Simplex space-time meshes in thermally coupled two-phase flow simulations of mold filling

The quality of plastic parts produced through injection molding depends on many factors. Especially during the filling stage, defects such as weld lines, burrs, or insufficient filling can occur. Numerical methods need to be employed to improve product quality by means of predicting and simulating the injection molding process. In the current work, a highly viscous incompressible non-isothermal two-phase flow is simulated, which takes place during the cavity filling. The injected melt exhibits a shear-thinning behavior, which is described by the Carreau-WLF model. Besides that, a novel discretization method is used in the context of 4D simplex space-time grids [2]. This method allows for local temporal refinement in the vicinity of, e.g., the evolving front of the melt [10]. Utilizing such an adaptive refinement can lead to locally improved numerical accuracy while maintaining the highest possible computational efficiency in the remaining of the domain. For demonstration purposes, a set of 2D and 3D benchmark cases, that involve the filling of various cavities with a distributor, are presented.Comment: 14 pages, 11 Figures, 4 Table

Enhanced SPH modeling of free-surface flows with large deformations

The subject of the present thesis is the development of a numerical solver to study the violent interaction of marine flows with rigid structures. Among the many numerical models available, the Smoothed Particle Hydrodynamics (SPH) has been chosen as it proved appropriate in dealing with violent free-surface flows. Due to its Lagrangian and meshless character it can naturally handle breaking waves and fragmentation that generally are not easily treated by standard methods. On the other hand, some consolidated features of mesh-based methods, such as the solid boundary treatment, still remain unsolved issues in the SPH context. In the present work a great part of the research activity has been devoted to tackle some of the bottlenecks of the method. Firstly, an enhanced SPH model, called delta-SPH, has been proposed. In this model, a proper numerical diffusive term has been added in the continuity equation in order to remove the spurious numerical noise in the pressure field which typically affects the weakly-compressible SPH models. Then, particular attention has been paid to the development of suitable techniques for the enforcement of the boundary conditions. As for the free-surface, a specific algorithm has been designed to detect free-surface particles and to define a related level-set function with two main targets: to allow the imposition of peculiar conditions on the free-surface and to analyse and visualize more easily the simulation outcome (especially in 3D cases). Concerning the solid boundary treatment, much effort has been spent to devise new techniques for handling generic body geometries with an adequate accuracy in both 2D and 3D problems. Two different techniques have been described: in the first one the standard ghost fluid method has been extended in order to treat complex solid geometries. Both free-slip and no-slip boundary conditions have been implemented, the latter being a quite complex matter in the SPH context. The proposed boundary treatment proved to be robust and accurate in evaluating local and global loads, though it is not easy to extend to generic 3D surfaces. The second technique has been adopted for these cases. Such a technique has been developed in the context of Riemann-SPH methods and in the present work is reformulated in the context of the standard SPH scheme. The method proved to be robust in treating complex 3D solid surfaces though less accurate than the former. Finally, an algorithm to correctly initialize the SPH simulation in the case of generic geometries has been described. It forces a resettlement of the fluid particles to achieve a regular and uniform spacing even in complex configurations. This pre-processing procedure avoids the generation of spurious currents due to local defects in the particle distribution at the beginning of the simulation. The delta-SPH model has been validated against several problems concerning fluid-structure interactions. Firstly, the capability of the solver in dealing with water impacts has been tested by simulating a jet impinging on a flat plate and a dam-break flow against a vertical wall. In this cases, the accuracy in the prediction of local loads and of the pressure field have been the main focus. Then, the viscous flow around a cylinder, in both steady and unsteady conditions, has been simulated comparing the results with reference solutions. Finally, the generation and propagation of 2D gravity waves has been simulated. Several regimes of propagation have been tested and the results compared against a potential flow solver. The developed numerical solver has been applied to several cases of free-surface flows striking rigid structures and to the problem of the generation and evolution of ship generated waves. In the former case, the robustness of the solver has been challenged by simulating 2D and 3D water impacts against complex solid surfaces. The numerical outcome have been compared with analytical solutions, experimental data and other numerical results and the limits of the model have been discussed. As for the ship generated waves, the problem has been firstly studied within the 2D+t approximation, focusing on the occurrence and features of the breaking bow waves. Then, a dedicated 3D SPH parallel solver has been developed to tackle the simulation of the entire ship in constant forward motion. This simulation is quite demanding in terms of complexities of the boundary geometry and computational resources required. The wave pattern obtained has been compared against experimental data and results from other numerical methods, showing in both the cases a fair and promising agreement

