Influence of soot aging on soot production for laminar propane diffusion flames

Fuel 210 (2017) 472–481

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Full Length Article

Influence of soot aging on soot production for laminar propane diffusion flames

MARK

⁎

J.P. Soussia, R. Demarcoa, , J.L. Consalvib, F. Liuc, A. Fuentesa a b c

Departamento de Industrias, Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso, Chile Aix-Marseille Université, IUSTI/ UMR CNRS 7343, 5 rue E. Fermi, 13453 Marseille Cedex 13, France Measurement Science and Standards, National Research Council, Building M-9, 1200 Montreal Road, Ottawa, Ontario K1A 0R6, Canada

A R T I C L E I N F O

A B S T R A C T

Keywords: Laminar diffusion flame Propane Oxygen index Soot aging effect Radiant fraction

A numerical analysis was conducted to investigate the effect of varying the Oxygen Index (OI) of the oxidizer stream between 21 and 35% on soot production and thermal radiation emitted by laminar axisymmetric propane diffusion flames at atmospheric pressure. The extended enthalpy defect flamelet model, an acetylene/benzenebased two-equation semi-empirical soot production model, and the Full-Spectrum correlated-k radiative property model were used in the numerical simulations. The focus of this study is to demonstrate that it is important to account for the soot aging effect to correctly predict how increasing OI affects the predicted soot production. Three soot surface growth rate models were considered. The first model neglects the soot aging effect and assumes the soot surface growth rate is linearly dependent on soot surface area. The second and third models account for the soot aging effect by assuming the soot surface growth rate is proportional to the square-root of soot surface area and assuming a particle size-dependent sublinear soot surface area, respectively. The predicted flame height, soot volume fraction, radially integrated soot volume fraction and radiant fraction were compared to available experimental data. The first soot model predicted a much higher soot loading increase with increasing OI than observed experimentally. The second and third soot models improve considerably the predicted general behavior of soot loading increase with OI. Soot and combustion gases make comparable contribution to flame radiation under the conditions studied. When the soot aging effect is properly taken into account, the relatively efficient numerical code assessed in this study becomes a suitable tool for predicting soot production and thermal radiation in laminar propane diffusion flames at different OI conditions. Moreover, increasing OI of the oxidizer stream is a remarkable way to enhance the flame radiation where the correct estimation of soot production is essential to predict the radiant fraction of the flame.

1. Introduction Since the combustion of fossil fuels was discovered, it has played a leading role in energy production and power demand of modern societies, although the associated pollution has undesirable health and environmental effects [1]. Despite the current efforts to increase the usage of renewable energy, the consumption of fossil fuels continues to grow along with energy consumption [2]. Therefore, an efficient management of this type of fuels is increasingly important at both industrial and domestic levels. This is mainly based on the pressing needs to further improve the combustion efficiency and at the same time to reduce combustion generated emissions. Industrial flames are in general turbulent and great efforts have been made in the last few decades to develop and improve models to simulate the interaction between chemistry and turbulence reliably and

⁎

Corresponding author. E-mail address: [email protected] (R. Demarco).

http://dx.doi.org/10.1016/j.fuel.2017.08.086 Received 13 April 2017; Received in revised form 19 August 2017; Accepted 25 August 2017 0016-2361/ Crown Copyright © 2017 Published by Elsevier Ltd. All rights reserved.

efficiently. One of the most effective models in this topic has been the laminar flamelet concept [3]. This approach is based on the assumption that the behavior of a turbulent flame can be described by an ensemble of laminar flames subject to different strain rates. The rationale of this hypothesis can be understood based on the existence of similarities between the scalar distributions in laminar and turbulent flames [4]. Laminar diffusion flames are often used as a model flame configuration to gain fundamental understanding of different physical and chemical mechanisms involved in the combustion process, which is the necessary first step towards addressing industrial combustion issues. At the same time, this type of flame is ideal to apply optical diagnostics to obtain high quality experimental data for model validation and to permit numerical simulation using detailed reaction mechanisms due to its good repeatability and relatively simple flow field. A distinct characteristic of non-premixed combustion is the formation

