Tank Ice Pressure Calculation 3

[WorcesterSorcerer]

Hi,

We have a large stainless steel storm tank (32m diameter but very shallow , 1m deep) that will be filled with water. We have calculated the hydro static pressue ok, but would like to calculate for the increased radial pressure if a thick layer of ice forms and expands .

Does anyone know of a factor or similar that we can apply to the hydrostatic pressure? A reference to a Eurocode or similar would be great too - thanks.

 

[LittleInch]

The factor is enormous, to the extent that your tank will simply break if you try to contain a single layer of ice. Usually it starts forming from the outside so if the level goes up and down you might be ok, but if its static then you need to find someway to prevent it.

You need to ensure that a single layer of ice cannot form and the expansion of the water into ice has somewhere to go, usually a small circular hole or two where you have a heating tube.

Or line the edge of the tank with something flexible to absorb the movement.

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[WorcesterSorcerer]

@LittleInch, thank you. Given it is an open top tank, I think your reccomendation of adding something flexible to the lip of the tank makes most sense. We could be chasing our tails otherwise.
Cheers.

 

[LittleInch]

Or you could have a gently sloping edge such that the expansion is then vertical or moves up and breaks?

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

 

[WorcesterSorcerer]

Thanks, we can look at that too. Out of interest, what order of magnitude are the factors that you would apply for ice expansion pressure?

 

[dold]

Out of interest, what order of magnitude are the factors that you would apply for ice expansion pressure?

Ice pressures are massive. I don't know much about ice in the simple "just freezing water in a tank" sense, but studies on frost heave in soils popped into my mind when I saw this post.

This paper indicates pressures from 25psi up to around 100psi. In the buildings world, one does not simply fight the pressure. The structure/soil must be protected from the phenomenon ever happening in the first place.

[URL unfurl="true"]https://onlinepubs.trb.org/Onlinepubs/hrr/1965/101/101-003.pdf[/url]

User CarlB has a bunch of good links in here too.

[URL unfurl="true"]https://www.eng-tips.com/viewthread.cfm?qid=43495[/url]

 

[dvd]

Interesting topic to ponder. I like the idea of a flared wall which might let expansion move upward instead of outward. Also asking myself when a 32 meter disk would buckle instead of expanding outward. The round tank would hopefully lend itself to hoop stresses for outward expansion, but wouldn't be too happy with shrinkage. Also curious about the phenomenon of the ice attaching itself to the stainless steel wall (is it stainless due to saline or other impurity of the water?). The attached paper has some information and it looks like there has been a lot of research conducted in this area.

 

[Geoff13]

Overly simplistic thought process

A typical stainless steel (say 316) has a yield of about 30 ksi. Converting this to strain S/E = 30ksi/30,000ksi gives 0.001 in/in, or 0.1%. However that's a circumferential strain limit, so we should convert to a radial growth limit, which would be 0.1%/2pi = 0.015%. Presuming we don't want to yield the shell perhaps limit this to 0.01% radial growth. My Googling suggest ice has a density of 0.92, and thus grows 8% in volume as it freezes, so about (1/0.92)^0.33 or 2.8% in each direction. Ice pressure must be prevented rather than resisted.
​

I expect in a large diameter tank like yours there would be some ice buckling like dvd suggested, but how much? Certainly a "thick" ice sheet would be needed to prevent this buckling so if where your tank is located isn't below freezing for extended periods perhaps a thick enough sheet can't form?

A sloped wall is interesting but my expectation would be that the initial ice would bond to the steel and not slide up later to relieve the pressure. This is an expectation, not knowledge.

A flexible protector is interesting, but no clue how to do this. Water can't get into or behind as that will freeze and defeat the purpose. It can't degrade due to continuous water, sun, temperature cycles, exposure, and that's difficult.

You've got an interesting problem. Good luck.
Geoff

 

[3DDave]

There are YouTube videos of attempts to contain ice expansion in very thick walled tubes. All the tubes ruptured.

https://www.youtube.com/watch?v=t5mdZD00POs

for example.

The engineering part is at this timestamp:

https://youtu.be/t5mdZD00POs?t=345

Practically, the force available is equal to the resistance available, so the limit is on the strain, which, but the numbers above is 2.8%.

Aeration is used around boats to keep them from getting crushed when ice forms around them at dock.

Slopes need to be extremely slick to avoid ice simply sticking to them, though if the walls are a 45 degree cone it may cause the ice to buckle upwards enough to avoid breaking the tank.

 

[BridgeSmith]

This paper indicates pressures from 25psi up to around 100psi.

Just from my observance/experience with frozen water pipes, I'm thinking that might be way low. What's the burst strength of a galvanized steel water line? Those pop like a soda can when they freeze.

