Imperial College London

Dr Stelios Rigopoulos

Faculty of EngineeringDepartment of Mechanical Engineering

Reader in Thermofluids
 
 
 
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Contact

 

+44 (0)20 7594 7108s.rigopoulos

 
 
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Location

 

620City and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
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59 results found

OSullivan D, Rigopoulos S, 2022, A conservative finite volume method for the population balance equation with aggregation, fragmentation, nucleation and growth, Chemical Engineering Science, Vol: 263, ISSN: 0009-2509

In the present paper, we present a method for solving the population balance equation (PBE) with the complete range of kinetic processes included: namely aggregation, fragmentation, nucleation and growth. The method is based on the finite volume scheme and features guaranteed conservation of the first moment by construction, accurate prediction of the size distribution, applicability to an arbitrary non-uniform grid, robustness and computational efficiency which is instrumental for coupling with computational fluid dynamics (CFD). The treatment of aggregation is based on the previous work by Liu and Rigopoulos (2019). An analysis of the aggregation terms in the PBE is made, and the source of conservation error in finite element/volume methods is elucidated. It is subsequently shown how this error is overcome in the present method via a coordinate transformation applied to the aggregation birth double integral resulting from the application of the finite volume method. The contributions to the birth term are delineated and their corresponding death fluxes identified. An aggregation map is then constructed for mapping birth and death fluxes, thus allowing the finite volume method to operate in terms of fluxes and achieve conservation of mass. The method is then extended to fragmentation, for which a map is also constructed to represent the birth and death fluxes. In the implementation, the aggregation and fragmentation maps are pre-tabulated to allow fast computation. It is also shown how the method can be coupled with a total variation diminishing (TVD) scheme for the treatment of growth with minimal numerical diffusion. The method is validated with a number of test cases including analytical solutions and numerical solutions of the discrete PBE for aggregation (theoretical and free molecule/Brownian kernels), fragmentation, aggregation-fragmentation and aggregation-growth. In all cases, the method produces very accurate results, while also being computationally effi

Journal article

Tang HY, Rigopoulos S, Papadakis G, 2022, On the interaction of turbulence with nucleation and growth in reaction crystallisation, Journal of Fluid Mechanics, Vol: 944, ISSN: 0022-1120

The objective of this work is to investigate the interaction of turbulence with the nonlinear processes of particle nucleation and growth that occur in reaction crystallisation, also known as precipitation. A validated methodology for coupling the population balance equation with direct numerical simulation of turbulent flows is employed for simulating an experiment conducted by Schwarzer <jats:italic>et al.</jats:italic> (<jats:italic>Chem. Engng Sci.</jats:italic>, vol. 61, no. 1, 2006, pp. 167–181), where barium sulphate nanoparticles are formed by mixing and reaction of barium chloride and sulphate acid in a T-mixer, with the spatial resolution resolved down to the Kolmogorov scale. A unity Schmidt number is assumed, since at present it is not possible to resolve the Batchelor scale for realistic Schmidt numbers (order of 1000 or more). The probability density function, filtered averages and spatial distribution of time and length scales are all examined in order to shed light on the interplay of turbulence and precipitation. Separate Damköhler numbers are defined for nucleation and growth and both are found to be close to unity, indicating that the process is neither mixing nor kinetics controlled. The nucleation length scales are also evaluated and compared with the Kolmogorov scale to show the importance of resolving nucleation bursts. In addition, zones of different rate-determining mechanisms are identified. The ultimate aim of precipitation is to obtain control over the product particle size distribution, and the present study elucidates the synergistic or competing roles of mixing, nucleation and growth on the process outcome and discusses the implications for modelling.

