Parametric and statistical investigation of the behavior of a lifted flame over a turbulent free-jet structure

Combustion and Flame 137 (2004) 458–477 www.elsevier.com/locate/jnlabr/cnf

Parametric and statistical investigation of the behavior of a lifted flame over a turbulent free-jet structure A. Cessou,∗ C. Maurey, and D. Stepowski CORIA—UMR 6614, CNRS, Université & INSA de Rouen, 76801 Saint Etienne du Rouvray cedex, France Received 9 September 2003; received in revised form 5 March 2004; accepted 14 March 2004 Available online 9 April 2004

Abstract Partially premixed combustion is involved in many practical applications, due to partial premixing of combustible and oxidant gases before ignition, or due to local extinctions, which lead to mixing of reactants and burned gases. To investigate some features of flames in stratified flows, the stabilization processes of lifted turbulent jet flames are studied. This work offers a large database of liftoff locations of flames stabilized on turbulence-free jets for different fuels and nozzle diameters studied over their flame stability domains. Methane, propane, and ethylene flames are investigated for nozzle diameters of 2, 3, 4, and 5 mm. Blowout velocities are measured and compared with an approach based on large-scale structures of the jet. The axial and radial locations of the flame base are measured by planar laser-induced fluorescence (PLIF) of the OH radical through high sampling (at least 5000 points). From this large database the average locations of the flame base are analyzed for the fuels investigated. The pdfs exhibit an evolution of their shapes according to the region of the turbulent jet where the flame stabilizes (potential core, transition to turbulence, or fully developed turbulence regions). This dependence is probably due to the interaction of the flame with the jet structures. This is confirmed by the comparison between the amplitude of the height fluctuations and the local size of the large-scale structures deduced from particle image velocimetry measurements and self-similarity laws for velocity. The results show the flame can be carried over a distance equal to the local diameter of the jet within the region of fully developed turbulence for propane and ethylene, and over a slightly larger distance for methane.  2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Diffusion flame; Liftoff; Blowout; Optical diagnostics

1. Introduction Flame stabilization is a phenomenon to be controlled in numerous industrial applications (furnace, boiler, rocket engine, turbine reactor, etc.). It requires the suitable mixing of fuel, oxidizer, and released heat. In industrial applications the flame is usually anchored at the nozzle to avoid flame instability (leading to pressure variation), extinction (leading to unburned * Corresponding author. Fax: 33-(0)-2-32-91-04-85.

E-mail address: [email protected] (A. Cessou).

hydrocarbon emission, etc.) and blowout for safety reasons. Partially premixed combustion is involved in more and more industrial applications to reduce NOx emission and fuel consumption. This mode of combustion exhibits particular properties and needs to be better understood. From a fundamental point of view, the turbulent lifted flame is an interesting configuration with which to investigate the properties of partially premixed combustion, as this phenomenon results from a balance of the effects of combustion and turbulence involving particular interactions between aerodynamics and mass and heat transfers. Upstream of the flame base the jet fluid mixes with the

0010-2180/$ – see front matter  2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2004.03.005

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ambient fluid, leading to partial premixing within the shear layer where the flame stabilizes. In this region the flame edge is submitted to high shear and mixture fraction gradients, leading to a complex phenomenon. In this context, numerous theories have been proposed in the past, as reviewed by Pitts [1]; they fall into two categories. One approach is based on turbulent flame propagation [2–5] and the other on extinction, considering either non-premixed flamelets [6,7] or the role played by large-scale structures [8,9]. More recently partially premixed propagation has been introduced in the description of turbulent lifted flame discussed in Peters’ review [10]. The stabilization of turbulent flames on jets is controlled by specific combustion properties at the flame base induced by the local mixture fraction gradients and their superimposition on local turbulence upstream of the reaction zone. In laminar flows, the flame base develops into a triple flame structure (fuellean and fuel-rich premixed branches and a trailing diffusion flame) across a mixture fraction gradient, and flame stabilization is controlled by the combined effects of mixture fraction gradient and aerodynamical flow properties, which influence the heat release and mass fluxes at the flame base [11,12]. In turbulent flows, these interactions and their consequences on flame behavior become very complex, and the triple flame becomes distorted, with branches overlapping into the trailing diffusion flame [13]. Numerous studies are still required to better understand the interaction between the flame edge and the turbulent flow, and to provide validation tools for numerical modeling. Recent experimental studies show that in turbulent flows the mixture at the flame base is within the flammable limits [14–16] and the velocity field in the stabilization region is slow enough to allow propagation of a leading-edge flame [17,18]. This was confirmed by the experimental observation of a leadingedge flame in turbulent jet flames [19]. Nevertheless the properties of the flame edge in turbulent fields are not well characterized and further investigations are required. The aim of the present study is to provide a large database of flame base locations (liftoff height and radius) for turbulence-free jets over their stability domain for different fuels (methane, propane, ethylene, and air-diluted ethylene) and different nozzle diameters (from 2 to 5 mm i.d.). The axial and radial locations of the flame base are measured by OH planar laser-induced fluorescence (PLIF). Blowout velocities are measured and their values are analyzed to determine whether the process can be described by a simplified model based on the large-scale structures of the jet. The locations of the flame base near the blowout condition are compared with those derived from the usual assumptions involved in the model proposed to

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describe the blowout condition [4,8]. Axial and radial locations of the flame base are measured and statistically analyzed over the stability diagrams of the flames investigated. The large database of flame base locations (probability density function (pdf), average, standard mean deviation) is examined and exhibits a correlation between flame base behavior and the region of the jet where flame stabilizes. These results show the role played by the large-scale structures of the jet in the fluctuations of the flame base. This role is confirmed by comparing the amplitude of the flame base fluctuations with the local size of the large scales deduced from PIV measurements. Despite the large database of flame base locations, physical phenomena governing the stabilization of turbulent lifted flames are not yet fully understood and there are still several directions for future investigation. 2. Experimental setup 2.1. Apparatus The burner consists of a stainless-steel tube with an inside diameter, D, of 2, 3, 4, or 5 mm. It is now well established that the basic jet velocity profile is a determining parameter of the instability that controls the development of the turbulence within the jet (Fig. 1). The basic velocity profile depends on the experimental conditions (nozzle contraction, Reynolds number, roughness, jet exit configuration). To obtain a flat velocity profile and a thin basic mixing layer from the small-diameter tubes, we chose straight, 200 mmlong tubes to allow an established turbulent pipe flow for all the velocities, fuel gases, and tube diameters. The minimum length of flow established is estimated from L = 4.4Re1/6 D [20]. We have chosen to investigate the flame stabilization in free jets for which the turbulence field is welldocumented. Results from the literature [21,22] show that confinement of the jet by walls does not disturb the jet dynamics if the distance between the walls is large enough (greater than 10 diameters) to avoid the development of new instabilities [22], which would modify the transition to turbulence. However, our experimental observations during firing have shown that a cylindrical confinement of even 25 diameters could disturb the flame stabilization. To avoid dynamic disturbance of the natural free jet flame, stabilization is investigated without any confinement. This is not a common experimental configuration as seeding (as required for velocity measurements) is more difficult to achieve. It is necessary to seed the ambient gas over the first diameters of the jet to avoid bias of velocity measurements within the mixing layer [23]. This is particularly important when studying the jet dynamics in the regions of the flame stabilization occurring

