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

Non Linear reaction rate.

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

Reply
 
LinkBack Thread Tools Display Modes
Old   March 16, 2005, 08:30
Default Non Linear reaction rate.
  #1
Burin'
Guest
 
Posts: n/a
Can someone explain why the fuel mass reaction rate expressed using the arrhenius law is highly non-linear. I have read that this is because it cannot be easily represented as a funciton of the mean mass fractions and density. I assume this is for RANS? The Arrhenius law looks fairly linear to me. What am I missing? What is the case in LES?

Thank you.
  Reply With Quote

Old   March 16, 2005, 09:00
Default Re: Non Linear reaction rate.
  #2
Z
Guest
 
Posts: n/a
it has Temperature T in exponential term. how can you make mean of a term which is exponential
  Reply With Quote

Old   March 16, 2005, 10:40
Default Re: Non Linear reaction rate.
  #3
Burin'
Guest
 
Posts: n/a
Why not? I am afraid I don't understand why I cannot calculate the mean of an exponential term. It doesn't seem to me to be non-linear. What is the mathemiatical reason for it being on-linear?

Thanks Z.
  Reply With Quote

Old   March 16, 2005, 10:45
Default Re: Non Linear reaction rate.
  #4
Z
Guest
 
Posts: n/a
expand the exponential terms using taylor series and then perform the mean. or check this in Poinsot book
  Reply With Quote

Old   March 16, 2005, 14:33
Default Re: Non Linear reaction rate.
  #5
Burnin'
Guest
 
Posts: n/a
Thank you. Can you tell where to find this in Poinsot's book...which page?
  Reply With Quote

Old   March 16, 2005, 14:41
Default Re: Non Linear reaction rate.
  #6
Burnin'
Guest
 
Posts: n/a
Its o.k., I found it on page 146-147 of Poinsot's book.

Thanks again.
  Reply With Quote

Old   March 17, 2005, 10:17
Default Re: Non Linear reaction rate.
  #7
Guillaume
Guest
 
Posts: n/a
In a turbulent flow, the RANS-predicted mean temperature may be 1500 K. But the real temperature encountered by the chemical term fluctuates and may be 1600 K or 1400 K (even if in mean T ~ 1500 K). Compute exp (-Ta/1400 K) and exp (-Ta/1600 K) with Ta very high (as in combustion), and take the mean. It is really different from exp (-Ta / 1500 K): the mean of the exp. is really different from the exp. of the mean...
  Reply With Quote

Old   March 20, 2005, 08:38
Default Re: Non Linear reaction rate.
  #8
Burnin'
Guest
 
Posts: n/a
Surely we are only interested in the mean of the exp though? So why would we care what the exp of the mean was?
  Reply With Quote

Old   March 20, 2005, 09:13
Default Re: Non Linear reaction rate.
  #9
Bak_Flow
Guest
 
Posts: n/a
Hi,

I think there are 2 fundamental issues here.

1. The Arrhenius theory for reaction rates. This is just a simple thery to explain what is happening on a mollecular level however fits many reactions over limited temperature ranges. As pointed out above this is non-linear in temperature. Any reaction mechanism applied strictly speaking to a homogenous system.....so no turbulence.

2. How do we inlude the above effects in a turbulent flow where we do not resolve all scales and times of the fluctuations of velocity, temp, mass fraction, etc. If we do a RANS simulation we only have mean values available (and a few statistics on our turbulence...k, eps, maybe u'T', etc). THAT is where the issue of the mean of a non-linear operator IS NOT the same as the operator applied to the mean of the independant variables. Many of the modern texts cover this well ie Warnatz, Peters, etc

Hope this helps,

Bak_Flow
  Reply With Quote

Old   March 21, 2005, 10:16
Default Re: Non Linear reaction rate.
  #10
Guillaume
Guest
 
Posts: n/a
You are interested in the mean of the exp., but your code will provide the exp. of the mean because this is what is computed (mean of T, U, Y...)
  Reply With Quote

Old   March 21, 2005, 14:42
Default Re: Non Linear reaction rate.
  #11
Burnin'
Guest
 
Posts: n/a
Is it possible to have a transport equation for the mean of the exp?
  Reply With Quote

Old   March 22, 2005, 10:15
Default Re: Non Linear reaction rate.
  #12
Guillaume
Guest
 
Posts: n/a
Sounds like turbulent modelling, does not it?

More exactly, concerning the (non-linear) reaction term, this is not a transport equation but a closure, sometimes based on transported quantities (CMC, Pdf,...)
  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
Segmentation fault in running alternateSteadyReactingFoam,why? NewKid OpenFOAM 18 January 20, 2011 17:55
solution diverges when linear upwind interpolation scheme is used subash OpenFOAM 0 May 29, 2010 01:23
surface reaction rate with udf yellow-stuff FLUENT 4 January 29, 2010 13:53
UDF changing the rate exponent of a reaction Stefan H Fluent UDF and Scheme Programming 0 September 16, 2009 13:20
chemical reaction - decompostition La S. Hyuck CFX 1 May 23, 2001 00:07


All times are GMT -4. The time now is 23:37.