2009 Fall Technical Meeting
Organized by the Eastern States Section of the Combustion Institute
and Hosted by the University of Maryland College Park
October 18-21, 2009
Numerical Simulations of Soot Kinetics
in Spherical Diffusion Flames
V.R. Lecoustrea, P.B. Sunderlanda, B.H. Chaob and R.L. Axelbaumc
aDepartment of Fire Protection Engineering, University of Maryland, College Park, USA
bDepartment of Mechanical Engineering, University of Hawaii, Honolulu, USA
cDepartment of Energy, Environmental & Chemical Engineering, Washington University,
St. Louis, USA
Detailed soot kinetics were numerically investigated in steady microgravity spherical diffusion flames. The flames involve an ethylene/nitrogen mixture flowing from a spherical burner into an oxygen/nitrogen mixture. A detailed chemistry model including intermediate elementary reactions up to pyrene is coupled with a description of the soot particle dynamics using the method of moments with interpolative closure. Radiative heat losses were modeled using the discrete ordinates method with a statistical narrow band method for gas species (CO2, H2O, and CO) and the Rayleigh approximation for soot particles. Soot volume fraction, rate of soot formation/destruction, and heat losses by radiation were studied for different locations of the outer boundary. The predicted soot concentrations are low. Soot radiation decreases temperatures, which favors the outward migration of PAH and soot owing to a decrease in H radical concentrations.
1. Introduction
Soot is observed in most hydrocarbon fuel combustion processes involving diffusion flames, including candle flames, large scale fires, diesel engines, coal burners, etc. While beneficial for some applications, soot can increase fire spread rates. The release of soot into the environment poses serious health risks [1] and environmental damage [2]. Thus soot formation and oxidation are areas of considerable research activity [3–11].
Soot particles consist of nearly spherical primary particles that form aggregates. Primary particles are relatively small, their size ranging between 5 – 80 nm. They consist almost exclusively of carbon [12], and their density is 1800 – 2000 kg/m3 [10].
The presence of soot in flames arises from a competition between its formation and destruction. It is generally accepted that the polycyclic aromatic hydrocarbons (PAH) created by fuel pyrolysis form the precursors of soot particles [8,13]. Soot kinetics include nucleation, coagulation, surface growth by addition of C2H2, aggregation, and oxidation, mostly by OH and O2. Soot motion arises from convection, diffusion and thermophoresis. Particle diffusivity is usually negligible, but thermophoresis can be significant [14].
While uncertainties remain, several models have been developed to predict soot processes in flames. These models can be classified as empirical, semi-empirical or detailed models [15]. Detailed models provide a fundamental description of the physics and soot chemistry without any assumptions about the soot particle size density function (PSDF). Different models have been developed to model the evolution of the PSDF: sectional methods [4,16-18], stochastic methods [19–21] and the method of moments [3,22–25]. The method of moments is used in this study.
Laminar spherical diffusion flames are one dimensional. The spherical geometry has several implications regarding the transport of mass, species and heat. In steady state, these flames have no stretch [26]. Flame structure can be characterized by the stoichiometric mixture fraction (given here for ethylene flames):
ZST=1+247YO2,OxYC2H4,f-1, (1)
and in these flames can be varied independently of convection direction, which is not the case in counterflow diffusion flames. The transient behavior of these flames has been observed by Sunderland et al. [27,28]. While many spherical diffusion flames have been numerically modeled, little attention has been dedicated to detailed modeling of their soot processes.
The present soot model is a detailed model based on the method of moments [3], coupled with a detailed chemistry model. Interactions radiation/soot particles are also considered.
2. Numerical
Flames similar to those considered here have been observed in microgravity drop facilities by Sunderland et al. [28]. The fuel is a mixture of 18% (by volume) ethylene in nitrogen. This was injected at 8.38 mg/s through a stainless steel porous burner of 6.4 cm diameter into a quiescent mixture of 28% (by volume) oxygen in nitrogen. The stoichiometric mixture fraction of this flame is ZST = 0.333 and its adiabatic flame temperature is Tad = 2306 K. The overall heat release rate is 71 W. Initially sooty, this flame is observed to reach its sooting limit 2 s after ignition [28].
Steady state modeling of the flame structure was predicted using the Appel, Bockhorn and Frenklach (ABF) detailed chemistry model [29]. This model includes 101 species and 544 reactions. Pyrolysis of C1 and C2 species is modeled, along with the formation of PAH up to four rings (pyrene), mainly through PAH collisions and the hydrogen abstraction carbon addition (HACA) mechanism.
