Numerical modelling of polydispersed flows using an adaptive-mesh finite element method with application to froth flotation

An efficient numerical framework for the macroscale simulation of three-phase polydispersed flows is presented in this thesis. The primary focus of this research is on modelling the polydispersity in multiphase flows ensuring the tractability of the solution framework. Fluidity, an open-source adaptive-mesh finite element code, has been used for solving the coupled equations efficiently. Froth flotation is one of the most widely used mineral processing operations. The multiphase, turbulent and polydispersed nature of flow in the pulp phase in froth flotation makes it all the more challenging to model this process. Considering that two of the three phases in froth flotation are polydispersed, modelling this polydispersity is particularly important for an accurate prediction of the overall process. The direct quadrature method of moments (DQMOM) is implemented in the Fluidity code to solve the population balance equation (PBE) for modelling the polydispersity of the gas bubbles. The PBE is coupled to the Eulerian--Eulerian flow equations for the liquid and gas phases. Polydispersed solids are modelled using separate transport equations for the free and attached mineral particles for each size class. The PBE has been solved using DQMOM in a finite element framework for the first time in this work. The behaviour of various finite element and control volume discretisation schemes in the solution of the PBE is analysed. Rigorous verification and benchmarking is presented along with model validation on turbulent gravity-driven flow in a bubble column. This research also establishes the importance of modelling the polydispersity of solids in flotation columns, which is undertaken for the first time, for an accurate prediction of the flotation rate. The application of fully-unstructured anisotropic mesh adaptivity to the polydispersed framework is also analysed for the first time. Significant improvement in the solution efficiency is reported through its use.Open Acces

A framework for polydisperse pulp phase modelling in flotation

Froth flotation is one of the most widely-used mineral processing operations. The pulp zone in flotation tanks is polydisperse in general and serves as a medium for the interaction between the solid particles and the gas bubbles in a liquid continuum, leading to particle–bubble attachment/detachment and bubble coalescence/breakage phenomena. To better predict the hydrodynamics and inform the design of e cient flotation equipment, it is therefore important to accurately model and simulate the evolution of the size distribution of the dispersed phases. This has created an urgent need for a framework that can model the pulp phase in an e cient manner, which is not currently available in the literature. The available software products are not e cient enough to allow for a tractable modelling of industrial-scale flotation cells and in some cases they cannot model the polydispersity of the dispersed phase at all. This work presents an e cient numerical framework for the macroscale simulation of the polydisperse pulp phase in froth flotation in an open-source finite element computational fluid dynamics (CFD) code that provides an e cient solution method using mesh adaptivity and code parallelisation. A (hybrid finite element–control volume) finite element framework for modelling the pulp phase has been presented for the first time in this work. An Eulerian–Eulerian turbulent flow model was implemented in this work including a transport equation for attached and free solid particles. Special care was taken to model the settling velocity of the free solids and the modification of the liquid viscosity due to the presence of these particles. Bubble polydispersity was modelled using the population balance equation (PBE), which was solved using the direct quadrature method of moments (DQMOM). Appropriate functions for bubble coalescence and breakage were chosen in the PBE. Mesh adaptivity was applied to the current problem to produce fully-unstructured anisotropic meshes, which improved the solution e ciency, while all simulations were executed on a multicore architecture. The model was validated for 2D simulations of a bubble column against experimental results available in the literature. After successful validation, the model was applied to the simulation of the pulp phase in a flotation column for monodisperse and polydisperse solids. Polydispersity of the solids was modelled for the first time in this work using three separate solid size classes. A clear dependence of the flotation rate on the particle size was noticed and the monodisperse solids simulations were shown to over-predict the flotation rate. Other than flotation, this open-source framework can be used for the simulation of a variety of polydisperse multiphase flow problems in the process industry

