TY - JOUR
T1 - An analysis of lower-dimensional approximations to the scalar dissipation rate using direct numerical simulations of plane jet flames
AU - Hawkes, Evatt R.
AU - Sankaran, Ramanan
AU - Chen, Jacqueline H.
AU - Kaiser, Sebastian A.
AU - Frank, Jonathan H.
PY - 2009
Y1 - 2009
N2 - The difficulty of experimental measurements of the scalar dissipation rate in turbulent flames has required researchers to estimate the true three-dimensional (3D) scalar dissipation rate from one-dimensional (ID) or two-dimensional (2D) gradient measurements. In doing so, some relationship must be assumed between the true values and their lower dimensional approximations. We develop these relationships by assuming a form for the statistics of the gradient vector orientation, which enables several new results to be obtained and the true 3D scalar dissipation PDF to be reconstructed from the lower-dimensional approximations. We use direct numerical simulations (DNS) of turbulent plane jet flames to examine the orientation statistics, and verify our assumptions and final results. We develop and validate new theoretical relationships between the lower-dimensional and true moments of the scalar dissipation PDF assuming a log-normal true PDF. We compare PDFs reconstructed from lower-dimensional gradient projections with the true values and find an excellent agreement for a 2D simulated measurement and also for a ID simulated measurement perpendicular to the mean flow variations. Comparisons of PDFs of thermal dissipation from DNS with those obtained via reconstruction from 2D experimental measurements show a very close match, indicating this PDF is not unique to a particular flame configuration. We develop a technique to reconstruct the joint PDF of the scalar dissipation and any other scalar, such as chemical species or temperature. Reconstructed conditional means of the hydroxyl mass fraction are compared with the true values and an excellent agreement is obtained.
AB - The difficulty of experimental measurements of the scalar dissipation rate in turbulent flames has required researchers to estimate the true three-dimensional (3D) scalar dissipation rate from one-dimensional (ID) or two-dimensional (2D) gradient measurements. In doing so, some relationship must be assumed between the true values and their lower dimensional approximations. We develop these relationships by assuming a form for the statistics of the gradient vector orientation, which enables several new results to be obtained and the true 3D scalar dissipation PDF to be reconstructed from the lower-dimensional approximations. We use direct numerical simulations (DNS) of turbulent plane jet flames to examine the orientation statistics, and verify our assumptions and final results. We develop and validate new theoretical relationships between the lower-dimensional and true moments of the scalar dissipation PDF assuming a log-normal true PDF. We compare PDFs reconstructed from lower-dimensional gradient projections with the true values and find an excellent agreement for a 2D simulated measurement and also for a ID simulated measurement perpendicular to the mean flow variations. Comparisons of PDFs of thermal dissipation from DNS with those obtained via reconstruction from 2D experimental measurements show a very close match, indicating this PDF is not unique to a particular flame configuration. We develop a technique to reconstruct the joint PDF of the scalar dissipation and any other scalar, such as chemical species or temperature. Reconstructed conditional means of the hydroxyl mass fraction are compared with the true values and an excellent agreement is obtained.
KW - Direct numerical simulation
KW - Non-premixed
KW - Reconstruction
KW - Scalar dissipation rate
KW - Syngas
UR - http://www.scopus.com/inward/record.url?scp=67649262157&partnerID=8YFLogxK
U2 - 10.1016/j.proci.2008.06.122
DO - 10.1016/j.proci.2008.06.122
M3 - Conference article
AN - SCOPUS:67649262157
SN - 1540-7489
VL - 32 I
SP - 1455
EP - 1463
JO - Proceedings of the Combustion Institute
JF - Proceedings of the Combustion Institute
T2 - 32nd International Symposium on Combustion
Y2 - 3 August 2008 through 8 August 2008
ER -