# Rossi Lugano/early demo's revisited. (technical)

• LDM ,

Do you mean that with everything else unchanged, a tube would run hotter with the fins (with a 2 cm valley bottom diameter), than a plain bare tube with a 2 cm diameter, notwithstanding the apparent extra surface area caused by the fins using the fin design used for the Lugano device?

For a bare tube the convective power can be calculated as :

Q = h x At x (Ts - Ta)

---------h--------Convective heat transfer coefficient

---------Q--------The power

---------At-------The area of the tube

---------Ts-------Temperature of the surface

---------Ta-------Ambient temperature

For the finned tube the power is calculated as :

Q = C x h x Af x (Ts - Ta)

---------C--------Convective heat transfer correction factor for the finned tube

---------h--------Convective heat transfer coefficient

---------Q--------The power

---------Af-------The area of the fins

---------Ts-------Temperature of the surface

---------Ta-------Ambient temperature

C, the correction factor has a value of .752

h is for both cases 13.28

At, the area of a bare tube of 20 mm diameter and 200 mm length is 0.0125 m^2

Af, the area of a finned tube is 0.0263 m^2

For the surface temperature we take 445 degree C

For the ambient temperature we take 21 degree C

The calculated powers for both cases are then

Qt-------------70.75 Watt for the bare tube

Qf------------111.36 Watt for the finned tube

Clearly with fins the dissipated power by convection is larger and thus the temperature lower.

As an additional comment : C x h = 9.99, the convective heat transfer coefficient I derived for the finned area.

Hope this explains it for you.

• LDM ,

Thanks.

I lost track of where we were on the long trail.

• Lugano dummy run recalculated - Final

The close agreement between applied electrical power and the confected and radiated thermal power makes it unlikely that the reported temperatures where inflated

Presented here is the, what I believe final, recalculation of the total convected and radiated power of the Lugano dummy run.

Compared to the first recalculation (post #226) the following changes have been implemented :

1. Stacked rod correction

In my first recalculation I included only on sets of rods while there are two sets.

This has been corrected.

2. Viscosity of air

In the calculation of the convective heat transfer coefficients I had wrongfully used the dynamic viscosity of air instead of the kinematic viscosity of air.

This has been corrected and all convective heat transfer coeffcients in the spreadsheet have been updated.

3. Convective heat transfer correction factor for the ribbed area

Due to having no spacing between the ribs, the convective heat transfer of the ribbed area is less efficient. Thus) a correction factor needs to be applied. This correction factor was, using CFD simulation (see post #389) , found to have a value of 0.752

The spreadsheet now includes this correction for the convective heat of the ribbed area.

The updated spreadsheet is included as an attachment to this post.

For information on additional changes compared to the original calculations of the Lugano report see the comments in the original post #226

The outcome of the spreadsheet calculation is that the difference between applied electrical power and the total convected and radiated thermal power is 1.62 %.

If the reported temperatures for the Lugano dummy run where inflated, then the difference would have been much larger. As such it is unlikely that the temperatures where inflated

## Files

• LDM ,

The correct Joule heating value for the dummy cables is 7.276 W, rather than the value supplied in the report, which failed to take into account the delta configuration (despite Rossi's tantrum claiming otherwise on JoNP).

The C2 cables are inside the delta, while the C1 ones are not. The C2 cables end up Joule heating at 2.182 W, rather than 1.6W, while the C1 cables produce 5.094 W when the corrections have been made.

It is a minor difference for the Dummy, but important for calculations for the Active Runs.

This simulation also shows that the MFMP thermal state report is deeply flawed in its conclusions about the dummy.

## Images

• If the reported temperatures for the Lugano dummy run where inflated, then the difference would have been much larger. As such it is unlikely that the temperatures where inflated

The reported Dummy temperatures were inflated, based on your work. Just not by much.

What is more interesting is the Dummy peak temperature. It is just below the point where emissivity-temperature errors really become apparent. Personally I doubt that is an accident.

## Images

• This simulation also shows that the MFMP thermal state report is deeply flawed in its conclusions about the dummy.

I find it a pitty that the MFMP did not cross check their measurements by calculating the convective and radiated thermal power and compare it with their electrical power setting.

If you do that you will see that the convective and thermal power is larger then their electrical power, which is indeed an indication that there is something wrong with their measurements.

Also I did in the past some thermal simulations with my thermal FEM program on my dogbone model and the temperatures the FEM program calculated where much lower then those reported by the MFMP.

For their 500 Watt run, about the power setting of the Lugano run, the simulated temperatures where close to the Lugano ones and thus much lower then those reportes by the MFMP.

