Simultaneous measurements of velocity and CH distributions. Part 1: jet flames in co-flow

Combustion and Flame 132 (2003) 565–590

Simultaneous measurements of velocity and CH distributions. Part 1: jet flames in co-flow Donghee Han, M.G. Mungal* Mechanical Engineering Department, Stanford University, Stanford, CA, USA Received 4 June 2001; received in revised form 19 September 2002; accepted 9 October 2002

Abstract Velocity field and CH distribution are measured simultaneously using particle-image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) of CH in piloted, turbulent, jet flames in coflow. The CH distribution is found to correspond well with the location of the stoichiometric velocity, U S , both instantaneously and on average. In addition, the CH distribution is observed to align with high-strain rate regions; however, significantly higher values of the maximum strain rates, compared to the mean value, are frequently observed. The residence time in the flame surface as represented by CH, ␶ F , remains nearly constant with axial distance downstream and is found to scale as ␶ F ⬃ d/U b , where d and U b are nozzle exit diameter and bulk nozzle-exit velocity, respectively. The mean value of the compressive principal strain rate is observed to decrease along the axial direction and shows a good correlation to a S ⬃ ( x/d) ⫺0.7 relation for a wide range of jet Reynolds numbers. Finally, the two-dimensional dilatation is not seen to be a good marker of the flame position, unlike the case for premixed flames. © 2003 The Combustion Institute. All rights reserved. Keywords: Turbulent diffusion flame, Experiments, PIV, PLIF

1. Introduction In non-premixed flames, the fuel and oxidizer are initially introduced separately into a burner. This characteristic is essential in many applications due to safety considerations. However, the mixing between the fuel and oxidizer limits the heat-release rate in non-premixed flames, and therefore, enhanced mixing between the fuel and oxidizer is achieved using turbulent flows. The applications of turbulent nonpremixed flames range from both small- and largescale industrial burners to various chemical processes. In addition to the practical interest, combustion processes of non-premixed flames are of

* Corresponding author. Tel.: ⫹1-650-725-2019; fax: ⫹1-650-723-1748. E-mail address: [email protected] (M.G. Mungal).

fundamental interest in combustion science. One of the most common configurations to introduce the fuel into a turbulent non-premixed flame is through a jet stream from a nozzle. The oxidizer can be stationary or flowing in the direction of the jet stream. Meanwhile, for enhanced mixing, the jets are often injected at a direction normal to the ambient flow, and even further, towards the ambient flow. In recent studies of the flame-surface dynamics using modern laser diagnostic techniques [1– 4], it has been revealed that the reaction of a turbulent non-premixed jet flame occurs in a relatively thin flame surface, which is comparable in thickness to that of a laminar-diffusion flame surface, even for a jet with Reynolds numbers as high as 20,000. For these flames, velocities and strain rates on this thin flame surface will determine the residence time and the reaction rate on the flame surface, and thus, will affect product and pollutant formation [5,6]. For this

0010-2180/03/$ – see front matter © 2003 The Combustion Institute. All rights reserved. S0010-2180(02)00515-1

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reason, understanding the interaction between the flame surface and the surrounding turbulent flow, such as velocities and the strain rates on the flame surface, will be critical to predict the combustion process. To investigate these characteristics of flames, the distribution of the flame surface has to be determined simultaneously with the velocity field. The attempt to image the instantaneous flame surface was initiated by the development of the planar laser-induced fluorescence (PLIF) technique. An overview of the PLIF technique and its application to combustion studies are given in the review papers by Hanson [7] and Hanson et al. [8]. In these reviews, OH was considered an indicator of burned gases, while CH was a marker of the reaction zone. Seitzman et al. [1] noted that OH can cause ambiguities in determining the flame surface, owing to its slow removal by three-body recombination reactions. They proposed CH or C2 as an alternative to OH for imaging the reaction zone. Contrary to OH, CH is formed and removed by faster two-body reactions, and therefore, is considered a better tracer for the reaction zone. However, due to its low concentration compared to OH and interference from polycyclic aromatic hydrocarbons (PAHs), single-shot imaging of CH has been a challenge. Paul and Dec [9] suggested a non-resonant scheme for CH PLIF, which excites the A 2 ⌬ 4 X 2 ⌸(1,0) band near 387 nm and detects the A ⫺ X(1,1) and (0,0) band near 431 nm. Carter et al. [10] used a different scheme, which excites the B 2 ⌺ ⫺ 4 X 2 ⌸(0,0) band near 390 nm and detects A ⫺ X and B ⫺ X(0,1) bands near 420 – 440 nm. These schemes enabled single-shot imaging of CH and therefore could be applied to non-sooting turbulent flames. Recently, the focus of reaction-zone imaging is to trace the heat-release rate. Najm et al. [11] assessed common reaction-zone tracers such as OH, CH, C*2, and CH* as a heat-release indicator in methane premixed flames and concluded that none of them are adequate for the purpose. For CH, its concentration is found to be not universally correlated with heat release and wrongly indicates breaks in the flame surface. They suggested HCO as a possible indicator but also noted that it is unlikely that PLIF of HCO would be applicable as a single-shot diagnostic, owing to the inherently low fluorescence signal. Single-shot reaction-zone-imaging techniques that use the product of two different species, such as [CH2O]*[OH] and [CO]*[OH], were recently developed by Paul and Najm [12] and Rehm and Paul [13]. In these studies, careful selection of transitions allowed the PLIF signal to mimic the rate of a specific reaction, such as CH2O ⫹ O 3 OH ⫹ HCO or CO ⫹ OH 3 CO2 ⫹ H. Even though there are arguments about the suitability of CH to mark the heat-release region as

