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1. Abstract

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.

2. Links

The following links are recommended. Individual sections are referenced in the text.

3. Steam Quality -- the Temperature-Enthalpy diagram

Steam is complicated stuff. For a quick summary, see Spirax : What is Steam?

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.

4. Steam Treated as Liquid Water plus an Ideal Gas

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.

5. Boiling in a Pan or Kettle

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.

See Nucleation

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.

6. Boiling in a Tube

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.

Extensive videos and theory are presented in CANDU Wolverine Tubes : Engineering Databook III (or A copy which works better in some PDF readers ), and in Corradini : Flow Boiling

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.

7. Dryout

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.

8. The eCat

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.

9. Experiments

This document refers to one experiment: Mats Lewan -- NyTeknik and as analyzed in Fakes Document - April 2011

Lewan specifically comments on the hose outlet :

During the April 28 test, we also checked the steam flow through the outlet hose regularly. Some steam was reasonably being condensed back into water in the three-meter-long tube that was exposed to air and was thus at a slightly lower temperature, and a small amount of water was observed coming out of the hose.

The amount of water coming out before boiling was clearly larger, and this was initially measured.

The experimental results were reported as:

If the steam quailty was very low then this would have produced 11 litres of water (almost 3 gallons).

In his report Test of Energy Catalyzer : April 28 Lewan says :

Condensed water and vapor from outlet hose was collected in a plastic bucket with the hose submerged in the water most of the time. Vapor bubbled from the hose under the water surface. After the test the mass of the water was about 5.4 kg.

Unfortunately it isn't possible to determine from this how much fluid water came out of the hose, and how much was from drops in the vapor, or from vapour condensing in the bucket. Lewan doesn't even state whether the bucket was emptied after the eCat warmed up.

A higher flow rate (7 litres/hr) was used for the Krivit demonstration.

In his introduction to his Report #3 New Energy Times Publishes Report #3 on Rossi Device Krivit says:

Our analysis shows a possible energy gain of one to two times. In other words, Rossi’s device probably produces Watts, not kilowatts, of power. It may, in fact, produce zero excess heat. We cannot know with confidence because of the poor data collection and reporting.

The NASA document (appendix 9) implies that any steam quality from 0 (zero excess heat) to 100% is possible.

 

10. Conclusion: Dryout and The eCat

The eCat can be described as a tube boiler.

The nature of the flow in the vertical and horizontal tubes depends on the Steam Quality.

There is a definite Dryout Steam Quality, Xdryout, estimated (by this author) to be between 75% Dry and 80% Dry.

If the eCat is operating BELOW Xdryout, then the flow contains fluid water: the chimney will fill with water and overflow down the outlet hose.

If the eCat is operating ABOVE Xdryout, then there will be NO fluid water in the output.


NOTE : I am still evaluating the following statements in the light of the experimental evidence.

During the start-up phase any water left in the chimney will probably be evaporated by the steam passing through it. When the system is stable the output will be a combination of water Vapour and Water droplets. (As assumed by the NASA calculation).

There is NO evidence that the chimney was full, or that substantial amounts of fluid water left the eCat.

The eCat was therefore operating above the Drypoint.

The steam quality was therefore at least 75%, and the Total energy was at least 4300W.

This is far in excess of the 770 W of input power used during the Krivit demonstration.

11. Work in Progress

The following is an attempt to obtain a numerical value for the Steam Quality at Dryout.

First, we need to consider flow regimes.


flow 7 L/hr = 0.0019444444444444 kg/sec
radius 1 cm area = 3.141589E-6 m2
mass flow = 618.93660960885 kg/sec m2

Wolverine Ch 10 analyzes the boiling stages, including the dryout point. Several different methods (and equations) are presented.

11.1. Baker Flow Regimes

Baker (195X) was the first to formulate flow regimes in 2-phase mixtures (a gas and a liquid) -- initially for the oil industry -- showing the type of flow on a map of Gas Flow (vertical) against Liquid Flow (Horizontal) -- in units of mass/(area second).

Corradini warns that the terms used in considering gas flow are NOT the same as those used in thermodynamics. In particular "Quality" is NOT "Steam Quality". And in this diagram "Bubbly" means bubbles created by the vapour blowing through the liquid, and "dispersed" (or "mist" in some versions) means droplets created by the "wind", not by evaporation.

This flow diagram does NOT apply directly to the water-steam case, where the medium can change from one phase to the other.

But we can get a subjective understanding of the general principles.

The broad red arrow shows a possible progression of Steam Quality from pure fluid flow (off the map at the bottom), through plug, slug, annular and dispersed modes, to pure vapour flow (off the map at the top).

Note that dispersed flow only happens at very high gas flows. (This will be used later to argue that atomization at low steam quality is unlikely).

11.2. Steam Flow Regimes

CANDU (2-phase flows p 14) warns : "Many flow-regime maps for vertical flow have been developed over the past two decades, but only a few of them are relatively useful. ... However, this may be regarded as no more than a rough guide, because the momentum fluxes alone are not adequate to represent the influence of fluid properties on the channel diameter." For example, CANDU regards the the simplified Taitel and Dukler map as the most useful:

Its interpretation of the use of this diagram in the eCat is left as an exercise for the reader.

