Download PROYECTO FONDECYT N° 1020578

PROYECTO FONDECYT 1050728
TITULO:
SIMULATION AND PARAMETER IDENTIFICATION FOR SUSPENSIONS IN
LABORATORY CENTRIFUGES AND SETTLING VESSELS.
Investigador Principal
Raimund Bürger (U. de Concepción)
Facultad/Depto.
Ciencias/Ciencias Básicas
E-Mail
[email protected]
Coinvestigadores
Anibal Coronel P.
OBJETIVOS:
- Implementation of an efficient numerical scheme for simulation of settling processes of
polydisperse suspensions.
- Characterization of entropy solutions of the direct problem of sedimentation of
polydisperse suspensions.
- Development of a numerical technique to solve parameter identification problems for
polydisperse suspensions.
- Mathematical analysis (including existence, uniqueness and convergence
applicable) of parameter identification schemes.
where
- Application to original experimental data and user-friendly implementation of the
parameter identification algorithm.
- Education of young researches (M.Sc. and doctoral students) and dissemination of
mathematical concepts that are available in highly specialized journals only.
RESUMEN Y RESULTADOS:
Laboratory devices for the analysis of the separation behaviour of suspensions under the
influence of eitheir gravity or a centrifugal body force are widely used in the medicine,
biotechnology, in wastewater treatment and in mineral processing. The settling tests that
can be performed with such equipment lead to concentration profiles under controlled
experimental conditions.
Practitioners urgently need material specific parameters of suspensions (for example, the
distribution of particle sizes and densities) for the simulation of scaled-up solid-liquid
separation processes in wastewater treatment plants, continuous thickeners and other units.
The applicant has specialized in the development, analysis and numerical simulation of
mathematical models for the solid-liquid separation of suspensions. Forward simulations
based on these models, which are given by convection-diffusion equations , are possible if
the material specific parameters and model functions are given. The aim of this project is
to provide the mathematical foundation of the identification of parameter from data
measured by laboratory devices.
We intend to treat the parameter identification problem by a Lagrangian formulation, and to
determine the parameter gradient by formal differentiation of discretized equations and by
their numerical solution. The decisive step in this method is the elimination of a gradient
that is usually difficult to determine by the solution of an additional adjoint problem.
Thus , the basic approach is to convert the parameter identification problem into an
optimization problem, which means that we try to minimize a cost function that measures
the “ distance” between the observed data (e.g.,a spatial concentration profile at a fixed
time) and the corresponding evaluation of the solution of the direct problem produced by
a given vector of parameters. The identification problem is in general ill-posed and admit
more than one solution .In particular, different initial setting for nonlinear conservation
laws could lead to the same solution.