[Cooling System Upgrade] 1-BAR Radiator Cap

Originally Posted by WDE46

I trust my math more than the intuition here. The math says that the system shouldn't experience any more than about 1.4 bar absolute pressure. That means the ET will experience a 0.4 bar maximum of pressure exerted on its inner surface. That is 1.6 bar below the cap's crack pressure. This never approaches 10-12 psi. Unless we are severely miscalculating something, I don't see why we have the 2 bar caps.

The only thing we haven't taken into account with the pressure calculation is water vapor in the ET air and the coolant expansion. The water expands by 3.8% (about 1/3 of a quart) when heated from 20C to 100C, so that could conceivably almost fill the ET depending on its size. It could be a very major factor. I need its dimensions, specifically air volume at min and max. We could find this, by topping off the ET with distilled water, then removing it into a measuring device until the max level, take a reading, then continue to the min. That is the easiest and most accurate way. If it so happens that the air volume is cut in half by the expansion of water, then we will find the system actually runs at around 2 bar. If this is the case, then I would recommend not filling the ET to maximum to reduce system pressure and extend ET life.

The most complex part of all this is the mixtures that are present. We have 50/50 water and antifreeze for our fluid mixture and a mix of water vapor/air/antifreeze vapor in the ET buffer volume.

The amount of water vapor in the expansion tank (hence the system) will not be more than 4% (even 100% humidity). It is negligible.

Originally Posted by TerraPhantm

Well... Assuming you start at 20ºC and end up at 95ºC the final volume would have to be ~42% of the starting volume to reach 3 bar. So if the coolant expanding by about 300mL causes the system to reach that point, that would mean the air space when cold is about 515mL. Which I suppose sounds reasonable enough.

So assuming the system is capable of reaching 3 bar - the question would now be why BMW wants such high pressures. Maybe it's due to a potential for cavitation, maybe it's due to a possibility of boiling coolant at localized hot spots. Or maybe it's something I can't think of.

But assuming any of those risks are legitimate, a better solution might be to use a lower temperature thermostat in conjunction with a 1-bar or 1.4 bar cap. From what I've read, the higher operating temperatures were chosen for emissions purposes.

What is the total coolant fill up to the min level for a well bled system? If we knew this, we could calculate the expansion of the coolant using 3.8% expansion rule much more accurately.

Not saying your numbers are not reasonable, but biasing the results to initial values doesn't seem too justifiable to me. We should be able to express things as state functions, meaning depending on the properties of the system at a given instant.

As a Chemical Engineer, there is so much misinformation in this thread I don't know where to start.

Tomorrow when I'm sober I'll poke through it.

edit: oh, looks like there's some smart people near the end, maybe I don't need to do much work.

I sorta trust the engineers at BMW. they seem to know what theyre doing. but anyways....sub'd

Originally Posted by SeanC

The amount of water vapor in the expansion tank (hence the system) will not be more than 4% (even 100% humidity). It is negligible.






What is the total coolant fill up to the min level for a well bled system? If we knew this, we could calculate the expansion of the coolant using 3.8% expansion rule much more accurately.

Not saying your numbers are not reasonable, but biasing the results to initial values doesn't seem too justifiable to me. We should be able to express things as state functions, meaning depending on the properties of the system at a given instant.

Him assuming initial values is the best way to do this kind of thing. We're just trying for a sanity check of the system's pressure. If the volume of air in the ET changes by 30-50% when heated, then we know the system actually does operate at a fairly high pressure. That's all I really want to know. Then the cap is justified, but we still don't know why they made the system higher pressure.

Originally Posted by WDE46

Him assuming initial values is the best way to do this kind of thing.

EDIT: I was wrong. You need to assume an initial and final temperature to calculate the expansion (see my calculation below). However, in order to calculate the pressure, the system we are dealing with is simple enough that everything can be expressed with state functions. Just to recap:

1. Only the knowledge of temperature of the coolant is needed to know the pressure.

2. Amount of water vapor in the ET is negligible in the calculation of the pressure.

3. Since fluids are incompressible, it follows that the gas pressure of the air in the ET is also the overall pressure in the system.

4. In order to calculate the expansion of the coolant in the ET accurately, we need to know the cold fill level, which should be very easy to find out.

[EDIT]: Apparently we also need to know some sort of an expansion coefficient, as well as a temperature change (I was wrong in assuming this being a state function. Pressure is, but expansion requires initial and final temperatures. The latter also requires the fill level though, which I will assume to be between 8 and 11 liters. You can do the extrapolation).

Now water has an expansion coefficient of 0.000214, and etylene glycol has 0.00057.. Since these two form a homogenous mixture, for a 50-50 mixture, the expansion coefficient will be average of the two: 0.000392.

Assuming a fill level of 8 liters, the maximum expansion will be 235 mL between 20-95 degrees. For a fill level of 11 liters, the expansion will be around 325 mL. Not too far from Terra's numbers.

