Posts by LDM


I have the definition for the derivation of n as used in the Optris equation somewhere. It also explains why n is 21 for the shortwave end of the IR spectrum, as in the image that Whyttenbach posted a long time ago. The number is not a fixed value, (as is represented in the image), but has to do with the relative proportion of the power that is contained in various wavelengths or spectral ranges within a true blackbody spectrum. I'll try and dig up the source so I don't muddy up the explanation further.
I am still interested in the explanation because doing some verifications it seems that the factor n could also be dependent on the measured temperature.
So I would appriciate if you can dig up the article for me.
LDM

I agree that incorporating more of the long wavelengths will reduce the integrated in band emissivity.
Perhaps since once a temperature is assigned to a particular emissivity using a particular bandwidth,
Are we talking about broad band or in band emissivities ?
And what do you consider bandwidth, the width of the band or the spectrum range of the band ?
translations to other emissivities at a new respective temperature using the same bandwidth is essentially independent of the bandwidth used.
If we are talking about the same spectrum range then indeed the radiant energy received in that band has to be constant and translating temperature with it's emissivity is for that spectrum range defined.
This is the basis of my in band radiant power matching scheme that I used in early calculations that ended up supporting Clarke's paper when I initially disagreed with it.
This assumes that the radiant power received by the detector is constant, no matter what the user selected emissivity setting and the respective temperature reported by the camera or pyrometer is.
Totally agree.
However the translation is also dependent on the ambient temperature and a factor "n"
See the formula for U on the righthand top of page 9 of the Optris IR basics document.
Since U is constant for a certain case (Constant radiant power received) , we can equate two times the same formula with each side having it's own emissivity and temperature. (The pyrometer temperature cancels out when equating).
For high temperatures we can discard the ambient temperature and the equation leads then to the conversion formula used by the MFMP in which they assume n to be 3.
For lower temperatures you can not discard the ambient temperature.
Also there is the question if n is indeed 3. Optris states that it is between 2 and 3.
Some calculations I did in the past gives me the impression that it is about 2.75, but the difference in calculations using 2.75 or 3 is only small.
I will attempt to email Mr. Rozenbaum and Mr. Manara and see if they are willing to share some spreadsheets of alumina spectral and total emissivity values.
Also ask about the transmittance of 9 %
Seems high to me, so I wonder if the Alumina they tested was partly doped or was processed to have a high density increasing the transmittance.
Again thanks for the work you put in your tests.
Combined with the short FEM simulation it shows that for calculations of Durapot the material data of Alumina can be used. (At least that is my conclusion)
I could not have come to that conclusion without your experimental data.
I will be going to Norway for two weeks and will start following the thread again after I return.

LDM ,
What alumina spectral emissivity curve are you using for your in band calculations?
Are you accounting for the broadening of the high emissivity area with increased temperature?
(See Figure 5, Manara et al 2009, from my earlier reference.)
I don't remember where I got them from, but incorprated it in a computer program for calculating the in band emissivity. And I used the program to calculate for 814 um.
However i found that there are two types of Alumina curves seen in Literature, some like the one you referred to which become broader with higher temperatures, but also others which are shifting to the right with higher temperatures.
I don't know why for the same material (Alumina) there are two type of curves, but the ones shifted give closer results to the recomended setting of .95 for the in band emissivity.
But also for the curve you supplied, if you shift the band from 7.513 um to 814um then you incorporate a larger part (on the righthandside) with lower values and as a result your in band emissivity will drop.

If I did my math correctly, the average temperature of the cylinder at the end of testing was 814 C, so about a 'COP" of 5 may have been accomplished.
That is using from left to right, 2.1 cm @ 727 C, 1.0 cm @ 850 C, 1.5 cm @ 894 C, 1.0 cm @ 880 C, 1.0 cm @ 767 C. (Measured carefully by pyrometer scanning and glow intensity).
The lengths of the cool outer ends are exaggerated somewhat, as they are the coolest temperatures recorded for each end, and as such are less than the actual averages over the ends.
I did a quick FEM simulation of your cylinder.
Material properties of Alumina where used.
Since I did not know the exact length and postion of the heater coil, I distributed it evenly over the full length. As a result my end temperatures are higher.
However the center temperature of the simulation was 892 degree C, very close to the 894 C measured.

