Thermodynamics of Chilling

Background

• Norman Pyle in HBD 1778 started a thread on "chillers" that I sympathize with. The thermodynamic terminology of homebrewers is esoteric and serves little technical purpose.
• Robert Brown in HBD 1780 attempts to coin an awesome nomenclature.
• Lee Allison in HBD 1780 wants to build a plate exchanger, I have a simple design.
• Tom Williams (refreshingly) identifies "chillers" as heat exchangers and introduces the correct technical description but wants to know why?

I left the Physics department for Literature 20 years ago, confident that the mysteries of thermodynamics would never torment me again. Alas, now I must dip my big toe in it again. I am constructing a 70 litre test model of a full mini-brewery for assembly in central Russia. To this end I have been pestering engineers, beer in hand.

FAQ: Why chill quickly?

I see two main reasons:

• To get from the Sterile Boiling Phase through the Warm Bacteria-Motel Phase to the Vigorously Fermenting-Protected by Krausen Foam or Airlock Phase without unwanted guests (bacteria), so time is important.
• Control of Sulphur flavours. The Di-Methyl Sulphide (DMS) flavour threshold in beer is about 30 micro grams/litre. DMS is produced from the malt's natural content of S-Methyl Methionine (SMM) and at temperatures greater than 70 C. In "Principals of Brewing Science", p 142, Professor George Fix describes the math of this. Apparently in the boil all DMS gets carried away with the exiting gases. But between boil and fermentation temperature the residual heat continues the reaction SMM to DMS with the DMS remaining in solution. Thus if cooling is prolonged, a pronounced sulphur taste enters the flavour profile.

FAQ: How quickly to chill?

The DMS flavour appears subjective, some like it in the tertiary flavour range of about half the flavour threshold of 30 micro grams/litre( ie nothing). Most beer seems to be in the secondary range of 20 to 60 micro grams. Some profiles have a higher concentration. How to control it?

Basically, some of the SMM converts to DMS in the boil and is carried away. Part of *what is left* is converted to DMS in solution, about 25% of which is then broken down in fermentation provided no DMS producing bugs are present.. So the final Sulphur flavour is determined by:

• the SMM fraction/gram of your malt
• the grams of malt/litre wort
• the boil time
• the cooling time
• bacteria free fermentation

Using George's examples I have created two tables, the first to calculate the concentration of SMM/litre Wort, and the second to calculate the % of this left as DMS in solution *after* fermentation.

      MICRO GRAMS of SMM/LITRE WORT BEFORE BOIL

 * Grain Bill/Vol*       * Micro Grams SMM/Gram of Malt *
Grams/Litre  Lbs/Gal    3    4    5    6    7     8     9
-----------------------------------------------------------
   150        1.125    450  600  750  900  1050  1200  1350
   200        1.5      600  800 1000 1200  1400  1600  1800
   300        2.25     900 1200 1500 1800  2100  2400  2700
   400        3       1200 1600 2000 2400  2800  3200  3600
   500        3.75    1500 2000 2500 3000  3500  4000  4500

This gives the initial concentration of SMM/litre in your mash.

 
 PERCENTAGE OF INITIAL SMM LEFT AS DMS AFTER FERMENTATION

*Boil Time*     *Chilling Time*  (100 C to 20 C)
                5    10     15    20    30    60    Minutes
-----------------------------------------------------------
    120        .5%   .9%   1.3%  1.7%  2.4%  4.2%
    105        .6%  1.2%   1.7%  2.2%  3.1%  5.5%
     90        .8%  1.5%   2.2%  2.8%  4.1%  7.1%
     75         1%  1.9%   2.8%  3.7%  5.3%  9.2%
 

Example: We have a 6 micro gram/gram SMM content malt, and a grain bill of 2.25 lbs/gal. We decide to boil for 90 minutes and our Supercyberchiller does the trick in 10 minutes.

DMS = 1800 x 1.5% = 27 micrograms/litre
(DMS is below the flavour threshold of 30, in lower secondary range).

If we cool for 15 minutes:
DMS= 1800 x 2.2% =40 micrograms/litre
(A slight malt/sulphur tone-quite agreeable).

Now we try some high SMM malt at 8 /gram and a high SG brew using 3lb/gal, a short boil of 75 minutes and a bathtub chiller which takes 30 minutes.
DMS= 3200 x 5.3%=170 micrograms/litre
(This would clear your sinuses!!)

I am not confident of these figures, could they be checked by Fix or someone more familiar with the labyrinths of chemistry? I will repost new tables if corrected.

FAQ: How do I chill it?

