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 Bo Busk Jensen May 21, 2003 03:53

Total shear rate in a 3 dimensional flow

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

 xueying May 22, 2003 14:43

Re: Total shear rate in a 3 dimensional flow

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,

 Bo Jensen May 23, 2003 03:00

Re: Total shear rate in a 3 dimensional flow

Hallo xueying

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

Regards

Bo

 xueying May 23, 2003 15:26

Re: Total shear rate in a 3 dimensional flow

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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