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of soot and its impact on flame properties, such as local temperature and thermal radiation [5,6]. In normal co-flow diffusion flames, like the ones analyzed in this research, soot particles are formed on the fuel side of the reaction zone, close to the high temperature regions. Then, these particles are transported downstream mainly by convection toward the tip of the flame, where they are oxidized by oxidative compounds such as O2 and OH under high temperature conditions [7,8]. One of the important parameters that directly affects the flame structure, soot production process, and the related radiation is the oxygen concentration in the oxidizer stream [9], known as the Oxygen Index (OI). This parameter has an important influence on combustion reactions and flame temperature. As the amount of oxygen in the oxidizer stream is increased, the fuel pyrolysis process is accelerated, temperature is increased, and consequently the soot formation reactions are greatly enhanced. In addition, because of the higher amount of oxygen molecules available, the overall oxidation rates of soot and combustion in general are also significantly enhanced [10,11], leading to shortened flame heights. The dual role played by the OI in soot production enables a competition between the formation and oxidation mechanisms that needs to be studied from both technological and fundamental points of view. In fact, investigation of the OI effects is highly relevant to oxy-fuel and oxygen-enriched combustion technologies and is critical to advance our understanding of the characteristics of oxy-fuel and oxygen-enriched combustion. From an industrial point of view, the strategy of using enriched oxygen for combustion to intensify reactions and to improve combustion efficiency is not new and has been implemented mainly within the context of oxy-fuel combustion with flue gas recirculation to reduce peak flame temperatures and pollutant emissions (both soot and NOx). The economic feasibility of oxy-fuel combustion has been discussed extensively such as in the edited books by Baukal [9] and Qi and Zhao [12]. Although oxy-fuel combustion with flue gas recirculation is likely the most promising technology for CO2 capture, it is recognized that oxygen-enriched combustion tends to enhance NOx emissions [13]. One of the gaseous hydrocarbons commonly used in industrial combustion systems, but not widely documented, is propane. Some domestic applications include the use of propane for heating homes, heating water, cooking, barbecuing and lighting. Propane is also widely used in industrial burners for air heating, fire tube boilers, steel forging, and glass processing. There has been relatively less fundamental research conducted in propane flames compared to that for methane and ethylene, although some studies have been carried out to understand the structure and combustion chemistry of propane diffusion flames [14–17]. In addition, the influence of oxygen enrichment on soot production [18] and radiative properties of propane coflow diffusion flames has been experimentally studied, demonstrating that higher radiation heat emission rate can be reached by increasing the OI of the oxidizer stream [19,20]. Despite the significant progress in our understanding of various soot formation processes in hydrocarbon flames and in soot formation model development [21], there is still a lack of robust and relatively simple soot models that perform equally well under different flame conditions or for flames fueled with different hydrocarbons. Although the soot inception step plays the bottleneck role in the overall soot formation process, it contributes negligibly to the total soot mass in comparison to the surface growth process. It has been well-known that soot particles gradually lose their surface reactivity as they become more mature [5,22–25]. This effect can be explained in terms of the decrease of active sites or defect sites on soot particle surface, and is normally called soot surface aging. It has been postulated that the soot aging effect is related not only to the local temperature but also to the residence time that the soot particles are subjected to, i.e., their thermal age [26]. However, the mechanism of soot surface aging has not been fully understood. Studies conducted so far have suggested that it is related to the carbonization/dehydrogenation processes of the soot particles [27]. At the surface of soot particles, the change in the chemical composition produces a decrease in the concentration of active C −H sites available

for reaction and therefore a decrease in the particle surface reactivity for growth. Different approaches have been proposed in the literature to account for the decrease in soot surface reactivity within the context of the hydrogen abstraction acetylene addition (HACA) mechanism for soot surface growth, e.g. Appel et al. [28] and Veshkini et al. [26]. Within the framework of the semi-empirical acetylene-based twoequation soot model, Liu et al. [29] have evaluated two soot surface growth models: one is proportional to the square-root of specific soot surface area (soot surface area per unit volume) and the other is proportional to the specific soot surface area. They showed that the soot surface growth model based on the square-root of soot specific surface area performs much better in terms of the predicted soot distribution and the pressure dependence of the peak soot volume fraction over a wide range of pressures for methane-air diffusion flames. They explained the sublinear dependence (here square-root) of the soot surface growth rate on soot specific surface area in terms of the soot surface aging phenomenon mentioned above and the shielding effect due to soot particle aggregation. In this study soot formation in laminar coflow propane diffusion flames was modeled, considering different OI in the oxidizer flow ranging from 21% to 35%. The simulations were carried out using a modified semi-empirical two-equation soot model and a detailed reaction mechanism of propane combustion. The numerical results were validated using experimental results obtained by Escudero et al. [20], analyzing flame height, soot loading and radiant fraction. Three soot surface growth models that have different functional expressions for soot surface area were used to demonstrate the importance of taking into account the soot aging effect on the predicted soot loading at different OI conditions. The present study intends to demonstrate that the account of the soot aging is important to accurately predict soot production. In this sense, study different OI conditions put in evidence the need to consider the aging effect in order to provide accurate soot content predictions. Finally, the present study proposes a modification in order to improve the predictive capabilities of the semi-empirical soot model. 2. Numerical model The overall continuity equation, the Navier–Stokes equations in the low Mach-number formulation, and transport equations for the mixture fraction (ξ ) and the total enthalpy (h) were solved in axysimmetric cylindrical coordinates. These equations were solved using a finite volume method on a staggered grid. Steady-state solutions were reached by time marching. The ULTRASHARP scheme was applied for the convective terms while a second-order central difference scheme was used for the diffusion terms. The pressure–velocity coupling was dealt with using the Iterative PISO algorithm [30]. 2.1. Combustion model Chemical reactions were modeled by using the Extended Enthalpy Defect Flamelet Model (E-EDFM) [31], which provides the state relationships for scalars based on mixture fraction (ξ ), scalar dissipation rate ( χ ) and an enthalpy defect parameter ( XR ). The extended version of this model stands for the calculation of production rates of the soot model within the flamelet generation. These production rates are used as input for the soot transport equations described later. During the solution of the transport equations, the local values of the mixture viscosity, density, diffusion coefficient, temperature, species and soot production rates were extracted interactively from the flamelet library. For the construction of the flamelet library a counterflow diffusion flame configuration was used, based on the OPPDIF code [32]. The code was modified in order to take into account the effect of thermal radiation into the energy equation. A strain rate ranging from about 10−1 s−1 up to the extinction value was considered. Regarding the 473