This also seems to indicate that the difference in detector emissivity sensitivity between the Optris camera (7 to 13.5 micron) and the pyrometer (8 to 14 micron) is negligible.
I was curious if indeed the differences are minor.
So I recalculated my in band emissivities for the 814 um range. See below
The numbers are for the 814 um range somewhat lower, which is what is to be expected since near the 14 um the Alumina spectral emissivity curves are dropping of, resulting in more lower values integrated.
T C)e Optris e 814 um
20.10.832 0.746
277.90.878 0.820
302.80.881 0.826
330.00.886 0.832
344.20.888 0.835
402.00.896 0.848
438.10.900 0.855
502.90.908 0.868
516.40.910 0.870
560.80.914 0.878
631.90.922 0.888
702.90.928 0.898
728.40.930 0.901
801.20.935 0.908
854.90.938 0.913
914.00.941 0.917
990.10.944 0.920

If I did my math correctly, the average temperature of the cylinder at the end of testing was 814 C, so about a 'COP" of 5 may have been accomplished.
That is using from left to right, 2.1 cm @ 727 C, 1.0 cm @ 850 C, 1.5 cm @ 894 C, 1.0 cm @ 880 C, 1.0 cm @ 767 C. (Measured carefully by pyrometer scanning and glow intensity).
The lengths of the cool outer ends are exaggerated somewhat, as they are the coolest temperatures recorded for each end, and as such are less than the actual averages over the ends.
Nice work !
What power setting did you use for these results ?

I just did a Spice simulation and it looked sketchy still.
Scrounging around for a 2:1 transformer...
What about using Kantal wire to make a series resistor ?

If I purchase the Aremco Pyro Paint (seems to be $100 US per pint, plus shipping), I may coat the Durapot devices and compare the emissivity changes.
Instead of using the Aremco Pyro Paint you could instead paint it with Aremco 840CM high emissivity paint which was also used by the MFMP.
Using high emissivity paint will give near accurate temperature readings with your pyrometer since Aremco gives for several temperatures the emissivity spectrum of the paint from which the in band emissivity can be estimated/calculated.
You can then make a callibration curve for the surface temperatures measured with the pyrometer and the thermocuple temperatures near the surface.
That makes it possible to translate the thermocuple temperatures measured with the Durapot cast to their approximate surface temperatures.
Then you will able to calculate back, after subtracting from the coil power the calculated convective power, the broad band emissivities for Durapot.
Using the established surface temperatures for the Durapot, you then also can adjust the in band emissivities of your pyrometer to match the established surface temperatures.
This will give you the in band emissivities to be used with your pyrometer when measuring the surface temperatures of Durapot.
That would answer some of the questions about the characteristics of Durapot.

LDM , what IR bandwidth is your alumina data referring to? 7.5 to 13 micron (Optris range)? 814 micron?
I calculated it for the Optris range
Edit: The in band emissivity of 0.878 was calculated for the temperature of 277.9 C.
For the temperature of 257.5 degree the value is .875.

Could you please produce a table, similar to the one I posted above, with your calculated emissivities for alumina at various temperatures?
See the table below with your temperatures and the emissivities I calculated for those temperatures.
Note that below 500 degree C the numbers are from an extrapolated curve fit and thus will be possible have a larger error then the ones above 500 degree C
I would like to compare the temperature variance of the alumina (paint?) to the Durapot at similar temperatures.
I won't bother with calculating power using the results, I just wan't see what the temperature difference might be.
For me it does not matter if you calculate power or temperatures with it. Feel free to use the numbers as you like.
T (C)e
 20.10.832
277.90.878
302.80.881
330.00.886
344.20.888
402.00.896
438.10.900
502.90.908
516.40.910
560.80.914
631.90.922
702.90.928
728.40.930
801.20.935
854.90.938
914.00.941
990.10.944


I am wondering what the purpose of your test is.
We know already that wrong emissivities used on the Optris will yield positive COP's for heater coil type devices.
Nevertheless if it is any aid for you then If you can supply a dimensional drawing of your device with also the dimensions and position of the heater coil I could make a CAD model of it and use that for a FEM thermal simulation.
That would give us also an idea how well the FEM modelling software fits the experiments.
The next days till after the weekend I am off to Berlin, but could maybe after that find some time for it.