A PHYSICS-BASED APPROACH TO MODELING WILDLAND FIRE SPREAD THROUGH POROUS FUEL BEDS

Wildfires are becoming increasingly erratic nowadays at least in part because of climate change. CFD (computational fluid dynamics)-based models with the potential of simulating extreme behaviors are gaining increasing attention as a means to predict such behavior in order to aid firefighting efforts. This dissertation describes a wildfire model based on the current understanding of wildfire physics. The model includes physics of turbulence, inhomogeneous porous fuel beds, heat release, ignition, and firebrands. A discrete dynamical system for flow in porous media is derived and incorporated into the subgrid-scale model for synthetic-velocity large-eddy simulation (LES), and a general porosity-permeability model is derived and implemented to investigate transport properties of flow through porous fuel beds. Note that these two developed models can also be applied to other situations for flow through porous media. Simulations of both grassland and forest fire spread are performed via an implicit LES code parallelized with OpenMP; the parallel performance of the algorithms are presented and discussed. The current model and numerical scheme produce reasonably correct wildfire results compared with previous wildfire experiments and simulations, but using coarser grids, and presenting complicated subgrid-scale behaviors. It is concluded that this physics-based wildfire model can be a good learning tool to examine some of the more complex wildfire behaviors, and may be predictive in the near future

Optimal computational parameters for maximum accuracy and minimum cost of Arnoldi-based time-stepping methods for flow global stability analysis

Global instability analysis of flows is often performed via time-stepping methods, based on the Arnoldi algorithm. When setting up these methods, several computational parameters must be chosen, which affect intrinsic errors of the procedure, such as the truncation errors, the discretization error of the flow solver, the error associated with the nonlinear terms of the Navier-Stokes equations and the error associated with the limited size of the approximation of the Jacobian matrix. This paper develops theoretical equations for the estimation of optimal balance between accuracy and cost for each case. The 2D open cavity flow is used both for explaining the effect of the parameters on the accuracy and the cost of the solution, and for verifying the quality of the predictions. The equations demonstrate the impact of each parameter on the quality of the solution. For example, if higher order methods are used for approaching a Fr\'echet derivative in the procedure, it is shown that the solution deteriorates more rapidly for larger grids or less accurate flow solvers. On the other hand, lower order approximations are more sensitive to the initial disturbance magnitude. Nevertheless, for accurate flow solvers and moderate grid dimensions, first order Fr\'echet derivative approximation with optimal computational parameters can provide 5 decimal place accurate eigenvalues. It is further shown that optimal parameters based on accuracy tend to also lead to the most cost-effective solution. The predictive equations, guidelines and conclusions are general, and, in principle, applicable to any flow, including 3D ones

Large scale cavity dissolution: From the physical problem to its numerical solution

Dissolution of underground cavities by ground water (or solutions) may cause environmental problems and geological hazards. Efficient modeling and numerical solving of such phenomena are critical for risk analysis. To solve the cavity dissolution problems, we propose to use a porous medium based local non-equilibrium diffuse interface method (DIM) which does not need to track the dissolution fronts explicitly as the sharp front methods (such as ALE). To reduce the grid blocks when using the DIM method, an adaptive mesh refinement (AMR) method is used to have higher resolutions following the moving fronts. An efficient fully implicit scheme is used by taking care of the velocities across the gridblock interfaces on the AMR grid. Numerical examples of salt dissolution under different flow conditions were performed to validate the modeling and numerical solving. Core-scale and reservoir-scale cases were carried out to study the mass transport and the evolution of the profiles of the dissolution fronts. Gravity-driven physical instabilities are found to be more strong in the infinite channel with upper and lower planes than in the 3D tube configuration under the same condition. The implementations with the AMR method also showed a very good computational efficiency, while obtaining good agreement with the finest-grid solutions