Population balance modelling of polydispersed particles in reactive flows

Polydispersed particles in reactive flows is a wide subject area encompassing a range of dispersed flows with particles, droplets or bubbles that are created, transported and possibly interact within a reactive flow environment - typical examples include soot formation, aerosols, precipitation and spray combustion. One way to treat such problems is to employ as a starting point the Newtonian equations of motion written in a Lagrangian framework for each individual particle and either solve them directly or derive probabilistic equations for the particle positions (in the case of turbulent flow). Another way is inherently statistical and begins by postulating a distribution of particles over the distributed properties, as well as space and time, the transport equation for this distribution being the core of this approach. This transport equation, usually referred to as population balance equation (PBE) or general dynamic equation (GDE), was initially developed and investigated mainly in the context of spatially homogeneous systems. In the recent years, a growth of research activity has seen this approach being applied to a variety of flow problems such as sooting flames and turbulent precipitation, but significant issues regarding its appropriate coupling with CFD pertain, especially in the case of turbulent flow. The objective of this review is to examine this body of research from a unified perspective, the potential and limits of the PBE approach to flow problems, its links with Lagrangian and multi-fluid approaches and the numerical methods employed for its solution. Particular emphasis is given to turbulent flows, where the extension of the PBE approach is met with challenging issues. Finally, applications including reactive precipitation, soot formation, nanoparticle synthesis, sprays, bubbles and coal burning are being reviewed from the PBE perspective. It is shown that population balance methods have been applied to these fields in varying degrees of detail, and future prospects are discussed

Hierarchical modelling of multiphase flows using fully resolved fixed mesh and PDF approaches

Fully–resolved simulations of multiphase flow phenomena and in particular particulate flow simulations are computationally expensive and are only feasible on massively parallel computer clusters. A 3D SIMPLE type pressure correction algorithm is implemented and extensively tested and parallelized to exploit the power of massively parallel computing clusters currently available. Domain decomposition and communication schemes applicable to a general unstructured or structured multi–block CFD codes are discussed and algorithms are proposed, implemented and tested. Several high–performance linear solvers and a multi–grid strategy for the current framework are implemented and the best types of solvers are identified. A 2D CFD code is developed by the author to test several possible fixed–mesh strategies. Variations of immersed boundary (IB) and fictitious domain (FD) methods are implemented and compared. FD methods are identified to have better properties especially if other transport phenomena are also considered. Therefore an FD method is adapted by the author for the SIMPLE type flow solvers and is extended to heat transfer problems. The method is extensively tested for the simulation of flow around stationary in addition to freely moving particles and forced motion where both natural and forced convection are considered. The method is used to study the flow and heat transfer around a stationary cylinder and a new high resolution correlation is devised for the estimation of the local Nusselt number curves. Free fall problem for a single circular cylinder is considered and the effects of internal heat generation and also long term behavior of single cold particle subject to natural convection are also studied in detail. A particle collision strategy is also adapted and tested for the particle–particle collision problems. The FD algorithm is extended to the 3D framework and the flow around single stationary sphere and also free fall of a single sphere are used to validate the FD algorithm in 3D. A unique polydispersed fluid-particle turbulent modelling process is reviewed and the closure problem for this framework is studied in detail. Two methods for the closure of the non–integer moments which results from the polydispersity of the particles are proposed namely PDF reconstruction using Laguerre polynomials and a unique direct method named Direct Fractional Method of Moments (DFMM). The latter is derived using the results of the fractional calculus by writing an equation for the fractional derivatives of the moment generating function. The proposed methods are tested on a number of problems consisting of analytical, experimental and DNS simulations to asses their validity and viability which shows that both methods provide accurate results with DFMM having more desirable properties.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Computational fluid dynamics multiscale modelling of bubbly flow. A critical study and new developments on volume of fluid, discrete element and two-fluid methods

