Also see :
eCat Steam Quality (with index)
eCat Steam Calculator

1. Introduction

See Report for a description of the experiment.

A SPICE simulation with 100C WATER indicates that the output temperature is affected by the fact that the output thermocouple is mounted on a brass manifold, which connects directly to the HOT inlet from the Ecat.

The most recent simulations indicate that this error is about +20% of the 6 C Delta-T.

Therefore it may invalidate the overall energy calculation.

This computed error value (1.19 C compared to the Output water temperature of 30C -- or about 4%) is probably less than the uncalibrated modeling/simulation accuracy.

It is not clear whether STEAM will give a significantly different value. (The modeling depends on whether we can use MASS flow, or VOLUME flow.)

A more accurate Spice simulation (with calibrated values, a finer mesh, and models of the pipe paste/gaskets between sections) could confirm this, but a Finite Element Model is really needed, as these have detailed properties, and correctly simulate the annular tubes.

In Rossi's favor, it has also been pointed out that the thermocouple to the INLET of the secondary may have poor thermal contact with the incoming water, and might therefore read a HIGHER temperature value (somewhere between the 25C input and 30C ambient), thus reducing the error in the recorded temperature difference.

2. Latest Results (Nov 9, 2011 setup)

The present model is for 100C WATER, not STEAM as the output of the eCat -- so that the heat transfer values between the HOT and COLD sections are identical.

The manifold model has been updated to reflect Bob Higgins' diagram.

This mesh is 0.5 cm (some older diagrams indicate 0.25 cm), which is very course.

The mesh is labeled by column :

Hot : H0 ... H9,HA ... HM
Mid: M0 .. M5
Cold: C0 .. C9,CA ... CS

The thermocouple is located at TCF (Top,Hot,Column F)

Spice Mesh Schematic:

Detail of the COLD side :

Overview : Simulation results showing the water flow, and the temperature of the top surface.

Water Flow

The water in the manifold starts off at ambient temperature (30C).

(A) The hot water initially cools down as it passes through the manifold, heating the copper.
(B) Due to conduction through the copper, water further down the pipe heats up.
(C) The temperature of the cold water outlet stabilizes.
(D) [Oops : not annotated] The Cold water heats up very slightly.

Final temperatures of the Hot and Cold water :

(A) Hot : Cools from 100C to 60.00 C
(B) Cold : Warms from 30C to 30.79 C

Temperature across the top of the manifold.

There is clear "banding" on the cold side, corresponding to the shape of the pipe.

The temperature of the Cold side only: again, there is some banding due to the shape.

 

The temperatures near the thermocouple :

(A) to left of Nut
(B) Thermocouple location -- showing similar temperature across the nut
(C) Cold Outlet

The temperature at the thermocouple and the Cold outlet

(A) Thermocouple TCF : temperature 31.96 C
(B) Outlet CS : temperature 30.78 C
Difference : 1.19 C

However, this error of 1.19 affects the Delta-T (Tout - Tin) of about 6 C -- representing a possible 19.8% error in the eCat output energy calculation.

This new result shows that the result varies with the placement of the thermocouple -- but since the actual measurements are not known, the results are speculative.

NOTE: this model has NOT been calibrated.

The temperature at the thermocouple varies only slightly with ambient temperature (0.01 C per degree).

It also depends on the heat transfer through the insulation or air to the ambient 30C..

Results with connection to "Air" removed : TCF : 32.02 CS : 30.80 Diff: 1.22 = 20.3%
Results with connection through insulators also removed : TCF: 32.23 CS : 30.86 Diff: 1.36 = 22.7%

Also, the effect of any pipe paste or the gasket between the sections has not been modeled. These will also affect the temperature and the heat flow.

The calculated temperature error of 1.19 C (or 3.8 % of the output temperature) is probably much smaller than the errors in the Spice model. A Finite Element Analysis is therefore recommended in order to resolve the issue.

Technical note for Nov 9, 2011 Runs

Hot : 100C Cold : 30C Ambient: 30C
Hot flow 1/40 slower than the cold flow.
Copper Mesh : R =1 C = 1 No connection to ambient.
Hot flow C1 = 10 C12 = 10 Rload = 10
Cold Flow C1 = 10 C12 = 10 Rload = 10
Insulator : 1000
Air : 500

 

3. Calibration

I did not calibrate this model -- I just plugged in nominal R and C values.