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carbon atoms in the incipient soot particle (60), Ca is the agglomeration rate constant (9.0), ρS is the soot density (2000 kg/m3 ) and WS is the molar mass (12.011 kg/kmol ) [35]. Symbol dp represents the soot particle diameter. The soot formation rates were calculated as:

chemical kinetics, a detailed scheme for propane combustion was used [16]. It consists of 70 species and 463 reactions and is optimized to predict up to C3 chemistry. Thermal radiation was introduced through the calculation of the enthalpy defect, using the method described by Carbonell et al. [31], following the expression:

XR =

h−had hu−had

(1)

f2 (AS ) =

(8)

AS

(9)

2/3

(10)

The primary soot particle diameter dp can be easily deduced from Eqs. (7) and (10). Primary soot particles are assumed spherical throughout the soot formation processes. If soot aging were neglected, the soot surface growth rate continues to increase as the primary soot particles become larger as a result of acetylene addition, which in turn accelerates the soot surface growth process until the soot oxidation process dominates the surface growth one as the soot particles travel towards the tip of the flame. This is what happens in the case of Model I. When the soot aging phenomenon is simulated using Models II or III, the surface growth rate of soot particles does not increase linearly with the soot surface area. In other words, the specific soot surface growth rate (on per unit surface area basis) actually decreases as primary soot particles become larger. Consequently, the primary soot particles in Models II and III grow at a lower rate than that in Model I and the soot surface area and soot volume fraction predicted by Models II and III are also expected to be lower. Nevertheless, Models II and III intend to simulate the soot aging process, but use different mathematical expressions. Model III was developed in this study through the trial and error of different aging formulations, aiming to reproduce the trends observed experimentally within increasing OI and also provide parameters that can be understood and interpreted physically. In this model the threshold soot surface area and the soot aging related limiting exponent were taken as a∗ = 2.2·10−15 m2 and n = 0.2 , respectively. These values were obtained through a sensibility analysis of this model, comparing the maximum values of the integrated soot volume fraction. The preexponential values and activation temperatures from the Arrhenius expression are in agreement with the values obtained by Lindstedt [35], except for k sg2 , where a different pre-exponential value was used. Reaction rate constants are summarized in Table 1. The soot oxidation rates are those of a previous numerical study [38]. As pointed out by Liu et al. in their study concerning the effect of pressure on soot formation [29], there is no reason why the soot aging

1/2

SYS = (ω̇n + ω̇sg ) WS−ω̇ O2−ω̇OH −ω̇O

(7)

6YS ⎞ ap = π ⎛⎜ ⎟ ⎝ πρS NS ⎠

This model considers the processes of particle nucleation, surface growth, coagulation and oxidation. The soot precursors are assumed to be acetylene and benzene, while soot surface growth is assumed to be due to acetylene reaction. Soot oxidation is based on the Nagle and Strickland-Constable [36] for O2 , and the Fenimore and Jones [37] model for O and OH. Coagulation of soot particles, decreasing the soot number density, is based on the normal square dependence [34]. The source terms for the two soot transport equations are given in Eq. (3) and Eq. (4) below.

