air laminar boundary layer diffusion flames

Combustion and Flame 191 (2018) 99–108

Contents lists available at ScienceDirect

Combustion and Flame journal homepage: www.elsevier.com/locate/combustflame

Numerical simulations of microgravity ethylene/air laminar boundary layer diffusion flames Jorge Contreras a,b,∗, Jean-Louis Consalvi a, Andrés Fuentes b a b

Aix-Marseille Université, IUSTI/UMR CNRS 7343, 5 rue E. Fermi, Marseille Cedex 13 13453, France Departamento de Industrias, Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso, Chile

a r t i c l e

i n f o

Article history: Received 10 January 2017 Revised 13 March 2017 Accepted 12 December 2017

Keywords: Laminar boundary layer diffusion flame Microgravity Radiative quenching Soot production Radiative property models

a b s t r a c t Microgravity ethylene/air laminar boundary layer diffusion flames were studied numerically. Two oxidizer velocities of 250 and 300 mm/s and three fuel injection velocities of 3, 4, and 5 mm/s were considered. A detailed gas-phase reaction mechanism, which includes aromatic chemistry up to four rings, was used. Soot kinetics was modeled by using a pyrene-based model including the mechanisms of nucleation, heterogeneous surface growth and oxidation following the hydrogen-abstraction acetylene-addition (HACA) mechanism, polycyclic aromatic hydrocarbon (PAH) surface condensation and soot particle coagulation. Radiative heat transfer from CO, CO2 , H2 O and soot was calculated using the discrete ordinate method (DOM) coupled to a wide-band correlated-k model. Model predictions are in quantitative agreement with the available experimental data. Model results show that H and OH radicals, responsible for the dehydrogenation of sites in the HACA process, and pyrene, responsible for soot nucleation and PAH condensation, are located in a thin region that follows the stand-off distance. Soot is produced in this region and, then, is transported inside the boundary layer by convection and thermophoresis. The combustion efficiency is significantly lower than 1 and is reduced as the flow residence time increasing, confirming that these sooting micro-gravity diffusion flames are characterized by radiative quenching at the flame trailing edge. In particular, this quenching phenomenon explains the increase in flame length with the oxidizer velocity observed in previous experimental studies. The effects of using approximate radiative-property models, namely the optically-thin approximation and gray approximations for soot and combustion gases, were assessed. It was found that the re-absorption and the spectral dependence of combustion gases and soot must be taken into account to predict accurately temperature, soot volume fraction, flame geometry and flame quenching. © 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction Nowadays microgravity combustion studies have been largely encouraged by the successful landing of Mars mission and the idea of conduct the first manned mission to this planet for 2030. In this sense, the fire safety plays an important role in order to maintain protected, during the mission, the crew and the spacecraft. The materials employed and ambient conditions should be therefore an important research subject. In fact, at the very early stages of space flight development, oxygen concentration in spacecraft was almost 100%, and combustible materials present in the spacecraft were flammable under such oxygen concentration, which resulted in high risk of fire. At present, the oxygen concentration in spacecraft is currently less, such as 21% normally established in the In∗ Corresponding author at: Departamento de Industrias, Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso, Chile. E-mail address: [email protected] (J. Contreras).

ternational Space Station (ISS) [1]. Flame behavior under microgravity conditions is quite different from that on the Earth due to the absence of buoyancy forces [2] and thus, understanding microgravity combustion to manage possible hazards associated with unwanted fires is crucial to minimize risks of future missions. A canonical scenario for the fire safety purpose in microgravity is the Laminar Boundary Layer Diffusion Flame (LBLDF) where a flame sets over a fuel plate supported by a low oxidizer flow blowing parallel to this surface. This situation can be analyzed theoretically by using the Emmons theory [3]. It is associated with flame spread over solid and liquid fuel flat-surfaces with opposed flow [4–9] and co-current flow [10–12], fabric materials [13,14] and electrical wires [15–18]. Also, it is of great importance to obtain insights on flame spread and extinction in materials used in the spacecraft infrastructure, payloads, crew member clothes and wires of electrical circuits. This configuration using a LBLDF at microgravity has been extensively studied by the group of researchers around Torero [19–25]. In some of these studies, the con-

https://doi.org/10.1016/j.combustflame.2017.12.013 0010-2180/© 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

100

J. Contreras et al. / Combustion and Flame 191 (2018) 99–108

Nomenclature fs g gk Ibη Iη k Lb Lf p Q˙ R tres T u Uox v VF wk x xi Y z

Soot volume fraction (ppm) Cumulative k-distribution function (–) kth quadrature points (–) Spectral blackbody intensity (W sr−1 m−1 ) Spectral intensity (W sr−1 m−1 ) Absorption coefficient variable (m−1 ) Porous burner length (m) Flame length (m) Pressure (Pa) Heat loss per unit volume by radiation (W m−3 ) Residence time (s) Temperature (K) Velocity in the x-direction (m s−1 ) Oxidizer injection velocity (m s−1 ) Velocity in the z-direction (m s−1 ) Fuel injection velocity (m s−1 ) kth quadrature weight (–) Coordinate along the plate (m) Molar concentrations of the ith gaseous species (–) Mass fraction (–) Coordinate in the vertical direction (m)

Greek letters χ Combustion efficiency (–) χR Radiant fraction (–) ε Emissivity (–) φ Scalar variable (–) η Wavenumber (m−1 ) κ Absorption coefficient (m−1 ) ρ Density (kg m3 ) Subscripts F Flame max Maximum ox Oxidizer R Radiative ref Reference s Soot ∞ Oxidizer η Wavenumber Abbreviations DOM Discrete ordinate method FVM Finite volume method OI Oxygen concentration in the oxidizer flow SOD Stand-off distance (m) WBCK Wide-band correlated-k WB Wide band NB Narrow band densed fuel was replaced by a porous gas burner which was justified by obtaining large experimental times, no fuel surface regression and because in this configuration the flame is easier to ignite and to control [23–26]. The absence of buoyancy normally enhances the residence time favoring the production of soot and increasing the radiative heat transfer to the detriment of convection. Consequently, the competing processes between soot formation and soot oxidation, and the resulting flame radiation, controls the flame length (Lf ) and the heat flux toward the solid surface. In particular, it was found that flame length increases mainly with the oxidizer velocity (Uox ) [23– 25,27]. This behavior is opposite to that expected when complete combustion occurs, suggesting that extinction takes place at the flame trailing edge [27], as expected from Ref. [28].