BUT the actual stable values will not be much different.

Here is a simple calibration model:

where water flows the entire length of the insulated pipe.

The temperature drop at the midpoint is :

(A) Temperature at top : 98.71 C
(B) Temperature of Water : 99.82 C
Difference : 1.11 C

With the mesh representing 0.5 cm, this is equivalent to a pipe of wall thickness 2 cm.

The water flow is 15 litres/hour (simulation clock tick of 1 second)

There are probably tables of data to compare the simulation with real results.

NOTE: I have regarded this as an axially-symmetric problem -- but the model actually represents a PLATE of copper over a river of water. This could be corrected using different values of R and C in the rows of the mesh.

This simulation presumes an input of 100 C hot water, but the profile is expected to be similar with steam.

The value of the "load" resistor should reflect the heat transfer coefficient from water-to-copper, or steam-to-copper.

Interface

Value
(W/m2 K)

water-copper-air 13
steam-copper-air 17
   

Note : Working on calibration:
Heat loss in uninsulated pipes (W/meter of run-length) 1-inch, 55C delta is 75 W/m Pic

http://wiki.answers.com/Q/Formula_for_Heat_loss_in_a_pipe

http://en.wikipedia.org/wiki/Heat_transfer_coefficient

http://www.engineeringtoolbox.com/convective-heat-transfer-d_430.html

http://physics.info/conduction/

spice, fem ... equations, no values

freiberg thesis RC ladder vs parallel RC

4. Time Log

A spreadsheet of the data :

This is more clearly shown in a graph:

The calculated input and output energies are:

However, the calculate output energy depends on the accurate measurement of the output temperature.

5. The Manifold and Output Thermocouple

Sketch of Manifold by Bob Higgins.

Note that he postulates pipe dope and a gasket between some of the sections, which will have high thermal resistance.

6. Spice and Thermal Modeling

Spice is a program for electrical circuit simulation ... calculating the voltages and currents in circuits composed of resistors, capacitors and many kinds of transistors.

It can also be used to simulate heat, with the following equivalences:

Electrical Thermal
Voltage Temperature
Charge Heat
Current Heat Flow
Resistance Thermal Resistance
Capacitance Specific Heat

Spice will be used to model the manifold of the heat exchanger.

I am using LT Spice , which includes a schematic editor and a waveform viewer.

(I will make my simulation files available for anyone who wants to try it out.) NOTE : I have not yet calibrated these models, so they will show the general "scope" of the problem, but not (yet) the exact numbers.


WARNING : results reported below this line have NOT been updated to reflect the latest models and Spice simulation settings. They are included to illustrate the methodology.


7. Models

I will start with a simple "Tube" model of the manifold:

Here is the Spice Network:

Hot, 100C water enters at the left, and departs at the middle. Cold, 30 C water enters at the middle and leaves at the right.

Heat propagates through the "mesh" ... which connects at the edge to a layer of insulation.

Here is a detail from the lower-left corner:

BLUE: The water flow is simulated by a "Charge Coupled" shift register. The initial voltage (100 C) is applied to the left, and is stored in the first cell as charge on a capacitor (proportional to the volume and the specific heat of water). With each "Tick" of the clock, this charge is transferred to the next stage.

ORANGE : Heat is conducted into the MESH, through a Resistor -- whose value represents the (technical term?) conductivity between water and brass.

YELLOW: Heat entering a mesh cell is used to WARM it up ( charge stored on the mesh capacitor), and also flows as current through the mesh resistors to adjacent mesh cells.

GREEN: at the edge of the mesh a resistor represents the insulation to the ambient temperature.

RED: As an alternative to a "transient" solution, a set of resistors can apply a DC Voltage (temperature).

Note : but Spice doesn't like to do this DC analysis... it slows down as the system converges.

Here are the details of the "Water" cell :

Charge is transferred onto the Capacitor C1, which then discharges through the resistor R1 to the bottom of the mesh. (Or, in the case of the "Cold" side, C1 can charge UP (gaining voltage or temperature).

The transfer of charge is done in two steps of the clock -- "tick" and "tock".

