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The issue of Steam Quality greatly impacts the calculations on the actual excess energy.
This issue is extensively analyzed by Steven B. Krivit in New Energy Times Issue 37
In particular, Appendix 9: NASA Electrical-Power-Only Steam Analysis reviews the performance of the eCat in relation to an Temperature-Entropy diagram, and states that the Steam quality could be any value between 0 and 1, so that the total output power could be anywhere between 770 W (NO excess energy), to slightly above Rossi's claimed value of 4900 W.
This article shows that NASA's analysis omits significant facts about the behaviour of steam.
First, we review some basic facts about steam, particularly the concept of steam quality, and the use of a temperature-enthalpy diagram. We then consider the detailed behavior of boiling water in a "Kettle" boiler and a "Tube" boiler.
In thermodynamics water is "liquid" or "vapour". But the liquid may be carried as droplets, or as bulk liquid. Following CANDU, we will refer to bulk liquid as Fluid water (which may contain bubbles), and the vapour part as Gas, which may contain drops of liquid water.
In a tube boiler, such as the eCat, the distribution of liquid water and water vapour depends directly on the Steam quality. As steam quality increases from 0 to 1 the flow changes in stages from pure fluid, bubbly fluid, plugs of gas/slugs of fluid to an annular arrangement of fluid water and vapour containing droplets. At a specific steam quality a "Dryout" occurs : there is no more fluid water in the output. Any remaining water will then be carried as droplets in the water vapour. This "Dryout Point" is estimated by the author to be between 75% dry and 80% dry.
If the eCat is operating with a steam quality BELOW the dryout point then fluid water will eventually fill the chimney and flow out of the outlet hose. If the eCat has steam quality ABOVE the dryout point, then the chimney will empty, and there will be no fluid water in the outlet hose.
The author believes that the experiments show that the chimney is NOT full of water, and that significant amounts of fluid water are NOT in the outlet stream. (Note ... Lewan's report makes this doubtful. )
The MINIMUM steam quality is thus ABOVE the dryout point, which means that the steam quality is above 75% Dry, and the total power is over 4300 W, much larger than the electrical input of 770 W.
Note 1 : this is a working draft. Some of these calculations have been "eyeballed", and will be replaced with more accurate numbers. Check back frequently for updates.
Note 2 : when researching "dryout" be sure to distinguish between "local dryout" (Leidenfrost), and "total dryout", when there is no more water.
- CANDU: Introduction to Thermodynamics
- Wolverine Tubes : Engineering Databook III (or A copy which works better in some PDF readers ).
- Corradini: Fundamentals of Multiphase Flow
- The official, international definitions of Steam : The International Association for the Properties of Water and Steam.
- Steam tables are available online at NIST: Thermophysical Properties of Fluid Systems
Just to set the stage, consider what happens in a closed system, viewed as a Temperature-Enthalpy diagram
The vertical axis is temperature, and the horizontal axis represents the energy added (usually expressed as enthalpy).
- Start at point A, with liquid water. As you add heat the water warms up, and you will move towards point B.
- What happens next depends on the pressure. When you reach point B, for a particular pressure, the water will start to boil.
- As you add more heat the temperature will not change, and you will move a point X horizontally towards point C. Along this line, you will have a mixture of water vapour and liquid water. The ratio of the mass of of the vapour to the total mass is expressed as the Quality of the steam, X, which varies from 0 (point B) to 1 (Point C). This Quality is expressed as a fraction, 0.95, or sometimes as a percentage -- eg "95% Dry" or even as the percentage of liquid water "5% Wet".
- When you reach point C there is no more liquid water, and the steam is said to be completely Dry : Quality 1.0, "%100% Dry" or "0% Wet".
- After point C the temperature will start to rise again, towards point D.
Now let's look at NASA's diagram:
As before, the vertical axis is temperature, but NASA has kindly scaled the X energy axis to indicate the power (W) required to raise the known volume of water (7 litres/hour) to the specified temperature.
The input power of 770W (for the Krivit demonstration) is enough to raise the water above boiling point, to what looks (by eye) to be about 5% Dry. Rossi calculated the energy, based on a quality of over 95%, to be 4900 W.
The yellow box in this diagram reads:
Again, once the water begins to boil and vapor starts to be produced, there are a wide range of input levels which will sustain an output of steam as some quality between 0 and 100%
The measured temperature of the steam at the output is reported to be at boiling point. So we have not yet entered the region of superheated steam (C-to-D on the first diagram.) The total energy input of 770 W includes 30W (measured in some of the experiments) to power the control box, and neglects any losses inside the eCat, which Rossi estimates at 80 W (assuming a 4900 W output).
NASA claims that the point X could be anywhere between the 770W mark (the electrical input energy), and the 5000W mark. On a theoretical basis, this is true. The actual output of the eCat could be in serious doubt.
Given a total mass of water, M which is made up of liquid, Mass Ml, and vapour, Mass Mv, the Steam Quality is expressed as
X = Mv / ( Ml + Mv)
An Ideal Gas follows the following law:
PV = NkT
where P is the pressure, V is the volume, N is the number of molecules, k is Boltzman's constant, and T is the temperature (In degrees Kelvin, ie starting at absolute zero).
