Modelling and numerical simulation of combustion and multi-phase flows using finite volume methods on unstructured meshes

The present thesis is devoted to the development and implementation of mathematical models and numerical methods in order to carry out computational simulations of complex heat and mass transfer phenomena. Several areas and topics in the field of Computational Fluid Dynamics (CFD) have been treated and covered during the development of the current thesis, specially combustion and dispersed multi-phase flows. This type of simulations requires the implementation and coupling of different physics. The numerical simulation of multiphysics phenomena is challenging due to the wide range of spatial and temporal scales which can characterize each one of the physics involved in the problem. Moreover, when solving turbulent flows, turbulence itself is a very complex physical phenomenon that can demand a huge computational effort. Hence, in order to make turbulent flow simulations computationally affordable, the turbulence should be modelled. Therefore, throughout this thesis different numerical methods and algorithms have been developed and implemented aiming to perform multiphysics simulations in turbulent flows. The first topic addressed is turbulent combustion. Chapter 2 presents a combustion model able to notably reduce the computational cost of the simulation. The model, namely the Progress-Variable (PV) model, relies on a separation of the spatio-temporal scales between the flow and the chemistry. Moreover, in order to account for the influence of the sub-grid species concentrations and energy fluctuations, the PV model is coupled to the Presumed Conditional Moment (PCM) model. Chapter 2 also shows the development of a smart load-balancing method for the evaluation of chemical reaction rates in parallel combustion simulations. Chapter 3 is devoted to dispersed multiphase flows. This type of flows are composed of a continuous phase and a dispersed phase in the form of unconnected particles or droplets. In this thesis, the Eulergian-Lagrangian approach has been selected. This type of model is the best-suited for dispersed multiphase flows with thousands or millions of particles, and with a flow regime ranging from the very dilute up to relatively dense. In Chapter 4, a new method capable of performing parallel numerical simulations using non-overlapping disconnected mesh domains with adjacent boundaries is presented. The presented algorithm stitches at each iteration independent meshes and solves them as a unique domain. Finally, Chapter 5 addresses a transversal aspect to the previously covered topics throughout the thesis. In this chapter, a self-adaptive strategy for the maximisation of the time-step for the numerical solution of convection-diffusion equations is discussed. The method is capable of determining dynamically at each iteration which is the maximum allowable time-step which assures a stable time integration. Moreover, the method also smartly modifies the temporal integration scheme in order to maximize its stability region depending on the properties of the system matrix.La present tesis està dedicada al desenvolupament e implementació de models matemàtics i mètodes numèrics amb l’objectiu de realitzar simulacions computacionals de fenòmens complexos de transferència de calor i massa. Diverses àrees i temes en el camp de la Dinàmica de Fluids Computacional (CFD) han sigut tractats i coberts durant el desenvolupament de la present tesi, en especial, la combustió i els fluxos multi-fase dispersos. Aquest tipus de simulacions de fenòmens multi-físics es desafiant degut al gran rang d’escales espaio-temporals que poden caracteritzar cada una de les físiques involucrades en el problema. D’altra banda, quan es resolen fluxos turbulents, la pròpia turbulència ja és un fenomen físic molt complex que pot requerir un gran esforç computacional. Per tant, amb l’objectiu de fer les simulacions computacionals de fluxos turbulents computacionalment assequibles, la turbulència ha de ser modelada. Per tant, durant aquesta tesis diferents mètodes i algoritmes han sigut desenvolupats e implementats amb l’objectiu de realitzar simulacions multi-físiques en fluxos turbulents. El primer tema abordat és la combustió turbulenta. El Capítol 2 presenta un model de combustió capaç de reduir notablement el cost computacional de la simulació. El model, anomenat el model Progress-Variable (PV), està basat en la separació d’escales espaio-temporals entre el fluid i la química. A més, amb l’objectiu de tenir en compte l’influencia de les fluctuacions a nivell sub-grid d’energia i concentracions d'espècies, el model PV s’acobla amb el model Presumed Conditional Moment (PCM). El Capítol 2 també mostra el desenvolupament d’un mètode intel·ligent de balanceig de càrrega per l'avaluació de el rati de reacció químic en simulacions de combustió paral·leles. El Capítol 3 està dedicat als fluxos multi-fase dispersos. Aquest tipus de fluids estan formats per una fase continua i una fase dispersa en forma de partícules o gotes inconnexes. En aquesta tesis, l’aproximació Euleriana-Lagrangiana ha sigut la seleccionada. Aquest tipus de model és el més adequat per fluxos multi-fase dispersos amb milers o milions de partícules, i amb règims que van des del molt diluït fins al relativament dens. Al Capítol 4, es presenta un nou mètode capaç de realitzar simulacions numèriques paral·leles utilitzant malles inconnexes no solapades que tenen fronteres adjacents. L’algoritme presentat cus a cada iteració les malles independents i les resol com un únic domini. Finalment, el Capítol 5 tracta un aspecte transversal a tots els temes coberts al llarg de la tesi. En aquest capítol es discuteix una estratègia auto-adaptativa destinada a la maximització del pas de temps per a la solució numèrica d’equacions de convecció-difusió. El mètode es capaç de determinar dinàmicament a cada iteració quin és el màxim pas de temps possible que assegura una integració temporal estable. A més, el mètode també modifica de forma intel·ligent la regió d’estabilitat en funció de les propietats de la matriu del sistema.Postprint (published version

