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01-14-2018 09:01 AM

Hi,

again I don't understand a certain behaviour ...

I want to calculate the temperature distribution within a furnace of a shell boiler. On the inner side you know the thermal load - there is a heat flux due to the flame which changes in the longitudinal direction of the furnace. I modelled this using a field.

On the outer side there is convection due to pool boiling. The heat transfer coefficient changes with the wall temperature. The governing equation is known. I defined a non-geometric element which I called water and defined its temperature at 184.07°C. I used a Thermal Coupling Simulation Object with a Secondary Region Override using the non-geometric element water. The temperature depency was modelled again by a field.

The results achieved are in my opinion correct - I worked for several years in this industry. The results are consistent with those of a rough calculation using paper and pencil.

Especially we find a minimum temperature of about 193°C and a maximum temperature of about 348 °C.

Then I tried to use the Constraint Type Convection to Enviroment instead of Thermal Coupling. I used the identical field as I used Thermal Coupling in order to define the temperatur depency of the heat transfer coefficient. The Enviroment Temperature was specified at 184.07°C, of course.

The results achieved are in my opinion not correct.

Especially we find a minimum temperature of about 199°C and a maximum temperature of about 358 °C.

If you compare the heat transfer coefficients calculated by an evaluation of the given equation with the heat transfer coefficients calculated by TMG using Thermal Coupling you find a good match.

If you do the comparison using the heat transfer coefficients calculated by TMG using Convection to Enviroment you find a bad match.

The abscissa values are the wall temperatures calculated by TMG in both cases.

Is there anything I could have done wrong? In my opinion, both methods should lead to identical results.

I am grateful for any hint.

Thank you in advance, many greetings

muppets

13 REPLIES

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01-15-2018 09:07 AM

The Convection to Environment constraint models the heat transfer using q=hA(Ts-Te).

What does the governing equation look like for the boiling water side?

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01-15-2018 10:16 AM - edited 01-15-2018 11:52 AM

The equation is based on Gorenflo's work, see VDI Heat Atlas Section H2. The equation is

h = 1.8682 * (temperature / 1C)^3 - 952.1708 * (temperature/1C)^2 + 160437.4626 * temperature / 1C - 8921515.0596,

which gives you the heat transfer coefficient with the unit W/(m² K). The temperature is the waterside wall temperature. This equation is valid for a pressure of 10 bar g (the corresponding saturation temperature is 184.07°C). I derived this eqution using the orginal equation of Gorenflo and fitting it just using Excel.

Please note that I used the above equation with Thermal Coupling, which produced the correct result and with Convection to Enviroment, which gave the wrong result.

Interesting could be that the calculated heat transfer coefficients with Convection to Enviroment are too small with a almost constant ratio h (correct) / h (Conv to Env) = 5.3 over the whole temperature range (refer also to the second graph in my first post).

Best regards

muppets

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01-16-2018 12:27 PM

In the first case, the non-geometric entity (i.e., "water") is thermally coupled to the surface. It's temperature therefore evolves over time.

In the second case, the convection to environment constraint is coupled to the environment, which is at a fixed temperature.

The two approaches will produce different results. The first is heat transfer to what is essentially a finite mass of water. The second is heat transfer to a large (effectively isothermal) reservoir.

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01-16-2018 02:31 PM

Thank you so much for your answer. I'm afraid I can't agree.

water is a modelling object of the type non-geometric. It doesn't have a mass und it's temperature doesn't change, please refer to the figure below.

Please consider also that the simulation is a steady state one.

It is to be stated that the results using thermal coupling with the non geometric modelling object water and the equation for the heat transfer mentioned in the previous post are correct whereas the results using convection to enviroment are n o t correct although the identical equation was used.

Best regards, thank you again

muppets

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01-17-2018 09:50 AM

You are correct. The NGE is indeed at a fixed temperature. My apologies for the confusion.

I created a simple model with a prescribed heat flux. In one solution, I use a NGE and in the other, a convection to environment constraint. They had the same heat transfer coefficients. The resulting temperatures were identical.

