| OCR Text |
Show Detailed soot modeling in turbulent kerosene/air diffusion flame: Sensitivity analysis of models using moment of methods. Ishan Verma1*, Rakesh Yadav2, Pravin Nakod1 and Stefano Orsino2 1 ANSYS Inc, India ANSYS Inc, USA 2 Abstract: Soot formation is a complex physical process and its modeling is quite challenging. Its complexity gets multi-fold in turbulent flows due to highly coupled interactions of turbulence, chemistry, soot particulate dynamics and associated radiative heat transfer. In this work, a comprehensive study is done in modeling soot formation for a turbulent Kerosene-air flame. The current modeling approach consists of four major components namely soot chemistry modeling, soot dynamics, turbulent-chemistry interactions and radiative heat transfer. For each component, the state of art methodologies and tools are investigated and used. The gas phase chemistry is represented by detailed mechanism comprising of 475 species and 4000 elementary reaction steps. The mechanism involves formation of polycyclic aromatic hydrocarbons (PAH), used as precursor for the soot nucleation. The soot is modeled using methods of moments with interpolative closure, which allows the prediction of particle size distribution. The coupling of gas phase chemistry and turbulence is modeled using steady diffusion flamelet model. The radiation from gas and soot particles are modeled using finite volume approach with weighted sum of gray gas model for calculation of radiative properties. The combined modeling approach is computationally demanding, and hence, in the current framework, the modeling is done using two equation turbulence models. The current results are compared against experimental data from Young et al. (Proc Combust Inst 25(1):609-617, 1994). The current predictions are in excellent match with experiments and offers a practical solution to the soot modeling for industrial combustors. The current computations are performed for operating pressure of 1 atm to study and investigate the sensitivity of the current modeling approach. In an attempt to optimize the current modeling method, a sensitivity analysis and parametric investigation is carried out for different modeling components like the number of moments, the soot nucleation precursors and effect of sootradiation interactions. Based on the current parametric investigation, an optimal solution strategy is proposed which allows high fidelity soot modeling in industrial application in an efficient manner. Keywords: kerosene flame, Soot, Radiation, Aggregation, Method of moment Introduction potent threat to environment and human health is from industrial and automotive soot production, a combustion-generated by-product that can be prevented with optimization of combustion systems1,2. Design engineers associated with task of mitigating soot emissions are often posed to challenges in understanding the complex combustion physics associated with soot formation, which is poorly understood even today. In addition to the physics of soot formation, the additional challenges come from accurate numerical estimation of soot formation due to involvement of complex multi-physics phenomenon that includes fluid mechanics, thermodynamics, heat transfer and multiphase flows3.A high fidelity numerical solution requires accurate modeling of various sub process of soot formation like soot inception, condensation, surface growth and oxidation of soot. In addition to this chemistry driven processes, the soot yield also depends heavily on coagulation and aggregation regimes. Therefore, the soot modeling for higher hydrocarbons like kerosene, which typically involves large thermo chemical solution, a detailed numerical solution is a daunting task. The practical considerations of soot modeling require simplified modeling of sub processes along with reduced dimension models of soot to have a tractable numerical solution. Hence, Computational Fluid Dynamic (CFD) modeling in reacting systems relies heavily on validating efficacy of reduced order models to predict such sub-processes associated with soot formation. A ANSYS Fluent allows to model soot with a family or reduced order models with different degree of approximation. In this family of various soot modeling methods present in Ansys Fluent, ranging from one-step, two-step, Moss-Brookes (MB), Moss-Brookes-Hall (MBH) and Method of Moments (MoM), this paper focuses on modeling soot formation in kerosene/ air sooting flame using detailed chemistry and MoM model for soot formation. Reacting flow model for sooting kerosene/air flame hence, is subdivided into three parts - gas phase chemistry, polymerization of PAH, and formation and growth of soot particles. The gas phase chemistry is represented by detailed mechanism comprising of 475 species and 4000 elementary reaction steps. This mechanism incorporates polycyclic aromatic hydrocarbons (PAH) formation, used as precursor for the soot inception. Surface growth and oxidation are modeled by commonly used simplified mechanism, known as Hydrogen Abstraction C2h2 Addition (HACA) mechanism. The soot is modeled using methods of moments with interpolative closure, which allows the prediction of particle size distribution. The coupling of gas phase chemistry and turbulence is modeled using steady diffusion flamelet model. The radiation from gas and soot particles is modeled using finite volume approach with a weighted sum of gray gas model for calculation of radiative properties. Standard 2 equation k-ε RANS turbulence model is used for modeling the turbulence. The current numerical results are compared against experimental data from Young et al. (Proc Combust Inst 25(1):609-617, 1994). The current computations are performed for operating pressure of 1 atm. To optimize the current modeling method, a sensitivity analysis and parametric investigation is carried out for different modeling components like the number of moments, the soot nucleation precursors and effect of soot-radiation interactions. Based on the current parametric investigation, an optimal solution strategy is proposed which allows high fidelity soot modeling in industrial application in an efficient manner. Test Case: Young et al. (Proc Combust Inst 25(1):609-617, 1994) Young et al.4 proposed a test case to benchmark soot formation in kerosene/sir flames. Prevaporised kerosene jet burns in a co-flow air stream. A 2D axisymmetric model was created with full quadrilateral mesh of around 3100 elements keeping into perspective the current computations. Multicomponent fuel was used as surrogate for experimental kerosene fuel. Operating condition of test case were P=1atm, fuel flow rate = 8g/min, fuel T=598K and air velocity= 0.23 m/s. Results and Discussions Moment convergence sensitivity Theoretically, a large number of moments are required to accurately capture the particle size distribution. However, with increased number of moments, the combine solution becomes stiff and higher order moments may pose challenge in smooth convergence and numerical stability. Therefore, it is required to find an optimal number of moments for optimization. In this section, insights into convergence of moments have been discussed. In addition to the numerical challenges, higher order hydrocarbon flames with high sooting often leads to convergence difficulties. Besides detailed kinetic modeling, resolution of Particle-Size Distribution (PSD) is required for accurate prediction of soot formation. The particle population balance methods, Smoluchouwski master equations utilizes PSD for modeling important sub-processes of soot formation. The solution of the population balance equations would require solving an infinite number of particle size classes, which can be achieved efficiently with method of moments model. For the particle of the size class I, its mass mi can be expressed as mi=im1, where m1 is the mass of a monomer, this is the smallest mass that can be added or removed from soot particles, i.e. a single carbon atom. The concentration moment Mr of the particle number density function, two moments are required: M0 which is total particle number density and M1 as total mass of the particles. Additional moments can be added to predict the shape of the distribution, e.g. M2 to calculate the variance and M3 to calculate the skewness. Moments are affected by convection and diffusion, transport equation for the moments is solved for Mr (rth moment of soot size distribution). ANSYS Fluent has interpolative closurebased implementation where unknown moments are interpolated from known ones. Details of model implementation are omitted here for the sake of brevity, but all details can be found in ANSYS Fluent Theory Guide5. Figure. 