Laminar pipeline flow of wastewater sludge: Computational fluid dynamics approach

A computational fluid dynamics (CFD) technique applied to laminar flow of wastewater sludge in horizontal, circular pipes is presented. The technique employs the Crank-Nicolson finite difference method in conjunction with the variable secant method, an algorithm for determining the pressure gradient of the flow. Head loss (pressure drop) and velocity profile are predicted using the technique. Numerical predictions of head loss and velocity profile for several combinations of flows, pipe sizes, and sludge solids concentrations are compared to exact analytical values, derived from the theory of laminar flow of Bingham-plastic fluids. The predicted values are in good agreement with the exact values. Comparisons are also made to head loss values for municipal wastewater sludge from the literature. The CFD technique has several advantages over the analytical calculations, including ease of use, time efficiency, and the ability to readily change boundary conditions, flow geometry, and the rheological model for the shear stress.