Lattice Boltzmann simulation of liquid-gas flows through solid bodies in a square duct

ArticleMathematics and computers in simulation. 72(2-6): 264-269 (2006)journal articl

Numerical investigation of particle-fluid interaction system based on discrete element method

This thesis focuses on the numerical investigation of the particle-fluid systems based on the Discrete Element Method (DEM). The whole thesis consists of three parts, in each part we have coupled the DEM with different schemes/solvers on the fluid phase. In the first part, we have coupled DEM with Direct Numerical Simulation (DNS) to study the particle-laden turbulent flow. The effect of collisions on the particle behavior in fully developed turbulent flow in a straight square duct was numerically investigated. Three sizes of particles were considered with diameters equal to 50 µm, 100 µm and 500 µm. Firstly, the particle transportation by turbulent flow was studied in the absence of the gravitational effect. Then, the particle deposition was studied under the effect of the wall-normal gravity force in which the influence of collisions on the particle resuspension rate and the final stage of particle distribution on the duct floor were discussed, respectively. In the second part, we have coupled DEM with Lattice Boltzmann Method (LBM) to study the particle sedimentation in Newtonian laminar flow. A novel combined LBM-IBM-DEM scheme was presented with its application to model the sedimentation of two dimensional circular particles in incompressible Newtonian flows. Case studies of single sphere settling in a cavity, and two particles settling in a channel were carried out, the velocity characteristics of the particle during settling and near the bottom were examined. At last, a numerical example of sedimentation involving 504 particles was finally presented to demonstrate the capability of the combined scheme. Furthermore, a Particulate Immersed Boundary Method (PIBM) for simulating the fluid-particle multiphase flow was presented and assessed in both two and three-dimensional applications. Compared with the conventional IBM, dozens of times speedup in two-dimensional simulation and hundreds of times in three-dimensional simulation can be expected under the same particle and mesh number. Numerical simulations of particle sedimentation in the Newtonian flows were conducted based on a combined LBM - PIBM - DEM showing that the PIBM could capture the feature of the particulate flows in fluid and was indeed a promising scheme for the solution of the fluid-particle interaction problems. In the last part, we have coupled DEM with averaged Navier-Stokes equations (NS) to study the particle transportation and wear process on the pipe wall. A case of pneumatic conveying was utilized to demonstrate the capability of the coupling model. The concrete pumping process was then simulated, where the hydraulic pressure and velocity distribution of the fluid phase were obtained. The frequency of the particles impacting on the bended pipe was monitored, a new time average collision intensity model based on impact force was proposed to investigate the wear process of the elbow. The location of maximum erosive wear damage in elbow was predicted. Furthermore, the influences of slurry velocity, bend orientation and angle of elbow on the puncture point location were discussed.Esta tesis se centra en la investigación numérica de sistemas partícula-líquido basado en la técnica Discrete Element Method (DEM). La tesis consta de tres partes, en cada una de las cuales se ha acoplado el método DEM con diferentes esquemas/solucionadores en la fase fluida. En la primera parte, hemos acoplado los métodos DEM con Direct Numerical Simulation (DNS) para estudiar casos de "particle-laden turbulent flow". Se investigó numéricamente el efecto de las colisiones en el comportamiento de las partículas en el flujo turbulento completamente desarrollado en un conducto cuadrado recto. Tres tamaños de partículas se consideraron con diámetros de 50, 100 y 500 micrometros. En primer lugar, el transporte de partículas por el flujo turbulento se estudió en la ausencia del efecto gravitacional. Entonces, la deposición de partículas se estudió bajo el efecto de la fuerza de gravedad normal a la pared, en el que se discutieron la influencia de la tasa de colisiones en re-suspensión de las partículas y la fase final de la distribución de partículas en el suelo del conducto, respectivamente. En la segunda parte, se ha acoplado los métodos DEM con Lattice Boltzmann Method (LBM) para estudiar la sedimentación de partículas en flujo laminar newtoniano. Un nuevo metodo combinado LBM-IBM-DEM se presentó y ha sido aplicado para modelar la sedimentación de dos partículas circulares bi-dimensionales en flujos Newtonianos incompresibles. Se estudiaron casos de sedimentación en una cavidad de una sola esfera, y sedimentación de dos partículas en un canal, las características de la velocidad de la partícula durante la sedimentación y cerca de la base fueron también examinados. En el último caso, un ejemplo numérico de sedimentación de 504 partículas fue finalmente presentado para demostrar la capacidad del método combinado. Además, se ha presentado un método "Particulate Immersed Boundary Method" (PIBM) para la simulación de flujos multifásicos partícula-fluido y ha sido evaluado en dos y tres dimensiones. En comparación con el método IBM convencional, se puede esperar con el mismo número de partículas y de malla un SpeedUp docenas de veces superior en la simulación bidimensional y cientos de veces en la simulación en tres dimensiones. Se llevaron a cabo simulaciones numéricas de la sedimentación de partículas en los flujos newtonianos basados en una combinación LBM - PIBM - DEM, mostrando que el PIBM podría capturar las características de los flujos de partículas en el líquido y fue en efecto un esquema prometedor para la solución de problemas de interacción fluido-partícula. En la última parte, se ha acoplado el método DEM con las ecuaciones promediadas de Navier-Stokes (NS) para estudiar el transporte de partículas y el proceso de desgaste en la pared de una tubería. Se utilizó un caso de transporte neumático para demostrar la capacidad del modelo acoplado. Entonces se simuló el proceso de bombeo de hormigón, de donde se obtuvo la presión hidráulica y la distribución de la velocidad de la fase fluida. Se monitoreó la frecuencia de impacto de las partículas en la tubería doblada, se propuso un nuevo modelo de intensidad de colisión promediado en tiempo para investigar el proceso de desgaste del codo basado en la fuerza de impacto. Se predijo la ubicación del daño máximo desgaste por erosión en el codo. Además, se examinaron las influencias de la velocidad de pulpa, la orientación y el ángulo de curvatura del codo en la ubicación del punto de punción.Postprint (published version