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Fig. 1. Experimental setup. Table 1 Domain of operating conditions for the three fuels investigated and four nozzle diametersa Fuel

i.d. (mm)

o.d. (mm)

Umin (m/s)

Remin

Umax (m/s)

Remax

Umax /Ubo (%)

Methane Propane Ethylene Ethylene (Yf = 0.9) Ethylene (Yf = 0.8) Methane Propane Ethylene Methane Propane Ethylene Methane Propane Ethylene

2 2 2 2 2 3 3 3 4 4 4 5 5 5

3 3 3 3 3 4 4 4 5 5 5 6 6 6

22 8 21 21 21 19 8 18 15 7 17 12 7 14

2700 3800 5000 4700 4500 3600 5700 6400 3700 6700 8000 3700 8400 8300

30 48 115 88 68 37 58 146 46 71 115 62 51 90

3,800 23,000 27,000 20,000 14,000 6,900 42,000 52,000 11,000 68,000 54,000 19,000 61,000 53,000

97 92 97 92 88 95 85 96 84 72 x 98 x x

Umin and Umax are the minimum and maximum jet velocities of our studies. Ubo is the value of jet velocity when blowout occurs. a Inside (i.d.) and outside (o.d.) diameters are indicated.

for very low mixture fractions, i.e., regions where the volume fraction of entrained air is large. For this reason, both the jet and a very slow surrounding co-flow are seeded. The co-flowing stream emerges from an annular concentric duct (i.d. of 120 mm) with velocity around 5 cm/s. To verify that such a low co-flow does not modify the flame stabilization, we measured the

liftoff location (height and radius) from fluorescence images, as explained in a later section, by a method already presented in a previous paper [24]. Jet flames of methane, propane, ethylene, and air-diluted ethylene are investigated for different jet diameters from the hysteresis conditions to flame blowout. Operating conditions are summarized in Ta-

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Table 2 Physical properties of fuels investigateda

Methane Propane Ethylene Ethylene (Yf = 0.9) Ethylene (Yf = 0.8)

ρ0 (kg/m3 ) 15 ◦ C, 1.013 bar

ρ0 /ρair

SLs (cm/s)

Zs

SLmb (cm/s)

ϕmb

Zmb

0.679 1.91 1.19 1.194 1.197

0.55 1.52 0.97 0.973 0.976

37.5 40 66 66 66

0.0548 0.06 0.0634 0.0704 0.0792

38.8 41.2 72.5 72.5 72.5

1.1 1.1 1.2 1.2 1.2

0.06 0.0656 0.0751 0.0835 0.0939

a ρ , fuel density; S , laminar burning velocity; Z, mixture fraction; ϕ, equivalence ratio. Subscript s defines the stoichioL 0 metric condition, and subscript mb, the condition of maximum laminar burning velocity.

ble 1. The three fuels were chosen because they have different densities. Thus, the flames stabilize on different jet structures depending on the variable density effects. The maximum burning velocity is identical for propane and methane, while it is greater for ethylene [25–28]. For the three fuels the burning velocity is maximum at an equivalence ratio of 1.1 for methane and propane and a ratio of 1.2 for ethylene. Table 2 summarizes the physical properties of the fuels investigated. All the flow rates are controlled through sonic nozzles. For the 2-mm-diameter jet of ethylene two cases of air dilution are investigated, for which the mass fractions of ethylene are 0.9 and 0.8. The small dilution values ensure that the injected mixtures are outside the flammability limits and make it possible to change the mixture fraction without modifying jet density and maximum flame propagation velocity. 2.2. Seedings To measure the potential core length, incense is injected just around the jet base and is entrained with air into the jet. When excited with UV laser radiation (see next section) incense emits fluorescence, so the potential core, where no air is entrained, appears black in the fluorescence images. These fluorescence images allow the instantaneous measurement of potential core length. Two seedings are used for PIV measurements. The jet is seeded with very small droplets of olive oil, and the co-flow is seeded with zirconium dioxide particles of 1-µm nominal diameter. An experiment had shown that the use of olive oil droplets to seed the jet fluid has no influence on the location of the flame base. Co-flow seeding by ZrO2 particles allows particle image velocimetry (PIV) measurements within the flame where these particles survive. This article focuses on the flow properties upstream of the flame, so all the PIV measurements presented here are performed in the cold flow, at a location that is up to two times the SD of liftoff height upstream of the mean liftoff height.

2.3. Laser-induced fluorescence OH PLIF images are used to provide the location of the reaction zone. OH is often considered as a poor marker of the reaction zone location [29], because, due to its recombination by slow three-body reactions, it can be transported by convection and diffusion outward from the primary reaction zone [24,30]. In a premixed combustion structure, OH rises steeply on the fresh mixture side and has a long tail in the burned gases. When using LIF, OH is, therefore, a good marker of the interface between fresh and burned gases in a premixed flame. In a non-premixed flame structure, OH diffuses slowly on either side of the reaction zone. Simultaneous images of OH and CH LIF [31] in such flames show that radicals indicate almost the same reaction zone. LIF of CH marks the rich side of the reaction zone, while LIF of OH is present in a lean mixture region in close contact with the CH zone. These simultaneous images show that LIF of OH or CH radicals is an accurate marker of the reaction zone. OH radicals and incense are excited by laser radiation (λ = 283.9 nm, t = 10 ns, E = 20 mJ/pulse) which is provided by the second harmonic of a dye laser pumped by the second harmonic of a Nd:YAG laser at 10 Hz. The OH ground state is laser probed by pumping the Q1 (6) line of the (0, 1) vibrational band of the (X2 Π − A2 Σ) electronic transition. Over the expected temperature range in the reaction zone (1200–1800 K) the relative population of the absorbing rotational level (J  = 6) is nearly independent of the temperature, so the global OH concentration can be inferred from that of the probed level [24]. OH fluorescence is detected via the (1, 1) and (0, 0) radiative relaxation bands (λ ∼ 315 nm) by interposing a highpass filter which removes the strong elastic scattering from particles. This scheme was chosen because it allows the removal of strong elastic scattering from particles when simultaneous measurements of PIV and OH fluorescence are performed [32]. The height of the laser sheet (400 µm thick) depends on the spatial fluctuations of the bottom of the