On estimating the interface normal and curvature in PLIC-VOF approach for 3D arbitrary meshes

Volume of fluid (VOF) method with its Piecewise Linear Interface Calculation (PLIC) reconstruction algorithm is one of the most popular approaches in numerical simulation of interfacial flows with a wide range of applications in different areas. In an effort to evaluate the similarity of the PLIC-generated planes in comparison with the exact interface, a point-cloud, based on the polygon centers of PLIC planes is extracted, which later is used to form a triangular grid that represents the estimated interface. The main objective of this article is to evaluate the interface geometrical properties based on the extracted triangular grid of the interface. The methods presented in this article, characterized by a higher spatially convergence ratio, are compared with the commonly used methods. The proposed methods are tested for two 3-dimensional general test cases, where an evident improvement is seen in calculation accuracy and spatial convergence of the errors of interface normal vector and curvature.This work has been financially supported by MCIN/AEI/10.13039/ 501100011033 Spain, project PID2020-115837RBI00. E. Schillaci acknowledges the financial support of the Programa Torres Quevedo (PTQ2018-010060).Peer ReviewedPostprint (author's final draft

A new statistical model for subgrid dispersion in large eddy simulations of particle-laden flows

This article is published under a CC BY licence. The Version of Record is available online at: http.//dx.doi.org/10.1088/1742-6596/745/3/032115Dispersed multiphase turbulent flows are present in many industrial and commercial applications like internal combustion engines, turbofans, dispersion of contaminants, steam turbines, etc. Therefore, there is a clear interest in the development of models and numerical tools capable of performing detailed and reliable simulations about these kind of flows. Large Eddy Simulations offer good accuracy and reliable results together with reasonable computational requirements, making it a really interesting method to develop numerical tools for particle-laden turbulent flows. Nonetheless, in multiphase dispersed flows additional difficulties arises in LES, since the effect of the unresolved scales of the continuous phase over the dispersed phase is lost due to the filtering procedure. In order to solve this issue a model able to reconstruct the subgrid velocity seen by the particles is required. In this work a new model for the reconstruction of the subgrid scale effects over the dispersed phase is presented and assessed. This innovative methodology is based in the reconstruction of statistics via Probability Density Functions (PDFs).Peer ReviewedPostprint (published version

Study of the conservation properties in two-way coupled dispersed multiphase flows using finite volume methods

In order to simulate dispersed multiphase flows, the coupling level must be determined according to the volume fraction in the system. The volume fraction is the ratio of the total volume of the dispersed phases over the total volume of the flow. In dilute flows, with volume fractions smaller than 10 -6 , only the influence of carrier phase over the dispersed phase is considered which is known as one-way coupling. Nonetheless, in dispersed flows with higher volume fractions, the effect of the dispersed phase over the continuous one should be taken into consideration, known as two-way coupling. This effect normally is applied as a source term in the conservation equations of the carrier phase. Depending on the numerical method and the discrete operators employed, these source terms can lead to some issues when aiming to preserve physical properties like mass, momentum or kinetic energy. Moreover, in order to validate the two-way coupling method, a particle-laden turbulent flow benchmark case with a mass loading of 22% is simulated by means of large eddy numerical simulation (LES). The aim of this work is to study the conservation properties of dispersed multiphase flows like momentum and kinetic energy through two-way coupling between dispersed and continuous phases.This research was supported by the Secretariat of Universities and Research of the Generalitat de Catalunya and the European Social Fund (FI AGAUR Grant). This work has also been developed within the EU H2020 Clean Sky 2 Joint Undertaking (JU) research project “A New proTection devIce for FOD – ANTIFOD” (grant agreement Nº 821352).Peer ReviewedPostprint (published version

Numerical analysis of conservative unstructured discretisations for low Mach flows