(ρNS )2

f1 (AS ) = AS = ap ρNS = πdp2 ρNS

In these expressions AS is the soot surface area per unit volume and ap is the surface area of a primary soot particle, which can be expressed as

(2)

NA 6k T ω̇n−2Ca dp1/2 ⎜⎛ B ⎟⎞ NC ⎝ ρS ⎠

(6)

ap f3 (AS ) = min ⎧ap,a∗ ⎛ ∗ ⎞ ⎫ ρNS ⎨ ⎝a ⎠ ⎬ ⎩ ⎭

Soot production is modeled by using a semi-empirical two-equation formulation based on a simplified soot formation mechanism introduced by Leung et al. [34] and later modified by Lindstedt [35]. Two transport equations are solved in this model: one for the soot number density, defined as the number of soot particles per unit mass of mixture (NS ), and the other for the soot mass fraction (YS ). Thermophoretic velocities of soot were included in these transport equations, following the expression:

S NS =

ω̇ sgi = 2k sgi fi (AS )[C2 H2]

n

2.2. Soot formation model

μ ∂T , x = r ,z ρT ∂x

(5)

where [C2 H2 ] and [C6 H6 ] represent the acetylene and benzene molar concentrations, respectively. Three different models for the functional dependence of the soot surface growth rate on the soot surface area fi (AS ) were assumed to investigate the importance of soot aging to the modeling of soot loading variation with OI: a lineal dependence (Model I), a square root dependence (Model II) following the recommendations of Leung et al. [34] and Liu et al. [29], and a hybrid sublinear dependence model (Model III) which only considers the soot aging effect when the soot particle surface area is larger than a prescribed threshold. In Model III, the increase in f3 (AS ) is limited by an assumed exponent n (n < 1) when the primary soot particle surface area ap exceeds the threshold a∗. These three models are expressed as:

where, had and hu corresponds to adiabatic and unburnt mixture enthalpies, respectively. For the calculations of the unburnt mixture enthalpy it is assumed that all the combustion energy is lost and the gaseous mixture is cooled down to ambient temperature. This formulation allows considering the energy lost by thermal radiation and the effect on the chemical reactions. The Enthalpy Defect Flamelet Model (EDFM), successfully implemented by Marracino and Lentini [33], proposes the idea of generating a set of flamelet profiles with different radiation source terms for a certain range of scalar dissipation rate χ . The first step for the flamelet library generation is to generate temperature and species profiles for a set of prescribed χ under adiabatic conditions, starting from the maximum temperature profile and ending with a profile close to the extinction. This is achieved by varying the strain rate of the axisymmetric opposed-flow diffusion flame used for each profile. According to the behavior of the generated library, the higher the strain rate, the greater the χ and the lower the flame temperature. Then, the non-adiabatic flamelet profiles are generated for each χ by solving the temperature and species flamelet equations using different values of volumetric radiative source term of the energy equation [31]. For generating these profiles, the volumetric radiative source term is multiplied by a δ factor which takes values from 0 (adiabatic conditions) to the maximum δ (highest radiative heat loss) to cover the entire range of possible degrees of radiation loss. It is important to mention that to achieve the objectives of this study it is necessary to generate a distinctive flamelet library for each OI considered.

VT ,x = −0.55

ω̇n = 2 kn1 [C2 H2] + 6 kn2 [C6 H6]

(3) (4)

(6.022·1026

particles/kmol) and kB is where, NA is Avogadross number the Boltzmann constant (1.38·10−23 J/K). Parameter NC is the number of 474

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mean velocity of 20.54 cm/s), 25% (80.0 L/min, 18.77 cm/s), 29% (69.0 L/min, 14.89 cm/s) and 35% (57.1 L/min, 12.32 cm/s). In these flames the oxygen flow rate was kept constant for all the cases, while the nitrogen flow rate was varied in order to obtain the desired OI. In the numerical simulations the fuel preheating effect associated with the heat transfer between the flame base and the fuel tube was neglected. A non-uniform staggered mesh was used with 89 × 320 cells to cover the solution domain of 2.5 cm × 12 cm in the radial and streamwise directions, respectively. The computational mesh was found fine enough to obtain grid-independent results. The parabolic velocity profile is assumed at the fuel stream, while a flat velocity profile is used for the oxidizer stream.

Table 1 Reaction rate constants for the soot production model, according to the expression kj = A e−Ta/ T T b,b = 0 (Units in K, m, s).

