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 Tim September 17, 2003 16:08

Non-Newtonian power law fluids

I am working with non-Newtonian power law fluids in PHOENICS and have come across a couple of uncertainties and I am simply going to throw these out and if anyone can help clarify them it would be greatly appreciated. I am trying to simulate simple pseadoplastic and dilitant fluids, which are given by the standard shear stress-shear rate equation of:

Tao = mu*(du/dy)^n

In polis, the calculation of the viscosity (kinematic) is given by

ENUL = ENULA*(LGEN1)^((ENULB-1)/2)/RAO and states that for ENULB = 1 the fluid is Newtonian (a value of n = 1 in the above equation). The whole part of using (ENULB-1)/2 is somewhat confusing, as it is not clearly stated why it is in this form. If, for example, I use B = 0.5, is this the same as n = 0.5?

I believe it is, but I would like some confirmation on this.

Polis states that LGEN1 is the strain rate squared. Why is this squared? Is it so that in the calculation of the viscosity it forces the viscosity to be positive? I assume that the following is the case:

shear stress = viscosity*strain rate

tao = {ENULA*((LGEN1)^2)^((ENULB-1)/2)}*(LGEN1)

where the ^2 is there to make sure that the viscosity stays positive (but the second du/dy is the *real* strain rate that allows for the correct sign for the shear stress)

this equaiton collapses to:

tao = ENULA*LGEN1^(2*(ENULB-1)/2)*LGEN1

and then to

tao = ENULA*LGEN^ENULB

and therefore ENULA = mu and ENULB = n

Is this correct?

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