A 1.5D numerical model for the start up of weakly compressible flow of a viscoplastic and thixotropic fluid in pipelines

We investigate the problem of the start up of a compressible flow in a pipeline filled with a viscoplastic and thixotropic material. The objective of this study is to examine the possibility that the flow can restart for a pressure drop below the value predicted by the conservative relation Δpˆ=4τˆyLˆ/Dˆ, where τˆy denotes the yield stress, Lˆ the pipe length and Dˆ the pipe diameter, thanks to the combined effects of compressibility and thixotropy. Our numerical model is a compromise between a fully 2D model and a fully 1D model, i.e., a 1.5D model. Only the velocity component in the direction of the pipe axis is assumed non-zero but it is allowed to vary both in axial and radial directions. We show that this intermediate model yields accurate results which are consistent with the predictions of the fully 2D model. The gain in computing time while keeping an equivalent reliability in the numerical predictions enables us to investigate the effects of the compressibility and thixotropy dimensionless numbers at a reasonable cost.