Bolus Contaminant Dispersion for Oscillatory Flow in a Curved Tube

Abstract

The dispersion of a bolus of soluble contaminant in a curved tube during volume-cycled oscillatory flows is studied. Assuming a small value of δ (the ratio of tube radius to radius of curvature), the Navier-Stokes equations are solved by using a perturbation method. The convection-diffusion equation is then solved by expanding the local concentration in terms of the cross-sectionally averaged concentration and its axial derivatives. The time-averaged dimensionless effective diffusivity, 〈Deff /D〉, is calculated for a range of Womersley number α and different values of stroke amplitude A and Schmidt number Sc, where D is the molecular diffusivity of contaminant. For the parameter values considered, the results show that axial dispersion in a curved tube is greater than that in a straight tube, and that it has a local maximum near α = 5 for given fixed values of Sc = 1, A = 5 and δ = 0.3. Finally it is demonstrated how the time history of concentration at a fixed axial position can be used to determine the effective diffusivity.