Looking at your plots once more, I noticed that the calculated heat transfer coefficient (based on the formula) is different in each case. Is this intended?

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01-17-2018 10:14 AM - edited 01-18-2018 11:00 AM

Again, thank you very much!

You are right, it could give the impression that heat transfer coefficient based in the formula is different in each case. Please not that the abscissa values on both diagrams are different, too. The heat transfer coefficient calculated by the formula is identical in both cases if you use identical temperatures.

~~I did some further detective work. I found out that the both heat transfer coefficients - formula and TMG / convection to enviroment are identical if you use a constant heat flux on the fire side. Only when you apply a local variable load on the fire side you get different values.~~

Edit 20170118: Strikethrough, because the error occurs also with constant heat flux.

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01-26-2018 11:11 AM

It took a bit of digging but here's what's happening. Thermal coupling with a non-geometric element does not support spatial distribution. Please see this documentation page: https://docs.plm.automation.siemens.com/tdoc/nx/12/nx_help/#uid:id627146

That said, there is another way to model the coupling. Instead of using an expression, use a formula field:

This will yield identical results for both thermal coupling to the NGE and convection to environment:

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01-28-2018 01:41 PM

Thank you so much for your efforts. I' m afraid we still haven't found the solution. I always used formula fields. I never tried a spatial distribution for the heat transfer coefficient. Always I used the temperature as independent variable. Please refer to the figure below. Please note that I used NX 10 when I started to examine the temperature distribution.

To symplify the issue I modelled only a small piece of the furnace subject to a constant heat flux load of 184,000 W/m². Then I derived a new equation for the heat transfer coefficient as a function of the temperature. The sole reason for this was that I wanted to be able to solve the problem analytically using paper and pencil. This would have been difficult with the first used 3rd order polynomial. However, the basis of the new equation and of the first used 3rd order polynomial is identical: the work of Gorenflo.

The analytically found result can be easily understood, see attachment analytic_solution.pdf. The wall temperature on the water side is 192.76 °C, the corresponding heat transfer coefficient is 21382.2 W/(m² K).

Using NX 10 and thermal coupling to a non-geometric element water having the temperature of 184.07°C yields exactly these results: 192.76°C and 21382.2 W/(m² K), please refer to the figures below.

Using the same formula field and convection to enviroment yields wrong results, see figures below.

The wrong results are 198.27°C for the wall temperature and 13100 W / (m² K) for the heat transfer coefficient.

It is particularly interesting that if one uses the temperature 198.27°C in the equation for the heat transfer coefficient, one doesn't receive 13100 W / (m² K), but 70607.2 W / (m² K). This is a factor of about 5.3 which I've seen already in my first examinations calculating the whole furnace, see my second post in this discussion.

If you are more interested I attached my NX-10 model in the file 4_6_gtac_10.zip.

The strangest still comes. We have installed NX 12 for a couple of weeks and of course I tried to solve the model using NX 12. In both cases - convection to enviroment and thermal coupling - the results are w r o n g ... The temperature is calculated at 198.27°C and the heat transfer coefficient at 13100 W / (m² K). I also attached my NX-12 model in the file 4_6_gtac_12.zip.

My confusion is maximum. I do know that 192.76 °C and 21382.2 W/(m² K) are correct ...

Best regards

muppets

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02-22-2018 10:56 AM

Muppets,

short ideas:

1. In your PDF post you did not use the absolut value function. But I think there is no influence to results because your ecpected values are larger than 184.07 C.

2. Maybe it's a measurement unit conversion problem. I can't solve your solution (no license rot NX Thermal/Flow) but I know that in NX NASTRAN - Termal , not NX Thermal/Flow there are all values converted into micro-Watt, mm and Celsius ...

Only a suggestion: Try to define your fourmula field in measurement units which are native for output unit system. What is written in your solution deck, I assume it's also a dat file. Can you find your formula there? Is it correct?

And I wonder if there is really an analytical formula inside. I think there is a table field definition. Could you check it?

Best wishes, Michael

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