Validation of Soot Formation and Oxidation models for a Kerosene Flame

Transcription

1 Validation o Soot Formation and Oxidation models or a Kerosene Flame F.Maniscalco 1, A. D Anna 1, P. Di Martino 2, G. Cinque 2, S. Colantuoni 2 1. Dipartimento di Ingegneria Chimica - Università Federico II, Napoli - ITALY 2. Avio Group, Pomigliano D Arco, Napoli ITALY 1. Introduction Aircrat Engine Emissions have been an environmental issue since the 197s. Concerns about the local eects on the air quality during LTO operations on the ground as well as about the global eects on climate change and on the ozone layer at altitude, have given rise to stringent regulatory requirements with respect to engine design and environmental perormance. Many research programmes on the subject have been set-up to tackle these issues through the development o a cleaner and proven aircrat propulsion technology. In this ramework, CFD numerical codes are gaining ever more importance as a tool that can be used to veriy the results o costly test measurements and even to predict them, i the code is reliable enough. The present paper is an illustration o the ongoing work on the development o such a numerical code, the AVIO in-house code Body3D. The ocus is on the implementation o a soot ormation model that is required to be ully coupled with the radiative balance equation in order to give simultaneous computation o the temperature and soot concentration ields. The tasks undertaken have included the critical evaluation o the available soot models in the literature, their implementation into the code and the identiication o suitable test-cases. The irst phase o the work has been ocused on the validation o the dierent embodiments o the code against the experimental data o a turbulent sooting non-premixed air/kerosene Jet-lame, the Cranield lame. The promising results obtained in this case have encouraged the passage to a subsequent phase that is currently underway: in this subsequent phase simulations o an industrial scale combustion chamber are perormed to asses the possibility o expand the range o application to more complicated geometries and low structures. The inal target is the set-up o a reliable calculating tool, capable o estimate the amount o soot ormed within an aircrat combustor and the related emission level. 2. Non-premixed sooting lames modelling strategies The presence o carbon particles in hydrocarbon lames is the result o two competitive processes: production and oxidation. Production occurs starting rom pyrolysis products generates by cracking o uel at high temperature (greater than 14 K) and poor oxygen conditions; successively these high molecular mass species may orm incipient particles by small nuclei condensation [1]. Those particles are subsequently subject to growing processes by two main mechanisms: surace growth, that proceeds by heterogeneous reactions o pyrolytic compounds on particle surace active sites, and coagulation, that involves coalescent collisions o particles, decreasing the number o particles without changing total particulate mass. Oxidation comprises surace reactions that reduce the mass and size o the particles; it takes place in regions o suiciently high temperature (greater then 11 K), where there is a signiicant concentration o oxidizing agents. The modelling o such processes or a turbulent non-premixed lame by means o a CFD code is a complex task; it entails the interplay o many dierent computational models in order to take into account the principal lame phenomena, such as convection, turbulent diusion, gas V-4, 1

2 31st Meeting on Combustion chemical kinetics, turbulent-chemistry interaction and radiation. The two principal eatures that connect soot model with the other component models are the nature o gas species associated with soot and the type o coupling with the energy balance equations. In act, computation o soot source terms requires the speciication o precursor and oxidizer concentrations in the gas phase. Soot models can dier with respect to the chemical nature o precursor gas species so that the associated gas kinetics scheme has to include the appropriate reaction network to carry out concentration computations. Moreover, soot into the lame can signiicantly modiy the radiative balance, because o its strong radiation emissions. Consequently, it can aect temperature distribution within the combustion apparatus, especially in the case o highly sooting uels, such as kerosene. Thus, a model approach able to perorm simultaneous predictions o temperature and soot concentration ields is highly desirable, especially in the case o kerosene burning aircrat applications. Two soot models have been taken into consideration in order to be implemented in the code Body3D: the Lund model [2], which is based on a detailed description o the gas phase reaction network, and the Cranield model [3], which, on the contrary, is based on a simpliied description o the soot ormation chemistry. Both o them have been developed with the aim o extend lamelet approach to sooting lames. In this case, soot will not be treated like other gas molecular species, since it exhibits a dierent behaviour with respect to the time scales o the mass diusion and the chemical reaction processes [4]. The models outlined overcome this limitation by plotting the soot source term proiles in the mixture raction space instead o the soot concentration proile and employing a balance equation or each soot parameter involved. The Lund model assume only one parameter to describe soot evolution: the soot volume raction (SVF), that is the volume-weighted irst order moment o the size distribution, so that it adds only one balance equation to the equations system. The dependence o the source terms on the detailed kinetics scheme is embedded in a lamelet library and their computation can be obtained by means o an appropriate subroutine by eeding the values o a certain number o input parameters, such as the inlet uel temperature, the inlet oxidizer temperature, the inlet pressure, the local mean mixture raction, the local mixture raction variance, the local mean scalar dissipation rate. The Cranield model employs two parameters in order to describe soot evolution: the soot volume raction and the soot number density (SND), that is the zero order moment o the size distribution. As a consequence it entails the addition o two balance equations. In this approach the source terms are calculated by means o semi-empirical expressions that speciy the unctional dependence on the soot controlling parameters: the local temperature, the local molar raction o precursor and oxidizer species and the local density. The model was originally developed to be used within a lamelet computational procedure: at irst, source term distributions are evaluated in the mixture raction space; subsequently they are multiplied by the presumed probability density unction and inally the product is integrated over the whole space. The main drawback o these computational methods is that they perorm only a partial coupling o the radiative equation with the soot balance equations, since the soot source terms are evaluated by means o a temperature-mixture raction relationship, that does not take into account the inluence o soot radiation on the temperature ield. In order to overcome this limitation typical o simplest lamelet approaches, dierent strategies have been proposed: multi-lamelet approach [3] is based on the extension o the lamelet library to include a radiation loss correction term. During the development work undertaken by our group a novel strategy has emerged, that is to employ the relation scheme provided by the Cranield model in a non-lamelet context: temperature, density and molar raction present in the semi-empirical expressions are taken equal to their mean values. This V-4, 2