Two mechanisms can lead to flame quenching. The first mechanism [29,30] (the kinetic extinction) occurs when the mixing time (or residence time) becomes significantly lower than the characteristic time for the chemical reactions (low Damkhöler number, Da). The other mode of quenching, opposite to the kinetic mode, is the radiative quenching. It exists only in the presence of radiative heat loss, and occurs at long residence times (large Da). The energy loss through radiation causes a decrease in flame temperature, leading to a reduction of the reaction rates. Quenching takes place when excess heat loss significantly lowers the reaction rate such that the flame can no longer sustain itself [31]. The radiative quenching has been less studied than the kinetic quenching because it is more difficult to observe on earth as the intrusion of buoyant force accelerates the flow and reduces the residence times. The microgravity environment offers unique conditions to investigate radiative flame quenching due to the large residence times encountered. Also, this phenomenon is expected to be enhanced by larger quantities of soot produced and reinforced radiation for this type of laminar diffusion flames. The main objective of the present study is to provide a better description of the structure for an ethylene LBLDFs generated in microgravity conditions and to demonstrate numerically the existence of flame quenching at the trailing edge of the flame providing also a better comprehension of this phenomenon. This work is carried out by using a numerical model involving detailed chemistry and advanced soot production and radiation models. Finally, different radiative property models are tested to evaluate the influence in the prediction of flame structure, soot production and quenching induced by the radiation heat loss mechanism. 2. Numerical model The overall continuity equation, the Navier–Stokes equations in the low Mach number formulation, and transport equations for gas-phase species mass fraction including the soot mass fraction, the soot number density per unit mass of mixture, and energy were solved in a 2D rectangular coordinates system (x, z) using a finite volume method (FVM) on a staggered grid. The gravitational term was set to zero to simulate the gravity reduced environment. Correction diffusion velocities in both x- and z-directions were used to ensure that the mass fractions of gaseous species and soot sum to unity. The thermophoretic velocities of soot in both the x- and z-directions were accounted for, as were the interactions between the gas-phase chemistry and the soot chemistry. The source term in the energy equation due to radiation heat transfer was calculated using the discrete ordinates method (DOM) with the absorption coefficients calculated from a wide-band correlatedk (WBCK) model as described below. The kinetic mechanism developed by Slavinskaya and Frank [32] to predict the formation of polycyclic aromatic hydrocarbons (PAH) and their growth up to four aromatic rings was used in present work. It consists of 94 species and 723 reactions. Transport properties are calculated from the CHEMKIN database [33]. 2.1. Soot model The soot model is, on the whole, the same as used by Guo et al. [34] and was based on the work of Apple et al. [35]. However, two major differences have been introduced. The steric factor for the H-abstraction-C2 H2 -addition (HACA) process is a constant set equal to 0.1 to be consistent to the works of Slavinskaya and coworkers [32,36,37]. In addition, the contribution of surface growth due to PAH-surface condensation has been added. The soot model assumes that soot particles are spherical and locally monodisperse, leading to a formulation involving two transport equations: one for the mass concentration of soot particles

J. Contreras et al. / Combustion and Flame 191 (2018) 99–108

and another for the soot number density [34]. The particle thermophoretic velocities in z- and x- directions are computed according to [38]. Mass concentration of soot particles depends on soot nucleation, surface growth, and oxidation by O2 and OH. The nucleation of a soot particle is assumed to result from the collision of two polycyclic aromatic hydrocarbons (PAH) and pyrene (A4 ) is assumed to be the only species responsible for soot nucleation. The surface growth and oxidation are assumed to follow the Habstraction and acetylene addition (HACA) reaction sequence given by Appel et al. [35]. Reactions of soot with O2 and OH are added into the HACA reaction scheme to account for soot oxidation. Oxidation by O2 is based on work of Frenklach and Wang [39]. Oxidation by OH is based on the Fenimore and Jones model [40]. The collision efficiency for OH oxidation is set to a value of 0.06 [34]. The soot number density evolves from a balance between particle nucleation and agglomeration [34].

 · q˙ = ∇

∞



κη 4π Ibη −





Iη d dη

(1)

4π

0

The spectral intensity (Iη ) is computed from the spectral RTE for an absorbing and emitting medium, expressed as [41]:

   dIη = κη φ Ibη (T ) − Iη ds

(2)

where Іbη and κ η are the Planck function and the absorption coefficient evaluated at the wavenumber η, respectively. T is the temperature and φ = (T , p, xi , fs ) is an array of state variables affecting the absorption coefficient, i.e. the temperature, the total pressure, p, the molar concentrations of the radiatively participating gaseous species, xi , and the soot volume fraction, fs . 2.3. Radiative properties The radiatively participating species considered in the present study are CO, CO2 , H2 O and soot and the spectral coverage range is 150–9300 cm−1 [42]. Soot particles are assumed to be spherical and small as compared to the wavelength. Rayleigh’s theory can then be applied to obtain the soot absorption coefficient. Scattering was ignored since it is negligible as compared with absorption within the limits of small particles [41]. The spectral absorption coefficient of soot, κ sη , is then expressed as κ s η = Cη fs η. The value of Cη depends on the refractive and absorptive indexes of the soot. In the present study, it is taken as a constant and is set equal to 5.5 [43]. The narrow-band correlated-k (NBCK) model was found to be too much time consuming to be applied in studies involving a detailed chemistry. In order to accelerate the solution of the radiative heat transfer problem a wide-band model was derived from the statistical NBCK. In this strategy [44], successive narrow bands are grouped together to form wider bands over which the RTE is solved. This model will be denoted as wide-correlatedk (WBCK) hereafter. Nine wide-bands (WB) with a non-uniform spectral resolution, ηWB , were considered. On each wide-band (WB) k-distributions were assembled from the k-distributions of the narrow bands (NB) that compose the WB by using a lumping strategy [44]:





gWB K, φ = i

NBi

ηNB, j j=1

ηWB



gNB k, φ j



i dIgk

ds

 