For our purposes, knowing the mass of a water molecule, we can replace the "Nk" term with "k1 M", so PV is proportional to the mass of the water vapour :
PV = k1 M T
Rearranging, we could write it as:
PV/T = k1 Mv
Finally, we plug in the steam Quality X and use the Total mass of water Mt, so the gas law for the Vapour part of the liquid/vapour mix is:
PV/T = k1 X Mt
Since the volume of steam at atmospheric pressure is about 1700 times larger than the volume of water, the overall calculation uses the volume from the vapour only, and presumes that the drops of water are just carried along with it.
It is sometimes convenient to consider the quality by the Volume of the liquid (Vl) and vapour (Vv). This is called the "Void Fraction" (The NASA paper calls this the "Volume Fraction").
a = Vv / ( Vl + Vv)
That's easy enough, right?
Everything you need to know to analyze an eCat (or a conventional nuclear reactor!) is in here : Introduction to Thermodynamics (You can skip the stuff about pumps).
THAT's easy enough, right? Yeah ... right. Everything is complicated, nonlinear and/or not fully determined.
As an interlude, let's see what happens when water boils.
You put a pan on a heater. Bubbles start forming on the bottom. Then they form streams, which reach the surface and break. Finally, you have a roiling, frothing boil. A couple of videos are here and here.
As usual, it's very complicated, and goes through several stages.
Boiling from a heated wire. (A bit got lost in the translation). As more heat is applied the following stages occur:
First, isolated bubbles appear. Very small bubbles are dominated by surface tension. In fact, the pressure inside a small bubble can be much larger than the ambient 1 atmosphere pressure.
The bubbles might not even rise to the surface. In an industrial kettle boiler the water increases slightly in volume, and is said to "swell". As bubbles get larger they rise to the surface, often streaming from a nucleation point.
This zone is also referred to as Superheating.
The bubbles get larger, and can form tubes, reaching the surface.
In stable film boiling, this photograph implies that droplets of water can be produced directly.
In a final stage vapour can form between the liquid water and the film, reducing heat transfer. This is the Leidenfrost Effect, which causes a droplet to skitter on a hot surface.
Further links : Corradini : Pool Boiling
There is general consensus [links..] that a kettle boiler will produce 95% Dry steam.
The Rossi eCat is clearly not a kettle boiler. It is a form of Tube Boiler, complicated by the coaxial "bulge" around the reactor core, and the fact that we don't know for sure how the heat transfer works.
Instead of heating the water from the bottom of a kettle, water is introduced from the left and flows to the right. If heat is introduced at a constant rate the liquid/vapour configuration will progress along the tube, from left to right:
This is generally recognized in the literature as a flow which progresses from pure fluid at one end (X=0) , to pure vapour at the other (X=1):
Note the progression from Single-phase-Liquid, to Bubbly Flow, Plug Flow, Slug Flow, Wavy Flow, Annular Flow and .. at the extreme right -- where there is no more FLUID, drop flow and finally, when the Steam Quality exceeds 1 -- superheated steam.
From Wolverine, here's a similar diagram for vertical tubes:
- On the right the vertical axis describes the physical height along the tube.
- On the left the vertical axis is the Steam Quality X.
Above a specific position marked "Dryout" there is NO MORE fluid water. All the water is carried as drops in the vapour.
The following diagram specifically scales the steam quality to the flow diagram and identifies the Dryout point "F", at a steam quality of approximately 80% Dry.
The conclusions of this paper are effectively obtained from these diagrams.
We can similarly identify this "Dryout" point for the horizontal case:
In the horizontal case the dryout is different, because gravity causes the fluid water to pool at the bottom of the tube:
If the heating section stops at a particular point, it is presumed that the final "flow" will continue in the same mode.
In the ecat there is a change from horizontal to vertical flow: any "pooled" fluid water will revert to annular (or even slug) form.
Dryout occurs at some definite value of Steam Quality, Xdryout.
Based on the Vertical diagram it appears to be at about 75% Dry.
The author is attempting to obtain a more accurate value for Xdryout, assuming the eCat operates as a horizontal tube boiler.
I will use the following diagram of the eCat, (crudely) adapted from Appendix 19: Anonymous Mechanical Engineer's Effective Method to Measure Power and Energy of Steam
1: Cooling water is pumped in
2. A "Start" heater (probably more than 300W) raises the water temperature.
3. A Heater band surrounds the reactor core
4. Hydrogen is introduced into the reactor core.
6. If the eCat is real, additional heating is produced by gamma rays, probably as they are absorbed in the copper pipe and/or the surrounding lead shielding. This section acts substantially as a tube boiler.
5. Water exits the reactor in the horizontal tube. The flow in this section depends on the Steam Quality. (Liquid water, bubbles, slugs, annular, drops ..).
7. The output tube becomes vertical. The flow structure is maintained, again depending on the Steam Quality.
8. It then expands into a chimney. Slugs or bubbles of vapor may become separated from any water liquid water. An instrument port penetrates the chimney, below the output level.
9. The output from the eCat is a mix of Fluid water, Water vapour and Drops of Water.
10. (Not illustrated). The water exits through a hose. Cooling in this section will result in a different Steam Quality and flow type at the end of the hose.