Method of moments for laminar dispersion in an oscillatory flow through curved channels with absorbing walls |
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Authors: | Sushil Kumar Girija Jayaraman |
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Institution: | (1) Centre for Atmospheric Sciences, Indian Institute of Technology, New Delhi, 110016, India |
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Abstract: | The unsteady dispersion of a solute, when the fluid is driven through a curved channel with absorbing walls by an imposed
pulsatile pressure gradient, is studied using the method of moments. The study examines the effect of oscillatory Reynolds
number, amplitude/frequency of the pressure pulsation and boundary absorption on the longitudinal dispersion. The methodology
involves a set of unsteady integral moment equations obtained by applying the Aris-Barton method of moments on the convective-diffusion
equation for a curved channel. Central moments are obtained from the moment equations which are solved by a finite-difference
implicit scheme. The effect of curvature and boundary absorption on the effective dispersion coefficient from the initial
to the stationary stage of the oscillatory flow is studied. Amplitude of the effective dispersion coefficient is found to
increase with curvature and decrease with frequency of the pressure pulsation. For large Peclet number and Schmidt number,
the amplitude of the dispersion coefficient can be 1.6 times that in a straight channel at large times. Also, for large times,
the amplitude of the dispersion coefficient is twice the amplitude of the dispersion coefficient as α, the frequency parameter
changes from 0.5 to 1.0. The axial distributions of mean concentration are determined from the first four central moments
by using the Hermite polynomial representation. The effect of curvature is to delay the stationary state and also the approach
to normality of the concentration distribution. The study has importance in understanding the spreading of pollutants in tidal
basins and natural current fields. |
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