discussed, the application of recently suggested methods, such as CH2O™OH and CO™OH techniques, would require an additional excitation and imaging system and thus, would be impractical for simultaneous particle-image velocimetry (PIV) and PLIF measurements. In addition, if the purpose of the investigation is not to study the extinction process in detail, CH would still be a useful marker of the reaction zone, and simultaneous PIV and CH PLIF experiments would provide significant insight into the non-premixed combustion processes. Simultaneous measurements of velocity and a reaction tracer, such as OH and CH, have enabled the possibility of assessing the strain rate and velocity on the flame surface quantitatively [10,14 –16]. Rehm and Clemens [15] performed simultaneous PIV and OH PLIF measurements in a hydrogen-diffusion flame and found relatively good correlation between the high compressive strain rate and OH level. Donbar et al. [3,17] quantitatively measured the strain rates on the CH layer at different axial positions and concluded that they are not decaying as expected from the scaling of the global strain rate. In addition, they found good correlation between the mean velocity on the CH layer and the stoichiometric velocity estimated by U s ⫽ Z S U b , where Z S and U b are the stoichiometric mixture-fraction and bulk nozzle-exit velocity, respectively. As a continuation of these previous efforts, this paper provides an experimental investigation of the velocity field and the distribution of the CH in piloted, turbulent, non-premixed jet flames in co-flow. This paper concentrates on the fully developed regime of the non-premixed flame rather than the stabilization region of the flame, with further details available in Han [18]. Due to the relatively simple geometry, turbulent jets in coflow have been the subject of many recent numerical computations and modeling. Through the extensive analysis of the velocity field on the CH layer, the interaction between the flame surface and turbulent flow will be investigated to improve our understanding of the turbulent non-premixed combustion process. The present results will be compared with the previous studies of Donbar et al. [3,17], with discussions on the similarities and differences among these studies.

2. Experimental method In this section, the experimental facilities and the two experimental techniques applied in this study, PIV and PLIF, are described. Issues related to the simultaneous acquisition of PIV and PLIF images are also discussed. Error analysis is performed, and interpretation of CH in diffusion flames is discussed.

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Fig. 1. Schematic diagram of the experimental setup for simultaneous PIV and CH PLIF.

2.1. Flow facility The coflow tunnel is an induced-draft wind tunnel with a rectangular test section of 30 cm ⫻ 30 cm and a height of 80 cm. A 4-to-1-area contraction is located in front of the test section, and the inlet flow is conditioned by one layer of 1-in.-thick honeycomb (1/8-in. cell size) and two layers of fine screens (30 mesh per inch). The maximum flow-speed inside the tunnel is 4.9 m/s, and the flow speed can be adjusted by controlling the flow rate through a bypass path located at the ceiling of the laboratory. The tunnel has 6% spatial non-uniformity in mean velocity and 1.3% turbulent intensity. Two walls on the test section are covered with Pyrex windows (30 cm ⫻ 80 cm and 0.63-cm thick), and one of the two other walls has a fused-silica window for optical access (5 cm ⫻ 25 cm and 0.4-cm thick) through which the UV and visible laser-beams enter. The jet and the pilot gas are injected from concentric stainless steel tubes, which are 120-cm long (l/d 0 ⬃ 260), at the center of the test section. The main jet originates from the inner tube (4.6-mm i.d. and 6.35-mm o.d.), while the pilot gas (H2) issues from the clearance between the inner and outer tube (7.7-mm i.d. and 9.5-mm o.d.). Nitrogen-diluted ethylene (C2H4) is used as the main jet. Even though it requires higher dilution to achieve a soot-free flame

than nitrogen-diluted methane (CH4) flames, it is found to provide a higher CH signal than nitrogendiluted methane flames with similar soot level. An additional advantage of using nitrogen-diluted ethylene over nitrogen-diluted methane is that the molecular weight of C2H4 and N2 are nearly identical, and therefore, any preferential diffusion effects would be minimized. 2.2. Simultaneous PIV and CH PLIF Fig. 1 shows the set-up of the simultaneous PIV and CH PLIF experiment used in this study. For the illumination of the particles, a Spectra physics PIV400 Nd:YAG laser is used. The time delay between the laser pulses can be precisely controlled using a SRS DG-535 delay generator. For the imaging of the particles, a Kodak ES 1.0 CCD array (1016 ⫻ 1008 pixels) is used. It is an inter-line CCD camera capable of exposing two consecutive images within 5 ␮s in the frame-straddling mode. The over-all repetition rate is ⬃15 Hz in this mode. The images from the CCD array are transferred to a PC through a PCI frame-grabber. The Insight software package from TSI is used for image acquisition. For image processing of the PIV images, the Matlab娀-based code “PIVlab” is used. It was developed based upon the image-processing techniques described in previous

