Effect of pipe inclination on internal structure of settling slurry flow at and close to deposition limit

Abstract

Pipeline systems transporting settling slurries often contain pipe sections inclined from the horizontal. The pipe inclination affects settling slurry flow and must be considered to assure safety of the system operation. Incline-induced changes in the internal structure of the slurry flow include variation in the distribution of solids in a pipe cross section and in the velocity of grains at the bottom of the pipe. We discuss results of experimental determination and model prediction of the effect of flow inclination on the solids distribution at flow velocities at and close to the deposition velocity at which first grains at the bottom of the bed stop moving and deposit starts to be formed. The effect of the pipe inclination on the deposition velocity is interrelated with the effect of the inclination on the solids distribution and it is discussed as well. We focus on partially-stratified flow for which a prediction of the effects is the most uncertain. Our experiment with the 0.87-mm sand in a 100-mm pipe contains measurements of solids distributions in flows inclined from – 45 to +45 degree and observations of the deposition velocity in flows from 0 to +45 degree. A new experimental method is introduced to detect the deposition velocity from a measured variation of local concentration of solids at the bottom of the pipe at velocities around the deposition limit. Flow predictions are carried out using our recent layered model for inclined partially stratified flow with an interfacial shear layer. The experiment confirms that the solids distribution in partially-stratified flow considerably varies with the flow slope. The model is able to successfully reproduce the variation. The model ability to predict also the deposition velocity is verified by our experiment and additional experimental results from the literature.Furthermore, the model results demonstrate how the widely used Wilson-Tse nomogram can be extended to include the effect of pipe inclination on the deposition velocity for flows different from fully-stratified flow. The model indicates that the original nomogram exaggerates the effect for flows in which the grain size is smaller than approximately 3% of the pipe diameter.