Journal article

Sun B, Rigopoulos S, 2022, Modelling of soot formation and aggregation in turbulent flows with the LES-PBE-PDF approach and a conservative sectional method, Combustion and Flame, Vol: 242, Pages: 1-19, ISSN: 0010-2180

The present paper presents a comprehensive approach for modelling soot formation in turbulent flows that incorporates a recently developed conservative finite volume sectional method for the solution of the population balance equation (PBE) into the Large Eddy Simulation - Probability Density Function (LES-PDF) framework for modelling turbulent reacting flows. The approach thus predicts the particle size distribution of soot and accounts for the complete set of aerosol dynamic processes (nucleation, surface growth, oxidation, condensation and aggregation) as well as for the interaction between turbulence, chemistry and soot. We employ a combination of gas-phase chemistry, soot kinetics and aerosol dynamics recently used by the authors in the context of a laminar co-flow diffusion flame and maintain the same kinetics without adjustments in order to focus on the modelling issues in turbulent sooting flame simulations. The results show that several features such as the location of the soot forming zones and the qualitative profiles of soot volume fraction and species concentrations can be predicted reasonably well, but there is a considerable underprediction in the magnitude of soot volume fraction. The possible reasons for this underprediction are discussed in the context of the aforementioned laminar flame simulation and the previous validation of the components of our methodology. The CPU time analysis shows that the solution of the PBE by the conservative sectional method and the associated transport of the discretised number densities account for less than 25% of the total CPU time, indicating that its incorporation in LES-PDF simulations of turbulent combustion is computationally feasible.

Journal article

Liu A, Gao Z, Rigopoulos S, Luo KH, Zhu Let al., 2022, Modelling of laminar diffusion flames with biodiesel blends and soot formation, Fuel, Vol: 317, Pages: 1-18, ISSN: 0016-2361

Modelling of soot formation and oxidation of biodiesel fuels is a challenge, due to the complexity of the chemical reactions and soot formation pathways. In this paper, the discretised population balance approach and a PAH-HACA based detailed soot model have been coupled with an in-house CFD code to simulate a laminar diffusion flame with blends of different components of oxygenated biodiesel fuel, and employed to predict combustion performance and soot formation. The simulation aims to reproduce a target experiment which investigated the effects of dibutyl ether (DBE) addition to the biodiesel surrogate (methyl decanoate, MD) by increasing the mole fraction of DBE from 0 to 40%. A combined and reduced MD–DBE–PAH mechanism developed from three sub-mechanism branches has been employed in the simulation. The simulation results show that temperature rises as the DBE percentage increases to 40%. The swallow-tail shape of the soot occurrence zone and the quantity of soot production are correctly predicted. Regarding the effect of soot suppression, the model has basically captured the reducing tendency of soot formation in the measurements as the DBE addition increases from 0% to 40%. Concentrations of PAHs and C3 species contributing to the formation of aromatic rings are slightly reduced due to the addition of DBE, which is a leading cause of soot suppression. However, on the whole, the numerical solution featured much smaller differences than those observed in the experiment among laminar flames with different MD/DBE ratios, because the combined MD–DBE–PAH mechanism only present a slight difference of concentrations of soot precursor species.

Journal article

Liu A, Luo KH, Rigopoulos S, Jones Wet al., 2022, Effects of the electric field on soot formation in combustion: a coupled charged particle PBE-CFD framework, Combustion and Flame, Vol: 239, ISSN: 0010-2180

In this article, a coupled PBE-CFD framework has been proposed to study counterflow non-premixed flames and soot formation under an external electric field. This framework integrates the population balance equation (PBE) for nanoparticle dynamics into an in-house CFD solver for the multicomponent reactive flows. Different electric properties have been considered in this model. An ion mechanism used in both fuel-rich and fuel-lean combustion is combined with a detailed chemistry for neutral gaseous species and small-size aromatics to retain the full chemistry. In order to model soot particles carrying charges and the movement of the reacting fluid medium in the electric field, a second PBE for the production and transport of charges on soot particles is introduced for the first time and incorporated into the original PBE for the number density of particles. Also, the electric force for the gas mixture is included in the momentum equations. The electric drift velocities for ions and soot particles are also considered in the transport equations of ions and the PBE of soot particles, respectively. The simulations have shown that the presence of the electric field modifies the stagnation plane of the counterflow flames and reduces the soot formation in both rich-fuel and lean-fuel conditions in agreement with experimental observations. The application of the soot particle charging model, accompanied by a proper electric correction factor on the nanoparticle processes of nucleation and surface growth, significantly improves the stability of the flame structure. The introduction of the electric correction factor reveals that the suppression of soot formation in an electric field is mainly caused by the inhibited chemical reactions of the PAH nucleation and particle surface growth, which is more important than the electric drift of the charged particles. Reducing the critical size of the particle charging process enhances the electric drift of nascent soot, thus lessening i

