Numerical simulation of non-isothermal viscoplastic waxy crude oil flows

This paper examines the numerical simulation of transient non-isothermal flows of a viscoplastic fluid in a pipe. The situation considered refers to the waxy crude oils transportation in a pipeline, where the flowing oil is cooled down due to extreme external temperature conditions. The rheological model used is an extension of the classical Bingham model in which plastic viscosity and yield stress are allowed to be temperature-dependent parameters. To solve the governing equations, we propose a decoupled transient solution algorithm. At each time step, the velocity-pressure problem and the temperature problem are solved sequentially. Particular attention is devoted to the velocity-pressure problem in which the “true” (without regularization procedure) Bingham model is accounted for by using Lagrange multipliers techniques and augmented Lagrangian/Uzawa methods. The mass, momentum, constitutive and energy equations are discretized using a Finite Volume method on a staggered grid with a TVD scheme for the convective term. The resulting numerical method highlights strong and robust convergence properties. Obtained results regarding the steady-state solution underline the influence of the temperature changes on the flow pattern, especially in terms of yielded/unyielded regions. In particular, in a pipe flow, as soon as the temperature field varies in the mean flow direction, the fluid is yielded.