Investigation of a hydrodynamic entrance region for a power-law fluid flow in a round pipe

The paper presents a study of the Ostwald-de Waele fluid flow in a round pipe with a uniform velocity profile specified at the inlet section. Mathematical formulation of the problem is presented using dimensionless variables. A numerical algorithm is developed on the basis of the finite volume method and SIMPLE procedure. Parametric studies of the flow are carried out for the Reynolds number varying from 0.1 to 80 and the power-law index varying from 0.2 to 1.5. It is shown that the flow can be distinguished into a developing flow zone in the inlet boundary vicinity and a fully developed flow zone in the rest part of the flow region. Dependency diagrams are plotted for the development length depending on the power-law index and Reynolds number. The first diagram is found to be non-monotonic. The development length is shown to be almost linearly dependent on the Reynolds number in the range from 1 to 80. In the region of low Reynolds numbers, the length remains almost uniform. The agreement of the obtained numerical results with data from other studies is shown.