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studies [16,19,20] and incorporates the iterative box offset feature as well as various filters to remove spurious vectors, which are known to increase the detectivity of particles and reduce the RMS errors. For CH PLIF, the excitation and collection method proposed by Carter et al. [10] is used: the Q 1 (7.5) line of the B 2 ⌺ ⫺ 4 X 2 ⌸ system is excited at 390.19 nm, and fluorescence is collected near 430 nm. The spectral width of the Q 1 (7.5) line computed by “LIF BASE” [21] is 0.013 cm⫺1, while the spectral width of the dye laser system is ⬃0.5 cm⫺1. Therefore, a spectrally broad source assumption can be made. In addition, assuming the collisional transfer rate, Q 21 ⬃ 10 9 , the saturation spectral intensity, approximated by I sat ⬃ Q 21 /B 12 , is I ␯sat ⬃ 6 ⫻ ␯ ⫺6 2 10 W/cm 䡠 Hz. Since the maximum spectral intensity of the current system is ⬃1.5 ⫻ 10⫺4 W/cm2 䡠 Hz, the ratio between the maximum spectral intensity and the saturation intensity, I ␯max /I ␯sat , is ⬃25. Therefore, CH fluorescence is highly saturated in some locations, but owing to the non-uniform laser energy profile, we cannot assume that the saturation limit is reached in the entire imaging region. The laser pulse for the CH excitation is generated by a dye laser (Lambda Physik, FL3002) pumped by a XeCl excimer laser (Lambda Physik, EMG 203 MSC). For the dye laser, Exalite 392a from Exciton is used with p-dioxane as the solvent. The excimer laser generated 300 –350 mJ/pulse at 308 nm, and the energy from the dye laser is 20 –25 mJ/pulse at 390 nm, with a pulse width of 20 ns. For the collection of the fluorescence signal, a Princeton Instruments PentaMAX system is used with a 512 ⫻ 1024-resolution CCD array from EEV. It is operated in frame-transfer mode, and the resolution in this mode of operation is 512 ⫻ 512. The intensifier is composed of a photocathode, a microchannel plate (MCP), and a phosphor screen. The intensifier is used to gate the fluorescence signal to achieve a higher signal-to-noise ratio. For the imaging, a Nikkor 50-mm f/1.2 lens is used with optical filters to block the elastic scattering from the seeding particles and the flame radiation. For the filters, Schott glass filters, KV-418 and BG-1 of size 50.8 mm ⫻ 50.8 mm and thickness of 3 mm, are used, as suggested by Carter et al. [10]. This combination of filters gives efficient rejection of the particle scattering, while ⬃65% transmission is achieved at 430 nm. Due to the short focal length, the actual image covers a larger area than the PIV imaging system, which results in a loss of resolution. However, since the resolution of the experimental system is limited by the PIV processing, it does not affect the over-all accuracy of the measurement. The laser sheet thicknesses measured by the fullwidth at half-maximum (FWHM) values are 380 ␮m and 320 ␮m, respectively, for the Nd:YAG laser and

the excimer-pumped dye laser system. The timing control of the laser pulse and the exposure of the cameras are critical to obtain a simultaneous PIV and PLIF image. To ensure the simultaneous acquisition, the laser pulse for PLIF is located between the two laser pulses for PIV. The synchronization is achieved by using three SRS DG-535 delay generators. Fig. 2 shows a sample image-set and a processed image typically obtained in the experiment. Fig. 2a shows the particle-scattering image for PIV. Fig. 2b is the corresponding CH PLIF image obtained simultaneously with Fig. 2a. Low-seeding-density regions are observed near the region where the CH level is high. In Fig. 2c, the CH level is represented by iso-contour lines on the processed velocity field. 2.3. Experimental conditions The experimental conditions are based upon a few criteria, which can be described as follows: Y The jet-exit Reynolds’ numbers should be high to initiate the turbulent flame. Y The flame should be relatively free of PAHs and soot, which can interfere with the LIF signal [10]. Y The jet-exit speed should be limited so that a small quantity of hydrogen pilot-flame gas (⬍1.5% of the jet-mass flux) can anchor the flame to the nozzle. Run conditions are summarized in Table 1. Jets with three different jet Reynolds numbers, Re d , are studied, which are approximately 4600, 9900, and 19,900. The jet fuel is composed of 14% ethylene (C2H4) in nitrogen by volume. Du and Axelbaum [22] have studied soot-particle inception in ethylene flames, and they found that a strong dependence on the stoichiometric mixture fraction, Z S , exists for the inception of soot particles. By diluting the fuel with nitrogen, or by increasing Z S , the soot-particle inception was found to be suppressed in laminar-diffusion flames in co-flow. In addition, it was found by Santoro et al. [23] and Gomez et al. [24] that the soot inception is essentially suppressed if the temperature is below 1300 K in diffusion flames. In the present case, the stoichiometric mixture-fraction is 0.33, and the flame is nearly soot-free, except for the flame-tip regions. For all three cases, pilot-to-jet mass flux ratio is ⬍1.2%, as shown in Table 2. We can estimate the ratio of heat flux from the pilot flame to that from ˙ pilot/Q ˙ jet, using: the main jet, Q ˙ pilot m Q ˙ pilot LHV pilot 䡠 ˙ jet ⫽ m ˙ jet LHV jet Q