What bugs me is what could have been gone wrong with their measurements.

• The reported Dummy temperatures were inflated, based on your work. Just not by much.

What is more interesting is the Dummy peak temperature. It is just below the point where emissivity-temperature errors really become apparent. Personally I doubt that is an accident.

What's important is that if they where inflated, what then the real input power must have been.

So the next thing for me to work on is making a spread sheet based on inflated temperatures and calculate what in that case the total convective and radiated thermal power would have been.

I think that the total power in that case is much lower. (But we will find out)

• What bugs me is what could have been gone wrong with their measurements.

The rods vs caps distribution of input power of the MFMP device was greatly different from the Lugano device, due mostly to the single heater wire (although that could have been mitigated).

This results in much less input power to the Caps, and the increased % of power into the Main Tube area because a single, straight through heater wire passes through the Caps instead of three as in Lugano. A few wraps in the Caps would have more closely reflected the input heat distribution in the MFMP replica. Roughly 30% of the heater wire in the Lugano device is outside of the Main Tube area, and is contained within the Caps and extensions beyond, attaching to the C2 cables.

In turn, this increases the MFMP Main Tube temperature relative to input power, skewing the simulation.

• In turn, this increases the MFMP Main Tube temperature relative to input power, skewing the simulation.

The simulation I did was on a model of the MFMP dogbone. (without rods)

The remark that the simulated temperatures where near the Lugano ones must be interpreted as that they where much closer to the Lugano ones then those of the MFMP, but indeed higher (skewed) then the Lugano ones.

However those simulations did at that time not take into the latest findings which I incorporated in my spreadsheet.

So If I can find time in the near future I can redo those simulation with my latest findings. But those simulations take a lot of my time.

• What's important is that if they where inflated, what then the real input power must have been.

The real input power, in my opinion, is very close to what was reported. It is consistent with the Active runs and the calculations of the resistance of the heater wires at all back-calculated input powers, within a reasonable variance.

Active Run 1 is a little "off" from the rest for some reason, (not sure why) but the rest are mutually consistent and are consistent with the Dummy.

• The real input power, in my opinion, is very close to what was reported. I

My feeling (For what it is worth) is otherwise, so let's wait for the recalculation and see who was right

• If you don't believe the electrical data, (such as it is) then the rest of the calculations are a waste of time.

The electrical data is one of the very few empirically measured things in the entire report (even if it is averaged over hours or days).

It is the fulcrum of all comparisons with other information supplied.

Even the reported dimensions of the Caps are suspect. Do they look "square", (4 cm x 4 cm) to you?.

## Images

• For the record, I will say the that the reported input power measurements in the Lugano Report are the best, most believable data ever reported on a Rossi device.

If there is an error, is the the most precise, internally consistent error ever made.

(The Dummy could have an input error of about 0.9% on the high side, in order to fit it to the Active Runs a bit better)

• If you don't believe the electrical data, (such as it is) then the rest of the calculations are a waste of time.

I think that the electrical data is about right, otherwise I could not have compared the convective and radiated power with the electrical power.

If I do a recalculation based on assumed inflated temperatures, then I convert those temperatures to their assumed correct ones.

I then do a new calculation of the convected and radiated thermal power.

If this newly calculated power differs much from the electrical power, then that is another argument that the temperatues where not inflated.

I don't see where in such a calculation I don't accept that the reported electrical power in the Lugano report is about right as you suggest.

And I disagree about the fact that calculations can be a waste of time. It has given me a lot of additional insight in the issues involved. You learn from it !

But let's have a real discussion if we have some data to discuss about

• LDM ,

If you end up with either 424.43 W or 160.3 W, that would be interesting.

Just going to try a few things here for a bit...

• Recalculating inflated temperatures when wrong emissivites where used

As a first approach to recalculate the Lugano dummy run for the case that the reported temperatures where inflated due to using wrong emissivity settings on the Optris thermal camera, we need to recalculate the temperatures to their real ones.

The procedure which can recalculate the temperatures is based on the following formula published by Optris which can be found on page 9 of their IR-basics document.

U = C · [ε Tobjn +(1 – ε) · Tambn – Tpyrn]

The meaning of the parameters is as follows :

---------U-----------The voltage from the thermal camera sensor

---------C-----------A constant

---------ε-----------The in band emissivity set on the Optris

---------Tobj------The temperature of the measured object in degree K

---------Tamb----The ambient temperature

---------Tpyr------The temperature of the camera sensor

---------n-----------A constant depending on the used sensor frequency band

We can use this formula for two situations, the first with the wrongly used emissivity ε1 and the accompanying measured temperature Tobj1, the second case with the correct emissivity ε2 to be used with the Optris and the correct temperature Tobj2.

