Thermal Dynamics of a IC

[ajdelange]

Your post is for a counterflow chiller, right ajdelange?

Yes, but the same model should serve for one in which wort and coolant flow in the same direction (not that one would want to operate a chiller that way).

 

[jaginger]

Yes, but the same model should serve for one in which wort and coolant flow in the same direction (not that one would want to operate a chiller that way).

Quite true.

I was thinking of immersion chillers earlier in the thread. The big difference between an IC and a CFC (in terms of heat dynamics) is that in the IC, a lack of wort movement means that you'll have cooler-than-average wort right next to the chiller, reducing the temperature gradient and slowing heat transfer.

 

[Shift]

One way to measure the total cooling effect could be to measure your flow (clocking a certain volume would be the easiest way) and compare the temperature of incoming and outgoing cooling water.

Heat capacity of water, time spent in tube by the water, and temperature difference (before and after) should result give you a number to, uhm, enjoy and reflect upon.

Lets say you have have a flow of 1L per minute, ingoing temp 15°C and outgoing 50°C

effect: (1000/60)*4.18*35 = ~2438 W
first term is grams per second (flow), the second is joule per gram and Kelvin, the last is the difference in temperature.
(to use imperial units you'd need some more numbers in there to compensate for fahrenheits and what not.)

Energy capacity can't really be modified, but the others can be changed. You could blast a ridiculous amount of water through the cooler with only a slight difference in temperature and still cool it more than a lower flow with a higher temperature difference.

It'll be different for different wort temperatures, so measure both and plot some sweet graphs of your cooling effect over time and/or wort temperature. :rockin:

disclaimer: Can't guarantee that this is correct.

It's still interesting, nonetheless that the heat flow into the chiller under these assumptions seems to just depend on the total rate of chiller water flow. Even though the parallel tubes start out by absorbing a lot more heat, the water in them heats up very quickly because the water flow through them is slow, thus lowering the temperature difference quickly.

But isn't lowering the temperature difference the point of cooling?
The smaller the difference is, the more heat has been absorbed by the water.

 

[jaginger]

Dude, that's a darn good point!

That's by far the easiest way to figure out and compare efficiencies of different coolers....thanks for sharing.

 

[DeafSmith]

But isn't lowering the temperature difference the point of cooling?
The smaller the difference is, the more heat has been absorbed by the water.

The object is to remove as much heat as possible quickly. Once the water in the chiller heats up so that there is not much temp. difference wrt the wort, there's not much heat energy being absorbed by the chiller water. Ideally, you'd want to have such a fast flow rate that the chiller water would hardly heat up at all, maintaining a very large temperature difference (and heat transfer) between the wort and the chiller water. At the other extreme, assume you only have a trickle of water through the chiller - the water heats up quickly and removes all the heat it is capable of, but then there is no more heat removed until more cool water comes through.

 

[Shift]

The object is to remove as much heat as possible quickly. Once the water in the chiller heats up so that there is not much temp. difference wrt the wort, there's not much heat energy being absorbed by the chiller water. Ideally, you'd want to have such a fast flow rate that the chiller water would hardly heat up at all, maintaining a very large temperature difference (and heat transfer) between the wort and the chiller water. At the other extreme, assume you only have a trickle of water through the chiller - the water heats up quickly and removes all the heat it is capable of, but then there is no more heat removed until more cool water comes through.

Ye, the point isn't to maximize the heat transferred to each unit of cooling water, but to maximize the heat transferred from the wort.
I kinda lost that somewhere while reading the thread.

Do you have any thoughts on the rest of my post above?

 

[kladue]

There are 4 basic factors involved, temperature difference between fluids, resistance of heat flow through tubing, surface area, and turbulence or movement of liquid over tubing. If you have large differential, surface area, low thermal resistance but no fluid movement over outside of tubing not much happens, stir the wort and things change dramatically. Parallel tubing immersion chillers will exploit higher temperature differential over shorter run, but if there is no stirring not much improvement over continuous tubing run of same length.
The plate heat exchangers work well in spite of high thermal resistance of stainless steel by creating turbulent flow on both sides of the heat exchange plates, and thin plates. Counter flow chillers offer similar results with constant flow over both surfaces and counter circulating coolant.

 

[ajdelange]

Motivated by this thread I dug out and posted (to www.wetnewf.org) my old notes on counterflow chillers. The bottom line is that each chiller's geometry, materials, length... give it a characteristic "capacity" or "size". This is a number expressed in units of flow rate e.g. gallons per hour. This capacity can be determined by establishing counter flowing "wort" (water for this determination) and coolant and then measuring the "efficiency" which is the difference between inlet and outlet wort temperature divided by inlet wort temperature minus inlet coolant temperature. Thus if outlet wort temperature is equal to inlet coolant temperature the chiller has done the best it possibly can and the efficiency is 100%. The efficiency and wort and coolant flow rates are sufficient to determine the capacity, Q. The performance of the chiller depends on the wort and coolant flows normalized by Q and the notes have a graph for various levels of efficiency. If coolant flow is equal to Q and wort flow to Q/5 the chiller will be 99% efficient. If wort flow is doubled for the same coolant flow efficiency drops to about 85%.

