---------- Forwarded Message ---------- Subject: [AR] Temperature analysis question Date: Saturday 13 October 2007 11:08 From: Robert Watzlavick To: AROCKET I have a question that I'd like some opinions on. On all of my recent regen tests, the wall and fuel temperatures never reached steady-state values. If I had a larger or better insulated LOX tank, I probably would have been able to get there but that will have to wait until the next set of tests. Less mass of the chamber would also have helped. If you look at the temperature data (here is an example), http://watzlavick.com/robert/rocket/regenChamber/tests/20071006-run1-re gen2-data.png you see that most of the wall thermocouples (Chamber Inside Temp 1, Chamber Inside Temp2) and the fuel exit temp (Fuel Exit Temp) appear to be approaching an asymptote. It looks like if I had been able to run the engine for about 10 more seconds, they would have leveled off. My question is: given this dataset (and my other similar ones), is it reasonable to assume that the temperatures would have continued along the existing trend and leveled off? You can see where I'm going with this. I'm trying to extract steady-state temperatures out of a short run. The notable exception for this run is the Exit Inside Wall Temp thermocouple. It is still rising pretty rapidly toward the end of the run and I suspect that is due to heat flowing from the chamber and throat areas toward the exit of the engine. It is also the coldest of the 3 embedded thermocouples so it makes sense that the entire engine would eventually reach equilibrium after the run. Thanks in advance, -Bob _______________________________________________ aRocket@exrocketry.net http://exrocketry.net/mailman/listinfo/arocket ------------------------------------------------------- ---------- Forwarded Message ---------- Subject: Re: [AR] Temperature analysis question Date: Sunday 14 October 2007 19:35 From: Robert Watzlavick To: David Gregory Cc: Arocket List For any mathmagicians out there who want to take a crack at it, here's the dataset we're looking at. If you plot the natural log of Temp vs. the natural log of time, it is very close to a line as David originally suggested. I threw out the points between 80 degF (ambient) and 180 degF because those didn't seem to match the curve that the later points had. I then offset the time to start at 180 deg. Time (s), Temp (degF) 0, 180 2, 240 4, 300 6, 335 8, 370 10, 395 12, 420 14, 440 16, 455 18, 470 20, 480 The iterative process David describes below would work, I'm just wondering whether there's any way to take the linear slope and offset from the ln(Temp) vs. ln(time) equation and back out the A and B terms in T(t) = A * e^ (-k*t) + B -Bob David Gregory wrote: > yes, i realized about 10 seconds after i hit send that ln(A + B) != > ln(A) + ln(B). > > I've spent alot of time fitting data of the form Y = A * e^(-k * t), > so I was trying to make that the solution. > > Most of the references i can find online actually write the lumped > model with T-Tinf on the left hand side, where Tinf is the steady > state temperature. > > So, the equation to fit would be > > T - Tinf = e^(-k *t) > > Then you have an iterative process where you guess a Tinf, fit the > curve, calculate Tinf, and then modify your guess. > > > > On 10/14/07, *Ian Woollard * > wrote: > > On 15/10/2007, *David Gregory* > wrote: > > ...ln ( A * e^ (-k *t) + B) > > = ln ( A * e^ (-k *t) ) + ln (B) > > > FWIW that's actually an invalid step e.g. ln(2+3) = 1.609 but > ln(2) + ln(3) = 1.792 > > But it may not matter- if you draw a graph on log paper you often > find you have two lines on it with a curve in between, and you > can use them to calculate A and B anyway (it's because different > terms dominate at different parts of the curve). But you would need > the data to be over a wide enough range for that to work. > > -David > > > -- > -Ian Woollard > > We live in an imperfectly imperfect world. If we lived in a > perfectly imperfect world things would be a lot better. _______________________________________________ aRocket@exrocketry.net http://exrocketry.net/mailman/listinfo/arocket -------------------------------------------------------