Secondary flows in straight ducts of rectangular cross section

In this paper we consider the “elastic effects” that a non-Newtonian fluid, a solution of 2% viscarin in water, can exhibit in fully developed laminar flow in straight ducts of rectangular cross section. The elastic effects associated with the nonlinear properties of constitutive equations are modelled by the CEF-equation.

Our main concern is the nature and magnitude of the secondary flows, determined both by numerical and experimental means. In contrast to earlier work, where a perturbation method has been used, the full non-linear equations are solved numerically by a finite volume method. It is shown that two vortices in each quadrant are observed for unity and moderate aspect ratios whereas three vortices are observed for the large aspect ratio of 16.

The effect of secondary flow on pressure drop is calculated using both the generalized Newtonian model and the CEF-model. At low flow rates the effect is small but significant effects are observed at high flow rates. This is partly verified through measurements of pressure drop. Calculated velocity fields are compared to data obtained by laser velocimetry and show general agreement within experimental uncertainty.