Analysis of Inertial Migration of Neutrally Buoyant Particle Suspensions in a Planar Poiseuille Flow with a Coupled Lattice Boltzmann Method-Discrete Element Method

In this study a hybrid numerical framework for modelling solid-liquid multiphase flow is established with a single-relaxation-time lattice Boltzmann method and the discrete element method implemented with the Hertz contact theory. The numerical framework is then employed to systematically explore the effect of particle concentration on the inertial migration of neutrally buoyant particle suspensions in planar Poiseuille flow. The results show that the influence of particle concentration on the migration is primarily determined by the characteristic channel Reynolds number Re0. For relatively low Re0 (Re0˂20), the migration behaviour can only be observed at a very low particle concentration (≤5%). However, when Re0˃20 the migration behaviour can be observed at a high concentration (≥20%). Furthermore, a focusing number Fc is proposed to characterise the degree of inertial migration. It was found that the inertial migration can be classified into three regimes depending on two critical values of the focusing number, Fc+ and Fc-: i) when Fc˃Fc+, a full inertial migration occurs; ii) when Fc˂Fc-, particles are laterally unfocused; iii) when Fc-˂Fc˂Fc+, a partially inertial migration takes place

Porous media drying and two-phase flow studies using micromodels

In this thesis, we report an investigation of porous media drying and steady-state two-phase flow behaviour at the pore scale using micromodels based on thin section images of real rocks. Fluid distributions (and the deposition of solid salt in the case of drying) were imaged in real-time using optical microscopy. Computer simulations of the two-phase flow was initially compared to micromodel experiments and then used to predict behaviour in geometries not available in the lab. We performed evaporation experiments on a 2.5D etched-silicon/glass micromodel based on a thin section image of a sucrosic dolomite carbonate rock at different wetting conditions. NaCl solutions from 0 wt% (deionized water) to 36 wt% (saturated brine) were evaporated by passing dry air through a channel in front of the micromodel matrix. For deionized water in a water-wet model, we observed the three classical periods of evaporation: the constant rate period (CRP) in which liquid remains connected to the matrix surface, the falling rate period (FRP) and the receding front period (RFP), in which the capillary connection is broken and water transport becomes dominated by vapour diffusion. The length of the deionized water CRP was much shorter for a uniformly oil-wet model, but mixed wettability made little difference to the drying process. For brine systems in water-wet and mixed-wet micromodels, the evaporation rate became linear with the square root of time after a short CRP. Although this appears similar to the RFP for water, salt continued to be deposited at the external surface of the matrix during this period indicating that a capillary connection was maintained. The reduction of evaporation rate appears to be due to the deposited salt acting as a partial barrier to hydraulic connectivity, perhaps allowing dry patches to grow on the evaporating surface. The mechanism causing the square root time behaviour is therefore unlike the case of deionized water where capillary disconnection from the fracture channel is followed by a diffusion controlled process. In completely oil-wet micromodels capillary disconnection prevented salt deposition in the fracture. The resulting permeability impairment was also measured, for the water-wet model, we observed two regions of a linear downward trend in the matrix and fracture permeability measurements. A similar trend was observed for the mixed-wet systems. However, for the oil-wet systems, fracture permeability only changes slightly even for 360g/L brine, a result of the absence of salt deposits in the fracture caused by the early rupture of the liquid wetting films needed to aid hydraulic connectivity. Overall, matrix permeability for all wetting conditions decreased with increasing brine concentration and was almost total for the 360g/L brine. Furthermore, drying with air was compared with drying with CO2 gas, with the latter