Pressure drop in converging flows in three-dimensional printing of concrete

The additive manufacturing technology of extrusion of concrete mixtures through a nozzle and deposition layer-by-layer is commonly called three-dimensional concrete printing (3DCP). Such materials are rheologically characterized by yield stress and viscosity. The Bingham model is a good approximation of their rheological behavior. We have developed approximate expressions for determination of pressure for flow through slightly tapered tubes and wedge-shaped extrusion dies, starting from the Buckingham–Reiner equation for flow of a Bingham fluid in a straight tube. The predictions are compared to numerical simulations for convergence half-angles (taper) from 0° to 30° and to analytical solutions available in the literature. Good comparison has been obtained for taper angles up to 15° but the agreement deteriorates as the angle increases. Some experimental data available in the literature have been analyzed, and the challenges for prediction of pressure drop in flow of concrete mixtures through tubes and dies, including entry flow losses, are discussed.