1(a-c) shows that temperature distribution along centerline and transverse direction at x=205mm & 300mm respectively. Sensitivity towards temperature distribution is less by increasing number of moments solved for size distribution. (a) (b) (c) Figure 1. Temperature distribution due to number of moments- a) axially along centerline, b) radially along x=205mm and c) radially along x=300mm. However, impact on converging size distribution by increasing number of moments can be seen on soot volume fraction, Figure 2 (a-c). As the number of moment transport equations increase, better convergence in soot predictions are seen due to less fluctuations in soot values. For higher order hydrocarbon flames, clearly more number of moments are required to obtain converged distribution. However, the impact of increasing number moment transport equations on predicting mixture fraction distribution was very small, Figure 3. Based on these studies, 6 moment transport have been used for high order hydrocarbon flames. Soot-radiation interaction: Absorption coefficient of soot In ANSYS Fluent, radiative transfer equation is solved by using Discrete Ordinates (DO) method with total emissivity coefficient of the gas calculated using a weighted sum of gray gases approach5. Soot-radiation interaction in ANSYSs fluent is modeled by using data from Sazhin et al.6, for a relation obtained by fitting to data based on the Taylor-Foster approximation7,8. Another popular approach reported by Modest et al.9, has been used in this paper to assess sensitivity of soot-radiation interaction, especially for higher order hydrocarbon flames. For primary soot particles ranging from 5nm to 100nm, scattering can be assumed negligible compared to absorption and the spectral absorption coefficient is given by kλ=Cofv/λ, where Co is a constant depending upon soot index of refraction, fv is the volume fraction and λ is the wavelength. (a) (b) (c) Figure 2. Soot [ppm] distribution due to number of moments -a) axially along centerline, b) radially along x=205mm and c) radially along x=300mm. Expression derived on these assumptions as reported by Modest et al.9, αsoot= 3.72fvCoT/C2 where C2=1.4388 cm-K. It's worth mentioning that there is great uncertainty associated with Co constant, which is a function of temperature, composition and particle aggregation, in addition to wavelength. As per the literature10,11, this value is between 2 to 10 as a result of differences in fuel, topology of flame and contrasting conditions between laboratory and realistic applications. In the present work, Co=2 was used since higher order hydrocarbon were being employed. (a) (b) Figure 3. Mean mixture fraction distribution due to number of moments- a) radially along x=205mm and b) radially along x=300mm. Figure 4 (a-c) shows comparison between two different approaches to model soot-radiation interaction by using relations from Modest et al.9and Sazhin et al.6, to compute soot absorption coefficient. Model proposed by Sazhin et al.6 returns lower radiative heat flux compared to Modest. (a) (b) (c) Figure 4. Temperature distribution comparison between different soot-radiation methods- a) axially along centerline, b) radially along x=205mm and c) radially along x=300mm. Figure. 5(a-c) shows sensitivity of soot-radiation interaction on soot predictions. It can be seen that soot formation has significant impact on soot-radiation interaction treatment, especially for sooting high order hydrocarbon flames. In further studies, soot-radiation interaction has been modeled using Modest et al.9 (a) (b) (c) Figure 5. Soot [ppm] distribution comparison between different soot-radiation methods- a) axially along centerline, b) radially along x=205mm and c) radially along x=300mm. Soot aggregation Coagulation phenomenon modeled within soot model promotes coalescent soot growth, where larger particles resulting from collision of two smaller particles are always spherical. In sooting, high order hydrocarbon flames soot growth is not limited to coagulation regime as the residence time could be short and therefore, the soot at the exit may be in form of aggregates or fractals. With modeling advances in ANSYS Fluent, capability to form chain like structures because of particles sticking together (aggregates) can be modeled using aggregation model5. Critical diameter, switching between coalescence and aggregation was specified as ~23nm. In Figure. 6-7 (a-c), impact of aggregation regime can be seen on temperature and soot distribution respectively. Comparative assessment between two regimes show that better experimental prediction can be seen with aggregation regime. (a) (a) (b) (c) Figure 6. Impact of aggregation on temperature distribution a) axially along centerline, b) radially along x=205mm and c) radially along x=300mm. Figure. 