**Lugano active run period 16 recalculation - The ECAT worked - COP was 4.98**

With the FEM model developed we can analyse, using finite element analyses, the thermal behavior of the dogbone shaped ECAT for an active run.

We are doing this analysis for the last active period 16.

The electrical power data for this period given by the Lugano report is :

Total power consumption was 906.31 Watt

Joule heating was 41.25 Watt

This leaves 906.31 - 41.25 = 865.06 Watt for heating coil wire.

Since about 4 cm of heating wires continue in the rods, the total power in the ECAT itself is somewhat less and is calculated as being 735.08 Watt

The average measured temperatures reported for active period 16 are

----------Temperature (C)-------Temperature (K)

Cap 1----------611.09-------------------884.24

Cap 2----------595.15-------------------868.30

Body--------- 1412.31-----------------1685.46

The report only gives for the active periods only the accumulated powers of the end caps , body and rods, not the seperate ones.

However using the average temperatures given above we can calculate the approximate powers.

We must indeed redo these calculations since for the body the Lugano team did not take into account the correct total area of the ribs, the view factor, the emissivity change due to the view factor and the correction needed for the convection of the ribbed surface. Also the temperature measurement of the body by the Optris camera was influenced by the change in emissivity due to the infinite reflection method.

So the first thing to do is recalculate the average body temperature to the correct one.

For the mentioned temperature the used emissivity on the Optris is .950

View factor between the ribs is 0.428

This changes the alumina in band emissivity to be used on the Optris from .950 to 0.971

Using both the original and the corrected emissivity we can calulate the correct body temperature.

The found body temperature is 1389.91 C ( n value 1.518).

Having found the correct average body temperature we can now determine the emissivity and the convective heat transfer coefficient for the ECAT body

Emssivity--------------------------------------------0.392

Convective heat transfer coefficient-----14.542

And with both values we can calculate the convective and radiated heat power of the body :

Radiated body energy-----------3453.17 Watt

Convective body energy----------523.55 Watt (uncorrected)

Convective body energy----------269.10 Watt (Corrected with factor .514 extrapolated from earlier simulations)

Total radiated and convected power of the body area is

3453.17 + 269.10 = 3722.27 Watt

For both caps we find :

Cap 1

----------Radiated cap energy------101.79 Watt----( e = 0.592 )

----------Convective cap energy-----34.05 Watt----( h = 11.481 )

Cap 2

-----------Radiated cap energy---------95.36 Watt----( e = 0.597 )

-----------Convective cap energy------33.06 Watt----( h = 11.457 )

The total thermal power comming from the ECAT after recalculation becomes then

3722.27 + 101.79 + 34.05 + 95.36 + 33.06 = 3986.53 Watt

This total power is much higher then the 2886.18 Watt reported and this increase is due to the recalculation of the power of the body area.

For the rods the Lugano report states a value of 88.47 watt due to radiation and 87.94 watt due to convection. The convection is overestimated since the testers used a correction of .667 instead of .561. Thus the convection shoud have been 87.94 x (.561/.667) = 74.00 Watt

Total rod power for one set of rods then becomes 88.47 +74.00 = 162.47 Watt

For two sets of rods the total power becomes 2 x 162.47 = 324.94 watt

Total power for both the rods and the ECAT then becomes 3986.53 + 324.94 = 4311.47 Watt

**The new calculated power leads to a COP of 4311.47/865.06 = 4.98** , higher then the COP of 3.74 mentioned in the report.

By now assigning the calculated ECAT power of 3986.53 Watt to the heating element of our FEM model, we can with the model calculate the approximate internal and surface temperatures and compare them with the data in the Lugano report. The results are :

---------------------------------------------Lugano---------FEM simulation----------Difference (%)

Setpoint temperature---------------1400----------------1436----------------------- 2.6

Average body temperature--------1412----------------1367----------------------- -3.3

Note that the actual average body surface temperature found by the FEM simulation was 1339 C

However for comparision with the Lugano report we must correct this temperature due to the misreading of the Optris as defined by the infinite reflection method.

The corrected temperature is 1367 degree C (n factor 1.570) and this is the temperature reported in the table above.

The setpoint temperature is the temperature in the inner core of the ECAT.

In the Lugano tests this setpoint temperature is measured by a thermocouple and by adjusting the power the testers where able to arrive at the required temperature setting.

Note that the setpoint temperature measured from the FEM data is close to the reported setpoint value of 1400 degree C the Lugano testers used for active period 16. Also the reported body temperature is close to the simulated temperature.

Note that the above calculations are approximations since they where based on average temperatures reported.

Despite using the average values in the above calculations my conclusion from the close agreement between reported data and the FEM simulation data is that the ECAT indeed produced excess energy with a COP of about 4.98 during period 16 of the Lugano report.