Lugano rods stacking dimensions
In order to calculate the convective heat transfer correction factor for the Lugano rods, we need to know what the distances between the tubes are.
I had thought that the distances between the tubes would still be rather large, in the range of 5 a 6 mm.
However if we look at the following picture where we have drawn the outlines of the tubes, we can already see that distances between the tubes are rather small.
To calculate the distances in an accurate way, a picture of the set up of the rods was loaded in a CAD program.
Using perspective information derived from the support frame to correct the view of the rods to a front view I was able to reconstruct the distances between the tubes.
Since only the placement of 2 tubes could be determined, it was assumed that the third one was symetrically placed with respect to the vertical axis.
The calculations showed that the rods where equilateral stacked with 1 mm spacing between the rods.
In principle we now could have calculated with the equivalent diameter method the correction factor (see earlier post in this thread).
However since the equivalent diameter method is intended for calculating the correction in bank of tubes, where the distances between the tubes are still rather large, I wonder if that method gives accurate results for such small distances.
The intention is now to simulate a single tube and also three stacked tubes in a CFD (Computional Fluid Dynamics) program in order to calculate an accurate convective heat transfer correction factor.
As stated earlier I still have to gain enough experience with the CFD program to do that, so it can take a while before there will be any results (Or maybe no results at all).

Influence of view factor on measuring the temperature of the top and bottom of a Lugano style fin.
In an earlier post we showed the effect of the view factor between fins on the thermal calculation. One of the factors is that the apparent emissivity changes by a factor
1/(1  F_{ff}(1ε))
The correction is dependent on both F_{ff}, the view factor between the fins and e the emissivity used, The recommended setting for e for the Optris being .95
The view factors can be calculated with the NIST program view3D by using an area around the circumfence of the fin with a small height compared to the height of the fin.
In our calculation we used a height of .05 mm for a circumfence at the top and the bottom.
The results of the calculation for the top and bottom of the fin are :
View factors (fin to fin)
Top0.007
Bottom0.747
Using the emissivity correction formula and the found view factors, the emissivity correction factors are :
Emissivity correction factors
Top1.0035
Bottom1.0388
And the corrected emissivities become :
Top0.950
Bottom0.987
Since the corrected emissivity at the top is the same as the used emissivity, the temperature shown by the Optris for the top will be correct.
For the bottom of the fin the higher emissivity means that the in band radiated power per area is a factor .987/.95 = 1.039 higher.
Since the temperature of the Optris is by approximation proportional to the power 1/3 of the power density it means that the Optris will show the temperature higher by a factor 1.039^(1/3) = 1.013. (temperature in degree Kelvin)
If we take as an example a temperature of 750 degree C or 1023.15 degree K, then the corrected temperature becomes 1023.15 * 1.013 = 1036.264 degree K or 763 degree C.
Thus the temperature shown by the Optris for the bottom of the fin will be 13 degree C higher then the real temperature (assuming in in band emissivity of .95 was set on the Optris). The total temperature difference between top and bottom of the fin as measure by the Optris now becomes the real difference plus the calculated correction.

Wat about casting a round tube with a heater coil embedded, say for example 10 cm long and then cast only one rib in the middle.
You can then measure easily with a thermocuple the temperature at the base of the fin by mounting a thermocouple on the tube next to the fin.
Since the thermal mass seen by the thermocuple is large, the deviation in temperature measurement will minor.
(You can also run the thermocuple wires for a short distance over the tube to reduce thermal drain from the tip)
The fin itself can be measured by a thermal camera pointing perpendicular to the surface of the fin if the thermal camera has enough resolution to resolve temperatures between bottom and top of the fin.
Since there are no opposing fins there will be almost no influence of view factors on the emissivity and thus the measured temperatures will be representative for the temperature distribution over the fin.

I don't think that the view factor has much effect for the camera, as long as the resolution is is not such that individual valleys and ribs can be clearly imaged. (And even then I wonder.)
As I stated I have seen a document of one thermal camera manufacturer in the past explicitly warning for the problem that the change in emissivity by ridges causes an additional error on the measured camera temperature. So while the camera will average the reading over the ridges, this reading will most likely be somewhat off.
Otherwise the Lugano reactor images of the main tube area would appear hotter in the middle (normal to the camera lens, valleys visible to the lens) and cooler towards the caps (oblique to the lens, valleys obscured by ribs)
What the effect is of not seeing the valleys to the end depends also on how large the temperature difference is between the tops and the valeys.
What I want to try if I can find time for it is to make with view3D an estimate of the view factor at the bottom and the top and then calulate the emissivity corrections.
That will give us an indication how much of the temperature difference between top and valley is due to the differences in emissivity.
It might be interesting to know this since it was stated somewhere in the past that the temperature difference between the top and valley could be near 100 degree C at higher temperatures.
If that is true then towards the caps where as you say the valleys are (partly) obscured, the temperature seen near the caps by the thermal camera should drop significantly.
However if the thermal camera by your statement is not seeing this temperature drop, then it would mean that the temperature differences between tops and valleys are much lower then that 100 degree C.
So I want to explore if some of the larger reported temperature differences can be explained by the differences in emissivities between top and bottom.
At least it will maybe tell us if it is something we need to take into account or not.

