Cross-dimensional isothermal model for the transient restart of weakly compressible laminar/turbulent flow of time-dependent non-Newtonian fluid in a long pipeline

Based on reasonable simplifications of three-dimensional governing equations, a cross-dimensional isothermal model for the transient flow restart of time-dependent non-Newtonian fluid in a long pipeline is established, in which conservation equations are in one-dimensional (1D) form and two key variables (average velocity and wall shear stress) in the 1D conservation equations are related to some two-dimensional (2D) equations. This model considers fluid compressibility, complex non-Newtonian rheological behavior, and flow pattern transition. A prediction-correction method and a trial calculation method are combined to solve the cross-dimensional model. The presented cross-dimensional simulation is validated from different perspectives using a theoretical formula, a mature empirical formula, and numerical results from 2D and 1.5-dimensional (1.5D) simulations. The presented cross-dimensional simulation is considered to have strong universality for predicting flow processes in long pipelines. Moreover, the complex flow restart in a long waxy crude oil pipeline is numerically simulated. The results indicate that the flow restart can be divided into three stages according to differences in various influence factors and flow features. These three stages include the laminar/turbulent flow in the yield front movement, the laminar/turbulent flow in the fluid structure breakdown and flow pattern transition, and the turbulent flow in the pure fluid structure breakdown. Analysis of flow processes in these three stages reveals the complex characteristics of the flow restart in a long pipeline.