3 Italian Section o the Combustion Institute represents a loss o accuracy since turbulence-chemistry interaction eects are not taken into account in this manner, and, in relation to this item, the computation constitutes a zero order approximation. To obtain a higher order approximation, a direct approach has been tested, eaturing the series expansion o the exponential Arrhenius terms present in the kinetics expression o the soot source terms. This approach consents to achieve the ully coupling between radiative and soot equation The details o the mathematical model implemented and the simulation results obtained or this particular embodiment o the code will be the subject o the ollowing sections. 3. Mathematical model Body3D is a CFD code tailored to perorm stationary RANS computations, o subsonic, twophase, reactive laminar or turbulent lows, within 3D geometry combustion chambers, employing body-itted structured meshes. The liquid phase is described in orm o an atomized spray o spherical droplets by means o balance equations that are treated in a Lagrangian ramework. The gas phase is described in an Eulerian ramework by means o a inite volume approach: balance equations are written in the density-weighted (Favre) ormalism, better suited or the description o compressible low. The turbulent lows are treated by means o the standard k-epsilon model; wall unctions in the near wall regions were used. Turbulent combustion is modelled by means o a two step inite rate reaction employing an Eddy Dissipation Model (EDM) approach. Radiation is taken into account by using a sixlux model with a sub-model o the gray-body type. The Cranield model solves two equations: one or the number o particles by unit mass o the gas ( n ), that is a scaled orm o soot number density, and one or the soot mass raction ( ). The evolution o these variables is described by two classical scalar balance equations, where the source terms are speciied by the ollowing expression: dρφ dt n dt dρφ 2 = α βρ φ = δ + 2 n 2 1/ 3 1/ 3 2 / 3 ( 36πN ρ s ) ργφn φ where N is the Avogadro number and s is the soot density. The parameters are expressed by the ollowing relations: α = C α β = C T γ = C ρx γ β δ = C α δ 2 ρ X FU FU T T exp( T exp( T γ where XFU is the molar concentration o the parent-uel that is assumed as a precursor in nucleation step and as the growing gas molecule in surace growing step. The values assigned to the constants appearing those expressions are reported in the ollowing table: α / T ) / T ) C/m 3 kg -2 K -1/2 s -1 C/m 3 K -1/2 s -1 C/mK -1/2 s -1 C/kgkmol -1 T/K T/K 6. x14 1.x (1) (2) V-4, 3

