Fun with Tempco
Fig 1 - 800W Hotplate, 1L water in 4qt pot, 180 second burn
Here are the results of a 3-minute burn with the 800W hotplate, a plain old cooking pot, and one meager liter of water. You can note several problems with this setup. First, the dead time before the water starts heating is quite long, about two minutes. Next, the ramp rate of temp is rather slow, even at full power. Finally, the overshoot is horrendous and with an uninsulated pot, the dropoff of temp is pretty strong. You don't even want to see the 1-gallon test, it's like watching grass grow.
Why does this suck? Well first, the transfer of heat from the hotplate is low (coil->plate->pot->water) and the time constant of the plate is large. Second, all the individual pieces of the system are leaking heat to the outside world. A good bit of heat produced is not even making it to the water, and more is sucked off from the sides and top of the pan. Let's investigate further.
Fig 2 - Hotplate Surface Temp during 1q boil test. Fig 3 - Water temp during 1q boil test.
In these plots, we drop a 1L pot of room-temp water onto the slightly-warm hotplate and turn it on full-power until it begins to boil. Although the plate easily reaches 200-300C, the thermal resistance from plate to water combined with the thermal inertia (specific heat) of water makes for a pretty slow system. The plate gets quite hot, so even if we turn it off it is going to continue heating our mash for quite some time. You can even see the temp of the plate FALL initially as it responds to the heavy load of the room-temperature water. A PID is going to hate this system, especially if we don't give it the plate temperature. In my SPICE simulations, the PID had to tickle the heat so gently to avoid overshoot that it was predicting 2+ hours to reach mash-in and respond to me dumping 10lbs of cold grain into the system. Sad!
So the hot-plate went back to the store, and I pondered heat transfer efficiency over a frosty cold brew. The system I saw as most efficient was CD's New RIMS, a very cool (or hot, rather) implementation using a low-density water heater element as the heating device inside a tube filled with wort. By continuously flowing the wort across the heater element, nearly all the heat produced by the element is transferred to the wort, and away it goes back into the tun. Hot wort is constantly replaced by cold wort, meaning that as long as the pump keeps running, it is very unlikely to scorch - the surface temperature of the heater is held to the present wort temp by the continuous flow. Now we just modulate the power dissipated in the heater element, and we can smoothly modulate the amount of heat delivered to the wort.
A low-density heater element is recommended, and I agree with this wholeheartedly. Theoretically, if you have a quick enough flow of wort you could use a high-density (little 7", 1500W) element, but without some fins or something to ensure good mixing, the surface of this element is likely to be much hotter than your desired setpoint. Although the average temperature of your mash will be right, the instantaneous temp at the surface of the heater may be higher, breaking down your poor enzymes and slowly filling your tun with impotent wort. So like Mr. Pritchard, I used the 70", 240V/5500W element driven at 110V for an output of about 1375W. However, I hate to lose any heat to the outside world, and I need a compact system for my small apartment, so I locate my heater tube inside the mash tun, and flow wort across it - pickup tubes bring wort in on the right end, and the pump brings wort out on the left end and returns it to the tun. Now any heat radiated by the heater tube assembly will be directed into the mash and we pick up another percent or two of efficiency.
So why do I believe that the surface temp of the low-density heater won't scorch? Well, once I built the heater bracket into the cooler, I did some simple testing consisting of running the heater with and without pumping. A temp probe attached to the heater surface said that with flow greater than about 0.5GPM, there was less than 1 degree of temp difference between the surface of the element and the bulk of the wort flowing past. Also, since the metal components of the system were GROUNDED and I was using a GFCI OUTLET, I happily held onto the heater element while playing with the flow. I curse mightily at about 140F, so if I can comfortably touch the element with 0.5GPM flow and 120F water, I believe the data.
Fig 4 - Now we're cookin! 4500W element at 110v, 1.5" copper tube enclosure, 30 minute burn
This plot shows the heater performance during a 30-minute burn with 5 gallons of water in the tun, and pump on continuously. Here I am measuring temp right at the pump, the exit of the heater tube. What is interesting is that when the heater is turned on, or shut off, there is about a 2-degree step. This is when we switch from heating wort to just recirculating it through the heater tube. From my old measurements of 1 degree difference between heater and wort, this tells us that the other 1 degree delta is the difference between "cold" wort entering and "hot" wort exiting. So we can estimate that when wort is sucked into the heater tube, it is heated to within 1 degree of the element, and the mixing in the tun at 1GPM is good enough to keep the entire tun within 1 more degree of this "hot wort" temp (although there is no grain in the tun here). That was better than expected. A few other nice points you can see are: The ramp rate of 5 gallons of water is about 1.3F/min at max power, and the falloff of temp is about 0.05F/minute. Thanks igloo for your nice work on that second parameter!
At this point, I found the new heater so predictable that PID was not necessary. Also, I was eager to get this bad boy regulating so the controller I designed was a simple hysteretic mode, like a generic house thermostat. The setpoint is programmed by the user, and the heater is applied until temp at the pump exceeds this temp by one degree, the delta from heater to wort. The heater is shut off until the temp at the pump falls to one degree below the setpoint, the delta from tun to heater chamber. By bouncing the pump output between these two limits, then theoretically we can keep the tun temp within one degree of the setpoint even with this very simple regulation. The key is the flow rate - slower flow will need more hysteresis between the ON/OFF points to avoid chatter. Now I find that in regulation, the heater is on for 8-10 second bursts, right where I want it.
One last note: I don't control the tun temperature because I want the hottest wort to be at my setpoint. If there is a difference in temp between the heater chamber output and the bulk of the tun, I will see it when I turn off the heater - the temp will fall by more than 2 degrees and the heater will restart. I feel this is better than trying to control the bulk of the tun - in that case, you don't know how hot the output of the heater chamber is; it could be very high if you are heating a big batch, denaturing the enzymes, while the bulk of the tun is still below regulation temp. This way, it's slow but sure. Maybe my next revision will predict the next heating cycle based on the bulk temp, but for now I find the regulation very suitable as-is.
The LOOP!
Fig 5 - Performance of the regulation loop, with setpoints 120F, 140F, 158F.
Fig 6 - Heater control during this test.
Here is the data from one of my "dry runs", using only water in the tun. The profile was 30min at 120F, 40 min at 140F, and 20 min at 158F. I didn't do a mash-in, mashout or sparge in this run, but it's a reasonable estimation of a mash run. The system was ready for grain!