Pergamon
Int. Comm. Heat Mass Transfer, Vol. 25, No. 3, pp. 321-330, 1998
Copyright © 1998 Elsevier Science Ltd
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PII S0735-1933(98)00019-0
TURBULENT PIPE FLOW OF HERSCHEL-BULKLEY FLUIDS
M.R. Malin
CHAM Limited
Wimbledon, London SW19 5AU
U.K.
(Communicated by J.P. Hartnett and W.J. Minkowycz)
ABSTRACT
A modified two-equation turbulence model is used to compute the turbulent flow of
Herschel-Bulkley fluids in smooth pipes. Numerical results are presented for the fully-
developed friction factor, and compared with existing empirical correlations. The model is
used to produce flow resistance curves over a wide range of values for the power-law index
and the generalised Reynolds and Hedstrom numbers. © 1998 Elsevier Science Ltd
Introduction
The transport of time-independent viscous non-Newtonian fluids through pipelines finds applications
in the process and wastewater industries] The turbulent flow of these fluids is not uncommon, as
turbulent conditions may be encountered in, for example, drilling hydraulics and sewage transport. The
present paper extends earlier computational work on the pipeline flow of Bingham-plastic [ 1] and power-
law [2] fluids to deal with the more general case of Herschel-Bulkley fluids [3]. The rheological model
of Herschel and Bulkley describes a large number of industrially important fluids, and it contains the
Newtonian, Bingham-plastic and power-law fluids as special cases.
For laminar flow, the friction factor for Newtonian, power-law, Bingham-plastic and Herschel-
Bulkley (HB) fluids can be obtained from a single theoretical relationship [4] involving the power law
index n, the generalised Reynolds number for a power-law fluid Re [5,6], and the generalised Hedstrom
number He [4,7,8]. However, several correlations have been developed for the turbulent friction factor
[4,6,9-12]. The majority of these have been examined by Garcia and Stette [12] with the conclusion that
the Hanks [4] correlation is the most comprehensive for HB fluids. This correlation deals with the
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