Michael Balthasar

A stochastic approach to calculate the particle size distribution function of soot particles in laminar premixed flames

We introduce an efficient stochastic approach to solve the population balance equation that describes the formation and oxidation of soot particles in a laminar premixed flame. The approach is based on a stochastic particle system representing the ensemble of soot particles. The processes contributing to the formation and oxidation of soot particles are treated in a probabilistic manner. The stochastic algorithm, which makes use of an efficient majorant kernel and the method of fictitious jumps, resolves the entire soot particle distribution (PSDF) without introducing additional closure assumptions. A fuel-rich laminar premixed acetylene flame is computed using a detailed kinetic soot model. Solutions are obtained for both, the stochastic approach and the method of moments combined with a modified version of the Premix, CHEMKIN code. In this manner, the accuracy of the method of moments in a laminar premixed flame simulation is investigated. It is found that the accuracy for the first moment is excellent (5% error), and mean error for rest of the moments is within 25%. Also the effect of the oxidation of the smallest particles (burnout) has been quantified but was found not to be important in the flame investigated. The time evolution of computed size distributions and their integral properties are compared to experimental measurements and the agreement was found to be satisfactory. Finally, the efficiency of the stochastic method is studied.

The Linear Process Deferment Algorithm: A new technique for solving population balance equations

In this paper a new stochastic algorithm for the solution of population balance equations is presented. The population balance equations have the form of extended Smoluchowski equations which include linear and source terms. The new algorithm, called the linear process deferment algorithm (LPDA), is used for solving a detailed model describing the formation of soot in premixed laminar flames. A measure theoretic formulation of a stochastic jump process is developed and the corresponding generator presented. The numerical properties of the algorithm are studied in detail and compared to the direct simulation algorithm and various splitting techniques. LPDA is designed for all kinds of population balance problems where nonlinear processes cannot be neglected but are dominated in rate by linear ones. In those cases the LPDA is seen to reduce run times for a population balance simulation by a factor of up to 1000 with a negligible loss of accuracy.

ANALYSIS OF A NATURAL GAS FUELLED HOMOGENEOUS CHARGE COMPRESSION IGNITION ENGINE WITH EXHAUST GAS RECIRCULATION USING A STOCHASTIC REACTOR MODEL

Abstract Combustion and emissions formation in a Volvo TD 100 series diesel engine running in a homogeneous charge compression ignition (HCCI) mode and fuelled with natural gas is simulated and compared with measurements for both with and without external exhaust gas recirculation (EGR). A new stochastic approach is introduced to model the convective heat transfer, which accounts for fluctuations and fluid-wall interaction effects. This model is included in a partially stirred plug flow reactor (PaSPFR) approach, a stochastic reactor model (SRM), and is applied to study the effect of EGR on pressure, autoignition timing and emissions of CO and unburned hydrocarbons (HCs). The model accounts for temperature inhomogeneities and includes a detailed chemical mechanism to simulate the chemical reactions within the combustion chamber. Turbulent mixing is described by the interaction by exchange with the mean (IEM) model. A Monte Carlo method with a second-order time-splitting technique is employed to obtain the numerical solution. The model is validated by comparing the simulated in-cylinder pressure history and emissions with measurements taken from Christensen and Johansson (SAE Paper 982454). Excellent agreement is obtained between the peak pressure, ignition timing and CO and HC emissions predicted by the model and those obtained from the measurements for the non-EGR, 38 per cent EGR and 47 per cent EGR cases. A comparison between the pressure profiles for the cases studied reveals that the ignition timing and the peak pressure are dependent on the EGR. With EGR, the peak pressure reduces and the autoignition is delayed. The trend observed in the measured emissions with varying EGR is also predicted correctly by the model.

