Hotwater tank theoretical energy

bluffit

The layering effect in a hot water tank intersts me.



If a thermostat is half way up the tank, and the maximum temperature in the tank is 100deg C, I'm assuming it would be possible to calculate the maximum theoretical energy able to be stored.



Other interesting questions arise.  If the thermostat reads x degs, what are the varying layers of heat in the tank i.e.  we will have x + n and x -n where n is the difference in temperature between layers at the extreme.   If a tank is layered evenly, and the thermostat is in the middle, then x would average out to itself, but if I want to calculate the temperature in the top 1/3 of the tank, what would be the maths?



Welcome your thoughts.

meplumber

Wow.

Way over my head.  But I will try and offer some information.

The stratification of domestic hot water tanks, or any water storage tank for that matter, varies with tank design.  Tanks with bottom coils layer differently than dual coils and tank-within-a-tank designs.  There are also large (800 gal +) insulated atmospheric tanks that are used with solid fuel and combination systems.  These layer in a completely different way.



From my perspective, as a lowly basement dweller, I just know how the tanks perform.  I don't have any charts to fall back on.  I know that by running a 79 gal Viessmann 300 tank at 140 degrees.  I get about 100 gal equivolent of domestic hot water to the house through a 120 degree mixing valve.  I know that TT tanks run hot in the top layers.  So 140 on the aquastat can be more like 155 out.



I am interested to see what you can calculate.



Good Luck

Mark Eatherton

As with any hydronic/water related question, the only correct answer is...

It DEPENDS!



Some storage tanks (tall, skinny) are more conducive to stratification that others, but as it pertains to potential energy, a BTU is a BTU, and it affects water the same way. It raises one pound one degree F.



If you had a circulation pump on the system, the tank would be kept in a homogenous mix, and stratification would be minimal. When the pump is turned off, the stacking potential kicks in, but is dependent upon the tanks geometry to become stratified.



Regardless, the IPC requires an anti-scald mixing device at the outlet of the tank to avoid end users getting scalded, and has done so since clear back in the year 2000, which is as far back as I could find in my local library...



Obviously, you are not in the US, but water is water and your code may be different, but you'd still be wise to reduce your liability by employing known means of scald protection.



ME

Larry Weingarten

assumptions

Hello:  I'm not sure you can assume layering is even.  Researchers use a "thermocouple tree" to determine temps vertically in a tank, but are finding now that horizontally things change too.



I imagine one way to accurately measure the energy stored in a tank would be to fill an unpressurized tank completely and run a tube from the top of the tank to a container to catch and measure the volume of thermal expansion.  Someone smarter than me could then calculate how much the tank volume had to heat to produce that much expansion.  It would be a way to account for the mixing or lack of in the tank.



Knowing what temperature you need the hot water to be would help in designing a strategy to store those BTUs.  Mixing the tank will likely give you greatest BTU capacity.  Keeping the bulk of the water at a lower temperature with a booster in line could yield lower tank heat loss along with the possibility of heat recovery or solar as a pre-heater... but then I may be designing the wrong system :~)



Yours,  Larry

jp_2

you answered it!

if you assume the manufacturer understands the different temps in a tank and determines the middle is the best place for the tstat, then the 100C is the value you use.

bluffit

Tank stratification calculations continued

Thanks for your replies.



I'm not sure I'm getting anywhere though.



Firstly, the hot water tanks in question are for central heating - they are low pressure, non-potable tanks and therefore anti scalding regulation does not apply.  In fact in terms of efficiency, I want to store the maximum possible heat in each tank.



Secondly, they range in diameter and height so it sounds like I need  a formula that takes this into account.



Finally, my main interest is in the ability to calculate the stratification as a function of the thermostat height.  In some tanks, the thermostat is at 50%, in others it is at the bottom.



I will be replacing the thermostats with PT100 sensors, so will want to calibrate each of the tanks such that I can estimate the temperature in say the top 33% of each tank.



Although there will be some circulation, we could assume for the purposes of the exercise there is zero.



Thanks again.

jp_2

Storing Heat??

that's kind of a odd comment?



 soon as the heating source is off, the tanks will start loosing heat, the higher the temp at the top, the faster that heats going to leave.



your only solution is to do test measurements.  measure the top of the tank, and sides at the top.   then measure down the side to the tstat.   I'd guess a linear equation will be accurate enough though its probably non linear in nature.



really do not think you will find an equation for this.  will have to make your own.

bluffit

Are you sure there's no equation?

Thanks, but measuring the tank at different spots is not practical. The tanks are well insulated and inaccessible, and I don't have sensitive enough equipment.



But given Height (H); Diameter (D); the height of the thermostat (h), and temperature (t) at h it should be possible to get a general equation to give tp i.e. the temperature at a given percentile (p) of the tank.



Is there not something of the form:



tp = .... 



Surely two cylinders of the same dimensions should behave the same, and should be able to be modelled?



Thanks

meplumber

I think that is what we are all getting at.

Because all of these tank manufacturers design the interior flow differently, they all stratify different.  Look at the manufacturer websites for Amtrol, Heat Transfer Products, Triangle Tube, Viessmann and you will see how different they all are.



You could possibly contact the manufacturers and they might head you in the direction of there specific equation, but I think you would find that each has their own equation.

bluffit

Thanks but ...

All my tanks are simple generic copper cylinders ....

jp_2

how good are you at differential equations?

I'm sure what you ask for is out there in some form.



look here:



http://en.wikipedia.org/wiki/Convection%E2%80%93diffusion_equation



for one, you would need to know the highest possible surface temp of the heat exchanger.  so then you could determine rates of velocity of convection currents.



seems to me there would be many variables here, differential water temps,  volume, insulation, air temps, pressure, height to wide ratios, distance from heat exchanger to tstat and top of tank.......



you could also do a host of experiments to determine convection velocities, horizontal heat transfer in water vs temp differentails, and determine vertical temp differentials.

bluffit

Very good.

Thanks for this! 



Just for the record, the tanks are not heat transfer systems per se, just simple hot water stores. Also, they are kept at atmospheric pressure.  Hopefully this will simply the maths.