Numerical simulation of turbulent diffusion flames using flamelet models on unstructured meshes

The present thesis aims at developing numerical methods and algorithms for the efficient simulation of diffusion flames in the flamelet regime. To tackle turbulent chemically reacting flows a double framework is used in the present thesis. On the one hand, flow description is performed in the context of Large Eddy Simulation (LES) techniques. On the other hand, thermochemistry is modelled by means of flamelet models. The flamelet regime is characterised by the split of the combustion process into a flame structure case and flow transport case. Therefore, to study chemically reacting flows it is required an algorithm for computing variable density flows and a model to describe chemical kinetics. In order to accomplish these goals the thesis is divided into five chapters, each one describing and analysing a specific aspect of the required numerical methods. In first place, in Chapter 1 the basic formulation for describing chemically reacting flows is detailed. Chemical kinetics are briefly described and transport terms for multicomponent flows are detailed. Then, an introduction to turbulent combustion is performed, where the challenges of simulating these flows using finite rate kinetics are stated. It is then argued that specific models are required. Before proceeding to describe the combustion model, an algorithm for the simulation of variable density flows is described and studied in Chapter 2. Furthermore, the study revolves around the use of unstructured meshes. A temporal integration scheme, specifically a multi-step scheme, and two spatial discretisation schemes, namely collocated and staggered schemes, are described and studied. In Chapter 3 a flamelet model for the simulation of diffusion flames is described. First, the flamelet regime is described and the flame equations in mixture fraction space are presented. Then, a Flamelet/Progress-Variable model is used to fully describe the flame. The two main parameters of the model are the mixture fraction and the progress-variable. Additionally, a finite differences method for the solution of the flamelet equations is presented. Since the target flames are turbulent, assumed probability density functions are introduced in order to restate the flamelet solutions as stochastic quantities. The model allows precomputing the flame thermochemistry and storing it into a database, which is accessed during simulations in physical space. The next two chapters deal with the parameters used to represent the flamelet database. First, Chapter 4 studies the definition of the progress-variable, which is required to unambiguously represent the chemical state. The definition of this parameter has been reported to be case sensitive. The present work evidences a dependence on the diffusion model. Definitions found valid for Fickian diffusion are shown to result in non-monotonic distributions when differential diffusion is considered. Furthermore, in the chapter two detailed chemical mechanism are considered. Tests include a CH4/H2/N2 diffusion flame and a self-igniting CH4 flame, where the fuel issues into a vitiated coflow. In the latter case, chemical mechanisms are shown to play a central role in the prediction of the flame stabilisation distance. Lastly, when turbulent flames are considered, the flamelet database is stated as a function of stochastic parameters. Among them, the mixture fraction variance, which represents mixing at the subgrid level, requires modelling. Since chemical reactions in the flamelet regime occur at scales smaller than the Kolmogorov scale, the correct characterisation of subgrid mixing is a critical issue. Hence, in Chapter 5 different models for the evaluation of the subgrid variance are studied. The study case is the methane/hydrogen/nitrogen diffusion flame. The study shows that correct description of the subgrid mixing is critical in accurately predicting the flame stabilisation.Aquesta tesi té com a objectiu desenvolupar mètodes numèrics i algoritmes per a la simulació eficient de flames de difusió en el règim flamelet. Per simular fluxos turbulents i químicament reactius és necessari un marc teòric doble. D'una banda, la descripció del flux es realitza en el context de tècniques Large Eddy Simulation (LES). D'altra banda, la termoquímica es modela per mitjà de models flamelet. El règim flamelet es caracteritza per la divisi ó del procés de combustió en l'estructura de la flama i el transport del flux. Per tant, per estudiar fluxos químicament reactius es requereix un algoritme per calcular fluxos amb densitat variable i un model per descriure la cinètica química. Per assolir aquests objectius, la tesi es divideix en cinc capítols, on cadascun descriu i analitza un aspecte específic dels mètodes numèrics requerits. Al Capítol 1 es detalla la formulació bàsica per descriure fluxos químicament reactius. La cinètica química, i els termes i coeficients de transport per a fluxos multicomponents es detallen. A continuació, es realitza una introducció a la combustió turbulenta, indicant les limitacions per a la simulació d'aquests fluxos quan s'usa cinètica finita, i argumentant la necessitat d'usar models específics. Abans de passar a descriure el model de combustió, en el capítol 2 es descriu i s'estudia un algoritme per a la simulació de fluxos de densitat variable. L'estudi es centra en l' ús de malles no estructurades. En el capítol es descriuen i estudien un esquema temporal d'integració, concretament un esquema multi-pas, i dos esquemes de discretització espacial, esquemes collocated i staggered. En el capítol 3 es descriu un model flamelet per a flames de difusió. En primer lloc s'introdueix el règim flamelet i les equacions de flama en l'espai fracció de mescla. Aleshores, el model Flamelet/Progress-Variable s'utilitza per descriure completament la flama. Els dos paràmetres principals del model són la fracció de mescla i la variable-progrés. A més, es presenta un mètode de diferències finites per a la solució de les equacions flamelet. Donat que les flames objectiu són turbulentes, s'usen funcions de densitat de probabilitat assumides per tal de parametritzar les solucions flamelet mitjançant quantitats estocàstiques. El model permet precomputar la termoquímica de la flama i emmagatzemar-la en una base de dades, la qual és accedida durant les simulacions en l'espai físic. Els dos capítols següents tracten sobre els paràmetres emprats per representar la base de dades flamelet. En primer lloc, al Capítol 4 s'estudia la definició de la variable de progrés, que ha de representar de forma inequívoca l'estat termoquímic. S'ha demostrat que la definició d'aquest paràmetre és depenent del cas. En el capítol es posa de manifest una dependència respecte del model de difusió. Definicions vàlides per a difusió "Fickian" es mostren que donen lloc a distribucions no monòtones quan es considera difusió diferencial. A més, es consideren dos mecanismes químics detallats. Els casos d'estudi inclouen un flama de difusió de CH4/H2/N2 i una flama de CH4 auto-encesa, on el combustible flueix dins un flux d'oxidant calent. En aquest últim cas, es mostra que el mecanisme químic juga un paper central en la predicció de la distància estabilització de la flama. Finalment, quan es consideren flames turbulentes, la base de dades "flamelet" es parametritza emprant variables estocàstiques. Entre ells, la variància de la fracció mescla, que representa la barreja en el nivell subgrid, ha de ser modelada. Ja que les reaccions químiques en el règim flamelet ocorren a escales menors que l'escala de Kolmogorov, és crítica la correcta descripció de la mescla subgrid. Per tant, en el Capítol 5 s'estudien diferents models per a l'avaluació de la variància subgrid

