Effects of heat release and imposed bulk strain on alignment of strain rate eigenvectors in turbulent premixed flames

Combustion and Flame 201 (2019) 290–300

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Effects of heat release and imposed bulk strain on alignment of strain rate eigenvectors in turbulent premixed flames Bo Zhou, Jonathan H. Frank∗ Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551, USA

a r t i c l e

i n f o

Article history: Received 29 August 2018 Revised 4 October 2018 Accepted 13 December 2018 Available online 11 January 2019 Keywords: Turbulent counterflow premixed flame Strain-flame alignment Bulk strain rate Heat release Tomographic PIV High-repetition-rate OH-PLIF

a b s t r a c t The impact of combustion heat release and bulk compressive strain on local alignment between the flame front normal and strain rate eigenvectors (principal strain rates) are investigated using simultaneous laser-induced fluorescence imaging of OH and tomographic particle image velocimetry in turbulent premixed CH4 /O2 /N2 counterflow flames with Karlovitz numbers (Ka) of 1.3 and 2.7. The bulk strain rate imposed by the counterflow introduces a preferential alignment of the most compressive principal strain rate, s3 , with the flame normal, n. Dilatation induced by heat release acts as a competing mechanism that promotes the alignment of the most extensive principal strain rate, s1 , with n. In the counterflow flames, the preferential s3 -n alignment prevails and remains dominant across the entire flame. This alignment stands in stark contrast to observations from previous studies in turbulent Bunsen flames or flames in isotropic turbulence, indicating the significance of bulk strain rate in determining local strain-flame alignment. The effects of increasing turbulence intensity on strain rate-flame front alignment are twofold; on the one hand, turbulence diminishes the s3 -n preferential alignment that is associated with the bulk strain field by increasing flame surface wrinkling and reducing the tendency of the flame front normal and s3 -eigenvectors to align with the axis of the counterflow. On the other hand, turbulence reduces the impact of heat release and enhances preferential s3 -n alignment approximately 1 mm ahead of the flame front, reflecting the characteristic alignment of compressive strain and scalar gradients in turbulent nonreacting flows. The effects of bulk strain are also observed in strain rate alignment statistics based on the fluctuating velocity fields, although the impact is less pronounced than for the statistics based on the full velocity fields. As a result of this complex interplay between heat release, turbulence, and bulk strain rate, the flametangential strain rate is on average extensive, and the flame-normal strain rate is dominantly compressive except for an approximately 0.8 mm wide region near the flame front where it is extensive due to dilatation. The compressive bulk strain in the counterflow was also shown to compress the length scales over which the strain rate and its alignment are affected by flame heat release. The present finding is important for developing turbulent flame models to accommodate the effect of bulk strain rate that is inherently associated with practical burner geometries, and the length scale dependence of the bulk strain effect could be a consideration for determining the cutoff scale in the context of large-eddy simulations. © 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction Scalar dissipation rate (Nc ) plays a critical role in turbulent flame models [1]. The effects of strain rate on Nc are manifest in the transport equation of the scalar dissipation rate in which the turbulence-scalar interaction term depends on the scalar-normal strain rate Sn = ni sij nj, where sij = 0.5(ui,j + uj,i ) is the strain rate tensor and n is the scalar-normal unit vector [2]. The eigenvalues of sij , also known as the principal strain rates (PSRs), si , are defined

∗

Corresponding author. E-mail address: [email protected] (J.H. Frank).

such that s1 ≥ s2 ≥ s3 , where s1 and s3 are the most extensive and compressive strain rates, respectively, and s2 is the intermediate strain rate. The scalar-normal strain rate can be expressed in terms of si as: Sn = s1 cos2 θ 1 + s2 cos2 θ 2 + s3 cos2 θ 3 , where θ i are the angles between the si -eigenvectors and scalar-normal. It is evident that Sn directly depends on the magnitudes of si and their alignments with the scalar-normal direction. In constant-density non-reacting turbulent flows, the most compressive eigenvector, s3 , preferentially aligns with n, resulting in the production of scalar gradients [3,4]. For reacting flows, direct numerical simulations (DNS) in an idealized system of freely-propagating flames interacting with isotropic turbulence [5–8] indicate that the strain alignment depends on the Karlovitz

https://doi.org/10.1016/j.combustflame.2018.12.016 0010-2180/© 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

B. Zhou and J.H. Frank / Combustion and Flame 201 (2019) 290–300

number (Ka), which is defined as the ratio of the characteristic flame time scale to the smallest time scales of turbulence, i.e. Kolmogorov scales. In low Karlovitz number flames, DNS studies have shown the preferential alignment of n with the most extensive eigenvector, s1 , near the flame front due to local dilatation [5,7]. However, at high Karlovitz numbers, alignment statistics become closer to those of non-reacting turbulent flows [8]. A limited number of experimental studies have investigated the strain rate alignment with the flame front. Hartung et al. [9] and Sponfeldner et al. [10] have shown the preferential alignment of n with s1 -eigenvectors in turbulent premixed bluff-body and Vflames using stereoscopic particle image velocimetry (SPIV) and planar laser-induced fluorescence (PLIF) of OH. However, Steinberg et al. [11] reported the alignment of n with s3 -eigenvectors in Bunsen-type premixed turbulent flames using SPIV with the flame front defined by the abrupt change in particle density. These different observations of alignment were attributed to differences in the methods for identifying the flame front location since the use of particle density in Ref. [11] explicitly excluded the region of dilatation [10]. Recently, Coriton and Frank [12] studied the strainflame front alignment in turbulent premixed Bunsen flames using OH-LIF imaging to identify the flame front and tomographic PIV (TPIV) to measure the complete strain rate tensor across the flame front region. They showed that the strain-flame front alignment indeed progresses from a weak preferential alignment with s3 -eigenvectors on the reactant side to a stronger alignment with s1 -eigenvectors at the flame front and extending several millimeters into the product region. They also showed that the preferential alignment weakens as the equivalence ratio (φ ) decreases from stoichiometric to lean conditions, resembling situations of increasing Ka number in DNS studies [8]. In practical systems, strain rate alignment with the flame front could involve several competing effects such as heat release, turbulence intensity, and bulk strain. Previous numerical and experimental studies of preferential si -n alignment in reacting turbulent flows have primarily focused on the effect of heat release, and the effect of imposed bulk strain has not been explicitly considered. In counterflows, high turbulence levels are produced by a turbulence generation plate [13], and a large bulk strain is imposed by the opposing flows, which provides a convenient platform for studying the effect of bulk strain with varying turbulence intensities. For accurate modeling of turbulent reacting flows, there is a need to understand the extent to which bulk strain rates influence the preferential si -n alignment. The present work studies the local si -n alignment in turbulent premixed CH4 /O2 /N2 counterflow flames using simultaneous TPIV and OH-LIF imaging for strain rate field quantification and flame front detection, respectively. The TPIV measurements provide access to the complete strain rate tensor, which is not available from planar or stereoscopic PIV measurements. Both reacting and non-reacting counterflows are considered in order to discern the effects of flame heat release. Simultaneous TPIV and OH-LIF measurements further allow for conditional statistics along the scalar-normal direction, which are essential for determining over what length scale the strain rate orientation is affected by flame heat release. The alignment of the strain rate eigenvectors based on both the full velocity field and the fluctuating velocity field are considered. The results are compared with those of a turbulent premixed Bunsen flame from our previous study [12] to elucidate the effect of inherent geometry-imposed bulk strain as well as its interaction with the effects of turbulence and heat release on the si -n alignment across the flame front. The paper is arranged as follows: first, the preferential orientations of the strain rate fields and the flame fronts with respect to the burner axis are investigated. Second, conditional statistics of strain rate fields along the scalar-normal direction are presented to address the relevant effects.

