Expansion vessel asettings and calculations

[chris w]

A few days ago, I posted the maths for the accumulator and showed that the optimim setting for the device was a couple of psi BELOW the pump's cut-in pressure.

 

I have now turned to looking at the expansion vessel (EV) both from a theoretical maths point of view and from a practical point of view.

 

I have now installed 2 pressure gauges, one on the cold pipe immediately after the pump and one on the hot feed just before the galley hot tap. Since the pump is under the galley sink, it means both gauges sit neatly side-by-side under the sink so that both can be observed simultaneously.

 

The gauges are marked off in 0.2 bar intervals. To be fair, I do not know their accuracy. However, I have measured the cold water cut-off pressure with a digital tyre gauge which gave 27.5psi (1.87 bar) and the installed gauge which read 1.9bar (27.9psi). So, although not an absolutely definitive test, it would appear, prima facie, that the gauges are very accurate.

 

I first measured the temperature of the cold water in the calorifier (having not been heated for several days) and it was 7 degC. I then switched on the Webasto and watched and waited whilst the temperature climbed and the pressure in the expansion vessel rose. I set the expansion vessel at 30 psig ie: just a couple of psi above the pump's cut-out pressure. I will explain why I set it at this pressure later when I show the maths. I have a non-return valve (NRV) between the calorifier and the water pump so the hot and cold systems are entirely isolated from one another.

 

The Webasto allows the water (in the Webasto) to reach 72degC before switching off and then allows the water to cool to 62degC before switching back on again. Therefore the average temperature of the water will be around 67degC. I switched off the radiators so that only the calorifier was being heated and after 3 hours the pressure rose no more in the EV. I then assumed the water in the calorifier and that in the Webasto had reached equilibrium.

 

The pressure on the hot gauge (and the cold gauge) showed 1.9 bar at the start. After 3 hours of heating the hot gauge had risen to 2.4 bar. (The cold gauge still showed 1.9 bar as expected).

 

Now I applied Boyle's Law and converted the gauge pressures (barg) to absolute pressures (bara) by adding 1 bar to them. My EV is 8 litres in size.

 

So, by Boyles Law P1V1 = P2V2

 

thus 2.9 x 8 = 3.4 x V2

 

Therefore V2 = 6.8 litres

 

But this is the volume of the AIR in the EV. The volume of the WATER in the EV (which was previously zero) is now 8 - 6.8 = 1.2 litres.

 

This is the amount by which the water has expanded due to heating and was a lot less than the percentages we were considering a couple of weeks ago in another post. I have a 60 litre calorifier so 1.2 litres expansion represents an expansion of 2%. This was half of the 4% figure we were using in the previous post (although we were considering 0degC to 100degC in that case).

 

So I googled for some density figures for water and came up with the following for the temperatures under consideration.

 

Density of water at 7degC in gm/ml = 0.999901

Density of water at 67degC in gm/ml = 0.979617

 

Thus, the density decrease over this temperature range is 0.020284 gm/ml, or virtually exactly a 2% decrease in density. Since the weight of the water in the system didn't change, this corresponds to a 2% increase in volume. Voilà...... exactly what I witnessed on the gauges.!

 

If I heat the water via the engine, it should get up to around 85degC when the engine is under load. The density at 85degC from tables is 0.969080 gm/ml. This represents a 3% change exactly in density (and therefore volume) from water at 7degC. The actual volume of water by expansion is 3% of 60 litres = 1.8 litres.

 

If we now plug that into our Boyle's Law equation, we can predict the worst case EV pressure (other than under fault conditions!).

 

Ergo, 2.9 x 8 = (8 - 1.8) x P2

 

therefore, P2 = 3.74 bara = 2.74 barg = 40.3 psig

 

Even at 85degC the pressure is still below the normal Pressure Release Valve (PRV) trip pressure of 42 psig and thus no water will leak from the PRV, the EV's having absorbed all the expansion. This shows that the EV is large enough and set at the correct pressure to do its job over the whole range of expected temperatures and pressures.

 

I then considered what would have happened had I set the EV pre-charge pressure BELOW the pump's cut-off pressure. In that case, the water pump would be able to pump an amount of water into the EV before its internal pressure was equal to the pump's cut-out pressure. let's look at a numerical example.....

 

Suppose we set the EV to 15psig (1 barg or 2 bara).

 

Applying Boyle's Law to the water pump expansion stage we get:

 

2.0 x 8/ 2.9 = 5.5 litres of AIR (ie: a decrease of 2.5 litres) due to the water pump's compressing the EV's air bag.

 

If we now allow a 3% expansion due to heating, ie: an additional 1.8 litres increase in water, from the density tables) leading to a 1.8 litre decrease in AIR in the EV, we get:

 

2.9 x 5.5/(5.5 - 1.8) = 4.3 bara = 3.3 barg = 49 psig.

 

This will cause the PRV to blow because PRV's are typically set at 42 psig (3 bar) and totally negates the effectiveness of the EV.

 

 

I then worked on the maths to come up with a general formula for any size EV, any pump pressure, any volume of expanded water and any PRV setting.

 

To prevent suicides, I won't set out the whole working, but am very happy to post it if anyone wants to see it.

 

Here then is the formula I derived..................

 

To prevent the PRV from blowing, the pre-charge pressure Ppc must be greater than:

 

Ppc > (Ew x Pco x Prv) / (V1 x (Prv - Pco))

 

where:

 

Ppc = the pre-charge pressure

Ew = water expansion in litres

Pco = the water pump cut-off pressure

Prv = the pressure release valve pressure blow point

 

Note that all pressures must be converted to absolute pressures by adding 1 bar to them to allow Boyle's Law to hold.