The study and modelling of two-phase flow, even the simplest ones such as the bubbly flow, remains a challenge that requires exploring the physical phenomena from different spatial and temporal resolution levels. CFD (Computational Fluid Dynamics) is a widespread and promising tool for modelling, but nowadays, there is no single approach or method to predict the dynamics of these systems at the different resolution levels providing enough precision of the results. The inherent difficulties of the events occurring in this flow, mainly those related with the interface between phases, makes that low or intermediate resolution level approaches as system codes (RELAP, TRACE, ...) or 3D TFM (Two-Fluid Model) have significant issues to reproduce acceptable results, unless well-known scenarios and global values are considered. Instead, methods based on high resolution level such as Interfacial Tracking Method (ITM) or Volume Of Fluid (VOF) require a high computational effort that makes unfeasible its use in complex systems. In this thesis, an open-source simulation framework has been designed and developed using the OpenFOAM library to analyze the cases from microescale to macroscale levels. The different approaches and the information that is required in each one of them have been studied for bubbly flow. In the first part, the dynamics of single bubbles at a high resolution level have been examined through VOF. This technique has allowed to obtain accurate results related to the bubble formation, terminal velocity, path, wake and instabilities produced by the wake. However, this approach has been impractical for real scenarios with more than dozens of bubbles. Alternatively, this thesis proposes a CFD Discrete Element Method (CFD-DEM) technique, where each bubble is represented discretely. A novel solver for bubbly flow has been developed in this thesis. This includes a large number of improvements necessary to reproduce the bubble-bubble and bubble-wall interactions, turbulence, velocity seen by the bubbles, momentum and mass exchange term over the cells or bubble expansion, among others. But also new implementations as an algorithm to seed the bubbles in the system have been incorporated. As a result, this new solver gives more accurate results as the provided up to date. Following the decrease on resolution level, and therefore the required computational resources, a 3D TFM have been developed with a population balance equation solved with an implementation of the Quadrature Method Of Moments (QMOM). The solver is implemented with the same closure models as the CFD-DEM to analyze the effects involved with the lost of information due to the averaging of the instantaneous Navier-Stokes equation. The analysis of the results with CFD-DEM reveals the discrepancies found by considering averaged values and homogeneous flow in the models of the classical TFM formulation. Finally, for the lowest resolution level approach, the system code RELAP5/MOD3 is used for modelling the bubbly flow regime. The code has been modified to reproduce properly the two-phase flow characteristics in vertical pipes, comparing the performance of the calculation of the drag term based on drift-velocity and drag coefficient approaches.El estudio y modelado de flujos bifásicos, incluso los más simples como el bubbly flow, sigue siendo un reto que conlleva aproximarse a los fenómenos físicos que lo rigen desde diferentes niveles de resolución espacial y temporal. El uso de códigos CFD (Computational Fluid Dynamics) como herramienta de modelado está muy extendida y resulta prometedora, pero hoy por hoy, no existe una única aproximación o técnica de resolución que permita predecir la dinámica de estos sistemas en los diferentes niveles de resolución, y que ofrezca suficiente precisión en sus resultados. La dificultad intrínseca de los fenómenos que allí ocurren, sobre todo los ligados a la interfase entre ambas fases, hace que los códigos de bajo o medio nivel de resolución, como pueden ser los códigos de sistema (RELAP, TRACE, etc.) o los basados en aproximaciones 3D TFM (Two-Fluid Model) tengan serios problemas para ofrecer resultados aceptables, a no ser que se trate de escenarios muy conocidos y se busquen resultados globales. En cambio, códigos basados en alto nivel de resolución, como los que utilizan VOF (Volume Of Fluid), requirieren de un esfuerzo computacional tan elevado que no pueden ser aplicados a sistemas complejos. En esta tesis, mediante el uso de la librería OpenFOAM se ha creado un marco de simulación de código abierto para analizar los escenarios desde niveles de resolución de microescala a macroescala, analizando las diferentes aproximaciones, así como la información que es necesaria aportar en cada una de ellas, para el estudio del régimen de bubbly flow. En la primera parte se estudia la dinámica de burbujas individuales a un alto nivel de resolución mediante el uso del método VOF (Volume Of Fluid). Esta técnica ha permitido obtener resultados precisos como la formación de la burbuja, velocidad terminal, camino recorrido, estela producida por la burbuja e inestabilidades que produce en su camino. Pero esta aproximación resulta inviable para entornos reales con la participación de más de unas pocas decenas de burbujas. Como alternativa, se propone el uso de técnicas CFD-DEM (Discrete Element Methods) en la que se representa a las burbujas como partículas discretas. En esta tesis se ha desarrollado un nuevo solver para bubbly flow en el que se han añadido un gran número de nuevos modelos, como los necesarios para contemplar los choques entre burbujas o con las paredes, la turbulencia, la