+ kik gk ,



Iη dη =

 i     φ + κsη,i Igk = kik gk , φ + ksη,i Ibη,i (T )

NG NWB

i Igk wk ηWB

(4)

(5)

i=1 k=1

In the energy transport equation, the radiation heat transfer is  · q˙  , considered through the divergence of the total heat flux, ∇ and it is expressed as:

 

where k is the absorption coefficient variable at state φ , NBi is the number of NB that compose the ith WB with a bandwidth ( ηNB ) of 25 cm−1 . gWB and gNB are the cumulative k-distribution over the i j ith WB and the jth NB, respectively. The statistical narrow band CK model and the NB parameters of the EM2C database [42] were used to determine gNB . j Since the cumulative k-distribution is smooth and increases monotonically, integration over g-space can be performed by using a Gauss quadrature scheme with few points. In the present study, the number of quadrature points is taken equal to 4 [45]. The RTE, for the ith WB and for the kth quadrature point and the total intensity are then expressed as:

I=

2.2. The spectral radiative transfer equation (RTE)

101

(3)

Ibη and κ sη were evaluated at the center of the WB. The WBCK model used in the present study was found to provide spectrallyintegrated quantities in very good accordance with those obtained with both NBCK and line-by-line models [44]. The radiative transfer equation (Eq. (4)) is solved by using the discrete ordinate method (DOM) along with a finite control volume strategy and a TN quadrature [46] for angular discretization. A T3 quadrature set, including 36 directions, was chosen in present study. Finally, an upwind scheme is used for the spatial discretization. 2.4. Numerical method The transport equations for mass, momentum, energy, gasphase species, soot mass fraction, soot number density are discretized using the finite volume method on a staggered grid. Diffusion terms in the transport equations are discretized by the central difference and the convection terms by the power law scheme [47]. The SIMPLE algorithm [47] was used to treat the pressure and velocity coupling. A pseudo-time marching method is used to achieve convergence. The momentum, pressure correction, energy and soot transport equations are solved in a segregated manner using the Tri-Diagonal Matrix Algorithm (TDMA) [47]. Since the gaseous species equations are closely coupled and stiff, they are solved simultaneously at each control volume [48] to deal effectively with the stiffness of the system and speed up convergence. The key point of this method is to linearize the current time step chemical reaction source terms by using Taylor series expansions based on the previous time step values and neglecting the second and higher order terms. The resulting Jacobian matrices are obtained by the perturbation method. A direct solver (Gauss elimination method) is used to solve the resulting linear system at each control volume. The species equations are solved control-volume-bycontrol-volume until the whole computational domain is covered. Because the solution of such a large number of highly nonlinear partial differential equations is very computationally demanding, parallel computation with a domain decomposition method was employed [48]. 3. Results and discussions 3.1. Computational details Some of the experimental laminar ethylene/air flames reported in Ref. [27] at atmospheric pressure were considered in this study. The fuel is injected through a porous burner of 5 × 5 cm2 located in a flat plate inside a boundary layer created by a laminar oxidizer flow parallel to this plate coming from left to right

102

J. Contreras et al. / Combustion and Flame 191 (2018) 99–108 Table 1 Boundary conditions. Boundary

Conditions

Radiative conditions

Left side (oxidizer inlet condition) Right side (outlet condition) Top side (free-slip) Bottom side Fuel inlet Flat-plate

u = Uox ; v = 0; φ = φ inj,ox Tox = 300 K; Yo2 , ox = 0.233; YN2 , ox = 0.766 ∂ u/∂ n = 0; ∂v/∂ n = 0; ∂φ /∂ n = 0; p = patm ; ∂ u/∂ n = 0; v = 0; ∂φ /∂ n = 0

ε = 1; T = Tox ε = 1; T = Tox ε = 1; T = Tox

u = 0; v = VF ; φ = 0; YC2H4, F = 1.0; TF = 300 K u = 0; v = 0; ∂φ /∂ n = 0

ε = 1; T = TF ε = 1; T = Tplate

Fig. 1. Computational domain and boundary conditions.

and with an oxygen index (OI) of 21%. Three flames with a constant Uox = 250 mm/s and VF of 3, 4 and 5 mm/s, and a flame with Uox = 300 mm/s and VF = 5 mm/s are considered. Analysis of the experimental data showed that the flow is essentially 2D along the burner, with 3D effects appearing after the burner trailing edge [27]. As a consequence, 2D simulations are considered with an overall computational domain of 26 cm (x) × 18 cm (z) (see Fig. 1). The burner is located at 5 cm from the plate leading edge where the oxidizer stream is injected. Uniform inlet temperatures of 300 K are assumed for both fuel and oxidizer streams. The computational domain is divided into 660 (x) × 364 (z) cells by using a non-uniform grid. The finest resolution (0.0125 cm) in the z-direction is between 0 and 3.5 cm. In the x-direction, the finest resolution is also about 0.0125 cm and takes place from x = −0.5 cm to x = 6 cm. It should be pointed out that the finest resolution includes the flame leading edge since the flame stabilization in this region may affect the region downstream [49]. Outside the region located between −0.5 cm and 6 cm, the grid is enlarged as the distance from the burner increases. A calculation with a finer grid involving 825 (x) × 455 (z) cells (finest resolution of 0.01 cm × 0.01 cm) was performed for VF = 5 mm/s and Uox = 250 mm/s and no-significant differences were observed on both stand-off distance and soot production. The boundary conditions are described in Table 1. Velocities in x- and z- directions are represented by u and v, respectively. In the solution of the radiative transfer equation, all the boundaries are assumed to be cold and black, except the plate that is only black. The assumption of black surface for the plate is justified since it was experimentally observed that the plate is normally covered by soot particles [23].

3.2. Comparison with available data The aim of this section is to compare the numerical predictions with the experimental data reported in Ref. [27]. The present calculations are 2D and, of course, the 3D effects on flame geometry and soot production are not captured. Consequently, the comparison between the numerical and the experimental results is limited to the region upstream the burner trailing edge (0 < x < 7.5 cm) where the flow remains 2D [27].

Fig. 2. Evolution of the stand-off distance as a function of the distance along the plate. (a) Influence of the Uox for a given VF of 5 mm/s, (b) influence of the VF for a given Uox of 250 mm/s.

