Numerical models and optimisation techniques for a circular cross-flow filtration device
thesisposted on 10.01.2021, 00:33 by Antonis Parasyris
The main goal of this thesis is the hydrodynamical analysis of a membrane-based water purification system for potable use that exploits a circular cross-flow design. To that end, a description of the device is introduced and multiphysics problems involving both incompressible fluid flows and porous media flows are solved. The results from two modelling approaches are compared, one based on a coupled system formed by the Navier–Stokes equations and by Darcy’s law with ad-hoc coupling conditions, the other involving Brinkman’s equation. The computations are conducted using COMSOL, a commercial Finite Element solver, and the results are validated using experimental data. Computational modelling permits to identify and quantify flow instabilities (Dean vortices) close to the membrane’s surface, that may improve filtration performance as also evidenced by experimental work. The computation of Dean numbers indicate that the vortices become more pronounced for higher inlet pressure and enlarged aspect ratio of the free flow channel. Even if Brinkman’s model is easier to implement, the coupled Navier–Stokes–Darcy model permits to better represent the slip velocity on the interface. Both models require a large computational time so that they can become prohibitive to study several configurations of the device for optimisation purposes. For this reason, the Proper Generalized Decomposition (PGD) is introduced. It is able to obtain solutions of boundary value problems in closed form with explicit dependence on parameters that can be varied to achieve the optimal configuration of the system one wants to study. The focus shifts on the membrane domain only, where the use of the PGD to obtain a parametric solution depending both on material properties (the permeability of the membrane) and on operational ones (the inflow flux) is studied. The convergence speed of the PGD is found to deteriorate as the number of parameters increase. To overcome this, the linearity of the problem is exploited to define an improved algorithm. Finally, possible techniques to combine PGD and domain decomposition methods are explored in order to obtain a parametric solution of a multiphysics problem in a complex domain. More specifically, both the classical Multiplicative Schwarz method accelerated by PGD and the overlapping Arlequin method are considered. A variant of the latter is proposed that provides similar results to the original method but has the advantage of not requiring to compute quantities on the overlapping region. This could possibly result in a simpler implementation and reduced computational cost, especially in 3D cases. The methods presented and developed in this thesis can be used as the foundation towards the parametric optimisation of the filtration device.
EPSRC Doctoral Training Programme (Award Reference: 1809172)
- Mathematical Sciences