kj

kn1

kn2

k sg1,3

k sg2

A

0.63·10 4 21,000

0.75·105 21,000

0.4·103 12,100

0.432·10 4 12,100

Ta

effect, i.e., the decrease in soot surface reactivity, is restricted to soot surface growth but not to soot oxidation. It is likely that the soot oxidation process is also affected in a similar way. However, in this study the linear dependence of soot oxidation rates was maintained, as has been the common practice in the literature, while further theoretical and experimental studies should be carried out to better understand the soot aging effect on both surface growth and oxidation. The first set of simulations was performed with the surface growth rate formulation according to the model used by Demarco et al. [38] (Model I), which neglected the soot aging effect and was shown to produce acceptable results for an OI of 21% (normal air conditions). With the purpose of demonstrating the importance of soot aging to soot production modeling at higher OIs, soot surface growth was also modeled using the other two expressions mentioned earlier, in which the surface growth rate is dependent on the soot surface area in sublinear fashions as an approximate way to simulate the soot aging effect (Models II and III given above). Thus, two additional sets of numerical calculations were carried out using Models II and III. Model II accounts for the soot aging effect on the soot surface growth rate by assuming that the active soot surface area for acetylene addition reaction is proportional to the square-root of the total soot surface area. This implies that as soot particles grow and increase in their total surface area, they become less reactive as far as the soot surface growth process is concerned. In Model III, the initial soot surface growth rate is the same as that in Model I, i.e., it is proportional to the soot surface area. However, as the primary soot particles grow in size and surface area to reach a threshold value a∗, the available soot surface area available for acetylene addition starts to deviate from the geometric soot surface area as imposed by the exponential expression given in Eq. (9). Correspondingly, the soot surface growth rate in Model III is lower than that of Model I.

4. Model validation In order to provide a validation of the soot surface growth modifications, two comparisons were carried out with the experimental data of Shaddix and Smyth [42] and Trottier et al. [43]. Even though these tests are limited because only data obtained at normal air condition (for 21% OI) are available in the literature (without error analysis), it is still very useful to validate the three soot models to ensure that they perform well at 21% OI. It is important to mention that the original model (Model I) predicted reasonably well the soot content at this OI, so the intention of this comparison is to show that the modifications to soot surface growth in Models II and III do not alter their ability to predict soot formation at 21% OI. Fig. 1 compares the predicted and measured radially integrated soot volume fractions, β , in laminar coflow propane diffusion flames investigated by Shaddix and Smyth [42], and Trottier et al. [43]. These flames have a similar layout to that of this study but were generated with higher fuel flow rates, and hence taller flames [42,43] were obtained. Comparison with experimental data shown in Fig. 1 indicates that the soot volume fraction predicted by the two soot models with aging effect (Models II and III) displays a reduction in the peak value and a decrease in the axial location where the peak occurs. This behavior of Models II and III improves the agreement between the model prediction and experimental data for the flame of Trottier et al., which has a higher oxidizer flow rate (1.98 cc/s fuel and 4700 cc/s air), but worsens the agreement for the flame of Shaddix and Smyth, which has a higher fuel flow rate (2.57 cc/s fuel and 694 cc/s air). Calculating the soot loading of these flames, an overall parameter of the soot content produced by the complete flame can be obtained. This parameter, denoted as hereafter, is estimated by integrating axially the β values within the flame. Experimental results and numerical estimations of the soot loading are summarized in Table 2. Given the limited experimental points available, the experimental profiles were fitted by a spline and then integrated. It is observed that for the flame of Shaddix and Smith [42] the relative error is reduced by Model II and III, compared to Model I, with a similar absolute magnitude between them. For the flame of Trottier et al. [43], Model III presents a clear reduction in the relative error, presenting a relative error of around 16%. Despite the differences between model predictions and measurements, the magnitude and general trend of the integrated soot volume fraction profiles predicted by Models II and III are in reasonable agreement with the experimental measurements and also similar to those predicted by Model I, which neglected the soot aging effect. Therefore, the modifications made in Models II and III to the soot surface growth rate expression do not seem to deteriorate the predictive capabilities of the soot model at normal air conditions.

2.3. Radiation model The Full Spectrum Correlated-K (FSCK) radiative property model was used to estimate the radiative transfer of the gaseous species [39], while the soot contribution to radiation was estimated through a Planck-mean absorption coefficient. Only CO2 and H2 O were considered as the participating gaseous species, disregarding the contributions of CO and hydrocarbon species. This approximation has been tested and found valid [40]. The radiative transfer equation (RTE) was solved by a finite volume method using the special mapping developed by Chui et al. for axisymmetric configurations [41]. Specific details on the radiation model and the parameters considered are given in Ref. [38]. 3. Flame conditions The flames simulated in this study are those investigated experimentally by Escudero et al. [20]. Experiments were carried out in a co-flow Gülder type burner [18] at atmospheric pressure. Pure propane (C3 H8 ) was injected through the central tube with an inner diameter of 10.9 mm and the oxidizer stream, consisting of a mixture of N2 and O2 , was delivered through the co-annular region between the fuel tube and the oxidizer tube (inner diameter of 100 mm). Both the fuel and the oxidizer were delivered to the burner at the room temperature (293 K). The volumetric flow rate of the fuel was fixed at 1.223 cm3/s (mean velocity of 1.310 cm/s) for all the cases. Four OI conditions were studied, at 21% (flow rate of 95.2 L/min and

5. Results and discussion 5.1. Flame height One of the most important parameters that characterize co-flow laminar diffusion flames is the flame height, which is defined as the 475

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Fig. 1. Variation of the integrated soot volume fraction with the height above the burner exit for propane laminar diffusion flames of (a) Shaddix and Smyth [42] and (b) Trottier et al. [43].