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lifted flame and ranges from 20 to 80 mm. To measure the location of the flame stabilization statistically, OH fluorescence is imaged at 90◦ onto a gated intensified video CCD camera (Proxitronic, t = 50 ns) with a 105-mm, f/4.5 UV lens (Nikkor). The video signal is digitized by a frame grabber board (Matrox MVP-AT, 512 × 512 × 8 bits) connected to a PC. The location of the flame base is measured from OH LIF images with a processing method previously developed to investigate a burning spray [24]. Here, we only briefly expound the principle of the processing, with more details available in the cited paper. The processing allows real-time measurements of the liftoff location from each instantaneous image of laser-induced fluorescence of the OH radical. The histogram of signal levels in the region where the turbulent flame stabilization takes place is analyzed to discriminate between the background and OH fluorescence levels. The two thresholds for a top-hat filter are objectively determined to binarize the image and extract the OH fluorescence contribution. Additional spatial filtering is required to erase some residues smaller than the impulse response of the detector. In such turbulent flames it has been checked that no correlation exists between the liftoff locations measured on opposite sides of the jet axis [33,34], so two independent measurements can be performed on each image. Therefore, real-time processing easily provides statistics over a large number of samples (several thousand). A processing window is placed so as to cover the region where flame stabilization can take place. The liftoff height is determined from this profile as the lowest elevation where the integrated count number is above the level associated with the spatial filtering. Once this height is measured the radial location of the liftoff is determined by using a thin processing window at the liftoff height and searching for the middle of the integrated signal over this horizontal window. Simultaneous fluorescence of incense and OH radicals is performed to measure the position of the flame base relative to the potential core length. Incense particles are excited with the same laser radiation as OH radicals (λ = 283.9 nm). Owing to this excitation, incense exhibits a broadband fluorescence from 300 to 640 nm with a peak at 410 nm. This fluorescence is red shifted and a high-pass filter in front of the detector removes the strong elastic scattering occurring at the particle interfaces. As the laser radiation is still tuned on the Q1 (6) OH rotational line, both the incense particles and OH radical are excited by the laser sheet. Fluorescence radiation from both species is imaged onto a slow-scan intensified CCD camera (Princeton, T = 50 ns) with a 105 mm UV lens. The effective dynamic range of the camera is 14 bits, as the fast A/D converter is used to acquire a statistical

sampling of the images. The wide dynamic range of the detector, wider than that used for single OH PLIF, distinguishes the incense signal from the OH signal, as illustrated in the next section by simultaneous measurements of liftoff height and potential core length. 2.4. Particle image velocimetry PIV measurements are performed to characterize the aerodynamic properties of the cold jet below the flame. The PIV calculations are performed under burning conditions for elevations smaller than the minimum liftoff height. Velocity fields are determined for the 4-mm i.d. nozzle and initial jet velocities close to the blowout conditions (44 m/s for methane, i.e., 80% of Ubo ; 60 m/s for propane, i.e., 60% of Ubo ; 90 m/s for ethylene) so as to cover a wide field of cold flow upstream of the flame base. The PIV apparatus consists of a two-pulse frequency-doubled Nd:YAG laser (SpectraPhysics, PIV400). The laser beam is focused with a spherical lens of 1-m focal length leading to a 200-µm-thick laser sheet that minimizes the out-of-plane motions of particles between two successive laser pulses. The delay between two laser pulses is 5 µs. The scattered light from particles (olive oil or ZrO2 particles) is imaged onto an interline CCD camera (Kodak, 1000HRS) that can acquire two successive images of 1008 × 1018 pixels2 . The images are digitized by an acquisition card and saved on a PC. The field-of-view of PIV images is 61 mm (H ) × 60 mm (V ), with a magnification factor of 59.5 µm/pixel. LaVision PIV software is used to compute the velocity field using an adaptive multipass calculation with increasingly smaller window sizes. The initial interrogation window size is 32 × 32 pixels2 and the final window size after five iterations is 16×16 pixels2 , with an overlap of 75%.

3. Results and discussion 3.1. “Blowout condition” For all fuels and nozzle diameters, when possible, lifted flames are investigated over a wide range of initial velocities, U0 , from velocities below the “liftoff velocity” (flame in the hysteresis region) to velocities leading to flame blowout. Some experimental limitations have been encountered for the highest velocities when the flame dimensions become too large for the dimensions of the experiment. The experimental determination of “blowout velocity” is delicate, because at this stage the flame is very sensitive to the large eddies passing by. We have defined this velocity, Ubo , as the jet velocity that extinguishes the flame after a few

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463

Table 3 Liftoff and blowout conditionsa Fuel

i.d. (mm)

o.d. (mm)

Ulo (m/s)

Relo

Ubo (m/s)

Rebo

Methane Propane Ethylene Ethylene–air (Yf = 0.9) Ethylene–air (Yf = 0.8) Methane Propane Ethylene Methane Propane Ethylene Methane Propane Ethylene

2 2 2 2 2 3 3 3 4 4 4 5 5 5

3 3 3 3 3 4 4 4 5 5 5 6 6 6

24 10 28 24 24 20 9 21 16 8 24 14 9 15

3,000 4,800 6,600 5,700 5,500 3,700 6,400 7,400 4,000 7,600 11,200 4,400 10,700 8,600

31 52 119 96 77 39 68 152 55 98 x 63 x x

4,000 25,000 28,000 22,000 16,000 7,500 49,000 54,000 14,000 94,000 x 20,000 x x

a Subscripts lo and bo defined liftoff and blowout conditions, respectively.

seconds (∼ 30 s). Table 3 lists “liftoff and blowout velocities” and the corresponding Reynolds numbers for all fuels and nozzle diameters investigated. Data in Table 3 show that the blowout velocity increases with jet diameter. Blowout velocities of propane flames are higher than those of methane flames, suggesting that an increase in density leads to an increase in blowout velocity, as SLmb and Zmb (Table 2) are roughly similar for the two gases. The high values of blowout velocity for ethylene, compared with propane and methane, can be attributed to the higher value of its burning velocity. The dependence of blowout velocity on physical parameters (injector diameter, burning velocity, and density) was previously observed by Kalghatgi [35], Broadwell et al. [8], and Tieszen et al. [4], and they proposed correlations for blowout based on these parameters. We examine the mechanism of blowout with the approach proposed by Broadwell et al. [8]. This description of blowout is based on the inviscid largescale motions observed in turbulent jets. This macroscopic description does not allow a fine analysis of the instantaneous phenomenon upstream of the flame when blowout occurs, but it has the advantage of introducing the important physical parameters and of predicting well blowout velocity as a function of jet radius for different fuels [36]. Flame stabilization requires molecular mixing between injected fuel and ambient air. From analysis of the mixing process from the large scale to the viscous scale, Broadwell and Breidenthal [37] have shown that the time required for the turbulent cascade from the largest scale to Kolmogorov’s scale is much longer than the time required for molecular mixing at Kolmogorov’s scale. Thus, in the process of turbulent mixing that occurs in the mixing layer of turbulent jets, the latter

time scale is neglected. This time analysis leads to a macroscopic description of flame stabilization, which is controlled by the large-scale mixing time. The blowout criterion proposed by Broadwell et al. [8] is thus that blowout occurs when the local large-scale mixing time is greater than a characteristic chemical time. This chemical time is characterized from the optimal condition for flame propagation (τch = κ/SL2 max , with κ the thermal diffusivity of air at

