Publications
71 results found
Tang H, Papadakis G, Rigopoulos S, 2019, Coupling direct numerical simulations with population balance modelling for predicting turbulent particle precipitation in a T-mixer, 11th International Symposium on Turbulence and Shear Flow Phenomena (TSFP11), Publisher: TSFP
In this study we develop a methodology for predicting the particle size distribution(PSD)inparticulate process, a process used for producing particulate materials,by coupling population balance modelling and direct numerical simulation. Itis employed in investigating the turbulent precipitation of BaSO4in a T-mixer.The high resolution allowed us to capture the dominating mechanisms.Particle formation is most intense in the impingementand the reactantconsumption in each precipitation mechanism depends on the mixing intensity.Different particle formation statesand their characteristics on the PSD in the early stage arethenidentified.Comparisonwith an ideal reactor showsthat the distribution can be controlled by altering the mixing environment.
Liu A, Rigopoulos S, 2019, A conservative method for numerical solution of the population balance equation, and application to soot formation, Combustion and Flame, Vol: 205, Pages: 506-521, ISSN: 0010-2180
The objective of this paper is to present a finite volume method for the discretisation of the population balance equation with coagulation, growth and nucleation that combines: (a) accurate prediction of the distribution with a small number of sections, (b) conservation of the first moment (or any other single moment) in a coagulation process, (c) applicability to an arbitrary non-uniform grid, and (d) speed and robustness that make it suitable for combining with a CFD code for solving problems such as soot formation in flames. The conservation of the first moment of a distribution with respect to particle volume is of particular importance for two reasons: it is an invariant during a coagulation process and it represents conservation of mass. The method is based on a geometric evaluation of the double integrals arising from the finite volume discretisation of the coagulation terms and an exact balance of coagulation source and sink terms to ensure moment conservation. Extensive testing is performed by comparison with analytical solutions and direct numerical solutions of the discrete PBE for both theoretical and physically important coagulation kernels. Finally, the method is applied to the simulation of a laminar co-flow diffusion sooting flame, in order to assess its potential for coupling with CFD, chemical kinetics, transport and radiation models. The results show that accurate solutions can be obtained with a small number of sections, and that the PBE solution requires less than one fourth of the time of the complete simulation, only half of which is spent on the discretisation (the remaining being for the evaluation of the temperature dependence of the coagulation kernel).
Sewerin F, Rigopoulos S, 2019, Algorithmic aspects of the LES-PBE-PDF method for modeling soot particle size distributions in turbulent flames, Combustion Science and Technology, Vol: 191, Pages: 766-796, ISSN: 0010-2202
In recent times, the LES-PBE-PDF framework has been developed to couple large eddy simulation (LES) and population balance models (PBE) for the description of soot formation in turbulent hydrocarbon flames. This approach is based on a modeled evolution equation for the LES-filtered probability density function (pdf) associated with the instantaneous gas composition and soot particle size distribution. Here, the interaction of turbulence with chemical reactions and soot formation can be represented without approximations on part of the chemical and soot formation kinetics, while effects due to turbulent transport and molecular diffusion require closure. In view of an efficient numerical solution scheme, we previously proposed to combine a statistically equivalent reformulation of the joint scalar-number density pdf based on Eulerian stochastic fields with a time-explicit adaptive grid discretization in particle size space and a fractional time stepping scheme. In this article, we present algorithmic aspects and relay implementational details for a consistent semi-discrete formulation of the PBE fractional step as well as an effective dynamic load balancing scheme for both the chemical reaction and PBE fractional steps. Considering soot formation in the Delft III turbulent diffusion flame as a test case, we show that the persisting load imbalance is almost negligible on average and give evidence of linear strong scaling on a modern high performance computer for moderate numbers of compute nodes.