Unfortunately, to utilize any of this you'll have to wade through quite a bit of algebra but at least you don't need to understand it at any more depth than is necessary to appreciate what the graph is telling you.

The big caveat here is that as flow transitions from laminar to turbulent, Q is going to change and the model does not account for that. If you measure Q in the turbulent region then you can use the model in the turbulent region but not in the laminar and vice versa. To further stir the pot on this issue note that wort could be laminar which coolant is turbulent and there are 3 other combinations.

 

[DeafSmith]

Ye, the point isn't to maximize the heat transferred to each unit of cooling water, but to maximize the heat transferred from the wort.
I kinda lost that somewhere while reading the thread.

Do you have any thoughts on the rest of my post above?

From your equation, you could determine the heat transfer with a given flow rate and temperature difference. Also, it is obvious that you could increase the heat transfer by increasing the flow rate or by increasing the temperature difference. The only way to increase the temperature difference is to either decrease the flow rate, or to increase the heat transfer coefficient of the chiller; i.e., more surface area, larger diameter, longer coil. Decreasing the flow rate will increase the amount of heat transferred per unit volume of water through the chiller, but will decrease the heat transferred per unit of time.
One way to look at this is to use the Log Mean Temperature Difference equation, or LMTD:

http://en.wikipedia.org/wiki/Log_mean_temperature_difference

Admittedly, this is more of a cross-flow situation, so a correction factor might be needed to account for that, but ignoring that for the moment, let's say we have a chiller with a certain transfer coefficient and we have a certain flow rate and temperature difference. Let's look at a single point in time where, for example, the wort temp. is 85º C, chiller water enters at 15ºC and leaves at 50ºC (also assume the wort is circulating around the outside of the chiller coils so the temperature of the wort in contact with the coils is everywhere 85ºC. So the LMTD or temperature driving force is:

(delta Ta - delta Tb)/ln(delta Ta/delta Tb) = ((85-15) - (85-50))/ln(70/35) =
35/ln(2) = 50.5ºC.

Now assume we double the flow rate, and assume for the moment that the heat transferred per unit time remained the same. If this were true, the temperature change in the chiller water would be half as great, or 17.5ºC instead of 35ºC and the chiller water would exit at 32.5ºC. This would mean the LMTD is ((85-15)-(85-32.5))/ln(70/52.5) = 17.5ºC/ln(1.33) = 60.8ºC. So there would be a greater temperature driving force in this case, which contradicts the assumption that the heat transfer is equal if we double the flow rate - in fact, the heat transfer would go up. So even though the water doesn't heat up as much with the faster flow, there is still more heat removed per unit time.

 

[Shift]

One way to look at this is to use the Log Mean Temperature Difference equation, or LMTD:
http://en.wikipedia.org/wiki/Log_mean_temperature_difference

Ooh, I remember that badboy from a course on interior climate about a year ago. (which nosed a bit on heat exchangers)

But I believe we more or less wrote the same, although you had a good explanation as to why it is that way
"You could blast a ridiculous amount of water through the cooler with only a slight difference in temperature and still cool it more than a lower flow with a higher temperature difference."
To clarify, the temperature difference referred to is between water going in and out of cooler. Not the one between coolant and wort.

More specifically what I was wondering was if you had any thoughts about making those measurements mentioned above and comparing the results?
I started to try and elaborate here but I lost track, not sure what you'd get out of comparing that in the end. But jaginger seemed to like the idea.

 

[DeafSmith]

Ooh, I remember that badboy from a course on interior climate about a year ago. (which nosed a bit on heat exchangers)

But I believe we more or less wrote the same, although you had a good explanation as to why it is that way
"You could blast a ridiculous amount of water through the cooler with only a slight difference in temperature and still cool it more than a lower flow with a higher temperature difference."
To clarify, the temperature difference referred to is between water going in and out of cooler. Not the one between coolant and wort.

More specifically what I was wondering was if you had any thoughts about making those measurements mentioned above and comparing the results?
I started to try and elaborate here but I lost track, not sure what you'd get out of comparing that in the end. But jaginger seemed to like the idea.

You could compare chiller efficiencies that way, but couldn't you basically do the same just by measuring the temperature of a known quantity of wort or water and see how fast the temperature drops? Assuming you don't care how much water you use for cooling, the rate of temp. drop of the wort is really all you care about. Maybe I don't understand just what you want to measure?

 

[Shift]

but couldn't you basically do the same just by measuring the temperature of a known quantity of wort or water and see how fast the temperature drops?

That's what I ended up with when I felt i had thought everything through.
I guess there's a reason why you see posts like "I cool a 5 gal batch in 10 mins with xx feet of tubing"
instead of "i have 4000 watts of cooling :rockin:"

Oh well, food for thought.