Direct numerical simulation of turbulence/radiation interaction in premixed combustion systems

An important fundamental issue in chemically reacting turbulent flows is turbulence/radiation interaction (TRI); TRI arises from highly nonlinear coupling between temperature and composition fluctuations. Here, a photon Monte Carlo method for the solution of the radiative transfer equation has been integrated into a turbulent combustion direct numerical simulation (DNS) code. DNS has been used to investigate TRI in a canonical configuration with systematic variations in optical thickness. The formulation allows for nongray gas properties, scattering, and general boundary treatments, although in this study, attention has been limited to gray radiation properties, no scattering, and black boundaries. Individual contributions to emission and absorption TRI have been isolated and quantified. Of particular interest are intermediate values of optical thickness where, for example, the smallest hydrodynamic and chemical scales are optically thin while the largest turbulence scales approach an optically thick behavior. In the configuration investigated, the temperature self-correlation contribution (emission) is primarily a function of the ratio of burned-gas temperature to unburned-gas temperature, and is the dominant contribution to TRI only in the optically thin limit. Even in the most optically thin case considered, the absorption coefficient–Planck function correlation and absorption coefficient–intensity correlation are not negligible. At intermediate values of optical thickness, contributions from all three correlations are significant.     

Three-angle scattering/extinction versus TEM measurements on soot in premixed ethylene/air flame

In this work, a three-angle scattering and extinction technique has been applied in order to study soot formation and growth in a rich ethylene/air premixed flame (Φ=2.34). The Rayleigh–Debye–Gans theory together with the fractal-like approach has been applied to derive soot parameters, in terms of volume concentration and morphology. A mathematical procedure is presented to obtain the radius of gyration by considering scattering signals collected at two supplementary angles. TEM measurements, carried out at different locations on the flame axis, are used to derive some parameters, such as fractal prefactor, fractal dimension and size distribution, to be entered in the mathematical treatment of optical data. The radius of gyration and the primary particle size as obtained by TEM and by optical measurements are compared. Good agreement has been found in the upper part of the flame investigated. Discrepancies observed low in the flame are discussed.     

Structural design of four-component optically compensated zoom lenses: Use of evolutionary programming

A new approach for ‘ab initio’ synthesis of thin lens structure of optically compensated zoom lenses is reported. This is accomplished by an implementation of evolutionary programming that explores the available configuration space formed by powers of individual components and inter-component separations to obtain globally or quasiglobally optimum solutions for the problem. Normalization of the variables is carried out to get an insight on the optimum structures. The method has been successfully used to get thin lens structures of optically compensated zoom lens systems by suitable formulation of merit function of optimization. Investigations have been carried out on four-component zoom lens structures. Illustrative numerical results are presented.     

On the dependence of the laser-induced incandescence (LII) signal on soot volume fraction for variations in particle size

“The laser-induced incandescence (LII) signal is proportional to soot volume fraction” is an often used statement in scientific papers, and it has – within experimental uncertainties – been validated in comparisons with other diagnostic techniques in several investigations. In 1984 it was shown theoretically in a paper by Melton that there is a deviation from this statement in that the presence of larger particles leads to some overestimation of soot volume fractions. In the present paper we present a detailed theoretical investigation of how the soot particle size influences the relationship between LII signal and soot volume fraction for different experimental conditions. Several parameters have been varied; detection wavelength, time and delay of detection gate, ambient gas temperature and pressure, laser fluence, level of aggregation and spatial profile. Based on these results we are able, firstly, to understand how experimental conditions should be chosen in order to minimize the errors introduced when assuming a linear dependence between the signal and volume fraction and secondly, to obtain knowledge on how to use this information to obtain more accurate soot volume fraction data if the particle size is known. PACS 42.62.-b; 44.40.+a; 61.46.Df; 78.70.-g; 65.80.+n     

Determination of temperature profiles from optically thick lines

A method for the evaluation of high-pressure discharge temperature profiles is proposed, which is based on a numerical solution of the radiative transfer equation. The measured quantities that have to be provided for the numerical evaluation are readily obtainable because only the absolute side-on intensity of a spectral line as a function of the lateral coordinate has to be measured. The method has been applied to several optically thick mercury lines. A comparison with temperatures obtained from optically thin lines shows good agreement. This method has the following two advantages: (i) temperature determination is possible in cases where no optically thin line is available, (ii) using optically thick lines of transitions with low excited states (e.g., resonance lines), the temperature profile can be determined for larger radii than from optically thin lines.     