3.2.1. Stand-off distance (SOD) Figure 2 shows the evolution of the calculated stand-off distance (SOD) as a function of the distance along the plate. Consistently with the experimental data, the stand-off distance is determined as the vertical location of the maximum value of the OH molar concentration and then can be used to observe the location of the primary combustion region [24,27,50]. The corresponding measurements [27] for the two flames are also plotted in Fig. 2. Experimental data shows that the stand-off distance decreases slightly as the oxidizer velocity is enhanced from 250 to 300 mm/s. On the other hand, Rouvreau et al. [20] showed that the reactive boundary layer is pushed away from burner plate as VF increases. This behavior is confirmed by both experimental data and numerical simulations. A fit of the numerical data for VF = 5 mm/s shows that, as expected from the LBL theory, the stand-off distance increases approximately with the square root of the distance along the plate (x1/2 ). The same behavior is observed for the other numerical simulation and the experimental data. The computed stand-off distances agree well with the experiments. 3.2.2. Soot volume fraction Figure 3 shows the predicted profiles of soot volume fraction, as a function of the z-coordinate for different locations along the plate. The corresponding measurements [27] are also plotted in this figure. This figure shows that, whatever the fuel and oxidizer

J. Contreras et al. / Combustion and Flame 191 (2018) 99–108

103

Fig. 3. Vertical profiles of soot volume fraction at different longitudinal positions.

velocities, the peak of soot volume fraction and the width of the sooting region increase with the distance along the plate. The increase in the width of the sooting region is mainly related to the increase in the stand-off distance with the distance along the plate. The numerical model reproduces correctly these trends although the peak of soot volume fraction is overestimated in the region located between the burner leading edge and x = 3.75 cm. The agreement between the numerical model and the experimental data concerning the peak of soot volume fraction is improved as the distance along the plate increases. The peak predictions become

on the whole within the experimental error bars at x = 5.00 and x = 6.25 cm. Nevertheless, the width of the sooting region is somewhat overestimated for VF = 3 and 4 mm/s (Fig. 3(a) and (b)). The diagrams (a)–(c) of Fig. 3 display the effects of the VF for a fixed Uox of 250 mm/s. At a given location along the plate, the experimental peak of soot volume fraction increases with VF . This behavior is more pronounced when VF is increased from 3 mm/s to 4 mm/s than when it is increased from 4 mm/s to 5 mm/s. Figure 3(c) and (d) display the effect of Uox for a fixed VF = 5 mm/s. Measured peaks of soot volume fraction tend to be-

104

J. Contreras et al. / Combustion and Flame 191 (2018) 99–108

∞

Fig. 4. Evolution of integrated soot volume fraction, defined as FV (x ) = ∫ f s (x, z )dz, 0

as a function of x-coordinate. (a) Effect of Uox for a given VF of 5 mm/s and (b) effect of the VF for a given Uox of 250 mm/s.

come slightly lower when the oxidizer velocity increases. Figure 4 shows the evolution of the integrated soot volume fraction, defined ∞

as FV (x ) = ∫ fs (x, z )dz, as a function of the distance along the plate. 0

Figure 4 shows that the integrated soot volume fraction (Fv ) increases as the Uox decreases and as the VF increases. These trends are well reproduced by the numerical model and a quantitative agreement between predictions and experimental data is observed. 3.3. Sooting flame structure In order to study the transport mechanisms controlling soot production inside a non-buoyant laminar diffusion flame, a qualitative description of the flame structure in terms of OH radicals, PAH and soot contours for the flame with VF of 3 mm/s and Uox of 250 mm/s is shown in Fig. 5. Similar trends are observed for the other flames. In Fig. 5(a), iso-contours of OH and PAH mole fraction equal to 0.0 0 01 and soot volume fraction equal to 3 ppm are used to locate the reaction, PAH and soot zones. The experimental contours of soot, OH radical and PAH in Fig. 5(b) are determined based on laser induced incandescence (LII), OH chemiluminescent and planar laser induced fluorescence (PLIF) signals, respectively. Figure 5(a) shows that that the SOD, defined as the vertical location of the maximum value of the molar concentration of OH radicals, agree well with the maximum temperature. Figure 5(a) shows also that the reaction zone, defined by the OH iso-contour, evolves with x1/2 as described previously (stand-off distance). Figure 5 shows that PAHs are located between the plate and the lower part of the OH radical zone where they are likely oxidized and soot particles are embedded in the PAH zone. The region occupied by soot is thinner in the z-direction than the PAH zone which suggests that PAHs are oxidized farther from the plate than soot. The appearance of soot is delayed along the plate as compared to that of PAH since its formation requires longer times. Figure 6(a) and (b) illustrate the soot production processes for the flame with VF of 3 mm/s and Uox of 250 mm/s. Figure 6(a) shows the streamlines, the line of maximum temperature, the region

Fig. 5. Interaction between reaction zone, soot formation and soot production for VF = 3 mm/s and Uox = 250 mm/s. (a) Numerical results: OH∗ and PAH zone correspond to iso-contours of OH and PAH mole fraction equal to 0.0 0 01 whereas the soot zone corresponds to iso-contour of soot volume fraction equal to 3 ppm. (b) Experimental results: OH∗ , PAH and soot contours are based on OH chemiluminescence, PLIF and LII signals.

where soot grows by inception, surface growth (HACA) and PAHsurface condensation, the region where soot is oxidized mainly by OH radicals, and the contours of soot volume fraction. As expected, the maximum temperature increases approximately with x1/2 in a similar manner as the stand-off distance. Model results show that soot is formed in a thin region located below the line of maximum temperature (fuel rich zone) and that this region follows the stand-off distance. The soot produced in this region is then transported along the streamlines but also by thermophoresis inside the boundary layer. It should be pointed out that the z-component of the thermophoretic velocity is about of the same order of magnitude as the z-component of the velocity but has an opposite sign being directed toward the cold plate surface. The soot oxidation zone also locates below the line of maximum temperature and follows the stand-off distance which is consistent with the contours of OH radical observed in Fig. 5(a). The locations of the species responsible for soot formation are represented in Fig. 6(b) in order to provide a better understanding concerning the shape of the soot formation region. Soot inception and PAH-surface condensation are directly related to the concentration of pyrene (A4 ). Figure 6(b) shows that A4 is contained in the zone where soot is produced. The HACA process results from the attack of H and OH radicals that produce de-hydrogenated active sites on the soot surface which allows the addition of acetylene. Figure 6(b) shows that the concentration of acetylene is significant inside the whole region delimited by the plate and the line of maximum temperature. On the other hand, OH and H radicals are located in the region where soot is produced, showing that these species delimit the region where the HACA process occurs. Figure 6(c) displays the integrated soot formation rate, defined as, the integration of

J. Contreras et al. / Combustion and Flame 191 (2018) 99–108

105

Table 2 Some characteristics of the flames.