Did you integrate the radiant power for the in band emissivity at various temperatures, and then determine a suitable in band emissivity, or just average the in band emissivity values?
I did it by numerical integrating over the in band frequency range the black body spectrum times the alumina emissivity devided by the black body spectrum.
From 0.86 to 0.95 over a very wide temperature range does not seem out of line, however.
Is that 3% error in temperature or in output power?
That is the change in temperature using the formula that the measured temperature changes by the power 1/3 for the Optris. (.86/.95)^1/3 = .967 or about 3% difference.
The same formula was used by the MFMP, however at lower temperatures it deviates.
With the Durapot, the apparent in band emissivity moved about 0.02  0.03 from 20 C to (I think) about 1200 C. I would have to review my notes to confirm that. I believe that I posted the results a while ago, immediately after testing it. There was a fairly sudden change, rather than gradual, at around 750  800 C, detectable both when increasing and decreasing the temperature.
From your post of nov 6th 2017:
I have only just done the emissivity test of Durapot 810, and it is only applicable to the 8 to 14 micron band. It was only one test, with one pyrometer, but over 10 temperature data points. It very slowly dropped from 0.9 to 0.87, in that band, from 300 C increasing to the maximum external temperature tested of 990 C. (0.88 at 500 C)
My point was more that the local temperature differences at any given time, for example between the ridges and valleys, would not have a large deviation in the in band (or even total) emissivity. It is not likely that immediately adjacent parts of a similar structure would have a large enough temperature gradient to require independent tuning of the local emissivity. Between the Caps and Main Tube, (obviously different structures), there could be a minor correction required.
I think that the correction would indeed only be minor.
I also still think that the measured difference between valley and top when using the Optris for the temperature measurement is influenced by the difference in view factor between the valey and top, resulting in different emissivity correction for the valey and top.
I am thinking about investigating these differences since with view3D I should be able to calulate the view factor for the valey and the top.
By your estimate, how much deviation in the in band emissivity is there from 450 C to 900 C?
.90 at 450 degree C
.94 at 900 degree C

I doubt that the in band emissivity required for the IR camera changes significantly with temperature.
Using emissivity curves for alumina taken at different temperatures I estimated once that the in band emissivity changes between about .86 at 200 degree C to .95 at 1100 degree C.
If you had used the .95 throughout then the error at 200 degree C would have been about 3%
I don't know if you consider this being significantly or not.
Wonder if you ever tried to determine the in band emissivity for different temperatures with your casts in order to arrive at the temperatures measured with the thermocouple.
Maybe that gives a better estimate/indication then my calculation.