2000 K, κ = 4.56 × 10−4 m2 /s [8]). Tieszen et al. [4] and Burgess and Lawn [5] have proposed this chemical condition applies to a blowout location different than that suggested by Broadwell and Breidenthal. Instead of considering that the flame stabilizes along the stoichiometric curve [2,38] and that blowout occurs where the stoichiometric curve reaches its maximum width [2,39], we consider that the flame stabilizes along the curve of mixture fraction, Zmb , corresponding to maximum laminar burning velocity and that blowout occurs when this curve reaches its maximum width [4,5]. To apply the approach of Broadwell, it is therefore necessary to express the large-scale turbulent mixing time, which is a function of the mean velocity field, the Zmb mixture fraction curve, and this curves maximum width. Following the method of numerous authors [4, 5,36], the mean velocity field and the mean mixture fraction distribution are computed from selfsimilarity laws of turbulent jet [40–42], U = U0 ·


d∗ exp −(r/ah)2 , Kh

(1)


d∗ (2) exp −(r/a  h)2 ,  Kh where r and h are the radial and axial coordinates, respectively; K, K  and a, a  are self-similarity conZ=

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Table 4 Radial (rlo ) and axial (hlo ) coordinates of the flame base near blowout conditions Fuel Methane

Propane

Ethylene

Ethylene–air (Yf = 0.9) Ethylene–air (Yf = 0.8)

i.d. (mm)

Umax (m/s)

Umax /Ubo (%)

Experimental results hlo /D

rlo /D

rlo / hlo

hbo /D

rbo /D

2 3 4 5 2 3 4 5 2 3 4 5 2 2

30 37 47 62 48 58 71 51 115 146 115 90 88 68

97 95 84 98 92 85 72 x 97 96 x x 92 88

32 33 31 34 52 45 38 25 39 38 20 14 33 27

6 5 5 6 8 7 6 4 6 7 3 3 6 5

0.188 0.152 0.161 0.176 0.154 0.156 0.158 0.16 0.154 0.184 0.15 0.214 0.182 0.185

37

3.5

57

5

40

4

stants for centerline decay and radial expansion, respectively; and d ∗ is the effective diameter. Han and Mungal [43] have shown that asymptotic entrainment behavior is observed between 35 and 40 diameters downstream from the injector. The self-similarity laws can be used for blowout description as our liftoff height measurements (see later) near blowout show that blowout occurs most of the time above 35 diameters (Table 4). In both of these expressions the virtual origins are neglected, because blowout generally occurs far downstream from the injector for all the hydrocarbons investigated in this article, and expression of the effective diameter is simplified to √ d ∗ = D ρ0 /ρ∞ , because so far downstream, the local density of the jet is close to the density of ambient air [44]. The large-scale turbulent mixing time, τmix , which is characterized by the local properties of the mixing layer, is given by the ratio of the jet diameter (δ = αh, 0.4 < α < 0.5, according to Dimotakis et al. [45]) and to the velocity difference across the mixing layer [37,46], i.e., Ucl = U0 d ∗ /Kh: τmix ≡ δ/Ucl = αKh2 /U0 d ∗ .

(3)

Experimental observations [2,39] show that blowout occurs around the location where the mixture fraction curve, corresponding to the maximum laminar burning velocity, reaches its maximum radius: Z = Zmb and (d/dh)(r(Zmb , h)) = 0. From Eq. (2) this condition leads to hbo = e−1/2 d ∗ /K  Zmb . Then, by combining Eq. (3) and the blowout condition τmix > τch , the blowout velocity can be expressed as Ubo = C

d ∗ SL2

mb

2 κZmb

,

(4)

Theory (Eq. (6))

Fig. 2. Blowout velocity versus Eq. (4). The gray symbols represent data from Kalghatgi [35].

where C is an empirical constant, C = (1/ε)(αKe−1 / K  2 ) with ε the critical value of the ratio τmix /τch leading to flame blowout. Fig. 2 shows the measured blowout velocity versus the right-hand side term of Eq. (4) with C = 0.268, obtained from linear regression. Agreement between measured values and Eq. (4) is good, particularly when considering the uncertainty in measurements of blowout velocity. We note that a slight reinterpretation of the location of blowout, where (d/dh)(r(Zmb , h)) = 0 instead of (d/dh) × (r(Zs , h)) = 0, leads to a minor change in the correlation obtained: Ubo = C(d ∗ SL2 s /κZs2 ), with C = 0.237, and the dispersion of the experimental points is identical, as Zmb is slightly greater than Zs for the fuels investigated, and the increase in SL is offset by the increase in Z. Eq. (4) is in good agreement with the correlation proposed by Broadwell et al. [8], Ubo ∝ d ∗ SL2 Ψs2 /κ, considering that blowout occurs at an axial distance proportional to the flame length, defined as the length

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required to mix jet fluid and ambient gas fluid in stoichiometric proportions. This agreement rests on the fact that from self-similarity laws (Eq. (2)) the axial distance of the maximum width of Zmb (h, r) or Zs (h, r) is proportional to the flame length, and that Ψs is related to Zs by 1 + Ψs = 1/Zs and Ψs 1 for the hydrocarbon jets investigated by Broadwell et al. [8], then Ψs ∼ 1/Zs . Eq. (4) is derived from a macroscopic description of the blowout process and gives only an approximation of the blowout velocity versus the physical properties of the fuels used in the present study. As mentioned by Pitts [36] this approach has the advantage of providing a good estimation of the blowout velocity from the global properties of the fuels. The good correlation obtained using Eq. (4) shows that the model incorporates some physical properties of the flame, d ∗ , SLmb , Zmb (or Zs ), but

465

the empirical determination of constant C proves that the description is not complete, as constant C still includes the critical value of the ratio τmix /τch , which is not expressed. In particular, this ratio is expected to depend on the flow properties, such as the mixture fraction gradient, at the flame base, and on the properties of the flame that are characteristic of the tip of a diffusion edge flame. In a recent paper Boulanger and Vervisch [11] showed that the Damköhler number at the tip of a diffusion edge flame is greater than the quenching Damköhler number of a diffusion flame, due to the additional fluxes of heat and mass at the tip. Then the influence of these additional fluxes must be included in the expression of the critical value of the Damköhler number, τmix /τch , at blowout. This influence can be observed on OH laser-induced fluorescence images, near blowout (Figs. 3d–3f) where

Fig. 3. Examples of OH laser-induced fluorescence images for methane, D = 4 mm. (a)–(c) At “liftoff condition”; (d)–(f) near blowout (U0 /Ubo = 91%).