Koniavitis P, Rigopoulos S, Jones W, 2018, Reduction of a detailed chemical mechanism for a kerosenesurrogate via RCCE-CSP, Combustion and Flame, Vol: 194, Pages: 85-106, ISSN: 0010-2180
Detailed mechanisms for kerosene surrogate fuels contain hundreds of species and thousands of reactions, indicating a necessity for reduced mechanisms. In this work, we employ a framework that combines Rate-Controlled Constrained Equilibrium (RCCE) with Computational Singular Perturbation (CSP) for systematic reduction based on timescale analysis, to reduce a detailed mechanism for a jet fuel surrogate with n-dodecane, methylcyclohexane and m-xylene. Laminar non-premixed flamelets are utilised for the CSP analysis for different strain rates and therefore different scalar dissipation rate, covering the flammable region of strain rates for the surrogate fuel.Two RCCE-reduced mechanisms are developed via an RCCE-CSP methodology, one with 17 and one with 42 species, and their accuracy is assessed in a range of cases that test the performance of the reduced mechanism under both non-premixed and premixed conditions and its dynamic response. These include non-premixed flamelets with varying strain rate, laminar premixed flames for a range of equivalence ratios and pressures, flamelets ignited by an artificial pilot or by hot air, and unsteady flamelets with time-dependent strain rate.The profiles of both major and minor species, as well as important combustion characteristics such as the ignition strain rate and the laminar flame speed, are investigated. The structure of non-premixed flamelets is very well predicted, while the premixed flames are overall well predicted apart from a few deviations in certain species and an underprediction in the laminar flame speed. Apart from the large reduction in dimensionality, the reduction in computational time is also considerable (up to 19 times). As the detailed mechanism comprises 367 species and 1892 reactions, this paper presents the first application of RCCE to a mechanism of this size, as well as a comprehensive validation in a set of cases that include non-premixed and premixed laminar flames, atmospheric and elevated pressur
Sewerin F, Rigopoulos S, 2018, An LES-PBE-PDF approach for predicting the soot particle size distribution in turbulent flames, Combustion and Flame, Vol: 189, Pages: 62-76, ISSN: 0010-2180
In this article, we combine the large eddy simulation (LES) concept with the population balance equation (PBE) for predicting, in a Eulerian fashion, the evolution of the soot particle size distribution in a turbulent non-premixed hydrocarbon flame. In order to resolve the interaction between turbulence and chemical reactions/soot formation, the transport equations for the gas phase scalars and the PBE are combined into a joint evolution equation for the filtered pdf associated with a single realization of the gas phase composition and the soot number density distribution. With view towards an efficient numerical solution procedure, we formulate Eulerian stochastic field equations that are statistically equivalent to the joint scalar-number density pdf. By discretizing the stochastic field equation for the particle number density using an explicit adaptive grid technique, we are able to accurately resolve sharp features of evolving particle size distributions, while keeping the number of grid points in particle size space small. Compared to existing models, the main advantage of our approach is that the LES-filtered particle size distribution is predicted at each location in the flow domain and every instant in time and that arbitrary chemical reaction mechanisms and soot formation kinetics can be accommodated without approximation. The combined LES-PBE-PDF model is applied to investigate soot formation in the turbulent non-premixed Delft III flame. Here, the soot kinetics encompass acetylene-based rate expressions for nucleation and growth that were previously employed in the context of laminar diffusion flames. In addition, both species consumption by soot formation and radiation based on the assumption of optical thinness are accounted for. While the agreement of our model predictions with experimental measurements is not perfect, we indicate the benefits of the LES-PBE-PDF model and demonstrate its computational viability.
