TY - JOUR
T1 - Estimates of the three-dimensional flame surface density and every term in its transport equation from two-dimensional measurements
AU - Hawkes, Evatt R.
AU - Sankaran, Ramanan
AU - Chen, Jacqueline H.
PY - 2011
Y1 - 2011
N2 - The flame surface density approach is one of the most established techniques for the modelling of turbulent premixed combustion. There has been considerable interest in the experimental measurement of the flame surface density and quantities involved in its transport equation, namely: strain, curvature, and displacement speed. Because of the difficulty involved in performing three-dimensional measurements, the vast majority of this work has been performed in two spatial dimensions. Therefore an assumption is required to relate the two-dimensional measurement to the three-dimensional reality. In the present article, new relationships are derived to relate the statistical mean values of measured two-dimensional quantities to those of the true three-dimensional quantity in the case of isotropic scalar fields and turbulence. The relationships are derived for the flame surface density as well as for every term in its transport equation. To assess the performance of the relationships, direct numerical simulations of turbulent, premixed, methane-air slot-jet flames are employed. In all cases considered, the agreement is very good away from a small region near the simulated burner exit. The agreement improves with downstream distance and with Reynolds number.
AB - The flame surface density approach is one of the most established techniques for the modelling of turbulent premixed combustion. There has been considerable interest in the experimental measurement of the flame surface density and quantities involved in its transport equation, namely: strain, curvature, and displacement speed. Because of the difficulty involved in performing three-dimensional measurements, the vast majority of this work has been performed in two spatial dimensions. Therefore an assumption is required to relate the two-dimensional measurement to the three-dimensional reality. In the present article, new relationships are derived to relate the statistical mean values of measured two-dimensional quantities to those of the true three-dimensional quantity in the case of isotropic scalar fields and turbulence. The relationships are derived for the flame surface density as well as for every term in its transport equation. To assess the performance of the relationships, direct numerical simulations of turbulent, premixed, methane-air slot-jet flames are employed. In all cases considered, the agreement is very good away from a small region near the simulated burner exit. The agreement improves with downstream distance and with Reynolds number.
KW - Coherent flame model
KW - Direct numerical simulation
KW - Flame surface density
KW - Premixed combustion
KW - Strain
UR - http://www.scopus.com/inward/record.url?scp=78650856467&partnerID=8YFLogxK
U2 - 10.1016/j.proci.2010.06.019
DO - 10.1016/j.proci.2010.06.019
M3 - Article
AN - SCOPUS:78650856467
SN - 1540-7489
VL - 33
SP - 1447
EP - 1454
JO - Proceedings of the Combustion Institute
JF - Proceedings of the Combustion Institute
IS - 1
ER -