Table 2 Soot loading and relative error for propane diffusion flames of Shaddix and Smyth [42] and (b) Trottier et al. [43]. Shaddix and Smyth [42]

Trottier et al. [43]

Data

Ψ (ppm cm3 )

Rel. Error

Ψ (ppm cm3 )

Rel. Error

Exp OI21 Model I Model II Model III

3.54 4.78 4.05 3.18

– 25.9% 12.6% −11.2%

2.20 3.49 3.50 2.61

– 37.0% 37.2% 15.7%

location of the reaction zone (peak heat release rate) on the flame centerline. This quantity is not only an important parameter of the flame shape, but also provides an indication of the residence time that soot particles experience from inception to begin fully oxidized. It is noticed that the flame height defined by the peak reaction zone on the flame centerline is in general very close to the visible flame height, which is defined by the flame centerline location where soot luminosity vanishes. This is because OH is a very effective soot oxidative species and soot cannot penetrate the OH layer. Although the visible flame height is the result of two competing processes between soot formation and soot oxidation, the efficient soot oxidation by OH implies that the visible flame height is largely determined by OH oxidation and is not sensitive to the soot surface growth sub-model. This point is supported by the numerical results shown in Fig. 1, where the predicted integrated soot volume fractions by all the three soot models vanish at very similar heights. Therefore, the predicted flame heights are largely insensitive to the soot surface growth sub-model as observed in Fig. 2. In the experimental study of Escudero et al. [20], the flame height was inferred based on the CH spontaneous emission, commonly used to determine the location of the reaction zone. Numerically, a similar estimation was obtained based on the maximum CH concentration on the flame axis. It is recognized that these two different ways to determine the flame height might cause some difference in the flame height, since measurements based on CH emission not only depends on the CH concentration but also on the local temperature; however, the difference is believed very small and can be neglected. A comparison between the measured and simulated flame heights is presented in Fig. 2. The predicted flame heights are in close agreement with the measured values at all the four OIs considered, regardless of the soot surface growth model. Model I, which assumes a linear dependency of soot surface growth rate on the soot surface area, slightly underestimates the flame height for all the OI considered, except at OI 35%, where the predicted flame height is in excellent agreement with the measurement. Model II and Model III, both

Fig. 2. Flame height at different OI.

considering the aging effect in soot surface growth, predict the flame heights in similar agreement with the measured values as Model I, except at 35% OI, where both models underestimate the flame height. These results show that the soot model, and consequently the predicted soot loading, has a minor influence on the predicted flame height.

5.2. Soot volume fraction Fig. 3 presents the simulated distributions temperature, soot surface growth rate, soot volume fraction, and the radiative source term by the three soot surface growth models at two OI conditions of 21 and 35%. As indicated before, the flame becomes shorter with increasing OI. At the same time, all the quantities displayed in Fig. 3 are significantly enhanced. These effects can be attributed to the significantly increased temperatures. Therefore, an increase in OI results in much higher soot formation rates and soot loading, which in turn greatly prompts flame radiation, i.e., an increased radiant fraction of the flame. By comparing the results of the three soot models it is clear that Model I predicts a much stronger increase in soot volume fraction with increasing OI than the other two models and also than the experimental results discussed later. On the other hand, Model II and III predict a much weaker enhancement in the soot production by increasing OI. At 35% OI the peak soot volume fraction calculated by Model I is 16.65 ppm, but it is only 5.21 ppm by Model II and 6.23 ppm by Model III. It is noticed that Model II predicts an earlier soot surface growth in 476

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Fig. 3. Computed distribution of temperature, surface growth formation rate, soot volume fraction and the divergence of the radiative flux for: Model I, II and III at OI 21% and 35%.

Based on the similarity in the distributions of radiative source term and soot volume fraction at both OIs (21 and 35%), it can be stated that soot is likely the main source of flame radiation in these propane diffusion flames. However, an examination of the relative importance of

the region just above the burner rim than Models I and III, Fig. 3. This is caused by the higher pre-exponential factor associated with Model II shown in Table 1, which had to be increased to compensate the weaker dependence of surface growth rate on soot surface area. 477

