I was curious about JC's claims about the temperature profile during the warm-up period. Since no one seems to be doing that (or did I miss something?) I have started analyzing the Oct. 28th temperature data in more detail.
I believe the data shows that initially the reactors are off, contain water and the pumps are off. The reactors are then turned on and their power increases linearly to ~475 kW. Thus temperature increases quadratically, until water starts to boil. A couple of liters boil off from each of the e-Cats, causing a rise in temperature (and pressure?). THEN pumps are turned on, causing an inrush of warm water into the reservoir and a corresponding increase in T_in. Stable regime follows. Peak power would be about 490 kW. Power profile : http://imgur.com/iUgJp.png Input temperature : http://imgur.com/PC7P7.png Output temperature : http://imgur.com/qQu0v.png SCENARIO, version 1 (caveat emptor) - At 10:36:07, e-Cats contain approximately 13.5 l of water each at 28.9 C. Pumps are off, reactors are off. The system is in thermal equilibrium. From now on, we assume that the output thermocouple temperature T_out reflects the temperature of the water/steam mixture in the reactors. - At 11:00:04, the reactors are turned on. - The 13.5 l of water they each contain start heating up. - The power level of the reactors rises linearly at a rate of 160 W / s. This can be deduced from the profile of the warm-up period, which is a quadratic function of time to a very good agreement: T_out = 20.37 + 1.423e-6 * t^2 where t is the time in seconds, and T_out is in degrees Celsius. - At 12:34:40 the water in the reactors reaches 100 degrees and starts boiling. - The reactors reach their peak power (492 kW or less) around 13:22:50. - From 12:34:40 to 13:22:50 about 631 l (2 l per module) of water has been boiled off the reactors. - At that moment, the pumps are turned on, causing water to flow at a rate of 675.6 l/h. This can be deduced from two facts. (1) The temperature of the water in the reservoir starts increasing linearly from 16.9 at 13:22:50 to 19.6 at 13:56:10 as 375 l of warm water is pumped back, according to T_in = 16.9 - 0.001351 * t where t is in seconds starting from 13:22:50. (2) The output temperature starts decreasing at the same time, as fresh water is pumped in. (3) Referring to my Nov. 24th post titled "E-Cat 1MW Demo Water Clog Theory", but counting both reservoirs as 2/3 full for a mass of m = 1200 l, we find that the average temperature of the water flowing back must be T_c = m (T_2 - T_1) / m_c + T_2 = 28.24 C which is quite close to the initial temperature. - Stable operation is attained at 13:56:10, with an average output temperature of 105.2 ± 1 C. Mean power is 461.4 ± 30 kW. Total energy produced from 13:56:10 is 8.55 GJ or 2 375 000 kWh. Notes. 1. This scenario doesn't take pressure into account. Because there was no pump after the condenser, a pressure increase of 0.5 to 1 m of water (about 50 to 100 kPa) can be expected. This may raise boiling temperatures by a couple of degrees. Also, pressure increases related to possible water clogs were not taken into account. 2. About the power profile. When boiling water, power transfer depends strongly and in a non-linear fashion on the temperature difference. This hasn't been taken into account. The formula used was : heating_power= ((min(T_out, T_boil) - T_in) * c_p_water + h_fg(T_out - T_boil) + max(0, T_out - T_boil) * c_p_steam) As you can see, this is only a class C^0 function in T_out: its derivative is discontinuous at T_boil. 3. Do not take these at face value. I am not familiar with thermodynamics. It would be nice if that kind of analysis was performed by a properly qualified and experienced person. -- Berke Durak
