A robust 3D particle tracking solver for in-flight ice accretion using arbitrary precision arithmetic

A particle tracking code is presented to compute droplet trajectories within a known Eulerian flow field for in-flight ice accretion simulations. The implementation allows for hybrid or unstructured meshes used by common CFD solvers. A known vicinity algorithm was devised to identify particles inside the mesh by computing the intersection between the particle trajectory and the faces of the mesh elements. Arbitrary precision arithmetic is used in the intersection evaluation in order to avoid errors when selecting the exit face if the intersection point is close to or coincident with a vertex or an edge. State-of- the-art wall interaction models are used to take into account droplet rebound, splash and spread at the walls. Non planar surface elements are assumed to improve the accuracy in evaluating the trajectory of secondary re-emitted particles. The software exhibits almost linear scaling when running in parallel on a distributed memory system. The particle tracking code is assessed against the experimental results regarding the impingement of Supercooled Large Droplets over a wing

Monte-Carlo simulation of colliding particles or coalescing droplets transported by a turbulent flow in the framework of a joint fluid–particle pdf approach

The aim of the paper is to introduce and validate a Monte-Carlo algorithm for the prediction of an ensemble of colliding solid particles, or coalescing liquid droplets, suspended in a turbulent gas flow predicted by Reynolds Averaged Navier Stokes approach (RANS). The new algorithm is based on the direct discretization of the collision/coalescence kernel derived in the framework of a joint fluid–particle pdf approach proposed by Simonin et al. (2002). This approach allows to take into account correlations between colliding inertial particle velocities induced by their interaction with the fluid turbulence. Validation is performed by comparing the Monte-Carlo predictions with deterministic simulations of discrete solid particles coupled with Direct Numerical Simulation (DPS/DNS), or Large Eddy Simulation (DPS/LES), where the collision/coalescence effects are treated in a deterministic way. Five cases are investigated: elastic monodisperse particles, non-elastic monodisperse particles, binary mixture of elastic particles and binary mixture of elastic settling particles in turbulent flow and finally coalescing droplets. The predictions using the new Monte-Carlo algorithm are in much better agreement with DPS/DNS results than the ones using the standard algorithm

Spray combustion model improvement study, 1

This study involves the development of numerical and physical modeling in spray combustion. These modeling efforts are mainly motivated to improve the physical submodels of turbulence, combustion, atomization, dense spray effects, and group vaporization. The present mathematical formulation can be easily implemented in any time-marching multiple pressure correction methodologies such as MAST code. A sequence of validation cases includes the nonevaporating, evaporating and_burnin dense_sprays

Numerical simulation of spray coalescence in an eulerian framework : direct quadrature method of moments and multi-fluid method

The scope of the present study is Eulerian modeling and simulation of polydisperse liquid sprays undergoing droplet coalescence and evaporation. The fundamental mathematical description is the Williams spray equation governing the joint number density function f(v, u; x, t) of droplet volume and velocity. Eulerian multi-fluid models have already been rigorously derived from this equation in Laurent et al. (2004). The first key feature of the paper is the application of direct quadrature method of moments (DQMOM) introduced by Marchisio and Fox (2005) to the Williams spray equation. Both the multi-fluid method and DQMOM yield systems of Eulerian conservation equations with complicated interaction terms representing coalescence. In order to validate and compare these approaches, the chosen configuration is a self-similar 2D axisymmetrical decelerating nozzle with sprays having various size distributions, ranging from smooth ones up to Dirac delta functions. The second key feature of the paper is a thorough comparison of the two approaches for various test-cases to a reference solution obtained through a classical stochastic Lagrangian solver. Both Eulerian models prove to describe adequately spray coalescence and yield a very interesting alternative to the Lagrangian solver

