Mathematical modeling of pulp washing on rotary drums and their numerical solution for various adsorption isotherms
The mechanism of the displacement washing of the bed of pulp fibers is mathematically modeled by the basic material balance equation. Linear as well as non-linear adsorption isotherms are used to describe the relationship between the concentration of the solute in the liquor and concentration of the solute on the fibers. In the present study, the numerical solutions are obtained of pulp washing model with different adsorption isotherms. For the numerical solution “pdepe” solver in MATLAB is applied on the axial domain of the system of partial differential equations. Numerical results thus obtained are compared with earlier workers analytically and numerically. The comparison shows that results are in good agreement with both analytically as well as numerically and also show the suitability of the isotherm coupling with the washing model. The technique used in the present investigation is simple, elegant and convenient for solving two point boundary value problems with varying range of parameters.
The diffusion model of longitudinal mixing in beds of finite length. Numerical values
Abstract Accurate numerical values are provided for the solution of the diffusion model of miscible fluid displacement in beds of finite length. The calculations presented here apply to the case in which a solute, uniformly distributed throughout the medium at the outset of the experiment, is displaced by a solvent which may itself contain some of the solute. Results are given in dimensionless form for (i) the instantaneous concentration of solute leaving the bed, and (ii) the average solute concentration in the bed at any instant. Various limiting cases are discussed.
Damage initiation and propagation in composite shells subjected to impact
Abstract The paper investigates the impact-induced damage initiation and propagation for laminated composite shells under low-velocity impact. A three-dimensional eight-node non-conforming element is described to analyze interlaminar stress distribution, and progressive failure. The damage analysis is performed by using Tsai–Wu quadratic failure criterion, Tsai’s damage modes and an additional delamination formula at all Gaussian points. The damage modes considered are matrix cracking, fiber breakage and delamination. The progressive failure is expressed by reducing stiffness of the material at all failed Gaussian points. Special attention is centered on curved laminates. Impact energy threshold for the onset of damage and transient damage size are predicted for composite shells. The analyses of the flat and curved laminates are compared for discussing their different damage mechanism. In addition, the influence of the stacking sequence, the thickness and the radius of curvature on damage behavior of composite shells are studied.