Project Overview
Thermoelectric coolers (TECs - as shown at left courtesy of Marlow Industries) and generators (TEGs) have been around more than 200 years, but they've been getting more press lately in the automotive industry, specifically BMW. They have been using TEGs for producing electricity from the temperature gradient from the exhaust pipe to the ambient air. In the reverse, by passing current through the two materials, typically n- and p-type semiconductors, you can pull heat from one side and reject it on the other, and use them in a cooling capacity.
I wanted to use this amazing effect for another hobby of mine, brewing beer. The main idea is to control the temperature of 5-6 gallons of fermenting wort without using a typical refrigerator system. This was as much for the challenge as it was for learning about these "cool" little devices. Overall for a system of this size or larger, a typical compression refrigeration system may be more efficient - but that wasn't the point of the project.
In this and subsequent blogs, I would like to trace my development of this system from start to finish. I will describe the system requirements, heat transfer analysis and resulting prototype circuit design and fabrication. Stage 1 - A Little Background
During the brewing process, the stage of converting the sweetened wort, with the help of yeast, to alcohol is called fermentation. Fermentation typically does not require real close temperature control; for many styles of beers fermentation at room temperature is good enough. Whe
re you get into trouble, however, is the fermenting lager style beers. This style of beer requires temperatures cooler than room temperature, roughly 50 deg F, and a refrigeration system to maintain this temperature for several weeks.
The refrigeration system consists of three main items - 1) the item to be cooled, wort, 2) the box/cabinet to contain and circulate the cooled air and 3) the device to do the cooling work. Items 1 and 2 are passively acting to counterbalance the work done by the cooling device (in this case a thermoelectric cooler). The energy balance needs to be calculated first of to size the cooling device.
Of course, all of my calculations can be sized for your application and could be used to cool or heat a number of various mediums.
Stage 2 - Heat Transfer AnalysisThe refrigeration system has to be able to overcome three major sources of heat in it's worst case condition - when the warm fermentation vessel is placed in the refrigerator. The overall energy balance is as follows:
where Q_boxloss [W] is the heat lost through the insulation of the refrigerator box to the ambient atmosphere, Q_ferm is the heat generated by the yeast converting sugars to alcohol, Q_cool is the amount of energy required to bring the temperature down from the yeast-pitching temperature to our ideal fermentation temperature over a given time and finally, Q_pumped is the heat pumped out of the system by the thermoelectric device.
What you are most interested in is this worst case scenario. The cooling device needs to be able to provide enough heat pumping to deal with this worst case or you will never get the temperature of the your wort down to your ideal temperature. As the wort cools down to the final fermentation temperature, you only have the insulation losses and fermentation heat to contend with, which will be less than the worst case.
Let's go through how to calculate these values:
where A [m^2] is the total area of the outside of the refrigerator box , T_b [deg C] is the ideal inside temperature of the box , T_a [deg C] is the ambient room temperature (again don't forget to make this the worst case scenario, i.e. 85 deg F on a hot day), K [W/m-C] is the thermal conductivity of the insulation and x [m] is the insulation thickness. If you want to get real precise, you could also add in the wood/plastic/metal outershell and it's conductivity, but for simplicity here, I only am looking at the insulation for a rough estimate.
We must cool the wort down from it's initial temperature to a it's final temperature and this will take energy as shown here:
where m_w [kg] is the mass of the wort (density x volume), T_i [deg C] is the initial temperature of the wort, T_f [deg C] is the final idel fermentation temperature of the wort, c_p [J/kg-C] is the specific heat of the wort (i used a value slightly less than water here since it is comprised partially of sugars) and t [sec] is the amount of time that you would like to have the wort go from the initial to final temperature. If the volume you are cooling is large, say 5-6 gallons, 24 hours might no be unreasonable. For smaller volumes, say 12 fluid oz, 15 minutes might be reasonable; the time to cool will be dictated by your requirements.
For the beer experts, this next section might be useful, but if you are not cooling fermenting wort or your medium is not generating heat, you can skip this equation. I wanted to make sure that the fermentation process itself was accounted for. It turns out that the heat generated by yeast can be quite negligible compared to the insulation losses (unless you have an amazingly thermally tight refrigerator). I will add it here, however, for completeness. I would also like to give my due respects to Spencer Thomas for these following equations.
The yeast will convert a portion of the sugars present in beer to alcohol and during this conversion will generate heat. If we assume that sugars being fermented release 140 kcal/kg or 586 J/kg (1 kcal = 4.184 J), we then must then figure out how much sugar is fermented and mulitply it by 586 J/kg and divide by the time they take to do this. The fermentation energy is then:
where t is the time of fermentation is seconds, which in our case would be maybe 1 week. The initial mass of the sugar, m_si [kg], can be calculated from the original gravity of the wort (OG) as follows:
where m_w [kg] is the mass of the wort and,
where OG is in points, i.e. 1.050 = 50 OG in points.
The final mass of the sugar, m_sf [kg] is a little more involved.
where FG is the final gravity of the beer in points. RE and AE deal with the attenuation of the beer, which is when the beer is no longer just water and sugar but is also alcohol as well. This composite has a different density and must be accounted for in the mass calculations when you are looking at the final gravity.
There you have it, all the heat transfer components to the left hand side of the energy balance equation. In my next blog, I will identify how to find Q_pumped and how to best to implement it. This will include specifying a thermoelectric cooler module and the heat sinks required to reach it's optimum performance.
Some points within the program that may not be so obvious. First, when we read the temperature from the LM34, the picaxe reads the analog voltage and converts it to a digital value with ten bits of resolution. This means that the value has 2^10 or 1024 divisions. The digital value can then be calculated back into a voltage in mV within our program. The ADC is converting based on a 5V range, or 5000 mV. This means that a digital value of 0 is equal to 0 mV and a digital value of 1024 is equal to 5000 mV. Taking this further, each digital division is equivalent to 5000/1024, or 4.88 mV. By the way, 4.88 mV is the same as 0.488 deg F, so the resolution of our program is ~0.5 deg F. You can see from the program that when we mulitply the digital value by 4.88, we will in essence be calculating the temperature in deg F mulitplied by ten. Since the temperature is read in tens of millivolts, the actual whole number value of the temperature can be read once we divide TE_Temp_10 by 10.
