An analysis of lower-dimensional approximations to the scalar dissipation rate using direct numerical simulations of plane jet flames

Chen, Jackie; Sankaran, Ramanan; Hawkes, Evatt R

Title: An analysis of lower-dimensional approximations to the scalar dissipation rate using direct numerical simulations of plane jet flames

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Abstract

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 (1D) 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 1D 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 particularmore »« less

Authors:

Chen, Jackie ^[1]; Sankaran, Ramanan ^[2]; Hawkes, Evatt R ^[1]

Sandia National Laboratories (SNL)
ORNL

Publication Date:: Fri May 01 00:00:00 EDT 2009

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). National Center for Computational Sciences (NCCS)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1007846

DOE Contract Number:: DE-AC05-00OR22725

Resource Type:: Journal Article

Journal Name:: Proceedings of the Combustion Institute

Additional Journal Information:: Journal Volume: 32; Journal Issue: 1; Journal ID: ISSN 1540-7489

Country of Publication:: United States

Language:: English

Subject:: 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; APPROXIMATIONS; FLAMES; ORIENTATION; COMBUSTION KINETICS; TURBULENT FLOW; COMPUTERIZED SIMULATION; THREE-DIMENSIONAL CALCULATIONS

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                    Chen, Jackie, Sankaran, Ramanan, and Hawkes, Evatt R. An analysis of lower-dimensional approximations to the scalar dissipation rate using direct numerical simulations of plane jet flames.  United States: N. p., 2009. 
        Web.

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                    Chen, Jackie, Sankaran, Ramanan, & Hawkes, Evatt R. An analysis of lower-dimensional approximations to the scalar dissipation rate using direct numerical simulations of plane jet flames.  United States.

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                    Chen, Jackie, Sankaran, Ramanan, and Hawkes, Evatt R. 2009.  
        "An analysis of lower-dimensional approximations to the scalar dissipation rate using direct numerical simulations of plane jet flames".  United States.

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@article{osti_1007846,

  title        = {An analysis of lower-dimensional approximations to the scalar dissipation rate using direct numerical simulations of plane jet flames},

  author       = {Chen, Jackie and Sankaran, Ramanan and Hawkes, Evatt R},

  abstractNote = {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 (1D) 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 1D 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.},

  doi          = {},

  url          = {https://www.osti.gov/biblio/1007846},
  journal      = {Proceedings of the Combustion Institute},

  issn         = {1540-7489},

  number       = 1,

  volume       = 32,

  place        = {United States},

  year         = {Fri May 01 00:00:00 EDT 2009},

  month        = {Fri May 01 00:00:00 EDT 2009}

}

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