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Why is surface average different from line average?
Posted 10 oct. 2013, 06:15 UTC−4 Heat Transfer & Phase Change, Computational Fluid Dynamics (CFD) 9 Replies
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Hello everyone,
I have a 2D axisymmetric model with a heat flux creating a temperature gradient.
When I use the Average Tool (Derived Values > Average) I get a significantly higher Surface Average temperature from a rotated boundary line than the Line Average temperature from the same boundary line.
Which average temperature is appropriate for the 2D axisymmetric model? And why?
So far the Surface Average gives me wrong results. But shouldn't be this more exact?!
Please help me with this. I am struggeling with this for a long time.
Thank you,
Fabian Holz
I have a 2D axisymmetric model with a heat flux creating a temperature gradient.
When I use the Average Tool (Derived Values > Average) I get a significantly higher Surface Average temperature from a rotated boundary line than the Line Average temperature from the same boundary line.
Which average temperature is appropriate for the 2D axisymmetric model? And why?
So far the Surface Average gives me wrong results. But shouldn't be this more exact?!
Please help me with this. I am struggeling with this for a long time.
Thank you,
Fabian Holz
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9 Replies Last Post 7 nov. 2013, 10:53 UTC−5
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Posted:
1 decade ago
Hi,
please note that the average over the line is mathematically not the same as over the surface (cut plane). Moreover, you actually do not need the cut plane in order to obtain the surface average of the revolved geometry. COMSOL provides the check box "Compute Surface Integral" in the "Integration settings" section of the "Line average" settings window. By using this, the result coinsides with the "Surface Average".
You may find some explanations in the chapter "Derived Values Common Settings" in the documentation.
Best regards
Bettina Schieche
please note that the average over the line is mathematically not the same as over the surface (cut plane). Moreover, you actually do not need the cut plane in order to obtain the surface average of the revolved geometry. COMSOL provides the check box "Compute Surface Integral" in the "Integration settings" section of the "Line average" settings window. By using this, the result coinsides with the "Surface Average".
You may find some explanations in the chapter "Derived Values Common Settings" in the documentation.
Best regards
Bettina Schieche
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Posted:
1 decade ago
Hi Bettina,
Thank you for your answer.
I do understand the mathematical difference between "Surface-" and "Line Average". Though I wonder which of them represents the "real" average mixed temperature of my simulated system. It need it to verify the developped temperature profile with the Nusselt number. This works only with the (simplified) "Line average" temperature, although from my point of view the "Surface Average" should represent the "real" average Temperature more.
Do you understand my problem? It could try to explain in German.
Best regards,
Fabian Holz
Thank you for your answer.
I do understand the mathematical difference between "Surface-" and "Line Average". Though I wonder which of them represents the "real" average mixed temperature of my simulated system. It need it to verify the developped temperature profile with the Nusselt number. This works only with the (simplified) "Line average" temperature, although from my point of view the "Surface Average" should represent the "real" average Temperature more.
Do you understand my problem? It could try to explain in German.
Best regards,
Fabian Holz
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Posted:
1 decade ago
Hi,
I agree with you that the surface average should represent the "real" average mixed temperature across the top surface. The fact that the value is slightly higher than the line average is as expected for your temperature profile. So, in terms of COMSOL and maths, everything seems to be correct. What do you mean by " This works only with the (simplified) "Line average" temperature"? Is this value rather the one you expect? Do you compare to measurements? How does the average correspond to the Nusselt number?
Regards,
Bettina
I agree with you that the surface average should represent the "real" average mixed temperature across the top surface. The fact that the value is slightly higher than the line average is as expected for your temperature profile. So, in terms of COMSOL and maths, everything seems to be correct. What do you mean by " This works only with the (simplified) "Line average" temperature"? Is this value rather the one you expect? Do you compare to measurements? How does the average correspond to the Nusselt number?
Regards,
Bettina
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Posted:
1 decade ago
Hi Bettiina,
thank you for your interest.
I need verify the simulation setup by comparing it with the local Nusseltnumber (Nu=alpha*diameter/conductivity) given in the common literature which tends to 4.364 at an infinitesimal long circular duct.
Nu depends mainly on the heat-transfer coefficient alpha (alpha=heatflux/(Twall-Tmixed)). Due to a higher mixed temperature (with the surface average method) in the end of my duct, alpha becomes to high (approx. 6). Considering the "line average" mixed temperature it is 4.3.
