Fluidized bed combustor modeling

A general mathematical model for the prediction of performance of a fluidized bed coal combustor (FBC) is developed. The basic elements of the model consist of: (1) hydrodynamics of gas and solids in the combustor; (2) description of gas and solids contacting pattern; (3) kinetics of combustion; and (4) absorption of SO2 by limestone in the bed. The model is capable of calculating the combustion efficiency, axial bed temperature profile, carbon hold-up in the bed, oxygen and SO2 concentrations in the bubble and emulsion phases, sulfur retention efficiency and particulate carry over by elutriation. The effects of bed geometry, excess air, location of heat transfer coils in the bed, calcium to sulfur ratio in the feeds, etc. are examined. The calculated results are compared with experimental data. Agreement between the calculated results and the observed data are satisfactory in most cases. Recommendations to enhance the accuracy of prediction of the model are suggested

The effect of Mach number on unstable disturbances in shock/boundary-layer interactions

The effect of Mach number on the growth of unstable disturbances in a boundary layer undergoing a strong interaction with an impinging oblique shock wave is studied by direct numerical simulation and linear stability theory (LST). To reduce the number of independent parameters, test cases are arranged so that both the interaction location Reynolds number (based on the distance from the plate leading edge to the shock impingement location for a corresponding inviscid flow) and the separation bubble length Reynolds number are held fixed. Small-amplitude disturbances are introduced via both white-noise and harmonic forcing and, after verification that the disturbances are convective in nature, linear growth rates are extracted from the simulations for comparison with parallel flow LST and solutions of the parabolized stability equations (PSE). At Mach 2.0, the oblique modes are dominant and consistent results are obtained from simulation and theory. At Mach 4.5 and Mach 6.85, the linear Navier-Stokes results show large reductions in disturbance energy at the point where the shock impinges on the top of the separated shear layer. The most unstable second mode has only weak growth over the bubble region, which instead shows significant growth of streamwise structures. The two higher Mach number cases are not well predicted by parallel flow LST, which gives frequencies and spanwise wave numbers that are significantly different from the simulations. The PSE approach leads to good qualitative predictions of the dominant frequency and wavenumber at Mach 2.0 and 4.5, but suffers from reduced accuracy in the region immediately after the shock impingement. Three-dimensional Navier-Stokes simulations are used to demonstrate that at finite amplitudes the flow structures undergo a nonlinear breakdown to turbulence. This breakdown is enhanced when the oblique-mode disturbances are supplemented with unstable Mack modes

Extraction of contact resistance in carbon nanofiber via interconnects with varying lengths

A method to extract the contact resistance and bulk resistivity of vertically grown carbon nanofibers (CNFs) or similar one-dimensional nanostructures is described. Using a silicon-compatible process to fabricate a terrace test structure needed for the CNF length variation, the contact resistance is extracted by measuring in situ the resistances of individual CNFs with different lengths and within a small range of diameters using a nanoprober inside a scanning electron microscope. Accurate determination of contact resistances for various combinations of catalysts and underlayer metals can lead to eventual optimization of materials’ growth and device fabrication processes for CNF via interconnects

Near-linear Time Algorithm for Approximate Minimum Degree Spanning Trees

Given a graph $G = (V, E)$, we wish to compute a spanning tree whose maximum vertex degree, i.e. tree degree, is as small as possible. Computing the exact optimal solution is known to be NP-hard, since it generalizes the Hamiltonian path problem. For the approximation version of this problem, a $\tilde{O}(mn)$ time algorithm that computes a spanning tree of degree at most $\Delta^* +1$ is previously known [F\"urer \& Raghavachari 1994]; here $\Delta^*$ denotes the minimum tree degree of all the spanning trees. In this paper we give the first near-linear time approximation algorithm for this problem. Specifically speaking, we propose an $\tilde{O}(\frac{1}{\epsilon^7}m)$ time algorithm that computes a spanning tree with tree degree $(1+\epsilon)\Delta^* + O(\frac{1}{\epsilon^2}\log n)$ for any constant $\epsilon \in (0,\frac{1}{6})$. Thus, when $\Delta^*=\omega(\log n)$, we can achieve approximate solutions with constant approximate ratio arbitrarily close to 1 in near-linear time.Comment: 17 page

Simulation of Thermal Transport in Open-Cell Metal Foams: Effect of Periodic Unit Cell Structure