Doctor of Philosophy

dissertationThe purpose of this research is the development of mathematical formalisms for the numerical modeling and simulation of multiphase systems with emphasis in polydisperse flows. The framework for these advancements starts with the William-Boltzmann equation which describes the evolution of joint distributions of particle properties: size, velocity, mass, enthalpy, and other scalars. The amount of statistical information that can be obtained from the direct evolution of particle distribution functions is extensive and detailed, but at a computational cost not yet suitable in usable computational fluid dynamics (CFD) codes. Alternatives to the direct evolution of particle distribution functions have been proposed and we are interested in the family of solutions involving the evolution of the statistical moments from the joint distributions. Rather than tracking every single particle characteristic from the joint distribution, transport equations for their joint moments are formulated; these equations share many of the properties of the regular transport equations formulated in the finite volume framework, making them very attractive for their implementation in current Eulerian CFD codes. The information they produce is general enough to provide the characteristic behavior of many multiphase systems to the point of improvement over the current Eulerian methodologies implemented on standard CFD modeling and simulation approaches. Based on the advantages and limitations of the solutions of the ongoing methodologies and the degree of the information provided by them, we propose formalisms to extend their modeling capabilities focusing on the influence of the size distribution in many of the related multiphase phenomena. The first methodology evolves joint moments based on the evolution of primitive variables (size among them) and conditional moments that are approximants of the joint moments at every time step. The second methodology reconstructs completely the marginal size distribution using the concept of parcel and approximate characteristic behavior of the rest of the conditional moments in each parcel. In both approaches, the representation of size distribution plays a fundamental role and accounts for the polydisperse nature of the system. Also, the numerics of the moment transport equations are to be consistent with the theory of general hyperbolic transport equations but the formulation of the discretization schemes are based on the properties of the underlying distribution. A final contribution is presented in the form of an appendix and it analyzes the role of maximum entropy-based methodologies on the formulation of Eulerian moment-based methods. Attempts to derive new transport equations on the framework of maximum entropy methodologies will be considered and reconstruction of distribution strategies will be presented as preliminary results that might impact future research on Eulerian moment-based methods

Influence of droplet collision modelling in Euler/Lagrange calculations of spray evolution

The numerical computation of spraying systems is favourably conducted by applying the Euler/Lagrange approach. Although sprays downstream of the breakup region are very often rather dilute, droplet collisions may still have a significant influence on the spray evolution and especially the produced droplet size spectrum. Consequently, they have to be reliably modelled in the Lagrangian tracking approach. For this purpose, the fully stochastic droplet collision model is applied, which is numerically very efficient. It is demonstrated that this model is largely independent of the considered flow mesh and hence grid size, as well as the number of tracked parcels and the Lagrangian time step size. Moreover, this model includes the impact efficiency which may remarkably reduce collision rates for a wide droplet size spectrum. An essential ingredient of any droplet collision model is the proper description of the collision outcome through the so-called collision maps (i.e. the non-dimensional impact parameter plotted versus collision Weber number; B = f(We)), where the outcome regions (i.e. bouncing, coalescence and stretching or reflexive separation) are demarked by appropriate, mostly theory-based boundary lines. There are a number of different correlations available which may be applied for this purpose. The structure of the collision maps strongly depends on the kind of liquid being atomised. Different types of boundary lines and collision map structures are analysed here in detail with regard to the conditional collision rates or numbers within a rather simple hollow cone spray. The comparison of the averaged Sauter mean diameters along the spray demonstrates the importance of droplet collisions and how strongly this result is affected by the presumed droplet collision maps. Crude approximations to such collision maps may result in large errors and wrong predictions of the produced droplet size spectrum. Moreover, it is demonstrated that the effective PDF (probability density function) of the colliding droplet size ratio has typically a maximum in the range 0.1 < Δ < 0.3, a condition where no experimental data are available so far and some of the commonly used boundary lines are not suitable. Naturally, the spray simulations are compared to experimental data for a water hollow-cone spray, showing excellent agreement if the droplet collision map is selected properly. This concerns profiles of both gas and droplet velocities as well as droplet concentration development and local droplet size distributions. Expectedly, the prediction of the velocities is less sensitive with respect to the presumed droplet collision ma

Large-eddy simulation of turbulent dispersed flows: a review of modelling approaches

In large-eddy simulation (LES) of turbulent dispersed flows, modelling and numerical inaccuracies are incurred because LES provides only an approximation of the filtered velocity. Interpolation errors can also occur (on coarse-grained domains, for instance). These inaccuracies affect the estimation of the forces acting on particles, obtained when the filtered fluid velocity is supplied to the Lagrangian equation of particle motion, and accumulate in time. As a result, particle trajectories in LES fields progressively diverge from particle trajectories in DNS fields, which can be considered as the exact numerical reference: the flow fields seen by the particles become less and less correlated, and the forces acting on particles are evaluated at increasingly different locations. In this paper, we review models and strategies that have been proposed in the Eulerian\u2013Lagrangian framework to correct the above-mentioned sources of inaccuracy on particle dynamics and to improve the prediction of particle dispersion in turbulent dispersed flows