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2. Experiment 2.1. Burner and flow conditions Experiments were performed in the Yale counterflow burner [14,15], which consisted of opposed 12.7-mm diameter axisymmetric nozzles with a nozzle separation distance (dnozzle ) of 16 mm. The counterflow burner provides a convenient configuration for studying the effects of bulk strain on the local strain rate alignment in turbulent flows since it imposes a controllable amount of mean bulk compressive strain along the burner axis. The flow conditions, which are summarized in Table 1, include isothermal (N2 vs-N2 ) and non-isothermal mixing (N2 -vs-product) cases as well as premixed stoichiometric flames (reactant-vs-product) with two turbulence intensities. The isothermal mixing cases were included to examine the alignment of strain rates with the burner axis while excluding heat release and density variation. For these cases, nitrogen flowed from the top and bottom nozzles with the same bulk momentum as the flame cases. For all cases, the flow rate from the top nozzle was 85 L/min at 294 K, corresponding to a mean bulk inlet velocity, Vbulk , of 11.2 m/s. The bulk strain rate, Kbulk , defined as 2Vbulk /dnozzle , was also kept constant at 1400 s−1 . Topnozzle flows with Reynolds numbers (Ret ) of 470 and 1050 were generated by positioning a high-blockage ratio turbulence generator plate (TGP) at different positions inside the nozzle [13,15]. Both top and bottom flows were seeded with 0.3 um aluminum oxide particles, which provided accurate flow tracking for the PIV measurements. For the non-isothermal mixing and flame conditions, the bottom nozzle delivered a stream of combustion products at 1850 K from a preburner within the nozzle using a stoichiometric premixed CH4 /O2 /N2 flame with an O2 /N2 ratio of 26/74. The nonisothermal mixing case used a N2 -vs-product configuration representing a reference condition of turbulent mixing between reactant and product streams. For the counterflow flames, the top flow was a stoichiometric mixture of CH4 /O2 /N2 with an O2 /N2 ratio of 30/70, which was characterized by a laminar burning velocity, SL , of 79.3 cm/s and a heat release parameter, τ = (Tb -Tu )/Tu = 7.6, where Tu and Tb are the reactant and product temperatures, respectively [15]. The Karlovitz numbers, Ka, were slightly larger than unity, suggesting that the flames resided in the thin reaction zone regime [16]. Table 1 also includes an isothermal non-reacting flow and a turbulent premixed flame in a Bunsen burner that were investigated in our previous study [12] and are used here for comparison with counterflows to discern the impact of an imposed bulk strain on the strain-flame front alignment statistics. 2.2. Diagnostics and data processing The experimental setup for simultaneous TPIV and OH-LIF measurements is shown in Fig. 1. The TPIV system consisted of a dual-head Nd:YAG laser and four high-speed CMOS cameras (Vision Research Phantom). The time delay within a TPIV pulse pair was 14.8 us bracketing the OH-LIF laser pulse. The four TPIV cameras collected signals on both sides of the beam path in the forward scattering direction at angles of 20° and 45° with respect to the laser-sheet normal direction (z-axis). The camera lenses were mounted at angles relative to the detector plane using Scheimpflug mounts to compensate for misalignment of the image and detector planes. Small camera lens apertures with f/22 and f/32 were employed for the cameras at angles of 20° and 45°, respectively, to provide the necessary depth of field throughout the probe volume while minimizing beam steering effects. The use of a forward-scattering detection configuration helped to offset the signal loss due to the small apertures. The TPIV cameras were operated at 20 kHz in a frame straddling mode with a projected pixel height of 18 um and a detection area of 748 × 800 px2 . A detailed

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B. Zhou and J.H. Frank / Combustion and Flame 201 (2019) 290–300 Table 1 Experimental flow conditions. Counterflow burner Isothermal mixing

Mixture

Ret

< |s|>

Kbulk

N2 -vs-N2

470 1050

4909 s−1 5924 s−1

1400 s−1 1400 s−1

Mixture

φ

Ret

τ

u /SL

Ka

Kbulk

470 470 1050

− 7.6 7.6

− 2.8 4.9

− 1.3 2.7

1400 s−1 1400 s−1 1400 s−1

Ka 0.79

Non-isothermal mixing Flames

N2 -vs-product 0.0 Reactant1.0 vs-product 1.0 Bunsen burner reference

Isothermal mixing

Mixture N2 Mixture

φ

Ret

τ

< |s|> 535 s−1 u /SL

CH4 /Air

1.0

250

6.5

1.8

Flame

Ret 250

Fig. 1. Experimental setup for simultaneous TPIV and OH-LIF imaging.