This topic came up in a discussion of the Lugano experiment. I do not recall where. Anyway 
In the Lugano experiment, I suggested that it would have been a good idea to confirm the IR camera temperature readings by comparing them to a thermocouple (TC) held to the surface of the cell. This was what Levi et al. did in the previous experiment. In the previous experiments, the IR camera agreed with the TC to within 2°C.
There are some possible issues with using a thermocouple to measure the temperature along the ridges in an Lugano like experiment.
First of all at the bottom of the fins on the tube there is more thermal mass then at the top of the fins.
Since the metal thermocoule wires are good thermal conductors, going to an environment with a much lower temperature, they will drain heat away at the tip of the thermocouple.
This will lower the temperature of the material measured and that of the tip of the thermocouple, especially if due to a lower thermal conductivity and thermall mass of the material measured, the lost heat can not be supllied fast enough.
Since there is less thermall mass at the top of the fin then at the bottom, the temperature due to the thermal drain of the thermal couple will be less at the bottom then at the top.
The effect will cause lower temperatures to be measured then the real temperatures and lower at the top then at the bottom.
Note that in the previous experiment you referred to, the thermall mass is much higher with no ridges and thus that situation is much more suited for calibrating with a thermocouple.
Secondly there is the effect of a changed emissivity due to the ridges.
As known, a small deep hole can be considered as a black body, independent of the material surrounding te hole. While the ridges are not holes, they create valeys which makes the material more gray then the flat material. This causes the emissivity to increase resulting in lower measured temperatures by the thermal camera. I have seen in the past one manufacturer of thermal camera's which in a document warned for this potentional measurement error.
The amount of increase of the emissivity can be calulated with the infinite reflection method if the view factors are known.
The change in measured temperature requires for an accurate temperature measurement calibration but as stated it is difficult to measure accurately with thermocouples due to the thermal drain.
Third the thermocuple measurement itself. Many people have no idea of the possible measurement errors when using thermocuples.
First of all, the temperature versus voltage curves for a type of thermocouple changes from thermocouple to thermocouple, the error often being a few percent. You can buy calibrated thermocouples which are supplied with a callibration curve to allivate this problem.
Then the thermocuple wires are connected at a certain point to normal wires, most of the time copper. That point is called the "cold junction" because it is normally at a place with a much lower temperature then the thermocuple tip.
The thermocuple measurement is dependent on the temperature of the cold junction, so you have to compensate for this effect and you can only compensate if the temperature of the cold junction is accurately known which requires another calibrated temperature measurement.
Then besides the cold junction, due to material dissimilarities in the electronics and wiring , we can have contact potentials resulting in offset voltages which are causing additional measurement errors.
And then we have the amplifier part where the thermocuple signal is amplified. This amplifier has also offset voltage errors and gain errors resulting in measurement errors.
Then we have also possible electromagnetic interference on the thermocuple signal, most of the time picking up 50/60 Hz magnetic fields which causes an ac voltage superimposed on the thermocuple voltage, again resulting in possible measurment errors if they are not filtered out.
The above problems can be largely deminished if adequate electronics (more complex and thus more expensive) are used.
For temperature measurements as in Lugano, where you can live with some limited inaccuracy in the temperature measurement I agree with Para that the averaging function of the Optris camera will give adequate results. However since also the in band emissivity to be set on the camera changes with temperature you will need to calibrate for this and then we have also to compensate for the increase in emissivity due to the grayer area caused by the fins. To allivate some of these problems I would suggest instead of using a thermocuple to measure with a dual or multiband pyrometer which automatically compensates for the emissivity (But averages the temperature also over the area as the Optris does) . That was indeed what the MFMP did by using a dual band Williamson pyrometer in addition to their Optris during their investigation of the Lugano Hotcat reactor.

Thermal expansion coefficient of air as applied to convective heat transferThe thermal exchange coefficient used in calculating the convective heat transfer is dependent on the Rayleigh number.
For horizental tubes the Rayleigh number is calculated with the following formula
Ra = gB(TsTa)D^3/va
In this formula B denotes the thermal expansion coefficient of air.
The Lugano testers in the report state about this coefficient :
β[K^{–1}] is the volumetric thermal expansion coefficient, which, for an ideal gas (applied here to air for simplicity) is= 1/T
Indeed, for ideal gases the thermal expansion coefficient is 1/T.
While for many calculations air can be treated as an ideal gas, this is not true for it's volumetric thermal expansion coefficient.
In those cases that the thermal expansion coefficient does not follow the ideal gas law 1/T the data can be found in tables. Such a table also exist for the thermal expansion coefficient of air.
The differences for air between the tabulated values and the ideal law can be found in the folowing figure.
As can be seen the difference between the ideal thermal expansion coefficient and the real value can be quite large. The errors are for different temperatures shown in the following table
TempError
K%
250 0.8
30012.8
35015.2
40012.4
45011.0
50010.6
These errors result in an incorrect calculated convective heat transfer coefficient.
However since in the final calculation of the convective heat transfer coefficient the Rayleigh numer is raised to the power .25 for the temperature ranges used in Lugano, the error will be lower and reduced to a value between 2.3 % and 4.2 %.
The question is if the Lugano testers applied 1/T for the thermal expension coefficient for simplicity only as they state in their example calculation in the Lugano report, only for the calculation of the dummy run, or for all calculations.
If they used 1/T throughout then their calculated convective heat transfer was somewhat under estimated.

The most likely version is that the reactor was painted with Aremco 634Al, rather than 634Zr.
If it was painted on the outside I agree.
That simplifies things a lot.
It does not make things simpler (except that we in that case possibly can use alumina emissivities in calculating radiated power, but that is possibly also dependent on the layer thickness of the paint)
Even if the outside was painted with Armenco 634Al, the samples analysed of the Lugano ridges would then also contain some of the underlying material and the contents of that material would have shown up in the results.
If that underlying material would have been Durapot 810 as per Dewey then the contents of Durapot 810 would have shown up. In that case we arive, based on the analysis in the Lugano report, to the conclusion that Durapot 810 does not contain any additives in adition to alumina / corundum.
So it is still interesting to know the contents of Durapot 810.
If it contains other materials then those which showed up in the Lugano report, then we know for sure that Durapot 810 was not used for the casting of the ridges.
If it only contains alumina and corundum in about the same relations as in the report , then we know that Durapot 810 was probably the casting material used.
Concerning your suspicion that the ingredients include manganese because of the pyrolusitelike stain, note that also corundum powders comes also in about the same colors as pyrolusite (At least that is what I make up after searching for some pictures), so corundum as a part of Durapot 810 is still an option.
I am curious to know how your Durapot 810 casts compare in color to the Lugano Ecat.

