqft edr radiator equates to 12,000btu and 1.25ft3 internal volume. Based on this I've calculated the pounds of steam the radiator can hold at once(assuming the water volume is negligible) and then calculated the total btus to condense and then to cool to 190f. This gives me 48btus for a full steam radiator to fully condense and drip out. Now, assuming that this condensate is not affected by the rest of the incoming steam that is all the btus for one full cycle. For the radiator to be at full load(12000btu/hr) that means there are 249 cycles/hr=4cycles/min.

So to summarize:

50edr=12,000btu/hr

1.25ft3 = 0.0481lb steam/cycle

Radiation/cycle of radiator=48btus

0.0058gal/cycle=1.48gal/hr condensate

Now, if the radiator is at half output, 6,000btu/hr, does it cycle at half the rate? Or does it cycle the same amount with less condensate/cycle?

Steamhead

The amount of air in a radiator varies according to the type of radiator. For example, a column-type rad has more internal volume than a small-tube type. Go here and scroll to page 14 of the PDF to see:

https://www.heatinghelp.com/systems-help-center/balancing-steam-systems-using-a-vent-capacity-chart/

HowardLong

@Steamhead Yep, I've got that as a variable in my calculation. I have a table I can put in the type and size of radiator and it will keep track of all of that. I need to see if my mode of thinking is correct. I assume that the difference in volume comes down to the efficiency of heat transfer of each radiator style. Some need more volume of steam to put out the same amount of radiation.

mattmia2

you really don't need to know the volume of the radiator, the edr is what is important, it tells you how much steam it can consume at a given ambient temp and steam pressure although in residential we assume the steam to be at around atmospheric pressure. if you are doing higher pressure systems that is more important to calculate than volume of the emitter.

the ratio of volume to surface area really isn't about efficiency, it is just construction style. you probably need to think about piping differences more than differences of ratio of edr to the radiator volume. probably a fixed ratio will be less error than other things that you can't measure.

Steamhead

@mattmia2 , when you're venting air from a rad, you need to know that. The rad won't get hot if air remains in it.

HowardLong

I'm trying to make a little "simulator" for the whole system, that will tell me time to steam from cold, how long it will take to vent each vent line and how quickly condensate will be generated. Is there a way for me to estimate the amount of times an hour a trap will cycle based on the edr and the load on the system?

mattmia2

https://forum.heatinghelp.com/discussion/comment/1899682#Comment_1899682

you do need some sort of estimate, but using a fixed ratio of volume to the edr is probably close enough, you will have to vary it based on the actual heat loss of the room and other errors like piping you can't see and piping in different ambient temps in your calculation anyhow, you aren't going to calculate it perfectly.

mattmia2

https://forum.heatinghelp.com/discussion/comment/1899683#Comment_1899683

once the radiator is full of steam you can calculate the condensate production from the edr and ambient temp(and steam temp if working at elevated pressures). i suppose if you wanted to figure out when the trap opened you would have to calculate how long it would take to collect 1/4"-1/2" of condensate over the trap which would depend on the profile of the bottom of the emitter, how the emitter connected to the trap, and the profile of the trap itself.

how long it takes steam to get to the trap is much more complicated because it is a function of how long it takes to heat each infinitesimally small piece of pie to steam temp then each increment of radiator to steam temp and of the rate of the radiator valve on a 2 pipe or the rate of the vent on one pipe. the steam won't progress until the surface just in front of it is the temp of the steam. it will produce a lot more condensate as this is happening vs steady state.

109A_5

I got a bit lost with the 'cycle' aspect of your simulation. Steam condensing in the radiator starts the moment steam enters the radiator and continues continuously until a bit after the steam supply to the radiator ceases. It's a continuous process, not cyclic. The boiler's operation producing the steam may be cyclic.

The return trap in a two pipe system may cycle, that cycle rate may change depending on environmental conditions and steam supply. I would not think it would affect the radiators dissipation much, assuming it is working correctly.

HowardLong

@109A_5

Yes, this is only for two pipe systems this isn't for one pipe radiator. That should be pretty continuous Flowback but I am thinking for a two pipe system we know that the traps normally open between 180 and 190° Fahrenheit. Based on that information I know that I could fill the radiator up completely with steam and I can calculate how many BTUs will be output from that steam condensing and then cooling to 190 degrees Fahrenheit. From there I can take the rated BTU output of the radiator per hour and divide that by the BTUs per cycle to see how many times the radiator should fill with steam and fully condense and cool. It is not perfect because steam will be more or less continuously flowing in even before trap opens because as the steam condenses it will lose volume and draw in fresh Steam. So there are limitations with this line of thinking.

Jamie Hall

Oh dear. Well, to start the heat output of the radiator or whatever to the space is determined by the surface temperature of the radiator, the airflow around it, and the effective area. If there is adequate steam supply, the entire radiator will approach the condensing temperature of the steam — 212 F at 14.7 psia — and the heat output will be, to a first approximation, 240 BTUh per square foot of effective area (the EDR).

The radiator will continuously accept steam at rate needed to produce that much heat output. If the steam supply is less, the radiator will cool; if the available steam supply is greater, no more heat is produced by the pressure may rise.

There is no cycling involved at all.

Depending entirely on the rate of steam supply and the effective area of the radiator, the output trap may or may not close. If the potential steam supply is greater than the condensing capacity of the radiator, eventually steam will reach the trap and it will close and then cycle to allow condensate to escape. How rapidly the trap will cycle at that point is a frankly insanely complex product of the power output of the radiator, the geometry of the bottom of the radiator, the design and characteristics of the trap element, the piping in that vicinity, and a few other factors. The overall cycle frequency and open/closed time ratio is potentially interesting… But has almost no effect on the heat output of the radiator or the total volume of condensate produced. It may be of academic interest to the trap designer, however…

HowardLong

• @Jamie Hall

I understand there's a lot of simplification going on here. I don't desire to do an ansys two phase simulation with the cast iron of the radiator and everything. I'm just making a 75% maybe 80% accurate simulation so I can just see how the system works a bit better in steady state. You're 100% correct there are a lot more variables that come into play. But I am simplifying everything. My input is that the radiator is putting out a specific number of BTUs I get that from what the manufacturer says that it will do and keeping the room about 70° from my understanding of edr.

As for the cycling. What I am trying to say is that just for an estimate we know how many btus go out of a radiator if it is completely full of steam and it's already at temperature so we don't have to take into account the heating of the cast iron. We know a certain volume of steam will fill that radiator. And I can calculate how many BTUs it takes to condensate and cool. Based on that regardless if it is actually cycling the Trap or not and it is really half open or something else. Based on that I can say that there are so many cycles in one hour based on the hourly heat output of the radiator. Although from what I've read it does sound like four Cycles a minute of the Trap internals cycling seems to be in the right ballpark.

And yes I understand this is academic. It's just for fun.