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Rostron Energy Analysis of Rossi Experiment
Appendix 8 to New Energy Times Report #3
By William Rostron
I have been following New Energy Times Editor Steven B. Krivit's reports about Andrea Rossi's invention, and LENR in general, with great interest for several years. After reading Krivit's account of his June visit to Italy, I had to weigh in on the analysis.
I work at a nuclear power plant in the U.S. and am very familiar with heat and power measurement, both electrical and thermal. My job for about 18 years was an engineer of the central control system of the nuclear plant. I now write simulator math code for power plant modeling. Heat transfer and power analysis are integral to what I do for a living.
I watched the Rossi demonstration video several times, and I can make a fair assessment of his claims, at least to an order of magnitude. Rossi made several statements that, with a little knowledge of thermodynamics, allow one could make an assessment of whether the device works as claimed.
Rossi did not give any precise numbers, so any evaluation is ballpark figures. Still, he is claiming results that are so significant that, even without great precision, the claims should be confirmed.
The first point that Rossi made is that the input power is, at most, 750 Watts (2 significant digits). He showed an ammeter reading of only 3.4 amperes, so right off the bat we can estimate the input power to no better than +/- 3%. I do not know the power factor involved, but if the power factor is not unity, then the input power would be less than 750 Watts, which would make the demonstration even more compelling than it is. I assume unity power factor for my assessment.
During the video, Rossi clearly stated that the flow rate was 7 kg/hr. That information is all that is needed, along with a qualitative assessment of the steam exiting the rubber hose, to make a ballpark determination of the validity of his claims.
The water source was at room temperature, which I estimate to be about 27ºC.
Seven kg/hr is about 2 g/sec. The enthalpy of water at 27ºC is 113 kJ/kg. The enthalpy of saturated liquid water at 1 bar is 417.5 kJ/kg. The enthalpy of saturated vapor at 1 bar is 2675.4 kJ/kg. The heat of vaporization for water at 1 bar is 2257.9 kJ/kg, so that gives some idea of the relative energy required to boil water as opposed to merely heating water to the boiling point.
I take Rossi at his word that the flow rate is 7kg/hr, delivered by a peristaltic pump. His statement about mass flow rate shows knowledge of the relevant thermodynamics. This is a constant flow rate of about 2g/sec, which is easily accommodated by the small tubing.
At a flow rate of 2g/sec, 750 Watts adds 325 J/g enthalpy, which raises the temperature of the water to saturation (100°C) and creates a slight amount of vapor. The resulting steam quality should be about 5%. The fluid at this point is hot at 100C, but it is mostly liquid by mass, not vapor. We in the power business would say that the steam quality is poor.
I studied the video before I had run any numbers (including the numbers above), so my initial reaction was that there was fairly clean-looking steam at the hose discharge. I tried to imagine what the steam velocity was, but I could not make out any clear picture in my mind. I could see turbulent vapor in the air, but that could have been merely condensation from heat transfer to the air. In short, Rossi's claims might be valid.
As I expected, the steam very quickly transferred heat to the atmosphere, which caused condensation to appear within a fraction of an inch of the hose discharge. The condensate was accelerated with some turbulent velocity along with the remainder of the steam at a rate exceeding a few inches per second. I was estimating this because I could not see the dimensions of anything. But this is clearly within an order-of-magnitude assessment and looked fairly normal. I knew that any condensate has a volume about 1/1,600 the volume of the vapor that it condensed from and that exit velocity is slowed down through conservation of momentum and from transfer of momentum to air. Also, the steam/vapor was difficult to see against the background of the walls. Only when the hose was backed by the dark T-shirt did the nature of the vapor discharge appear. Dry steam is a gas and is clear; however, there is a normal optical refraction because of fluid density boundary effects.
So I decided that, if the steam quality at the exit was anywhere near 100%, there must be significantly more heating in Rossi's device than can be achieved by the electrical input power. At 100% steam quality, that additional power is about 5.5 times the power required to heat the water to saturation that is accomplished by resistance heating alone.
The idea that this could be the case was exhilarating for a while. But I've been taught to validate assumptions and look for independent confirmation. So there had to be a sanity check. As Richard Feynman famously said, "The principle thing is to not be fooled, and you are the easiest person to fool."
Up to this point, I had not calculated what 100% quality steam discharge would look like. Everything so far was just sort of, well, "that looks about right."
So I thought about the kinds of validations that I could do. One was to see what the steam quality would be if there were nothing but resistive heating at 750 W. I had calculated based on the heat of vaporization of water and the initial enthalpy of 113 kJ/kg that water would be completely vaporized with 0.3g/sec flow rate, or 1 kg/hr. I kept the calculations ballpark because of the uncertainty of the numbers. Rossi showed 3.4 amperes of current and said 7 kg/hr. So the uncertainties are rather high.
But, if the flow rate were as stated, and if the steam quality were near 100%, then about 5kW of power had to be generated in the E-Cat device, which is about 5.5 times the input power.
I wrote a letter to New Energy Times stating the above, as a realistic assessment of what I saw at the time.
After I sent the letter, which was done late at night, I went to retire for the night. But I couldn't sleep. Something in the back of my mind just didn't seem quite right.