However, the reactor (including ridges) was cast from Durapot 810, which is not made of 100% alumina, nor is it 99.9 % alumina with no detectable other elements in concentrations to make up the 0.1% , although it is alumina based.
So we now have three possible materials with their respective emissivities to choose from
1. Durapot 810 (stated by Dewey ?).
2. Zirconiumoxide coating over the potting (also by Dewey ?)
3. Analysis of the material of the ridges by x ray crystallography, giving as a result that it was almost 100 % pure Alumina.
Note that the x ray christallography analysis did not detect any signals on positions 28 and 32 which are the main peaks for zirconiumoxide.
So in the samples analyzed there was indeed no zirconiumoxide present .
The German safety sheet of Durapot 810 says that it is made up of only two components, Alumina and the solvent.
That would make Durapot 810 after casting also a 100% alumina cast.
However how did they increase the thermal conductivity compared to Durapot 801 ? Is the casted Durapot 810 denser ?
In that case the specific weight of Durapot 810 should be higher.
Did they do that by adding synthetic corundum particles?
In that case it explains that also Al2O3 with the corundum crystal structure was found by the xray chrystallography in the Lugano report.
In my opinion it is not likely that the x ray christallography equipment is giving incorrect results but that al least contradicts point 2.
So what information are we missing , is incompete or wrong ?
I think I did so because it is still inconclusive.
Agree that it is inconclusive
The "fragments" analysed would not be all paint, and might in fact contain no paint at all.
Seems very unlikely to me that the samples would not contain some coating material if it had been coated.
So, given the reactor was painted, we don't have much info, unless as P says above we are sure that the ridges were not case from something that bakes to 99% alumina.
The x ray christallography equipment has no interest in this story.
It will tell the composition without trying to cheet on us and it told us it was more then 99% alumina.
I have no doubt about that, but as mentioned above, maybe Durapot 810 is also 100% alumina.
Para has Durapot 810 ?
Would it then be possible for someone with acces to x ray chrystallography equipment to test a casted sample for it's contents ?
Many universities seem to have x ray chrystallography equipment.

Not I think inconsistent
The Lugano report says that the alumina sample was taken from one of the rods, not the reactor body.
THH
The following quote is from appendix 2 of the report
In order to determine the nature of the material covering the reactor, a sample from one of the ridges was analyzed.
As far as I know the rods had no ridges, but the reactor body had

Although the error % seems large for the coolest end of the rods, the final W difference, in terms of the total power budget, should still be rather minor. I believe that I had a similar result when I did it, and it did seem to be rounding that made the difference.
I agree, except for the dummy run where convected and radiated power are of the same order.
The calculations for working out the Rod segment temperatures and Rod temperature gradient, and therefore power, during the active period is much more complex. There're is very little in the report to go on, since just the final total power is reported for each run.
Agreed. And that also means that I have currently no plans to do any calculations for estimating the COP of the active runs.
You should be close enough, however, with your model that it should be possible to test if the 2/3 factor was in fact applied, or not, to the active period Rod power in the report, since a total 33% overestimate error should be obvious. (It is my opinion that the 2/3 adjustment was not made to the active period Rod power in the report, and therefore the Rod power reported is too high for all active runs. (Easily fixed, since they lump those results into two periods anyways, an indication of how concerned the Professors were about the Rods contribution)).
First of all can you explain what you mean by my model ?
Any ideas how to test with my model if the 2/3 factor was applied ?
If the Lugano testers made the error as per your opinion then indeed the COP value would be less.
But in a previous posts we showed that they made an other error, being that they did not calculate with the fin area combined with the view factor to the background and also did not correct the emissivity for the reflection between the fins. And that total correction has about the same value as when the 2/3 factor was not applied, but with the opposite polarity.
So we end up with about the same power budget
Don't forget the minor Joule heating in the rods added in the report from the cables,
Thanks for the warning . I was already aware of it
and consider carefully the contribution of the heater coil extensions entering the Rods for 4 to 5 cm, which affect calculations for both the temperature of the initial Rod segments (Cap end) and the power budget of the Main Tube since these wire extensions, six in all, reduce the amount of input Joule heat available to the Main Tube and Caps, possibly explaining a portion of the previously calculated excess (COP 1.2 or similar)
Good point !
Once, here in the Forum, I calculated exactly the parameters of the twisted 15 ga Kanthal resistance wire for the three parallel coils, from which the 6 X 4 cm (estimated) could be subtracted so that the end lead power % of the entire heater windings could be correctly attributed. Off the top of my head, each of the 3 coils have about 1.5 m of wire, which is twisted to make a precoiled length of slightly less than half of that. Probably better for me to look it up again. I believe that the Caps and wire extensions combined contain about 30% of the total calibrated resistance heater wire, and therefore the wire extensions could net about 15% of the Total input power.
I am still wondering about the heater wire seize of AWG15 they supposedly used.
AWG15 wire has a diameter of 1.45 mm. But they seem to have been braided with two wires.
Twisting two wires will double the diameter, thus 2.9 mm
For about 70 windings total, without inter winding spacing, the length of the heater coil would have been 70 x 2.9 mm = 203 mm. But the photographs of the heated Ecat gives me the impression that a reasonable spacing was used between the windings.
Proper engineering practice for heater coils uses strech factors between 2.5 to 4 for the inter spacing between the coil windings to prevent shortages due to the coil windings moving when heated.
Using a stretch factor of 2.5 (the minumum) gives a minimum length of the coil of 2.5 x 203 = 507 mm. That is much longer then the total Ecat length of 280 mm.
Or is my calculation wrong ?