Soot particles were modeled as carbon spheres. Soot density was assumed to be ρsoot = 1800 kg/m3. Nascent particles were modeled to originate from coalescent collisions of pyrene molecules. Coagulation was modeled by coalescent collisions of soot particles in free, transitional and continuum regimes. Aggregation was not modeled. The model included surface growth by the HACA mechanism and PAH condensation, and soot oxidation by OH and O2. The steric factor proposed by ABF [29], accounting for the loss of soot particle reactivity due to particle aging, was used for both the surface HACA mechanism and oxidation by O2. The rate of surface reactions by C2H2, O2 and OH were identical to those in Ref. [29]. Soot oxidation by OH was modeled using a collision efficiency of 0.13 [30].
The PSDF governing the evolution of the soot particle population was solved using the method of moments with interpolative closure (MOMIC). Further details can be found in Ref. [31]. The rth moment Mr of the PSDF, with r a real number, is defined by:
Mr=i∞irNi, (2)
where i is the number of carbon atoms in a particle of class i and Ni is the particle density number of class i. Without any assumptions of the shape of the PSDF, the dynamic evolution of soot populations is solved through the evolution of its moments. The first 6 moments, M0 – M5, were considered in this study.
Transport of particles by bulk convection and thermophoresis was considered. Particle diffusion induced by soot concentration gradients was neglected. The thermophoresis velocity, UT , which is independent of the particle size, was computed using [14]:
UT=-3ν41+απ8∇lnT, (3)
where the accommodation coefficient is α = 0.925 and ν is the mixture kinetic viscosity.
The General Dynamic Equation governing the evolution of each class density function is then expressed as:
∂Ni∂t+∇·NiU+∇·NiUT=Ni, (4)
where Ni is the rate of class i particle creation/destruction and U is the bulk velocity. Multiplying the above equation by ir and summing over i gives the conservation equation of the moment Mr. This equation, expressed in spherical coordinates after multiplying by A(r) = 4πr2, in steady state, is written:
ddrmρ-0.55νAr∂lnT∂r Mr=ArMr, (5)
where Mr is the combined rate of nucleation, coagulation and surface reaction given by MOMIC. The term m represents the mass flow rate from the burner. For each of the six moments, Eq. (5) was discretized and solved as an additional conservation equation. This solution used a modified version of Sandia’s PREMIX code [32]. Further details about the numerical code can be found in Refs. [33,34]. Mixture averaged transport coefficients were considered. Steady-state solutions were computed using the Sandia’s TWOPNT program [35]. The temperature at the burner surface and at the outer boundary was held constant at 300 K. Burner surface radiative heat losses were neglected. Gas-phase species flux balances were observed at the burner surface. At the outer boundary, the mass fractions of O2 and N2 were held constant. The computational boundaries were considered to be sink terms for the soot moments. Adaptive mesh spacing was used to insure smoothness of the solution. The inner boundary was located at r = 0.32 cm to simulate the burner surface. The location of the outer boundary was varied from 1.2 – 3.0 cm.
Radiative heat losses were obtained by solving the radiative transfer equation using the discrete ordinates method [36,37] with Gaussian-Legendre quadrature. The solution involved 21 ordinates. The participating species were H2O, CO2, CO, and soot. The spectral species absorptivities were computed using a statistical narrow band model with a resolution of 25 cm-1 for wavenumbers between 150 – 9300 cm-1. The radiative properties of CO2, H2O and CO were taken from the HITRAN database [38], averaged over a spectral band considering a Lorentz spectral line shape of random spacing and strength, and used a exponential-tailed inverse probability distribution [39].
