Heat Loss of Cold, Clean water in CPVC pipe (uninsulated) 5

[Tris4K]

Hi All,

I've had a look through the forums and there are 2 similar threads, but both have variables that mean I'm personally unable to apply the answers to my particular problem.

The situation is that I have a pipe that passes from a heated space into a (potentially) unheated space. The problem is that the 'heated' and 'unheated' space temperatures are considerably variable, but for the purposes of this should be assumed to be:

Heated area: 17°C (62.6°F)
Unheated Area: -4°C (24.8°F) or 0°C (32°F)

The pipe length in the heated are is to be assumed to be 15M in length.
The pipe in question is 22.199mm ID, 26.670mm OD (so 2.2355mm wall). Material is CPVC with thermal conductivity (BTU/hr./ft.(squared)/°F/in): 0.95
The water is stagnant, with no additives.
The pipe into the unheated space is a dead-end.

Heat will conduct within the pipe (from heated space, through pipe wall, and through stagnant water)

What i need to know is the length of pipe within the unheated space before the water sill reach <4°C due to heat loss (i.e. the maximum pipe length before i need to consider lagging and/or trace heating to prevent freezing).

Thereafter I need to know to apply the same but with the pipe in the unheated space being insulated with 20mm insulation foil-faced, mineral wool insulation(Rockwool Rocklap: 0.84 kJ/kgK (nom.) at 20°C, and 0.033W/mK @ 10°C). Average air gap between pipe and inside of insulation is 0.165mm.

Rightly or wrongly, I've typically assumed <500mm of uninsulated pipe is acceptable, and <1000mm of insulated pipe (insulation as per spec noted above) before trace heating is needed. this was based on advice from a superior some years ago, but now i'm responsible for the design and implementation of these systems I need to have a better understanding of how this conclusion was reached, and actually if it's even correct.

I'll hold my hands up and say that the formulae and methodology I've found to solve this is beyond my capabilities. So any help anyone could offer to dumb this down to my level would be greatly appreciated.

Thank you in advance, please let me know if you need more information.

 

[LittleInch]

Unless the pipe is vertical up into the unheated space, you will get virtually no heat transfer into the liquid from the heated side.

For a 25mm pipe I would guess about 100mm max from the heated edge.

If there is no flow it matters little how much insulation you have - given sufficient time the water will reach ambient conditions, but may take a little longer if you insulate it.

Why have you got a pipe exposed to the outside air with no flow? Doesn't make any sense.

I suspect your superior was talking about a flowing pipe, but impossible to second guess.

Insulate and trace heat the lot that is outside of your heated area.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[Latexman]

No flow and dead-ended into unheated space?

Why not cut it and cap it in the heated space. It's only 1" CPVC and water. A DIY'er could do it.

Good Luck,
Latexman

 

[Tris4K]

Firstly, thank you for the very quick responses! Much appreciated.

When you say 'virtually no heat transfer" i need more specificity than that, i.e. i need too know exactly how much transfer there will be. There must be some, and some arbitrary tests (involving a length of pipe and a freezer!) show that the water does not freeze even at home freezer temperatures (Circa -18'C) but that would be about 400mm in length.

Avoidance is, of course, the ideal, but the situation is that it is necessary. I should have explained that this is for use in a domestic fire sprinkler system, so the pipe terminates with a sprinkler head.

Think of it like a pipe existing a house, into a conservatory terminating in a bib-tap. These are simply insulated even when installed outdoors and using copper pipe and do not freeze, so i know there will be some heat transfer despite stagnant state, and CPVC will perform better than copper of course.

Actual use case is: The 'unheated' space is an enclosed balcony in a flat within a tower block, technically it is outside the heated envelope of the flat(s), but the anticipated temperature inside the 'balcony' should always be above 4'C (as the outer panel/glazing is always at least double (or triple) glazed UPVC or Aluminium composite with min 100mm insulation in panels, and the 'inner' glazing separating heated/unheated space is typically single glazing (sometimes Georgian wired, but more often simple single glazing) with either timber or steel frame) so i'm sure the indoor temperature in the unheated space will be significantly higher than the outdoor temperature, and closer to the temp of the heated space, however, erring on the side of caution i need to prove it with hard numbers.

I should also state this is not a single instance, and occurs 50+ times in a building, and I will be applying it to around 10,500 flats! hence the requirement for absolute surety.