velocidad vista por las burbujas, la distribución del intercambio de momento y masas con el fluido en las diferentes celdas por cada una de las burbujas o la expansión de la fase gaseosa entre otros. Pero también se han tenido que incluir nuevos algoritmos como el necesario para inyectar de forma adecuada la fase gaseosa en el sistema. Este nuevo solver ofrece resultados con un nivel de resolución superior a los desarrollados hasta la fecha. Siguiendo con la reducción del nivel de resolución, y por tanto los recursos computacionales necesarios, se efectúa el desarrollo de un solver tridimensional de TFM en el que se ha implementado el método QMOM (Quadrature Method Of Moments) para resolver la ecuación de balance poblacional. El solver se desarrolla con los mismos modelos de cierre que el CFD-DEM para analizar los efectos relacionados con la pérdida de información debido al promediado de las ecuaciones instantáneas de Navier-Stokes. El análisis de resultados de CFD-DEM permite determinar las discrepancias encontradas por considerar los valores promediados y el flujo homogéneo de los modelos clásicos de TFM. Por último, como aproximación de nivel de resolución más bajo, se investiga el uso uso de códigos de sistema, utilizando el código RELAP5/MOD3 para analizar el modelado del flujo en condiciones de bubbly flow. El código es modificado para reproducir correctamente el flujo bifásico en tuberías verticales, comparando el comportamiento de aproximaciones para el cálculo del término dL'estudi i modelatge de fluxos bifàsics, fins i tot els més simples com bubbly flow, segueix sent un repte que comporta aproximar-se als fenòmens físics que ho regeixen des de diferents nivells de resolució espacial i temporal. L'ús de codis CFD (Computational Fluid Dynamics) com a eina de modelatge està molt estesa i resulta prometedora, però ara per ara, no existeix una única aproximació o tècnica de resolució que permeta predir la dinàmica d'aquests sistemes en els diferents nivells de resolució, i que oferisca suficient precisió en els seus resultats. Les dificultat intrínseques dels fenòmens que allí ocorren, sobre tots els lligats a la interfase entre les dues fases, fa que els codis de baix o mig nivell de resolució, com poden ser els codis de sistema (RELAP,TRACE, etc.) o els basats en aproximacions 3D TFM (Two-Fluid Model) tinguen seriosos problemes per a oferir resultats acceptables , llevat que es tracte d'escenaris molt coneguts i se persegueixen resultats globals. En canvi, codis basats en alt nivell de resolució, com els que utilitzen VOF (Volume Of Fluid), requereixen d'un esforç computacional tan elevat que no poden ser aplicats a sistemes complexos. En aquesta tesi, mitjançant l'ús de la llibreria OpenFOAM s'ha creat un marc de simulació de codi obert per a analitzar els escenaris des de nivells de resolució de microescala a macroescala, analitzant les diferents aproximacions, així com la informació que és necessària aportar en cadascuna d'elles, per a l'estudi del règim de bubbly flow. En la primera part s'estudia la dinàmica de bambolles individuals a un alt nivell de resolució mitjançant l'ús del mètode VOF. Aquesta tècnica ha permès obtenir resultats precisos com la formació de la bambolla, velocitat terminal, camí recorregut, estela produida per la bambolla i inestabilitats que produeix en el seu camí. Però aquesta aproximació resulta inviable per a entorns reals amb la participació de més d'unes poques desenes de bambolles. Com a alternativa en aqueix cas es proposa l'ús de tècniques CFD-DEM (Discrete Element Methods) en la qual es representa a les bambolles com a partícules discretes. En aquesta tesi s'ha desenvolupat un nou solver per a bubbly flow en el qual s'han afegit un gran nombre de nous models, com els necessaris per a contemplar els xocs entre bambolles o amb les parets, la turbulència, la velocitat vista per les bambolles, la distribució de l'intercanvi de moment i masses amb el fluid en les diferents cel·les per cadascuna de les bambolles o els models d'expansió de la fase gasosa entre uns altres. Però també s'ha hagut d'incloure nous algoritmes com el necessari per a injectar de forma adequada la fase gasosa en el sistema. Aquest nou solver ofereix resultats amb un nivell de resolució superior als desenvolupat fins la data. Seguint amb la reducció del nivell de resolució, i per tant els recursos computacionals necessaris, s'efectua el desenvolupament d'un solver tridimensional de TFM en el qual s'ha implementat el mètode QMOM (Quadrature Method Of Moments) per a resoldre l'equació de balanç poblacional. El solver es desenvolupa amb els mateixos models de tancament que el CFD-DEM per a analitzar els efectes relacionats amb la pèrdua d'informació a causa del promitjat de les equacions instantànies de Navier-Stokes. L'anàlisi de resultats de CFD-DEM permet determinar les discrepàncies ocasionades per considerar els valors promitjats i el flux homogeni dels models clàssics de TFM. Finalment, com a aproximació de nivell de resolució més baix, s'analitza l'ús de codis de sistema, utilitzant el codi RELAP5/MOD3 per a analitzar el modelatge del fluxos en règim de bubbly flow. El codi és modificat per a reproduir correctament les característiques del flux bifàsic en canonades verticals, comparant el comportament d'aproximacions per al càlcul del terme de drag basades en velocitat de drift flux model i de les basades en coePeña Monferrer, C. (2017). Computational fluid dynamics multiscale modelling of bubbly flow. A critical study and new developments on volume of fluid, discrete element and two-fluid methods [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/90493TESI