With a heat exchanger of course. All our contraptions of copper, plastic and water are heat exchangers. Heat exchanging is a highly advanced industry that knows what it is doing, so why do we reinvent the wheel? The most common classes of heat exchangers are:

• "parallel flow" in which the two fluids(or gases) flow parallel and in the same direction.
• "crossflow" in which they flow across each other's path,usually 90 degrees
• "counterflow" is parallel flow in oposite directions

The reason for this terminology is that different mathematical formulas are used to calculate the heat transfer in these different configurations, heat exchangers are named by *how the two fluids move in relation to each other*. The "Cu tube in a hose" is a counterflow heat exchanger. The coolant water should run opposite to the wort because this is by far the most efficient. It is possible to cool the wort to below the exit temperature of the water. The "Cu tube in a bucket/bathtub of ice water" is a crossflow exchanger. It should be continously stirred and because the flow is not parallel to the Cu wall, boundary layers are not a problem outside the tube. The "cold coil in wort" system is also crossflow.

The kettle in a snow drift (my Russian grandmother-in-laws method) is a non flow system and fraught with temperature stratification problems and the transmission coefficient of water. (stir vigorously and it has the same properties as crossflow.)

FAQ: What is best?

Well, let us look at some of the basics. Heat must flow from wort to coolant. The main barrier is the metal wall. *Wrong!*

The first trap I fell into was confusing "coeficients of heat transfer" with "coeficients of heat transmission". Heat travels through things and most high school kids could find out that Cu is 7 times better at this than steel. But the heat *transmission* properties of water are lousy and in a laminar flow situation a boundary layer forms on the wall of you tube, becoming an insulator. As well, the interface between liquid/metal and then metal/liquid has it's own resistance called the coeficient of heat *transfer*. The actual bit of metal (if its under 3mm) contributes much less than 10% to the "overall coeficient of heat transfer".

The rate of heat transfer depends on a few vital factors:

• The area of you exchanger (ie length of tube)
• Getting rid of the boundry layer by achieving "turbulent flow" (dramatic improvement, convection replaces transmission)
• The thermal pressure, known as the "logarithmic mean temperature difference". (always greater for counterflow)
• The overall coeficient of heat transfer, which depends a lot on b/

Without trying to understand Prandtl and Renyolds numbers, turbulent flow is achieved in a 1/2 " tube at .11 m/sec, in a 3/8" tube at .14 m/sec, and in a 1/4 " tube at .22 m/sec, which quite simply means in each case:

*put 5 gallons through your (1/2":3/8":1/4") exchanger in under (22:31:46) minutes and you have turbulent flow*, (Charlie's Law)

The overall coeficient of transfer jumps from about 1.25 KW/m2 K to about 12.5 KW/m2 K ! Fast flow systems rule, OK?

Example:
Now 5 gallons of wort at 100 C cooled to 20 C needs to loose about 6300 KJ of energy, If the temp difference (dT1) at exit of coolant and entrance of wort (same end) is 30 C (run the hose fast) and at wort exit (dT2) = 5 C the the log mean temp difference O = (dT1-dT2)/(loge (dT1/dT2)) = 13.8 C
Now Q=U A O (Q=heat transfer rate, U= coeficient, A= area, O= log mean temp diff)

If we want to cool in 10 minutes we need a rate of 10.5 KW which translates theoretically into about 8 feet of 3/8 tube in a hose. Extra area in heat exchanges can't hurt and gives more control, so buy 12 feet. But tap water is seldom 5 C below the desired final temperature, especially for lager brewers. A crossflow "finishing" exchanger of 4 feet of tube in a ice bucket will pull it down a further 8 > 12 C without need to change the ice coolant.

The "tap water in a hose around a tube of wort" and "tap water in a coil in stirred wort" are thermodynamically efficient, but suffer from the limitation of the tap temperature as some thermal pressure is needed to drive the heat exchange.

The "coil in an ice bucket/bathtub" systems on their own need coolant changes and constant stirring.

The combination counterflow, crossflow exchanger avoids most of this except the stirring, the tap water receives most of the energy, preventing the rapid heating of the ice bucket.

To control you cooling for DMS results, the siphon height or outlet constriction will adjust your flow rate of wort and thus your cooling time. The tap water flow rate will adjust your final temperature to the desired figure. Record your results and taste the difference.

FAQ: How do I clean it?

Simple, a fishing sinker and some 40 lb line. Drop it down your tube propelled by water pressure and then pull through a rag with whatever cleaning agent you prefer. Those with military training with recognise the rifle pull-through technology.

Pubs force tennis-size foam balls through their beer lines under pressure.

FAQ: What is a Plate exchanger?

If anyone wants to build a simple plate exchanger, please post me. Plate exchangers have coolant and wort flowing on alternate sides of many plates of metal with gasket spacers, a sort of thermodynamic sandwich. Their advantages are massive surface area, good turbulent flow and you can take them apart to clean them! They are run counterflow and can be configured as very efficient heat-recovery pastuerizers.

I'll work out how to send my drawings on this Internet thingame.

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