Encyclopaedia Index

Turbulent mixing and chemical reaction; the multi-fluid approach


Brian Spalding, CHAM Ltd, London, England

A lecture , 1998

Historical note.The original of this lecture is one delivered in Moscow, in May 1997, at The International Symposium on the Physics of Heat Transfer in Boiling and Condensation.
Its content was expanded for delivery in the Institute of Professor Hanjalic of the University of Delft during the following year; and further additions have been made for later occasional deliveries, so that it is now too long to be delivered, in toto, in a single session anywhere.
Nevertheless, it has seemed best to preserve it as a record of the author's thoughts about MFM during 1997 and 1998.


Discretization of scalar-variable space, in the same manner as is customary for geometric space, makes possible the simulation of many turbulent single- and multi-phase flow phenomena for which conventional turbulence models fail, especially those influenced by body forces, or by chemical reaction.

This opportunity is exploited by the Multi-Fluid Model (MFM) of turbulence, which may be regarded as an extension and generalization of the "PDF-transport" model of Dopazo, O'Brien, Pope, et al. It is also the successor to, and generaliser of, numerous two- fluid models of the kind which were already envisaged by Reynolds and Prandtl.

MFM uses a conventional finite-volume method for computing the discretized PDFs, which may be one-, two- or multi-dimensional.

The lecture explains the nature and practical utility of MFM. Examples of its application are presented to both chemically-inert and chemically-reactive flow phenomena.

Contents of the lecture

  1. The task to be performed: computing the PDF
  2. Efforts to avoid computing the PDF
  3. Pioneering efforts to compute the PDFs
  4. The multi-fluid model (MFM) approach to PDFs
  5. First steps towards MFM for combustion: the four-fluid model
  6. Application of MFM to the ideal well-stirred reactor
  7. Application of MFM to 3D processes in engineering equipment
  8. The plane uniform-density mixing layer
  9. The future of MFM
  10. References
Appendix: governing equations and underlying assumptions