Solid-Liquid Pipeflows – Holdup and the Two-Layer Model

*Trevor Frank Jones*

## **Abstract**

The relative delay of the flow of solids in a pipe, *holdup*, is shown to be an important factor in the evaluation of the flow of settling particle-bearing liquids. Holdup can be determined using a new, modified interpretation of the *two-layer model*, originally published in the 1970s. In the original model, particles in the upper layer of the flow are supported by hydrodynamic forces only, while those in the lower layer are also supported by hindered settling and wall reactions. This concept has been retained in the new model. An initial approximated value of holdup can be refined to allow an increasingly accurate value to be calculated. Innovative coding of the new model overcomes instability and interface positioning problems. Applications for determinations of holdup and the model are examined. Pressure loss, flow rate and the prediction of the pipe velocity to avoid a stationary bed are established. The model allows a locus of stationary bed conditions to be plotted for a family of holdup values. A method to obtain the *centre of concentration* in the cross section is demonstrated. The *locus of centre of concentration (LCC)* gives an indication of the position and size of the particle burden as conditions change.

**Keywords:** solid-liquid pipe flow, two-layer model, holdup, stationary bed locus, center of concentration
