Pulsating flow of viscoelastic fluids in straight tubes of arbitrary cross-section - Part II: Secondary flows

The secondary flow field in the pulsating flow of a constitutively non-linear fluid, whose structure is defined by a series of nested integrals over semi-infinite time domains, in straight tubes of arbitrary cross-sections is investigated. The transversal field arises at the second order of the perturbation of the non-linear constitutive structure, and is driven by first-order terms which define the linearly viscoelastic longitudinal flow in the hierarchy of superposed linear flows stemming from the perturbation of the constitutive structure. The unconventional conduit contours are obtained through a novel approach to the concept of domain perturbation. Time-averaged, mean secondary flow streamline patterns are presented for triangular, square and hexagonal pipes.