Posts by LDM

    MFMP dogbone thermal test, earlier FEM simulation result

    In support of the finding that the MFMP dogbone thermal power is not in agreement with the applied power, I post here the result of an early FEM simulation (Was I think posted on ECW before I moved to LF) that was in my opinion accurate enough to be indicative for the relationship between temperature and power.

    Below is shown the FEM model of the dogbone created.

    With that model the temperature versus power curve was calculated and combined in a single graph with the results of the MFMP dogbone thermal test.

    The graph is shown below

    From the graph it can be seen that the temperatures measured by the MFMP are much higher then those calculated by the FEM simulation program.

    For the about 480 watt power of the Lugano dummy run the temperature is about 500 degree C while the MFMP measured about 700 degree C.

    Note that the 500 degree C is not too far of from the about 450 degree C measured in the Lugano test.

    The conclusion of the simulation is that the temperatures measured by the MFMP are not representative for the Lugano ECAT.

    I will now starting work on upgrading the FEM model with the latest findings for view factor and convective heat correction and taking into account the power dissipated into the rods.

    I also intend to increase the number of different sections the model is made up from in order to increase the accuracy of the simulations.

    After doing so I expect that the simulated temperatures will be even closer to the ones in the Lugano report.

    MFMP dogbone thermal versus applied power. A case study

    In post #445 in this forum thread we have shown that for the second MFMP dogbone thermal test the applied electrical power differs largely from the calulated thermal power.

    This can be possibly due to one of the following reasons :

    Wrong power measurement

    Wrong temperature measurement

    Emissivity of the casting material is different

    Concerning the power measurement we can state that for the first MFMP dogbone thermal test we are able to calculate from the posted data the heater coil resistance for each setting.

    This resistance has about the same value for each run and calculating the wire resistance from the supplied heater coil winding data gives about the same value.

    Thus it is likely that the power measurments of the MFMP where correct.

    Concerning the temperature measurment we know that at least during one of the MFMP thermal tests the temperatures where measured with the Optris thermal camera and the Williamson pyrometer.

    Both where in close agreement and as such the measured temperatures with the Optris are supposed to be (near) accurate.

    The differences between applied power and calculated thermal power can also be explained if the emissivity of the material used to cast the dogbone is much lower then that for standard alumina.

    This possibility will now be investigated in this case study.

    Using the data in post #445 a rough estimate was made by which factor the emissivities of the 900 Watt run had to be lowered to bring the applied power in line with the total thermal power.

    This factor was about .7 . This means that emissivities for the high temperatures would have been closer to .30 then to the .45 for the ribbed area.

    The question now is which ceramic material can have such low emissivity values. A likely candidate is Magnesia (Magnesium Oxide, MgO).

    Total emissivity of magnesia as a function of temperaure is given in the following figure which was taken from the


    For magnesia the handbook gives the following figure :

    The dots in the figure are representing measured emissivities by several sources. As can be seen there is a wide spread between those measured values.

    The curve represents the curve fit for all these measurements. The curve is in the document also presented as a table and we take that data as a starting point .

    We now do a linear transformation on the published emissivity values of magnesia such that for the MFMP dogbone thermal tests for 500, 700 and 900 Watt the applied power is about in agreement with the thermal power. The translation used was :

    ε' = 1.02 x ε - 0.04

    The part of the original curve between 200K and 1800K together with the translated curve is given in the following figure :

    The new curve has almost the same shape as the original curve but is somewhat lower but falls largely within the upper and lower limits shown by the measurements dots in the first figure.

    We now apply the translated emissivity values of magnesia to our calculations of the thermal powers of the MFMP 500, 700 and 900 Watt runs and determine the difference between applied powers and thermal powers.

    The table below shows the differences between the calculated applied power and thermal power for both the original calculation with alumina and for the translated magnesia curve

    Run-------------Difference alumina (%)----------Difference magnesia (%)

    500 Watt-----------------16.3-----------------------------------0.94

    700 Watt-----------------27.3-----------------------------------0.09

    900 Watt-----------------33.9-----------------------------------0.95

    Conclusion of this case study is that the large differences between the applied and calculated thermal powers of the MFMP dogbone thermal test almost disappear if the MFMP dogbone was casted from a lower emssivity ceramic then alumina. Especially magnesia is a good candidate to bring applied and calculated thermal powers in line.