(1)

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Fig. 2. A typical sample-image-set and processed image. (a) Particle-scattering image obtained for PIV analysis. (b) CH PLIF image obtained simultaneously with the particle image shown in (a). (c) Processed image which shows the position of the CH layer and velocity-field simultaneously.

where LHV pilot and LHV jet represent the low heating value of the pilot and jet fuel, respectively. For the pilot-to-jet mass flux ratio of 1.2%, the heat-flux ratio between the jet and pilot becomes 22%, which is a significant amount of heat release from the pilot flame. However, if the momentum ratio between the pilot and main jet is computed, it is ⬍0.23% for all cases. Since the pilot-flame momentum is negligible

compared to that of the main jet, the effect of the pilot flame would be confined to near the nozzle exit, where most of its heat release would occur. As discussed by Mastorakos et al. [25] and Bourlioux et al. [26], a mixture-fraction with the fastest reaction rate, Z MR , could be different from the stoichiometric mixture-fraction, Z S , near the stabilization region, especially when stabilization is achieved

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Table 1 Run conditions for jet flames in co-flow Case

x C2 H4

Re d

U b,0 (m/s)

U c,0 (m/s)

U c,0 /U b,0

U 0 /U b,0

1 2 3

0.14 0.14 0.14

4600 9900 19900

14.0 30.0 60.7

22.0 40.0 73.7

1.57 1.33 1.21

1.168 1.091 1.056

Case

U 0 (m/s)

␳0 (kg/m3)

U CF (m/s)

ZS

U S (m/s)

m ˙ p /m ˙0

1 2 3

16.3 32.8 21.8

1.145 1.145 1.145

1.0 1.0 1.0

0.33 0.33 0.33

6.1 11.5 21.8

0.009 0.012 0.012

xC2H4: mole fraction of C2H4 Ub,0: bulk nozzle exit velocity U0: momentum averaged velocity ␳0: nozzle exit density US: stoichiometric velocity

Red: jet Reynolds number Uc,0: centerline nozzle exit velocity UCF: coflow velocity ZS: stoichiometric mixture fraction m ˙ p, m ˙ 0: mass flux of pilot and main jet

with a pilot flame. This could affect the determination of the flame surface location with CH near the nozzle, where the influence of the pilot flame is great, and introduce systematic bias to the correlations. Therefore, it is important to confine the influence of the pilot flame to a small region near the nozzle, by limiting the pilot-flame momentum flux. 2.4. Error estimation The sources of error can be summarized as follows:

Y Generic PIV error, in the experiment and the subsequent processing. Y Resolution of the experiment. Y Interpretation of the CH distribution. Each effect is discussed in the following paragraphs. 2.4.1. PIV error The error in the PIV results can be divided into the generic error originating from the experiment itself, such as particle lag or thermophoresis, and the errors from the image-processing procedure, espe-

Table 2 Estimated dissipative length-scale for jet flames in co-flow Re d 4600

9900

19,900

x/d 6 15 26 37 48 6 15 26 37 48 6 15 26 37 48

T (K) 471 762 1080 1410 1740 471 762 1080 1410 1740 471 762 1080 1410 1740

U c (m/s) 20.6 17.8 13.5 11.1 8.9 37.4 33.4 24.3 18.3 13.8 70.3 65.4 46.4 36.1 25.7

␦ (mm) 5.9 9.4 13.4 18.1 23.1 5.2 8.8 12.7 20.1 25.8 5.9 8.1 13.4 19.5 26.4

␯ (m2/s) ⫺5

3.14 ⫻ 10 7.11 ⫻ 10⫺5 1.29 ⫻ 10⫺4 2.02 ⫻ 10⫺4 2.89 ⫻ 10⫺4 3.14 ⫻ 10⫺5 7.11 ⫻ 10⫺5 1.29 ⫻ 10⫺5 2.02 ⫻ 10⫺5 2.89 ⫻ 10⫺5 3.14 ⫻ 10⫺5 7.11 ⫻ 10⫺5 1.29 ⫻ 10⫺4 2.02 ⫻ 10⫺4 2.89 ⫻ 10⫺4

⌳ B ⫽ 11.5 (Buch and Dahm 1998), ␭ T ⫽ ␭ B Re ␦1/4 T: estimated centerline temperature Uc: centerline velocity ␦: FWHM width of jet ␯: estimated kinematic viscosity Re␦: local Reynolds number ␭T, ␭B: Taylor and Kolmogorov scale

Re ␦

␭ T (mm)

␭ B (mm)

3852 2364 1403 993 711 6234 4121 2401 1818 1231 13152 7443 4827 3479 2345

1.09 2.23 4.10 6.61 9.97 0.76 1.57 2.98 5.42 8.46 0.59 1.08 2.21 3.80 6.27

0.14 0.32 0.67 1.18 1.93 0.09 0.20 0.43 0.83 1.43 0.05 0.12 0.27 0.50 0.90

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cially for digital PIV, such as the sub-pixel-accuracy issue. PIV methods measure the Lagrangian velocities of particles and therefore, are based upon the assumption that the particles follow the surrounding fluid motion. According to the analysis of Raffel et al. [27], the relaxation time of a particle to a step change in the fluid velocity is given as:

␶ s ⫽ d p2

␳p 18 ␮

(2)

If the relaxation time is computed assuming a particle size of 1 ␮m, ␳ p ⬃ 3500 kg/m3, and a temperature of 1500 K, it is ⬃0.84 ␮s. The smallest time-scale of the current experimental system obtained by ␦ r /U c,0 , where ␦ r , the spatial resolution of the experimental system ( ␦ r ⬃ 1.1 mm; see next paragraph), is 15 ␮s. Therefore, the error from the particle lag is not significant for the current experimental resolution. Besides the dynamic relaxation time, ␶ s , there are additional considerations when PIV is applied to a reacting flow, which are the thermophoretic effect and the effect of particles upon the chemical reactions or thermal transport in the flame. Mun˜ iz et al. [28] found that thermophoretic velocities can be as high as 15 cm/s for the case of a 2000 K/mm temperature gradient at 1300 K. According to the analysis of Hasselbrink [16], the thermal lag-time, ␶thermal, at 1000 K is ⬃4 ␮s. It is also important to note that the surface of the particles can terminate reactions and induce additional radiative loss to the flame, which has not been quantified. In digital PIV, the sub-pixel displacement is estimated by the values of three adjacent points [19], using a Gaussian peak fit. The RMS error from the conventional cross-correlation PIV analysis varies with the displacement, but for a particle-image diameter of 2 pixels, it ranges up to around 0.05 pixels. However, by shifting the box and therefore reducing the apparent displacement, the RMS error can be reduced [20]. Since the jet-flow field has a high dynamic range, 兩v兩 max/兩v兩 min, it limits the ability to achieve uniform relative accuracy along the image: relative RMS errors can be high in the co-flow region where the flow speed is low compared to the jet center. For the region near the nozzle exit with the highest Reynolds number, the dynamic range is as high as 70, and the corresponding relative RMS error in the ambient flow is ⬃7%, according to the Monte Carlo simulation result of Westerweel et al. [20]. Due to the same sources that cause errors in velocity determination, errors result in the derived quantities such as strain rate and two-dimensional dilatation. Assuming the thermophoretic force and PIV processing error are the dominant sources of

571

errors, the derived quantities such as strain rate or two-dimensional dilatation would have an error on the order of 200 –300 s⫺1. However, as shown in the Results sections, the mean strain rates on CH in most locations are an order of magnitude greater than the error margin of the current experimental system. 2.4.2. Experimental resolution The spatial resolution of the experimental system in this experiment is limited by the PIV resolution and can be improved by using a smaller interrogation-window size in the processing algorithm. However, it will reduce the number of particles in the interrogation region, and thus, the signal-to-noise ratio of the correlation will be reduced. Therefore, the size of the interrogation region has to be chosen as a compromise between the resolution and the accuracy or the detectivity of vectors. In this study, the interrogation-window size of 32 ⫻ 32 pixels was consistently used with 50% overlap between the adjacent interrogation region. In physical dimension, the spatial spacing between the vectors ranged from 580 to ⬃670 ␮m. Therefore, the smallest scale that can be resolved by the PIV system ranges from 1.16 to ⬃1.34 mm. All derived quantities, such as the vorticity and strain rates, are computed using the central-difference method. The experimental resolution has to be compared with the smallest scale that exists in physical space. Dowling [29] suggested that the regions of highest dissipation are observed in the Taylor scale, which can be represented as:

␭T ⬅ ⌳ TRe ␦⫺1/ 2Sc ⫺1/ 2 ␦

(3)

Buch and Dahm [30], however, found that both the largest and the smallest dissipation layer follow Kolmogorov scaling, such as:

␭B ⬅ ⌳ BRe ␦⫺3/4Sc ⫺1/ 2 ␦

(4)

In the recent three-dimensional measurement by Su and Clemens [31], evidence for both Taylor and Kolmogorov scaling was observed. Table 2 summarizes the computed-length scales for the jets studied. For the constant ⌳ B , 11.5 is used as suggested by Buch and Dahm [30], and the Taylor scale is estimated by ␭ T ⫽ ␭ B Re ␦1/4 , or assuming ⌳ B ⫽ ⌳ T . In some positions, the current experimental system fails to resolve one or both of the scales discussed above. However, the experimental system is capable of locating the distribution of the CH layer and the velocity on the layer, which are the main interests of the current study. In addition, according to Hasselbrink [16], a significant portion of the tur-

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bulent energy is measured, even though it is not resolving all scales. Furthermore, since the temperature near the flame surface becomes high, typically ⬎1500 K, the resolution requirement is expected to become less severe near the flame surface owing to the increased viscosity. 2.4.3. Interpretation of the CH distribution There are different views in interpreting the CH distribution in a non-premixed flame. Najm et al. [11] found that CH is not universally correlated to heat release and can show false breaks in methane premixed flames. They have noted that the main oxidation path for the methane flame is: CH4 3 CH3 3 CH2O 3 HCO 3 CO 3 CO2

(5)

while CH is formed mainly from the following paths: CH4 3 CH3 3 CH*2 or

CH2 3 CH

3 CO 3 CO2

(6)

or CH4 3 CH3 3 C2H6 3 C2H5 3 C2H4 3 C2H3 3 C2H2 3 CH

(7)