Multi-diagnostic soot measurements in a laminar diffusion flame to assess the ISF database consistency

Control of soot emission raises fundamental issues and has important practical implications requiring a full understanding of soot production and oxidation processes. The research reported in the present paper intends to contribute to the studies carried out within the frame of the International Sooting Flame workshop (ISF) on laminar sooting flames. The objective is to identify and quantify sources of experimental errors and to extend the existing database for the Yale laminar diffusion burner flame. This will especially enable more comprehensive comparisons among different experimental techniques and numerical simulations. To this end, a combined use of Modulated Absorption/Emission (MAE) and Laser Induced Incandescence (LII) techniques is presented in this work. Results are compared with already existing experimental data in terms of soot volume fraction, soot temperature and primary particle size distribution, highlighting the high variability of the experimental data depending on the measurement techniques as well as the underlying assumptions and post-processing methods. These complementary original data may serve to guide the validation of numerical modeling in this configuration.     

Simulations of sooting turbulent jet flames using a hybrid flamelet/stochastic Eulerian field method

The stochastic Eulerian field method is applied to simulate 12 turbulent C₁?C₃ hydrocarbon jet diffusion flames covering a wide range of Reynolds numbers and fuel sooting propensities. The joint scalar probability density function (PDF) is a function of the mixture fraction, enthalpy defect, scalar dissipation rate and representative soot properties. Soot production is modelled by a semi-empirical acetylene/benzene-based soot model. Spectral gas and soot radiation is modelled using a wide-band correlated-k model. Emission turbulent radiation interactions (TRIs) are taken into account by means of the PDF method, whereas absorption TRIs are modelled using the optically thin fluctuation approximation. Model predictions are found to be in reasonable agreement with experimental data in terms of flame structure, soot quantities and radiative loss. Mean soot volume fractions are predicted within a factor of two of the experiments whereas radiant fractions and peaks of wall radiative fluxes are within 20%. The study also aims to assess approximate radiative models, namely the optically thin approximation (OTA) and grey medium approximation. These approximations affect significantly the radiative loss and should be avoided if accurate predictions of the radiative flux are desired. At atmospheric pressure, the relative errors that they produced on the peaks of temperature and soot volume fraction are within both experimental and model uncertainties. However, these discrepancies are found to increase with pressure, suggesting that spectral models describing properly the self-absorption should be considered at over-atmospheric pressure.     

Numerical investigation of heat transfer augmentation through geometrical optimization of vortex generators

In this paper a two-dimensional numerical simulation of a steady incompressible and turbulent model has been carried out to study the effects of vortex generators in a compact heat exchanger in a curvilinear coordinate system. The mesh which is applied in this study is boundary fitted and has been smoothed by a Laplace operator. Experimental data of a former study has been applied to validate the numerical results. The effects of geometrical variation are studied by adjusting vortex generators’ inclination and relative cross location. The major issue of this study is the optimal trade-off by selecting an optimal geometric, considering the opposite influences of geometrical variation on Nusselt number and pressure drop.     

Simulation of pumping beams self focusing and defocusing in NH3 Raman laser

High power IR pumping beams self focusing and defocusing in NH₃ Raman laser is investigated by numerical methods on the basis of the solution of nonlinear quasioptical equations. The analysis of self focusing have been done for a wide range of parameters of radiation and of active medium. Spatial evolution of the beam configuration have been investigated for different regimes of nonlinear diffraction. Developed model enables to allow exactly for the spectroscopic features of active molecules and may be applied to the analysis of the properties of powerful optically pumped FIR lasers.     

Investigations of soot formation in an optically accessible gasoline direct injection engine by means of laser-induced incandescence (LII)

This study presents the results of laser-induced incandescence (LII) measurements in an optically accessible gasoline direct injection engine. The focus was to evaluate LII as a particle measurement technique which is able to provide a deeper understanding of the underlying reaction and formation processes of soot in order to optimize the injection system to reduce exhaust gas emissions. A comparison of time-resolved LII, based on the model described by Michelsen, with an Engine Exhaust Particle Sizer (EEPS) was performed. In this context, the air–fuel ratio, the injection pressure and the injection timing have been varied while applying the measurement techniques in the exhaust system. In case of a variation of the air–fuel ratio, two-dimensional LII has been performed in the combustion chamber additionally. For each measurement, the Filter Smoke Number (FSN) was taken into account as well. Finally, a good agreement of the different techniques was achieved. Moreover, we found that by combining time-resolved LII and EEPS a differentiation of primary particles and agglomerates is possible. Consequently, a determination of the processes in the combustion chamber and agglomeration in the exhaust gas is feasible.     