8 shows distribution between coalescence and aggregation regimens. With aggregation, soot destruction in downstream region of flame can be seen which occurs due to reduction in soot volume fraction and soot diameter. PAH Precursor Precursor is the key for nucleation and whole soot formation is built upon it. Therefore, understanding and finding the correct precursor is of crucial importance in accurate soot modeling. Here, we have used two major precursors, independently. These precursors are pyrene (C16H10, a4) and naphthalene (C10H8, naph). Based on contribution of precursor in flamelet, sticking coefficients which are used to scale rates based on kinetic theory are computed automatically. Sticking coefficient of naph=0.00100549 and a4 was reduced to 0.0031171. Interaction of radiation with soot models involving aggregation becomes challenging since kinetic rates of associated precursors are effected. By individually studying precursors for soot nucleation, more understanding of combustion-soot model coupling can be done. Figure 9-10 (ac) show distribution of temperature and soot respectively. a) (a) (b) (c) Figure 7. Impact of aggregation on soot [ppm] distribution a) axially along centerline, b) radially along x=205mm and c) radially along x=300mm. Figure 8. Impact of aggregation regime on centerline distribution of soot diameter. With the impact of radiation dominant after x>100mm, fundamental aspects of flame have been captured. Low soot concentration region of 100mm < x < 200mm leads to larger prediction of flame temperature whereas x>200mm reduction in temperature is seen both in computational predictions and experimental data. Figure. 11-12 shows comparison between two precursors for soot mean diameter and spatial distribution of temperature and soot volume fraction. Mean diameter of soot particles with a4 as inception peaks around ~x=400mm where soot volume fraction is reducing rapidly. This is completely different than soot diameter distribution with naph as inception PAH molecule. ) (a) (b) (c) Figure 9. Impact of precursors on temperature distribution a) axially along centerline, b) radially along x=205mm and c) radially along x=300mm. Conclusion In this work, soot formation in Kerosene/Air flame has been modeled using detailed chemistry with Steady diffusion flamelet model, coupled with Method of Moments for soot modeling. Final results show good qualitative and quantitative match of temperature and soot concentration with experimental data. Temperature prediction is greatly influenced by radiative properties of gas and soot. While WSGM was used to estimate gas absorptivity, sensitivity study for soot absorptivity was done. The radiative heat losses could not be accurately accounted by gray radiation, leading to over-prediction in flame temperature during low soot concentrations. It was seen that for high order hydrocarbon flames, large sooting requires modification to soot absorption. Aggregates of carbon formed during soot formation and destruction have been successfully modeled. Impact of PAH precursor was seen on soot formation with impact of inclusion of multiple PAH precursor yet to be studied. (a) (b) (c) Figure 10. Impact of precursors on soot [ppm] distribution a) axially along centerline, b) radially along x=205mm and c) radially along x=300mm. Figure 11. Impact of PAH precursor species on soot diameter distribution along centerline. (a) (b) Figure 12. Comparisons between a) temperature and b) soot volume fraction for "naph" & "a4" PAH preccursors. References 1. Mahowald N, Ward DS, Kloster S, Flanner MG, Heald CL, Heavens NG, Chuang PY (2011) Aerosol impacts on climate and biogeochemistry. Annu Rev Env Resour 36(1):45 Mueller ME 2. Pöschl U (2005) Atmospheric aerosols: composition, transformation, climate and health effects. Angew Chem Int Edition 44(46):7520-7540 3. Stephen R Turns (2000) An introduction to combustion: concepts and applications. McGraw-Hill 4. K.J. Young, C.D. Stewart, J.B. Moss, Twenty-Fifth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1994, p. 609. 5. ANSYS Fluent Theory Guide, Release 19.0. ANSYS, Inc.; 2018. 6. S. S. Sazhin. "An Approximation for the Absorption Coefficient of Soot in a Radiating Gas". Manuscript. Fluent Europe, Ltd. 1994. 7. P. B. Taylor and P. J. Foster. "Some Gray Weighting Coefficients for Soot Mixtures". Int. J. Heat Transfer. 18. 1331-1332. 1974. 8. T. F. Smith, Z. F. Shen, and J. N. Friedman. "Evaluation of Coefficients for the Weighted Sum of Gray Gases Model". J. Heat Transfer. 104. 602-608. 1982. 9. Modest, M. F. 2003. Radiative Heat Transfer, , 2nd edition, New York: Academic Press. 10. Wang H, Du DX, Sung CJ, Law CK (1996) Experiments and numerical simulation on soot formation in opposed-jet ethylene diffusion flames. Proc Combust Inst 26(2):2359- 2368 11. Wen Z, Yun S, Thomson MJ, Lightstone MF (2003) Modeling soot formation in turbulent kerosene/air jet diffusion flames. Combust Flame 135(3):323-340 |