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gas and soot radiation to the radiant fraction (fraction of energy loss by thermal radiation over the total energy release of combustion) does not support this statement. Numerical calculations using Model III indicate that by neglecting neglect of the effect of soot radiation led to a reduction in radiant fraction by 35.4% and 40.9% at 21% and 35% OI, respectively. Similar results were also obtained using Model II. This implies that it is vital to correctly predict not only the soot loading in the flame but also the radiative heat transfer by combustion gases (CO2 and H2 O ) radiation in order to accurately estimate the amount of energy loss through thermal radiation. To demonstrate the consequences of using the three different soot surface growth models to the predicted soot production at different OIs, it is necessary to compare the simulated soot volume fractions against the experimental measurements of Escudero et al. [20]. The predicted radial distributions of soot volume fraction are compared with the experimental data at two non-dimensional flame height of 0.6 hf and 0.75 hf in Figs. 4a and 4b for OI = 21 and 35%, respectively. These two non-dimensional flame heights are chosen for comparison because soot concentrations at these flame heights are high and can better illustrate the importance of accounting for the soot aging effect to soot prediction. It is shown in Figs. 4a and 4b that all the three soot models, with or without including the aging effect, predict much lower soot concentrations in the flame centerline regions than measured experimentally. This behavior is systematically observed in all simulations and is characteristic of this kind of simplified model. Previous studies, using both the semi-empirical soot models, e.g. Liu et al. [29] and PAH-based soot models, Dworkin et al. [44], have shown that this inability to correctly predict the soot concentration levels in the flame centerline region is an indication that soot growth along the flame centerline is poorly modeled. Despite the very low soot concentrations predicted at the centerline by the soot models, three soot models reproduced reasonably well the soot volume fractions at these two flame heights at 21% OI, Fig. 4a. However, this is no longer the case at 35% OI, Fig. 4b, where Model I predicted much higher soot volume fractions than Models II and III and the experimental data. When the OI is increased from 21 to 35%, the experimental measurement showed that the peak soot volume fraction increases modestly from less than 3 ppm to about 6 ppm, i.e., by a factor of 2. For the same increase in OI, Model I predicted about a factor of 5 increase in the peak soot volume fractions at these two flame height. On the other hand, the peak soot volume fractions at these two flame heights predicted by Models II and III are in much closer agreement with the measured values. The results shown in Fig. 4a and Fig. 4b suggest that it is critical to account for the soot aging effect in the soot surface growth rate to correctly capture the soot production enhancement due to the increase in OI. To further demonstrate the importance of accounting for the soot aging effect in soot surface growth process to soot formation modeling, the predicted and measured peak soot volume fractions at the two nondimensional flame heights over the entire range of OI (21–35%) are compared in Fig. 4c. It is interesting to observe that the predicted and measured peak soot volume fractions at these two heights all exhibit a fairly linear increase with increasing OI, albeit at different rates. Although all the three soot models predicted similar peak soot volume fractions to the experimental results at 21% OI, which is expected from the results shown in Fig. 4a, they predicted very different increase rate with respect to OI. It is evident that Model I, which neglects the sooting aging effect on soot surface growth process, predicted a drastically higher increase in the peak soot volume fraction than the other two soot models and the experimental data by more than 100% relative error at all the three higher OIs investigates, i.e., OI = 25, 29, and 35%. When the soot aging effect is taken into account in Models II and III, though only approximately, the predicted increases in the peak soot volume fractions with increasing OI at the two flame heights are close to each other and only slightly higher than the experimental data. It is

Fig. 4. Soot volume fraction radial profiles at 0.6 and 0.75 of each flame height at: (a) OI 21% and (b) OI 35%. (c) Maximums of soot volume fraction at 0.6 and 0.75 of each flame height for different OI.

important to note that Models II and III predicted similar radial distributions of soot volume fraction and its increase with OI, shown in Fig. 4, despite their different ways to model the soot aging effect.

5.3. Integrated soot volume fraction The radially integrated (over the flame cross-section at a given height) soot volume fraction, β , is a useful quantity to assess the influence of the OI on the overall soot production. Fig. 5a shows a direct 478