    Note that if instead of alumina magnesia or an other low emissivity ceramic was used it would also result in the higher surface temperatures measured during the MFMP test.

    Update for typo error : Constant factor in emissivity translation is -.04 instead of -.03

    Update 08-11-2018 : Added Excel sheet with calculation

    I'm fast awake. No. we didn't need to change anything -Russ realised we had been playing cat and mouse all the while, but we did change the way we applied the heat a little

    Let me quess.

    Instead of applying heat by a continuous pulse width modulated voltage to the heater coil you are now applying power in a more burst like fashion ?

    Radiated and convective power calculation of the MFMP Dogbone thermal simulation 500W, 700W and 900W runs.

    In the attached spreadsheet the total radiated and convective power of the second MFMP dogbone thermal test was calculated.

    Temperatures of the same sections as in the Lugano report where taken from the Ravi files made available by the MFMP. This was done by replacing the embedded profile in the Ravi files by a Lugano style profile.

    The dogbone did not show up totally horizental on the Optris thermal pictures and as such the Lugano profile did not match the camera picture perfectly.

    I did not correct the profile for this. since the introduced errors where in my opinion not very significant for this comparison.

    From each file (500, 700 and 900 Watt) the temperatures for all sections where taken at the 5 minute mark .

    Then the average temperature of the ribbed area of each run was taken and this value was used to do new CFD simulations to determine the convective heat correction factor of the ribbed area for that average temperature. This since the fin spacing where the maximum heat transfer occurs is temperature dependent and this optimum spacing increases with increasing temperature.

    Otherwise stated, due to the optimal spacing shift to the right with increasing temperatures, the correction factor decreases with increasing temperatures, but is also dependent on the change in the convective heat transfer coefficient.

    For the MFMP 500,700 and 900 watt runs the correction factor was found to be relative constant with an average value of about .695

    With the above established convective heat correction factor for the ribbed area and the section temperatures the total thermal power (convective and radiated) for each run was calculated

    These thermal powers where then compared with the input powers.

    The results are :

    Run Input power (Watt)-------------Thermal power (Watt)------- Error (%)

    500 Watt-------------502------------------------- 591.14----------------------16.3

    700 Watt-------------713--------------------------916.67----------------------27.3

    900 Watt-------------895------------------------1208.77----------------------33.9

    The results confirm the earlier statement in a previous post that for the MFMP dogbone thermal test the total convective and radiated power is much more then the applied power.

    Update 3-11-2018

    For the 500 watt run the error was stated as 6.3%, however it was 16.3 %

    Initially that didn't work also

    If I loaded another profile then the one embedded in the Ravi file, then the colored temperature information disappeared.

    Also the configuration menu was not properly working and I had many crashes.

    This all without warnings.

    Have now installed the software on another, almost identical computer, and it is now working properly.

    Could also load the Lugano profile and use it on the MFMP Ravi data

    Thanks for the above link


    'm not saying you are making stuff up.

    That's what Zeus46 already explained.

    I think I need to fly over to Liverpool to visit family and upgrade my understanding of the English language. (Have already an invitation)

    I'm saying the long list of experimental bad practice from Lugano is so extravagant that you could not make it up.

    I agree that they where very sloppy.

    Don't know if that was in general the case or that they rushed out their report too fast and made a lot of errors in it.

    However the calculation of the convective and radiated power matches up with the applied power.

    Don't know if that is that is just coincidence or not.

    On the other hand in earlier FEM simulations of the MFMP dogbone I got temperatures already close to the reported ones in the Lugano report.

    That's why I with the aquired knowledge want to recalculate the convective and radiated power of their 500W run and maybe after that a new FEM simulation.

    Maybe it will tell us somewhat more.

    I took this horizental profile from the Ravi 500W file

    And think indeed that this is a profile measured with an in band Optris emissivity setting of 1

    Your picture with the different sections as in Lugano is nice and gives the average section temperatures

    However when I want tot create my own sections such as in your picture above then the program refuses and states that it can not connect to the camera.

    So I think I need to spend some time on the manual.

    But I could save some time if you could supply the average section temperatures for each section for the 500 Watt situation.

    That because I want to calculate the total convective and radiated power for the 500 W case and see if after all the calculation updates, there is still more convective and radiated power then the aupplied power of 500 Watt.