From my point of view the "surface average" method should represent the "real" local mixed temperature in the duct more. I checked every step of the calculation twice. I don't want to question the Nusseltnumber from the literature. Is there the possibility that the COMSOL simulation is calculated in an "infinitesimal small" plane and the result extruded around the axis of the circular duct, so it corresponds only with the "line average" mixed temperature?
Regards,
Fabian
thank you for your interest.
I need verify the simulation setup by comparing it with the local Nusseltnumber (Nu=alpha*diameter/conductivity) given in the common literature which tends to 4.364 at an infinitesimal long circular duct.
Nu depends mainly on the heat-transfer coefficient alpha (alpha=heatflux/(Twall-Tmixed)). Due to a higher mixed temperature (with the surface average method) in the end of my duct, alpha becomes to high (approx. 6). Considering the "line average" mixed temperature it is 4.3.
From my point of view the "surface average" method should represent the "real" local mixed temperature in the duct more. I checked every step of the calculation twice. I don't want to question the Nusseltnumber from the literature. Is there the possibility that the COMSOL simulation is calculated in an "infinitesimal small" plane and the result extruded around the axis of the circular duct, so it corresponds only with the "line average" mixed temperature?
Regards,
Fabian
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Posted:
1 decade ago
Hi Fabian,
for 2D axi COMSOL takes a 3D equation and performs a transformation to a polar coordinate system. This results in a 2D equation in the coordinate system (r,z). This equation is actually solved and can be seen when enabling the equation view.
Regards,
Bettina
for 2D axi COMSOL takes a 3D equation and performs a transformation to a polar coordinate system. This results in a 2D equation in the coordinate system (r,z). This equation is actually solved and can be seen when enabling the equation view.
Regards,
Bettina
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Posted:
1 decade ago
Hi Fabian,
I believe you are using the wrong definition of the mean temperature Tmixed. It should be the mean temperature of the fluid passing through the cross-section. That means the surface integration of T*w (the z component of velocity) divided by the surface integration of w.
Nagi Elabbasi
Veryst Engineering
I believe you are using the wrong definition of the mean temperature Tmixed. It should be the mean temperature of the fluid passing through the cross-section. That means the surface integration of T*w (the z component of velocity) divided by the surface integration of w.
Nagi Elabbasi
Veryst Engineering
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Posted:
1 decade ago
for 2D axi COMSOL takes a 3D equation and performs a transformation to a polar coordinate system. This results in a 2D equation in the coordinate system (r,z). This equation is actually solved and can be seen when enabling the equation view.
Thank you, Bettina. This made it clear to me, that my COMSOL settings were right.
Hi Nagi,
I didn't understand your sugggestion of how to calculate the mean temperature. I want to calculate it from a cross-section with a infinitesimal short length dz. Due to the fact that the system is stationary, is there any influence of the fluid velocity at all?
Best regards,
Fabian
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Posted:
1 decade ago
Hi Fabian,
Yes the fluid velocity should influence the mean temperature. Basically what you need is the mean temperature of the fluid and the regions of the cross-section which have a higher velocity will transport more fluid.
Nagi Elabbasi
Veryst Engineering
Yes the fluid velocity should influence the mean temperature. Basically what you need is the mean temperature of the fluid and the regions of the cross-section which have a higher velocity will transport more fluid.
Nagi Elabbasi
Veryst Engineering
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Posted:
1 decade ago
Hey Nagi,
thank you so much that you gave me this hint with the velocity. I finally found a formula to calculate my mean Temperature and this is in fact affected by the velocity although it is part of a stationary system!
The formula for the mean temperature is:
Tm=2/(Vavg*R²)*INTEGRAL[0;R]T(r)*u(r)*r*dr with
Vavg= 2/R²*INTEGRAL[0;R]u(r)*r*dr
Thank you two for your help :)
Greetings from Germany,
Fabian
thank you so much that you gave me this hint with the velocity. I finally found a formula to calculate my mean Temperature and this is in fact affected by the velocity although it is part of a stationary system!
The formula for the mean temperature is:
Tm=2/(Vavg*R²)*INTEGRAL[0;R]T(r)*u(r)*r*dr with
Vavg= 2/R²*INTEGRAL[0;R]u(r)*r*dr
Thank you two for your help :)
Greetings from Germany,
Fabian