IH built the Lugano reactors, three of them, and were surprised by the paint, so your theory doesn't work.
The argument goes also otherwise. The outside of the ECAT was by analyses almost 100% Alumina.
So in the same way we can argue that the theory that it was painted with Zr paint doesn't work.
So the question is who is right and who is wrong.
On that question I don't know the answer.

I understand now why the manufacturer of the IR cam advise to calibrate, and not to trust any emissivity number...
Alain,
While radiated heat transfer is part of the calculated power and emissivity can then be important, the above posts are about convective heat transfer.
As far as calculating radiated heat transfer, then indeed if you measure the temperature with the Optris, then for a correct temperature measurement you need to use the correct in band emissivity.
Hoevever for the in band emissivity often a fixed value of .95 is quoted, but in reality the in band emissivity is also somewhat dependent on temperature.
In an earlier post I showed that you can also calculate the power using the Optris without calibration. see
Revisiting the power calculation in the Lugano report
We cannot replicate the active rod, but maybe can Dewey Weaver obtain a dummy from the stock? or Maybe is the dogbone of MFMP not far enough from the shape (maybe it can be painted with the ZrO2 paint cited by Dewey Weaver ) to give interesting approximation of emmissivity over temperature?
The ZrO2 paint from Aremco is a special paint which is as Armeco says specially fitted for fixing heater coils. So they could have fixed the heater coil with it before casting the ECAT with Alumina.
That would fit both Dewey's story and also fit the analysis of the Lugano report that the outher casting was almost pure Alumina.

Newtons law of cooling is likely too oversimplified to give an accurate result, especially over a wide variation in temperatures. It assumes that each unit area transfers the same amount of heat (And also that h isn't affected by T).
The thermal exchange coefficient h is affected by T, but in an indirect way.
First of all the Rayleigh number is calculated with :
The volumetric thermal expansion coefficient
The kinemathic viscosity
The thermal diffusity
All three are dependent on the temperature.
Then using the Raleigh number to calculate h, we also multiply by k, the thermal conductivity of air, also temperature dependent. Thus the calculated value of h is largely depent on temperature.
But I agree that we work with an average temperature and that h over the area is constant.
That is indeed a simplified approach, which however gives for situations which have been researched many times in literature, such as horizental tubes, adequate results.
An other approach would be to use CFD (Computional Fluid Dynamics) software to calculate the convective heat transfer of a part of the rod for a given temperature. Additional we can then also calculate h.
I have CFD software, but have still to learn how to use it beyond the basics. But I have seen in literature several quite complex simulations with CFD software which give errors of 1% to 2 % compared to the real measured data. This because CFD is not using approximations in calculating the convective heat transfer coefficient, but is instead solving the differential equations governing the heat transfer. So maybe this is the way to go.
Instead of using h = Q/(A(TsTa)), the more accurate method is to calculate an average h (taking the shape of the object into account)  done by first working out the Prandtl, Raleigh & Nusselt numbers for the system.
Using h = Q/(A(TsTa)) is using the forumula as used by the Lugano team in a reverse way using their data. As such that should give the exact value of h they used.
Can't paste the formula's for those easily, but this should give you what's needed:
I had the link myself, but must concede that I did not look at the contents lately.
The formula showed in the link is somewhat different from the one the Lugano team and I used.
If time allows it migh be an idea to use the formula in the link and see how much the data differs.
But there are many formula's for calculating the convective heat transfer coefficient of a horizental tube (or round heated wires).
The formula used by the Lugano testers is normally used for much larger Rayleigh numbers then those valid for the Lugano case.
As such it might be worth the effort to find a better (more accurate) formula for the lower Rayleigh numbers.