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

Intermediate wake characteristics behind a circular cylinder

The intermediate wake of a circular cylinder at Reynolds number 3300 is studied by means of highly resolved large eddy simulations. The domain spans 100 cylinder diameters D downstream of the cylinder. The intermediate wake is taken here as the region between 6D and 50D downstream of the cylinder. Initially, the velocity deficit shows a marked decrease. This rate of decrease diminishes in the region 10D to 20D downstream of the cylinder centre. Thereafter, it starts to evolve following the far-wake behaviour. The wake half-width exhibits a marked increase in the region 20D to 40D. It is in this region where the von Kárman vortex street looses its coherence.J. Fröhlich and J. Ventosa-Molina acknowledge the funding by the Deutsche Forschungsgemeinschaft (DFG), through FR1593/15-1 within PAK948. I. Rodriguez and J. Ventosa-Molina acknowledge funding by AGAUR through grant 2021 SGR 01051. The authors thank Jan Wissink for providing the inflow signals. Part of the computations were performed at the Centre for Information Services and High Performance Computing (ZIH) at TU Dresden. The authors thankfully acknowledges the computer resources at Altamira and MareNostrum Supercomputers and technical support provided by Santander Supercomputacion support group at the University of Cantabria and Barcelona Supercomputing Center - Centro Nacional de Supercomputación (RES-IM-2023-1-0016, RES-IM-2023-2-0021).Peer ReviewedPostprint (published version

Large eddy simulation of a turbulent diffusion flame: some aspects of subgrid modelling consistency

