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

D. A. Mamazova ; K. E. Ryltseva ; G. R. Shrager

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 79 (2022), pp. 120-134

Résumé

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.

Détail

Keywords: non-isothermal flow, Ostwald-de Waale model, power-law fluid, axisymmetric flow, expansion, Reynolds number, Peclet number.
Mots-clés : circulation zone