I don't know how this will drive the pressure to near 3 bars provided the system is not filled above the max fill level [/EDIT].



My feeling is that system will NEVER operate near the 3 bar maximum pressure even after the expansion is taken into account provided the system is filled between min and max levels.

Originally Posted by SeanC

My feeling is that system will NEVER operate near the 3 bar maximum pressure even after the expansion is taken into account provided the system is filled between min and max levels.

I will go against your feeling with my feeling. I will try getting around to proving it at some point.

Just as a clarification, what variables are you using to figure out this maximum pressure?

Originally Posted by mkodama

I will go against your feeling with my feeling. I will try getting around to proving it at some point.

Great, looks like people in the community has too much "street" knowledge, but when it comes down to actually calculating numbers, there is only WDE46, Terra and myself who are doing the work. I will look forward to your proof.

Originally Posted by mkodama

Just as a clarification, what variables are you using to figure out this maximum pressure?

In my calculation of the pressure (without taking into account expansion), I used ideal gas law (PV=nRT), along with the knowledge of maximum operating temperature of 96 degrees Celcius. This gives a pressure of 1.3614 bars as the operating pressure (i.e. 0.3614 cap should suffice). For details and justification, read my posts above.

Now that we have an interval for the expansion (235-325 mL, we still don't know the absolute fill, hence we don't know the absolute expansion), we can start thinking about how this will effect the pressure that was calculated to be 1.3614 bars without taking into account the expansion. I still don't think it will effect it much, unless you're a clueless BMW owner (as most are), and top off your coolant as you would do on a domestic car.

So at this point, it seems to me that BMW is trying to minimize a possible premature ET failure by using a 2 bar cap. However, that's a good reason only for those clueless owners who tend to top things off, and I fail to see the advantages for the rest of us.

Originally Posted by SeanC

Assuming a fill level of 8 liters, the maximum expansion will be 235 mL between 20-95 degrees. For a fill level of 11 liters, the expansion will be around 325 mL. Not too far from Terra's numbers.

Glad you are starting to consider expansion of liquid in the system as it heats. That is why there is an expansion tank. System contains "about" 8.4 liters of liquid. The remaining unknown is the volume of air in the expansion tank.

Originally Posted by dknightd

Glad you are starting to consider expansion of liquid in the system as it heats. That is why there is an expansion tank. System contains "about" 8.4 liters of liquid. The remaining unknown is the volume of air in the expansion tank.

That is not too difficult to guesstimate. If expansion lowers the volume by a factor of 2 (for example, assume .5 mL initial empty space, for 8.4 liters of fill level, the expansion will be about .25mL), at constant maximum operating temperature of 96 degrees Celcius, this relation will apply: P1/V1 = P2/V2. Pressure will be doubled to 2.72 bars... Hah, that justifies the use of a 2-bar cap lol!

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Originally Posted by SeanC

That is not too difficult to guesstimate. If expansion lowers the volume by a factor of 2 (for example, assume .5 mL initial empty space, for 8.4 liters of fill level, the expansion will be about .25mL), at constant maximum operating temperature of 96 degrees Celcius, this relation will apply: P1/V1 = P2/V2. Pressure will be doubled to 2.72 bars... Hah, that justifies the use of a 2-bar cap lol!

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But to those of us who dont just top it off, a 1 bar cap would be fine

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fvck... i may be going off topic a little but its urgent..

is putting too much coolant in the tank bad?

Originally Posted by tehcbass

fvck... i may be going off topic a little but its urgent..

is putting too much coolant in the tank bad?

Yes, you may not allow enough expansion space for the coolant. ET will blow.

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Originally Posted by sedanpowersc

But to those of us who dont just top it off, a 1 bar cap would be fine

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Apparently not. You need a really low fill (quite possibly even lower than the minimum level) not to risk anything with a 1-bar cap.

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Originally Posted by SeanC

Apparently not. You need a really low fill (quite possibly even lower than the minimum level) not to risk anything with a 1-bar cap.

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I don't understand why running a 1 bar cap would be a risk at normal coolant levels (asides for possible cavitation or boiling at localized hot spots... Which is a risk at any level). When the coolant expands, the air would just vent once the pressure started to go beyond 2 bar

Originally Posted by SeanC

at constant maximum operating temperature of 96 degrees Celcius, this relation will apply: P1/V1 = P2/V2. Pressure will be doubled to 2.72 bars... Hah, that justifies the use of a 2-bar cap lol!

Sent from my SGH-I997 using Bimmer App

Why do you assume a maximum operating temperature of 96 degrees Celsius?
That would be the ideal. Thermostat should be fully open by then. 96 in the block, less than that (on average) in the radiator. But if you are beating on the car in a hot climate it is very possible that the thermostat is always open, then the average temperature could exceed 96. If the average temp was 96 deg C then you would not need a pressurized system at sea level. I assume BMW designed a system that would work on any road, at any elevation, and any likely ambient temperature. But that type of system may not be ideal for some of us.

