A numerical study of the effect of nonisothermality on the power-law fluid flow characteristics in a sudden pipe expansion

In this paper, a steady laminar non-isothermal flow of a power-law fluid in an axisymmetric sudden pipe expansion is numerically simulated. The rheological behavior of the fluid is described by the modified Ostwald-de Waele law; the apparent viscosity is an exponential function of temperature. The equations are written in terms of dimensionless stream function - vortex - temperature. No-slip conditions and zero temperature are used on the solid wall. At the inlet boundary, the velocity and temperature profiles correspond to a one-dimensional steady non-isothermal flow of the considered fluid. “Soft” boundary conditions are assigned at the outlet boundary. The formulated problem is solved using the finite-difference method.
The structure of the flow through a sudden pipe expansion is shown to include one- and two-dimensional flow zones with a recirculation region occurring in the inner corner vicinity. The variation in the two-dimensional flow zone length is analyzed with respect to a power-law index and dimensionless criteria of the problem. Distributions of the velocity, temperature, and apparent viscosity are presented at various Peclet and Reynolds numbers for dilatant and pseudoplastic fluids.