This is followed by several pages of equations and correction factors.

Recent papers have moved to numeric simulations.

CANDU (p 28) : "Two phase flow is an area of continuous research and development. The
introduction of new calculation tools does not prevent the necessary knowledge
of experimental results on which the numerous correlations are based on. The
careful selection of the solution scheme along with the use of appropriate
correlations is of utmost importance when solving two phase phenomena."

11.3. Dryout Point Calculation

These, and the associated calculation of the dryout point, depend on a large number of factors (including power flux, surface roughness of the tubes, slip ratios, 2-phase friction ...) which are beyond the expertise and resources of the present author.

The author's estimate of the dryout point as "75% to 85%" remains an estimate of what might be obtained in a typical tube boiler.

 

 

11.4. The Tube Boiler Revisited.

The author has the temerity to suggest that these flow regimes (and the corresponding regime maps for steam) are incompletely specified. The water is contained in several states:

  • Fluid Water "F"
  • Vapour contained in small bubbles "B" (where surface tension is dominant, and the internal pressure is above ambient)
  • Drops "D"" of liquid water carried in the Vapour (Gas)
  • Vapour forming the Void "V" (including large bubbles where surface tension is negligible, so pressure is ambient).

The flow patterns probably contain (based on this diagram) :

Flow Pattern Contains Comments
Fluid F Uncompressible fluid
Bubbly Flow F+B Compressible fluid (swollen)
Plug/Slug Flow F+B+V Compressible Fluid plus Vapour
Wavy: Drop Formation starts F+B+V+D Compressible Fluid plus Gas
Annular with bubbles F+B+V+D Compressible Fluid plus Gas
Annular F+V+D Bubbles stop
Post-Dryout V+D No more fluid -- Gas
Superheating V No more drops -- Vapour

The initiation of each stage is associated with a specific Steam Quality and a specific volume of Fluid.

In the absence of a direct measurement of Steam Quality, the amount of Fluid leaving the eCat can be used to set limits on the Steam Quality.

11.5. Pressure Drop

NASA's analysis assumes that the pressure is constant through the system.

CANDU (2-phase flow, p22) notes :

When a coolant expands or contracts because of heat exchange, it has to
accelerate as it travels through a channel. There will therefore be a force F equal
to the change in momentum of the fluid. This force equals an acceleration
pressure drop times the cross-sectional area of the channel. This pressure drop is
usually small in single-phase flow, but can be quite large in two-phase flow.

This is partly due to friction with the walls and, if the eCat is full of water, gravity.

In order to calculate the change of static pressure along a two-phase flow system,
it is essential to obtain the void fraction of the mixture at every point in the flow.
The number of void fraction correlations that have been developed is extensive.
At present, there are over thirty different methods of correlating void fraction
with other flow parameters. Most of these relationships are based on one and
two component adiabatic flow data. Systematic comparisons have been made
between accepted correlations and data banks containing void fraction or
density measurements. Ten parameters may be considered to affect the void
fraction of the mixture for two-phase flow in a round, straight pipe under
adiabatic correlations: ....

Again, the author regrets he is unable to derive numbers for the eCat.

However, where NASA says that the eCat is at atmospheric pressure, and progresses A-B-X (and does not reach C):

The following is more likely, taking pressure into account:

NOTE : This is NOT to SCALE

The pressure near the reactor core is higher than atmospheric pressure. Therefore the eCat goes A-B-E1, where it starts boiling, at a higher temperature than atmospheric. It then moves horizontally from E1 towards E2 as the input energy is increased and the Steam Quality changes with it.

But as it flows through the horizontal and vertical pipes of the eCat and into the wider chimney, it expands adiabatically (a vertical line on the E-H diagram) to a lower pressure at point E3 -- which is the instrument port-- still above atmospheric pressure.

It finally exits through the hose, and drops to atmospheric pressure at the end of the hose, at point E4.

If we take into account the heat losses in the reactor body (80W) and the hose (80W/meter) then we have (NOT TO SCALE) :

We have temperatures for A (input water temperature), E3 (Instrument port) and (I think, from Lewan) the Outlet (E4).

In progress ... I'll get a properly scaled EH diagram and do some calculations.

Since point B on the NASA chart is very close to the measured electrical energy (particularly if we subtract the power of the control box) I expect that the temperature at E1 will demonstrate that the ECat MUST have been producing excess energy in order to boil any water.

12. Future Work

Try to calculate the Drypoint and/or find references to it.

Note : Dryout is a big problem in BWR reactors -- it can lead to tube burnout

Some distinguish between local or partial dryout (eg under a slug or annular film) compared to total dryout, which is what I'm using. The reported qualities for local dryout still have fluid water.

Determine whether an eCat which starts full of water will dry out due to the steam passing through it.

Next up : Some have suggested that even at very low steam quality (5% Dry) the fluid water could be atomized and carried out with the vapour flow. I'll try to quantify this.

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