Turbulent mixing and chemical reaction; the multi-fluid approach

by

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.

Abstract

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
   • EBU: the eddy-break-up model
   • EDC: the eddy-dissipation concept
   • 2FM: the two-fluid model
   • Presuming the shape of the PDF
   • Presuming that a few statistical properties will suffice
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
   • The flame-spread-in-a-plane-duct problem
   • Transient flame spread in a baffled duct
   • Explosion in an off-shore oil platform
6. Application of MFM to the ideal well-stirred reactor
   • With uniform fuel-air ratio; the 1D population
   • With non-uniform fuel-air ratio; the 2D population
   • Concluding remarks about the stirred-reactor results
7. Application of MFM to 3D processes in engineering equipment
   • Transient flow in a paddle-stirred reactor
   • Smoke generation in a gas-turbine combustor
   • Prediction of turbo-machinery flows
8. The plane uniform-density mixing layer
   • The problem and its solution
   • Discussion of the results
9. The future of MFM
   • Concluding remarks about the nature of MFM
   • Mathematical and computational tasks
   • Tests of realism
   • Conceptual developments
10. References