Browsing by Author "McKibbin, R."

Now showing 1 - 7 of 7
  • Thumbnail Image
    Item
    Agglomerate properties
    (Massey University, 2003) Rynhart, P.R.; Jones, J.R.; McKibbin, R.
    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.
  • Thumbnail Image
    Item
    A comparison of some numerical methods for the advection-diffusion equation
    (Massey University, 2006) Thongmoon, M.; McKibbin, R.
    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.
  • Thumbnail Image
    Item
    Leaf area index and topographical effects on turburlent diffusion in a deciduous forest
    (Massey University, 2012) Kimura, S.; McKibbin, R.; Ogawa, J.; Kiwata, T.; Komatsu, N.; Nakamura, K.
    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.
  • Thumbnail Image
    Item
    Solution of the Young-Laplace equation for three particles
    (Massey University, 2003) Rynhart, P.R.; McLachlan, R.; Jones, J.R.; McKibbin, R.
    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.
  • Thumbnail Image
    Item
    Source release-rate estimation of atmospheric pollution from a non-steady point source - Part 2: Source at an unknown location
    (Massey University, 2003) Kathirgamanathan, P.; McKibbin, R.; McLachlan, R.I.
    This paper presents an inverse modelling procedure to estimate the location and release rate of atmospheric pollution. The input to this model requires measured pollution concentration at a minimum of three observation sites on the ground and meteorological conditions such as wind speed and cloud cover. The inverse model is formulated as a least squares minimisation problem coupled with the solution of an advection-diffusion equation for a non-steady point source model. Since the minimisation problem has a combination of linear and non-linear parameters the problem is solved in two steps. Non-linear parameters are found by constructing an iterative procedure using an optimisation routine such as MATLAB’s lsqnonlin and at each iteration, the linear subproblem is solved to estimate the linear parameters. Finding the linear parameters is an ill-posed problem and consequently its solution is extremely sensitive to errors in the data. Tikhonov regularisation, which stabilises the process of the solution, is used to overcome the ill posedness of the problem and the regularisation parameter is estimated using the properties of the non-linear L-curve, linear L-curve and generalised cross validation. Finally, the accuracy of the model is examined by imposing normally-distributed relative noise into concentration data generated by the forward model.
  • Thumbnail Image
    Item
    Source release-rate estimation of atmospheric pollution from a non-steady point source - Part I: Source at a known location
    (Massey University, 2003) Kathirgamanathan, P.; McKibbin, R.; McLachlan, R.I.
    The goal is to build up an inverse model capable of finding the release history of atmospheric pollution by using measured gas concentration data at just one location on the ground and identify the factors which affects the accuracy of the model predictions. The problem involves a non-steady point source of pollution at a known location in the atmosphere. This problem of finding the release rate is an ill-posed inverse problem and its solution is extremely sensitive to errors in the measurement data. Special regularisation methods, which stabilise the process of the solution, must be used to solve the problem. The method described in this paper is based on linear least-squares regression and Tikhonov regularisation, coupled with the solution of an advection-diffusion equation for a non-steady point source. The accuracy of the method is examined by imposing normally-distributed relative noise into the concentration data generated by the forward model as well as some real experimental data.
  • Thumbnail Image
    Item
    Source term estimation of pollution from an instantaneous point source
    (Massey University, 2002) Kathirgamanathan, P.; McKibbin, R.; McLachlan, R.I.
    The goal is to develop an inverse model capable of simultaneously estimating the parameters appearing in an air pollution model for an instantaneous point source, by using measured gas concentration data. The approach taken was to develop the inverse model as a non-linear least squares estimation problem in which the source term is estimated using measurements of pollution concentration on the ground. The statistical basis of the least squares inverse model allows quantification of the uncertainty of the parameter estimates, which in turn allows estimation of the uncertainty of the simulation model predictions.