    So now we reach the point where we see in the report that the emissivity curve, shown in Plot 1, was “adapted” to the type of alumina used, after comparing the results of the 0.95 emissivity Kapton “dots” (maximum temperature 380 C, tested on the Rods, since they would not stick to the actual reactor). Whatever that means, since there is no other mention of this in the report, nor any plot that shows this emissivity curve adaptation.

    The text in the report is :

    We therefore took the same emissivity trend found in the literature as reference; but, by applying emissivity reference dots along the rods, we were able to adapt that curve to this specific type of alumina, by directly measuring local emissivity in places close to the reference dots (Figure 7).

    They talk about an emissivity trend found in literature they used as reference, but did not state what kind of trend they referred to.

    Was it the broadband emissivity trend of Alumina they referred to or the in band emissivity trend for alumina ?

    As usual the report is very vague about this and as such makes it for the reader of the report indeed another controversial point.

    So you are right that we don't know what it means.

    Besides the above a question for you.

    If I take a horizental temperature profile from a MFMP dogbone thermal test 2, then what emissivity was used to measure those temperatures.

    My guess is that it is 1.

    I am almost sure you can tell me what it was.


    The report says the dummy run used thermocouples for temperature (which were not used for the active runs).

    You just can't make this stuff up!

    Sure they used thermocouples in preparation of the dummy run.

    (Actual one, the one as they stated which was normally used for the ambient temperature measurement)

    But the actual temperature measurements during the dummy where done by the Optris Camera.

    However they used the ambient thermocouple to compare the measured temperature by the Optris of a reference dot on a rod with that of the thermocouple and noted that they where in close agreement.

    Then they adjusted the emissivity of the Optris to give for the rod the same reading and this should have given them for that temperature the right emissivity setting of the Optris for the type of alumina used for the rods(Which by the other density of the alumina rods could have been a little bit off)

    Having done so I would find it very strange that in that situation, when they saw that the emissivity setting they found differed very much from the broadband emissivity that they would have used during the dummy run broadband emissivities on the Optris for the ribbed area.

    And the recalculation showed that there is a large likelyhood that indeed they used the correct emissivities.

    So I can't agree with you that I am making stuff up.

    This because "the stuff" is the outcome of calculations and simulations, not something I dream up.

    Reference about the application of thermocouples in the Lugano report is given below :

    Page 3

    A thermocouple probe, inserted into one of the caps, allows the control system to manage power supply to the resistors by measuring the internal temperature of the reactor.

    This is the internal thermocouplw which is used for temperature control

    It has not to do anything with measuring surface temperatures.

    Page 4

    The IR cameras, on the other hand, were focused on circular tabs of adhesive material of certified emissivity (henceforth referred to as “dots”). The relevant readings were compared to those obtained from a thermocouple used to measure ambient temperature, and were found to be consistent with the latter, the differences being < 1°C

    Here is stated that they used a thermocouple to verify that the measured temperatures by the Optris from the thermal dots was in agreement with a thermocouple which normally was used for reading the ambient temperature.

    Page 7

    We also found that the ridges made thermal contact with any thermocouple probe placed on the outer surface of the reactor extremely critical, making any direct temperature measurement with the required precision impossible

    Here is stated that they found that measuring of the ridges with a thermocouple was very critical and would make direct temperature measurement impossible.

    As such they used the Optris for indirect measurement.

    Lugano dummy run with supposed Optris emissivity error recalculated

    In the attached Excel spreadsheet the total radiated and convective power of the Lugano test for the situation in which the Lugano testers would have used broadband instead of in-band emissivities on the Optris is calculated.

    Using broadband emissivities instead of Optis in band emissivities leads to the measured temperatures to be inflated and it has been assumed by many that these inflated temperatures are the reason for the positive COP values reported in the Lugano report.

    Since we have found in this forum thread some errors with respect to how radiative and convective powers have to be calulated, we can now apply the correct calculation methods to the Lugano data.

    We have done this already for the situation where we assume that the temperatures where measured correctly and have found that in that case the applied power is almost in agreement with the calculated radiative and convective power.

    In the included Excel spreadsheet to this post we do the same calculation for the case where the Lugano testers would have used broadband instead of in band emissivities when measuring temperatures with the Optris thermal camera.