LES of certain droplet size effects in fuel sprays

This thesis belongs to the field of mechanical engineering, more precisely to computational fluid dynamics and fuel injection modelling. This type of problems have been extensively studied because of their practical importance, for example, in combustion processes of automotive industry. Novel challenges are reduction of exhaust gas emissions in the present diesel fuel-based and also in bio diesel-based concepts. The problem studied in this work is of generic nature and it can be related to many real world problems. A model problem of droplet-laden jet is studied to emulate a fuel spray. The most essential parameter that is studied is fuel droplet size. More precisely, the ratio of droplet timescale and fluid timescale i.e. the Stokes number. Mathematically, the studied system can be formulated in terms of the Navier-Stokes equation with a spray momentum source term at low Mach number regime. A feature characteristic to this study is to use large scale computer simulation to simulate the system. For adequate modelling, this work makes use of a method called Large-Eddy Simulation (LES) to simulate the motion of the turbulent gas and Lagrangian Particle Tracking (LPT) to simulate the motion of the droplets. The main computational tool used in this work is the OpenFOAM software. In fact, the present work is one of the first computational studies on LES/LPT diesel spray modeling in which droplet-level phenomena are discussed in light of the global behavior of the spray jet in an extensive manner. In view of the literature on this topic the results of the work seem to be realistic. The dependence of spray shape on droplet size (Stokes number) is studied and differences between the shapes are consistently explained. It is noted that mixing inside the spray depends significantly on the fuel droplet size. Quantitative and statistical analysis methods are developed in order to explain the connection between spray shape and mixing. The presented analysis explains the results and, on its behalf, the analysis explains the practical observation on the decrease of soot emissions together with decreasing nozzle diameter and increasing injection pressure

Numerical simulation and analysis of multi-scale cavitating flows

Cavitating flows include vapour structures with a wide range of different length scales, from micro-bubbles to large cavities. The correct estimation of small-scale cavities can be as important as that of large-scale structures, because cavitation inception as well as the resulting noise, erosion and strong vibrations occur at small time and length scales. In this study, a multi-scale cavitating flow around a sharp-edged bluff body is investigated. For numerical analysis, while popular homogeneous mixture models are practical options for large-scale applications, they are normally limited in the representation of small-scale cavities. Therefore, a hybrid cavitation model is developed by coupling a mixture model with a Lagrangian bubble model. The Lagrangian model is based on a four-way coupling approach, which includes new submodels, to consider various small-scale phenomena in cavitation dynamics. Additionally, the coupling of the mixture and the Lagrangian models is based on an improved algorithm that is compatible with the flow physics. The numerical analysis provides a detailed description of the multi-scale dynamics of cavities as well as the interactions between vapour structures of various scales and the continuous flow. The results, among others, show that small-scale cavities not only are important at the inception and collapse steps, but also influence the development of large-scale structures. Furthermore, a comparison of the results with those from experiment shows considerable improvements in both predicting the large cavities and capturing the small-scale structures using the hybrid model. More accurate results (compared with the traditional mixture model) can be achieved even with a lower mesh resolution

Transient simulation of gaseous particle/droplet laden flows in industrial-scale devices for flue gas cleaning including two-way mass and enthalpy coupling

Paper presented at the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 1-4 July, 2007.The method of computational fluid dynamics (CFD) is applied to spraying processes with strong enthalpy coupling. Focus is brought to industrial scale applications in the field of environmental engineering. A transient 3D finite volume solver is used, wherein the disperse phase is modeled within an Lagrangian framework. Two-way mass and enthalpy coupling is taken into account. Resulting limitations of the traditional sequential model droplet integration approach are discussed, which potentially lead to thermodynamically inconsistant or oscillatory solutions, especially in zones of dense spray. As an alternative a combined sequential-simultaneous solution algorithm is proposed. Thus obtained results show sufficient aggreement with a validated test case. Application to industrial scale reactors in the field of flue gas cleaning are demonstrated exemplarily.cs201