TURBULENT TRANSITION SIMULATION AND PARTICULATE CAPTURE MODELING WITH AN INCOMPRESSIBLE LATTICE BOLTZMANN METHOD

Derivation of an unambiguous incompressible form of the lattice Boltzmann equation is pursued in this dissertation. Further, parallelized implementation in developing application areas is researched. In order to achieve a unique incompressible form which clarifies the algorithm implementation, appropriate ansatzes are utilized. Through the Chapman-Enskog expansion, the exact incompressible Navier-Stokes equations are recovered. In initial studies, fundamental 2D and 3D canonical simulations are used to evaluate the validity and application, and test the required boundary condition modifications. Several unique advantages over the standard equation and alternative forms found in literature are found, including faster convergence, greater stability, and higher fidelity for relevant flows. Direct numerical simulation and large eddy simulation of transitional and chaotic flows are one application area explored with the derived incompressible form. A multiple relaxation time derivation is performed and implemented in a 2D cavity (direct simulation) and a 3D cavity (large eddy simulation). The Kolmogorov length scale, a function of Reynolds number, determines grid resolution in the 2D case. Comparison is made to the extensive literature on laminar flows and the Hopf bifurcation, and final transition to chaos is predicted. Steady and statistical properties in all cases are in good agreement with literature. In the 3D case the relatively new Vreman subgrid model provides eddy viscosity modeling. By comparing the center plane to the direct numerical simulation case, both steady and unsteady flows are found to be in good agreement, with a coarse grid, including prediction of the Hopf bifurcation. Multiphysics pore scale flow is the other main application researched here. In order to provide the substrate geometry, a straightforward algorithm is developed to generate random blockages producing realistic porosities and passages. Combined with advection-diffusion equations for conjugate heat transfer and soot particle transport, critical diesel particulate filtration phenomena are simulated. To introduce additional fidelity, a model is added which accounts for deposition caused by a variety of molecular and atomic forces. Detailed conclusions are presented to lay the groundwork for future extensions and improvements. Predominantly, higher lattice velocity large eddy simulation, improved parallelization, and filter regeneration

Nonlinear enthalpy transformation for transient convective phase change in Smoothed Particle Hydrodynamics (SPH)

A three-dimensional model is presented for the prediction of solidification behavior using a nonlinear transformation of the enthalpy equation in a Smoothed Particle Hydrodynamics (SPH) discretization. The effect of phase change in the form of release and absorption of latent heat is implemented implicitly as variable source terms in the enthalpy calculation. The developed model is validated against various experimental, analytical, and numerical results from the literature. Results confirm accuracy and robustness of the new procedure. Finally, the SPH model is applied to a study of suspension plasma spraying (SPS) by predicting the impact and solidification behavior of molten ceramic droplets on a substrate

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

High performance computing for multiphase fluid flows

Multiphase fluid flows are very common in engineering and science applications. Examples include air ow on water surface, metallurgical flow and blood flow in the body. In these flows, fluids are separated by a sharp interface and form different phases. The flow is characterized by the movement of this interface. Accurate modelling of the interface movement is a fundamental problem in the numerical simulation of these flows. Velocities for the movement are provided by the numerical solution of the Navier-Stokes (N-S) equations. These equations are discretized and converted into linear systems of equations. Research in the direction towards solving these systems efficiently has been the main focus of many researchers in the field of Computational Fluid Dynamics (CFD). A modified Volume of Fluid (VOF) method for modelling two phase flows is implemented using an analytic relation for its reconstruction step. The Finite Volume Method (FVM) is utilized, by incorporating a staggered grid, to discretize the two-dimensional (2-D) N-S equations. A preconditioned Krylov-Subspace iterative method, namely, the Bi-Conjugate Gradient Stabilized (Bi-CGSTAB) method is employed to solve the linear systems of equations. Solving the linear system usually consumes most of the simulation time for multiphase flow problems. Novel algorithms for the Incomplete LU Threshold (ILUT) preconditioner, forward and backward substitution and other matrix operations for penta-diagonal matrices are proposed here by adopting a diagonal sparse matrices format. The novel algorithm for ILUT reduces the computational complexity from O(n3 − n2) to O(n) in comparison to dense format. Further, it brings down the communication overhead, consequently facilitating parallelization. Parallel versions of these algorithms are developed using a new load balancing scheme. The MPI C++ communication library is utilized to develop the parallel version. The 2-D VOF code is applied to shape advection problems and results are found to be in good agreement with those available in literature. In the case of translation of a square box, it provides more accurate results than other VOF methods. The code for the VOF method and the parallel iterative solvers are integrated with 2-D N-S code in C++. The whole code is then implemented to simulate several two phase flow problems: dam breaking with and without an obstacle, rising of an air bubble and lid driven cavity flows. Speedup data from parallel programs implemented on these problems are generated