LAMINAR-FLOW IN TWISTED DUCTS

Fully developed flow of an incompressible Newtonian fluid through a du ct in which the orientation of the cross section is twisted about an a xis parallel to an imposed pressure gradient is analyzed here with the aid of the penalty/Galerkin/finite element method. When the axis of t wist is located within the duct, flow approaches limits at low and hig h torsion, the spatial frequency tau by which the duct is twisted. For small torsion, flow is nearly rectilinear and solutions approach prev ious asymptotic results for an elliptical cross section. For large tor sion, flow exhibits an internal layer structure: a rotating circular-c ylinder core with a nearly parabolic axial velocity profile, an intern al layer of thickness tau-1 along the perimeter of the largest circula r cylinder that can be inscribed in the duct, and nearly quiescent flo w outside of the circular cylinder. The maximum rate of swirl in the c ore of a square duct is found to be at moderate torsion. The primary e ffect of inertia is an increase in pressure with distance from the axi s, due to centrifugal acceleration. When the duct is offset from the a xis of twist, inertia leads to one, two, or three primary vortices wit hout apparent bifurcation of steady states, although stability of stea dy flows is lost beyond detected Hopf points.