description of the TPIV data processing and analysis is available in Ref. [17], and only a brief overview is given here. The particle scattering images from each camera were pre-processed and reconstructed into an 18 × 14.3 × 1.7 mm3 probe volume using a multiplicative algebraic reconstruction tomography (MART) algorithm [18]. The full 3D velocity field was calculated using volumetric cross-correlation with interrogation region dimensions of 24 × 24 × 24 px3 (400 × 400 × 400 um3 ) and 75% overlap of neighboring regions, resulting in 100 um vector spacing. A smoothing filter equivalent to a 4 × 4 × 4 moving average filter was applied to the 3D velocity field, which was further refined using a 4th order Runge–Kutta algorithm [19] to take advantage of the resolved temporal dynamics of the measurements. The fluctuating flow field was calculated by subtracting the mean of 20 0 0 velocity field measurements from the instantaneous full velocity field. The principal strain rates associated with the full velocity field and the fluctuat ing velocity field are denoted as si and s i , respectively. For the OH-LIF measurements, the second harmonic of a Nd:YAG-pumped dye laser delivered 60 uJ/pulse at 10 kHz to excite the Q1 (7) transition of the A-X(1,0) band of OH at 283.3 nm. The laser beam was formed into a 25-mm high sheet in the x-y plane centered in the TPIV probe volume, and the OH-LIF signal was collected orthogonal to the beam using a high-speed intensified CMOS camera of 640 × 480 px2 with a projected pixel size of 38 um. The OH-LIF and TPIV measurement regions were spatially matched by recording images of targets on all cameras. Figure 2 shows snapshots of x-y-plane projections of s3 eigenvectors calculated from the full velocity field superimposed on simultaneous OH-LIF images for (a) the N2 -vs-product mixing case (φ = 0.0, Ret = 470) and (b) the stoichiometric flame with the same Reynolds number (φ = 1.0, Ret = 470). The OH-LIF signal was

used to identify the flame front and the gas mixing layer interface (GMLI) following the procedure in Ref. [15]. The GMLI corresponds to the boundary of the product stream from the lower nozzle, and the region between the flame-front and the GMLI contours is the flame product zone. Vectors normal to the flame-front and GMLI contours were calculated for the reacting cases and N2 -vs-product mixing case, respectively. 3. Results and discussion In order to discern the effects of flame heat release on the strain rate alignment, we compare strain rate statistics in the nonreacting isothermal counterflows, the non-reacting N2 -vs-product counterflow, and turbulent counterflow flames. Statistics for each case were calculated using 20 0 0 single-shot TPIV/OH-LIF measurements to ensure statistical convergence. First, probability density functions (PDFs) of the principal strain rates from the N2 vs-N2 counterflows and the non-reacting Bunsen flow provide an overview of the strain rate distributions without heat release. Second, for alignment studies, we investigate the preferential orientation of the strain rate, GMLI, and flame front relative to the counterflow burner axis and then investigate the strain rate alignment relative to the flame/GMLI-normal direction. Strain rate fields calculated from the full velocity field and the fluctuating velocity field are considered, and the results are also compared with those obtained in the Bunsen burner (cf. Table 1) to highlight the influence of bulk strain on strain rate alignment in the counterflow. Third, the flow divergence along with the flame-normal and tangential strain rates that the flames experience from the full velocity fields are further characterized as a function of the distance from the flame/GMLI front.

B. Zhou and J.H. Frank / Combustion and Flame 201 (2019) 290–300

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Fig. 2. Simultaneous OH-LIF images and s3 -eigenvectors calculated from the instantaneous full velocity field with vector lengths scaled by the magnitude, |s3 |, (1 out of 9 eigenvectors displayed) for (a) N2 -vs-product mixing case (φ = 0.0, Ret = 470) and (b) flame (φ = 1.0, Ret = 470). (c) zoomed-in full eigenvector display of region marked by the blue square in (b). Red and black curves indicate the GMLI contour and the flame front, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 3. PDFs of the principal strain rates for (a) isothermal non-reacting counterflows with Ret = 470 (solid) and Ret = 1050 (dashed) and (b) isothermal non-reacting Bunsen flow. The principal strain rates are normalized by the corresponding mean strain tensor norm (Table 1).

3.1. Principal strain rate distributions in isothermal turbulent flows The PDFs of the principal strain rates, si , from the full velocity field for turbulent non-reacting isothermal flows for the counterflow and Bunsen burners are plotted in Figs. 3a and 3b, respectively. The values of si are normalized by the corresponding mean value of the strain rate tensor norm, defined as < |s| > = (s1 2 + s2 2 + s3 2 )1/2 . The values of < |s | > are 4909 s−1 and 5924 s−1 for the Ret = 470 and 1050 isothermal counterflows, respectively, which are an order of magnitude larger than that of the Bunsen flow (< |s | > = 535 s−1 ) [12] (Table 1). Despite this significant difference in < |s| > , the normalized PDF profiles of si in the counterflows are similar to those of the Bunsen flow except that the peak value of the PDF of s3 is larger than that of s1 in the counterflows, which is consistent with the dominantly compressive mean bulk strain. In both the counterflow and Bunsen configurations, the mean value of s2 is positive, indicating the intermediate principal strain rate is extensive on average and its distribution is slightly skewed towards positive values, in agreement with previous studies of non-reacting turbulence [20]. For the counterflows, the mean value of s2 is 462 s−1 and 257 s−1 for Ret = 470 and Ret = 1050, respectively. The relative ratios between the principal strain rates, s1 /s2 :1:s3 /s2 , provide insight into the structure of the strain rate field. To determine the most probable s1 /s2 and s3 /s2 ratios,

Table 2 Relative ratios between the principal strain rates.

