Friction Factors For Pipe Flow Of Xanthan- Based Concentrates Of Fire Fighting Foams

Abstract

In this paper we develop a friction factor correlation to predict the pressure drop during pumping and induction of concentrates of fire fighting foams containing around 1% of xanthan gum. Such concentrates are highly elastic, display small yield stress and exhibit significant thinning upon shearing. We demonstrate that in the turbulent regime, the Blasius equation normally used for Newtonian fluids seems to correlate well the friction factor with the Metzner-Reed Reynolds number. Our development provides an example of how the methodology used to develop the friction factor correlation can be applied to analyse a set of experimental data to verify its internal consistency. The friction factors developed in the paper can be applied to other foam concentrates that include a similar content of xanthan gum in their formulation, to predict pressure drop as a function of a flow rate and pipe diameter, provided that there exists an appropriate viscosity model. Subsequently, the paper presents experimental measurements of apparent viscosity for one foam concentrate and develops relevant viscosity models. We observe that the rheology of the concentrate is governed by the behaviour of xanthan gum. Although, the foam concentrate considered in the article is yield pseudo plastic (i.e., it follows the Herschel-Bulkley model), for the shear stresses normally encountered during pipe flow, the viscosity of the material can be described by a power law model. Over the temperature range of between 0 and 40 o C, the apparent viscosity displays only a weak dependence on temperature. Subsequent calculations of pressure drop with temperature demonstrate minor variation in pressure drop with temperature, but only in the turbulent flow regime. This suggests that induction systems intended to operate under widely varying temperature conditions should be designed to function in the turbulent flow regime.

Pressure-Loss Correlations for Designing Foam Proportioning Systems

“…The effective viscosities of types 4 and 5 of FC 600 concentrates lie significantly higher as recently reported by Dlugogorski et al [3] The effective viscosity of Artic Foam 600 from Solberg Scandinavian, a concentrate that has a similar chemical make up to that of FC 600, also exceeds the effective viscosity of Equation (9) [6].…”

“…We believe that the data illustrated in Figures 1 and 2 originated in 1970s, and correspond to type 2 or 3 formulation of Light Water concentrate. Subsequently, in 1993, an independent engineering laboratory in Australia performed additional measurements, with the results presented in Figures 3 and 4 as type 4 FC 600 [3]. Recently, the present authors have measured, using a cone and plate viscometer, the apparent viscosity of type 5 FC 600 concentrate as function of temperature, developing power-law and Bulkley-Herschel (i.e., yield pseudoplastic) models of the material.…”

“…In practical pressure-loss calculations, a small yield stress (in the order of 5 Pa), also displayed by the concentrate, can be neglected, with a simple power-law description of the apparent viscosity yielding quite satisfactory predictions [3]. This means that, the flow curve or rheogram of FC 600 concentrate can be described by Equation (1)…”

“…Recently, the present authors have measured, using a cone and plate viscometer, the apparent viscosity of type 5 FC 600 concentrate as function of temperature, developing power-law and Bulkley-Herschel (i.e., yield pseudoplastic) models of the material. These measurements have then served to develop the effective-viscosity (see Equation (7)) and pressure-loss correlations, which are also illustrated in Figures 3 and 4 [3].…”

“…Viscosity of the solution of xanthan-gum concentrates is a weak function of temperature [3,7], a phenomenon that would necessitate unrealistically high heating (in the order of 30 • C) during experiments with each consecutive pipe. Time-dependent rheopectic fluids show a dependence of the relationship between the nominal shear rate and shear stress at the wall on pipe diameter, which is similar to that illustrated in Figure 8 (compare with Figure 5.4 of ref.…”