Dynamic modeling and model predictive control of a continuous pulp digester

This work explores the design of a model predictive controller of the continuous pulp digester process consisting of the co-current zone and counter-current zone modeled by a set of nonlinear coupled hyperbolic partial differential equations (PDEs). The distributed parameter system of interest is not spectral, and slow–fast dynamic separation does not hold. To address this challenge, the nonlinear continuous-time model is linearized and discretized in time utilizing the Cayley–Tustin discretization framework, which ensures system theoretic properties and structure preservation without spatial discretization or model reduction. The discrete model is used in the full state model predictive controller design, which is augmented by the Luenberger observer design to achieve the output constrained regulation. Finally, a numerical example is provided to demonstrate the feasibility and applicability of the proposed controller designs.     

Heat transfer of dry granular materials in a bladed mixer: Effect of thermal properties and agitation rate

Agitated drying of pharmaceuticals remains a challenging manufacturing step due to the simultaneous heat transfer, mass transfer, and physicochemical changes occurring during the process. This work focuses on the heat transfer component by implementing the discrete element method to model dry particles in a heated bladed mixer. Simulations varying material conductivities and impeller agitation rates were conducted to evaluate the influence on the mean bed temperature and distribution. The results indicated that increasing the agitation rate generally improved heat transfer up until a critical agitation rate where the rate of heat transfer plateaued. The magnitude of this improvement in heat transfer depended on the material's thermal properties. We observed three regimes: a conduction-dominated regime where particles heated quickly but with an annular temperature gradient, a granular convection-dominated regime where particles heated slowly but uniformly, and an intermediate regime. The results were nondimensionalized to enable predictions and help inform drying protocols.     

Fictitious particle method: A numerical model for flows including dense solids with large size difference

Large solids coexist with small solids in a number of dense gas‐solid flow applications such as fluidized beds and pneumatic conveyers. A new numerical model that is based on the discrete element method–computational fluid dynamics mesoscopic model and extended by introducing an idea appearing in volume penalization method is presented. In computational cells including large and small solids, the amount of momentum exchange between the fluid and the solids is estimated by assuming that a large solid consist of small, dense fictitious particles. We describe the proposed model in detail and show the optimal model parameters found through a number of parameter‐dependency studies. Validation study is performed for the motion of a large sphere in a bubbling fluidized bed and good agreements are confirmed for floating and sinking motions of the sphere between the present model and the experiment. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1606–1620, 2014     

Darcy's law for two‐dimensional flows: Singularities at corners and a new class of models

As is known, Darcy's model for fluid flows in isotropic homogeneous porous media gives rise to singularities in the velocity field for essentially two‐dimensional flow configuration, like flows over corners. Considering this problem from the modeling viewpoint, this study aims at removing this singularity, which cannot be regularized via conventional generalizations of the Darcy model, like Brinkman's equation, without sacrificing Darcy's law itself for unidirectional flows where its validity is well established experimentally. The key idea is that as confirmed by a simple analogy, the permeability of a porous matrix with respect to flow is not a constant independent of the flow but a function of the flow field (its scalar invariants), decreasing as the curvature of the streamlines increases. This introduces a completely new class of models where the flow field and the permeability field are linked and, in particular problems, have to be found simultaneously. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Boundary conditions for collisional granular flows of frictional and rotational particles at flat walls

Collisions between frictional particles and flat walls are determined using Coulomb friction and both tangential and normal restitution, and pseudothermal states of particles are described by both the translational and rotational granular temperatures. Then, new models for the stresses and the fluxes of fluctuation energy for the collisional granular flows at the walls are derived. These new models are tested and compared with the literature data and models. The ratio of rotational to translational granular temperatures is shown to be crucial on accurately predicting the shear stress and energy flux and is dependent on the normalized slip velocity as well as the collisional parameters. Using a theoretical but constant value for this ratio, predictions by the new models could still agree better with the literature data than those by the previous models. Finally, boundary conditions are developed to be used within the framework of kinetic theory of granular flow. © 2014 American Institute of Chemical Engineers AIChE J 60: 4065–4075, 2014