Quasisimilarity of helical flow of power-law fluids in concentric annuli

摘要

Helical,steady-state,laminar,isothermal flow of incompressible power-law fluids through a concentric annulus is analysed for a stationary outer cylinder with the inner pipe rotating with constant torque.Pressure is applied in an axial direction.Using dimensionless analysis,a quasisimilarity solution was derived for a sufficiently broad region of rheological,geometrical and dynamical parameters.The relation between flow rate and the pressure gradient can be determined in this region using six graphs presented in the contribution.First,a dimensionless flow rate is determined from these graphs,and then a real flow rate is obtained from a simple linear proportionality between dimensionless and real flow rates.No numerical calculations are needed.Moreover,these six graphs illustrate(for the given pressure gradient)the functional dependence of flow rate on an aspect ratio of the inner-to-outer cylinders,parameters in the power-law rheological model,and torque.The above procedure was applied to the experimental data published in the literature and a good agreement was found.