Gravity-driven laminar flow in a partially-filled pipe

The Boundary Element Method (BEM) is used to evaluate the integral and local flow properties of gravity-driven laminar flow in a partially filled pipe accounting for the correct free surface shape. With the BEM, any interface shape can be specified and only the solution values on the interface are evaluated, minimizing the computational time and storage space. Only three parameters, namely the Bond number, the contact angle and the holdup, are required to describe the flow system. Results are presented for the volumetric flow rate, the wall shear stress and the velocity profiles on the interface and the symmetry plane of the pipe for different interface shapes when the key parameters are altered, it is concluded that the Boundary Element method offers great flexibility and accuracy in addressing this class of flows.