[q__]

Hello,



could you explain to me what is the interpretation of the so-called "strain rate" used in non-premixed combustion (not to be mistaken with the rate of strain tensor). In many textbooks the formal definition is simply a=dv/dy. But this applies only to simple 2d configuration of a counterflow. Is there a similar concept for 3d flow field?



Best Regards

[LuckyTran]

Take the norm of the strain-rate tensor and you have the "strain rate"


dv/dy is technically a vector. You can see that even in the simple definition, the concept of magnitude/norm has already been utilized implicitly.

[q__]

Originally Posted by LuckyTran

Take the norm of the strain-rate tensor and you have the "strain rate"


dv/dy is technically a vector. You can see that even in the simple definition, the concept of magnitude/norm has already been utilized implicitly.

Thank you for your interest.


By the magnitude do you mean the square root of the dyadic product of the strain rate tensor by itself?


Second question. I am not sure about that but I have already read about the concept of the principal directions along which the so-called principal "strain rates" act. So it appears to me that the concept of the "strain rate" is related to a particular direction and should have 3 components rather than single scalar magnitude in 3d case. Could you please comment on that?



Thank you.

[LuckyTran]

Yes, magnitude means square root of dyadic double dot product.


You can indeed decompose the strain rate tensor into two parts: one which is an isotropic expansion/compression and another which is the symmetric shear. Both of these each act in three orthogonal directions. But you still need to be careful whether you are talking about the strain rate tensor and its properties, or just the magnitude of the strain rate tensor.