Detailed Modeling of soot formation in a partially stirred plug flow reactor

The purpose of this work is to propose a detailed model for the formation of soot in turbulent reacting flow and to use this model to study a carbon black furnace. The model is based on a combination of a detailed reaction mechanism to calculate the gas phase chemistry, a detailed kinetic soot model based on the method of moments, and the joint composition probability density function (PDF) of these scalar quantities. Two problems, which arise when modeling the formation of soot in turbulent flows using a PDF approach, are studied. A consistency study of the combined scalar-soot moment approach reveals that the molecular diffusion term in the PDF-equation can be closed by the IEM and Curl-type mixing models. An investigation of different kernels for the collision frequency of soot particles shows that the influence of turbulence on particle coagulation is negligible for typical flame conditions and the particle size range considered. The model is used as a simple toot to simulate a furnace black process, which is the most important industrial process for the production of carbon blacks. Despite the simplifications in the modeling of the turbulent flow reasonable agreement between the calculated soot yield and data measured in an industrial furnace black reactor is achieved although no adjustments were made to the kinetic parameters of the soot model. The effect of the mixing intensity on soot yield and different soot formation rates is investigated. In addition the influence of different operating conditions such as temperature and equivalence ratio in the primary zone of the reactor is studied. (Less)

Detailed soot modeling in turbulent jet diffusion flames

An approach for modeling the interaction between the formation and oxidation of soot, the radiative heat loss, and the flowfield in turbulent jet diffusion flames is presented. These interactions are modeled by the flamelet library approach in the framework of prescribed probability density functions (PDFs). The formation and oxidation of soot is calculated from a detailed chemical soot model. The laminar flamelet concept is applied to model the rates of soot particle inception, soot volume dependent surface growth, and oxidation, as well as species and temperature fields, Radiative heat transfer from the soot particles and the gas-phase species, CO2 and H2O, decreases the peak flame temperature, which in turn influences the flamelet structures. Experiments from Young et al. on a turbulent ethylene diffusion flame are used to validate the modeling approach. The calculated fields of mean mixture fraction, temperature, and soot volume fraction are found to be in agreement with the experimental data. The spatially resolved rates of soot inception, surface growth, and oxidation are presented. The maximum rates of the surface independent production occur in the fuel-rich region at a radial position of about 10 mm. In contrast, the maximum rates of surface growth and oxidation are found on the centerline with the oxidation occurring at a higher location in the flame. The total rate has its maximum on the centerline, whereas soot formation and destruction balances on the slightly rich side near the stoichiometric contour. This shows the strong interaction of soot formation and oxidation in the flame. A sensitivity analysis of the calculated soot volume fraction on different model parameters is presented. The rate coefficient of the heterogeneous surface growth reaction is the most sensitive parameter. A 20% increase of this rate leads to a 65% increase of the calculated maximum soot volume fraction.

MODELING DIESEL SPRAY IGNITION USING DETAILED CHEMISTRY WITH A PROGRESS VARIABLE APPROACH

In this work, a progress variable approach is used to model diesel spray ignition with detailed chemistry. The flow field and the detailed chemistry are coupled using the flamelet assumption. A flamelet progress variable is transported by the computational fluid dynamics (CFD) code. The progress variable source term is obtained from an unsteady flamelet library that is evaluated in each grid cell. The progress variable chosen is based on sensible enthalpy. By using an unsteady flamelet library for the progress variable, the impact of local effects, for example variations in the turbulence field, effects of wall heat transfer etc. on the autoignition chemistry can be considered on a cell level. The coupling between the unsteady flamelet library and the transport equation for total enthalpy follows the ideas of the representative interactive flamelet (RIF) approach. The method can be compared to having an interactive flamelet in each computational cell in the CFD grid. The results obtained using the proposed model are compared to results obtained using the RIF model. Differences are exhibited during the autoignition process. After ignition, the results obtained using the proposed model and RIF are virtually identical. The model was used to study lift-off lengths in sprays as function of nozzle diameter and injection pressure. A good agreement between model predictions and experimental trends was found.

A computational study of the thermal ionization of soot particles and its effect on their growth in laminar premixed flames

The effect of thermal ionization on the growth of soot particles has been analyzed by detailed kinetic modeling of a low-pressure premixed acetylene flame. The detailed kinetic model considers the oxidation of fuel, the formation and growth of polycyclic aromatic hydrocarbons, and particle inception, coagulation, as well as mass growth via surface reactions. A numerical method has been developed, which considers the production of charged particles by thermal ionization as well as coagulation and surface reactions of these particles. The enhancement of coagulation by collisions between charged-charged and charged-neutral particles is rigorously accounted for in the numerical model. The particle size distribution functions for both neutral and charged particles were solved using the method of moments. The computed relative soot volume fractions for neutral and charged soot particles were compared to measurements and found to be in good agreement with them. The results show also that omitting of thermal ionization of soot particles does not lead to significant errors in the simulation of soot formation in the acetylene flame, as long as the nature of the surface reactions between charged particles and gaseous molecules remains the same as that for neutral particles. This result can be generalized to most laboratory laminar premixed and counterflow diffusion flames with flame temperatures not exceeding 2100 K.