Unconditioned Conditioned on s ≥ < s>

Case

Bunsen flow

Counterflow (Ret = 470)

s1 /s2 s3 /s2 s 1 /s2 s3 /s2

8.0 −9.0 7.6 −8.6

4.9 −5.9 3.0 −4.0

Counterflow (Ret = 1050) 10.9 −11.9 4.8 −5.8

we employed the same method described in Ref. [21] using PDFs of the normalized intermediate principal strain rate, defined as sn2 =s2 /(|s|2 /6)0.5 , where the factor of 60.5 is introduced to bound the values of sn2 within [−1 1]. To investigate the structural differences in the high strain rate regions, we evaluated unconditional PDFs of sn2 over a 3 × 8 mm2 region centered in the probe volume and PDFs conditioned on regions in which the strain rate norm |s| is greater than its mean value, < |s| > . For counterflows, the regions of |s| ≥ < |s | > are primarily concentrated near the stagnation plane. The corresponding conditional and unconditional values of the s1 /s2 and s3 /s2 ratios are listed in Table 2 for the counterflows and Bunsen flows. In isotropic turbulence, the most probable ratios are approximately 3:1:−4 [22]. The conditional ratios for the counterflows are smaller than those of the Bunsen flow and more comparable to the ratios in isotropic turbulence, implying

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Fig. 4. PDFs of cosine angles of si -eigenvector (or s i -eigenvectors) with respect to y-axis, θ s- y , for non-reacting (a) N2 -vs-product counterflow with Ret = 470 (b) N2 -vs-N2 counterflow with Ret = 470 (c) N2 -vs-N2 counterflow with Ret = 1050 and (d) the Bunsen Flow. The first and second rows show alignment statistics of strain rate fields based on the full velocity fields and the fluctuating velocity fields, respectively.

that high strain rates near the stagnation plane are preferentially sheet-forming with a single axis of compressive strain and two axes of extensive strain. The unconditional ratios of counterflows include regions of the bottom stream of hot products, which is nearly laminar, resulting in a bias towards larger |s1 /s2 | and |s3 /s2 | ratios. 3.2. Alignment with burner axis The bulk flow field can introduce a preferential orientation of the principal strain rates, flame front, and GMLI with respect to the burner axis, which impacts the relative alignment of these quantities. Probability density functions of the cosine angles (θ s-y ) of si with respect to the counterflow burner axis (y-axis) are shown in Fig. 4 (a1–c1) for the three non-reacting cases. The use of cos(θ s-y ) instead of θ s-y accommodates the spherical coordinates such that an isotropic angular distribution results in a flat PDF with a value of unity. PDF values greater than unity indicate preferential alignment. The peaks in the PDFs of s3 at cos(θ s-y ) = 1 indicate that the most compressive strain, s3 , is strongly aligned with the y-axis for the three cases, while s1 and s2 are preferentially aligned orthogonal to the y-axis with overlapping distributions for each case. The azimuthal angle distributions of si in the x-z plane (data not shown) are nearly isotropic, as expected from the axial symmetry. The PDF of s3 for the non-reacting mixing of N2 -vs-product (φ = 0, Ret = 470) has the largest peak, indicating significantly stronger preferential alignment of s3 with the y-axis than the isothermal flow with the same Ret due to the dampening of turbulent fluctuations by the high temperature products. The alignment in the isothermal flow is diminished further as Ret increases from 470 to 1050 due to larger fluctuations in the strain field orientation. In contrast to the counterflow, the si alignment relative to the burner axis (y-axis) in the Bunsen flow, shown in Fig. 4(d1), is very minor with s2 (s1 and s3 ) being slightly preferentially aligned (orthogonally) with the y-axis.

The second row of Fig. 4 shows the same cosine angle PDFs based on the strain rate fields calculated from the fluctuating velocity fields. The PDFs in Fig. 4(a2–c2) show that preferential alignment of the fluctuations in the compressive strain,  s 3 , with the y-axis due to flow geometry is significantly re duced but still present. The reduced s 3 -eigenvector alignment is accompanied by an increased preferential alignment between  s 1 -eigenvectors and the y-axis. This result indicates that both   the s 1 and s 3 -eigenvectors are intermittently aligned with the counterflow burner axis, which differs from the dominance of the s3 -eigenvector alignment for the full velocity field, as seen in the PDFs of Fig. 4 (a1–c1). In contrast to the counterflow, the alignment statistics based on the full and fluctuating velocity fields of the Bunsen flows in Fig. 4 (d1–d2) show rather trivial differences due to lack of geometry-imposed bulk strain, and the  alignment between s 3 and the y-axis is nearly random. We next consider the alignment of the GMLI and flame front with respect to the counterflow burner axis. Fig. 5(a) shows PDFs of the alignment of the GMLI-normal and flame-normal vectors with respect to the y-axis in the OH-LIF measurement plane (x– y plane) for the N2 -vs-product case and the two flames, respectively. All three PDFs have a peak at θ F-y = 0°, indicating preferential alignment of the surface normal with the y-axis. The GMLI in the non-reacting mixing case has a stronger preferential alignment than that of the flame front in the two flames. In the flames, the preferential flame front alignment becomes less pronounced as the Reynolds number increases as a result of the increased surface wrinkling at higher turbulence intensities. In contrast, the flame front alignment in the Bunsen flame shown in Fig. 5(b) exhibits preferential alignment of n orthogonal to the y-axis to a modest extent. The combination of Figs. 4 and 5 shows that the counterflow geometry reinforces the alignment of the s3 -eigenvectors with the flame-normal and GMLI-normal vectors through their preferential alignment with the y-axis, while the Bunsen flows exhibit much weaker preferential alignment imposed by its geometry due

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Fig. 5. PDFs of (a) the angles of the GMLI or flame front normal with the y-axis in the x-y plane, θ F- y , for counterflows and (b) Bunsen burner flow (right column). Black dash-dot line indicates the probability density for an isotropic angular distribution.

