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What's the formulation of "mechanical energy flux" in COMSOL?

Posted 2012年8月8日 GMT+8 22:39 Results & Visualization, Structural Mechanics Version 4.2, Version 4.2a, Version 4.3 8 Replies

Ting-Wei Liu
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There are "mechanical energy flux," "complex mechanical energy flux"
which I can derive or plot in the result.
They are cool but still I want to know the definitions of them, how it calculates, and I did not find them in the user manuals.
Could somebody tell me? Thanks.
8 Replies Last Post 2016年8月23日 GMT+8 22:25
COMSOL Moderator

Hello Ting-Wei Liu

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Guilhem Viallet
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Posted: 1 decade ago 2013年5月23日 GMT+8 22:12
Hi,

Nobody answer you? because i'm also interested to kwow more about this indicator and to what is the formulation difference between «mechanical energy flux» and «complex mechanical energy flux».
Hi, Nobody answer you? because i'm also interested to kwow more about this indicator and to what is the formulation difference between «mechanical energy flux» and «complex mechanical energy flux».
Henrik Sönnerlind COMSOL Employee

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Posted: 1 decade ago 2013年5月24日 GMT+8 14:29
Hi,

The mechanical energy flux is a vector formed by the multiplication of the stress tensor and the velocity vector. Mathematically:



The reason to have the minus sign in the definition is that if you put a pressure on an external boundary, and it moves in the direction of the load, then a positive power input in the direction of the load is obtained.

In time domain, the expression above is sufficient, but in frequency domain, there are two flavors:

The "Complex mechanical energy flux" is now the complex vector formed by the operation above, but with the velocity replaced by its complex conjugate.



The "Mechanical energy flux" in frequency domain is a real quantity; the cycle average of the "Complex mechanical energy flux"



In the appended screenshots you can see the definitions as displayed in Equation View in time and frequency domain.

Thanks for pointing out that this is not properly documented. It will be improved in upcoming versions.

Regards,
Henrik
Hi, The mechanical energy flux is a vector formed by the multiplication of the stress tensor and the velocity vector. Mathematically: [math] I_i =- \sigma_{ij} v_j [/math] The reason to have the minus sign in the definition is that if you put a pressure on an external boundary, and it moves in the direction of the load, then a positive power input in the direction of the load is obtained. In time domain, the expression above is sufficient, but in frequency domain, there are two flavors: The "Complex mechanical energy flux" is now the complex vector formed by the operation above, but with the velocity replaced by its complex conjugate. [math] I_i =- \sigma_{ij} v_j^* [/math] The "Mechanical energy flux" in frequency domain is a real quantity; the cycle average of the "Complex mechanical energy flux" [math] I_i =\frac{1}{2}Re(- \sigma_{ij} v_j^*) [/math] In the appended screenshots you can see the definitions as displayed in Equation View in time and frequency domain. Thanks for pointing out that this is not properly documented. It will be improved in upcoming versions. Regards, Henrik
Ting-Wei Liu
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Posted: 1 decade ago 2013年5月24日 GMT+8 15:54
Thank you for the explanation, the definition (stress dot velocity) looks as people's exception for mechanical energy flux.
But in the COMSOL of my computer (COMSOL 4.3), the (complex) mechanical energy flux has the unit of W/m^3, where I saw it using "point evaluation," and it was W/m for surface integration!?
Shouldn't they be W/m^2 & W in the sense of energy flux (and also the definition)?
Where did I miss it?
Thank you!

Liu
Thank you for the explanation, the definition (stress dot velocity) looks as people's exception for mechanical energy flux. But in the COMSOL of my computer (COMSOL 4.3), the (complex) mechanical energy flux has the unit of W/m^3, where I saw it using "point evaluation," and it was W/m for surface integration!? Shouldn't they be W/m^2 & W in the sense of energy flux (and also the definition)? Where did I miss it? Thank you! Liu
Henrik Sönnerlind COMSOL Employee

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Posted: 1 decade ago 2013年5月24日 GMT+8 19:45


But in the COMSOL of my computer (COMSOL 4.3), the (complex) mechanical energy flux has the unit of W/m^3, where I saw it using "point evaluation," and it was W/m for surface integration!?
Shouldn't they be W/m^2 & W in the sense of energy flux (and also the definition)?



You are right. The unit for this quantity was wrong in versions prior to 4.3b. This does not affect the values (only the unit display) as long as results are displayed in the unit system of the model, but unit conversions will be wrong. To get the automatic unit conversion to work you can, as an example, evaluate solid.IX*1[m] instead of just solid.IX (assuming that the SI system is used).

Regards,
Henrik
[QUOTE] But in the COMSOL of my computer (COMSOL 4.3), the (complex) mechanical energy flux has the unit of W/m^3, where I saw it using "point evaluation," and it was W/m for surface integration!? Shouldn't they be W/m^2 & W in the sense of energy flux (and also the definition)? [/QUOTE] You are right. The unit for this quantity was wrong in versions prior to 4.3b. This does not affect the values (only the unit display) as long as results are displayed in the unit system of the model, but unit conversions will be wrong. To get the automatic unit conversion to work you can, as an example, evaluate solid.IX*1[m] instead of just solid.IX (assuming that the SI system is used). Regards, Henrik
Guilhem Viallet
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Posted: 1 decade ago 2013年5月24日 GMT+8 20:30
Thank you for these explanations!
Thank you for these explanations!
Ting-Wei Liu
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Posted: 1 decade ago 2013年5月25日 GMT+8 12:32
Thank you very much!!
Thank you very much!!
Mohan Shen
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Posted: 9 years ago 2016年8月14日 GMT+8 22:01
Hi Henrik,
In my case I also need to calculate the energy flux through a face in piezoelectric module, but why the energy flux through a free boundary condition face is not zero?
Thank you!
Hi Henrik, In my case I also need to calculate the energy flux through a face in piezoelectric module, but why the energy flux through a free boundary condition face is not zero? Thank you!
Henrik Sönnerlind COMSOL Employee

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Posted: 9 years ago 2016年8月23日 GMT+8 22:25
The stresses are not exactly zero on a free boundary since they are a result computed from the gradients of the displacements.

As a consequence, the energy flux may also be non-zero. It should be small when compared to the flux at other places in the model, though.

How close to zero the stresses are on a free boundary depends on the mesh size.

Regards,
Henrik
The stresses are not exactly zero on a free boundary since they are a result computed from the gradients of the displacements. As a consequence, the energy flux may also be non-zero. It should be small when compared to the flux at other places in the model, though. How close to zero the stresses are on a free boundary depends on the mesh size. Regards, Henrik

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