Abstract
The secondary flow and dispersion of a tracer substance in a fluid flowing through a curved tube are studied numerically. The system consists of an infinitely long conduit defined by two concentric curved circular pipes. Thus the two phases correspond to a flowing fluid phase and the annular wall comprised of a stationary homogenous medium. The solute is soluble in the annular region and is assumed to satisfy a linear equilibrium relationship at the interface. Flow in the fluid phase is calculated using the finite difference scheme as described by Collins and Dennis [9]. The scheme is of second order accuracy with respect to grid sizes over the entire laminar flow region and reveals the asymptotic nature of the solution for large values of Dean number D. Further, a central difference scheme is used to solve the convection diffusion equation in both the phases with the condition that the injective solute is highly soluble in the wall layer according to a linear equilibrium relationship at the interface. Results for small Dean number are first verified with our earlier results (Jayaraman et al. [17]) which were based on Dean's solution [12,13]. The numerical calculations are then extended for larger Dean number and Schmidt number. The results are consistent with experimental results that the influence of secondary flows on dispersion is reduced if the tracer is very soluble in the wall. It is found that the effective longitudinal diffusivity falls below its straight tube value by an amount, which depends on the absorption coefficient, Dean number and the diffusivity in the wall. For large Dean number dispersion becomes negligible.
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