Implementation and validation of a new soot model and application to aeroengine combustors

The modeling of soot formation and oxidation under industrially relevant conditions has made significant progress in recent years. Simplified models introducing a small number of transport equations into a CFD Code have been used with some success in research configurations simulating a reciprocating diesel engine. Soot formation and oxidation in the turbulent flow is calculated on the basis of a laminar flamelet library model. The gas phase reactions are modeled with a detailed mechanism for the combustion of heptane containing 89 species and 855 reactions developed by Frenklach and Warnatz and revised by Mauss. The soot model is divided into gas phase reactions. the growth of polycyclic aromatic hydrocarbons (PAH) and the processes of particle inception, heterogeneous face growth, oxidation, and condensation. The first two are modeled within the laminar flamelet chemistry, while the soot model deals with the soot particle processes. The time scales of soot formation are assumed to he much larger than the turbulent time scales. Therefore rates of soot formation are tabulated in the flamelet libraries rather than the soot volume fraction itself. The different rates of soot formation, e.g., particle inception, sinface growth, firagmentation, and oxidation, computed on the basis of a detailed soot model, are calculated in the dissipation rate space and further simplified by fitting them to simple analytical functions. A transport equation for the mean soot mass fraction is solved in the CFD code. The mean rate in this transport equation is closed with the help of presumed probability density functions for the mixture fraction and the scalar dissipation rate. Heat loss due to radiation can be taken into account by including a heat loss parameter it? the flamelet calculations describing the change of enthalpy due to radiation, but was not used for the results reported here. The soot model was integrated into an existing commercial CFD code is a post-processing module to existing combustion CFD flow fields and is very robust with high convergence rates. The model is validated with laboratory flame data and using a realistic three-dimensional BM V Rolls-Royce combustor configuration, where test data at high pressure are available. Good agreement between experiment and simulation is achieved for laboratory flames, whereas soot is overpredicted for the aeroengine combustor configuration by 1-2 orders of magnitude.

Modeling Diesel Engine Combustion With Detailed Chemistry Using a Progress Variable Approach

In this work, we present an unsteady flamelet progress variable approach for diesel engine CFD combustion modelling. The progress variable is based on sensible enthalpy integrated over the flamelet and describes the transient flamelet ignition process. By using an unsteady flamelet library for the progress variable, the impact of local effects, for example variations in the turbulence field, effects of wall heat transfer, etc., on the autoignition chemistry can be considered on a cell level. The coupling between the unsteady flamelet library and the transport equation for total enthalpy follows the ideas of the representative interactive flamelet approach. Since the progress variable gives a direct description of the state in the flamelet, the method can be compared to having a flamelet in each computational cell in the CFD grid. The progress variable approach is applied to high-EGR, late injection operating conditions, and we demonstrate that the model can be applied for 3D engine simulations. (Less)

Role of Late Soot Oxidation for Low Emission Combustion in a Diffusion-controlled, High-EGR, Heavy Duty Diesel Engine

Soot formation and oxidation are complex and competing processes during diesel combustion. The balance between the two processes and their history determines engine-out soot values. Besides the efforts to lower soot formation with measures to influence the flame lift-off distance for example or to use HCCI-combustion, enhancement of late soot oxidation is of equal importance for low-λ diffusion-controlled low emissions combustion with EGR. The purpose of this study is to investigate soot oxidation in a heavy duty diesel engine by statistical analysis of engine data and in-cylinder endoscopic high speed photography together with CFD simulations with a main focus on large scale in-cylinder gas motion. Results from CFD simulations using a detailed soot model were used to reveal details about the soot oxidation. A particular objective of the present study was to investigate the importance of enhancing soot oxidation after End of Injection (EOI) when temperature and NOx formation rapidly decreases. Geometrical measures to control flame propagation and different flame interactions were investigated. Such measures contribute to conserve available kinetic energy until late in the combustion period in an efficient way. Based on this combustion strategy it is possible to reach near zero engine-out soot emissions. Copyright