# Hershel-Bulkley viscosity

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 October 4, 2001, 05:57 Hershel-Bulkley viscosity #1 Atholl Guest   Posts: n/a 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

 October 4, 2001, 10:06 Re: Hershel-Bulkley viscosity #2 Anthony Wachs Guest   Posts: n/a 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=2*mu*D+(2*D/gamma)*tau_0 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 : mu_a=mu+tau_0/gamma 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 : mu_a=mu+(1-exp(-m*gamma))*tau_0/gamma 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... Anthony Upyoung likes this.

 April 3, 2013, 11:51 #3 New Member   lei Join Date: Apr 2013 Posts: 1 Rep Power: 0 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

 February 4, 2014, 02:41 #4 Member   Satish Gupta Join Date: Jun 2012 Posts: 30 Rep Power: 7 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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