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the reaction zone is thicker than at the “liftoff condition” (Figs. 3a–3c). These observations are in agreement with the results of Han and Mungal [47] from CH LIF images. Near blowout the flame sometimes exhibits (Fig. 3f) complex structures with a lot of local extinction, but most of the time the flame base is wide with a sharp gradient of OH fluorescence. This sharp gradient of OH fluorescence is a characteristic of premixed reaction zones [32]. Thus, near blowout, the flame finds a larger premixed region than for upstream stabilization locations (Figs. 3a–3c) and usually it burns in a premixed regime as indicated by the intense gradients of OH fluorescence. These enlarged flame bases in the premixed regime resemble the combustion regime observed in laminar lifted flames near blowout (Fig. 8 in [11]), but in turbulent cases, local extinction and high perturbation of the flame sometimes occur (Fig. 3f) due to jet intermittency. These two situations are characterized by a different edge flame aspect ratio, f , defined in [11] as the ratio of the local thickness of the mixing layer (in the direction normal to the iso-Zs surface) to the thermal thickness tangential to the iso-Zs surface. Premixed reaction zones at the flame base are characterized by a low value of edge flame aspect ratio, while for high values (f ∼ 1) full quenching is observed. The feature of the OH fluorescence images near blowout shows that this edge flame aspect ratio is usually small, and sometimes local extinction occurs when its value is large due to local and instantaneous high strain and high mixture fraction gradient. These observations show the complexity of the flame structures near blowout where premixed aspects and extinction of the flame are both present. Some authors analyze flame stabilization as the balance between turbulent flame propagation and mean local flow velocity, and blowout as the condition where this balance is lost. Thus Tieszen et al. [4], using an approach based on turbulent flame propagation as first introduced by Vanquickenborne and Van Tiggelen [2], propose a correlation very similar to Eq. (4): Ubo =

∗ 2 0.013 d SLmb . 2νb Z 2

(5)

mb

Based on turbulent flame propagation, their approach is dependent on interactions of small-scale turbulent properties and combustion and on the local Reynolds number in front of the flame. Thus, their correlation depends on the local kinematic viscosity, while the inviscid approach of Broadwell et al. [8] adopted in the present article introduces the thermal diffusivity of burned gases. But it is worth noting that an identical model of blowout is obtained from these two different approaches.

Comparison of the term 0.013/2νb [4] with the value of C obtained in the present study from experimental data (Fig. 2) leads to a relative error of 40%. This difference is quite small considering the difficulty in estimating the blowout velocity. Moreover, the description assumes that self-similar behavior of the axial turbulent fluctuations is reached at the blowout location [4], which is not always the case. Despite the differences in the two approaches, one based on inviscid large-scale motion, the other depending on small-scale turbulent properties of the flow, they provide very similar results. These approaches are both derived from a description, from self-similarity laws, of the mixing process in the jet. On average, they provide a good prediction of the blowout behavior, but this agreement does not make it possible to reach any conclusion concerning a physical explanation for the blowout phenomenon. Although the approach of Tieszen et al. [4] provides a correct estimation of blowout velocity, some improvements of their description are still required. First, they consider that the flame always propagates within the intermittency limit r/ h = 0.11 [4,48], a region where the fluid is well premixed at the flame base. But the measurements (see next section) of the axial and radial coordinates of the liftoff location (Table 4) show that r/ h is close to 0.17 near the blowout condition. Thus, near blowout the flame stabilizes in a highly intermittent region and at a given instant the mixture fraction gradient can still be intense. This stratification of the flow upstream of the flame should therefore be taken into account by choosing a correlation for the turbulent burning velocity that includes the effect of the mixture fraction gradient. These approaches based on average balance between turbulent flame propagation and local flow velocity are interesting as they could be linked to the mechanism of blowout proposed by Han and Mungal [47]: the flame blows out when the flame base cannot sustain the high value of the stoichiometric velocity. But the correlation of turbulent burning velocity used in these approaches must include the properties of partially premixed flame as mentioned above. The location where the Z = Zmb surface reaches its maximum width is determined from a self-similarity law of the isothermal jet (Eq. (2)): hbo =

e−1/2 d ∗ , K  Zmb

rbo =

a  e−1/2 d ∗ √ . K  2 Zmb

(6)

And rbo / hbo = 0.094. The values of hbo /D and rbo /D corresponding to our experimental conditions are reported in Table 4, with K  = 0.2 and a  = 0.132 [41,49]. While the theoretical values of hbo /D

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are very close to experimental values near blowout, the theoretical values of rbo /D are underestimated. The experimental value of rbo / hbo is roughly constant, but the value is almost two times greater than the theoretical value derived from Eq. (6). All the descriptions [2,4,5,8] of blowout or liftoff of turbulent jet flames assume the flame does not disturb the upstream cold flow. This assumption is correct up to a certain limit just in front of the flame. Due to heat release, the flow diverges in front of the flame; this phenomenon explains the higher propagation speed of a triple flame compared with that of a premixed flame [50]. The deflection of the flow in front of the flame has been observed by other groups [18,43], but it is still necessary to determine if the flow deflection can change the location of the flame base estimated from the properties in the upstream cold flow. The flow deflection in front of the flame leads to a change in the location of the isosurface Z = Zmb and of the dynamic condition surface at stabilization (τmix = ετch [8], U = St [4], or Utur = St [5]). Recently Boulanger et al. [51] showed that the flow deflection induced by heat release brings the laminar flame much closer to the burner and at larger radial locations than expected from the cold flow assumption under the flame. The heat release

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effect induces a complete reorganization of the flow under the flame and completely changes the position where suitable conditions of mixture and velocity conditions are found. As the radial location of the flame base is underestimated, the flow deflection under the flame, and therefore the mixture fraction gradients, must be taken into account in the description of turbulent flame stabilization, even for a blowout description. 3.2. Statistical measurements of liftoff location The axial (hlo ) and the radial (rlo ) coordinates of the bottom of the flame are measured from OH laser-induced fluorescence using the real-time image processing presented previously. This real-time and automatic detection of the liftoff location allows statistical sampling, at least 5000 measurements for each operating condition. The large number of samples permits calculation of the pdf of the liftoff height and radius for each operating condition. Examples of height and radius pdfs are presented in Fig. 4 for three operating conditions representative of low, medium, and high jet velocity conditions. At low velocities (Figs. 4a, 4d) the height and radius pdfs are very narrow and asymmetric; the curves show a rapid rise and

Fig. 4. Pdfs of normalized liftoff height and radius for methane, D = 4 mm. (a), (d) U0 = 16 m/s, (b), (e) U0 = 20 m/s, (c), (f) U0 = 31 m/s.

