ON THE VELOCITY-FIELD AND TRACER PATTERNS IN A TWISTED DUCT FLOW

The laminar flow in a twisted square duct is studied numerically to analyze the formation and reorganization of Dean roll cells under abrupt curvature change. The flow geometry consists of four 90° bends, the curvature plane of each making a 90° angle with that of its neighbor. Straight ducts are inserted between successive bends. The flow geometry studied here is a basic element of a twisted duct flow in which chaotic advection has been observed [Jones, Thomas, and Aref, J. Fluid Mech. 209, 335 (1989)]. Steady incompressible full Navier-Stokes equations have been solved by an approximate factorization technique. Vector plots of the secondary flow (Dean roll cells) show upstream diffusion of curvature effects. The upstream propagation is weak, however, and the Dean roll cells adopt the rotation protocol of the bend immediately at its entrance. Farther downstream, roll cells continue to develop and reach an axially invariant state before leaving the bend. A passive tracer was also introduced at the center of the entrance to the twisted duct. Tracer distribution was followed in the downstream direction and was visualized every 30°. Comparison of the secondary flow velocity vector plots and the corresponding tracer patterns shows that the tracer distribution lags behind the velocity field in adjusting to changes in curvature. Tracer patterns show strong stretching and folding, which lead to mixing enhancement. © 1995 American Institute of Physics.