Fluidization and soot filtration in a rotating fluidized bed

A horizontal rotating fluidized bed (RFB) has been investigated for the removal of soot from diesel engine exhaust. This requires necessitating an understanding of the nature of fluidization, particle mixing and filtration in the RFB. In an RFB, particles are subject to a centrifugal force which can be much larger than the force of gravity. Therefore the Geldart classification for conventional fluidized beds must be modified for rotating fluidized beds. A theoretical analysis shows that group A particles (minimum bubbling velocity Umb \u3e minimum fluidization velocity Umf can shift to group B Umb = Umf and group C particles (agglomerating) can shift to group A under a centrifugal force. Therefore, certain group C particles can be fluidized in rotating fluidized beds. However, for very high g , such particles shift to group D (spouting) and cannot be fluidized. This was verified experimentally by successfully fluidizing 7 µm alumina particles in the RFB which behave as group C in a conventional fluidized bed. Thus an important and unique feature of RFB technology is that it enables the use of very fine bed particles in a fluidization mode. Since the RFB works as a shallow bed, the distributor plays an especially important role in its fluidization behavior. The pressure drop in an RFB was measured using slotted, perforated and sintered metal cylindrical gas distributors as a function of rotating speed, gas velocity and bed thickness with both polydisperse alumina particles and nearly monodisperse glass beads. The measured pressure drop for the different distributors depends strongly on the distributor design. A theoretical model available in the literature is used to calculate the minimum fluidization velocity and the pressure drop as a function of rotating speed, mass loading and gas velocity which are then compared to the experimental results. Particle motion in an RFB was studied by observing the mixing of two layers of particles of different color and different density. Experiments show that bubbles are responsible for particle motion and mixing for layers of the same material. When a layer of denser particles is placed on the distributor, the mixing behavior is similar to that observed for layers of the same material. However, when a layer of less dense particles is placed on the distributor, mixing is dominated by differences in density and occurs before bubbles are visible. A horizontal rotating fluidized bed filter (RFBF) charged with either polydisperse alumina granules or nearly monodisperse glass beads, was used to capture soot from diesel engine exhaust. The mass average filtration efficiency, calculated on the basis of the total mass of soot that was captured in the bed, was found to be up to 90% at the start of filtration at steady state flow conditions. Time and equipment limitations did not permit obtaining data with a build up of soot in the bed or the exploration of the effect of varying engine load conditions. A critical factor in obtaining high filtration efficiency is the use of fine sized bed particles (high surface area/volume), which is enabled by the use of an RFB. The filtration efficiency increased with increasing gas flow rate as the bed passes from the packed bed to the fluidized bed mode. The filtration efficiency also varied as a function of agglomerated soot size, showing a minimum for soot particles in the 0.3 to 0.6 µm range. This is a consequence of particles larger than 0.6 gm being removed mainly by inertial impaction and interception and smaller particles mainly by diffusion. Distributor plugging and fines generation due to attrition of the bed media were identified as critical issues and need to be addressed for realizing improvements in this area

A Study of the Navier-Stokes Equations with the Kinematic and Navier Boundary Conditions

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a domain in $\R^3$ with compact and smooth boundary, subject to the kinematic and Navier boundary conditions. We first reformulate the Navier boundary condition in terms of the vorticity, which is motivated by the Hodge theory on manifolds with boundary from the viewpoint of differential geometry, and establish basic elliptic estimates for vector fields subject to the kinematic and Navier boundary conditions. Then we develop a spectral theory of the Stokes operator acting on divergence-free vector fields on a domain with the kinematic and Navier boundary conditions. Finally, we employ the spectral theory and the necessary estimates to construct the Galerkin approximate solutions and establish their convergence to global weak solutions, as well as local strong solutions, of the initial-boundary problem. Furthermore, we show as a corollary that, when the slip length tends to zero, the weak solutions constructed converge to a solution to the incompressible Navier-Stokes equations subject to the no-slip boundary condition for almost all time. The inviscid limit of the strong solutions to the unique solutions of the initial-boundary value problem with the slip boundary condition for the Euler equations is also established.Comment: 30 page

New Approach for Vorticity Estimates of Solutions of the Navier-Stokes Equations

We develop a new approach for regularity estimates, especially vorticity estimates, of solutions of the three-dimensional Navier-Stokes equations with periodic initial data, by exploiting carefully formulated linearized vorticity equations. An appealing feature of the linearized vorticity equations is the inheritance of the divergence-free property of solutions, so that it can intrinsically be employed to construct and estimate solutions of the Navier-Stokes equations. New regularity estimates of strong solutions of the three-dimensional Navier-Stokes equations are obtained by deriving new explicit a priori estimates for the heat kernel (i.e., the fundamental solution) of the corresponding heterogeneous drift-diffusion operator. These new a priori estimates are derived by using various functional integral representations of the heat kernel in terms of the associated diffusion processes and their conditional laws, including a Bismut-type formula for the gradient of the heat kernel. Then the a priori estimates of solutions of the linearized vorticity equations are established by employing a Feynman-Kac-type formula. The existence of strong solutions and their regularity estimates up to a time proportional to the reciprocal of the square of the maximum initial vorticity are established. All the estimates established in this paper contain known constants that can be explicitly computed.Comment: 27 page

Using the teach-back method to improve postpartum maternal-infant health among women with limited maternal health literacy : a randomized controlled study

Peer reviewe

The Navier-Stokes Equations with the Kinematic and Vorticity Boundary Conditions on Non-Flat Boundaries

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in $\R^n$ with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure $p$ can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition (without the incompressibility condition), which establishes a velocity mapping. Then we develop \emph{apriori} estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in $\R^n (n\ge 3)$ with nonhomogeneous vorticity boundary condition converges in $L^2$ to the corresponding Euler equations satisfying the kinematic condition.Comment: 31 page

Nitrogen Release Characteristics of a Bag Controlled Release Fertilizer

Slow release fertilizers are designed to enhance crop yield and minimizing the loss of nitrogen (N) to environment. However, N release in leaching and loss in ammonia emission from bag controlled release fertilizers have not been previously evaluated under the standardized conditions in soil. Accordingly, a laboratory study was conducted to evaluate the characteristics of N release from a bag controlled fertilizer with 1, 3, 5 and 7 rows of hole (B-1, B-3, B-5, B-7) and a kraft bag without hole (B-W). The results showed that the amount of N leaching of B-1, B-3, B-5, B-7 and B-W were significantly lower than urea fertilizer without bag (U). The maximum N release from the fertilizers followed the order: U (83.16%) > B-7 (54.61%) > B-5 (54.02%) > B-W (51.51%) > B-3 (48.87%) > B-1 (38.60%) during the experimentation. Compared with U treatment, ammonia volatilization losses were significantly decreased by B-1, B-3, B-5, B-7 and B-W treatments. Based on N release and loss, a suitable bag with holes should be considered in practice when using the bag controlled fertilizer to meet an environment good objective. The evaluation method merits further study combined with field experiment