Alternative Measures of Dispersion Applied to Flow in a Convoluted Channel

Abstract Steady flow in a convoluted channel is studied via Particle Tracking Velocimetry. The channel is constructed from a sequence of closed parallel cylindrical tubes welded together in plane which are then sliced down the lateral mid-plane and the lower complex is laterally shifted relative to the upper complex. Flow is induced in the lateral direction normal to the axis of the tubes. The a-time, T-a, finite-size Lyapunov exponent, lambda(a), and the real-space self-and distinct-part of the intermediate scattering functions, G(s) and G(d), and the pair density function, G(p), are computed from the data. Particle trajectories, velocity maps and streamlines show the channel has two prominent recirculation zones and a main flow region. The first passage time probability density function of tagged particles past a plane transverse to the mean flow illustrates how particles are delayed by recirculation zones. The delay caused by fluid element folding is manifested in single particle statistics such as the first passage time and the slowing increase in horizontal evolution of G(s). G(p) describes initial particle distribution and allows areas in the flow domain trapping particles to be identified and visualized. G(d) Shows the evolution of the average separation of pairs of particles and when examined in a recirculation zone, it evolves little because of fluid element rotation. lambda(a) gives information on what transpires at a fixed scale and provides an estimate of the rate at which particles initially separated by a distance x separate to a distance ax as opposed to G(d) which allows one to view changes over time. At small separations, lambda(1.3) approaches a constant and for intermediate separations it scales as x(-0.8).