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 Home Brew Forums > Thermodynamic approach to Wort Chilling
09-27-2012, 04:21 PM   #1
jgalati
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 Thermodynamic approach to Wort Chilling

First post! Woo!

After reading what feels like every post on this forum, I've noticed there's a lot of misconceptions about wort chilling and what's most efficient.
Thus I propose treating this concept like any other engineering problem.

Summary is at bottom.

What is heat transfer?
A complex study of removing energy from one substance and transferring it to another. At a basic level, we are transferring heat from our wort, to a fluid contained within copper, stainless steel, aluminum, or any other conductive material.

What affects heat transfer?

• Specific Heat of Wort (constant)
• Specific Heat of Cooling Fluid (constant)
• Surface Area of Chiller (constant)
• Gauge of Chiller Material (constant)
• Viscosity of Fluids (constant)
• Velocity of Wort
• Velocity of Cooling Fluid
• Kettle/Keggle Material (constant)
• Ambient Air Temperature
• Thermal Conductivity of Chiller (constant)
• Surface Area of Wort to Ambient Air (constant)
• Temperature of Chilling Fluid
*Constants based on your current equipment, or physical properties

Equations
We are not so much interested in solving for the specific amount of time it takes to chill 10 gallons of boiling water, but rather, what system provides optimal cooling abilities at the lowest cost.

We will assume a simple system (no loss to outside world):
1/(m0*A) = (1/(h1*A1))+dx/(k*A)+1/(h2*A2)

where m0 = Heat transfer coefficient
A=Surface Area of fluid to conductive material (note this is different on each side because materials have thickness)
h = Individual convection heat transfer coeffecient
k = Thermal Conductivity (sometimes denoted as sigma)

From this we can say:
1) More surface area = more heat transfer
2) Thinner conductive walls = more heat transfer (lighter gauge)
3) A higher thermal conductivity of the material = more heat transfer

Defining Individual convection heat transfer
This value changes based on the type of system used, i.e. counter flow, heat exchanger, immersion chiller. It also depends on length of pipe, resistance to water flow, laminar values, etc.
At an utmost simplistic view we will define h as:
h = (thermal conductivity)/(Dh)*(N)
where Dh = hydraulic diameter (we will assume this value to be at a maximum i.e. water fills the entire conductive piping.
N = Nusselt number based on Reynolds number, and Prandlt Number (we will not calculate these values, rather look at what properties of our system maximize heat transfer).

Reynolds number =
(density)*(velocity)*(Linear_length_traveled)/(dynamic_viscosity).
Prandlt number = (dynamic_viscosity*density*specific_heat)/(density*thermal conductivity)

What values maximize h?
Based on values we can control:
More velocity across conductive material = more heat transfer
More conductive tubing = more heat transfer

Laminar vs Turbulent Motion
For our purposes, we will assume chilling water is laminar.
Wort can either be move in a Laminar or Turbulent fashion.

To motivate this discussion, let's imagine we have water at 200 degrees F.
If you leave it sitting by itself on a stove, you will see steam coming off of the surface, and eventually it will come to equilibrium with the surrounding air.
Now, imagine the same water at 200 degrees F: If you start stirring the water, even slowly, what happens? More steam escapes from the surface, which means the water will cool quicker. Why is this?
If you were to look at the surface of the water at a microscopic level, you would see a very thin layer of air acting as an insulator to the outside air, and a very thin layer of water acting as an insulator to the water below it. And we know that insulation decreases speed of heat transfer. Thus, turbulence, or siring the pot, will remove that insulating layer, improving heat transfer to the outside world.

Great... How does this apply to Wort Chilling?
Let's assume we have a 20' immersion chiller and a 20' counter-flow chiller. We all know that the counter-flow chiller will cool the wort faster without agitating the wort surrounding the immersion chiller. This is because we reduce the laminar buildup on the outside of the chiller using a counter-flow chiller. We can express this quantity as v2 or the velocity of the wort against the conductive material. Let's assume that v1 (the velocity of the cooling fluid is constant for both chillers). The Reynolds number will be higher, thus making the h2 value for the counter-flow higher than the immersion chiller.

Immersion vs Counter-Flow vs Plate Heat Exchanger
The pros and cons list of each of these would go on forever, again, based on the values we have discussed above. I'm not going to derive optimal values for each of these, because you can probably determine, for yourself, the optimal values.

Summary
Values in your control: Make your cooling water as cold as possible, increase water pressure either by pump or faucet to maximum value possible, remove insulation from keg (if possible) while cooling.
Maximum Efficiency: Heat Exchanger. The surface Area and thickness of the plates provides maximum efficiency. Also, velocity of wort can easily be increased by using a higher pressure pump.

What I do
Immersion chiller all the way baby.
1) Simplicity simplicity simplicity
2) USE A PAINT STIRRER.

Why Immersion
An immersion chiller gives me the best of all worlds. Using this paint stirrer, 1)I can oxygenate my wort the entire time it's spinning. If I wanted, I could have froth spilling over the top of the keggle.
2)At full speeds, the velocity of the wort over my coil is faster than that of a counter-flow chiller and heat exchanger.
3) Simplicity and Extra Low Cost.
4) The outside of the Keg acts as a heat exchanger to the outside air. So not only are you cooling the wort on the immersion chiller, you're cooling it against the keg walls.
5) Huge amounts of steam escape by destroying the laminar layer between the wort and outside air.
6) Cheap and effective way to BOTH oxygenate and cool wort at the same time.
7) Less parts to sanitize.
8) Keep it simple.

