Journal of Fluid Mechanics

The Fanno model for turbulent compressible flow

H. OCKENDON a1, J. R. OCKENDON a1 and S. A. E. G. FALLE a2
a1 OCIAM, Mathematical Institute, Oxford University, 24–29 St Giles', Oxford OX1 3LB, UK
a2 Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK


The paper considers the derivation and properties of the Fanno model for nearly unidirectional turbulent flow of gas in a tube. The model is relevant to many industrial processes. Approximate solutions are derived and numerically validated for evolving flows of initially small amplitude, and these solutions reveal the prevalence of localized large-time behaviour, which is in contrast to inviscid acoustic theory. The properties of large-amplitude travelling waves are summarized, which are also surprising when compared to those of inviscid theory.

(Received May 10 1999)
(Revised May 8 2001)