having important applications in CO2 sequestration processes. We observed that using CO2 rather than air as carrier gas makes the brine phase somewhat more wetting especially in the deionized water case, with the result that hydraulic connectivity was maintained for longer in the CO2 case compared to dry-out with air. Steady-state two-phase flow experiments were also conducted to study the effect of viscosity ratio, flow rate and capillary number on flow regimes and displacement processes using a 2.5D etched-silicon/glass micromodel based on a thin section image of a Berea sandstone rock. Of particular interest here was a new type of pore-scale behaviour, termed dynamic connectivity, previously identified in steady-state two-phase flow experiments in real rocks at the transition to ganglia flow by X-ray tomography. Micromodels have the potential to resolve the dynamics of these displacement processes due to the high speed resolution of optical techniques. Depending on the mean-size, prevalence, and connectivity of the non-wetting phase, four flow regimes were identified: connected pathway flow (CPF), big ganglia flow (BGF), big-small ganglia flow (BSGF) and small ganglia flow (SGF). These flow regimes move from CPF to SGF as the capillary-viscous balance of the system is altered by increasing the total flow rate of the system. The boundaries of the flow regimes are indistinct, however the domain of the BGF increases (and/or SGF decreases) with a decrease in the viscosity ratio of the system. That is the BGF regime persisted to higher capillary number for the water/squalane system than the water/decane system because it is harder for big blobs to split into smaller blobs at low viscosity ratio. However, dynamic connectivity was not observed in these micromodel experiments even after replicating the experiments with the same fluid pair (Nitrogen/Deionized water) used in the real porous media experiment. Therefore, we speculate that the constant depth of the micromodel used in this study does not provide a suitable geometry for dynamic connectivity to develop. One potential reason for this is the compressed range of capillary pressures due to the single etch depth. Hence, a multi-depth non-repeat micromodel was designed based on a single confocal image of a Bentheimer sandstone. Prototypes of small sections of the multi-depth model were produced by 3D printing but it was not possible to fabricate a functioning model due to time constraints. Simulation was therefore used to explore the multiphase flow behaviour of the new geometry. Initially a Lattice Boltzmann code (developed in another project) was applied to simulate flow in a small region of the single depth geometry and compared to the experimental results as a validation step. The LB model was then used to predict flow behaviour in the multi-depth geometry, however only connected pathway and ganglia flow regimes were seen unambiguously. It is therefore likely that the lack of 3D connectivity rather than capillary pressure limitations prevent the appearance of dynamic connectivity.Open Acces

Numerical simulation of dynamic behavior of droplet on solid surface by the two-phase lattice Boltzmann method

The dynamic behavior of a droplet on a solid surface is simulated by the lattice Boltzmann method (LBM) for two-phase fluids with large density differences; the wetting boundary condition on solid walls is incorporated in this simulation. By using the method, the dynamic behavior of a droplet impinging on a horizontal wall is investigated in terms of various Weber numbers. The dynamic contact angle, the contact line velocity, and the wet length are calculated, and found to be in good agreement with available experimental data. In addition, the method is applied to simulations of the collision of a falling droplet with a stationary droplet on a solid surface. The behavior of the droplets and the mixing process during their collision are simulated in terms of various impact velocities and several static contact angles on the solid surface. It is seen that mixing occurs around the rim of the coalescent droplet due to the circular flows. Also, the relationship between the mixing rate of the primary coalescent droplet and Weber number is investigated.ArticleCOMPUTERS & FLUIDS. 40(1):68-78 (2011)journal articl