Journal article

Schlander R, Rigopoulos S, Papadakis G, 2022, Analysis of wall mass transfer in a turbulent pipe flow combining extended POD and FIK identity, Physical Review Fluids, Vol: 7, ISSN: 2469-990X

We combine extended proper orthogonal decomposition (EPOD) together with the Fukagata-Iwamoto-Kasagi (FIK) identity to quantify the role of individual coherent structures on the wall mass transfer in a turbulent pipe flow. Direct numerical simulation at a Reynolds number of 5300 (based on bulk velocity) is performed with the passive scalar released at the pipe inlet. The proper orthogonal decomposition (POD) eigenvalues show that the scalar field can be described by a more compact set of modes compared to the velocity field, and that these modes are skewed towards higher azimuthal wave numbers. POD modes for the scalar and EPOD modes for the velocity are visualized in the cross-stream plane to infer the capacity of each mode to transport scalar to and from the wall. A form of the FIK identity is derived for the wall mass transfer coefficient (Sherwood number, Sh) and employed to separate the contributions of the mean and fluctuating velocity and scalar fields. The FIK decomposition shows that the turbulent velocity/scalar correlations account for up to 65.8% of the total Sh. The contribution of each POD and EPOD mode to the Sh number is also computed; it is found that, using azimuthal wave numbers m=1–15 and POD modes n=1–10, it is possible to reconstruct 49% of the turbulent component of Sh, with the velocity modes containing only 31% of the turbulent kinetic energy. Quadrant analysis shows that these modes are related to ejection and sweep events near the wall, with the ejection events dominating.

Journal article

Tsagkaridis M, Rigopoulos S, Papadakis G, 2022, Analysis of turbulent coagulation in a jet with discretised population balance and DNS, Journal of Fluid Mechanics, Vol: 937, Pages: 1-31, ISSN: 0022-1120

The objective of the present study is to investigate turbulence-coagulation interaction via direct numerical simulation (DNS) coupled with the population balance equation (PBE). Coagulation is an important process in several environmental and engineering applications involving turbulent flow, including soot formation, gas-phase synthesis of nanoparticles and atmospheric processes, but its interaction with turbulence is not yet fully understood. Particle dynamics can be described by the PBE, whose Reynolds de-composition leads to unclosed terms involving correlations of number density fluctuations. In this work, we employ a discretisation (sectional) method for the solution of the PBE, which is free of a priori assumptions regarding the particle size distribution (PSD), and couple it with a DNS for the flow field in order to study the behaviour and significance of the unknown correlations. At present, it is not feasible to resolve the Batchelor scales thatresult from diffusion at high Schmidt number, hence a unity Schmidt number is employed. The investigation is conducted on a three-dimensional planar jet laden with monodisperse nanoparticles, and coagulation in the free-molecule regime is considered. The correlations due to turbulent fluctuations of the particle number density are calculated at several points in the domain and found to be positive in most cases, except close to the jet break-up. The transport equation for the moments of the PSD is also studied, and itis found that the correlations make a considerable contribution to the time-averaged coagulation source term, up to 20% on the jet centreline and 40% close to the edges.