NUMERICAL MODELING OF OPTICALLY CONTROLLED DIELECTRIC REASONATORS

To analyze the optically controlled dielectric resonators accurately, an efficient numerical modelling technique is proposed in this paper. By using alternating-direction implicit finite-difference time-domain method and conformal technique, the resonant frequency of a dielectric resonator is calculated. In addition, an optical generation of plasma is used as a possible means of controlling the resonate frequency, and the effect that solid state plasmas have on the resonator’s frequency is described. The numerical results agree very well with measurements in estimation of the optically induced resonator’s frequency-shift.     

A Trefftz-based numerical modelling framework for Helmholtz problems with complex multiple-scatterer configurations

The aim of the work presented in this paper is the numerical solution of low- and mid-frequency time-harmonic acoustic multiple-scattering problem. A novel so-called ‘multi-level’ modelling approach is proposed which is applicable to the study of a configuration of well separated obstacles of arbitrary shape on which any type of acoustic boundary condition can be applied. The generic character of the method is obtained by embedding the superposition principle for the multiple-scattering influence in a state-of-the-art acoustic modelling technique, the so-called Wave Based Method. The resulting approach successfully alleviates the geometrical limitations of the underlying Trefftz-based method and preserves the method’s computational efficiency, resulting in a generic multiple-scattering modelling framework with a superior computational efficiency in the low- as well as the mid-frequency range. Several numerical validation examples show that the proposed approach is as accurate as the classical single-scattering Wave Based Method and illustrate the computational efficiency as compared to Boundary Element Methods.     

Relationship between soot volume fraction and LII signal in AC-LII: effect of primary soot particle diameter polydispersity

Theoretical analysis and numerical calculations were conducted to investigate the relationship between soot volume fraction and laser-induced incandescence (LII) signal within the context of the auto-compensating LII technique. The emphasis of this study lies in the effect of primary soot particle diameter polydispersity. The LII model was solved for a wide range of primary soot particle diameters from 2 to 80 nm. For a log-normally distributed soot particle ensemble encountered in a typical laminar diffusion flame at atmospheric pressure, the LII signals at 400 and 780 nm were calculated. To quantify the effects of sublimation and differential conduction cooling on the determined soot volume fraction in auto-compensating LII, two new quantities were introduced and demonstrated to be useful in LII study: an emission intensity distribution function and a scaled soot volume fraction. When the laser fluence is sufficiently low to avoid soot mass loss due to sublimation, accurate soot volume fraction can be obtained as long as the LII signals are detected within the first 200 ns after the onset of the laser pulse. When the laser fluence is in the high fluence regime to induce significant sublimation, however, the LII signals should be detected as early as possible even before the laser pulse reaches its peak when the laser fluence is sufficiently high. The analysis method is shown to be useful to provide guidance for soot volume fraction measurements using the auto-compensating LII technique.     

An efficient finite volume method for electric field–space charge coupled problems

The goal of this paper is to introduce some recently developed finite volume schemes to enable numerical simulation of electric field–space charge coupled problems. The key features of this methodology are the possibility of handling problems with complex geometries and accurately capturing the charge density distribution. The total variation diminishing (TVD) scheme and the improved deferred correction (IDC) scheme are used to compute the convective and diffusive fluxes respectively. Our technique is firstly verified with the computation of hydrostatic solutions in a two coaxial cylinders configuration. The homogeneous and autonomous injection from the inner or outer electrode is considered. Comparison has been made with the analytical solution. The numerical technique is also applied to the problem of corona discharge in a blade-plane configuration. The good agreement between our numerical solution and the one obtained with a combination approach of Finite Element Method (FEM) and Method of Characteristics (MoC) is shown.     