4 31st Meeting on Combustion In addition to the ormation model an oxidation model must be assumed: instead o the classical Nagle and Strickland-Constable model, here a more eicient model has been assumed proposed by Leung and co-workers [7], with the ollowing ormulation: w ox 4 = 1 T ρy exp( 1968 / T ) W It implicitly assumes that molecular oxygen is the only oxidizer. An extra source term must be added to the balance equation o soot mass raction: O2 O2 (3) dρφ dt ox = 2 1/ 3 1/ 3 2 / 3 ( 36πN ρ s ) ρwoxφn φ (4) 4. Validation test-case The validation work is based on a set o measurements perormed on a conined co-lowing kerosene/air jet lame coniguration [5]. The turbulent lame is contained within a borosilicate glass tube o 155 mm diameter and 6 mm length. The burner is comprised o a 1.5 mm diameter cylindrical nozzle, surrounded by a coaxial annulus,.25mm wide, on which is burnt a laminar premixed lames to rim stabilize the turbulent kerosene jet lame. The kerosene uel is pre-vaporised in a small resistively-heated pre-camber, maintained at a temperature o 9 K. The dataset provided comprise measurement executed or three scalar variables: mean temperature, mean soot volume raction, mean mixture raction. The measurements have been taken along the axis, until about 45 mm rom the mouth o the burner (axial proiles), and along our axial stations, at 1mm, 15mm, 21mm and 4mm (radial proiles).the CFD computational domain is a 2-degree circular wedge with symmetry conditions on its two sides. Grid employed was o dimensions 122x42x12, respectively in the axial, radial and angular direction; axial and radial directions ollow a logarithmic growth. The number o live cells, whereby low computations are executed, is about Results and Discussion Results are presented in table I, where radial proiles are reported or temperature and soot volume raction in the irst three measurement stations (1mm, 15mm, 21mm). For reasons o clarity, only two comparisons between simulations and experimental data are here reported. That one indicated with the name (in blue) illustrates the results o the computation executed with the proposed soot model coupled with the standard component model o the Body3D. As can be seen radial temperature proiles are not very ar rom experimental data with respect to the peak position and the order o magnitude is well captured. However, it seems that the amplitudes o the predicted proiles are too large and predicted temperature gradients are too gentle. The mean SVF proiles, are also in a good agreement with experimental data with respect to order o magnitude and peak position, but exhibit a marked dispersion o soot burning zone, related to a gentler gradient. Thus it seems possible to suppose that there is a signiicant correlation between temperature gradient and soot gradient. Looking or the reason o this gentler gradient, our group may have probably ound a possible explication [6]. The standard k-epsilon model implemented with the usual value o its and applied to round-jet lows constants give rise to an over-prediction o turbulent diusion and consequently the scalar gradients are decreased. The suggestion is given to decrease the value o the constant C2e in order to increase the dissipation rate o turbulent kinetic energy and decrease the turbulent viscosity [6]; smaller diusions should V-4, 4

5 Italian Section o the Combustion Institute lead to a sharper gradient. Following this suggestion, the value o the C2e has been changed rom 1.92 to1.65 and the result o the related simulation are outlined in the red proiles, named. As can be seen in Fig. 1 temperature gradient are sharp and strictly ollow the experimental data. SVF proiles also are subject to a better itting o the experimental data, which is both quantitative and qualitative. This results show that the approach undertaken is very promising, since i the low ield is suiciently accurately modelled, it is able to predict soot and temperature ields with suicient accuracy. 6. Conclusion A novel strategy to tackle the non-premixing sooting lame modelling has been proposed, which is based on the semi-empirical Cranield model, applied in a non-lamelet context. Although the soot kinetic scheme is quite simple, assuming the parent-uel as the soot precursor, the predictions obtained can be considered suiciently accurate. This indicates that, at least in cases such as the one examined, turbulence eects play a major role than kinetic scheme. A model o this kind is very interesting in view o the application to the CFD simulations o complex combustion equipment, since it is not very CPU-expensive. 7. Reerences 1. Glassman I.: Proceedings o The Combustion Institute, 22:295(1988). 2. Bai, X., Balthasar, M., Mauss, F., and Fuchs, L.: Proceedings o The Combustion Institute, 27:1623(1998). 3. Young, K. and Moss, J.: Combust. Sci. Technol. 15(1):33 (1995) 4. Kent, J. and Honnery, D.: Combust. Sci. Technol. 54(1):383 (1987) 5. Young, K., Stewart, C., Syed, K., and Moss, J.: Tenth International Symposium on Air Breathing Engines, Nottingham, England, p. 239 (1991). 6. Coelho, P., Farias, T., Pereira, J., and Carvalho,: AGARD, Fuels and Combustion Technology or Advanced Aircrat Engines 16 p( N ). (1993) 7. Leung, K., Lindstedt, R., and Jones, W.: Combust. Flame 87(3-4):289 (1991) V-4, 5

6 31st Meeting on Combustion Mean Temperature / C X=1 mm T_expe Mean Soot Volume Fractionx1 7 X=1 mm sv_expe Mean Temperature / C X=15 mm T_expe Mean Soot Volume Fraction x 1 7 X=15 mm sv_expe X=21 mm X=21 mm sv_expe Mean Temperature / C T_expe Mean Soot Volume Fraction x Fig.1 : Comparison between experimental data (dots) and numerical predictions (lines) or mean temperature mean soot volume raction radial proiles at dierent heights above the burner. Blue lines: simulation n 1, without turbulent diusion correction. Red lines: simulation n 2, with turbulent diusion correction V-4, 6