Franke LLC, Chatzopoulos AK, Rigopoulos S, 2017, Tabulation of combustion chemistry via Artificial Neural Networks (ANNs): methodology and application to LES-PDF simulation of Sydney flame L, Combustion and Flame, Vol: 185, Pages: 245-260, ISSN: 0010-2180
In this work, a methodology for the tabulation of combustion mechanisms via Artificial Neural Networks (ANNs) is presented. The objective of the methodology is to train the ANN using samples generated via an abstract problem, such that they span the composition space of a family of combustion problems. The abstract problem in this case is an ensemble of laminar flamelets with an artificial pilot in mixture fraction space to emulate ignition, of varying strain rate up to well into the extinction range. The composition space thus covered anticipates the regions visited in a typical simulation of a non-premixed flame. The ANN training consists of two-stage process: clustering of the composition space into subdomains using the Self-Organising Map (SOM) and regression within each subdomain via the multilayer Perceptron (MLP). The approach is then employed to tabulate a mechanism of CH4-air combustion, based on GRI 1.2 and reduced via Rate-Controlled Constrained Equilibrium (RCCE) and Computational Singular Perturbation (CSP). The mechanism is then applied to simulate the Sydney Flame L, a turbulent non-premixed flame that features significant levels of local extinction and re-ignition. The flow field is resolved through Large Eddy Simulation (LES), while the transported Probability Density Function (PDF) approach is employed for modelling the turbulence-chemistry interaction and solved numerically via the Stochastic Fields method. Results demonstrate reasonable agreement with experiments, indicating that the SOM-MLP approach provides a good representation of the composition space, while the great savings in CPU time allow for a simulation to be performed with a comprehensive combustion model, such as the LES-PDF, with modest CPU resources such as a workstation.
Sewerin F, Rigopoulos S, 2017, An LES-PBE-PDF approach for modeling particle formation in turbulent reacting flows, Physics of Fluids, Vol: 29, ISSN: 1070-6631
Many chemical and environmental processes involve the formation of a polydispersed particulate phase in a turbulent carrier flow. Frequently, the immersed particles are characterized by an intrinsic property such as the particle size, and the distribution of this property across a sample population is taken as an indicator for the quality of the particulate product or its environmental impact. In the present article, we propose a comprehensive model and an efficient numerical solution scheme for predicting the evolution of the property distribution associated with a polydispersed particulate phase forming in a turbulent reacting flow. Here, the particulate phase is described in terms of the particle number density whose evolution in both physical and particle property space is governed by the population balance equation (PBE). Based on the concept of large eddy simulation (LES), we augment the existing LES-transported probability density function (PDF) approach for fluid phase scalars by the particle number density and obtain a modeled evolution equation for the filtered PDF associated with the instantaneous fluid composition and particle property distribution. This LES-PBE-PDF approach allows us to predict the LES-filtered fluid composition and particle property distribution at each spatial location and point in time without any restriction on the chemical or particle formation kinetics. In view of a numerical solution, we apply the method of Eulerian stochastic fields, invoking an explicit adaptive grid technique in order to discretize the stochastic field equation for the number density in particle property space. In this way, sharp moving features of the particle property distribution can be accurately resolved at a significantly reduced computational cost. As a test case, we consider the condensation of an aerosol in a developed turbulent mixing layer. Our investigation not only demonstrates the predictive capabilities of the LES-PBE-PDF model but also indicate
Koniavitis P, Rigopoulos S, Jones WP, 2017, A methodology for derivation of RCCE-reduced mechanisms via CSP, Combustion and Flame, Vol: 183, Pages: 126-143, ISSN: 0010-2180
The development of reduced chemical mechanisms in a systematic way has emerged as a potential solution to the problem of incorporating the increasingly large chemical mechanisms into turbulent combustion CFD codes. In this work, a methodology is proposed for developing reduced mechanisms with Rate-Controlled Constrained Equilibrium (RCCE) via a Computational Singular Perturbation (CSP) analysis of counterflow non-premixed flamelets. An ordering of species for variable strain rates is derived by integrating over mixture fraction space a modified CSP pointer that depends on the timescale and mass fraction of each chemical species. Subsequently, a global set of kinetically controlled species is identified from weighting the local ordering for each strain rate. RCCE simulations with the derived reduced mechanisms for methane with 16 species and for propane with 27 species are compared with the integration of the detailed mechanisms GRI 1.2 and USC-Mech-II respectively. The applicability of the methodology is demonstrated in non-premixed flames for several strain rates, in non-premixed flames ignited with a pilot in order to test the dynamics and ignition of the reduced schemes, in premixed flames for different equivalence ratios and subsequently in perfectly stirred reactors for ignition delay times for varying temperature, pressure and equivalence ratio. Overall very good agreement is obtained, indicating that the methodology can produce reliable mechanisms for different fuels and for a wide range of conditions, including dynamical behaviour and conditions different from those employed for the derivation of the mechanism.