    Recalculated supposed inflated temperatures due to using broadband instead of in band emissivities where imported from the spreadsheet with the recalculated temperatures (see post # 413 ) and incorporated as a separate page in the Excel file.

    The result of the recalculation is that the total convective and radiated power is 414.95 Watt, a difference of -13.50 % with respect to the applied electrical power.

    This difference of -13.50 % compared to the a difference of 1.62 % when we assume that the the temperatures where not inflated is another indication that the reported temperatures of the Lugano dummy run where likely correct.

    Nice work !

    From which MFMP test did you use the Ravi data ?

    The 700 Watt or 900 Watt run ?

    The minimum temperature set for the color display was somewhat high in the MFMP Ravi file and as such the cap temperatures where a flat profile showing the minimum set temperature.

    Don't know if that can be adjusted afterwards so that the real temperatures show up.

    As I stated in an earlier post the cooler cap temperatures for the MFMP run can possibly be explained by the Lugano device having its heater coil windings continue under the end caps.

    Since most issues for a calculation are now known, I could in the future do two FEM simulations. One without the heater coil extending under the end caps and one with extended heater coils.

    Maybe from the resultsing temperature profiles we can then determine what is the most likely case.

    Concerning the gaps, it does depends on what emissivity was set for the background ?

    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.

    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.

    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.


    • n

      (7.86 kB, downloaded 17 times, last: )

    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

    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


    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.

    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

    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.

    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)

    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.

    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

    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.

    Lugano ECAT convection correction

    Due to the close spacing of the ribs of the Lugano ECAT, the convective heat transfer of the ribs is less effective. Thus there needs to be applied a correction to the calculated convective heat transfer of the ribs.

    Without a correction the convective heat transfer is calculated based on the calculated convective heat transfer coefficient for the base tube with a diameter of 20 mm.

    The convected power is then calculated by multiplying the convective heat transfer coefficient of the tube by the area of the fins and the difference temperature of the surface and the ambient temperature. The formula :

    Q = h x Af x (Ts - Ta)

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

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

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

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

    However due to the fins being close to each other and their respective convective heat flows interacting, the convective heat transfer will be less effective and will result in a lower convected power.

    Evaluating the above formula it means that the convective heat transfer coefficient has a lower value then one would expect when calculating it based on a bare tube. (which is the basis for the calculation in the Lugano report). The question now is how to determine the correct value of the convective heat transfer coefficient for a finned area as used on the Lugano ECAT.

    The method followed was to calculate with the CFD software the convected power for two different section lengths of a finned area, the second section having halve the length of the first section.

    The sections where simulated with a temperature of 445 degree C and an environmental temperature of 21 degree C.

    Subtracting from the power of the longer section the power of the halve section yields the power of a halve section.

    Since for both simulated sections the convected power of the sides at the ends is equal, this power of the sides is then automaticcaly removed by the subtraction and only the power of the finned area is calculated in this way.

    Deviding the calculated convected power of the halve section by the fin area of the halve section and by the difference between section temperature and ambient temperature gives the convective heat transfer coefficient.

    This convective heat transfer coefficient obtained in this way was found to have a value of 9.99

    Since the value for a bare tube of 20mm diameter, tube temperature of 445 degree C and an ambient temperature of 21 degree C is 13.28 the convective heat correction factor becomes :

    -------------------------Correction factor = 9.99/13.28 = .752

    The conclusion is that due to having the fins next to each other without additional spacing in between, the convective heat transfer of the finned area is lower then one would expect based on the calculation in the Lugano report.

    Simulating convection with CFD - update 2

    In my previous post I wrote :

    Next step now is to do some additional simulations to gain more insight on the effect of using higher levels of meshes (smaller mesh sizes) instead of using a boundery layer. This since if the smallest mesh size is less then the thicknes of the first (smallest) boundery layer, the simulation results are expected to be to be as good as with a boundery layer. (But the calculation overhead much larger due to the greater amount of meshes)

    Thus I started simulating the bare tube again using meshing levels 1, 2, 3 and 4 and without a boundery layer. A higher messing level then 4 was not possible due to exceeding the maximum number of meshes allowed for my version of the program.

    I did not do a rerun for level 1, since that was already simulated and the result presented in my previous post. For all 4 meshing levels a cross sectional view was made. These are presented in the following figure.