This is a copy of the author 's final draft version of an article published in the journal Flow turbulence and combustion. The final publication is available at Springer via http://dx.doi.org/10.1007/s10494-017-9813-2In the context of Large Eddy Simulation (LES) solely for the momentum transport equation there may be found several models for the turbulent subgrid fluxes. Furthermore, among those relying on the eddy diffusivity approach, each model may be based on different invariants of the strain rate. Besides, when heat and mass transfer are also considered, closures for the subgrid turbulent scalar fluxes are also required. Hence, different model combinations may be considered. Additionally, when other physical phenomena are included, such as combustion, further subgrid modelling is involved. Therefore, in the present study a LES simulation of a turbulent diffusion flame is performed and different combination of subgrid models are used in order to analyse the numerical effects in the simulations. Several models for the turbulent momentum subgrid fluxes are considered, both constant and dynamically evaluated Schmidt numbers. Regarding combustion, in the context of the Flamelet/Progress-Variable (FPV) model, with an assumed probability density function for the turbulent-chemistry interactions and four different closures for the subgrid mixture fraction variance are considered. Hence, a large number of model combinations are possible. The present study highlights the need for a consistent closure of subgrid effects. It is shown that, in the context of an FPV modelling, incorrect capture of subgrid mixing results in a flame lift-off for the studied flame (DLR A diffusion flame), even though experimentally an attached flame was reported. It is found that a consistent formulation is required, that is, all subgrid closures should become active in the same regions of the domain to avoid modelling inconsistencies. In contrast, when the classical flamelet approach is used, no lift-off is observed. The reason is that the classical flamelet includes only a limited subset of the possible flame states, i.e. only includes burning flamelets and extinguished flamelets for scalar dissipation rates past the extinction one.The present work has been financially supported by the Ministerio de Economía y Competitividad of the Spanish government through project ENE2014-60577-R. We would also like to thank the reviewers for their helpful comments which have led to an improved article. The authors declare that they have no conflict of interest.Peer ReviewedPostprint (author's final draft

Analysis of the Near-Wall Flow in a Turbine Cascade by Splat Visualization

Turbines are essential components of jet planes and power plants. Therefore, their efficiency and service life are of central engineering interest. In the case of jet planes or thermal power plants, the heating of the turbines due to the hot gas flow is critical. Besides effective cooling, it is a major goal of engineers to minimize heat transfer between gas flow and turbine by design. Since it is known that splat events have a substantial impact on the heat transfer between flow and immersed surfaces, we adapt a splat detection and visualization method to a turbine cascade simulation in this case study. Because splat events are small phenomena, we use a direct numerical simulation resolving the turbulence in the flow as the base of our analysis. The outcome shows promising insights into splat formation and its relation to vortex structures. This may lead to better turbine design in the future.Comment: Accepted at IEEE Scientific Visualization (SciVis) 2019. To appear in IEEE Transactions on Visualization and Computer Graphic

Visual analysis of the impact of periodic wakes on the pressure side of a turbine blade

The version of record of this article, first published in Journal of visualization, is available online at Publisher’s website: https://doi.org/10.1007/s12650-023-00930-6Turbines are core components in jet engines for flight propulsion, power plants, and other important energy conversion processes. They are composed of successive rows of blades so that wakes of upstream blades reach subsequent blades where they perturb the flow in an unsteady manner. At the point where a wake reaches the downstream blades, the perturbation forms a so-called negative jet. In this work, we show that the negative jet partially fulfills the conditions of an anti-splat. Based on this finding, we enhance an anti-splat detection algorithm developed by the present authors in previous work and apply it to direct numerical simulation data of a turbine cascade with unsteady wakes. This provides a sound framework and suitable visualization approaches to investigate the phenomenon even in very complex conditions, as is the alteration of the boundary layer flow along the pressure side of a turbine blade. The approach allows a very clear visualization of this interaction, which was not possible to evidence with previous methods, providing new insight into the physics of this flow. The use of flow paths shows up to which point wakes affect the boundary layer along the blade. The reported physical analysis, made possible by the proposed approach, demonstrates the usefulness of the method for the application domain. The generalization to flows in compressors, pumps, and blade-tower interaction in wind engineering and other fields is possible.This work was funded by the German Federal Ministry of Education and Research within the project Competence Center for Scalable Data Services and Solutions (ScaDS) Dresden/Leipzig (BMBF 01IS14014B). JF and JVM acknowledge funding by DFG under FR1593/15-1 within PAK948.Peer ReviewedPostprint (published version