Journal article

Tian B, Liu A, Chong CT, Fan L, Ni S, Hull A, Hull A, Rigopoulos S, Luo KH, Hochgreb Set al., 2021, Measurement and simulation of sooting characteristics by an ATJ-SKA biojet fuel and blends with Jet A-1 fuel in laminar non-premixed flames, Combustion and Flame, Vol: 233, Pages: 1-15, ISSN: 0010-2180

We investigate the sooting propensity of an Alcohol-to-Jet-Synthetic Kerosene with Aromatics (ATJ-SKA) biojet fuel. The soot volume fraction and primary particle size in the pre-vaporised diffusion flames using ATJ-SKA biojet and blends with Jet A-1 at atmospheric conditions were measured experimentally and compared to numerical simulations. The measurements were conducted using extinction calibrated laser induced incandescence (LII). The soot volume fractions measured using the ATJ-SKA fuel do not show significant differences relative to measurements with Jet A-1. A comparison of the chemical composition of the fuels suggests that the Degree of Unsaturation (DoU) may not determine the sooting propensity of biojet fuels. The SEM analysis shows that diffusion flames using neat Jet A-1 produce finer soot particles and larger number density compared to the biojet and biojet surrogate. The soot model employs a semi-detailed chemical kinetic mechanism and a physical model which integrates the population balance equation governing the soot particle size distribution with an in-house reactive flow solver for multicomponent ideal gases. The model predicts the maximum soot volume fraction (SVFm) in the neat biojet case and the blended cases with Jet A-1 fuels within an error margin of 13% of the measured values. However, the predicted soot volume fraction distribution patterns differ from the measured one and the possible causes are discussed.

Journal article

Papadakis G, Rigopoulos S, Mikhaylov K, 2021, Reconstruction of large scale flow structures in a stirred tank from limited sensor data, AIChE Journal, Vol: 67, Pages: 1-16, ISSN: 0001-1541

We combine reduced order modelling and system identification to reconstruct the temporal evolution of large scale vortical structures behind the blades of a Rushton impeller. We performed Direct Numerical Simulations at Reynolds number 600 and employed proper orthogonal decomposition (POD) to extract the dominant modes and their temporal coefficients. We then applied the identification algorithm, N4SID, to construct an estimator that captures the relation between the velocity signals at sensor points (input) and the POD coefficients (output). We show that the first pair of modes can be very well reconstructed using the velocity time signal from even a single sensor point. A larger number of points improves accuracy and robustness, and also leads to better reconstruction for the second pair of POD modes. Application of the estimator derived at Re=600 to the flows at Re=500 and 700, shows that it is robust with respect to changes in operating conditions.

Journal article

Ding T, Readshaw T, Rigopoulos S, Jones WPet al., 2021, Machine learning tabulation of thermochemistry in turbulent combustion: An approach based on hybrid flamelet/random data and multiple multilayer perceptrons, Combustion and Flame, Vol: 231, Pages: 1-23, ISSN: 0010-2180

A new machine learning methodology is proposed for speeding up thermochemistry computations in simulations of turbulent combustion. The approach is suited to a range of methods including Direct Numerical Simulation (DNS), Probability Density Function (PDF) methods, unsteady flamelet, Conditional Moment Closure (CMC), Multiple Mapping Closure (MMC), Linear Eddy Model (LEM), Thickened Flame Model, the Partially Stirred Reactor (PaSR) method (as in OpenFOAM) and the computation of laminar flames. In these methods, the chemical source term must be evaluated at every time step, and is often the most expensive element of a simulation. The proposed methodology has two main objectives: to offer enhanced capacity for generalisation and to improve the accuracy of the ANN prediction. To accomplish the first objective, we propose a hybrid flamelet/random data (HFRD) method for generating the training set. The random element endows the resulting ANNs with increased capacity for generalisation. Regarding the second objective, a multiple multilayer perceptron (MMP) approach is developed where different multilayer perceptrons (MLPs) are trained to predict states that result in smaller or larger composition changes, as these states feature different dynamics. It is shown that the multiple MLP method can greatly reduce the prediction error, especially for states yielding small composition changes. The approach is used to simulate flamelets of varying strain rates, one-dimensional premixed flames with differential diffusion and varying equivalence ratio, and finally the Large Eddy Simulation (LES) of /air piloted flames Sandia D, E and F, which feature different levels of local extinction. The simulation results show very good agreement with those obtained from direct integration, while the range of problems simulated indicates that the approach has great capacity for generalisation. Finally, a speed-up ratio of 12 is attained for the reaction step.