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Fig. 5. Average (top) and SD (bottom) of height and radius of flame base for methane versus jet velocity.

a moderate falloff. The pdfs tend to a minimum height showing the flame cannot stabilize below a minimum height where the strain rate and mixture fraction gradient are becoming too high. In the medium velocity domain, the pdfs are shifted to greater height and radius values and are wider and more symmetric (Figs. 4b, 4e). For high velocity, the pdfs become totally symmetric, while the height and radius are higher (Fig. 4c, 4f). This observation for high liftoff heights is in agreement with measurement of Hammer and Roshko [52]. In the high velocity domain, the higher the velocity, the greater the height and radius, and the broader the pdfs. It will be shown in the next section that for high jet velocities, the flame stabilizes in a fully developed turbulent region where the pdfs of liftoff height and radius are found to be symmetric. From these pdfs different order moments such as average and mean standard deviation can be worked out. Figs. 5, 6, and 7 present the variations of the average and mean standard deviation of liftoff height and radius versus jet velocity, U0 , for methane, propane, and ethylene, respectively. The liftoff height domain is the same for all the fuels investigated; it ranges from 2 to around 170 mm, for the same range of jet velocities of methane and propane, but for higher velocities with ethylene. The averages and fluctuations of height and radius increase with jet velocity.

Liftoff height shows a nonlinear rise for small velocities before it increases linearly at higher velocities; this change is particularly clear for ethylene flames (Fig. 7). At a given value of U0 , the fluctuations of height and radius are clearly smaller for ethylene than for propane, and more especially than for methane. At low velocities for methane, the minimum liftoff height is greater, and the range of the height fluctuations is wider than for propane or ethylene. For each fuel, average and mean standard deviation of height and radius increase moderately with nozzle diameter. For a given axial distance, the liftoff radius is identical for all fuels. In Fig. 8 the normalized coordinates of the liftoff location are presented for all the fuels and injector diameters under all the operating conditions investigated. This figure shows that the stabilization location occurs on the same straight line for all of the hydrocarbons used: 
hlo − h0 /D = 6.8rlo /D.

(7)

The value of h0 = −4.5D is of the same order of magnitude as the virtual origin in the similarity laws of turbulence-free jets [41,53]. This expression is only a first-order approximation and cannot highlight the dependence of the stabilization location on the physical properties of the fuel. In Fig. 8 the isolines Z = Zmb are presented for pure methane, propane,

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Fig. 6. Average (top) and SD (bottom) of height and radius for propane versus jet velocity.

Fig. 7. Average (top) and SD (bottom) of height and radius for ethylene versus jet velocity.

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Fig. 8. Normalized liftoff coordinates for all the operating conditions investigated.

and ethylene jets as deduced from self-similarity laws (Eq. (2)). As noted for blowout, the experimental radial location for liftoff is greater than the theoretical radius, especially for distances greater than 20D from the injector, where the similarity laws are normally valid. The circles represent the theoretical locations of blowout (Eq. (6)), for which we have previously seen that the height is correctly estimated, while the radius is underestimated. For liftoff, Fig. 8 shows the radius is still underestimated, whereas no conclusion can be drawn for height from the similarity laws alone. But it can be seen that the assumption that the flame stabilizes on average along the iso-Zmb defined by self-similarity in the cold jet is not validated. This result means that further investigation on the turbulent mixing process in front of the flame is required. Concentration field measurements in front of lifted flames [14,15,54–56] have shown that the flame stabilizes in a region where the mixture is almost stoichiometric. These results suggest that the assumption of a stoichiometric mixture in front of the flame is valid. The discrepancy between iso-Zmb surface values determined from the similarity laws for cold jets and the experimental flame base locations may then be attributed to the effect of heat release in the region directly in front of the flame base. Heat release leads to flow deflection in front of the flame [50]. For laminar lifted flames Boulanger et al. [51] have shown that this flow deflection brings the flame much lower than has been expected from self-similarity laws for laminar jets. This disagreement with theoretical prediction has been previously observed in the experimental work of Chung and Lee [57]. From direct numerical simulation of a laminar flame lifted on a round jet, Boulanger et al. [51] have shown that the flame

is located on the stoichiometric surface, and the flow deflection induced by heat release leads to a stabilization location closer to the nozzle and at a larger radius. They have also observed that these heat release effects increase with the Reynolds number of the jet. In turbulent jets, such heat release effects may explain the discrepancy between the iso-Zmb location and the experimental location of the flame base. It would be interesting to evaluate such heat release effects for turbulent jet flames and, particularly, for flames of low and high Reynolds number, i.e., low and high values of h/D. Whether the flame stabilization in a mixture close to stoichiometric is a valid assumption under all operating conditions should also be investigated. Measurements of mixture fraction in front of the flame base have been performed by different authors [14–16,54–56] but the conclusions depend on the value of the Reynolds number of the jet and on the measurement method, especially on the method used to identify the flame. Some works confirm this assumption [54,55] whereas others show that the mixture in front of the flame base can be in lean proportion [14,16,56]. Kelman et al. [14] have shown from Raman measurements that fuel sometimes exists only on the jet side of the reaction zone and does not surround the flame base. Mixture fraction measurements in front of the flame base will be very helpful in determining whether the stoichiometric mixture assumption is valid over the entire stability diagram. In particular, with high jet Reynolds numbers, close to the blowout condition, the local velocity increases along the stoichiometric isoconcentration surface [47]; this could possibly make it easier for the flame to stabilize along a leaner isosurface.

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Fig. 9. Example of instantaneous measurement of the liftoff height and potential core length from simultaneous LIF images of OH radical and incense.

Fig. 10. Pdfs of the simultaneous liftoff height and potential core length and their difference, , for two operating conditions: (top) methane, D = 4 mm, U0 = 15 m/s; (bottom) methane, D = 4 mm, U0 = 21 m/s.