Transport in complex systems : a lattice Boltzmann approach

Celem niniejszej pracy jest zbadanie możliwości efektywnego modelowania procesów transportu w złożonych systemach z zakresu dynamiki płynów za pomocą metody siatkowej Boltzmanna (LBM). Złożoność systemu została potraktowana wieloaspektowo i konkretne układy, które poddano analizie pokrywały szeroki zakres zagadnień fizycznych, m.in. przepływy wielofazowe, hemodynamikę oraz turbulencje. We wszystkich przypadkach szczególna uwaga została zwrócona na aspekty numeryczne — dokładność używanych modeli, jak również szybkość z jaką pozwalają one uzyskać zadowalające rozwiązanie. W ramach pracy rozwinięty został pakiet oprogramowania Sailfish, będący otwarta implementacja metody siatkowej Boltzmanna na procesory kart graficznych (GPU). Po analizie szybkości jego działania, walidacji oraz omówieniu założeń projektowych, pakiet ten został użyty do symulacji trzech typów przepływów. Pierwszym z nich były przepływy typu Brethertona/Taylora w dwu- i trójwymiarowych geometriach, do symulacji których zastosowano model energii swobodnej. Analiza otrzymanych wyników pokazała dobra zgodność z danymi dostępnymi w literaturze, zarówno eksperymentalnymi, jak i otrzymanymi za pomocą innych metod numerycznych. Drugim badanym problemem były przepływy krwi w realistycznych geometriach tętnic dostarczających krew do ludzkiego mózgu. Wyniki symulacji zostały dokładnie porównane z rozwiązaniem otrzymanym metoda objętości skończonych z wykorzystaniem pakietu OpenFOAM, przyspieszonego komercyjna biblioteka pozwalająca na wykonywanie obliczeń na GPU. Otrzymano dobra zgodność między badanymi metodami oraz pokazano, że metoda siatkowa Boltzmanna pozwala na wykonywanie symulacji do ok. 20 razy szybciej. Trzecim przeanalizowanym zagadnieniem były turbulentne przepływy w prostych geometriach. Po zwalidowaniu wszystkich zaimplementowanych modeli relaksacji na przypadku wiru Kidy, zbadano przepływy w pustym kanale oraz w obecności przeszkód. Do symulacji wykorzystano zarówno siatki zapewniające pełną rozdzielczość aż do skal Kolmogorova, jak i siatki o mniejszej rozdzielczości. Również w tym kontekście pokazano dobrą zgodność wyników otrzymanych metodą siatkową Boltzmanna z wynikami innych symulacji oraz badaniami eksperymentalnymi. Pokazano również, że implementacja LBM w pakiecie Sailfish zapewnia większą stabilność obliczeń niż ta opisana w literaturze dla tych samych przepływów i modeli relaksacji

Solid-Particles Deposition Through a Turbulent Impinging Jet Using Lattice Boltzmann Method

Solid particle distribution on an impingement surface has been simulated utilizing a graphical processing unit (GPU). An in-house computational fluid dynamics (CFD) code has been developed to investigate a 3D turbulent impinging jet using the lattice Boltzmann method (LBM) in conjunction with large eddy simulation (LES) and the multiple relaxation time (MRT) models. This work proposed an improvement in the LBM-cellular automata (LBM-CA) probabilistic method. In the current model, the fluid flow utilizes the D3Q19 LBM lattice model, while the particles movement employs the D3Q27 one. The particle numbers are defined at the same regular LBM (fluid) nodes, and the transport of particles from one node to its neighbouring nodes are determined in accordance with the particle bulk density and velocity by considering all the external forces. The previous CA models distribute particles at each time step without considering the local particles number and velocity at each node. The present model overcomes the deficiencies of the previous LBM-CA models and, therefore, can better capture the dynamic interaction between particles and the surrounding turbulent flow field. Despite increasing popularity of the LBM-MRT model in simulating complex multiphase fluid flows, this approach is still expensive in term of memory size and computational time required to perform 3D simulations. To improve the throughput of simulations, a single GeForce GTX TITAN X GPU is used in the present work. The CUDA parallel programming platform and the CuRAND library are utilized to form an efficient LBM-MRT-CA algorithm. The LBM-MRT fluid (i.e. no particles) model results were compared with two benchmark test cases ones. The first case is a turbulent free square jet, and the second one is a circular turbulent impinging jet for L/D=2 at Reynolds number equals to 25,000, where L is the nozzle-to-surface distance and D is the jet diameter. The LBM-CA simulation methodology was first validated against a benchmark test case involving particle deposition on a square cylinder confined in a duct. The flow was unsteady and laminar at Re=200 (Re is the Reynolds number), and simulations were conducted for different Stokes numbers. The GPU code was then used to simulate the particle transport and deposition in a turbulent impinging jet at Re=10,000. The effect of changing Stokes number on the particle deposition profile was studied at different L/D ratios, i.e. L/D=2, 4, and 6. The current model was finally used to simulate the particle impaction pattern from a circular jet for L/D=0.5, where the effect of changing Stokes and Reynolds numbers on the particle transport and deposition was examined. The present LBM-CA solutions agree well with other results available in the open literature. For comparative studies, another in-house serial CPU code was also developed, coupling LBM with the classical Lagrangian particle dispersion model. Agreement between results obtained with LBM-CA and LBM-Lagrangian models and the experimental data for the impinging jet case of L/D=0.5 is generally good, and the present LBM-CA approach on GPU achieves a speedup ratio of about 150 against the serial code running on a single CPU. Another new model was proposed to incorporate the solid particle phase effect (i.e. two-way coupling) on the fluid flow. The LMB-Lagrangian approach was used in this model to track solid particles in the computational domain. The solid particle phase was considered as a porous medium moving in the computational domain. The impact of the porous medium (i.e. the solid particle phase) on the fluid flow characteristics (e.g. fluid velocity) is a function of the particle phase volume fraction and velocity in the LBM. Particle-particle collision (i.e. four-way coupling) was also considered in this model by utilizing the discrete element method (DEM). This approach can numerically capture the multi-particle collision behaviours in dense particle suspension problems. This model data were compared with the numerical study ones for a single bubble injected in a fluidized bed, and the results of the bubble diameters at different injection velocity were in good agreement