At the next "tick" of the clock the charge from C1 is COPIED onto a holding capacitor, C12.

At the following "tock" of the clock, it is copied from C12 onto C1 of the NEXT stage.

For the "DC" solution, we apply a voltage directly onto the load :

NOTE this has changed. C1 connects directly to the load resistor.
The DC input E2 and switch SW3 connect to C1 (and similarly, to C12).

The ratio ladder can be used to pre-load the pipe with temperatures close to the final result.

This completely bypasses the CCD capacitors.

A MESH cell looks like this :

The other two resistors forming the mesh are contained in adjacent cells.

Note : the actual values are contained in subcircuits, so they can be changed everywhere at the same time.

Finally, the insulation layer provides resistors to the ambient temperature:

An "Air" resistor is used at a surface where there is no insulation.

8. Simulation of the Tube Model

Here is the LtSpice screen : The Waveforms (voltage vs time) are at the top, and part of the schematic is at the bottom:

NOTE : this model has NOT yet been scaled correctly, so the times shown are not actual real-time seconds. Since we are only concerned with the final steady state, this does not matter.

First, consider the simulation of the flow of water through the tube, which starts "empty"

A: The Voltage (temperature) of the first cell starts at the Ambient temperature of 25 C. (RED Trace)

B: At the first clock cycle one "packet" of water at 100 C enters the first cell.

C: So its voltage/temperature immediately rises to 100C.

D: It immediately starts discharging into bottom of the manifold.

E: At the NEXT clock cycle, the charge from the first cell is MOVED onto the next cell (Green Trace), and the first cell gets a NEW charge at 100 C.

If we look at the bottom of the Mesh :

we can see the temperature rising more smoothly from the ambient. (A and B), and at the top of the tube, it is smoother still:

Now let's look at the complete flow in the Hot and Cold sides:

A: On the HOT side the temperature rises slowly from ambient (because it is warming up the manifold).

B: On the COLD side, which started closer to ambient, the water only warms up a little.

C: Once it is stable, we can see a large drop of temperature on the HOT side (the left side is at the TOP)

D: and on the COLD side we can see a small rise in temperature (Left side is at the bottom).

The reason for this difference is that the HOT side is flowing 10X slower than the HOT side (the caption saying 40X is wrong). This is achieved by providing a FAST (1 second) clock to the cold side, and a slow (10-second) clock to the hot side.

But now let's look at the temperatures on the TOP of the tube:

NOTE Nov 9, 2011 : this has not been run with the latest Spice settings (mostly, precision).

Houston ... we have a problem !!!

The water in the cold side is only at 30C (plus a little heating through the manifold) ... but the temperature at the END of the top of the tube (A) is 48 C !!!!!

And as we move it from the end of the tube towards the center, it gets even worse.

9. Tube with 40X Flow

The previous section set the Hot flow to be 10X slower than the Cold Flow.

Here is the water temperature at 40X ... the simulation is a little course, so the HOT water shows a distinct "sawtooth" pattern. The COLD water shows an even smaller temperature rise than for the 10X example.

And here is the temperature at the top of the manifold :

This is a little better .... but it is still a major error compared to the cold water temperature.

Perhaps it will be better if we use a slightly more accurate model.

10. Stepped Manifold

The varying sized pipes are represented by stepping the tube radius. Here is the Spice Model:

NOTE: the caption says the grid is 1/4 cm ... but it's closer to the actual manifold if we use a 1/2 cm grid.

The water flow is similar to the tube model :

But the temperature along the top of the manifold is not very different:

We still have a 10C ERROR even with the thermocouple at the extreme right.

NOTE : See the UPDATE at the top of this document. With the new wider manifold model the temperature difference is down to 3.4 C at the extreme right.

NOTE: Bob Higgin's diagram suggests that the inside of the pipe is also stepped. This is used in the "final" model.

11. Next Steps

This model shows that there is a possible problem with the placement of the secondary output thermocouple.

The accuracy of the model can be improved by

a) Calibrating the various components.

b) Modeling a more accurate geometry -- but to do that I would need a better estimate of the size of the manifold. (I would generate a net list with a program). UPDATE : a wider model has been made.

However, Finite Element Model simulators would do a better job, and they have built-in properties for the various components.

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