Fig. 6. Soot production interaction in the LBLD flame with VF = 3 mm/s and Uox = 250 mm/s, (a) soot formation (nucleation, surface condensation and surface growth) and oxidation (by OH) processes. The iso-contour of soot formation and oxidation rates are selected equal to 7 × 10− 5 and 2 × 10− 6 g/cm3 /s whereas the isocontours of soot volume fraction labeled by 2 and 4 correspond to 2 and 4 ppm, respectively, (b) precursors for soot formation. The regions of existence of H∗ , A4 and C2 H2 are delimited by iso-contour of the mole fraction of these species equal to 0.0 0 012, 6 × 10− 7 and 0.01, respectively, and (c) integrated soot formation rates as a function of x-coordinate for VF = 3 mm/s and VF = 4 mm/s flames with a fixed oxidizer velocity of 250 mm/s.

inception, surface growth and PAH-surface condensation rates over the z-coordinate, as a function of the distance along the plate. Results show that the integrated soot formation rate increases rapidly close to the leading edge of the burner, mainly due to higher local concentration of soot precursors, reaching a peak around x = 1 cm. Beyond x = 1 cm it decreases slowly as x increases. As expected, the soot formation rate is found to increase with the fuel velocity. 3.4. Radiative quenching at the trailing edge The effects of fuel and oxidizer velocities on the flame quenching at the trailing edge are analyzed based on the data provided in Table 2. The third column in Table 2 is relative to Lf . Flame length

Uox

VF

Lf

χ

tres

Q˙ R

χR

(χR )soot/χR

(mm/s) 300 250 250 250

(mm/s) 5 5 4 3

(mm) 222.1 192.0 140.8 129.2

(–) 0.53 0.61 0.73 0.85

(s) 0.740 0.768 0.563 0.516

(W/m3 ) 54.4 50.5 46.8 41.9

(–) 0.37 0.34 0.39 0.45

(–) 0.64 0.61 0.60 0.57

is determined as the distance along the x-axis between the burner leading edge and the farthest location reached by the iso-contour at 1400 K. It should be pointed out that the choice of this temperature threshold to define the flame length does not affect the conclusions. It has been selected because it corresponds approximately to the temperature below which soot ceases to be oxidized and can then be considered as an indicator of the luminous flame [51,52]. In agreement with the experimental data reported in Ref. [27], Lf increases with both VF and Uox . In particular, the evolution of Lf with Uox follows an opposite trend as compared to that expected in the case where all the fuel is consumed at the flame tip [27] and is a consequence of the flame quenching at the trailing edge. It should be pointed out that the simulations are 2D whereas 3D effects are expected beyond the burner trailing edge [21–23]. This shows that the 3D effects are not responsible for the increase of Lf with Uox and the quenching process. The fourth column represents the combustion efficiency (χ ), defined as the ratio between the actual heat released by the combustion process and the theoretical heat release rate. In the case where all the fuel is consumed at the flame tip, χ should be equal to 1. The results reported in Table 2 shows that the values of χ are significantly lower than 1, confirming that the reactions quench at the flame tip. The fifth column in Table 2 concerns tres , defined as the ratio between the Lf and the Uox . It increases with the VF due to an increase in Lf (third column) and it is reduced as the Uox increases. The results in Table 2 show clearly that χ decreases as tres increases for a fixed VF . This can be interpreted as follow: as tres becomes longer, more time is available to loss energy by radiation. As a consequence, the flame quenching process occurs comparatively sooner and less fuel is oxidized. The radiant fraction (χ R ), defined as the ratio between the total radiative loss of the flame and the theoretical heat release rate, measures the part of the heat released by the chemical reaction radiated away from the flame. The radiant fractions are given in the penultimate column of Table 2. The first important point is that the radiant fractions computed for the present flames are higher than those observed in axi-symmetric laminar flames at normal gravity that do not exceed about 0.3 even for heavily sooting flames [52] which can be explained by the higher tres encountered in micro-gravity configurations (see Table 2 and Ref. [53]). The second important point is that although the heat radiated away from the flame, Q˙ R , increases with the fuel velocity (see the sixth column), the radiant fraction decreases, implying that the increase in radiative loss is weaker than the increase in the heat release rate (HRR). This behavior is opposite to that observed in closed-tip axisymmetric laminar diffusion flames [53] and may be interpreted as a characteristic of the nature of the present flames that exhibit radiative quenching at the trailing edge. The last column of Table 2 provides the contribution of soot radiation, defined as the ratio between Q˙ R,soot computed by considering only the contribution of soot particle to radiation (ignoring the contribution of gas radiation) and Q˙ R computed by considering both soot and gas radiation. Both Q˙ R were computed in decoupled radiative calculation based on the converged fields of mole fraction of gaseous species, soot volume fraction and temperature as input thermal field. The contribution of soot to total radiation ranges from 57% to 64%, showing both soot and gas radiation must

106

J. Contreras et al. / Combustion and Flame 191 (2018) 99–108

models result from the spectral dependence of gaseous radiatively participating species, namely CO, CO2 and H2 O. (v) The opticallythin approximation (OTA) where the re-absorption of both participating gases and soot is neglected. The analysis is carried out by considering the flame with Uox of 250 mm/s and VF of 3 mm/s. Similar trends were observed for the other flames.