In their study, they found that the heat-release rate corresponds well with the HCO concentration, since the oxidation path shown in Eq. (5) is dominant. In addition, noting that HCO is a fast-dissociating species and thus, that its concentration is proportional to the production rate, Paul and Najm [12] proposed that [CH2O]*[OH] be used as a marker of the heat-release rate by choosing a spectral line that mimics the reaction coefficient of the HCO-forming reaction. As an attempt to interpret CH in diffusion flames, an opposed-flow laminar-diffusion flame computation is performed for the current fuel using OPPDIF [32]. The oxidation path for ethylene would be different from that of the methane flame, and CH would have a different meaning in diluted ethylene flames. For the chemical reactions, C2 and C3 mechanisms proposed by Qin et al. [33] are used, which is composed of 70 species and 463 elementary reactions. For comparison, laminar premixed flame calculations are also performed using the premixed flame code, PREMIX [34]. The result from the opposed-flow laminar-diffusion flame calculation is given in Fig. 3a. The fuel is composed of 14% C2H4 and 86% N2 and the oxidizer is air. The maximum strain rate is ⬃350 s⫺1, and the temperatures of the fuel and oxidizer are 1000 K and 300 K, respectively. The peak and width of the [CH] and [HCO] profiles are essentially identical. In addition, the absolute-concentration level is similar for both [CH] and [HCO], while [HCO] is ⬃20 times

higher in a diluted ethylene premixed flame (25% C2H4 and 75% N2, ␾ ⫽ 1, where ␾ is the equivalence ratio) computed via PREMIX. OH stays closer to the oxidizer side compared to the other species. Donbar et al. [4] reported similar results for their diluted methane-air diffusion flame. The temperature profile in Fig. 3b shows that the peaks of [CH] and [HCO] correspond well with the peak of the temperature profile. Furthermore, Watson et al. [35] performed simultaneous CH and OH PLIF, and confirmed that CH exists when the reaction sustains or the OH exists, even though the concentration can be significantly reduced. In summary, the CH is produced by some of the hydrocarbon-oxidation paths. In premixed flames, these paths are not dominant, and it is plausible that the CH falsely indicates breaks while the reaction sustains. However, in ethylene diffusion flames, the peak of [CH] occurs essentially at the same position as that of [HCO], and its concentration level is also comparable to [HCO], which implies that reaction paths through CH become important. A single species that can represent all oxidation paths has not been found; however, CH remains a useful indicator of the reaction zone, especially in ethylene diffusion flames, and the CH distribution will be considered as the flame surface in this study.

3. Results and discussion In this section, experimental results on the velocity and strain rate measurements of CH are presented. Both qualitative observations and statistical analysis are performed. The concept of stoichiometric velocity will be introduced for interpretation of the results. 3.1. Stoichiometric velocity, US In their study of simultaneous velocity and CHfield measurement in non-premixed flames, Donbar et al. [17] noted that the velocity on the flame surface is close to Z S U b , where Z S is the stoichiometric mixture-fraction and U b is the bulk nozzle-exit velocity. Hasselbrink [16] also reported similar observations in his simultaneous PIV and OH PLIF results in jet flames in cross-flow. These observations suggest that the velocity on the flame surface has a characteristic velocity, which can be determined from global conditions. To investigate this concept further, the governing equations of the mixture fraction and the axial velocity are examined [36,37]:

冉

⭸ ⭸ ⭸ ⭸Z 共 ␳ Z兲 ⫹ 共 ␳ u iZ兲 ⫽ ␳D ⭸t ⭸ xi ⭸ xi ⭸ xi

冊

(8)

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573

Fig. 3. Spatial profile of (a) flame-zone markers (OH, CH, and HCO) and (b) temperature profile for an opposed-flow diffusion-flame between a fuel (14% C2H4, 86% N2) and air computed by the OPPDIF code.

and

冉

冊

⭸u 1 ⭸ ⭸ ⭸p ⭸ 共 ␳ u 1兲 ⫹ 共 ␳ u iu 1 兲 ⫽ ⫺ ⫹ ␳␯ ⭸t ⭸ xi ⭸ x1 ⭸ xi ⭸ xi

(9) In Eq. (9), the subscript 1 indicates the axial direction. Eqs. (8) and (9) have similar formal structure except for two aspects, which are the pressure-gradient term, ⭸p/⭸ x 1 , and transport-property values, D

and ␯, where D is the molecular diffusion coefficient and ␯ is the kinematic viscosity. Therefore, if we can assume uniform-pressure conditions and unity Schmidt number (Sc ⫽ ␯ /D), the two equations become identical. Furthermore, if the Reynolds number increases, the relative importance of the molecular diffusion and viscous term reduces, and thus, non-unity Schmidt number would not affect the similarity significantly. It is also important to note that

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Fig. 4. Comparison of boundary conditions of the (a) mixture-fraction and (b) axial velocity at the nozzle exit.

