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May 21, 2003, 04:53 |
Total shear rate in a 3 dimensional flow
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#1 |
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Hallo All
The shear stress on a fluid element in a unidirectional flow is given by du/dy (y the distance from the wall). Is it then correct that the total shear rate on a fluid element in a 3 dimensional flow is expressed by the shear rate tensor (a 3 times 3 matrix)?? Regards Bo |
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May 22, 2003, 15:43 |
Re: Total shear rate in a 3 dimensional flow
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#2 |
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I think it's not completely correct. rate-of-strain tensor 2D = \Delta \vec{v} + (\Delta \vec{v})^T
shear rate is equal to sqrt(-II_{2D}). where II_{2D} is the second invariant of the rate of strain tensor, |
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May 23, 2003, 04:00 |
Re: Total shear rate in a 3 dimensional flow
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#3 |
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Hallo xueying
Could you please elaborate on the equations... I cannot make out what they mean.. Regards Bo |
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May 23, 2003, 16:26 |
Re: Total shear rate in a 3 dimensional flow
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#4 |
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Sorry, I wrote it in latex format.
To calculate the shear rate, first you need rate-of-strain tensor (let's say 2D); then you need to calculate the second invariant of the tensor 2D (let's say II_2D); finally your shear rate equals to square root of the negative second invariant. Where rate-of-strain equals to gravient v + transpose of gravient v; note gravient is a tensor. |
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