Fig. 7. Flame shape (iso-contours) for the different radiative property models. The green lines correspond to simulations carried out without taking account soot radiation (dashed line) and gas plus soot radiation (solid line). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

be considered. The model results show that contribution of soot increases both with the fuel velocity and oxidizer velocity. 3.5. Effects of approximate radiation models The objective of this section is to investigate the effects of using simplified radiation model on flame geometry, soot production and radiative quenching at the flame trailing edge. Calculations run with the WBCK are used as reference. Other calculations were run by considering the following approximate radiative property models: (i) disregarding the radiative contribution of both participating gases and soot (no radiation), (ii) disregarding the radiative contribution of soot (no soot), (iii) assuming soot is a gray species by using its Planck-mean absorption coefficient. This model will be referred as gray soot in the following, (iv) assuming both soot and participating gases are gray species. The Planck-mean absorption coefficient was considered for each radiating species. This model will be denoted as gray hereafter. To be consistent with the reference model, the Planck mean absorption coefficients considered in models (iii) and (iv) are computed from the WBCK model. It should be pointed out that the differences between gray soot and gray

3.5.1. Flame geometry and combustion efficiency Figure 7 shows the iso-contour 1400 K computed by using the different radiation models investigated. In the reference solution, flame length is 12.92 cm and the flame stand-off distance at the flame trailing edge is 2.09 cm. The results observed when radiation (no radiation) and soot radiation (no soot) are disregarded demonstrate that the influence of radiation and soot radiation cannot be neglected in this type of flames. The flame geometry is completely modified as compared to the reference case. Firstly, it is much larger due to higher temperature and then thermal expansion. Secondly, the flame is much taller since no quenching occurs at the trailing edge. The use of the other approximate models affects also the flame geometry and the combustion efficiency. The OTA enhances the radiative losses as compared to the reference case and, as a consequence, favors flame quenching at the trailing edge. This results in a significantly shorter flame of about 9.26 cm, showing that this approximation leads to non-negligible discrepancies. The combustion efficiency is also significantly reduced to 49% as compared to 71% for the reference model. The flame length is increased from 12.92 cm for the reference case to 13.38 cm and decreased to 11.36 cm for gray soot and gray cases, respectively. The influence of these approximate radiative models is also pronounced on the stand-off distance at the flame tip which is increased from 2.09 cm (reference case) to 2.33 cm and 2.56 cm for the gray soot and gray cases, respectively. The use of these radiative models tends to overpredict the combustion efficiency (74% for the gray soot model and 81% for the gray model). The phenomenon of flame quenching at the trailing edge of LBLDFs under microgravity conditions is a typical case of radiative quenching. Table 2 revealed the significant contribution of soot ra-

Fig. 8. Fields of reference temperature and error predicted for different radiative property models.

J. Contreras et al. / Combustion and Flame 191 (2018) 99–108

107

Fig. 9. Fields of reference soot volume fraction and relative error for different radiative property models.

diation on this process. Therefore, only the influences of the approximate models (iii)–(v) on flame temperature and soot formation will be discussed in the following. 3.5.2. Influence on temperature predictions Figure 8 shows the distribution of temperature obtained with WBCK and the relative errors induced by the other radiative models. On each figure, the reaction zone is defined by an iso-contour at 1400 K and the deviation is quantified by the temperature difference between the model investigated and the reference model ( T = Tmodel − Tref ). The effect of neglecting the spectral dependency of the soot is displayed in Fig. 8(b) where four regions can be observed. The gray soot model overpredicts the temperature in the region under the flame reaction zone with a maximum discrepancy of 88 K in the middle of the flame. On the other hand, the gray soot model underestimates the temperature above the flame reaction zone with a maximum discrepancy around 60 K. Beyond the flame tip this trend in inversed, and discrepancies become higher. These results show clearly that the spectral dependence of soot has to be taken into account. The large discrepancies induced by the gray model present clearly two zones (Fig. 8(c)). It overpredicts the temperature above the flame zone and underpredicts temperature between the flame zone and the plate. Comparison with the discrepancies observed in the case of gray soot (Fig. 8(c) vs. (b)) allows to quantify the influence of the spectral dependence of gaseous participating species. Figure 8(d) shows the effects of the radiation absorption. The use of the OTA underestimates on the whole significantly the temperature over all the computational domain. 3.5.3. Influence on soot volume fraction To analyze the effects of radiation models on soot volume fraction, the following definition of the relative error is adopted: Er, fs = ( fs,model − fs,ref )/ fs,max [54]. The fs, max is the maximum value of the soot volume fraction over the entire computational domain in the reference case. The previous analysis of the mechanism leading to soot formation in laminar boundary layer flame has revealed that soot is produced in a thin region located in the fuel rich side

and following the stand-off distance. The soot particles were then transported along streamlines inside the boundary layer by convection and thermophoresis. As a consequence, the distribution of soot inside the boundary layer depends on both the soot formation processes and the flow dynamic. Previous results have shown that the use of approximate radiative models affects, on the one hand, the temperature field which has a direct influence on the soot production processes and, on the other hand, the flame geometry which influences the flow dynamic. Consequently, the relative error on soot volume fraction results from these two effects. Figure 9(b)–(d) show the relative error in soot volume fraction predicted by the gray soot model, the gray model, and the OTA, respectively. These simplified radiation models lead to significant discrepancies on the soot volume fraction, with the maximum relative error being 19%, 79%, and 110% for the gray soot, gray and OTA models, respectively. 4. Conclusions Microgravity ethylene/air laminar diffusion flames with different fuel and oxidizer velocities were simulated by considering a detailed chemistry, an advanced soot model based on PAH and a WBCK radiative model coupled with DOM to solve the RTE. Numerical results are in quantitative agreement with the available experimental data. Soot is formed in a thin region following the stand-off distance where OH, H and A4 are located and is transported inside the boundary layer by convection and thermophoresis. The combustion efficiency is significantly lower than 1, indicating that flame quenches at the trailing edge. In addition, it was found to decrease as the residence time increases. This quenching phenomenon explains the increase in flame length with the oxidizer velocity observed in previous experimental studies [23–27]. Radiant fractions, which measure the level of radiative loss, are higher than those encountered in normal gravity flames due to longer residence times. In addition, they are found to decrease as the fuel velocity increases. The influence of approximate radiative property models, namely the gray soot model, the gray model with soot and combustion

