Abstract
Traveling wave analysis of a recently developed two-fluid model for bubbly flow in lab-size packed beds is used to propose a constitutive closure for the effective viscosity, a nonzero parameter that is needed in the liquid momentum balance to avoid the prediction of disturbances with an infinite growth rate. Near-solitary wave profiles are predicted over a range of velocity parameters consistent with linear stability analysis. Centimeter-scale periodic disturbances are predicted in the near-pulsing regime. Preliminary estimates of average pulse properties compare well with typically reported experimental values. Initial comparison with time integration subject to periodic boundary conditions shows agreement of the liquid saturation profiles but differences in the liquid velocity profiles.
Highlights
Introduction e volume averaged two-fluid model [1, 2] has been successfully applied in the literature to predict key engineering quantities that are needed for the design of packed beds with cocurrent and downward gas-liquid flow
As pointed out in a recent paper [5], the scaling argument used by Dankworth et al to obtain a closure for the effective viscosity is based on the assumption that typical variations in the interstitial liquid velocity, a mesoscale quantity, occur over distances that are of the order of the packing diameter
Preliminary results show that the closure predicts centimeter-scale periodic disturbances in this regime
Summary
Elimination of the pressure gradients in equations (3) and (4) leads to the following equation for the variables εl and vl:. We ask if it is possible to integrate equations (1), (9), and (10) in time, starting from the linear stability solutions, and asymptotically (after saturation at large time) reach the finite-amplitude periodic profiles predicted from the traveling wave analysis. Another available method for generating finite-amplitude periodic solutions consists of solving equations (1), (9), and (10) with periodic boundary conditions in “boxes” that have dimensions equal to the wavelengths of the linear modes. Both methods are based on different assumptions/restrictions, it would be interesting to compare their predictions, at least in a preliminary fashion in this work
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