CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Main CFD Forum

About the Hershel-Bulkley model of Non-Newtonian fluids

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Display Modes
Old   October 24, 2013, 23:47
Question About the Hershel-Bulkley model of Non-Newtonian fluids
  #1
New Member
 
Join Date: Oct 2013
Posts: 2
Rep Power: 0
tiger0004 is on a distinguished road
Hi,everyone!
Lately I have been using the Herschel-Bulkley model to model the behaviors of a Non-Newtonian 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!
tiger0004 is offline   Reply With Quote

Old   October 25, 2013, 16:43
Default
  #2
Member
 
Reza
Join Date: Mar 2009
Location: Appleton, WI
Posts: 99
Rep Power: 8
triple_r is on a distinguished road
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 \dot{\gamma} > 0. Now, the equation shows exactly the same behavior, if you have a \dot{\gamma} 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 non-Newtonian fluid flow text books.

By the way, in the constitutive equation that you have, neither tau, nor \dot{\gamma} can be negative. They are "magnitudes" of tensors. Usually they are defined as:

\dot{\gamma}=\sqrt{\frac{1}{2}\dot{\gamma}:\dot{\gamma}}

and

\dot{\tau}=\sqrt{\frac{1}{2}\dot{\tau}:\dot{\tau}}

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 double-inner product of tensors (multiply corresponding components with each other, and then sum all of the products).

Hope this helps.
triple_r is offline   Reply With Quote

Old   October 25, 2013, 22:43
Default
  #3
New Member
 
Join Date: Oct 2013
Posts: 2
Rep Power: 0
tiger0004 is on a distinguished road
Quote:
Originally Posted by triple_r View Post
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 \dot{\gamma} > 0. Now, the equation shows exactly the same behavior, if you have a \dot{\gamma} 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 non-Newtonian fluid flow text books.

By the way, in the constitutive equation that you have, neither tau, nor \dot{\gamma} can be negative. They are "magnitudes" of tensors. Usually they are defined as:

\dot{\gamma}=\sqrt{\frac{1}{2}\dot{\gamma}:\dot{\gamma}}

and

\dot{\tau}=\sqrt{\frac{1}{2}\dot{\tau}:\dot{\tau}}

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 double-inner product of tensors (multiply corresponding components with each other, and then sum all of the products).

Hope this helps.

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?
tiger0004 is offline   Reply With Quote

Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Use of k-epsilon and k-omega 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 IƱigo 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


All times are GMT -4. The time now is 12:48.