108

J. Contreras et al. / Combustion and Flame 191 (2018) 99–108

gases treated as gray species, and the optically-thin approximation, was evaluated. The following conclusions can be drawn: (a) Soot radiation accounts for about 50% of the total radiative heat loss in this flame and plays a significant role in the phenomenon of flame quenching at the trailing edge. (b) Gray soot and Planck mean models cause significant discrepancies in temperature and soot volume fraction distributions and moderate discrepancies in the flame shape. The level of error is higher for the Planck mean model. (c) OTA neglects the absorption of radiation which affects significantly the temperature, the soot volume fraction and the flame shape, and the radiative quenching at the flame tip. (d) All the approximate radiative property models introduce significant discrepancies in the predicted temperature, soot volume fraction, flame geometry and quenching processes. They should be avoided in the study of such kind of flames. Acknowledgments J. Contreras wishes to thank the CONICYT Chile for financial support through its BECAS-CHILE program (“Doctorado en el Extranjero” #72130544) and FONDECYT Iniciación #11161045. References [1] O. Fujita, Solid combustion research in microgravity as a basis of fire safety in space, Proc. Combust. Inst. 35 (2015) 2487–2502. [2] H.D. Ross, Microgravity combustion: fire in free fall, Academic Press, 2001. [3] H.W. Emmons, The film combustion of liquid fuel, ZAMM 36 (1956) 60–71. [4] S. Bhattacharjee, W. Tran, M. Laue, C. Paolini, Y. Nakamura, Experimental validation of a correlation capturing the boundary layer effect on spread rate in the kinetic regime of opposed-flow flame spread, Proc. Combust. Inst. 35 (2015) 2631–2638. [5] S. Bhattacharjee, M. Laue, L. Carmignani, P. Ferkul, S. Olson, Opposed-flow flame spread: A comparison of microgravity and normal gravity experiments to establish the thermal regime, Fire Saf. J. 79 (2016) 111–118. [6] S.L. Olson, Mechanisms of microgravity flame spread over a thin solid fuel: oxygen and opposed flow effects, Combust. Sci. Technol. 76 (1991) 233–249. [7] C. Fernandez-Pello, Flame spread modeling, Combust. Sci. Technol. 39 (1984) 119–134. [8] D.B. Bullard, L. Tang, R.A. Altenkirch, S. Bhattacharjee, Unsteady flame spread over solid fuels in microgravity, Adv. Space Res. 13 (1993) 171–184. [9] S. Bhattacharjee, C.P. Paolini, F. Miller, R. Nagarkar, Radiation signature in opposed-flow flame spread, Prog. Comput. Fluid Dyn. 12 (2012) 293–301. [10] J.S. T’ien, D.W. Foutch, Extinction of a stagnation-point diffusion flame at reduced gravity, AIAA J. 25 (1987) 972–976. [11] A. Fuentes, G. Legros, P. Joulain, J.P. Vantelon, J.L. Torero, Evaluation of the extinction factor in a laminar flame established over a PMMA plate in microgravity, Microgravity Sci. Technol. 17 (2005) 10–14. [12] T. Vietoris, J.L. Ellzey, P. Joulain, S.N. Mehta, J.L. Torero, Laminar diffusion flame in microgravity: the results of the minitexus 6 sounding rocket experiment, Proc. Combust. Inst. 28 (20 0 0) 2883–2889. [13] A.F. Osorio, C. Fernandez-Pello, D.L. Urban, G.A. Ruff, Limiting conditions for flame spread in fire resistant fabrics, Proc. Combust. Inst. 34 (2013) 2691–2697. [14] J.E. Kleinhenz, J.S. T’ien, Combustion of nomex® iii fabric in potential space habitat atmospheres: cyclic flame spread phenomenon, Combust. Sci. Technol. 179 (2007) 2153–2169. [15] S. Takahashi, H. Ito, Y. Nakamura, O. Fujita, Extinction limits of spreading flames over wires in microgravity, Combust. Flame 160 (2013) 1900–1902. [16] M. Nagachi, F. Mitsui, K. Kizawa, J.-M. Citerne, H. Dutilleul, G. Jomaas, G. Legros, O. Fujita, Effect of flow direction on the extinction limit of spreading flame over wire insulation, 46th International Conference on Environmental Systems (2016). [17] J.-M. Citerne, H. Dutilleul, K. Kizawa, M. Nagachi, O. Fujita, M. Kikuchi, G. Jomaas, S. Rouvreau, J.L. Torero, G. Legros, Fire safety in space – investigating flame spread interaction over wires, Acta Astronaut. 126 (2016) 500–509. [18] L. Hu, Y. Zhang, K. Yoshioka, H. Izumo, O. Fujita, Flame spread over electric wire with high thermal conductivity metal core at different inclinations, Proc. Combust. Inst. 35 (2015) 2607–2614. [19] J.L. Torero, T. Vietoris, G. Legros, P. Joulain, Estimation of a total mass transfer number from the standoff distance of a spreading flame, Combust. Sci. Technol. 174 (2002) 187–203. [20] S. Rouvreau, P. Joulain, H.Y. Wang, P. Cordeiro, J.L. Torero, Numerical evaluation of boundary-layer assumptions used for the prediction of the standoff distance of a laminar diffusion flame, Proc. Combust. Inst. 29 (2002) 2527–2534. [21] G. Legros, P. Joulain, J.P. Vantelon, A. Fuentes, D. Bertheau, J.L. Torero, Soot volume fraction measurements in a three-dimensional laminar diffusion flame established in microgravity, Combust. Sci. Technol. 178 (2006) 813–835.