Lugano rods convection heat transfer coefficients
The convective heat transfer coefficients used in calculating the convective powers for the rods can be calculated.
We do this by using Newtons law. Newtons law is given by the following formula :
Q = hA(TsTa)
Q being the power
h the convective heat transfer coefficient
A the surface area
Ts the surface temperature
Ta the ambient temperature
h can then be calculated as
h = Q/(A(TsTa))
Since the convective data for the rods in the Lugano report give the values for the power (Q), the value of the area of each section (A) being 4.71E3 m2, the section temperatures Ts and the ambient temperature (21 degree C), we can for each section calculate the convective heat transfer coefficient used for each section.
Tthe results of these calculations can be found for both the upper and lower rods in the following tables
Upper rod h values
AreaTu (C)Conv (W)h
1151.525.849.50
2125.134.459.07
390.852.818.54
468.171.727.74
558.261.287.29
654.121.117.12
746.330.806.71
840.020.566.25
935.340.405.92
1031.820.285.49
Lower rod h values
AreaTd (C)Conv (W)h
1147.985.659.45
2118.894.138.96
387.712.668.47
468.151.727.75
558.211.287.30
652.821.067.07
745.060.756.62
838.890.526.17
934.300.365.75
1031.090.265.47
Since I wanted to know if I could correctly calculate the convective heat transfer coefficients myself, I did the calulation of the convective heat transfer coefficients of the rods myself.
The result was that they differed from the values calculated back from the report.
To understand how I did the calculations we recalculate the convective heat transfer coefficients for area 3 of the lower rods.
For the calculation we use the data from the following table which gives k (thermal conductivity), alpha (thermal diffusivity) and v (kinematic viscosity) as function of the film temperature.
(These values are from the same table in the book Fundamentals of heat and mass transfer as the Lugano testers used)
film tempkalphav
E3E6E6
1009.342.52.00
15013.805.84.43
20018.1010.37.59
25022.3015.911.44
30026.3022.515.89
35030.0029.920.92
40033.8038.326.41
45037.3047.232.39
50040.7056.738.79
For a temperature of 300K the tabulated values are in agreement with the values mentioned at the bottom of page 11 of the Lugano report.
The reported ambient temperature during the dummy run was 21 degree C (284.15K) and the surface temperature of the rod was 87.81 degree C (360.86K)
Thus the film temperature is (284.15 + 360.86) / 2 = 327.51 K
The closest tabulated value is 350K and we now take this value, one value lower in the table and one value higher.
For the thermal conductiveity k this gives :
Tk
30026.30
35030.00
40033.80
We now do a 3 point curve fit with the Newton method to solve the k value for the temperature of 327.51.
This gives a k value of 0.0283. In the same way the values for v ( 1.978E05 ) and alpha ( 2.645E05 ) can be obtained.
Using for the Fluid thermal expansion coefficient B the value of 1/T_{film }as specified in the Lugano report and doing the same calculations with the same formulas as used in the report, we obtain a value of the convective heat transfer coefficient h of 8.12.
The value we obtained as being used by the test team was 8.47. The difference is 4.1 %.
The outcome of the calculations for all zones of both the upper and lower rods are presented in the following tables.
Upper rod differences
Areahmy hError %
19.509.570.7
29.079.060.1
38.548.213.9
47.747.473.5
57.297.053.3
67.126.853.7
76.716.414.4
86.255.964.7
95.925.566.1
105.495.185.7
Lower rod differences
Areahmy hError %
19.459.510.7
28.968.920.4
38.478.124.1
47.757.473.6
57.307.053.5
67.076.784.1
76.626.324.5
86.175.874.9
95.755.465.0
105.475.097.0
As can be seen especially for the lower temperatures the differences become quite large.
A possible explenation might be that the Lugano testers in the report used in the calculation of the convective heat transfer most of the values in two digit accuracy while i used three digits.
With two digits accuracy the error margin become then quite large and can then possibly add up to the errors in the ranges calculated above.
Suggestions for other reasons why the values differ are welcome.