In my simple brain, as long as the heat transfer is higher than the loss in through the pipe, then it's OK (as water volume and therefore surface area increases, there will be a tipping point of course). I understand this may be quite complex as the temperature of the water will decrease along the length, therefore heat-loss may vary depending on differential between outer and inner temperature (complete guess there as i don't profess to understand much at all about thermal transfer physics and coefficients).

 

[chicopee]

The main mode of heat transfer thru the tubing wall and within the stagnant water that has accumulated in the small diameter of the tubing laid horizontally. There will be also an increase in the internal energy of the tubing and the accumulated stagnant water. So you have two equations that you can apply to the situation that you described. Any segment of vertical tubing that has accumulated stagnant water, the principal mode of heat transfer will be convection even for small diameter tubing.

 

[Tris4K]

Thanks Chicopee.
I’d not considered that heat transfer will differ in vertical versus horizontal but it’s pretty obvious that convection will come into it when vertical.
All the pipe in the above situation is horizontal though.
Are you able to guide me on how to calculate the energy (or heat) losses to get to the position indicated in the original post please?

 

[LittleInch]

what sort of "test" did you do?? PVC is actually quite a good insulator on its own so it might have taken a little while but it would freeze if you left it long enough.

However regardless of this if this is a fire sprinkler supply I'm not sure you really should be trying to cut corners here.

BTW did you mean ten THOUSAND flats?? That's a small town.

The downside of PVC is that it doesn't transmit heat in the same way copper would do so, so is actually worse not better.

Also it sounds like your space is actually being heated by the adjacent heated area.

You cannot state that pipes exposed will not freeze - that is simply not true. Now at around 0C it might take quite a while and if you maintain a flow in the pipe you might stop it freezing, but if left long enough water below 0C will FREEZE. Physical fact of life.

I think what you're trying to do is skimp on a few mm of insulation and trace heating. If the temperature really is -4C for long periods, this won't be able to be calculated. Too many assumptions and coefficients and changes in temperature.

And if you get a freeze plug which stops the sprinkler working and the building burns down, I think the saving of a few mm pales into comparison.

I admire you're trying to get hard numbers, but sometimes you need to understand that hard numbers sometimes just don't exist without so much effort and essentially guessing certain factors that your answer isn't worth the computer screen it is written on.

Just insulate and trace heat the lot.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[danschwind]

I think OP's ultimate goal is to comply with a NFPA 13 requirement to mathematically prove that the portion of the outside pipe will not be below 4ºC at any given time.

Maybe you could try solving this by disregarding the pipe altogether and solving only for the balcony's mean temperature? If it is enclosed, this problem becomes a HVAC problem, where the balcony is surrounded by the outside and inside conditions, with known thermal resistances as boundaries. If you can prove that the balcony's mean temperature is above 4ºC at the worst possible condition (maximum heat transfer possible from the outside and minimum from the inside), then maybe it is enough? It will be your judgement...

 

[Compositepro]

Another option is dry sprinkler heads or piping, which does add to cost. CPVC is very prone to bursting if it freezes. PEX is much more robust against freezing.

The bib valves you mention are dry in the section where freezing is possible.

 

[Tris4K]

@littleinch Thanks for your input, i'll answer each part directly to be concise:
The test was over several days, and was from a pipe fed from a heated area (kitchen). The short section of pipe was around 300mm long IIRC, but i cannot recall if it was insulated in all honesty. This was not conducted by myself, but was reported to me by a highly respected member of the sprinkler community some time ago. So the point was that there MUST be some horizontal heat transfer, although i fully accept the fact the pipe is CPVC harms heat transfer too. I just need to know how to work it out. There has to be a formula out there, and someone that understands how to use it.
To be clear, I'm not trying to cut corners. Quite the opposite! It is 10,500 flats, and its all of the high rise social housing of a large city actually. We believe it's the biggest such project (Retro-Fit) in the world (certainly Europe), hence the need to ensure it's right BUT without unnecessary costs to the end client. 10,500 lots of trace heating and lagging will add £millions! I agree that if it was a single block, or a single dwelling, the cost would not justify it, but we are talking big numbers here, and ultimately someone has to pay for it so it has to be justifiable either way.
You are right, the space is (sort of) heated, but it's so difficult to know what the temperatures will be, so if we start by assuming it will drop to/below 0'C, then that's a starting point. If it's proved that we can use up to 1000mm (for example) of pipe, then we can design the systems to hit this maximum in all circumstances.
Stating pipe did not freeze: I have to say this is possible. The pipe was left for many days, at sub-zero temperatures, and tested (opening valve inside freezer) at increasing intervals. I do not have information as to what intervals, but i believe it was several days in the end. Again, I am not sure of all of the parameters, the point was simply to show that there has to be some horizontal heat transfer within the stagnant water, and that there must be someone out there that can work out how much energy is transferred and lost.
Skimp: is a strong word. As above, we are talking big numbers. To me it does not really matter as i will get paid, and so will my company, but the end client WILL suffer and if it's unnecessary, then i could be open to litigation later due to over-specification and artificially increased costs if i work on assumptions alone.
If the numbers do not exist, then i will have to carry out physical tests myself in a similar method to that which i mentioned before, but with better records, and controlled variables. Calcs are better though!