[22] A. Fuentes, S. Rouvreau, P. Joulain, J.P. Vantelon, G. Legros, J.L. Torero, C. Fernandez-Pello, Sooting behavior dynamics of a non-buoyant laminar diffusion flame, Combust. Sci. Technol. 179 (2007) 3–19. [23] A. Fuentes, G. Legros, A. Claverie, P. Joulain, J.P. Vantelon, J.L. Torero, Interactions between soot and CH radicals in a laminar boundary layer type diffusion flame in microgravity, Proc. Combust. Inst. 31 (2007) 2685–2692. [24] G. Legros, A. Fuentes, S. Rouvreau, P. Joulain, B. Porterie, J.L. Torero, Transport mechanisms controlling soot production inside a non-buoyant laminar diffusion flame, Proc. Combust. Inst. 32 (2009) 2461–2470. [25] G. Legros, J.L. Torero, Phenomenological model of soot production inside a non-buoyant laminar diffusion flame, Proc. Combust. Inst. 35 (2015) 2545–2553. [26] E.P. Volchkov, V.V. Lukashov, V.V. Terekhov, K. Hanjalic, Characterization of the flame blow-off conditions in a laminar boundary layer with hydrogen injection, Combust. Flame 160 (2013) 1999–2008. [27] J. Contreras, J.-L. Consalvi, A. Fuentes, Oxygen index effect on the structure of a laminar boundary layer diffusion flame in a reduced gravity environment, Proc. Combust. Inst. 36 (2) (2017) 3237–3245. [28] S. Bhattacharjee, R.A. Altenkirch, Radiation-controlled, opposed-flow flame spread in a microgravity environment, Symp. (Int.) Combust. 23 (1991) 1627–1633. [29] A. Liñán, The asymptotic structure of counterflow diffusion flames for large activation energies, Acta Astronaut. 1 (1974) 1007–1039. [30] J.S. T’ien, D.W. Foutch, Extinction of a stagnation-point diffusion flame at reduced gravity, AIAA J. 25 (1987) 972–976. [31] K. Santa, B. Chao, P.B. Sunderland, D. Urban, D. Stocker, R. Axelbaum, R, Radiative extinction of gaseous spherical diffusion flames in microgravity, Combust. Flame 151 (2007) 665–675. [32] N.A. Slavinskaya, P. Frank, A modelling study of aromatic soot precursors formation in laminar methane and ethene flames, Combust. Flame 156 (2009) 1705–1722. [33] R.J. Kee, G. Dixon-Lewis, J. Warnatz, M.E. Coltrin, J.A. Miller, A FORTRAN computer code package for the evaluation of gas-phase multicomponent transport properties, 1986, pp. 3–39. Sandia Rep. SAND86-824. [34] H. Guo, F. Liu, G.J. Smallwood, Ö.L. Gülder, Numerical study on the influence of hydrogen addition on soot formation in a laminar ethylene–air diffusion flame, Combust. Flame 145 (2006) 324–338. [35] J. Appel, H. Bockhorn, M. Frenklach, Kinetic modeling of soot formation with detailed chemistry and physics: laminar premixed flames of C2 hydrocarbons, Combust. Flame 121 (20 0 0) 122–136. [36] S.B. Dworkin, Q. Zhang, M.J. Thomson, N.A. Slavinskaya, U. Riedel, Application of an enhanced PAH growth model to soot formation in a laminar coflow ethylene/air diffusion flame, Combust. Flame 158 (2011) 1682–1695. [37] V. Chernov, Q. Zhang, M.J. Thomson, S.B. Dworkin, N.A. Slavinskaya, U. Riedel, Soot formation with C1 and C2 fuels using a novel chemical mechanism for PAH growth, Combust. Flame 161 (2014) 592–601. [38] L. Talbot, R.K. Cheng, R.W. Schefer, D.R. Willis, Thermophoresis of particles in a heated boundary layer, J. Fluid Mech. 101 (1980) 737–758. [39] M. Frenklach, H. Wang, Detailed mechanism and modeling of soot particle formation, in: H. Bockhorn (Ed.), Soot Formation in Combustion, Springer, Berlin, Heidelberg, 1994, pp. 165–192. SE - 10. [40] C.P. Fenimore, G.W. Jones, Oxidation of soot by hydroxyl radicals, J. Phys. Chem. 71 (1967) 593–597. [41] M.F. Modest, Radiative heat transfer, Academic Press, San Diego, 2013. [42] A. Soufiani, J. Taine, High temperature gas radiative property parameters of statistical narrow-band model for H2 O, CO2 and CO, and correlated-K model for H2 O and CO2 , Int. J. Heat Mass Transfer 40 (1997) 987–991. [43] W.H. Dalzell, A.F. Sarofim, Optical constants of soot and their application to heat-flux calculations, J. Heat Transfer 91 (1969) 100–104. [44] H. Chu, J.-L. Consalvi, M. Gu, F. Liu, Calculations of radiative heat transfer in an axisymmetric jet diffusion flame at elevated pressure using different gas radiation models, J. Quant. Spectrosc. Radiat. Transfer 197 (2017) 12–25. [45] R. Demarco, J.L. Consalvi, A. Fuentes, S. Melis, Assessment of radiative property models in non-gray sooting media, Int. J. Therm. Sci. 50 (2011) 1672–1684. [46] C.P. Thurgood, A. Pollard, H.A. Becker, The TN quadrature set for the discrete ordinates method, J. Heat Transfer 117 (1995) 1068–1070. [47] S. Patankar, Numerical heat transfer and fluid flow, Taylor & Francis, 1980. [48] Q. Zhang, H. Guo, F. Liu, G.J. Smallwood, M.J. Thomson, Implementation of an advanced fixed sectional aerosol dynamics model with soot aggregate formation in a laminar methane/air coflow diffusion flame, Combust. Theory Model. 12 (2008) 621–641. [49] C-H. Chen, J.S. T’ien, Diffusion flame stabilization at the leading edge of a fuel plate, Combust. Sci. Technol. 179 (2007) 3–19. [50] K.T. Walsh, M.B. Long, M.A. Tanoff, M.D. Smooke, Experimental and computational study of CH, CH∗ , and OH∗ in an axisymmetric laminar diffusion flame, Symp. (Int.) Combust. 27 (1998) 615–623. [51] G.H. Markstein, J. De Ris, Radiant emission and absorption by laminar ethylene and propylene diffusion flames, Symp. (Int.) Combust. 20 (1985) 1637–1646. [52] J.H. Kent, A quantitative relationship between soot yield and smoke point measurements, Combust. Flame 63 (1986) 349–358. [53] R. Demarco, F. Nmira, J.L. Consalvi, Influence of thermal radiation on soot production in Laminar axisymmetric diffusion flames, J. Quant. Spectrosc. Radiat. Transfer 120 (2013) 52–69. [54] F. Liu, H. Guo, G. Smallwood, Effects of radiation model on the modeling of a laminar coflow methane/air diffusion flame, Combust. Flame 138 (2004) 136–154.