Implementation and test of a turbulent-flame-speed-closure model for
premixed turbulent flame calculations

F. Dinkelacker, S. Hoelzler, K.-P. Helbig, A. Leipertz
Lehrstuhl fuer Technische Thermodynamik, Univ. Erlangen,
Am Weichselgarten 8, D-91058 Erlangen, Germany
E-Mail: fdi@ltt.uni-erlangen.de
Fax: xx49 / 9131 / 85 99 01


Abstract

For numerical calculations of the near field region of turbulent premixed
flames a simple and efficient numerical model is not straightforward, since
turbulent flow and reaction can have strong interactions, where especially
fluctuating small scale effects can be important. While for the numerical
calculation of turbulent nonreacting flows typically 6 coupled partial
differential equations are solved for mass, momentum and turbulence (k-e
model), additional N+1 equations might be necessary, if N chemical species
and energy are involved in reacting flows. Due to strong nonlinearities a
formal approach with the averaged equations would lead to totally wrong
results, if higher order correlation's and modeling terms are not handled
with great care. An essential simplification is possible for turbulent
premixed flames due to the experimental observation of correlation's between
temperature and major species. Here only one additional transport equation
is necessary, describing the reactive and thermal processes in terms of a
reaction progress variable. In an approach following Zimont et al. [1, 2]
the reaction term of this equation is closed with one algebraic equation for
the turbulent flame speed, including different effects of the interaction
between turbulent flow and chemistry and flame extinction.

These equations have been implemented as subroutines into a commercial
computational fluid dynamics (CFD) code. In order to check the model,
numerical results are compared with experimental data from a turbulent
premixed V-shaped flame, where the conditions of the approaching turbulent
flow and of the chemical processes have been varied separately and
systematically [3]. The comparison shows that the calculated flame location
and flame width fits surprisingly well with the experimental data for the
different flow rates and equivalence ratios, without tuning on fitting
constants. Calculations of larger turbulent premixed flames, a turbulent
premixed Bunsen-type flame of 100 kW and a premixed swirl burner of the type
of a gas turbine [2] shows that the agreement between calculation and
experiment is reasonable well also for these flames of industrial relevance.

[1]     V. Zimont, A. Lipatnikov, Chem. Phys. Reports 14(7), 993-1025 (1995)
[2]     V. Zimont, W. Polifke, M. Bettelini, W. Weisenstein, ASME Turbo Expo,
Orlando (1997)
[3]     A. Soika, Diploma thesis, Lehrstuhl für Technische Thermodynamik,
Universität Erlangen (1996)