Journal article

Sun B, Rigopoulos S, Liu A, 2021, Modelling of soot coalescence and aggregation with a two-population balance equation model and a conservative finite volume method, Combustion and Flame, Vol: 229, Pages: 1-19, ISSN: 0010-2180

The objective of the present paper is to develop a population balance approach for modelling soot formation that distinguishes between coalescence and aggregation and accounts for finite-rate fusing of primary particles within aggregates, while providing a numerically accurate description of primary particle surface growth and oxidation within aggregates. To this end, the recently developed conservative finite volume sectional method for the solution of the population balance equation (PBE) due to Liu and Rigopoulos (2019, Combust. Flame 205, 506–521) is extended to a two-PBE approach that allows for a more accurate modelling of primary particle surface growth and oxidation and furthermore involves a timescale for the fusing of primary particles. The accuracy of the numerical method is first tested by calculating the self-preserving distributions of aggregates with varying fractal dimension. Subsequently, the one-PBE and two-PBE approaches are coupled with CFD and applied to the simulation of the Santoro laminar non-premixed co-flow sooting flame. The results show that both approaches can provide good prediction of the soot volume fraction, but the two-PBE approach yields a significant improvement in the prediction of soot morphology. At present, the information available for modelling the gradual fusing of soot primary particles is based on experiments on silica and titania nanoparticles, and therefore a comprehensive study of the impact of the sintering model parameters is conducted. Finally, conclusions are drawn regarding the predictive potential of the one-PBE and two-PBE approaches.

Journal article

Readshaw T, Ding T, Rigopoulos S, Jones WPet al., 2021, Modeling of turbulent flames with the large eddy simulation–probability density function (LES–PDF) approach, stochastic fields, and artificial neural networks, Physics of Fluids, Vol: 33, Pages: 1-17, ISSN: 1070-6631

This work proposes a chemical mechanism tabulation method using artificial neural networks (ANNs) for turbulent combustion simulations. The method is employed here in the context of the Large-Eddy Simulation (LES)–Probability Density Function (PDF) approach and the method of stochastic fields for numerical solution, but can also be employed in other methods featuring real-time integration of chemical kinetics. The focus of the paper is on exploring an ANN architecture aiming at improved generalization, which uses a single multilayer perceptron (MLP) for each species over the entire training dataset. This method is shown to outperform previous approaches which take advantage of specialization by clustering the composition space using the Self-Organizing Map (SOM). The ANN training data are generated using the canonical combustion problem of igniting/extinguishing one-dimensional laminar flamelets with a detailed methane combustion mechanism, before being augmented with randomly generated data to produce a hybrid random/flamelet dataset with improved composition space coverage. The ANNs generated in this study are applied to the LES of a turbulent non-premixed CH4/air flame, Sydney flame L. The transported PDF approach is used for reaction source term closure, while numerical solution is obtained using the method of stochastic fields. Very good agreement is observed between direct integration (DI) and the ANNs, meaning that the ANNs can successfully replace the integration of chemical kinetics. The time taken for the reaction source computation is reduced 18-fold, which means that LES–PDF simulations with comprehensive mechanisms can be performed on modest computing resources.

Journal article

Ma C, Zou X, Li A, Li H, Rigopoulos S, Zhu L, Zhen Het al., 2021, Evolution of MoO3 nanobelts and nanoplatelets formation with flame synthesis, Proceedings of the Combustion Institute, Vol: 38, Pages: 1289-1297, ISSN: 0082-0784

A co-flow premixed flat flame is applied to form MoO3 nanobelts and nanoplatelets in the gas phase. An experimental study is conducted with a thermophoretic sampling particle diagnostic (TSPD) technique to reconstruct the evolution of nanostructure formation. In order to investigate the growth mechanism of the nanobelts and nanoplatelets, samples were directly taken along the centerline at different positions in the flame to represent the essential morphological variations of material. Based on the sample information collected by TEM, a growth mechanism of nanobelts and nanoplatelets is proposed. The results indicate that nanobelts and nanoplatelets with well-defined structure are successfully synthesized in premixed flame. The precursor temperature has a significant impact on the morphology by affecting the vapor concentration in the flame. For synthetic nanobelts,the intermediate particles tend to grow along a specific direction with small surface energy, and the final morphology is determined by particle attachment. In contrast, the initial growth of the nanoplatelets is mainly characterized by vapor surface deposition/growth, and the formation of the final morphology relies on the coalescence of large particles and small particles.

