Conditional-moment Closure with Differential Diffusion for Soot Evolution in Fire

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Hewson, J.
Ricks, A.
Tieszen, S.
Kerstein, A
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Fox, Rodney
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Chemical and Biological Engineering

The function of the Department of Chemical and Biological Engineering has been to prepare students for the study and application of chemistry in industry. This focus has included preparation for employment in various industries as well as the development, design, and operation of equipment and processes within industry.Through the CBE Department, Iowa State University is nationally recognized for its initiatives in bioinformatics, biomaterials, bioproducts, metabolic/tissue engineering, multiphase computational fluid dynamics, advanced polymeric materials and nanostructured materials.

The Department of Chemical Engineering was founded in 1913 under the Department of Physics and Illuminating Engineering. From 1915 to 1931 it was jointly administered by the Divisions of Industrial Science and Engineering, and from 1931 onward it has been under the Division/College of Engineering. In 1928 it merged with Mining Engineering, and from 1973–1979 it merged with Nuclear Engineering. It became Chemical and Biological Engineering in 2005.

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1913 - present

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  • Department of Chemical Engineering (1913–1928)
  • Department of Chemical and Mining Engineering (1928–1957)
  • Department of Chemical Engineering (1957–1973, 1979–2005)
    • Department of Chemical and Biological Engineering (2005–present)

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The conditional-moment closure (CMC) equation for the evolution of a large Lewis number scalar, soot, is derived starting from the joint probability density function (pdf) equation for the gas-phase mixture fraction, ξ g , and the soot mass fraction, Y s . Unlike previous approaches starting with the joint pdf, the residual terms that result from the typical closure models were retained. A new formulation of the one-dimensional turbulence (ODT) model suitable for spatially evolving flows with buoyant acceleration and radiative transport in participating media was employed to carry out simulations of a prototypical ethene fire. The resulting ODT evolution of ξ g and Y s was used to assess the significance of various terms in the CMC equation including the residual correlations. The terms involving differential diffusion are found to be important along with the soot source terms and the large-scale evolution of both ξ g and Y s . Of particular importance in the regions in mixture-fraction space around the soot production and consumption is a residual term, not previously identified, related to the correlation between the differential diffusion and Y s . This term results in a diffusion-like behavior of Y s in the mixture fraction coordinate that has an apparent Lewis number near unity. In scenarios where the large Lewis number component is a non-negligible component of the mixture fraction (i.e., large soot loading), it is found easier to employ a mixture fraction neglecting this component. Such a mixture-fraction variable has a chemical source term, but this appears easier to model than the differential diffusion and dissipation terms that result when the large Lewis number component is retained in the mixture-fraction definition.


This article is from Proceedings of the 2006 Summer Program-Center for Turbulence Research, Stanford, CA, pp.311-323.