
[Sponsors] 
October 24, 2013, 23:47 
About the HershelBulkley model of NonNewtonian fluids

#1 
New Member
Join Date: Oct 2013
Posts: 2
Rep Power: 0 
Hi,everyone!
Lately I have been using the HerschelBulkley model to model the behaviors of a NonNewtonian fluid. The model states that if the stress of the fluid is less than the yield stress tau0,then the fluid would act like rigid(pseudoplastic). The mathematical description of the HB model is tau=tau0+k*gamma^n,in which tau is the stress, tau0 is the yield stress,gamma is the shear rate and k and n are fluid constants. Here is the question. In some fluid field, if I don't previously know in which area the shear stress would be smaller than tau0 (plug area), how can I find it out? I mean, according to the HB equation, because gamma and tau, tau0 point to the same direction, so no matter what value set gamma to be, the absolute value of tau is always no less than that of tau0. (tau,tau0 and gamma always have the same sign.) For example, if k=1,n=1,gamma>0, then tau(positive)=tau0(positive)+gamma(positive), tau>tau0;if gamma<0, then tau(negative)=tau0(negative)+gamma(negative),abs(t au)>abs(tau0). In both case, there would be no plug area in the fluid. Can anyone help me? Thanks! 

October 25, 2013, 16:43 

#2 
Senior Member
Reza
Join Date: Mar 2009
Location: Appleton, WI
Posts: 115
Rep Power: 8 
As you said, when shear stress is higher than the yield stress, then and only then the fluid will experience shear deformation. In other words, if tau > tau0, then > 0. Now, the equation shows exactly the same behavior, if you have a that is non zero, then you must have had a shear stress that was higher than the yield stress.
In order to see the plug flow region, you must write the equations in terms of shear stress, and not strain. For an example, you can take a look at some of the solutions for a Bingham plastic fluid in most nonNewtonian fluid flow text books. By the way, in the constitutive equation that you have, neither tau, nor can be negative. They are "magnitudes" of tensors. Usually they are defined as: and in these definitions, the left hand side symbols are scalars (and these are the ones that appear your constitutive equation), and the right hand side symbols are tensors. also, means doubleinner product of tensors (multiply corresponding components with each other, and then sum all of the products). Hope this helps. 

October 25, 2013, 22:43 

#3 
New Member
Join Date: Oct 2013
Posts: 2
Rep Power: 0 
Quote:
Thank you triple_r! I know sometimes my fundamental concepts are ambiguous. I referred to some text books and scientific papers, and found out that usually the shear rate is calculated first and then then shear stress is calculated with the constitution equation. In some simple cases, like in a tube or between two plates, the shear stress can be obtained when knowing the pressure distribution. Is this always the way to find out the shear stress without the shear rate? 

Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Use of kepsilon and komega Models  Jade M  Main CFD Forum  12  June 2, 2015 13:16 
Atomization and Breakup model  xck1986  OpenFOAM  4  May 31, 2014 04:43 
herschel Bulkley rheological model into fluent  hamina  FLUENT  4  February 17, 2006 10:28 
spraying non newtonian fluids  IĆ±igo  Main CFD Forum  0  October 4, 2005 09:36 
Non newtonian power law model in pipe annulus  Poly  FLUENT  0  March 24, 2005 16:12 