Originally Posted by tehcbass

fvck... i may be going off topic a little but its urgent..

is putting too much coolant in the tank bad?

YES - never overfill. Always keep between min and max

Originally Posted by TerraPhantm

I don't understand why running a 1 bar cap would be a risk at normal coolant levels (asides for possible cavitation or boiling at localized hot spots... Which is a risk at any level). When the coolant expands, the air would just vent once the pressure started to go beyond 2 bar

While not being 100% sure, maybe a system constantly venting is not a healthy one. Think about the venting system being stuck open or in the worse but less likely case, stuck closed.

Originally Posted by dknightd

Why do you assume a maximum operating temperature of 96 degrees Celsius?
That would be the ideal. Thermostat should be fully open by then. 96 in the block, less than that (on average) in the radiator. But if you are beating on the car in a hot climate it is very possible that the thermostat is always open, then the average temperature could exceed 96. If the average temp was 96 deg C then you would not need a pressurized system at sea level. I assume BMW designed a system that would work on any road, at any elevation, and any likely ambient temperature. But that type of system may not be ideal for some of us.

96 degrees is not the temperature in the block, it is what the coolant temperature sensor in the lower radiator hose measures. I used this value as an approximation of the coolant temperature inside the ET, which will maximize the pressure. We were trying to put a ceiling on the highest pressure, so as to err on the cautious side.

Temperature is probably much higher in the block, but of course not higher than the boiling point. Oil temperature might give a better estimation of that. INPA does have the capability of reading the oil temp.

Originally Posted by SeanC

Great, looks like people in the community has too much "street" knowledge, but when it comes down to actually calculating numbers, there is only WDE46, Terra and myself who are doing the work. I will look forward to your proof.



In my calculation of the pressure (without taking into account expansion), I used ideal gas law (PV=nRT), along with the knowledge of maximum operating temperature of 96 degrees Celcius. This gives a pressure of 1.3614 bars as the operating pressure (i.e. 0.3614 cap should suffice). For details and justification, read my posts above.

Now that we have an interval for the expansion (235-325 mL, we still don't know the absolute fill, hence we don't know the absolute expansion), we can start thinking about how this will effect the pressure that was calculated to be 1.3614 bars without taking into account the expansion. I still don't think it will effect it much, unless you're a clueless BMW owner (as most are), and top off your coolant as you would do on a domestic car.

So at this point, it seems to me that BMW is trying to minimize a possible premature ET failure by using a 2 bar cap. However, that's a good reason only for those clueless owners who tend to top things off, and I fail to see the advantages for the rest of us.

lol, your posts are much longer than they need be.

So for your ideal gas law, you are only acknowledging the air within the expansion tank, and your variables are:

P=variable you're solving for
V=?
n=?
R=?
T=coolant temperature

I think we are all in agreement that if you completely top off the expansion tank with coolant, you will get the 2bar relief pressure on the expansion tank cap?

Originally Posted by SeanC

While not being 100% sure, maybe a system constantly venting is not a healthy one. Think about the venting system being stuck open or in the worse but less likely case, stuck closed.



96 degrees is not the temperature in the block, it is what the coolant temperature sensor in the lower radiator hose measures. I used this value as an approximation of the coolant temperature inside the ET, which will maximize the pressure. We were trying to put a ceiling on the highest pressure, so as to err on the cautious side.

Temperature is probably much higher in the block, but of course not higher than the boiling point. Oil temperature might give a better estimation of that. INPA does have the capability of reading the oil temp.

Would it be constantly venting? I would think it'd just let out air until the pressure drops, at which point it would stop venting since it'd be at equilibrium. Now it would constantly take in and release some air as the temperatures change, but isn't that true even when the system reaches 3 bar? I suspect that it wouldn't be any worse than any other car that comes with a 1(ish) bar cap from the factory.


As far as oil temperatures go - in my experience it is highly variable on ambient temperature. On cooler days, I may barely reach 75C, but on warmer days it'll easily get to 100C. In both cases, my coolant temperature will be at around 80 degrees.

Originally Posted by SeanC

While not being 100% sure, maybe a system constantly venting is not a healthy one. Think about the venting system being stuck open or in the worse but less likely case, stuck closed.



96 degrees is not the temperature in the block, it is what the coolant temperature sensor in the lower radiator hose measures. I used this value as an approximation of the coolant temperature inside the ET, which will maximize the pressure. We were trying to put a ceiling on the highest pressure, so as to err on the cautious side.

Temperature is probably much higher in the block, but of course not higher than the boiling point. Oil temperature might give a better estimation of that. INPA does have the capability of reading the oil temp.

If you want an example of a venting system that is open, you can look into heavy trucks. I forget the reasons, but they run a non-pressurized open cooling system.

Incorrect on the coolant temperature location. The lower radiator hose sensor is only used for control of the fans. The actual coolant temperature sensor used for engine operation is on the intake side of the head.