3.3. Liftoff location over the jet structure Fig. 4 shows that the symmetry of the liftoff height pdfs depends on the distance downstream from the injector where the flame stabilizes. The pdfs are asymmetrical for low mean liftoff height and become symmetrical for stabilization elevations greater than 10D. To examine how the symmetry properties of these

pdfs are linked to the region of the turbulent jet where the flame stabilizes, the simultaneous and instantaneous liftoff height (hlo ) and the potential core length (Lpc ) are compared. These quantities are obtained from fluorescence images (Fig. 9) induced by the same laser sheet; the instantaneous liftoff height is deduced from OH LIF images and the potential core length from LIF of a particulate tracer (incense) in-

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Fig. 11. Nondimensional liftoff height fluctuations (σh /D) versus the nondimensional mean liftoff height (hlo /D) for all the operating conditions.

jected just around the jet. From these images the instantaneous difference,  = hlo − Lpc , is calculated. Fig. 10 shows the pdfs of hlo and Lpc , and the corresponding pdf of  for two operating conditions, one with a low mean liftoff height (methane, D = 4 mm, U0 = 15 m/s) and the other with a greater mean liftoff height (methane, D = 4 mm, U0 = 21 m/s). For the low liftoff height case, with asymmetric hlo -pdf, the flame stabilizes in the “initial region” [58] of the jet (distance from the injector lower than Lpc ) and  is often negative. For the case with higher liftoff height (symmetric hlo -pdf) the flame stabilizes above the initial region and  is positive most of the time. This result shows that the symmetry properties of the pdf of liftoff height are linked to the region of the turbulent jet and to the mixing layer properties where the flame stabilizes. Moreover these pdfs are asymmetric when the flame frequently stabilizes at elevations lower than the potential core length, in a region where the mixing layer is very thin. This is confirmed in Fig. 11 showing the scaled fluctuations of the height of the flame base (σh /D) versus the scaled distance from the injector where the flame stabilizes on average (hlo /D). Fig. 11 exhibits three zones corresponding well to the different regions of the turbulent jet: the initial region, or potential core region, a transition region, and the “main region” [58], where the turbulence is fully developed. The data for propane and ethylene are superimposed: for small distances from the injector (h/D < 5–6), σh /D exhibits a linear increase; downstream (h/D > 12) the increase rate of σh /D is still constant, but lower than in the initial region. Between these two regions (6 < h/D < 12), σh /D is almost constant and equal to one. These data show

that the height fluctuations of the flame base are specific to each region of the turbulent jet, with a linear increase in the “initial region” and the fully developed region, and a value almost constant within the region of transition to the developed turbulence. We can note that near blowout (U0 /Ubo > 95%) the value of σh /D deviates from the linear curve (the two highest points for ethylene). Hammer and Roshko [52] have made the same observation of increase in fluctuation of liftoff height near blowout. For methane, the behavior of the flame base is globally the same as for propane and ethylene, but the amplitude of fluctuations is greater, with the same slope in the region of fully developed turbulence (h/D > 12) as for propane and ethylene. The value of the slope is in agreement with the ratio of σh / hlo measured by Hammer and Roshko [52]; their values of σh / hlo fall between 0.05 and 0.08, whereas in our study the values of σh / hlo are roughly equal to 0.08 for h/D > 12. Schefer et al. [59] have shown from double-pulse LIF images that the flame is carried downstream by the large-scale structures of the jet, and returns to an upstream location by propagation. In view of their observations and our measurements of σh /D, it seems interesting to investigate whether a quantitative relation exists between the amplitude of the fluctuations of the flame base and the local size of the large-scale structures in the jet, as suggested by the linear growth of σh /D. The local size of the large-scale structures results from the width over which the shear is sustained, i.e., the local jet radius. This means that the local jet radius should be compared with the entire range of fluctuations of liftoff height. Both these quantities are difficult to measure experimentally, and we prefer to compare the mean standard deviation of the liftoff

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height scaled by the injector diameter with the full width at half maximum (FWHM) radius, r1/2 , of the local mean axial velocity profiles. We note that if the velocity profiles and the hlo -pdfs are gaussian, this comparison amounts to comparing the range of the liftoff height fluctuations with the local jet radius. The flame does not always stabilize at elevations where the effect of variable density and the virtual origins in the self-similarity laws can be neglected. Thus Eq. (1) is not always correct. The quantity r1/2 has been measured from PIV for the 4-mm nozzle for the three fuels investigated. The velocity field is measured in the cold jet below the flame up to 15 diameters downstream of the nozzle. This elevation is lower than the minimum liftoff height for the three operating conditions chosen, so the PIV measurements are not biased by the presence of the flame. To compare the r1/2 values with the mean standard deviation of the liftoff height over the entire stability diagram of the flame, it is necessary to know r1/2 at higher elevations than 15D. Thus to obtain the values of r1/2 as a function of the elevation above the injector, we used a model proposed by Abramovitch [58]. This model takes into account the variation of density due to entrainment and includes virtual origins for the description of the fully developed region. From the balance equation of mass and momentum it provides an expression for the axial decrease of the velocity and for the radial expansion of the jet:    √ n2u z0 ρ0 R(z) − R(z0 ) c(h − h0 ) = D √ ρ∞ 2 0.134 z √  1 + 2kz0 − (8) , (1 + z0 ) 

√ n2u z ρ0 √ ρ∞ 2 0.134 z0    ρ∞ z × 1 + 0.745k −1 , ρ0 z0

r =D

(9)

where z U = cl , z0 U0  z0 =

R(z) =

 ρ∞ k −1 , ρ0 2 √ (k − 1) z arctan 1 + 2kz − 2 √ 2k − 1 √ 1 + 1 + 2kz , − z ln √ 1 − 1 + 2kz

√  1 + 2kz √ 2k − 1

c = 0.22 is an empirical constant [58], n2u =

D/2 2U02 /DU02 dr takes into account the nonuni0 max formity of the initial velocity profile, and k = 0.745/

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n2u . From PIV measurements, n2u = 0.95. The value of r1/2 is determined by dividing the local radius of the jet, r, by 2.72 [58]. The values of Ucl versus the elevation above the nozzle are calculated from Eq. (8). In the fully developed region (h/D > 12) a comparison with the experimental values (white symbols in Fig. 12) allows us to determine the virtual origins (h0 = 1.8D for methane, h0 = −0.5D for propane, h0 = D for ethylene). The r1/2 values derived from Eq. (9) with these virtual origins are compared with the experimental values (white symbols in Fig. 13). The good agreement between the model and the experimental results shows that Abramovich’s model for r1/2 can be used for operating conditions where the flame stabilizes in the fully developed region (h/D > 12). In Fig. 11 the values of r1/2 /D calculated from Abramovich’s model are superimposed on the measured values of the mean standard deviation of liftoff height, σh /D. For ethylene and propane, the mean standard deviations of liftoff height are equal to r1/2 in the “fully developed region.” For methane, σh /D is greater than r1/2 /D, but its rate of increase with elevation above the nozzle is the same. These results show the quantitative relation between the fluctuations of the flame base and the local size of the largescale structures in the jet. The fluctuation of the liftoff height increases as the large-scale structures grow. For ethylene and propane the amplitude of fluctuations of liftoff height is equal to the local diameter of the jet (assuming the hlo -pdf is gaussian, which is true within the fully developed region). This result is in agreement with the observation of Schefer et al. [59], who noted from double-pulse LIF images that the large-scale vortical structures can cause an excessive stretch leading to transport of the flame downstream by a vortex and that the flame can return to an upstream location by propagation. From Fig. 11 we can see that the flame can be carried over a distance equal to the local diameter of the jet within the fully developed region. For methane, the fluctuation amplitudes of liftoff height are greater than the local jet diameter, but the growth rate with downstream distance is the same as that for jet diameter. This result for methane shows that further investigations are still required to elucidate the role of flame interaction with the flow, especially the flow properties, which can be modified by the behavior of the flame edge. As mentioned by Buckmaster [60], in turbulent flows, numerous parameters could affect the velocity of the edge flame: stretch; curvature, which depends on the velocity and mixture fraction gradients; scalar dissipation rate; and mixture intermittency. All these parameters are functions of the local properties of the flow and modify the velocity of the flame edge. Thus these parameters and the physical properties of fuels influence fluctu-