Fig. 6. Velocity normal to the GMLI/flame front (vn ) as a function of xn for the non-reacting N2 -vs-product case (green curve) and two turbulent premixed flames with Ret = 470 (red curve) and Ret = 1050 (blue curve). Green dashed lines mark vn = 0 m/s and the corresponding xn for the N2 -vs-product case. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

to the lack of inherent bulk strain rate alignment with the burner axis. Although the geometry effect of the counterflow is significantly less pronounced in the fluctuating velocity field, the fact  that the s 3 -eigenvectors remain preferentially aligned with the yaxis suggests that the geometry effect could impact the strain rate alignment statistics. 3.3. Flame/GMLI-normal conditional statistics Conditional statistics of the velocity and strain rate are evaluated across the GMLI and flame front to determine the flow field structure near these interfaces. At each position along the GMLI or flame front contour, the velocity and strain rate are evaluated along the surface normal direction, xn , where positive and negative values of xn correspond to the reactant and product regions, respectively. Each sampled point is associated with the nearest GMLI/flame front contour to avoid ambiguity caused by surface wrinkling. We first evaluate the velocity normal to the GMLI/flame front (vn ) as a function of xn for the turbulent counterflow cases of N2 -vs-product and stoichiometric flames at two Reynolds numbers, as shown in Fig. 6. In a traverse from the reactant side (xn = 3 mm) toward the GMLI or flame front (xn = 0 mm), the magnitude of vn for all three cases decreases with a similar slope of approximately vn /xn = 1900 s−1 , which is somewhat higher than the

bulk strain rate of Kbulk = 1400 s−1 (Table 1). For the non-reacting case (green curve), the flow stagnates (vn = 0 m/s) within 300 um of the GMLI front, indicating that the OH-LIF signal provides a good marker of the GMLI position. On the product stream side of the GMLI (xn < 0), the gradient of the normal velocity increases to 40 0 0 s−1 as a result of the momentum balance between the top and bottom flows. In contrast, the velocity profiles in the flames (red and blue curves) exhibit a region of flow acceleration due to heat release near the flame front (xn = 0), while the deceleration trend resumes further into the product region (xn < −0.5 mm). PDFs of the si -eigenvector alignment with the flame/GMLInormal vectors were computed at the flame/GMLI front (xn = 0) as shown in Fig. 7 (a1–c1). For the N2 -vs-product mixing case (cf. Fig. 7(a1)), the large peak in the PDF at cos(θ 3 ) = 1 indicates very strong preferential alignment of s3 -eigenvectors with the GMLInormal vectors as a result of imposed bulk strain and the fact that turbulence tends to promote the s3 -n alignment in non-reacting flows [8]. The peaks in the PDFs for the most extensive and intermediate strain rates at cos(θ 1 ) = 0 and cos(θ 2 ) = 0, respectively, in Fig. 7(a1) indicate that the s1 and s2 -eigenvectors are preferentially aligned orthogonal to the GMLI-normal. The effect of heat release is identified by comparing the N2 -vs-product mixing case in Fig. 7(a1) to the flame with the same Ret in Fig. 7(b1). Although the s3 -eigenvectors in the flame (c.f. Fig. 7(b1)) are preferentially aligned with the flame front normal, n, the extent of this alignment is significantly diminished by the presence of heat release as well as the increased level of surface wrinkling as shown in Fig. 2. Similarly, the propensity for s2 to align orthogonal to n persists in the flame but is less pronounced than in the non-reacting flow. In contrast, the s1 -n alignment is modified significantly by the heatrelease-induced extensive strain near the flame front, such that the PDF of cos(θ 1 ) approaches a random distribution with s1 -n alignment angles near cos(θ 1 ) ≈ 0.7 (i.e. θ 1 ≈ 45 o ) having a slightly greater probability. This result differs significantly from most previous strain-flame front alignment studies, in which the dilatation from heat release dominated the alignment statistics resulting in a high probability of s1 -n alignment. For example, results from our studies of a turbulent Bunsen flame shown in Fig. 7(d1) indicate a strong s1 -n alignment by the large peak at cos(θ 1 ) = 1. This difference is the consequence of a competition between the effects of heat-release-induced extensive strain and the imposed bulk compressive strain of the counterflow. The turbulence intensity also plays a role in determining the strain-flame front alignment. A comparison of Fig. 7(b1) and (c1) shows that as Ret increases from 470 to 1050, the PDFs of the s1 -n and s3 -n alignments exhibit modest increases at cos(θ 1 ) = 0 and cos(θ 3 ) = 1, respectively, indicating a shift towards the distributions of the non-reacting flow in Fig.

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Fig. 7. (a1–d1) PDFs of the alignment between strain rate eigenvectors (based on the full velocity fields) and the flame/GMLI-normal vectors at the flame/GMLI front (xn = 0). (a2–d2) conditional probabilities for θ i < 45° as a function of flame-normal coordinate, xn , across the flame/GMLI front. From the left to right columns are the counterflow cases of N2 -vs-product and the flames with Ret = 470 and 1050, respectively, and the Bunsen flame. Black dash-dot line indicates the probability for an isotropic angular distribution.

7(a1). This increased preferential alignment may seem counterintuitive since the PDFs in Fig. 4(b1–c1) and Fig. 5(a) indicate that an increase in Ret tends to scramble the orientations of the strainrate eigenvectors and flame front, resulting in a reduced alignment with respect to the burner axis. However, the increased turbulence partially counteracts the effects of heat release on the strain-rate alignment. As the effects of heat release diminish, the strain-rate alignment characteristics of non-reacting turbulent flows become more prominent. For example, in turbulent non-reacting flows, the compressive strain eigenvector tends to be aligned normal to contours in the scalar field, which is consistent with a stronger s3 -n alignment. The results in the second row of Fig. 7 show the si -n alignment conditioned on the distance from the flame front or GMLI for the counterflows and the Bunsen flame. The extent of preferential alignment, defined as the probability that the angle between the si -eigenvectors and the flame/GMLI normal is less than 45°, P(θ i < 45°), was computed as a function of xn . The dash-dot line at P(θ i < 45°) = 0.29 corresponds to an isotropic angular distribution of a three-dimensional vector field, and a probability above this line indicates preferential si -n alignment. For all three counterflow cases in Fig. 7(a2–c2), preferential s3 -n alignment is observed across the entire flame/GMLI front with local variations resulting from the interplay between heat release, turbulence, and the bulk strain. For clarity, the following discussion focuses on the alignment of the s3 -eigenvector but remains highly relevant to the alignment of the s1 -eigenvector. At sufficient distance from the flame/GMLI front (e.g., xn = ± 3 mm), the strain rate fields are less sensitive to the density variation or heat release near the flame/GMLI front. At these locations, the preferential s3 -n alignment is primarily determined by the bulk flow properties. For the counterflows, as shown in Fig. 7(a2–c2), the plateaus of the P(θ 3 < 45°) profiles near xn = ± 3 mm are well above the line that identifies an isotropic angular distribution. For the counterflow flame with Ret = 1050