Journal article

Cheng X, Gao Z, Ren F, Rigopoulos S, Zhu L, Huang Zet al., 2021, Experimental and kinetic modeling study on sooting tendencies of alkylbenzene isomers, Fuel, Vol: 283, ISSN: 0016-2361

Alkylbenzenes are major aromatic constituents of real transportation fuels and important surrogate components. In this study, 4 kinds of C8H10 and 8 kinds of C9H12 alkylbenzenes were tested in a laminar diffusion flame to investigate the influence of chemical structure on sooting tendency. The laser induced incandescence (LII) technique was applied to obtain the 2D distribution of soot volume fraction for calculating the yield sooting index (YSI) of test fuels. The processes of fuel oxidation and soot formation were simulated by a detailed chemical kinetic mechanism. The mechanism includes all C8H10 and C9H12 alkylbenzenes and includes species ranging from reactant to carbon particle. The simulation results of defined YSI were in good agreement with the experimental values. A database of sooting tendencies was established by experimental data, which shows that the number of substituents is positively correlated with the sooting tendency and that the sooting tendency of meta-substituent species is higher than other isomers. Through the analysis of reaction pathway and sensitivity, it was found that the main production pathway of A4 (pyrene) is via alkylbenzenes combination reactions at the early stage of combustion. The experimental database presented in this study is systematic and comprehensive for C8H10 and C9H12 alkylbenzenes, and is thus expected to be useful for soot model development and validation.

Journal article

Tian B, Liu AX, Chong CT, Fan L, Ni S, Ng J-H, Rigopoulos S, Luo KH, Hochgreb Set al., 2021, Experimental and numerical study on soot formation in laminar diffusion flames of biodiesels and methyl esters, Proceedings of the Combustion Institute, Vol: 38, Pages: 1335-1344, ISSN: 1540-7489

Biodiesel and blends with petroleum diesel are promising renewable alternative fuels for engines. In the present study, the soot concentration generated from four biodiesels, two pure methyl esters, and their blends with petroleum diesel are measured in a series of fully pre-vapourised co-flow diffusion flames. The experimental measurements are conducted using planar laser induced-incandescence (LII) and laser extinction optical methods. The results show that the maximum local soot volume fractions of neat biodiesels are 24.4% - 41.2% of pure diesel, whereas the mean soot volume fraction of neat biodiesel cases was measured as 11.3% - 21.3% of pure diesel. The addition of biodiesel to diesel not only reduces the number of inception particles, but also inhibits their surface growth. The discretised population balance modelling of a complete set of soot processes is employed to compute the 2D soot volume fraction and size distribution across the tested flames. The results show that the model also demonstrates a reduction of both soot volume fraction and primary particle size by adding biodiesel fuels. However, it is not possible to clearly determine which factors are responsible for the reduction from the comparison alone. Moreover, analysis of the discrepancies between numerical and experimental results for diesel and low-blending cases offers an insight for the refinement of soot formation modelling of combustion with large-molecule fuels.

