The flow behaviour of non-Newtonian sludges
A large body of data is analysed of the flow of concentrated sewage sludge through straight pipes. Mathematical models are obtained of the laminar and turbulent flow of each main category of sewage sludge. The sludges are modelled as time-independent, non-Newtonian relations between shear stress, rate of shearing strain, and solids concentration. Due to the inhomogeneity of sewage sludge, error analysis becomes pivotal to the data analysis, and options are examined for reducing the error of each model with one or more user-fitted parameters. Parameter estimation is discussed for viscous, time-independent, non-Newtonian, laminar and turbulent flow models. Due to extensive requirements of the data analysis, the parameter estimation methods are robust, and generally suitable for any shear flow relation. The difficulties of estimating parameters of shear flow models from pipe flow data are addressed. Numerical algorithms are presented for modelling the flow of time-independent, non-Newtonian, viscous fluids through a straight pipe. Laminar, critical and turbulent flow algorithms are developed to offer predictions such as pressure gradient, mean cross-sectional velocity, and the velocity distribution. To handle the requirements of the data analysis, the algorithms impose few restrictions on the type of shear flow relation, the flow velocity, and the pipe diameter. Suitable pipe flow equations are chosen, and are manipulated mathematically into forms that would yield robust and efficient schemes. The appropriate use of numerical methods for the algorithms is investigated. Mathematical models of sludge are for use by the sewage industry to give an idea of the flow behaviour of sludges for any relevant application. The parameter estimation techniques and pipe flow algorithms are not constrained to any particular pipe, fluid or flow conditions, so they would be useful for any relevant application.