@danschwind It's not NFPA13 (It's BS9251:2014, which is far inferior to NFPA13R/D in my opinion), however, i believe NFPA13R/D standard is the best Resi standard in the world, and we often use it (as an industry) when our 'less mature' standard here in the UK does not cover it. You are right with the numbers though. We need to maintain 4'C in the pipe. Absolutely agree about proving temperatures, but that would take a lot of time (a year at least to ensure we find the lowest outdoor temp) and we have a lot of variables (internal construction separating enclosed balcony with heated space, and external construction separating balcony from atmosphere). The buildings are not all the same, and even from flat-to-flat within a building internal construction/layout can be different. You have just triggered a thought though! Perhaps we can better control the temperature by simply opening up part of the balcony to he heated space (removal of a door for example!)

@Compositepro We cannot use PEX. restrictions of the UK standard, and also to specify it would suggest we expect it to freeze which is a no-go (if we expect it to freeze, we need to protect it). Technically we could use dry pipe BUT, there are no suitable heads for use in resi systems without having significant consequences on water supply and distribution network which would then be a higher cost than trace heat/lag.

I'm not sure what more info I can add, so it may be a case of taking some sample temperatures in Jan/Feb this year on a particularly cold day/night in the worst construction conditions i can find (good internal construction, and lower grade external) and see what we find. If that's above 4'C then the issue goes away completely. Failing that, it's a case of chopping a freezer up, and simulating sub-zero (technically sub 4'C) conditions and simply measuring different circumstances.

As an aside, i have sprinklers in my home, and i have an uninsulated wet 20mm CPVC pipe (same as suggested in OP), about 2.5 M in length (but vertical, and fed from heated space above) at the front of my garage about 1M away from the single-ply steel door (approx 1.5mm steel) without a door-seal (cold air can get in easily) and that pipe has never burst in 5 years. The garage is not heated and is beside, and under a heated space separated by an insulated floor (above) and a solid brisk wall (no air gap) along it's length, and i'm sure that never drops below 0'C (cannot be sure about 4'C though to be absolutely honest). I've not actually flow tested it during cold spells, I cannot assume it's never frozen just because it's never split. To that end, perhaps i'm under-estimating the potential temperature in the enclosed balconies (i.e. assuming it will go below 4'C when actually it's unlikely).

 

[danschwind]

Tris4K,

Where I live I'm able to obtain some easy-to-find data on temperature, so I think you may be able to gather this data without measuring it (and it would be more representative due to larger inputs).

My suggestion was with the premises that all balconies were identical. Maybe you can work out those thousands of cases into groupings of similar construction? It would be labor-intensive, but at least you would have some analytical/empirical method to calculate the temperature in the balcony.

Apart from that, two other options that may apply:

- Get in contact with some heat transfer professor that will be able to to this analytically.

- Use FEA.

Although I never used FEA for heat transfer, I reckon that this problem while pretty hard to solve by hand may be quite easy to model in a robust FEA software. There are some FEA-gurus here in the forum that will perhaps clarify.

 

[Tris4K]

@Danschwind thank you kindly. I've got absolutely no experience with FEA (had to look up what it meant!), so without third party input that's a no-go. I was already considering a professor or university bod of some sort, just not quite sure how to go about that. I'll contact the 2 local universities to see if i can make any headway.