Strongly coupled fluid-particle flows in vertical channels. II. Turbulence modeling

In Part I, simulations of strongly coupled fluid-particle flow in a vertical channel were performed with the purpose of understanding, in general, the fundamental physics of wall-bounded multiphase turbulence and, in particular, the roles of the spatially correlated and uncorrelated components of the particle velocity.The exact Reynolds-averaged (RA) equations for high-mass-loading suspensions were presented, and the unclosed terms that are retained in the context of fully developed channel flow were evaluated in an Eulerian–Lagrangian (EL) framework. Here, data from the EL simulations are used to validate a multiphase Reynolds-stress model (RSM) that predicts the wall-normal distribution of the two-phase, one-point turbulence statistics up to second order. It is shown that the anisotropy of the Reynolds stresses both near the wall and far away is a crucial component for predicting the distribution of the RA particle-phase volume fraction. Moreover, the decomposition of the phase-average (PA) particle-phase fluctuating energy into the spatially correlated and uncorrelated components is necessary to account for the boundary conditions at the wall. When these factors are properly accounted for in the RSM, the agreement with the EL turbulence statistics is satisfactory at first order (e.g., PA velocities) but less so at second order (e.g., PA turbulent kinetic energy). Finally, an algebraic stress model for the PA particle-phase pressure tensor and the Reynolds stresses is derived from the RSM using the weak-equilibrium assumption