Soot particle spectral absorptivity coefficient assumed Rayleigh behavior. The spectral absorption coefficient αλ,i for a spherical particle of diameter di is given by [40]:
αλ,i= -4 πdiλπdi24Im2-1m2+2, (6)
where m is the complex refractive index of the particle, expressed by m = n−ik, I denotes the imaginary part of its complex argument, and di is the class i particle diameter. The soot refractive index was taken to be m = 1.57 − 0.56i [41]. Because soot particles were modeled as spheres of constant density whose mass is defined by the number of carbon atoms, the following relation held:
π6ρsootdi3=imC, (7)
with mC the mass of a carbon atom. The spectral absorption coefficient of the cloud of soot particles is the sum of the individual contribution of each particle:
αλ=i∞αλ,iNi, (8)
which gives:
αλ=π2λ6mCπρsoot6nkn2+k22+4n2-k2+4M1. (9)
Recognizing that:
fv=mCρsootM1, (10)
and replacing n and k by their assigned value gives the final expression of the soot spectral absorptivity:
αλ=C1λfv, (11)
where
C1=4.8622 . (12)
3. Results and Discussion
Steady state solutions were obtained for three different radii of the outer boundary: 1.2, 2.0, and 3.0 cm. The resulting flame characteristics are summarized in Table 1. The flame temperature Tf is defined as the peak temperature in the computational domain. The radius associated with this temperature is defined as the flame radius, rf . The radiative losses are denoted Qr. Results from Table 1 show that, when the flame is constrained in the smallest domain, heat losses by radiation are drastically reduced. The radius of the flame increases when the outer boundary radius increases. The increase of flame radius leads to increased radiative heat losses, as illustrated by Santa et al. [33]. The largest flame has the greatest radiative heat losses, which represents nearly a third of the heat released by combustion. The peak of soot volume fraction is on the order of 10-8. This low concentration of soot contributes little to the radiative heat losses.
Figure 1 plots the flame temperature and the soot volume fraction profiles for the three flames considered. Temperature profiles show a broad distribution of high temperature, with steep temperature gradients at the inner (burner surface) and outer boundary. These gradients are reduced as the domain radius increases, implying a diminution of heat losses by conduction at the burner surface and outer boundary. This also decreases thermophoresis. The decrease of heat losses by conduction is counteracted by the increase of radiative heat losses from gas species. The radiating gases, i.e., CO2, H2O, and CO, form a radiative layer outside the flame in regions of high temperature, thus increasing radiative heat losses. In addition, the increase of domain radius allows the volume of radiating gases to increase.
Figure 1 shows that soot concentrations peak inside the peak temperature and that no soot is predicted beyond the peak temperature. Comparing the smallest and largest flames, the peak soot volume fraction decreases by 25% when the peak temperature decreases by 14%. The soot layer thickness is 1 – 2 mm and increases with increased domain size.
Figure 2 plots predicted mole fractions of H, OH, O2, C2H2, and pyrene for the 1.2 and 3 cm domains versus local carbon to oxygen atom ratio (C/O). The C/O ratio is defined as the local ratio of number of carbon atoms divided by number of oxygen atoms. The local C/O ratio tends to infinity near the fuel side and tends to 0 near the oxidizer side. For ethylene flames, the peak temperature is located near C/O = 1/3. The use of the local C/O ratio is particularly helpful for the study of flames using the same fuel but having different ZST .
Figure 2 also shows temperature profiles and regions where soot volume fraction exceeds 10-9. The soot layer shifts toward the oxidizer side of the flame as flame size and radiative heat losses increase. The predicted soot profile for the highest flame temperature case (domain 1.2 cm) spans from C/O = 0.43 – 0.645, with a peak at C/O = 0.5. The flames with the highest heat losses (domain 3.0 cm) has a predicted soot profile spanning from C/O = 0.4 – 0.51 with a peak at C/O = 0.42.
The reduction of the extent of the soot volume fraction in C/O space is attributed to the decrease of scalar dissipation rate in the largest domain. The computed scalar dissipation rate, defined by χ=2αdZdr2, with α the thermal diffusivity and Z the mixture fraction, is 8 ´ 10-4 s-1 at the flame location for the largest domain, and 4 ´ 10-3 s-1 for the 1.2 cm domain. This decrease in mixing rate is associated with a decrease in gradient of C/O ratio. Therefore the soot layer extent is reduced in C/O space whereas it is increased in physical space.
Figure 2 indicates that the flame with the highest radiative heat losses contains lower OH concentrations than does the flame with lower heat losses. Moreover, the extent of the OH profile for these conditions is restricted to low C/O ratio. This decrease of OH radical is attributed to the lower flame temperature predicted in the 3.0 cm domain. This reduces soot oxidation rates, since OH is the main soot oxidizer, and allows the presence of soot at low C/O ratio.
Another effect of lower flame temperature is the shift of acetylene and pyrene mole fraction peaks toward lower C/O ratio. This shift is attributed to the reduction of H radicals at high C/O ratio for the largest domain. Hydrogen radical is the main species responsible for the activation of radical sites of intermediate species and PAH needed for growth through the HACA mechanism. Owing to lower temperatures, H radicals are present is smaller quantities and remain confined to C/O locations close to the peak temperature.