the density change by heat release affects both equations in the same manner, and therefore, the similarity between Eqs. (8) and (9) remains valid even in the presence of heat release. The boundary conditions are also a crucial element. As shown in Fig. 4, the mixture-fraction has a top-hat exit profile near the nozzle exit, while the velocity has a turbulent pipe flow profile. Furthermore, the mixture-fraction value will be zero at the ambient flow, while the ambient fluid is flowing at a

finite co-flow speed. It is expected that the difference in the nozzle-exit profile will become insignificant far downstream, since the jet will approach the limit of a point source, where only the momentum flux is a significant factor; however, the co-flow carries momentum throughout the flow, and the co-flow momentum will remain important in determining the velocity on the flame surface. From the above discussions, the velocity of the stoichiometric mixture can be formulated. Fig. 5

Fig. 5. Conceptual sketch of the ideal mixing process in a uniform-pressure condition. The mixture velocity is the stoichiometric velocity, U S ⫽ Z S U 0 ⫹ (1 ⫺ Z S )U CF .

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shows a conceptual sketch of the ideal molecularmixing process in a uniform-pressure environment. If Z S kg of fuel traveling at speed U 0 mixes at the molecular level with (1 ⫺ Z S ) kg of oxidizer traveling at U CF , the mixture velocity, U S , can be computed from momentum conservation as: U S ⫽ Z SU 0 ⫹ 共1 ⫺ Z S兲U CF

(10)

For a non-uniform nozzle-exit-velocity profile such as in the present case, the most appropriate value for the fuel-jet velocity, U 0 , will be a momentum-averaged velocity, which represents the momentum flux for a unit-mass flux of the jet fluid; i.e., the momentum-averaged velocity can be expressed as: U0 ⫽

J0 m ˙0

(11)

where J 0 and m ˙ 0 are the initial momentum and mass fluxes of the jet from the nozzle, given by: J0 ⫽

冕

R

␳ u 22 ␲ r dr

(12)

␳ u2 ␲ r dr

(13)

0

and m ˙0⫽

冕

R

0

at x ⫽ 0. For a top-hat velocity profile, U 0 should be the same as the bulk velocity, U b , where the bulk velocity for a uniform density fluid can be defined as: Ub ⫽

1 ␲R2

冕

R

u2 ␲ r dr

(14)

0

However, for a flow from a tube, the two values are different. For a laminar pipe flow with a parabolic velocity profile and U c /U b ⫽ 2, U 0 /U b can be computed as 4/3, where U c represents the center-line velocity. For a turbulent-pipe flow with U c /U b ⫽ 1.31, U 0 /U b reduces to 1.085, as can be deduced from the direct numerical simulation result of Eggels et al. [38]. The center-line exit velocities, U c , are 22.0 m/s, 40.0 m/s, and 73.7 m/s, respectively, for the three different cases studied, which yields U c /U b ratios of 1.57, 1.33, and 1.21, as summarized in Table 1. Since the axial-velocity profile at the nozzle exit is not available, the ratio between the momentum-averaged velocity and the bulk velocity, U 0 /U b , is estimated from using the three known cases discussed above, which are the top-hat-profile case (U 0 /U b ⫽ 1 at U c /U b ⫽ 1), the laminar parabolic-profile case (U 0 /U b ⫽ 4/3 at U c /U b ⫽ 2), and a turbulent case from DNS (U 0 /U b ⫽ 1.085 at U c /U b ⫽ 1.31). From a parabolic curve-fit to the known three points,

575

the U 0 /U b ratios of 1.168, 1.091, and 1.056 are obtained for U c /U b of 1.57, 1.33, and 1.21, respectively. Another aspect of Eq. (10) is revealed if it is arranged as: U S ⫺ U CF ⫽ Z S共U 0 ⫺ U CF兲

(15)

This represents the velocity on the stoichiometric surface in a reference frame moving at constant coflow speed, U CF , with assumptions of top-hat profile, unity Schmidt number, and uniform-pressure distribution according to Eqs. (8) and (9). Considering the various assumptions involved in the concept of stoichiometric velocity, the validity of U S to represent a characteristic axial velocity on the flame surface has to be assessed. 3.1. Instantaneous velocity and the CH field In this section, instantaneous images of the velocity and CH field are presented. Figs. 6 through 8 show the instantaneous velocity and strain rate field superimposed with the location of the CH layer for all three cases studied. The interaction between the CH layer and the flow, which is represented by the velocity and strain rate field, are discussed. 3.1.1. Instantaneous-velocity field The focus of the discussion here is to assess the relevance of the stoichiometric velocity to represent the velocity on the CH layer. For all Reynolds numbers and positions shown in Figs. 6 – 8, the correlation between the position of the CH layer and the stoichiometric velocity-contour are good in general. Despite generally good correlations, there also exist positions where the CH distribution deviates from the U S contour as observed in Figs. 6(a-2, a-3), 7(a-3), and 8(a-3), which will be discussed more in the next paragraph. Even for the highly turbulent and contorted cases [Figs. 6(a-3), 7(a-2), and 8(a-3)], the CH layer stays close to the U S contour. With all the limitations discussed in the previous section, the good correlation between the CH distribution and the U S contour in a turbulent-reacting jet implies that the molecular-mixing process sketched in Fig. 5 is an appropriate approximation for non-premixed jet flames in coflow throughout the flame with nearuniform-pressure conditions. As the jet Reynolds number grows, the contortions in the CH distribution as well as in the U S contour increase, and the breaks in the CH distribution become frequent especially, at down-stream positions. 3.1.2. Instantaneous-strain rate field Owing to the two-dimensional nature of PIV, only limited components of the strain rate can be obtained.