Simulations of Nanoparticle Synthesis in Laminar Stagnation Flames

A new implementation of a multidimensional solver for studying nanoparticle synthesis in laminar flames is presented. The governing equations are convective-diffusive-reactive partial differential equations that are discretised using the finite volume method. Detailed chemical source terms and transport coefficients are used to close the equations. The implementation of these governing equations is discussed and the numerical algorithm used to solve them is presented. The new solver is verified against analytic solutions and numerical solutions from 1D models for counterflow diffusion flames. The new solver was used to calculate the flame location, shape and temperature of laminar premixed ethylene jet-wall stagnation flames when the equivalence ratio, exit gas velocity and burner-plate separation distance are varied. The simulation results were compared to new experimental 2D measurements of CH* chemiluminescence and temperature. The 2D simulations showed excellent agreement, and correctly predicted the flame shape, location and temperature as the experimental conditions were varied. The new solver was used to study growth of inorganic nanoparticles in premixed, jet-wall stagnation flames. Titanium dioxide, also known as titania and TiO2, is a white powder than has many uses as a pigment, including in paper and cosmetics, and was selected as the system to apply the new solver. TiO2 nanoparticles formed from titanium tetraisopropoxide (TTIP) were simulated using a two step methodology, which enabled insight into the variations of particle properties as a function of the deposition radius. Two different TTIP loadings (280 and 560~ppm) were studied in two flames, a lean flame (equivalence ratio 0.35) and a stoichiometric flame (equivalence ratio 1.0). First, the growth of particles was described with a spherical particle model fully coupled to the conservation equations of chemically reacting flow. Second, particle trajectories were extracted from the 2D simulations and post-processed using a detailed particle model solved with a stochastic numerical method. The simulation produced gas phase predictions of flame location that are in good agreement with available literature. The particle morphologies and size distributions were examined and found to be dependent on the deposition radius. Particles began to have different size distributions at a deposition radius of approximately one and a half times the nozzle radius (1.0 cm), which should be kept in mind when synthesising and modelling nanoparticles for novel applications. This coincided with the growth of total residence time along particle trajectories. It is suggested that experiments critically examine the radially uniformity of deposited particles do not affect the performance for their intended application.Gates Cambridge Foundation, Gates Cambridge Scholarship (OPP1144

Population balance modelling of soot formation in laminar flames

In this thesis, a discretised population balance eqaution (PBE) with a comprehensive model of soot formation processes has been coupled with the computational fluid dynamics (CFD) to predict the soot evolution in laminar diffusion flames. Contributions have been made in terms of methodology, modelling and applications. First of all, a conservative finite volume method is proposed to discretise the PBE with regard to the coagulation process. This method rigorously calculates the double integrals arising from the coagulation terms via a geometric representation, and exactly balances the coagulation source and sink terms to conserve moments. It proves that the proposed method is able to accurately predict the distribution with a small number of sections and conserve the first moment (or any other single moment) in the coagulation process, in an extensive test of various coagulation kernels, initial distributions and 'self-preserving' distributions, by comparison with analytical solutions and direct numerical solutions of the discrete PBE. Moreoever, the method is also flexible to an arbitrary non-uniform grid. Later on, the proposed method is also coupled with the CFD program to simulate Santoro flame, a laminar ethylene diffusion flame, for the validation on its accuracy, economy and robustness. Furthermore, the simulation results have been compared with simultaneous multiple diagnostics measurements drawn from a single data source, providing guidance on soot kinetic models. Three well-established PAH-based chemical reaction mechanisms, ABF, BBP and KM2, are employed to model the inception of soot precursors and oxidants. The physical model involves the nucleation by PAH dimerisation, surface growth by HACA mechanism and PAH condensation, size-dependent coagulation. Experimental signals are directly modelled, including the line-of-sight attenuation (LOSA) for the integrated soot volume fraction, planar OH laser-induced fluorescence (OH-PLIF) and elastic light scattering (ELS) for the soot distribution. The comparisons between model predictions and experimental measurements reflect the predictive capability for soot formation in laminar diffusion flame in terms of the flame structure, soot appearance and amount of soot production. The background gas phase chemistry clearly affects the soot modelling and a sensitivity analysis suggests that coordinating the rates of nucleation and surface growth help adjust the soot production on the centreline and sooty wings. Finally, the same soot model has been extended to two studies of diffusion flames with blends oxygen-containing surrogates: (1) methyl decanoate (MD) with the addition of dibutyl ether (DBE); (2) four practical methyl ester-based real biodiesels and their blends with petroleum diesel. In the first case study, aiming to reproduce an experiment which was to investigate the effects of dibutyl ether (DBE) addition to the biodiesel surrogate (methyl decanoate, MD), a combined and reduced MD-DBE-PAH mechanism from three sub-mechanism sources has been employed in the simulation. Due to the heavy molecular weight of the biodiesel fuel, the terms of the effect of molecular weight, thermophoresis and Dufour effect in the energy equation exhibit a similar magnitude with the original diffusion term, especially in the region of high temperature and a large gradient of the average molecular weight. Predicted temperature profiles are in good comparison with the experiment in terms of position and absolute value. The swallow-tail shape of the soot region and the absolute soot production are correctly predicted by the simulation. In terms of soot suppression, the model predicts 33\% reduction of soot as the DBE addition ranges from 0\% to 40\%, in contrast to around 55\% reduction measured in the experiment. In the second study, a semi-detailed kinetic mechanism for the pyrolysis and combustion of a large variety of biodiesels fuels are considered. The model successfully captures the reduction of soot formation by addition of biodiesels, but not necessarily the rate of decrease with blending. The current investigation offers pioneer and encouraging results on modelling soot formation in biodiesel flames, which has been fewly explored.Open Acces

