Theoretical Investigation of the Flow Behavior of Gelled Fuels of the Extended Herschel Bulkley Type

Kurzfassung

Gelled fuels are shear-thinning fluids, which have in many cases a distinct yield stress at low shear rates and a constant viscosity at high shear rates. The viscosity behavior in a wide range of shear rates can be described by an extended formulation of the Herschel-Bulkley equation with an additional term containing the theoretical constant viscosity value of the high shear rate range. In this paper the flow behavior of such fluids is numerically derived for steady, fully developed and laminar flow conditions in tubes of constant cross sectional area. Shear rate and velocity distributions are shown for different fluids and boundary conditions in comparison to the theoretical flow behavior of the common Herschel-Bulkley and Bingham fluids. The velocity distribution of an Extended Herschel-Bulkley fluid (HBE-fluid) depends upon a characteristic shear rate “g”, a dimensionless factor “f” (both determined by fluid properties) and the ratio of yield stress to wall shear stress. The flow behavior of fluids of the common Herschel-Bulkley and Bingham fluids are the limits to which the flow behavior of extended Herschel-Bulkley fluids tends for distinct boundary conditions.