Longitudinal dispersion of turbulent oscillatory pipe flows

Abstract

In the present study, we examine the longitudinal dispersion of oscillatory pipe flows in the turbulent range which is not well covered before. An analytical analysis was first performed using the homogenization approach (i.e. multiple scale perturbation analysis) to predict the magnitude of the longitudinal dispersion induced by a turbulent oscillatory flow forced by a sinusoidal pressure gradient inside a circular pipe. An axisymmetric co-axial eddy viscosity model was adopted to resolve the radial distribution of velocities and turbulent shear stresses. Based on the derived kinematic characteristics, the longitudinal dispersion coefficient for the turbulent oscillatory pipe flow was then quantified. The results demonstrated that a dimensionless parameter α , which is the ratio of the oscillatory velocity amplitude divided by the frequency and pipe radius, determines the flow structure as well as the magnitude of the induced longitudinal dispersion coefficient. Experiments were also conducted to quantify the longitudinal dispersion coefficient under different frequencies and oscillatory velocity magnitudes. The measurement approaches were based on the non-invasive laser imaging techniques of particle image velocimetry and planar laser induced fluorescence. The experimental conditions covered a relatively wide range of boundary Reynolds number (Re δ ) from 100 to 1,000, and included both laminar and turbulent flow regimes. The results showed that when the flow enters the conditional turbulence regime, i.e. Re δ ≥500 , the longitudinal dispersion coefficient increases drastically. The analytical predictions based on the homogenization approach in the present study agree well with the measured longitudinal dispersion coefficients.