shown in Fig. 7(c2), the plateau on the reactant side (i.e. xn = 3 mm) occurs slightly beyond the 3-mm interrogation range due to the greater impact of turbulence. In all three counterflow cases, the plateau value in the product region (Pb ) is higher than that in the reactants (Pu ) as a result of the disparity in turbulence intensity of the opposing streams. The hot product stream is practically laminar, resulting in a stronger preferential alignment of s3 with the y-axis and therefore with n. An intuitive illustration of this observation is reflected in the snapshot of the OH-LIF signal and strain rate field of s3 in Fig. 2(a). Comparing Fig. 7(a2–c2) suggests that the overall influence of the bulk flow properties diminishes from the N2 -vs-product mixing case to the comparable reacting case, and further with increasing turbulence in the reacting flows. Accordingly, Pu drops from 70% in the N2 -vs-product mixing case to 66% and to 50% in the flames with low and high turbulence, respectively. This observation is a direct consequence of the increased wrinkling of the surface, which becomes more randomly oriented, as shown in Fig. 5(a). The decrease in Pb from Fig. 7(a2) to (b2) is primarily due to the different sampling regions associated with the product stream and the flame product zone for the non-reacting and reacting cases, respectively. We next consider how s3 -n alignment evolves across the GMLI and flame front relative to the alignment at the extrema of xn = ± 3 mm. In a traverse of the counterflow profiles in Fig. 7(a2–c2) from reactants to products, P(θ 3 < 45°) initially increases with a local maximum occurring slightly on the reactant side at xn = 0.5 mm in the N2 -vs-product case and at xn = 1.0 mm in the flames. In the lower turbulence flame (cf. Fig. 7(b2)), the peak in P(θ 3 < 45°) slightly ahead of the flame front is largely counteracted by the effect of heat release. The dilatation that is induced by heat release reduces the s3 -n alignment while enhancing the s1 -n alignment, creating a dip in the P(θ 3 < 45°) profile and a corresponding peak in the extensive strain alignment, P(θ 1 < 45°), profile within the region spanning ± 1 mm around the flame front. Near xn = 0 mm in Fig. 7(b2),

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Fig. 8. (a1–d1) PDFs of the alignment between strain rate eigenvectors (based on the fluctuating velocity fields) and the flame/GMLI-normal vectors at the flame/GMLI front (xn = 0). (a2–d2) conditional probabilities for θ i < 45° as a function of flame-normal coordinate, xn , across the flame/GMLI front. From the left to right columns are the N2 -vs-product mixing case and the flames with Ret = 470 and 1050, respectively, and the Bunsen flame. Black dash-dot line indicates the probability for an isotropic angular distribution.

an unusual si -n alignment is observed in which both s1 and s3 -eigenvectors are preferentially aligned with n as a result of the competition between the heat release and bulk strain. The s1 and s3 -eigenvectors near the flame front are intermittently aligned with n such that on average they both show preferential alignment. In the Ret = 1050 flame (cf. Fig. 7(c2)), the higher turbulence counteracts the influence of heat release and therefore enhances the preferential s3 -n alignment near the flame front. Consequently, the dip in the PDF of s3 -n alignment at xn = 0 mm is less pronounced than in the lower turbulence flame (cf. Fig. 7(b2)). The corresponding peak in P(θ 1 < 45°) of Fig. 7(c2) is also suppressed and falls below the line for a random distribution. As the role of turbulence-induced alignment increases and the impact of extensive strain from the heat release decreases, the shapes of the si -n alignment profiles transition towards those of the non-reacting case in Fig. 7(a2). Overall, the dominant preferential s3 -n alignment is observed throughout the entire 6-mm profile in these counterflow flames, which have Ka numbers of 1.3 and 2.7. In previous studies of strain-rate alignment in flames, the dominance of preferential s3 -n alignment has only been reported in numerical simulations of highly turbulent flames with isotropic turbulence and Ka1 [6,7]. This difference highlights the importance of considering bulk strain in determining strain rate alignment with the flame normal. As will be shown towards the end of this section, the observed si -n alignments have a direct impact on the flame-normal strain rate, Sn , which plays a key role in determining scalar dissipation, local flame burning properties, and flame extinction. The underlying physical mechanisms that affect the strain-flame front alignment are the same in the turbulent counterflow and Bunsen flames with the exception of the imposed bulk strain, which is absent in the Bunsen flame. As a result, the P(θ i < 45°) profiles for the Bunsen flame (c.f. Fig. 7(d2)) share similar overall shapes to those of the counterflows but have different magnitudes and stand on different baselines such that the strain-rate alignment in the Bunsen flame is nearly random at ± 3 mm on ei-

ther side of the flame front. The preferential s1 -n alignment for xn ≤ 1 mm dominates the profiles in Fig. 7(d2) as a consequence of flow acceleration induced by the flame heat release. Although the Bunsen flame has a lower heat release parameter than that of the counterflow flames, the extensive strain alignment dominates in the absence of a counteracting bulk compressive strain. The preferential s3 -n alignment at 1 mm < xn < 3 mm is likely the result of the heat-release-induced dilatation slightly compressing the reactants just ahead of the flame front. For the remainder of the profile, the compressive and intermediate strain rates exhibit preferential alignment orthogonal to the flame front. To further understand the effect of bulk strain, we recomputed the same alignment statistics as Fig. 7 using the fluctuating velocity field, and the results are shown in Fig. 8. In comparison  with the corresponding PDFs in Fig. 7, preferential s 3 -n alignment  is greatly reduced and s 1 -n alignment is increased for all the counterflow cases. For the counterflow flame of Ret =470 at xn = 0,  there is no preferential s 3 -n alignment (cf. Fig. 8(b1)), and the  heat release dominates, resulting in preferential s 1 -n alignment. For the counterflow flame of Ret = 1050 at xn = 0, intermittency in   the alignment of s 1 - and s 3 -eigenvectors with n results in similar   PDFs of s 1 and s 3 shown in Fig. 8(c1). In comparison to Fig. 7(a2– c2), Fig. 8(a2–c2) shows that subtraction of the mean bulk strain field of the counterflow leads to a shift in the P(θ 1 < 45°) and P(θ 3 < 45°) profiles towards the line for an isotropic distribution. In contrast, due to the lack of bulk strain in the Bunsen flame, the differences between the P(θ i < 45°) profiles in Fig. 8(d2) and Fig. 7(d2) are much less pronounced. These results are consistent with the alignment PDFs of θ s- y for the non-reacting flows in Fig. 4, which shows that the effect of subtracting the mean field is much more significant for the counterflow than for the Bunsen flow. Despite the changes in the absolute values of the P(θ i < 45°) profiles in Fig. 8(a2–c2), the overall shapes of the corresponding P(θ i < 45°) profiles exhibit similarities to the distributions for the full strain rate shown in Fig. 7(a2–c2), suggesting the same