Development of a Prototype Lattice Boltzmann Code for CFD of Fusion Systems.

Designs of proposed fusion reactors, such as the ITER project, typically involve the use of liquid metals as coolants in components such as heat exchangers, which are generally subjected to strong magnetic fields. These fields induce electric currents in the fluids, resulting in magnetohydrodynamic (MHD) forces which have important effects on the flow. The objective of this SBIR project was to develop computational techniques based on recently developed lattice Boltzmann techniques for the simulation of these MHD flows and implement them in a computational fluid dynamics (CFD) code for the study of fluid flow systems encountered in fusion engineering. The code developed during this project, solves the lattice Boltzmann equation, which is a kinetic equation whose behaviour represents fluid motion. This is in contrast to most CFD codes which are based on finite difference/finite volume based solvers. The lattice Boltzmann method (LBM) is a relatively new approach which has a number of advantages compared with more conventional methods such as the SIMPLE or projection method algorithms that involve direct solution of the Navier-Stokes equations. These are that the LBM is very well suited to parallel processing, with almost linear scaling even for very large numbers of processors. Unlike other methods, the LBM does not require solution of a Poisson pressure equation leading to a relatively fast execution time. A particularly attractive property of the LBM is that it can handle flows in complex geometries very easily. It can use simple rectangular grids throughout the computational domain -- generation of a body-fitted grid is not required. A recent advance in the LBM is the introduction of the multiple relaxation time (MRT) model; the implementation of this model greatly enhanced the numerical stability when used in lieu of the single relaxation time model, with only a small increase in computer time. Parallel processing was implemented using MPI and demonstrated the ability of the LBM to scale almost linearly. The equation for magnetic induction was also solved using a lattice Boltzmann method. This approach has the advantage that it fits in well to the framework used for the hydrodynamic equations, but more importantly that it preserves the ability of the code to run efficiently on parallel architectures. Since the LBM is a relatively recent model, a number of new developments were needed to solve the magnetic induction equation for practical problems. Existing methods were only suitable for cases where the fluid viscosity and the magnetic resistivity are of the same order, and a preconditioning method was used to allow the simulation of liquid metals, where these properties differ by several orders of magnitude. An extension of this method to the hydrodynamic equations allowed faster convergence to steady state. A new method of imposing boundary conditions using an extrapolation technique was derived, enabling the magnetic field at a boundary to be specified. Also, a technique by which the grid can be stretched was formulated to resolve thin layers at high imposed magnetic fields, allowing flows with Hartmann numbers of several thousand to be quickly and efficiently simulated. In addition, a module has been developed to calculate the temperature field and heat transfer. This uses a total variation diminishing scheme to solve the equations and is again very amenable to parallelisation. Although, the module was developed with thermal modelling in mind, it can also be applied to passive scalar transport. The code is fully three dimensional and has been applied to a wide variety of cases, including both laminar and turbulent flows. Validations against a series of canonical problems involving both MHD effects and turbulence have clearly demonstrated the ability of the LBM to properly model these types of flow. As well as applications to fusion engineering, the resulting code is flexible enough to be applied to a wide range of other flows, in particular those requiring parallel computations with many processors. For example, at present it is being used for studies in aerodynamics and acoustics involving flows at high Reynolds numbers. It is anticipated that it will be used for multiphase flow applications in the near future