So I got up and spent the next several hours doing some different kinds of energy calculations to try and validate the visual cues in Krivit's Rossi video. When I got through, I was convinced that the E-Cat could not be working as claimed. But I also recognized that the uncertainties were so large that it could have been working with some sort of additional reaction, just not to the degree claimed by Rossi.
At this point, I had estimated that the discharge hose was about the size of a man's finger, and I set the ID at 7 mm. From that, I calculated that the discharge velocity of 100% quality steam at 2g/sec was nearly 200 mph! Clearly, something was very wrong. There was simply no way that kind of energy was present. But I wondered, Was the hose that small, or was it larger, which would justify the obviously slower exit velocity?
New Energy Times was good enough to send me some high-resolution photographs of the E-Cat, and from them, I was able to determine the hose dimensions more correctly. Based on the components mounted on the E-Cat device, there was a ½ NPT valve fitting on top that could be used as a dimensional reference. From that, and from a frame shot of the video hose end, I determined that the ID of the hose was very near 10mm. This is almost exactly ⅜ inch, which is a standard hose dimension from Parker Fittings.
From this dimension, I could calculate a reasonable expectation for fluid velocity at the exit. The area of the hose is:
(10mm/2)^2 * pi /(100mm^2/cm^2) = 0.79 cm^2
The specific volume of saturated vapor of water at 100ºC, 1bar, is 1.696 m^3/kg. Translating units, this is 1,696 cm^3/g. The exit velocity of dry saturated steam from the discharge hose would then be:
(1,696 cm^3/g) / (0.79 cm^2 )* 2g/s = 4,319 cm/s
or 43 m/sec. [97 mph]
This is closer to what is in the video, but frankly, this exit velocity requirement strains the credibility of Rossi's claim. As a reference, because I had determined the water flow rate that 750 watts would completely vaporize, the exit velocity for dry saturated steam at a rate of 0.3 g/sec would be a more modest 6.1 m/sec [14 mph]. This is a lot closer to what I saw on the video than 97 mph, based on Rossi's claims.
Because the steam velocity at the discharge was so obviously lower than expected, and the uncertainties in the figures so large, Rossi's claims appear to have completely disappeared. But there are more ways to validate the visual cues.
Another way to assess the claims is to look at the power delivery of the system. I had determined previously that it takes 5 kW of power to turn room-temperature water into dry saturated steam at a flow rate of 2 g/sec. 5 kW is the equivalent of 6.5 hp.
Many of us are familiar with the power density of ordinary electric motors, and a 6.5 hp motor is "quite a hoss," as they say where I live. That kind of power will plane a 12-inch-wide yellow pine board ⅛ inch deep at 3 inches/sec. That is also about the power of a high-powered engine steam cleaner. Somehow, I don't think that's what we saw from the video taken in Bologna, Italy.
So, reluctantly, I have come to the conclusion that the demonstration of the steaming rate of the water is more consistent with a power input of 750 Watts than of 5 kW.
In my assessment, I neglected loss of heat through the discharge hose walls. Some loss of heat is inevitable, and that would certainly lower the discharge steam quality. I thought about the dissipation of rubber hose and decided that it was easiest to neglect that factor, because the other uncertainties of input power and flow rate were so large. But just to be fair, any heat loss to ambient from the hose is in favor of Rossi's claims. Loss of heat through the hose walls would be a fair explanation of reduced steam quality at the discharge. But even there, the heat of vaporization of water is about 8 times the heat required just to bring the water to the boiling point, and I couldn't imagine that much heat loss.
There is, of course, a way to lay the power claims to rest, and that is with a precision heat balance. Power companies do this all the time. They use precision instrumentation, calibrated and certified to international standards. Nuclear power plant reactors are licensed for certain maximum thermal power. This requires high assurance that this licensed power value is not exceeded, because safety limit analyses are based on this power. This requires well-maintained precision equipment, backed by certified measurement uncertainty calculations. Such instrumentation and engineering work is expensive but necessary. If there is to be integrity in the scientific process, there can be no substitute for precision and accuracy.
The easiest way to do a relatively precise heat balance with Rossi's device is to use a variable speed pump and a precision scale. With Rossi's device in service, the pump flow rate would be adjusted to obtain slightly superheated steam at one atmosphere pressure, as we saw in the video. There must be enough superheat above instrument uncertainty to verify temperature well above saturation so that there is no doubt about steam quality. Alternatively, one could increase the flow rate to assure that the fluid remains sub-cooled. One should achieve the largest possible temperature differential that meets the fluid phase requirement and addresses the temperature instrument uncertainty.
The internal pressure of the E-Cat must be measured to compensate for changes in water properties, using IP97 Steam Tables for reference. The temperature and pressure of the feed water at the immediate inlet to the E-Cat must be measured, to exclude heat added by the feed pump. The flow rate is determined by weighing the water tank periodically. A heat loss term must be included, based on calculation of realistic test geometry and validated by measurement in control runs with no LENR present. Only after these controls are in place can the input power be matched to the measured heat added to the water. Any excess heat must come from a reaction in Rossi's device.
Brief Biography of William Rostron (South Carolina)
William Rostron is a controls systems expert with 37 years of experience in the nuclear power industry. At his plant, he had lead technical responsibility for digital upgrade to the Integrated Control System and other process controllers. He writes modeling software for the nuclear power plant operator training simulator.
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