A predictor–corrector algorithm for the coupling of stiff ODEs to a particle population balance

In this paper a novel predictor–corrector algorithm is presented for the solution of coupled gas-phase – particulate systems. The emphasis of this work is the study of soot formation, but the concepts can be applied to other systems. This algorithm couples a stiff ODE solver to a Monte Carlo population balance solver. Such coupling has been achieved previously for similar systems using a Strang operator splitting algorithm, however, that algorithm demonstrated several numerical issues which resulted in a high computational cost to acquire adequate precision. In particular a source-sink instability was identified whereby a large-magnitude source term present in the ODE system was competing with a similarly sized sink term in the population balance. This instability required that the splitting step size was very small in order to keep numerical error sufficiently low. A predictor–corrector algorithm has been formulated to negate this instability. An additional efficiency is gained with this algorithm as a principal computational cost of the Strang splitting algorithm is removed: the requirement to re-initialise the ODE solver every splitting step. The numerical convergence of the new algorithm is demonstrated, and its efficiency is compared to that of the Strang splitting algorithm. Substantial computation time savings are demonstrated, which allow a fixed error in three studied system functionals to be achieved with an order-of-magnitude reduction in computation time.     

On applying the extended intrinsic mean spin tensor to modelling the turbulence in non-inertial frames of reference

Modelling the turbulent flows in non-inertial frames of reference has long been a challenging task. Recently we introduced the notion of the “extended intrinsic mean spin tensor” for turbulence modelling and pointed out that, when applying the Reynolds stress models developed in the inertial frame of reference to modelling the turbulence in a non-inertial frame of reference, the mean spin tensor should be replaced by the extended intrinsic mean spin tensor to correctly account for the rotation effects induced by the non-inertial frame of reference, to conform in physics with the Reynolds stress transport equation. To exemplify the approach, we conducted numerical simulations of the fully developed turbulent channel flow in a rotating frame of reference by employing four non-linear K-ε models. Our numerical results based on this approach at a wide range of Reynolds and Rossby numbers evince that, among the models tested, the non-linear K-ε model of Huang and Ma and the non-linear K-ε model of Craft, Launder and Suga can better capture the rotation effects and the resulting influence on the structures of turbulence, and therefore are satisfactorily applied to dealing with the turbulent flows of practical interest in engineering. The general approach worked out in this paper is also applied to the second-moment closure and the large-eddy simulation of turbulence.     

Modelling nongrey gas-phase and soot radiation in luminous turbulent nonpremixed jet flames

Much progress has been made in radiative heat transfer modelling with respect to the treatment of nongrey radiation from both gas-phase species and soot particles, while radiation modelling in turbulent flame simulations is still in its infancy. Aiming at reducing this gap, this paper introduces state-of-the-art models of gas-phase and soot radiation to turbulent flame simulations. The full-spectrum k-distribution method (M.F. Modest, 2003, Journal of Quantitative Spectroscopy & Radiative Transfer, 76, 69–83) is implemented into a three-dimensional unstructured computational fluid dynamics (CFD) code for nongrey radiation modelling. The mixture full-spectrum k-distributions including nongrey absorbing soot particles are constructed from a narrow-band k-distribution database created for individual gas-phase species, and an efficient scheme is employed for their construction in CFD simulations. A detailed reaction mechanism including NO _x and soot kinetics is used to predict flame structure, and a detailed soot model using a method of moments is employed to determine soot particle size distributions. A spherical harmonic P₁ approximation is invoked to solve the radiative transfer equation. An oxygen-enriched, turbulent, nonpremixed jet flame is simulated, which features large concentrations of gas-phase radiating species and soot particles. Nongrey soot modelling is shown to be of greater importance than nongrey gas modelling in sooty flame simulations, with grey soot models producing large errors. The nongrey treatment of soot strongly influences flame temperatures in the upstream and the flame-tip region and is essential for accurate predictions of NO. The nongrey treatment of gases, however, weakly influences upstream flame temperatures and, therefore, has only a small effect on NO predictions. The effect of nongrey soot radiation on flame temperature is also substantial in downstream regions where the soot concentration is small. Limitations of the P₁ approximation are discussed for the jet flame configuration; the P₁ approximation yields large errors in the spatial distribution of the computed radiative heat flux for highly anisotropic radiation fields such as those in flames with localized, near-opaque soot regions.     

