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Total shear rate in a 3 dimensional flow

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Old   May 21, 2003, 03:53
Default Total shear rate in a 3 dimensional flow
  #1
Bo Busk Jensen
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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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Old   May 22, 2003, 14:43
Default Re: Total shear rate in a 3 dimensional flow
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xueying
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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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Old   May 23, 2003, 03:00
Default Re: Total shear rate in a 3 dimensional flow
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Bo Jensen
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Hallo xueying

Could you please elaborate on the equations... I cannot make out what they mean..

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Bo
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Old   May 23, 2003, 15:26
Default Re: Total shear rate in a 3 dimensional flow
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xueying
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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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