 

[EngDM]

Hypothetically speaking if your only option was to reinforce the tank, you'd have to look at the phase diagram for water and determine the pressure you'd need to be able to withstand for whatever lowest temperature the tank would be experiencing. If you could pressurize the tank this would be easier to determine since you could pressurize above the freeze-melt curve, but since you're probably just at atmospheric pressure to start, you'd need to somehow design the wall to accomodate ice expansion such that the pressure in the remaining liquid water then exceeds the freezing melting curve at that point such that no more liquid water can phase change. Then you'd have to make sure that there is little to no deformation in the tank so that the pressure isn't released and more ice is allowed to form. Not to mention the seals would need to be designed for this pressure, and some sort of system to be able to open the tank without it just exploding due to coming down to atmospheric and letting the remaining water turn to ice.

I don't even know where you would begin to actually analyze this.

 

[WorcesterSorcerer]

Thanks for all the comments and suggestions everyone. We've since been able to confirm with the user that the tank will not be full for long enough, for it to freeze completely. I agree that it is ikely the 32m span of ice would buckle/crack during forming before it can exert a damaging force on the tank walls. However, all comments have been very useful as I'm sure we'll have a similar scenario to assess in future where a tank's content can indeed freeze completely. Given we're in England, its not a common challenge. I would however be interested to understand how such challenges are dealt with by others in locations such as Canada, where the winters are long and very very cold!

Thanks all.

 

[JStephen]

You have a POTENTIAL problem. Whether it's an actual problem, I'm not so sure about.
In the past, in water tank seminars, the problems of ice in tanks has been discussed at some length. One problem is that a big slug of ice in a tank will move up and down with the water level, but will hang on internal ladders, etc., and pull them loose. One problem is that ice can freeze asymmetrically in a tank, causing a large moment if the water is drained from around it (which can collapse an elevated tank). Of course, loss of function is a problem. But what has NOT come up in those seminars was the topic of tanks splitting down the middle due to ice pressure.
I think the issue is that the sequence of freezing is different than being assumed above. The ice freezes from top down or outside in or whatever, but doesn't instantly all freeze at once. So just calculating radial growth assuming a solid block of water turns to a solid block of ice doesn't represent what actually goes on.
Example: Ice cube trays. The cubes don't pop out as they freeze, even through the sides are tapered. Nor do they split the ice cube trays open.
But, that said, I do not have a definitive answer for how much pressure should be designed for.

 

[LittleInch]

This is a bit different to a water tank as I'm assuming the water is just at a fixed level. Water tanks tend to go up and down or if fixed have a regular flow of water circulating

Having said that 32m is a big distance and getting a completely flat ice sheet which wouldn't itself break or buckle is looking low possibility. But even a little bit of pressure on an atmospheric tank will break it as they tend to be designed to very thin thicknesses at the top.

Ice cubes tend to grow upwards as they freeze and are often sloped to create this. Plus the trays are PE and they flex before breaking.

The ice in the tanks seems to grow from the outer edge into the centre. So if you can create a small warm spot with a little water heater that's all you need. Floating heaters are very common on fish ponds and the like. A flexible say 8" pipe filled with air all the way round the outside might be enough as well to absorb any movement.



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

 

[1503-44]

I don't see where anyone has actually mentioned the bulk modulus of ice.

The bulk modulus of water ice ranges from 11.3 GPa at 0 K up to 8.6 GPa at 273 K.

1 GPa is 145 Ksi 8.6 GPA = 1.25 MegaPSI
Water expands [in volume] by 10% when frozen. A rather large strain to accommodate.

I have no experience of a disk of ice buckling, but it probably generates considerable pressure before it does. Counting on it to buckle at a pressure low enough to save your tank is probably difficult to guarantee.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

 

[dvd]

I believe that the 10% expansion cited by 1503-44 is a volumetric expansion. The discussion below addrresses linear expansion.

A typical stainless steel (say 316) has a yield of about 30 ksi. Converting this to strain S/E = 30ksi/30,000ksi gives 0.001 in/in, or 0.1%. However that's a circumferential strain limit, so we should convert to a radial growth limit, which would be 0.1%/2pi = 0.015%. Presuming we don't want to yield the shell perhaps limit this to 0.01% radial growth. My Googling suggest ice has a density of 0.92, and thus grows 8% in volume as it freezes, so about (1/0.92)^0.33 or 2.8% in each direction. Ice pressure must be prevented rather than resisted.

 

[ThomasH]

I was involved in a project with water frezing a few years ago. A number I remember is that when water is confined and starts to expand (freeze) there is a pressure of more than 1000 MPa. Or, you create room for the expansion .