 

[MintJulep]

The equations are relatively simple and straight-forward. Found in any heat transfer text book.

However, because there is so much uncertainty about every variable and coefficient involved in the calculation the results will be somewhat short of "proof" of anything.

Isolate the relatively few factors that actually control this and design an experiment to derive an empirical model of the system.

 

[georgeverghese]

These calculations will be simplified considerably if you were to assume that heat transfer along the pipe walls is negligible in comparison to the internal and external modes of heat transfer. This is the premise used in most Uni textbook heat transfer mode expressions. Recently there was a query on the internal heat transfer coeff when the internal stream is stagnant. Ask a senior process or mechanical engineer familiar with these calcs to assist if required.

 

[chicopee]

Somehow my sentence"The main mode of heat transfer thru the tubing wall and within the stagnant water that has accumulated in the small diameter of the tubing laid horizontally..." are missing the words "...is conductive"

 

[moon161]

What if you put a slight rise on the stub so that you have a high point at the end? Then you'll get convection going and pulling heat to the end.

 

[LittleInch]

Tris4K,

I do admire the desire to provide some information based on hard technical data.

However your desire to do this falls at the first hurdle which is determination of the required temperature and the conditions in which this pipe is installed.

In the UK we don't get the really long prolonged low temperatures other parts of Europe and the US get, but even then once in while we can get two to three weeks of frozen ground, hard frosts and burst pipes in unheated houses and flats (aka "the beast from the East..."). Currently we're having a pretty mild winter, but global warming could actually result in harder winters if the Gulf stream slows down which is what keeps us warmer than say parts of the US at the same latitude.

So even if this ( a hard sustained frost) is once every 10 years, do you really want to have even one of these exposed lines burst ( maybe the adjacent flat is unheated for some reason) or maybe they leave the outer window open. The impact of one burst pipe on the rest of the block of flats would wipe out any savings you get.

If this was up to me I would say you need to insulate any pipe not inside a heated building. If the pipe is not exposed to wind or other high conduction cold air moving past it then that should be enough without needing to trace heat it.

The latent heat of fusion for water is quite high compared to heat capacity, so temperature would fall to zero quite quickly, but actual freezing can take a long time if you add insulation.

You would probably need to use CFD (Computational Fluid Dynamics) to show how long and for what distance your pipe would remain fluid at different outside temperatures and length from the heated portion. The kitchen experiment you refer to is difficult to use without more scientific rigour and not knowing if the pipe was insulated or not is only the start.

SO in short I think you're looking for a precision which doesn't exist or is really needed.

But good luck and retrofitting of sprinkler systems post Grenfell is a good thing to do.


Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[Tris4K]

LittleInch,

I couldn't agree more! And that is my default position, but I am just mildy nervous about the potential risk. Having done some VERY rough tests recently with a digital thermometer, and i'm seeing a bigger differential between outdoor temp and balcony temp versus balcony/indoor temp, so I am actually now more confident that it's unlikely temperatures will drop below 4'C (yet to be proven though). It's unclear if the differential shifts (as a %) with a lower outdoor temp and i won't know until the temps drop outside.
Going back to my A-Level Physics day, but are you referring to "latent heat capacity". Whilst this is a good point, we have to maintain 4'C (or more) in the pipe.

Thanks for the comments and wishes. Most appreciated. It seems a good-old field test is necessary, but i am at the mercy of mother nature for a cold spell. I have got a temperature data logging system in my possession now, so i'll be deploying that in several locations and just waiting for a cold day to see what happens. Given the time of year it should happen fairly soon. Fingers crossed.

 

[georgeverghese]

In outdoor potable water distribution systems( for safety showers, drinking water), it is a HSE requirement to install a self operated TCV on the supply line to the faucet. This device keeps the supply line cool by bleeding out a trickle flow of water to dispose of accumulated solar heat in the pipe. I forget the name used for these TCV devices (usually fitted on DN20mm lines). Could this same device, modified suitalby, act as an antifreeze valve in this safety sprinkler application? Could we ask the supplier?

 

[Tris4K]

Thanks George, but that's not an option we can use as it will cause the pumps to run too often, which will (in turn) cause a fault on the monitoring system due to continual (or regular) loss of pressure. It also introduces requirement for drainage, and cost of parts, so we'd probably be at similar cost to trace heating in the end in any case.