A comparison of some numerical methods for the advection-diffusion equation

This paper describes a comparison of some numerical methods for solving the advection-diffusion (AD) equation which may be used to describe transport of a pollutant. The one-dimensional advection-diffusion equation is solved by using cubic splines (the natural cubic spline and a ”special” AD cubic spline) to estimate first and second derivatives, and also by solving the same problem using two standard finite difference schemes (the FTCS and Crank-Nicolson methods). Two examples are used for comparison; the numerical results are compared with analytical solutions. It is found that, for the examples studied, the finite difference methods give better point-wise solutions than the spline methods

Agglomerate properties

Modelling of wet granulation requires the rate of agglomerate coalescence to be estimated. Coalescence is dependent on the frequency of collisions that occur, and the fraction of collisions which result in coalescence. The collision rate is a function of granulator kinetics and powder properties, while the coalescence success rate is dependent on factors including the Stokes number and particle geometry. This work investigates an aspect of the geometry by examining the distribution of liquid on the surface of agglomerates in the capillary state. Agglomerates are created by adding particles, one at a time, about a central tetrahedral arrangement of four primary particles. For a given agglomerate, the wetted fraction of surface area, defined as the wetness, is evaluated using an approximate fluid surface. Packing density and binder saturation parameters are incorporated into the model. Given a number of primary particles and the volume of binder in a particle, the agglomerate wetness is able to be estimated using computational geometry

Solution of the Young-Laplace equation for three particles

This paper presents the solution to the liquid bridge profile formed between three equally sized spherical primary particles. The particles are equally separated, with sphere centres located on the vertices of an equilateral triangle. Equations for the problem are derived and solved numerically for given constant mean curvature H0, contact angle , and inter-particle separation distance S. The binding force between particles is calculated and plotted as a function of liquid bridge volume for a particular example. Agreement with experiment is provided

Convection and heat transfer in layered sloping warm-water\ud aquifers

What convective flow is induced if a geologically-tratified groundwater aquifer is subject to a vertical temperature gradient? How strong is the flow? What is the nett heat transfer? Is the flow stable? How does the convection affect the subsequent species distribution if a pollutant finds its way into the aquifer? This paper begins to address such questions. Quantitative models for buoyancy-driven fluid flow in long, sloping warm-water aquifers with both smoothly- and discretely-layered structures are formulated. The steady-state profiles are calculated for the temperature and for the fluid specific volume flux (Darcy velocity) parallel to the boundaries in a sloping system subjected to a perpendicular temperature gradient, at low Rayleigh numbers. The conducted and advected heat fluxes are compared and it is shown that the system acts somewhat like a heat pipe. The maximum possible ratio of naturally advected-to-conducted heat transfer is determined, together with the corresponding permeability and thermal conductivity profiles

Development of compressor end seals stator interstage seals, and stator pivot seals in advanced air breathing propulsion systems. Part 2: Experimental data and analysis

Performance tests of compressor seals and stator pivot seals used with air breathing propulsion systems - Part

Solid performance at Tenth District banks

Commercial banks in Tenth District states performed well in the first half of 1997. Profitability and loan quality remained high, while loans continued to grow at a healthy pace. The only negative was that deposits grew sluggishly, adding to liquidity pressures. Banks in district states slightly outperformed banks nationwide in profitability and loan quality, while matching them in loan growth and deposit growth.Federal Reserve District, 10th

Changes in the depository industry in Tenth District states

Recent development in Congress and the courts have focused attention on the relative roles of commercial banks, thrifts, and credit unions. As concern mounted last year about the state of the thrift deposit insurance fund, Congress required commercial banks to share the burden of recapitalizing the fund. In return, Congress promised to come up with a plan for merging the bank and thrift charters, a move the banking industry has long favored. About the same time, a federal appeals court ruled against a major source of credit union growth since the early 1980s - the acceptance of new members with a common bond different from the original members. The Supreme Court later agreed to hear the case, sparking a renewed debate in Congress about the proper role of credit unions in the financial system. ; These recent actions by Congress and the courts follow a decade and a half of dramatic changes in the depository industry in Tenth District states. Some of these changes have been due to shifts in laws and regulations. First, there has been a significant decline in the number of district depository institutions - a decline in which banks, thrifts, and credit unions have all shared. Second, total deposits have declined when adjusted for inflation or measured relative to economic activity. Third, the share of thrifts in total deposits has plummeted relative to that of banks and credit unions. And fourth, while banks, thrifts, and credit unions still specialize in different loans and investments, the three types of institutions do not look as different today as at the beginning of the 1980s. ; Such changes are important because they affect the thousands of depository institutions in the district and the supply of credit and other financial services to district households and businesses. With those effects in mind, Keeton and McKibbin show how the district depository industry has changed since 1979, explain the factors behind each change, and suggest what further changes may lie ahead.Banks and banking ; Credit unions ; Savings and loan associations ; Federal Reserve District, 10th

Development of compressor end seals stator interstage seals, and stator pivot seals in advanced air breathing propulsion systems. Part 1: Screening studies and analysis

Design and characteristics of 28-inch diameter seals for air breathing propulsion systems - Part

Leaf area index and topographical effects on turburlent diffusion in a deciduous forest

In order to investigate turbulent diffusion in a deciduous forest canopy, wind velocity measurements were conducted from late autumn of 2009 to early spring of 2010, using an observation tower 20 m in height located in the campus of Kanazawa University. Four sonic anemometers mounted on the tower recorded the average wind velocities and temperatures, as well as their fluctuations, at four different heights simultaneously. Two different types of data sets were selected, in which the wind velocities, wind bearings and atmospheric stabilities were all similar, but the Leaf Area Indexes (LAI's) were different. Vertical profiles of average wind velocities were found to have an approximately exponential profile in each case. The characteristic length scales of turbulence were evaluated by both von Karman's method and the integral time scale deduced from the autocorrelation from time-series analyses. Both methods produced comparable values of eddy diffusivity for the cases with some foliage during late autumn, but some discrepancy in the upper canopy layer was observed when the trees did not have their leaves in early spring. It was also found that the eddy diffusivities generally take greater values at higher positions, where the wind speeds are large. Anisotropy of eddy diffusivities between the vertical and horizontal components was also observed, particularly in the cases when the canopy does not have leaves, when the horizontal eddy diffusivities are generally larger than the vertical ones. On the other hand, the anisotropy is less visible when the trees have some foliage during autumn. The effects of topography on the turbulent diffusion were also investigated, including evaluation of the non-zero time-averaged vertical wind velocities. The results show that the effects are marginal for both cases, and can be neglected as far as diffusion in the canopy is concerned