This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. https://authorservices.wiley.com/author-resources/Journal-Authors/licensing-and-open-access/open-access/self-archiving.htmlUnstructured meshes allow easily representing complex geometries and to refine in regions of interest without adding control volumes in unnecessary regions. However, numerical schemes used on unstructured grids have to be properly defined in order to minimise numerical errors. An assessment of a low-Mach algorithm for laminar and turbulent flows on unstructured meshes using collocated and staggered formulations is presented. For staggered formulations using cell centred velocity reconstructions the standard first-order method is shown to be inaccurate in low Mach flows on unstructured grids. A recently proposed least squares procedure for incompressible flows is extended to the low Mach regime and shown to significantly improve the behaviour of the algorithm. Regarding collocated discretisations, the odd-even pressure decoupling is handled through a kinetic energy conserving flux interpolation scheme. This approach is shown to efficiently handle variable-density flows. Besides, different face interpolations schemes for unstructured meshes are analysed. A kinetic energy preserving scheme is applied to the momentum equations, namely the Symmetry-Preserving (SP) scheme. Furthermore, a new approach to define the far-neighbouring nodes of the QUICK scheme is presented and analysed. The method is suitable for both structured and unstructured grids, either uniform or not. The proposed algorithm and the spatial schemes are assessed against a function reconstruction, a differentially heated cavity and a turbulent self-igniting diffusion flame. It is shown that the proposed algorithm accurately represents unsteady variable-density flows. Furthermore, the QUICK schemes shows close to second order behaviour on unstructured meshes and the SP is reliably used in all computations.Peer ReviewedPostprint (author's final draft

On the Interpolation Problem for the Poisson Equation on Collocated Meshes

The appearence of unphysical velocities in highly distorted meshes is a common problem in many simulations. In collocated meshes, this problem arises from the interpolation of the pressure gradient from faces to cells. Using an algebraic form for the classical incompressible Navier-Stokes equations, this problem is adressed. Starting from the work of F. X. Trias et. al. [FX.Trias et al. JCP 258: 246-267, 2014], a new approach for studying the Poisson equation obtained using the Fractional Step Method is found, such as a new interpolator is proposed in order to found a stable solution, which avoid the appearence of these unpleasant velocities. The stability provided by the interpolator is formally proved for cartesian meshes and its rotations, using fully-explicit time discretizations. The construction of the Poisson equation is supported on mimicking the symmetry properties of the differential operators and the Fractional Step Method. Then it is reinterpreted using a recursive application of the Fractional Step Method in order to study the system as an stationary iterative solver. Furthermore, a numerical analysis for unstructured mesh is also provided.This work has been financially supported by the Ministerio de Economía y Competitividad, Spain (project ref. ENE2017-88697-R). D. Santos acknowledges a FI AGAUR-Generalitat de Catalunya fellowship (2020FI B 00839), and N. Valle also acknowledges a FI AGAUR-Generalitat de Catalunya fellowship (2017FI B 00616). The authors thankfully acknowledge these institutions.Peer ReviewedPostprint (published version

A dynamic load balancing method for the evaluation of chemical reaction rates in parallel combustion simulations

The development and assessment of an efficient parallelization method for the evaluation of reaction rates in combustion simulations is presented. Combustion simulations where the finite-rate chemistry model is employed are computationally expensive. In such simulations, a transport equation for each species in the chemical reaction mechanism has to be solved, and the resulting system of equations is typically stiff. As a result, advanced implicit methods must be applied to obtain accurate solutions using reasonable time-steps at expenses of higher computational resources than explicit or classical implicit methods. In the present work, a new algorithm aimed to enhance the numerical performance of the time integration of stiffsystems of equations in parallel combustion simulations is presented. The algorithm is based on a runtime load balancing mechanism, increasing noteworthy the computational performance of the simulations, and consequently, reducing significantly the computer time required to perform the numerical combustion studies.Peer ReviewedPostprint (published version

New parallel method for adjacent disconnected unstructured 3D meshes

A new parallel method for simulations with non-overlapping disconnected mesh domains but adjacent boundaries is presented and studied. This technique allows simulations using 3D unstructured meshes that are independent.Peer ReviewedPostprint (author's final draft

An efficient strategy of parcel modeling for polydispersed multiphase turbulent flows

A three-dimensional particle-laden two-phase turbulent flow by employing the Eulerian-Lagrangian method using multiphase Particle-In-Cell model is implemented to analyze the effects of parcel modeling. In order to achieve an optimal trade-off between accuracy and computational cost, a hybrid approach is proposed. This approach is a combination of two typical models: the volume fixed model, in which each parcel has the same volume, and the number fixed model, in which each parcel has the same number of particles. This approach is studied for the particle-laden turbulent flow benchmark case of Boreé et al. [1], with a mass loading of 22%, by using large eddy simulation through a two-way coupling between continuous and polydispersed phases.Linda Bahramian acknowledges the financial support from the Secretariat of Universities and Research of the Generalitat de Catalunya and the European Social Fund, FI AGAUR Grant (2019 FI B 01205). Carles Oliet, as a Serra Húnter lecturer, acknowledges the Catalan Government for the support through this Programme.Peer ReviewedPostprint (published version

Assessment of numerical aspects using LES in particle separation devices

Numerical simulations can be a powerful tool for the design and optimization of Foreign Object Debris (FOD) protection and separation devices. This work aims to study the relevance and influence of different modelling and numerical aspects in simulations of FOD devices using Large Eddy Simulation (LES) modelling. The results show that in LES some numerical aspects can be critical and must be carefully considered aiming to obtain accurate and reliable results. It is presented how some models affect the physics of the phenomena involved in these kind of flows as well as their impact on the accuracy of the simulations.Peer ReviewedPostprint (published version