Sewerin F, Rigopoulos S, 2017, An explicit adaptive grid approach for the numerical solution of the population balance equation, Chemical Engineering Science, Vol: 168, Pages: 250-270, ISSN: 0009-2509
Many engineering applications, such as the formation of soot in hydrocarbon combustion or the precipitation of nanoparticles from aqueous solutions, encompass a polydispersed particulate phase that is immersed in a reacting carrier flow. From a Eulerian perspective, the evolution of the particulate phase both in physical and in particle property space can be described by the population balance equation (PBE). In this article, we present an explicit solution-adaptive numerical scheme for discretizing the spatially inhomogeneous and unsteady PBE along a one-dimensional particle property space. This scheme is based on a space and time dependent coordinate transformation which redistributes resolution in particle property space according to the shapes of recent solutions for the particle property distribution. In particular, the coordinate transformation is marched in time explicitly. In comparison to many existing moving or dynamic adaptive grid approaches, this has the advantage that the semi-discrete PBE does not need to be solved in conjunction with an additional system governing the movement of nodes in particle property space.By design, our adaptive grid technique is able to accurately capture sharp features such as peaks or near-discontinuities, while maintaining the semi-discrete system size and adhering to a uniform fixed grid discretization in transformed particle property space. This is particularly advantageous if the PBE is combined with a spatially and temporally fully resolved flow model and a standard Eulerian solution scheme is applied in physical space. In order to accommodate localized source terms and to control the grid stretching, we develop a robust scheme for modifying the coordinate transformation such that constraints on the resolution in physical particle property space are obeyed.As an example, we consider the precipitation of BaSO4 particles from an aqueous solution in a plug flow reactor. Our findings demonstrate that for a given accuracy o
Garcia Gonzalez CE, Sewerin F, Liu A, et al., 2017, Predicting and measuring soot formation and particle size distributions in a laminar diffusion flame, European Combustion Meeting 2017, Publisher: The Combustion Institute
We present the results from a joint experimental and modelling investigation of a laminar diffusion flame on a Santoroburner. The experimental techniques include laser diagnostic measurements and extractive thermophoretic sampling.In order to predict the spatial evolution of the primary soot particle size distribution throughout the flame, we employa detailed population balance model. From the model predictions, “modelled” laser diagnostic signals are obtainedwhich we directly compare with the experimental laser diagnostic images. This allows us to assess the validity ofthe model with reduced uncertainty by reducing the set of assumptions commonly made when recovering physicalmagnitudes from experimental signals.
Akridis P, Rigopoulos S, 2016, Modelling of soot formation in laminar diffusion flames using a comprehensive CFD-PBE model with detailed gas-phase chemistry, Combustion Theory and Modelling, Vol: 21, Pages: 35-48, ISSN: 1741-3559
A discretised population balance equation (PBE) is coupled with an in-house computational fluid dynamics (CFD) code in order to model soot formation in laminar diffusion flames. The unsteady Navier–Stokes, species and enthalpy transport equations and the spatially-distributed discretised PBE for the soot particles are solved in a coupled manner, together with comprehensive gas-phase chemistry and an optically thin radiation model, thus yielding the complete particle size distribution of the soot particles. Nucleation, surface growth and oxidation are incorporated into the PBE using an acetylene-based soot model. The potential of the proposed methodology is investigated by comparing with experimental results from the Santoro jet burner [Santoro, Semerjian and Dobbins, Soot particle measurements in diffusion flames, Combustion and Flame, Vol. 51 (1983), pp. 203–218; Santoro, Yeh, Horvath and Semerjian, The transport and growth of soot particles in laminar diffusion flames, Combustion Science and Technology, Vol. 53 (1987), pp. 89–115] for three laminar axisymmetric non-premixed ethylene flames: a non-smoking, an incipient smoking and a smoking flame. Overall, good agreement is observed between the numerical and the experimental results.
