Commun. Comput. Phys., 8 (2010), pp. 304-326.


On the Necessary Grid Resolution for Verified Calculation of Premixed Laminar Flames

Ashraf N. Al-Khateeb 1, Joseph M. Powers 1*, Samuel Paolucci 1

1 Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana 46556-5637, USA.

Received 9 July 2009; Accepted (in revised version) 2 November 2009
Available online 12 March 2010
doi:10.4208/cicp.090709.021109a

Abstract

We consider the grid resolution necessary to resolve combustion in a mixture of calorically imperfect ideal gases described by detailed kinetics and multicomponent transport. Using the steady premixed laminar flame as a paradigm, the required spatial discretization to capture all detailed physics in the reaction zone is found via 1) determination of the finest grid used in a standard software tool which employs adaptive mesh refinement, 2) examination of peak values of intermediate species mass fractions in the flame zone as a function of grid size, 3) a formal grid resolution study, and 4) a robust new eigenvalue analysis developed to estimate the finest length scale. Application to laminar premixed flames in hydrogen-air flames reveals that the finest length scale is on the order of $10^{-4}$ cm for combustion at atmospheric pressure. Resolution at this scale is shown to be necessary to capture detailed species mass fraction profiles; other features such as steady flame speeds and equilibrium thermochemical properties do not have such a stringent length scale requirement.

AMS subject classifications: 65, 76, 80

Notice: Undefined variable: pac in /var/www/html/issue/abstract/readabs.php on line 164
Key words: Length scales, premixed flames, detailed kinetics.

*Corresponding author.
Email: aalkhate@gmail.com (A. N. Al-Khateeb), powers@nd.edu (J. M. Powers), paolucci@nd.edu (S. Paolucci)
 

The Global Science Journal