Controlled crystallization of Mn12 single-molecule magnets by compressed CO2 and its influence on the magnetization relaxation

6 pages, 6 figures, 2 tables.Micro- and sub-micro particles of complex [Mn12O12(O2CC6H5)16(H2O)4] ( 1) with controlled size and polymorphism have been prepared by dense-gas crystallization techniques, showing a remarkable particle size influence on the magnetization relaxation rates.This work was supported by DGI (Spain) under projects MAT2002-0043 and MAT2003-04699 and by the European Commission under the NoE MAGMANET (Contract NMP3- CT-2005-515767) and QUEMOLNA Marie Curie RTN (Contract MRTN-CT-2003-5044880). Javier Campo and Nora Ventosa thank the Ramon y Cajal Program of Ministerio de Educación y Tecnología (Spain) for their contracts. Maria Muntó thanks the Consejo Superior de Investigaciones Científicas (CSIC) for her PhD bursary and Jordi Gómez- Segura thanks the European Community for his PhD grant.Peer reviewe

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

Artificial compressibility method for high-pressure transcritical fluids at low Mach numbers

Supercritical fluids possess unique properties that makes them relevant in various scientific and engineering applications. However, the experimental investigation of these fluids is challenging due to the high pressures involved and their complex thermophysical behavior. To overcome these limitations, computational researchers employ scale-resolving methods, such as direct numerical simulation and large-eddy simulation to study them. Nonetheless, these methods require substantial computational resources, especially in the case of low-Mach-number regimes due to the disparity between acoustic and hydrodynamic/thermal time scales. This work, therefore, addresses this problem by extending the artificial compressibility method to high-pressure transcritical fluids. This method is based on decoupling the thermodynamic and hydrodynamic parts of the pressure field, such that the acoustic time scales can be externally modified without severely impacting the flow physics of the problem. In addition, the method proposed has two key characteristics: (i) the splitting method presents low computational complexity, and (ii) an automatic strategy for selecting the speedup factor of the approach is introduced. The effectiveness of the resulting methodology is demonstrated through comprehensive numerical tests of increasing complexity, showcasing its ability to accurately simulate a wide range of high-pressure transcritical flows including turbulence. The results obtained indicate that the approach proposed can readily lead to computational speedups larger than without significantly compromising the accuracy of the numerical solutions.This work is funded by the European Union (ERC, SCRAMBLE, 101040379). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.Peer ReviewedPostprint (published version

Near-Wall Flow in Turbomachinery Cascades—Results of a German Collaborative Project

This article provides a summarizing account of the results obtained in the current collabora-tive work of four research institutes concerning near-wall flow in turbomachinery. Specific questions regarding the influences of boundary layer development on blades and endwalls as well as loss mech-anisms due to secondary flow are investigated. These address skewness, periodical distortion, wake interaction and heat transfer, among others. Several test rigs with modifiable configurations are used for the experimental investigations including an axial low speed compressor, an axial high-speed wind tunnel, and an axial low-speed turbine. Approved stationary and time resolving measurements techniques are applied in combination with custom hot-film sensor-arrays. The experiments are complemented by URANS simulations, and one group focusses on turbulence-resolving simulations to elucidate the specific impact of rotation. Juxtaposing and interlacing their results the four groups provide a broad picture of the underlying phenomena, ranging from compressors to turbines, from isothermal to non-adiabatic, and from incompressible to compressible flows.The investigations reported in this article were conducted within the framework of the joint research project “Near-Wall Flow in Turbomachinery Cascades” which was funded and supported by the Deutsche Forschungsgemeinschaft (DFG) under grant number PAK 948. The responsibility for the contents of this publication lies entirely by the authors.Peer ReviewedPostprint (published version