My Results
Using this technique, in the summer, where my hose water is about 63 degrees F. I can usually cool 5 gal of wort in less than 11 minutes. The best I've ever done, in the winter, was 6 minutes. I use a 20' coil of 3/8" copper tubing from home depot that i coiled myself. I use my hose water. I've also never had to oxygenate my wort other than letting it fall from the top of the carboy to the bottom because the paint stirrer does that for me along with helping cool the wort.

Thanks guys and I hope I didn't make too many errors.
Anyways, post your thoughts below and/or experiences.
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09-27-2012, 04:58 PM   #2
cheezydemon3
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Honestly, I feel that the "ICE in the wort" method may be simpler and as efficient (sorry, no supporting formula )

first off. AWESOME POST!!!!

Even AG, I brew 4 gallons from a 5 gallon recipe, dump that on 1 gallon of sanitary ice.

Amazing cold break, awesome clear beer.

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09-27-2012, 05:32 PM   #3
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Did you ever check out Jamil's whirlpool chller?

Similar principle, though a more elegant and hands-off approach. I get my wort to 120F in 3min, and to source water temp in 20min in the dead of summer.

Kudos for taking the time to work out the calculations

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09-27-2012, 07:09 PM   #4
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It's this simple. GPM X TD X 500 = BTUs. That's the way the refrigeration requirements for a chiller are determined. 12,000 BTU = one ton of ice melting or in power 750 watts or in HP, 1. You know, kinda like what Jimmy Watt invented. However, the formula doesn't work when it comes to change of state. Oh, just so you know, steam doesn't come off 200 degree water unless the boiler is maybe on Mt. Everest. That's the change of state thing. But, I know what you were getting at. You're figures and explanation are great, they are sensible and easily understood. I enjoyed reading them. Keep up the good work.

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09-27-2012, 07:53 PM   #5
jesserizzo
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Most of your post went over my head, so I can't comment. But...

Quote:
 Originally Posted by jgalati 6) Cheap and effective way to BOTH oxygenate and cool wort at the same time.
Quote:
 Originally Posted by jgalati I've also never had to oxygenate my wort other than letting it fall from the top of the carboy to the bottom because the paint stirrer does that for me along with helping cool the wort.
So I assume you've looked into and aren't worried about hot side aeration?
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09-27-2012, 09:18 PM   #6
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Quote:
 We are not so much interested in solving for the specific amount of time it takes to chill 10 gallons of boiling water, but rather, what system provides optimal cooling abilities at the lowest cost.
if you were talking about efficiency of the chiller, you should mention flow rate of the water thru the coil, and legnth of coil. having an immersion chiller 100 feet long isnt necessarily perform better than a 20 foot chiller if the cooling water reaches equlibrium with the wort temperature after 10 or 15 feet. maximizing efficiency is a balancing act between flow rate (and volume of waste water), temperature differential of incoming water and the wort, and legnth of tubing/surface area of the chiller.

Quote:
 Originally Posted by jesserizzo So I assume you've looked into and aren't worried about hot side aeration?
yea, i would only start the paint stirrer after the wort has chilled almost all the way down (probably around 100 degrees or below). not only theoretically, but ive also personally noticed that adding oxygen at even moderately elevated temparature that results in off flavors.

it does depend on what malt you use though, as the no-chill brewing guys know about.
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10-02-2012, 01:56 AM   #7
jgalati
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As to Hot Side Aeration: Oxidation is a function of time, heat, and surface area exposed to oxygen. If my wort is being oxygenated for maybe 4 minutes at these higher temperatures, then I guess I can live with an increased oxidation rate for those 4 minutes. Past that, all chemical reactions will take place as they normally do. Thus, the cooler your wort is, the less any chemical reactions like oxidation will occur, which is exactly why we store hops air tight and at very cold temps. Also, a hotter liquid means less diffusivity. If my liquid is boiling, I can stir it all I want, but it will never increase it's oxygen levels.

In short, no I don't think hot side aeration means anything, because the amount of oxygen your introducing during this time is 1) small compared to the oxygen you can add at cooler temperatures and 2) limited in it's oxidation effects to the wort because it's only at these higher temperatures for such a small amount of time.

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10-02-2012, 02:19 AM   #8
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One thing I tried this weekend which worked amazingly well on a 5 gallon all-grain batch. I have a homemade 3/8" 20 or 25' copper wort chiller (I can't recall the exact length). I purchased a 650 GPH submersible pump from Harbor Freight and stuck it in a cooler full of ice water for the first 5-10 minutes or so I let the hot water returning from the chiller to run onto the lawn while keeping the cooler remain full from the hose. Once I got to the point where I had no more ice to add tossed the output line from the chiller back into the cooler and let it continue to recirculate. I tried to keep the cooler about half full of ice and half full of water. Within 20 minutes or so I was down below 60F. It was cold enough that the side of the boil kettle had condensation forming on it not to mention an awesome cold break. I let the chiller continue to run as a siphoned off the wort. The last batch I did using ground water took over an hour to get it down to 80F.

So I'm going it at from the thermal gradient and temperature of the cooling fluid approach. I'd like to look into the paint stirrer approach as well because I notice temperature gradients in the boil kettle and I think a stirrer would help negate that as well.

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