Analysis of fluid-dynamical and multiphase flow aspects of capillary membrane backwashing

The number of industrial applications has increased exponentially in the last decades and the need for effective water treatment methods has become more essential as demand for pure water has increased. It is no longer possible to fulfil the rapidly growing demand worldwide using natural water resources. Low pressure membrane filtration with inside-out dead-end driven UF-/ MF- capillary membranes has been widely inserted in water and wastewater treatment plants to remove colloids and suspended particulate matter. However, the implementation of this technology has been limited by several factors. These include concentration polarisation, membrane fouling and particles which remain inside the capillary after backwashing. An efficient backwash process is a determining factor in ensuring effective membrane filtration and enhance the separation of the particles in the capillary membrane. By optimising the backwash process, hydraulical irreversible membrane fouling can be minimised and membrane permeability recovered, and the operating costs of the filtration process can consequently be controlled. In the context of this thesis, a numerical approach to the detailed description of the fluid dynamics process in capillary membrane during backwashing is developed and partially validated by experiments. Moreover, the study contributes to a better understanding of the conditions for potential formation of agglomerates inside the capillary, which lead to increased operating pressure during the process and may clog the capillary. The presented model investigates a variety of parameters associated with the backwash process in dead-end capillary membrane, such as operation parameters, in particular the operating pressure as a function of time, particle properties (size and density) and initial particle distribution in addition to capillary arrangement (vertical/horizontal). The evaluation of these data concentrates on observation and analysis of particle behaviour and distribution in a cross-sectional plane and along the capillary length. Based on the fluid flow and particle distribution, the eventual formation of particle plugs inside the capillary membrane is predicted. For this purpose, a multiphase flow model was developed to describe the fluid flow and particle motion inside the capillary membrane. The numerical model considers the interaction between the involved phases in terms of lift, virtual mass and drag forces. The simulations are carried out using different configurations of the initial particle distribution, homogeneous distribution, evenly and unevenly deposited particles. The model is coupled with a population balance equation to account for particle agglomeration and breakage. Furthermore, the pressure drop as well as the shear stress on the membrane surface inside the capillary during the backwash process are estimated. Based on the fact that during the backwash there are tightly adhered layers which cannot be removed, the influence of these layers on the process is taken into account. The simulation results show a good agreement with the experimental data in terms of the flow rate during the backwash process and particle removal at certain operating pressures