LES models for turbulent non-premixed combustion usually require knowledge of the filtered density function of the conserved scalar, and we propose to use a simple top-hat function. Such top-hat distributions were developed as probability density functions for RANS applications in the 1970s but were soon surpassed by the $\beta$ function. We find that in the context of LES, the top-hat distribution provides an excellent alternative to the now much more common $\beta$ function. The top-hat function is assessed through a phenomenological analysis of Direct Numerical Simulation (DNS) data from a planar jet and of experimental data from a turbulent opposed jet. The approach is then tested a posteriori for a piloted diffusion flame (Sandia Flame D). Advantages of the top-hat function are the ease of implementation and the reduced dimensionality of look-up tables. The present paper also discusses inconsistencies of sub-grid $\beta$-FDFs, the FDFs sensitivity on implicit filtering, and the regime in which a $\beta$ assumption can be a valid filtered density function for LES.
%0 Journal Article
%1 ubo_mods_00030512
%A Floyd, J.
%A Kempf, Andreas Markus
%A Kronenburg, A.
%A Ram, R. H.
%D 2009
%J Combust. Theo. Mod.
%K itvak
%P 559--588
%T A simple model for the filtered density function for a passive scalar in combustion LES
%U https://www.tandfonline.com/doi/full/10.1080/13647830802632200
%V 13
%X LES models for turbulent non-premixed combustion usually require knowledge of the filtered density function of the conserved scalar, and we propose to use a simple top-hat function. Such top-hat distributions were developed as probability density functions for RANS applications in the 1970s but were soon surpassed by the $\beta$ function. We find that in the context of LES, the top-hat distribution provides an excellent alternative to the now much more common $\beta$ function. The top-hat function is assessed through a phenomenological analysis of Direct Numerical Simulation (DNS) data from a planar jet and of experimental data from a turbulent opposed jet. The approach is then tested a posteriori for a piloted diffusion flame (Sandia Flame D). Advantages of the top-hat function are the ease of implementation and the reduced dimensionality of look-up tables. The present paper also discusses inconsistencies of sub-grid $\beta$-FDFs, the FDFs sensitivity on implicit filtering, and the regime in which a $\beta$ assumption can be a valid filtered density function for LES.
@article{ubo_mods_00030512,
abstract = {LES models for turbulent non-premixed combustion usually require knowledge of the filtered density function of the conserved scalar, and we propose to use a simple top-hat function. Such top-hat distributions were developed as probability density functions for RANS applications in the 1970s but were soon surpassed by the $\beta$ function. We find that in the context of LES, the top-hat distribution provides an excellent alternative to the now much more common $\beta$ function. The top-hat function is assessed through a phenomenological analysis of Direct Numerical Simulation (DNS) data from a planar jet and of experimental data from a turbulent opposed jet. The approach is then tested a posteriori for a piloted diffusion flame (Sandia Flame D). Advantages of the top-hat function are the ease of implementation and the reduced dimensionality of look-up tables. The present paper also discusses inconsistencies of sub-grid $\beta$-FDFs, the FDFs sensitivity on implicit filtering, and the regime in which a $\beta$ assumption can be a valid filtered density function for LES.},
added-at = {2018-04-27T17:01:05.000+0200},
author = {Floyd, J. and Kempf, Andreas Markus and Kronenburg, A. and Ram, R. H.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2ba09221e87841beb70bd7e68452e2e01/itv-puma},
interhash = {2d138801e26cc7919c557b02ffa16fbf},
intrahash = {ba09221e87841beb70bd7e68452e2e01},
journal = {Combust. Theo. Mod.},
keywords = {itvak},
pages = {559--588},
timestamp = {2018-07-24T13:51:40.000+0200},
title = {A simple model for the filtered density function for a passive scalar in combustion LES},
url = {https://www.tandfonline.com/doi/full/10.1080/13647830802632200},
volume = 13,
year = 2009
}