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Fig. 9. Top row: Flame/GMLI-normal profiles of the mean principal strain rates < si > (solid) and their projections (dashed) onto the flame/GMLI-normal direction. Bottom row: divergence ࢞ (red), flame-normal strain rate Sn (green) and flame-tangential strain rate St (blue). Curves are normalized by the corresponding mean strain rate tensor norms (see Table 1). From the left to right columns are the counterflow non-reacting mixing case and the counterflow flames with Ret = 470 and 1050 as well as the Bunsen flame. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)



underlying effect of heat release on the s i alignment statistics.  The reduction of the s3 -n or s 3 -n alignment near the flame front due to heat release is reflected as a dip in the corresponding P(θ 3 < 45°) profile. It has been shown in our previous study [12] that the dip in the P(θ 3 < 45°) profile for the Bunsen flame (cf. Fig. 8(d2)) gradually converges to an isotropic distribution as the effect of heat release is reduced by adjusting the equivalence ratio. For the counterflow flames, the dip in the P(θ 3 < 45°) profiles shifts from below to slightly above the isotropic alignment from Fig.  8(b2) to Fig. 8(c2), indicating an increase in s 3 -n alignment as the turbulence is increased and the effect of heat release is reduced. The width of the dip in the P(θ i < 45°) profiles in Fig. 8(b2–c2), which indicates the length scale of the local heat release impact, is narrower in the counterflow flames than in the Bunsen flame. This is consistent with the compressive bulk strain confining the extent of the extensive strain induced by flame heat release. Overall, these results indicate that the bulk strain in the counterflows influences the alignment statistics based on the fluctuating velocity fields. The impact of these preferential alignments between the principal strain rates and the flame front or GMLI depends on the strain rate magnitude and the projection of the principal strain rates onto the normal and tangential directions of these surfaces. The top row of Fig. 9 shows the mean profiles of the principal strain rates (solid curves), < si > , and their projections onto the flame/GMLI-normal direction (dashed curves) normalized by the corresponding mean strain rate norms. For the counterflow nonreacting mixing case (cf. Fig. 9(a1)), peak magnitudes of < si > are located near xn = 0 and are primarily associated with streamwise compression for < s3 > and radial expansion for < s1 > and < s2 > . A comparison of the non-reacting counterflow with its reacting flow counterpart (cf. Fig. 9(b1)) shows that the flame heat release shifts the peaks of all the < si > curves towards positive values in the vicinity of the flame front. As the turbulence is increased in

the counterflow flame from Fig. 9(b1) to (c1), the magnitude of this shift is systematically reduced. For the Bunsen flame results in Fig. 9(d1), the peaks in the < si > profiles are quite pronounced with a maximum extensive strain of approximately twice the norm of the strain rate tensor. The combined effects of the preferential si -n alignment and the strain rate magnitude across the flame can be analyzed by projecting the si -eigenvectors onto the flame/GMLI-normal direction, as shown by the dashed lines in Fig. 9(a1–d1). Each dashed line represents the contribution of the corresponding si component to the flame-normal strain rate, Sn . Accordingly, the contribution of each si component to the tangential strain rate, St , corresponds to the difference between the respective solid and dashed curves. In the counterflows, the dominant contribution to Sn comes from s3 over a large portion of the profiles with an increasing contribution from s1 near the flame front as a result of dilatation. In contrast, s3 contributes comparably less to Sn in the Bunsen flame shown in Fig. 9(d1) due to its orthogonal preferential alignment with n, as indicated by the relatively small projection of s3 onto the flame normal direction. Profiles of the mean values of the normal strain rate, < Sn > , tangential strain rate,< St > , and the divergence, <  > , across the GMLI and flame front surfaces are shown in Fig. 9(a2–d2). The divergence is determined from the definition  = s1 + s2 + s3 = Sn + St , which is zero for non-reacting incompressible flows and nonzero in reacting flows due to dilatation. As expected, near-zero values of <  > are observed in the reactant region for xn ≥ 2 mm for all three counterflows. The values of <  > are slightly above zero in the product region (xn ≤ −1 mm). It is suspected that the non-zero divergence in this region is a result of local density variations due to turbulent mixing for the N2 -vs-product case, and slow CO and H2 oxidization reactions [14] that can extend up to a several millimeters downstream of the reaction zone in the counterflow flames. In the absence of heat release,

