Dear Madam/Sir I am a research student of Ecole Polytechnic of Nantes, I'm working about "laminar heat transfer for thermally developing flow of Herschel-Bulkley fluide in square duct". For this studies I use FLUENT code. My difficult is to adapt this code to my studies i.e. taking into acount the yield stress. Is there somebody who deals whith this problem? I'll apraciate your help. Regards.

Hi,

I have been working in the field of non-newtonian fluid mechanics for some years and I have already experienced performing calculations related to the flow of yield stress fluids, particularly with FLUENT.

The method retained consists merely to modify the viscosity using an UDF (user defined function) in FLUENT. For instance, as a Bingham fluid is involved, the shear stress tau is given by

tau=tau_0+mu*gamma (1)

where mu stands for the shear viscosity and gamma the shear rate.

Thus the apparent viscosity mu_a is

mu_a=mu+tau_0/gamma (2)

Since the relation is a non smooth function, you need to regularize the model to obtain a well defined problem to be solved. Using for instance the regularization model of Papanastasiou, the apparent viscosity can be written as :

mu_a=mu+(1-exp(-m*gamma))*tau_0/gamma

where m is a numerical parameter of the model.

You can easily verify that the greater m, the closer to the exact model the regularized equation.

Well, I expect that you have now all the informations to program the fair UDF in FLUENT and to perform yours simulations.

Besides, I encourage you to have a look at the following papers :

J. Blackery & E. Mitsoulis "Creeping motion of a sphere in tubes filled with a Bingham plastic fluid", Journal of non-Newtonian Fluid Mechanics, 70, 59-77, (1997).

M. Beaulne & E. Mitsoulis "Creeping motion of a sphere in tubes filled with Herschel-Bulkley fluids", Journal of non-Newtonian Fluid Mechanics, 72, 55-71, (1997).

G.R. Burgos & A.N. Alexandrou "Flow development of Herschel-Bulkley fluids in a sudden 3D square expansion", Journal of Rheology, 43(3), 485-498, May/June 1999.

Hope it could help,

Good luck for your study,

Regards,

Anthony

Thanks you very much for your kindly help. I am deeply appreciated. yes I did the regularized model of Papanastasiou, but when I get to program the UDF, I need to accede to the parameter gamma (shear rate). Does it exist already in the laboratory of fluent or are obliged to calculate it from the derivative components of the velocity (C_DUDX(c,t), C_DUDY(c,t)…)? Thanks again for what you have done.