Journal article

Tang HY, Rigopoulos S, Papadakis G, 2020, A methodology for coupling DNS and discretised population balance for modelling turbulent precipitation, International Journal of Heat and Fluid Flow, Vol: 86, ISSN: 0142-727X

In this paper, we present a methodology for simulating nanoparticle formation in a turbulent flow by coupling Direct Numerical Simulation (DNS) and population balance modelling. The population balance equation (PBE) is solved via a discretisation method employing a composite grid that provides sufficient detail over the wide range of particle sizes reached during the precipitation process. The coupled DNS/PBE approach captures accurately the strong interaction between the dynamics of turbulent mixing and particle formation processes. It also allows the calculation of the particle size distribution (PSD) of the product and enables an investigation on how it is controlled by turbulent mixing. Finally, it provides the statistics of kinetic processes and their timescales so that further analysis can be performed. The methodology is applied to the simulation of experiments of hydrodynamics and nanoparticle precipitation in a T-mixer (Schwertfirm et al., 2007, Int. J. of Heat and Fluid Flow 28, pp. 1429-1442; Schwarzer et al., 2006, Chem.Eng. Sci. 61, pp. 167-181), and the agreement with the experimental results is very good.

Journal article

Liu A, Garcia CE, Sewerin F, Williams BAO, Rigopoulos Set al., 2020, Population balance modelling and laser diagnostic validation of soot particle evolution in laminar ethylene diffusion flames, Combustion and Flame, Vol: 221, Pages: 384-400, ISSN: 0010-2180

Laminar diffusion flames present an elementary configuration for investigating soot formation and validating kinetic models before these are transferred to turbulent combustors. In the present article, we present a joint experimental and modelling investigation of soot formation in a laminar co-flow burner. The diffusion flames are analysed with the aid of laser diagnostic techniques, including elastic light scattering (ELS), planar laser-induced fluorescence of OH (OH-PLIF) and line-of-sight attenuation (LOSA), to measure the spatial distribution of soot, gas phase species and the line-of-sight integrated soot volume fraction (ISVF), respectively. The experimental dataset is supplemented by location-specific TEM images of thermophoretically sampled soot particles. The simulation of the sooting flames is carried out with a recently developed discretisation method for the population balance equation (Liu and Rigopoulos, 2019, Combust. Flame 205, 506-521) that accomplishes an accurate prediction of the particle size distribution, coupled with an in-house CFD code. By minimising numerical errors, we ensure that the discrepancies on the modelling side are mainly due to kinetics and are able to carry out an investigation of alternative models. We include a complete set of soot kinetics for PAH-based nucleation and condensation, HACA-based surface growth and oxidation as well as size-dependent aggregation, and consider three different gas phase reaction mechanisms (ABF, BBP and KM2). Based on predictions of the gas phase composition and particle size distribution of soot, modelled counterparts of the laser diagnostic signals are computed and compared with the experimental measurements. The approach of directly predicting signals circumvents the difficulties of explicitly representing the OH concentration in terms of the measured OH-PLIF data and avoids using ‘hybrid’ modelled and measured values to approximate the OH concentration. Moreover, the LOSA signal is

Journal article

Rigopoulos S, 2019, Modelling of soot aerosol dynamics in turbulent flow, Flow, Turbulence and Combustion, Vol: 103, Pages: 565-604, ISSN: 1386-6184

Aerosol dynamics plays an important role in the modelling of soot formation in combustion processes, as it is responsible for predicting the distribution of size and shape of soot particles. The distribution is required for the correct prediction of the rates of surface processes, such as growth and oxidation, and furthermore it is important on its own because new regulations on particulate emissions require control of the number of smaller particles. Soot formation is strongly dependent on the local chemical composition and thermodynamic conditions and is therefore coupled with fluid dynamics, chemical kinetics and transport phenomena. Comprehensive modelling of soot formation in combustion processes requires coupling of the population balance equation, which is the fundamental equation governing aerosol dynamics, with the equations of fluid dynamics. The presence of turbulence poses an additional challenge, due to the non-linear interactions between fluctuating velocity, temperature, concentrations and soot properties. The purpose of this work is to review the progress made in aerosol dynamics models, their integration with fluid dynamics and the models for addressing the turbulence-soot interaction.

Journal article

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.

Conference paper

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).

Journal article

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.

Journal article

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

Journal article

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.

Journal article

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.

Journal article

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

Journal article

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.

Journal article

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

Journal article

Garcia Gonzalez CE, Sewerin F, Liu A, Rigopoulos S, Williams BAOet 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.

Conference paper

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.

Journal article

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.

Journal article

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