Elbahloul S, Rigopoulos S, 2015, Rate-Controlled Constrained Equilibrium (RCCE) simulations of turbulent partially premixed flames (Sandia D/E/F) and comparison with detailed chemistry, Combustion and Flame, Vol: 162, Pages: 2256-2271, ISSN: 1556-2921
This paper investigates the potential of the RCCE mechanism reduction approach for modelling turbulent flames within the framework of transported PDF methods. For this purpose, PDF simulations are performed with an RCCE-reduced mechanism via direct integration of the RCCE ODEs, without any tabulation, and comparison is made with both the experimental results and those from a PDF simulation with direct integration of the detailed mechanism. The flames simulated are the Sandia flames D/E/F and the simulations are carried out with a RANS approach and a Lagrangian particle method for solving the transported joint-scalar PDF equation. The detailed mechanism is the well known GRI 3.0 CH4 combustion mechanism. The turbulence closure employed is the k–ε model, while the micromixing closure in the PDF transport equation is the Interaction with the Mean (IEM) model. The RCCE-reduced mechanism incorporates 18 constraints, selected from the original 53 species based on laminar flamelet simulations. Excellent agreement was observed between the RCCE simulations and direct integration, indicating that the reduced mechanism can reproduce very well the features of the full mechanism. Agreement with experimental results is also very good, given the turbulence and mixing models employed.
Sewerin F, Rigopoulos S, 2015, A methodology for the integration of stiff chemical kinetics on GPUs, COMBUSTION AND FLAME, Vol: 162, Pages: 1375-1394, ISSN: 0010-2180
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- Citations: 17
Akridis P, Rigopoulos S, 2015, Modelling of soot formation in a laminar coflow non-premixed flame with a detailed CFD-Population Balance model, 7th World Congress on Particle Technology (WCPT), Publisher: ELSEVIER SCIENCE BV, Pages: 1274-1283, ISSN: 1877-7058
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- Citations: 3
Sewerin F, Rigopoulos SR, 2014, Integration of stiff chemical kinetics on a CPU-GPU pair - Application to a turbulent, non-premixed flame, Ninth Mediterranean Combustion Symposium
Chatzopoulos AK, Rigopoulos S, 2013, A chemistry tabulation approach via Rate-Controlled Constrained Equilibrium (RCCE) and Artificial Neural Networks (ANNs), with application to turbulent non-premixed CH4/H-2/N-2 flames, PROCEEDINGS OF THE COMBUSTION INSTITUTE, Vol: 34, Pages: 1465-1473, ISSN: 1540-7489
Navarro-Martinez S, Rigopoulos S, 2011, Differential Diffusion modelling in LES with RCCE-reduced chemistry
Navarro-Martinez S, Rigopoulos S, 2011, Large Eddy Simulation of a Turbulent Lifted Flame using Conditional Moment Closure and Rate-Controlled Constrained Equilibrium, FLOW TURBULENCE AND COMBUSTION, Vol: 87, Pages: 407-423, ISSN: 1386-6184
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- Citations: 16
Di Veroli GY, Rigopoulos S, 2011, Modeling of aerosol formation in a turbulent jet with the transported population balance equation-probability density function approach, PHYSICS OF FLUIDS, Vol: 23, ISSN: 1070-6631
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- Citations: 21
Lovas T, Navarro-Martinez S, Rigopoulos S, 2011, On adaptively reduced chemistry in large eddy simulations, PROCEEDINGS OF THE COMBUSTION INSTITUTE, Vol: 33, Pages: 1339-1346, ISSN: 1540-7489
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- Citations: 18
Rigopoulos S, 2010, Population balance modelling of polydispersed particles in reactive flows, Progress in Energy and Combustion Science, Vol: 36, Pages: 412-443, ISSN: 1873-216X