 

For the 1.8 expansion litres above and using the same EV (8 litres) and the same pump (1.9 barg) and the same PRV (3 barg), we can calculate that

 

Ppc > (1.8 x 2.9 x 4)/(8 x (4 - 2.9)) > 2.37 bara > 1.37 barg > 20 psig

 

Thus if we set the EV a couple of psi ABOVE the pump's cut-off pressure, no EV volume is wasted by the pump's being able to push water into the EV before the heating cycle starts. This setting will give the most effective use of the EV's volume.

 

If we assume, for the sake of slightly easier maths, that we set the EV at the same pressure as the pump cut-out, we can then solve for Ew (the water expansion). This will give us the maximum water expansion with which we can cope before the PRV blows and, from density tables, the temperature at which this will happen.

 

So setting Ppc = Pco and solving for Ew gives Ew(max) = 2.2 litres. This represents a 3.7% expansion percentage for a 60 litre calorifier which would occur at a temperature of around 94degC (from density tables) and assuming a 7degC starting point.

 

Of course, in warmer months, the temperature difference between cold and hot will not be as great and so the expansion of water will be less. But these calculations give closer to worst case conditions and so are very useful (IMHO).

 

Bottom line........ set the EV pressure to just above the pump's cut-off pressure.

 

Chris

PS: the density tables for water from 0degC to 100degC may be found here

Edited November 26, 2008 by chris w

[RLWP]

.........

 

I have now installed 2 pressure gauges, one on the cold pipe immediately after the pump and one on the hot feed just before the galley hot tap. Since the pump is under the galley sink, it means both gauges sit neatly side-by-side under the sink so that both can be observed simultaneously

 

.........

Chris

 

(Imagines Chris sat in cupboard under the sink with torch, pencil and clipboard)

 

Richard

[chris w]

(Imagines Chris sat in cupboard under the sink with torch, pencil and clipboard)

 

Richard

Got it exactly......

 

At least it was getting warmer on the boat as the experiment progressed!!

Edited November 26, 2008 by chris w

[RLWP]

Got it exactly......

 

At least it was getting warmer on the boat as the experiment progressed!!

 

Have you got a white lab coat with lots of pens in the top pocket?

 

Richard

 

Rule of thumb - set you EV pressure to about the cut-out pressure on the label on the pump?

[chris w]

Have you got a white lab coat with lots of pens in the top pocket?

 

Richard

 

Rule of thumb - set you EV pressure to about the cut-out pressure on the label on the pump?

Yes that'll do it. I actually advocate a couple of psi higher than that to ensure absolutely that no volume is wasted by the pump's cut-out pressure pushing some water into the EV.

 

Chris

[alan_fincher]

Oh don't!

 

In course of doing the plumbing I've been doing, I needed to pass some pipes though a very compact hanging wardrobe between engine room and bedroom.

 

My cupboard has only a small door well above bed height, and I needed to drill holes and attach things low down, but couldn't reach. Stupidly I thought if I got in there I might be able to get to the problem area, (I think my brain had stopped working at this point!)

 

To cut a long story short, I had something to climb on to get in, but having forced my bulk through a small aperture, then had nothing to climb on to get out again.

 

I didn't go into blind panic, and was too embarrassed to try summoning help, but spent what seemed like an age, (but was probably only about 15 minutes), trying to plan my escape. I did get out, but it was a near thing. Cath was due up in about 3 hours, but I don't think I'd have cared to be there that long.

 

Needless to say, once in there, it was so tight that I had no chance of getting to what I wanted. And a bit of thought would have told me that before I blundered in!

[Nickhlx]

Imagines someone finding a clothed skelton hanging in a cupboard several months later....

 

The dangers of working alone !

 

Nick

[Bullfrog]

Imagines someone finding a clothed skelton hanging in a cupboard several months later....

 

Bones is working on this on another thread!

 

David

[smileypete]

Interesting stuff, how much pressure/volume would the 8 litre EV need to lose before the PRV operates?

 

cheers,

Pete.

[chris w]

Interesting stuff, how much pressure/volume would the 8 litre EV need to lose before the PRV operates?

 

cheers,

Pete.

That's easy to answer because it's just a question of rearranging my formula to make V1 the subject. The question the answer also gives is "given the data in my example, what is the minimum size of EV in order for the PRV not to blow."

 

So:, since Ppc > (Ew x Pco x Prv) / (V1 x (Prv - Pco))

 

where:

 

Ppc = the pre-charge pressure

Ew = water expansion in litres

Pco = the water pump cut-off pressure

Prv = the pressure release valve pressure blow point

 

(Note that all pressures must be converted to absolute pressures by adding 1 bar to them to allow Boyle's Law to hold.)

 

then V1 > (Ew x Pco x Prv) / (Ppc x (Prv - Pco))

 

using Ew = 1.8 litres (ie: water heated to engine temp of 85degC

Ppc = 1.9 barg

Pco =1.9 barg

Prv = 3 barg

 

then V1 > 6.6 litres showing that an 8 litre EV ( a standard available size) is perfect for this role on a 60 litre calorifier.

 

Chris

[Gibbo]

then V1 > 6.6 litres showing that an 8 litre EV ( a standard available size) is perfect for this role on a 60 litre calorifier.

 

That ties in with what I was told. I need 13 litres of EV for my 2 X 60 litre calorifiers. But the nearest size won't physically fit in the available so I've got 2 X 8 litres. Next week's project.

 

Gibbo

[chris w]

Having now done the "Special Relativity" bit (separate EV and accumulator isloated by an NRV, I will undertake "General Relativity" by attempting to explain mathematically what happens if one just has an accumulator and no NRV and tries to use it for both functions.

 

I'm off back into the cosmos........