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as shown in Fig. 9(a1) for the counterflow non-reacting mixing case, < Sn > remains compressive across the entire profile with greater compression on the product side, and < St > remains extensive with greater extension on the product side. In the counterflow flame profiles shown in Fig. 9(b2–c2), dilatation induces a shift of < Sn > and <  > towards positive values that is most noticeable within 1 mm of the flame front. However, the effects of heat release on < St > are less pronounced because the changes due to dilatation are primarily associated with the density jump along the flame-normal. Comparison of Figs. 9(b2) and (c2) shows that the effect of dilatation on < Sn > and <  > is reduced with increasing turbulence, while the < St > profile is less affected. The values of < St > in the counterflow flames are positive across the entire flame front region, thereby contributing to stretching of the flame front. The < Sn > profiles are dominantly compressive (negative) except for a small region of approximately 0.8 mm near the flame front where < Sn > is slightly extensive (positive). Therefore, scalar gradients are enhanced by both tangential stretching and normal compression of the fluid parcels, although the compression is somewhat overcome by dilatation near the flame front. In contrast to the counterflow flames, the < Sn > profile for the Bunsen flame shown in Fig. 9(d2) is extensive (positive) over the region xn ≤ 1.2 mm due to dilatation, contributing to reduction of scalar gradients along the flame normal [12]. A comparison of the widths of the peaks in the <  > , < Sn > and < St > profiles in Fig. 9 as well as in the P(θ i < 45°) profiles in Fig. 7 for the Bunsen and counterflow flames shows that the counterflow flames exhibit narrower profile widths. Note that the profile widths were not affected by the flame brush since the statistics were performed on a flame-based coordinate. Instead, the profile width corresponds to the length scale affected by heat release, which is on average more compressed in the counterflow flames. 4. Conclusions The present work investigated the effects of an imposed bulk strain rate on the local strain rate alignment and its interaction with heat release and turbulence in turbulent non-reacting and reacting counterflows. Results were compared with those of a Bunsen burner flame in which the bulk strain rate is negligible. Simultaneous tomographic PIV and OH-LIF imaging provided measurements of the strain rate eigenvectors, si , and their alignment relative to the flame-front normal and GMLI-normal. Consistent with previous work, the presence of heat release enhanced the alignment of extensive strain, s1 , with the flame-normal, n. However, the counterflow introduced an additional preferential alignment of compressive strain, s3 , with the flame front normal. As a result, a preferential s3 -n alignment was observed throughout the counterflow flame front despite the large heat release parameter in these flames. This result represents a significant departure from flames in idealized isotropic turbulence, which require substantially higher turbulence intensities to achieve such a strong s3 -n alignment, indicating the importance of the bulk flow field. The effect of turbulence on the alignment was twofold: on the one hand, increases in turbulence intensity reduced the preferential s3 -n alignment imposed from the bulk flow by increasing surface wrinkling and scrambling the orientation of the flame front and strain rate eigenvectors with respect to the burner axis; on the other hand, higher turbulence counteracted the effect of heat release and promoted preferential s3 -n alignment slightly ahead of the flame front. In the counterflows, the effects of bulk strain on alignment statistics based on the fluctuating velocity field were also detected but were less pronounced than those based on the full velocity field. In the Bunsen flame, the alignment statistics based on the

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full and fluctuating velocity fields were very similar. The persistence of the influence of the bulk flow on the fluctuating strain is dependent on the flame conditions and the flow geometry, which could impact the treatment of strain rate fluctuations in turbulent combustion models. In the context of large-eddy simulations, the extent to which the bulk flow geometry influences the strain rate fluctuation statistics would depend on the choice of the cutoff length scale that separates the resolved and subgrid scales. As a result of preferential alignments of s3 parallel to n and s1 orthogonal to n, the mean flame-tangential strain rate, < St > , was extensive and the mean flame-normal strain rate, < Sn > , was dominantly compressive except for a small region near the flame front where < Sn > became slightly extensive due to strong dilatation. The existence of compressive bulk strain in the counterflows was also shown to compress the length scale over which the strain rate and its alignment are affected by flame heat release. These observations are distinct from previous studies in showing the significant impacts of the bulk flow field in determining local strain rate alignment, which ultimately affects flame stretching and dissipation rates. For proper modeling of turbulent flames, the effect of the bulk flow field should be carefully considered, particularly since the extent of this effect is length scale dependent. Acknowledgments The authors thank Dr. Bruno Coriton for helpful discussions and Mr. Erxiong Huang for technical assistance in the laboratory. The support of the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences is gratefully acknowledged. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0 0 03525. The views expressed in the article do not necessarily represent the views of the U.S. Department of Energy or the United States Government. References [1] H. Kolla, J.W. Rogerson, N. Chakraborty, N. Swaminathan, Scalar dissipation rate modeling and its validation, Combust. Sci. Technol. 181 (2009) 518–535. [2] N. Swaminathan, K.N.C. Bray, Effect of dilatation on scalar dissipation in turbulent premixed flames, Combust. Flame 143 (2005) 549–565. [3] K.K. Nomura, S.E. Elghobashi, Mixing characteristics of an inhomogeneous scalar in isotropic and homogeneous sheared turbulence, Phys. Fluids A-Fluid 4 (1992) 606–625. [4] G.K. Batchelor, The effect of homogeneous turbulence on material lines and surfaces, Proc. R. Soc. Lon. Ser. A. Math. Phys. Sci. 213 (1952) 349–366. [5] N. Swaminathan, R.W. Grout, Interaction of turbulence and scalar fields in premixed flames, Phys. Fluids 18 (2006) 045102. [6] N. Chakraborty, N. Swaminathan, Influence of the Damkohler number on turbulence-scalar interaction in premixed flames. II. Model development, Phys. Fluids 19 (2007) 045104. [7] N. Chakraborty, N. Swaminathan, Influence of the Damkohler number on turbulence-scalar interaction in premixed flames. I. Physical insight, Phys. Fluids 19 (2007) 045103. [8] P.E. Hamlington, A.Y. Poludnenko, E.S. Oran, Interactions between turbulence and flames in premixed reacting flows, Phys. Fluids 23 (2011) 125111. [9] G. Hartung, J. Hult, C.F. Kaminski, J.W. Rogerson, N. Swaminathan, Effect of heat release on turbulence and scalar-turbulence interaction in premixed combustion, Phys. Fluids 20 (2008) 035110. [10] T. Sponfeldner, I. Boxx, F. Beyrau, Y. Hardalupas, W. Meier, A.M.K.P. Taylor, On the alignment of fluid-dynamic principal strain-rates with the 3D flamelet-normal in a premixed turbulent V-flame, Proc. Combust. Inst. 35 (2015) 1269–1276. [11] A.M. Steinberg, J.F. Driscoll, N. Swaminathan, Statistics and dynamics of turbulence-flame alignment in premixed combustion, Combust. Flame 159 (2012) 2576–2588. [12] B. Coriton, J.H. Frank, Impact of heat release on strain rate field in turbulent premixed Bunsen flames, Proc. Combust. Inst. 36 (2017) 1885–1892. [13] G. Coppola, A. Gomez, Experimental investigation on a turbulence generation system with high-blockage plates, Exp. Therm. Fuild Sci. 33 (2009) 1037–1048.

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