Polydispersed particles in reactive flows is a wide subject area encompassing a range of dispersed flows with particles, droplets or bubbles that are created, transported and possibly interact within a reactive flow environment - typical examples include soot formation, aerosols, precipitation and spray combustion. One way to treat such problems is to employ as a starting point the Newtonian equations of motion written in a Lagrangian framework for each individual particle and either solve them directly or derive probabilistic equations for the particle positions (in the case of turbulent flow). Another way is inherently statistical and begins by postulating a distribution of particles over the distributed properties, as well as space and time, the transport equation for this distribution being the core of this approach. This transport equation, usually referred to as population balance equation (PBE) or general dynamic equation (GDE), was initially developed and investigated mainly in the context of spatially homogeneous systems. In the recent years, a growth of research activity has seen this approach being applied to a variety of flow problems such as sooting flames and turbulent precipitation, but significant issues regarding its appropriate coupling with CFD pertain, especially in the case of turbulent flow. The objective of this review is to examine this body of research from a unified perspective, the potential and limits of the PBE approach to flow problems, its links with Lagrangian and multi-fluid approaches and the numerical methods employed for its solution. Particular emphasis is given to turbulent flows, where the extension of the PBE approach is met with challenging issues. Finally, applications including reactive precipitation, soot formation, nanoparticle synthesis, sprays, bubbles and coal burning are being reviewed from the PBE perspective. It is shown that population balance methods have been applied to these fields in varying degrees of detail
di Veroli G, Rigopoulos S, 2010, Modeling of Turbulent Precipitation: A Transported Population Balance-PDF Method, AICHE JOURNAL, Vol: 56, Pages: 878-892, ISSN: 0001-1541
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- Citations: 32
Rigopoulos S, Lovas T, 2009, A LOI-RCCE methodology for reducing chemical kinetics, with application to laminar premixed flames, PROCEEDINGS OF THE COMBUSTION INSTITUTE, Vol: 32, Pages: 569-576, ISSN: 1540-7489
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- Citations: 28
Di Veroli G, Rigopoulos S, 2009, A study of turbulence-chemistry interaction in reactive precipitation via a population balance - transported PDF method, 6th International Symposium on Turbulence, Heat and Mass Transfer, Publisher: BEGELL HOUSE, INC, Pages: 749-752
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- Citations: 3
Rigopoulos S, 2007, PDF method for population balance in turbulent reactive flow, CHEMICAL ENGINEERING SCIENCE, Vol: 62, Pages: 6865-6878, ISSN: 0009-2509
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- Citations: 45
Rigopoulos S, 2007, The rate-controlled constrained equilibrium (RCCE) method for reducing chemical kinetics in systems with time-scale separation, INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING, Vol: 5, Pages: 11-18, ISSN: 1543-1649
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- Citations: 9
Jones WP, Rigopoulos S, 2007, Reduced chemistry for hydrogen and methanol premixed flames via RCCE, COMBUSTION THEORY AND MODELLING, Vol: 11, Pages: 755-780, ISSN: 1364-7830
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- Citations: 32
Rigopoulos S, 2006, Reduced flame kinetics via rate-controlled constrained equilibrium, 6th International Conference on Computational Science (ICCS 2006), Publisher: SPRINGER-VERLAG BERLIN, Pages: 18-25, ISSN: 0302-9743
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- Citations: 1
Jones WP, Rigopoulos S, 2005, Rate-controlled constrained equilibrium: Formulation and application to nonpremixed laminar flames, COMBUSTION AND FLAME, Vol: 142, Pages: 223-234, ISSN: 0010-2180
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- Citations: 57
Jones A, Rigopoulos S, Zauner R, 2005, Crystallization and precipitation engineering, 14th European Symposium on Computer Aided Process Engineering (ESCAPE-14), Publisher: PERGAMON-ELSEVIER SCIENCE LTD, Pages: 1159-1166, ISSN: 0098-1354
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- Citations: 30
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