Since the measured sensor voltage U is only dependent on the amount of radiation coming from the object under observation, this value is the same for both situations.

Thus we can fill in the above formula for both situation and then equate them.

This is written out below

C · [ε1 Tobj1n + (1 – ε1) · Tambn – Tpyrn] = C · [ε2 Tobj2n + (1 – ε2) · Tambn – Tpyrn]

Simplifying this gives :

ε1 Tobj1n + (1 – ε1) · Tambn = ε2 Tobj2n + (1 – ε2) · Tambn

Or

ε2 Tobj2n = ε1 Tobj1n + (ε2 - ε1) · Tambn

Tobj2n = (ε1/ε2) Tobj1n + (1 - ε1/ε2) · Tambn

Tobj2 = [(ε1/ε2) Tobj1n + (1 - ε1/ε2) · Tambn ] 1/n

The last formula above will be used in a spreadsheet to recalculate the assumed inflated temperatures to the assumed real temperatures.

Note :

For high temperatures the term (e1/e2)Tobj1n is much larger then the term

(1 - ε1/ε2) · Tambn and the last term can in that case be discarded.

(Note that the term with Tamb can not be discarded for lower temperatues since the errors become quite large)

This leads the to the following formula also used by the MFMP to be used for high temperatures :

(Tobj2/Tobj1) = (ε1/ε2)1/n

The MFMP verified this formula at higher temperatues to be working with a value of n=3.

• LDM - the basic physics means that the value of n is highly temperature dependent. MFMP verified this n ~ 3 at just one temperature (where indeed numerically n ~ 3), and if you talk to them they will say they did not validate at other temperatures because they broke the camera. That is why their high temperature results were wrong (though much less wrong than the Lugano authors).

Remember the key equation here (T=temp, Pb = power in a given passband) is the Planck curve, and this changes as Pb ~ T^1 (in extreme low frequency approx) to Pb ~ T^n where n -> infinity as frequency increases for the high frequency (above hump) case.

The LF case, n=1, is well studied as the Rayleigh - Jeans approximation.

the high frequency case (n -> infinity) is also studied as the Wien approximation. That shows:

Pb ~ exp(-C/(kT)).

that goes up faster than an exponential in T where C >> kT (the high frequency case). Unfortunately it is not a nice expression to deal with algebraically.

There are a whole load of simple approximations of which S ~ T^A is the least accurate:

https://en.wikipedia.org/wiki/…%E2%80%93Hattori_equation

You can easily validate how n changes with T yourself numerically from the Planck curve.

• LDM - the basic physics means that the value of n is highly temperature dependent. MFMP verified this n ~ 3 at just one temperature (where indeed numerically n ~ 3), and if you talk to them they will say they did not validate at other temperatures because they broke the camera. That is why their high temperature results were wrong (though much less wrong than the Lugano authors).

Thanks THH,

Will investigate this further.

If you have more info how to calculate n, then I would be gratefull to receive it

• Thanks THH,

Will investigate this further.

If you have more info how to calculate n, then I would be gratefull to receive it

You can do a numerical integration of the Planck curve spectral power over the camera frequency passband, and note how that changes with T. Specifically Accuracy would require knowing the Optris spectral response which may be difficult to find data on. Or you could get an approximate answer by evaluating the Planck function at just one frequency - say the mid-point of the stated response band. A good compromise would be to integrate uniformly over the stated band. Clarke used integration over a typical IR bolometer response graph found by Higgins (referenced in link). The results are not VERY dependent on what you use for this.

Her eis how you do the (reasonably good) uniform rectangular passband response calculation. For the more complex version you multiply by the bolometer response inside the integration. The idea is that B(T) is the total power received by the detector. there is also a constant (independent of T or nu) factor but this does not matter, it drops out when you calculate n.

EDIT multiply by T to get n

Here nu1 - nu2 are the bounds of the bolometer quoted response (converted to frequency nu2 > nu1).

n for a given value of T can be found by (numerically) integrating to get a function B(T). Then numerically differentiating B to get its polynomial in T approximation at any given T, note that n, dB/dT, and B are all functions of T (I've omitted the explicit dependence as in normal).

EDIT - sorry I've lost the latex source, but n should be T(dB/dT)/B (multiply by T). Sorry for the typo.

• Thanks again

I wrote in the past already a VB program which integrates the Planck function over a bandwith range.

Will play with it or adapt it to find n for the Optris band as a function of the temperature

• Note typo now corrected with edit.