    Each case was again simulated with a tube temperature of 445 degree C and an environmental temperature of 21 C.

    From the reported heat flux for each simulated case the heat tranfer coefficient was calculated.

    The results can be found in the following table :

    Level-----------heat transfer coefficient-------------deviation (%)

    ---1------------------------10.84------------------------------- -18.4

    ---2------------------------12.84--------------------------------- -3.4

    ---3------------------------13.03--------------- ----------------- -1.9

    ---4------------------------13.24--------------------------------- -0.3

    The reported deviation is the deviation from the value calculated with the method used in the Lugano report, the value being 13.28

    For the smallest grid simulated, the deviation from the value derived from the calculation method used in the Lugano report is only -0.3%

    Level 4 simulation with one layer per mesh size

    Meshing a ribbed area requires many more meshes then for a bare tube as used in the simulations above.

    This is because the area between the ribs must be meshed with a small mesh size for proper simulation of the convective heat between the ribs.

    In order to reduce the number of meshes in order to stay within the limits of my program I deceided for the bare tube to do an experiment with one layer of meshes per mesh size instead of the 4 layers as used in the examples shown in the figure above. This reduces the number of total meshes.

    The result of that simulation was that the calculation of the convective heat transfer coefficient had for this case a value of 13.28, the same as the value calculated with the method in the Lugano report.

    My conclusion is that a level 4 simulation without a boundery layer will give results very close to the values obtained with the method used in the Lugano report.

    Simulating convection with CFD - update 1

    As a first approach to simulating natural convection for a ribbed tube I started with simulating convection of a bare tube.

    I used the bare tube case since calculating natural convection for a bare tube is a standard case which is well researched and as such the calculation of the convective heat transfer coeefficients are near accurate using established formula's such as the ones used in the Lugano report. This makes it possible to compare the value of the calculated heat transfer coeffcient with those of the simulations.

    The case simulated was for a bare tube with a diameter of 20 mm. Tube temperature was set to 445 degree C (About the central temperature of the Lugano ECAT during the dummy run) and an environmental temperature of 21 degree C.

    For the meshing of the fluid (Air) a level 1 grid was used (2 seizes of meshes). For the meshing of the tube a level 1 was used (2 seizes of meshes).

    Then the heat flux from the tube by natural convection was simulated for two cases, the first being with the original derived mesh, the second with the original mesh but with an added boundery layer mesh at the surface of the tube for improved simulation accuracy of the convective heat transfer.

    A cross sectional view of both cases is shown in the following figure.

    The properties of the fluid (Air) where simulated with the janaf formula's for the thermodynamic properties of air and with the sutherland approach for the transport coefficients.

    (I had found somewhere that using these gives the best results when calculating convective heat transfer)

    First I calculated, following the method outlined in the Lugano report, the convective heat transfer coeffcient for the tube. For the mentioned temperatures the coefficient had a value of 13.28

    For the case without the boundery layer mesh I calculated back from the total heat flux from the tube as reported by the CFD program a convective heat transfer coefficient of 10.82

    For the simulated case with the added boundery layer mesh the obtained value was 13.74, the difference with the Lugano calculation method being 3.7 %.

    The conclusion is that even with a coarse mesh grid for the fluid, but with the addition of a boundery layer mesh, the calculated value of the convective heat transfer is close to the value obtained by existing formula's such as the ones used in the Lugano report.

    Maybe the accuracy can be improved somewhat more by adapting the janef and sutherland material coeffcients such that they give a closer match in the temperature range of the simulation.

    Currently the error is in my opinion quite acceptable, also taking into account that a convective heat transfer correction factor for the ribbed area of the ECAT will be based on a ratio calculation.

    Since for both a bare tube and a ribbed tube for the same temperatures, the deviations of thermal coefficients used by the CFD program will be equal for both cases, the ratio calculation will limit the error somewhat.

    Next step now is to do some additional simulations to gain more insight on the effect of using higher levels of meshes (smaller mesh sizes) instead of using a boundery layer. This since if the smallest mesh size is less then the thicknes of the first (smallest) boundery layer I used in the example above, the simulation results are expected to be to be as good as with a boundery layer. (But the calculation overhead much larger due to the greater amount of meshes)