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Atholl October 4, 2001 05:57

Hershel-Bulkley viscosity
Can anyone tell me how to go about modifying the non-Newtonian Power-Law viscosity in Fluent to include a true yield stress, which would make it a Herschel Bulkley viscosity? I know this would be via a UDF, but is there any way I can get access to the existing code for Power-Law viscosity and then modify it as a UDF? Or do I have to start a UDF from scratch myself, and if so, how? Thanks in advance

Anthony Wachs October 4, 2001 10:06

Re: Hershel-Bulkley viscosity
Hi Atholl,

I have been working for a long time in the area of viscoplastic fluids and have already experienced to include this kind of models (Bingham or Helschel-Bulkley) in Fluent. Concerning that point, I have two news for you : a good one and a bad one

1. good new : implementing visoplastic fluids in Fluent works very well !! and besides is very easy to handle. You only have to write an UDF for the viscosity.

2. bad new : for confidentiality reasons (I am currently working for a private company), I cannot forward you the UDF.

Nevertheless, I encourage you to try too because you are now absolutely sure that it will work (if you trust me of course). And I can show you how to consider the model in Fluent because obviously, after a deep look in the literature, you would probably find it by yourself, so I expect that the following tips will enable you to save some time.

Consider the Bingham constitutive equation in 3D (the generalization to HB model is straightforward) :


tau=stress tensor

mu=shear viscosity

D=rate-of-strain tensor

gamma=(second invariant of D)=sqrt(2*tr(D**2))

tau_0=yield stress

If you write this relation in terms of apparent viscosity mu_a, it yields :


An other thing to keep in mind is that the relation tau=f(D) or tau=f(gamma) in 1D (in that case, gamma is the shear rate) is discontinuous in gamma=0 and tau cannot be evaluated (for gamma=0, tau in [0,tau_0]). A popular solution consists in using any of the following regularization models :

1. bi-viscosity model

2. exponential model

3. model with a parameter epsilon

I chose to use the exponential model which can be written as :


with m=numerical parameter

If m is great enough (typical values verify m>100), the regularized law fits well the real consitutive equation. Thus, your regularized law exhibit now good properties : continuous (stress can be computed everywhere e.g. tau in [0,infinity]) and is differentiable everywhere too e.g. is C^infinity.

This method to tackle viscoplastic problems is well known and works very well with Fluent too either in 1D or in 2D-3D problems.

Have a look to those papers : 1. T.C. Papnastasiou "Flow of materials with yield", Journal of Rheology, 31, 385-404, (1987).

2. E. Mitsoulis, S.S. Abdali, N.C. Markatos, "Flow simulation of Herschel-Bulkley fluids through extrusion dies, Canadian Journal of Chemical Engineering, 71, 147-160, 1993.

3. 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.

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

5. I.C. Walton, S.H. Bittleston, "The axial flow of a Bongham plastic in a narrow eccentric annulus", Journal of Fluid Mechanics", 222, 39-60, (1991).

With all those informations, I am quite sure you will succeed !! The only remaining thing to do by yourself is to write the UDF for the apparent viscosity (forget about the non-newtonian power law that is not suited to handle yield stress), that is an easy and quick duty.

Hope it might help you...


djb13110 April 3, 2013 11:51

hi, Do you know whether liquefied iron ore powder is the viscoplastic fluid\?
I think I should do some steps:
1: do some experiments about the material
2: build the constitutive equation using the UDF

Rahul123 February 4, 2014 02:41

I am also trying to solve a similar problem. where should I attach the udf in fluent because if I attach it to viscosity, I don't find any place to enter the value of power n and consistency index K

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