• Recalculating inflated temperatures when wrong emissivites where used- Determining n

Inresponse to my previous post on the subject THH correctly mentioned that the factor n, used in the Optris forumla (see previous post #406) is as he stated highly temperature dependent.

He also supplied the basics for calculating n, which in hindsight is logically.

So I updated my VB program which integrates the Planck curve at a certain temperature between two frequencies, in our case the low and high limit of the Optris thermal camera.

The updated program does this calculation for a user defined temperature range and temperature step. The resulating data is written out to a text file which I then imported in Excel.

In Excel the derivative was calcualted at each temperature and using the derivative, the in band power B(T) and the temperature the factor n was calculated.

The Excel file with the data is supplied as an attachment to this post.

The calculated value of n as a function of the temperature is shown in the following figure :

There are two things standing out.

Optris stated that the value of N would be between 2 and 3, but the figure shows a larger range.

Especially at low temperatures the value of n is much higer.

Other point is that the MFMP used a fixed value of 3 to convert their measured temperatues to the supposedly inflated ones.

As we can see from the figure above this is incorrect since the factor n is very dependent on the temperature.

Having found the value of n as a function of the temperature aloows us to recalculate supposedly inflated temperatures of the Lugano dummy run to their approximate real ones.

## Files

• n factor.zip

(7.86 kB, downloaded 9 times, last: )
• Recalculated Lugano temperatures when temperatures where inflated

In post #406 the formula to be used for recalculating temperatures between two emissivity value settings on the Optris thermal camera has been established.

The factor n needed in that formula was as a function of the temperature determined in post #412.

With both we can now recalculate the reported Lugano temperatures if we assume that these temperatures where inflated.

For a recalculation of a temperature we start with the inflated incorrect temperature.

That causes a problem since we can not use this temperature for determining the value of n. This because n is based, by the use of the Planck curve integration,on the real temperature, not the wrong inflated one.

To solve for the correct temperature and the value of n belonging to that temperature we have to apply an iterative procedure for finding the correct temperature and it's value of n.

By applying such an iterative approach the supposed Lugano inflated temperatures where recalculated.

The results are presented in the Excel file supplied as an attachment ot this post.

Besides the recalculated temperatures I also added for each recalculated temperature in the Excel file the found value of n.

As a last remark, the recalculation assumes that the proper in band emissivity setting of the Optris is .95.

While this value give good approximate values, we also know that the Optris in band emissivity for Alumina is somewhat temperature dependent.

Using a fixed value is in my opinion however adequate for calculations if we take into account that the results of those calculations is a (close) approximation.

• LDM ,

I just compared a couple of those temperatures to the Optris software results for the same emissitivty-temperature.

Your n results are really close to the software with a heated MFMP dogbone.

I would like to test a higher temperature to make sure that it holds together.

Optris:

451.0 @ 0.695 ---> 374.0 @ 0.95 (LDM 377.66)

412.1 @ 0.731 ---> 353.4 @ 0.95 (LDM 355.95)

• Thank's for your checking that theory and practice are about in line, at least for the lower temperatures.

Really appreciate it because I was not sure if we where overlooking something.

What I do not understand is how Optris determines what value of n to use when converting their received heat flux to a temperature.

Maybe you know ?

I now intend to do a new Lugano dummy run recalculation, now based on inflated temperatures.

Have to find some time to work on that.

• LDM ,

As I understand it, n is related to the area of the Planck curve detectable by the camera compared to the total Plank curve area for a given temperature.

In practice, this is empirically determined by calibration to a black body source at the Optris factory, since it also depends on the signal generated by the bolometer array for various temperatures of the black body.

According to Optris:

## Images

• Chapter 11 (from link below) has some handy calculations and a cool table of BB radiation functions (page 570, PDF page 10)

• Chapter 11 (from link below) has some handy calculations and a cool table of BB radiation functions (page 570, PDF page 10)

That one I didn't know !

Thank's for the link

• MFMP DB2 Validation, Before and After, using the Lugano re-iterative method on the cells.

Note that hottest T in the reiterative version exceeds the max T for the Optris, and so defaults to 1524.7 C. I'm not sure how that affects the cell average. I meant to avoid that effect.

Note also that the caps are cool relative to the Lugano device (Fig 10, Lugano Areas image below), and barely show up in the MFMP .RAV file.

Cell 3 is used for the temperature displayed on the upper RH side of my images.

## Images

• Regarding Figure 10, Lugano Report, the gaps between the IR measurement area boxes can be used to determine qualitatively the level of "enrichment" of the temperature.

If the box(es) is(are) brighter than the immediately adjacent gap, then there has been an upward temperature adjustment (by lowering the measurement area emissivity function).