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The initial increase in β close to the burner exit is the result of soot nucleation and subsequent surface growth. With the increase in height along the flame, soot oxidation gradually plays an increasing role to limit the peak value of β and then becomes dominant over soot growth at certain flame height. This causes the decrease of β after the peak value until soot is fully oxidized. An examination of the numerical results reveals that soot is mainly oxidized by OH radicals. The peak values of β predicted by Models II and III are in reasonable agreement with the experimental data at all the four OIs. Regarding the position of the peak β , both models predicted an upstream shift compared to the experimental measurements, i.e., the predicted position of the peak β is closer to the burner exit, and the shift becomes more pronounced with increasing OI. In addition, Model II predicted a significantly higher rise rate β at the burner exit than Model III and the measurements. The faster rise in β in the results of Model II is attributed to its higher soot surface growth rates at the burner exit region displayed in Fig. 3. On the other hand, the rise rates of β along the height predicted by Model III are in much better agreement with the measurements, especially at 21 and 25% OI. The better agreement in β between Model III and experiments suggests that the overall soot aging effect is better modeled by Model III than Model II. It is noticed that soot surface growth rate depends on not only the soot surface area, but also the kinetic parameters given in Table 1. To illustrate the improvement of Models II and III in the prediction of β in a quantitative manner, the variation of the predicted and measured peak β with OI are compared in Fig. 5b. As expected from the results shown earlier, the predicted β values by all three soot models, without or with soot aging effect, are in good agreement with the experimental data at 21% OI. The overall observation from Fig. 5b is similar to that from Fig. 4c, i.e., Model I drastically overpredicted the radially integrated soot volume fraction and the results of Models II and III agree well with the experimental data within the experimental error. It is important to mention that the measured βmax was used as the target to tune the parameters of Models II and III. This explains the little differences between both aging models in this figure. In order to complement the analysis, the soot loading is presented in Fig. 5c. This quantity indicates to total soot volume fraction within by the flame zone. In this case a more different behavior is observed between Models II and III. Model II tends to overestimate at the lower OI values studied, while Model III tends to overestimate more at the higher OI values. In any case, both models improve the predictive capabilities of the soot model, independent of the formulation considered. 5.4. Radiant fraction The radiant fraction is a global parameter of the flame to quantify the percentage of thermal radiation heat loss from the total combustion heat release. It is a measure of the overall quality of flame modeling in terms of flame structure, soot production, flame radiation, and combustion heat release. Thus, it is useful to evaluate the predicted radiant fractions by the three soot models against the measured data. The measured and predicted radiant fractions at the four OIs are compared in Fig. 6. It is seen that the flame radiation loss increases with increasing OI, which is consistent with the enhanced soot production with increasing OI. The predicted radiant fractions are persistently higher than the experimental data, regardless of the soot model. At the three higher OIs (25, 29 and 35%), Model I significantly overpredicted the radiant fraction, especially at 35% OI, mainly due to the much higher soot loadings predicted by this soot model, while Models II and III predicted radiant fractions in closer agreement with the experimental data. Model II an III predicted similar radiant fractions at all OI studied, Model II predicted a slightly lower increase rate with OI than Model III. Despite the difference in magnitude, the trend displayed in the results of Model II is somehow closer to the experimental data than Model III, following the same behavior observed in the maximum of the integrated soot volume fraction βmax in Fig. 5b. Comparing the results of

Fig. 5. (a) Integrated soot volume fraction at different OI. (b) Maximums of the integrated soot volume fraction at different OI. (c) Soot loading at different OI.

comparison of the predicted and measured distributions of the radially integrated soot volume fraction along the flame height for the four OIs investigated. Since the results of Model I are drastically higher than the experimental data, they are not included in this comparison for clarity. In both the numerical and experimental results at any OI, the radially integrated soot volume fraction first increases with the flame height to reach a peak and then starts to decrease continuously until it vanishes. 479

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Fig. 6. Radiant fraction at different OI.

radiant fraction and the integrated soot volume fraction it can be observed that although the former is directly related to the overall soot loading, the differences in XR are relatively small despite the fairly large differences in β . 6. Conclusions A numerical study was carried out in order to demonstrate the importance of accounting for the soot aging effect in the soot surface growth process to soot formation modeling in a laminar coflow propane diffusion flame over a wide range of oxygen index (OI) from 21 to 35%. A semi-empirical soot model was incorporated into the framework of a modified extended enthalpy defect flamelet model with thermal radiation taken into account. A detailed reaction mechanism for propane combustion was used to generate the flamelet library in the counterflow diffusion flame configuration. To illustrate the impact of soot aging effect, three soot surface growth models with different treatments in the soot surface growth rate were implemented and their results are compared to available experimental data. Regarding the flame height, all three soot models predicted similar flame heights and a decreasing trend with increasing OI, in qualitative and relatively good quantitative agreement with the experiments. These results indicate that (1) the flame chemistry is well reproduced at different OI and (2) soot model has a minor influence on the predicted flame height. Although Model I (without considering soot aging effect) performed reasonable well in soot modeling in the propane diffusion flame at 21% OI, it drastically overpredicted soot production at higher OIs. Despite their simplicity, the other two soot models, which take into account the soot aging effect in approximate manners, quantitatively capture the increasing trend of soot production with increasing OI, although there are still deficiencies in the predicted soot distributions. In addition, Models II and III predicted the radiant fractions at different OIs in better agreement with the experimental data than Model I. The results presented in this work clearly demonstrate that it is critical to include the soot aging effect in modeling the soot surface growth rate in order to better quantify the enhancement of soot production caused by increasing the oxygen concentration in the oxidizer stream. The reduction in the soot surface reactivity as soot particles age can compensate the significant increase in the soot formation rates caused by increase in oxygen concentration in the oxidizer. The results presented in this study are encouraging for implementing and improving the soot surface aging models in other applications. Acknowledgements Authors would like to acknowledge financial support from Chilean 480

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