Direct simulation of thermal transport in open-cell metal foams is conducted using different periodic unit-cell geometries. The periodic unit-cell structures are constructed by assuming the pore space to be spherical and subtracting the pore space from a unit cube of the metal. Different types of packing arrangement for spheres are considered—body centered cubic, face centered cubic, and the A15 lattice (similar to a Weaire-Phelan unit cell)—which give rise to different foam structures. Effective thermal conductivity, pressure drop, and Nusselt number are computed by imposing periodic boundary conditions for aluminum foams saturated with air or water. The computed values compare well with existing experimental measurements and semiempirical models for porosities greater than 80%. The effect of different foam packing arrangements on the computed thermal and fluid flow characteristics is discussed. The capabilities and limitations of the present approach are identified

A Two-Temperature Model for the Analysis of Passive Thermal Control Systems

Passive control of steady and unsteady thermal loads using effective thermal conductivity enhancers, such as metal foams, internal fins and metal filler particles, is being explored for a variety of electronics applications. The interstices are filled with air, phase change materials, or other fluids. Local thermal equilibrium between the solid filler and the matrix is not ensured in such systems since their thermal diffusivities are frequently very different. The use of a single volume-averaged energy equation for both the phases cannot be justified in such situations. A two-medium approach is used in the present work to account for the local thermal non-equilibrium. Separate energy equations are written for the solid and fluid respectively, and are closed using a steady-state interphase heat transfer coefficient between the two phases. A general momentum equation which includes the Brinkman-Forchheimer extension to Darcy flow is employed. The resulting equations are solved implicitly using a fully transient method on fixed orthogonal co-located finite volumes. Unsteady natural convection in a metal-foam filled cavity is computed. The influence of various parameters such as the ratios of solid-to-fluid thermal conductivities and heat capacities, Rayleigh number, Prandtl number and Darcy number on the thermal and flow fields is investigated. The results illustrate that local thermal equilibrium is not assured, either during the transient or at steady state for the range of parameters considered. Furthermore, even if the steady-state solid-to-fluid temperature differences are small, large temperature differences are seen during the unsteady response

Direct Simulation of Transport in Open-Cell Metal Foams

Flows in porous media may be modeled using two major classes of approaches: (a) a macroscopic approach, where volume-averaged semiempirical equations are used to describe flow characteristics, and (b) a microscopic approach, where small-scale flow details are simulated by considering the specific geometry of the porous medium. In the first approach, small-scale details are ignored and the information so lost is represented in the governing equations using an engineering model. In the second, the intricate geometry of the porous structures is accounted for and the transport through these structures computed. The latter approach is computationally expensive if the entire physical domain were to be simulated. Computational time can be reduced by exploiting periodicity when it exists. In the present work we carry out a direct simulation of the transport in an open-cell metal foam using a periodic unit cell. The foam geometry is created by assuming the pore to be spherical. The spheres are located at the vertices and at the center of the unit cell. The periodic foam geometry is obtained by subtracting the unit cell cube from the spheres. Fluid and heat flow are computed in the periodic unit cell. Our objective in the present study is to obtain the effective thermal conductivity, pressure drop, and local heat transfer coefficient from a consistent direct simulation of the open-cell foam structure. The computed values compare well with the existing experimental measurements and semiempirical models for porosities greater than 94%. The results and the merits of the present approach are discussed

A Two-Temperature Model for Solid/Liquid Phase Change in Metal Foams

Transient solid-liquid phase change occurring in a phase-change material (PCM) embedded in a metal foam is investigated. Natural convection in the melt is considered. Volume-averaged mass and momentum equations are employed, with the Brinkman- Forchheimer extension to the Darcy law to model the porous resistance. Owing to the difference in the thermal diffusivities between the metal foam and the PCM, local thermal equilibrium between the two is not assured. Assuming equilibrium melting at the pore scale, separate volume-averaged energy equations are written for the solid metal foam and the PCM and are closed using an interstitial heat transfer coefficient. The enthalpy method is employed to account for phase change. The governing equations are solved implicitly using the finite volume method on a fixed grid. The influence of Rayleigh, Stefan, and interstitial Nusselt numbers on the temporal evolution of the melt front location, wall Nusselt number, temperature differentials between the solid and fluid, and the melting rate is documented and discussed. The merits of incorporating metal foam for improving the effective thermal conductivity of thermal storage systems are discussed