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Fig. 12. Axial velocity versus elevation above the nozzle. Symbols are experimental values. Black symbols: “initial region” of the jet, gray symbols: “transition region,” white symbols: “fully developed region.” Lines are results from Eq. (8), with virtual origins h0 = 1.8D for methane, h0 = −0.5D for propane, h0 = D for ethylene.

Fig. 13. r1/2 values. Symbols are experimental values. Cray symbols: “transition region,” white symbols: “fully developed region.” Lines are results from Eq. (9), with virtual origins determined from Fig. 12.

ation of the flame height. The difference in the range of height fluctuations observed for methane as compared with propane and ethylene is a consequence of the influence of all these parameters, and it seems difficult to isolate them in such a complex turbulent flow as the free jet where the interactions are strong. These effects can be separated into two categories, one due to mixture because of the difference in values of Zmb (or Zs ) for the three fuels [16], and another due to particular effects of heat release at the flame edge [12,60–64]. The difference in liftoff height fluctuations for methane could be due to its lower mixture fraction value at maximum burning velocity, Zmb (or at stoichiometry Zs ) (Table 2). Due to this lower value the CH4 flame must stabilize in a more oxidizing region than for the other two fuels, where it is submitted to

higher intermittency leading to larger height fluctuations. Measurement of mixture fraction at the flame base for the three fuels would be required to analyze this possible influence, but we can note that in Fig. 11 there is no difference in flame behavior for propane and ethylene (pure or air diluted) despite the fact that Zmb (or Zs ) is greater for pure and diluted ethylene. Laminar edge flames are submitted to great heat release because, at the edge, heat is released through directions that are parallel and perpendicular to the stoichiometric line [11,12]. Due to the curvature of the flame at the edge, effects due to hydrodynamic stretch and curvature and effects of thermodiffusive instabilities are highly probable, as are the effects of preferential diffusion induced by the local mixture fraction gradients where the flame stabilizes. All these effects depend on the Lewis number of the fuel. It is

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interesting to note that the difference in fluctuations of liftoff heights is observed for methane, which has a Lewis number that is slightly smaller than unity, whereas propane and ethylene have Lewis numbers greater than unity. Asymptotic theories [12,63] have shown that Lewis number effects on the propagation velocity of the laminar flame edge can be different according to whether the flame advances or retreats in the flow. So, if these effects occur in strongly turbulent flows, where the velocity field is time variant, if these effects occur, they can be very complex. At this stage it is not possible to determine the influence of such effects described for laminar flames on the properties of the turbulent flames we observed in Fig. 11. We have also asked whether the heat release at the flame edge is affected by the effects of stretch and preferential diffusion in the same manner as premixed flames are. Due to the effect of preferential diffusion, flame temperature is elevated for rich propane/air and lean methane/air mixtures (Le < 1), leading to flames that are more resistant to extinction. The flames in mixtures with a Lewis number smaller than unity require larger values of stretch to be extinguished. Thus, for methane, the flame is more resistant to extinction for lean mixture fractions, while its maximum burning occurs for mixture fractions slightly above stoichiometry [65]; for propane, however, the maximum resistance to stretch is obtained for almost the same mixture fraction as for maximum burning. It would be interesting to investigate the influence of such effects on the edge flame, especially in turbulent flows where the flame can be submitted to high values of stretch in a mixture where its propagation is fastest but its resistance to extinction is not maximum. For methane, the behavior observed may result from competition between the condition necessary for a mixture for giving the fastest propagation and the condition necessary for a mixture giving the greatest resistance to extinction. This competition does not occur for propane and ethylene and might explain the difference in the fluctuation amplitudes of liftoff height (Fig. 11) observed for methane.

4. Conclusions and summary A parametric investigation of turbulent lifted flames has been carried out for three fuels and various nozzle diameters. Blowout velocities are determined and experimental data are compared with an approach proposed by Broadwell et al. [8] based on the role of inviscid large-scale structures of turbulent jets. From this approach it is possible to propose an expression of blowout velocity without a detailed description of the blowout phenomenon. Measurements of flame base location near blowout conditions show that further

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investigation into the local condition of mixture and velocity fields in front of the flame base is required to fully understand the blowout phenomenon of turbulent jet flames. The location of the flame base has been measured over the stability diagram extended from hysteresis to blowout using PLIF of OH radicals. Instantaneous radial and axial coordinates of flame base location are measured with sufficient sampling to determine pdfs of height and radii of liftoff locations, and hence their average and standard mean deviation values. Average values of height and radius provide a large database over the flame stability diagrams of methane, propane and ethylene for nozzles 2, 3, 4, and 5 mm in diameters. Liftoff height and radius increase nonlinearly with exit jet velocity. The stabilization location occurs along a unique straight line for all the hydrocarbons investigated. The radial location of the flame base is greater than the theoretical location of the isoline Z = Zmb in a cold jet deduced from similarity laws. Further investigation is required to determine whether this discrepancy may be attributed to the nonvalidity of the assumption of stabilization along the iso-Zmb (or iso-Zs ) surface in the cold jet or to heat release effects (in this case whether the assumption Z = Zmb is valid or not) while keeping valid the assumption of stabilization. The shape of the pdfs of liftoff height changes according to the region of flame stabilization over the jet structures. The pdfs are not symmetric when the flame stabilizes in the “potential core region” (h/D < 6) and there is a minimum height below which the flame cannot stabilize. Within the fully developed region (h/D > 12) the pdfs are symmetric. The analysis of flame base fluctuations versus the elevation above the nozzle reveals three zones corresponding to the region of the turbulent jet where the flame stabilizes. Within the fully developed region the fluctuations of the flame base increase linearly with the elevation above the nozzle. For propane and ethylene, fluctuations of liftoff height are the same for a given elevation. Methane exhibits larger fluctuations, but the same dependence on downstream distance as propane and ethylene. Comparison with similarity laws of velocity shows that the mean standard deviation of liftoff height is equal to the local diameter of the jet and is slightly greater for methane. The behavior of methane flames would require further investigation in an experimental configuration where all the parameters affecting the velocity of the edge flame could be independently controlled.

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