Modeling nongray gas-phase and soot radiation in luminous turbulent nonpremixed jet flames

Much progress has been made in radiative heat transfer modeling with respect to treatment of nongray radiation from both gas-phase species and soot particles, while radiation modeling in turbulent flame simulations is still in its infancy. Aiming at reducing this gap, this paper introduces state-of-the-art models of gas-phase and soot radiation to turbulent flame simulations. The full-spectrum k-distribution method (Modest, M.F., 2003, Journal of Quantitative Spectroscopy & Radiative Transfer, 76, 69–83) is implemented into a three-dimensional unstructured CFD code for nongray radiation modeling. The mixture full-spectrum k-distributions including nongray absorbing soot particles are constructed from a narrow-band k-distribution database created for individual gas-phase species, and an efficient scheme is employed for their construction in CFD simulations. A detailed reaction mechanism including NO _x and soot kinetics is used to predict flame structure, and a detailed soot model using a method of moments is employed to determine soot particle size distributions. A spherical-harmonic P₁ approximation is invoked to solve the radiative transfer equation. An oxygen-enriched, turbulent, nonpremixed jet flame is simulated, which features large concentrations of gas-phase radiating species and soot particles. Nongray soot modeling is shown to be of greater importance than nongray gas modeling in sooty flame simulations, with gray soot models producing large errors. The nongray treatment of soot strongly influences flame temperatures in the upstream and the flame-tip region and is essential for accurate predictions of NO. The nongray treatment of gases, however, weakly influences upstream flame temperatures and, therefore, has only a small effect on NO predictions. The effect of nongray soot radiation on flame temperature is also substantial in downstream regions where the soot concentration is small. Limitations of the P₁ approximation are discussed for the jet flame configuration; the P₁ approximation yields large errors in the spatial distribution of the computed radiative heat flux for highly anisotropic radiation fields such as those in flames with localized, near-opaque soot regions.     

Assessment of LES of intermittent soot production in an aero-engine model combustor using high-speed measurements

Soot production in turbulent flames is an extremely intermittent phenomenon since it is the result of specific thermochemical conditions occasionally occurring in space and time. In realistic configurations such as the swirling flames used in gas-turbines, the presence of large-scale flow motions can additionally affect soot formation processes, leading to even more pronounced intermittency. Classically, the validation of numerical simulations is performed by comparing time-averaged results with experimental data of the phenomenon under investigation. This comparison can be considered as rigorous only if a statistically converged numerical representation is obtained. In case of sporadic events such as intermittent soot formation in turbulent flames, this means to perform the simulation over thousands of milliseconds of physical time, which can have extremely high CPU demands when performing Large Eddy Simulation (LES). In this work, a possible strategy to overcome this issue is proposed based on the use of high-speed measurements and numerically synthesized signals from LES. To illustrate the approach, numerical and experimental soot light scattering signals are considered here by looking at the model aero-engine combustor developed at DLR for the study of pressurized swirled sooting flames. The light scattering signal is numerically synthesized from an LES. Experimental high-speed measurements are used to statistically account for the high temporal and spatial variability of soot when considering time intervals similar to what is today achievable with LES. The feasibility of this approach is finally demonstrated by comparing numerical results to the ensemble of possible soot production states observed experimentally in the DLR burner allowing to eventually validate the present LES results.     

Soot visualisation by use of laser-induced soot vapourisation in combination with polarisation spectroscopy

A novel approach to the visualisation of soot is presented. It relies on a combination of laser-induced soot vapourisation and consecutive polarisation spectroscopy. Upon soot vapourisation, molecular fragments (for example, C₂) emerge, and may serve as effective tracers for soot. In this study we demonstrate that saturated polarisation spectroscopy on photo-induced C₂ can be exploited for soot detection. Signal maps featuring high signal-to-noise ratios were readily recorded in ethyne-rich flames and any spurious background, for example, caused by Rayleigh scattering, was successfully suppressed by means of spatial filtering. Additionally, investigations were carried out addressing how the attained signals correlate with local soot volumne fractions. For this purpose, height profiles of C₂ number densities inferred from the polarisation spectroscopy signal maps were compared with profiles of the soot volumne fraction inferred from measurements with laser-induced incandescence. For low soot volumne fractions, the shapes of the height profiles from our approach agree rather well with the latter; they do not agree for higher soot volumne fractions. Further investigation is required to resolve this discrepancy. Scattering from particles in the Mie scattering range may hamper the application of this approach, and avenues are suggested for extending the applicability of the approach presented to large soot particles. PACS 42.62.Fi; 82.80.Dx