A steady-state laminar flow of a viscoplastic fluid through an axisymmetric sudden pipe contraction under non-isothermal conditions has been studied numerically. Mathematical formulation of the problem is given using stream function – vorticity – temperature variables. Rheological properties of the fluid are described by the Herschel–Bulkley model, which implies an unyielded region formation in the flow. Viscous dissipation effects and temperature dependence of the viscosity are taken into account when simulating the process. An asymptotic time solution of unsteady flow equations is used to obtain a steady-state solution to the initially formulated problem. The finite-difference method based on the alternative directions scheme is applied to solve the problem numerically. Regularization of the rheological equation is performed to provide a through computation of the flow with unyielded regions. A parametric investigation of the flow structure, which includes dead zones and yielded/unyielded regions, is implemented in order to show the impact of main dimensionless parameters.

在非等温条件下，通过轴对称突然的管道收缩，对粘塑性流体的稳态层流进行了数值研究。使用流函数-涡度-温度变量给出了问题的数学公式。流体的流变特性由Herschel-Bulkley模型描述，这暗示了流中未屈服的区域形成。在模拟过程时，应考虑粘性耗散效应和粘度的温度依赖性。使用非定常流动方程的渐近时间解来获得对初始公式问题的稳态解。应用基于交替方向方案的有限差分方法来数值求解该问题。进行流变方程的正则化以提供具有未屈服区域的流动的完整计算。为了显示主要无量纲参数的影响，对流动结构进行了参数研究，其中包括死区和屈服/未屈服区域。