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Fig. 6. Examples of processed images for Re d ⫽ 4600. (a) Solid lines show the contour of the CH layer and dashed lines show the contour of stoichiometric velocity, U S . (b) Black solid lines show the contour of the CH layer, and the color map represents shear-strain rate, S rx .

In Figs. 6 – 8, the contour of the shear-strain rate component, S rx , is shown with the CH layer, where S rx is computed by:

S rx ⫽

1 2

冉

冊

⭸u r ⭸u x ⫹ ⭸x ⭸r

(16)

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577

Fig. 7. Examples of processed images for Re d ⫽ 9900. (a) Solid lines show the contour of the CH layer and dashed lines show the contour of stoichiometric velocity, U S . (b) Black solid lines show the contour of the CH layer, and the color map represents shear-strain rate, S rx .

For the cases shown in Figs. 6 – 8, the correlation between the high-strain rate regions and the CH layer are generally good. Similar experimental observa-

tions were made by Rehm and Clemens [15], where they found that the compressive principal strain rate aligns with the high-OH-concentration region. Espe-

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Fig. 8. Examples of processed images for Re d ⫽ 19,900. (a) Solid lines show the contour of the CH layer and dashed lines show the contour of stoichiometric velocity, U S . (b) Black solid lines show the contour of the CH layer, and the color map represents shear-strain rate, S rx .

cially for the positions where the CH distribution deviates from the U S contour, it is often the case that CH stays in high-strain regions, as observed in Figs.

6(a-2, a-3), 7(a-3), and 8(a-3). In the large-eddysimulation (LES) result of a turbulent partially premixed flame (Sandia flame D) by Pitsch and Steiner

D. Han, M.G. Mungal / Combustion and Flame 132 (2003) 565–590

579

Fig. 9. Interaction between the strain rate and flame surface. In this figure, S 1 and S 2 represent the principal strain rates (S 1 ⬎ S 2 ).

[39], it was found that regions of high-strain rate align with regions of a narrow temperature maximum, which is possibly the reaction zone. They also noted that the high-scalar dissipation rate regions tend to align with the stoichiometric mixture-fraction surface. To explain the alignment between the CH layer and the regions of high strain rate, a simple schematic shown in Fig. 9 can be used. First, the alignment of the CH layer with the high-strain rate region implies that there exist high-velocity gradients across the flame surface. In addition, since the shear-strain rate is dominant, the fluid element inside the flame surface is tilted, as shown in Fig. 9. If this deformation is observed in the principal strain rate axis, it becomes similar to a counter-flowing diffusion-flame situation, where shear-strain rates bring fuel and oxidizer together. Higher strain rate will induce higher reaction rate unless the reaction is quenched by an excessive strain rate. In summary, strain rates on the flame surface bring fuel and oxidizer into the reaction zone and enhance combustion, unless the flame surface is extinguished by excessive strain rates. In Fig. 10, the velocity and vorticity fields are shown for the cases shown in Figs. 6 – 8, but the stoichiometric velocity, U S , is subtracted from the

axial-velocity component. In this frame of reference, the axial-velocity component is zero along the stoichiometric velocity-contour shown as dashed lines in Fig. 10. Evidence for flame-surface stretching and entrainment of ambient flow near the stoichiometric velocity-contour are observed more clearly in this frame of reference. It is also interesting to observe the instantaneous-vorticity field, computed by:

␻⫽

⭸u x ⭸u r ⫺ ⭸r ⭸x

(17)

The vorticity field generally appears similar to the corresponding strain rate field, which implies that the axial-velocity-gradient term, ⭸u x /⭸r, is dominant in Eqs. (16) and (17). Pure vorticity without strain rate does not induce deformation of fluid elements and is not expected to enhance the reaction. 3.2. Mean velocity and the CH field In this section, the mean velocity and strain rate of the CH layer are investigated. The mean axial velocity on CH is compared with U S obtained from Eq. (10). The mean residence-time in the flame surface is also estimated from the characteristic radial velocity.

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Fig. 10. Instantaneous velocity and vorticity fields for (a) Re d ⫽ 4600, (b) Re d ⫽ 9900, and (c) Re d ⫽ 19,900. In the velocity field, the stoichiometric velocity, U S , is subtracted from the axial-velocity component.

3.2.1. Mean axial velocity on the CH layer Fig. 11 shows the mean center-line velocity obtained by ensemble-averaging instantaneous-velocity fields and the velocity on the CH layer obtained by

averaging the points where the CH level exceeds the threshold that is ⬃20% of the maximum CH level. The open symbols indicate the mean axial velocity on the flame surface marked by the CH distribution,

D. Han, M.G. Mungal / Combustion and Flame 132 (2003) 565–590

Fig. 23. Color versions of Figs. 6, 7, and 8 from top to bottom.

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Fig. 12. Ratio of the velocity on the flame surface, U Flame, and the mean center line velocity, U c , for different Reynolds numbers in x/L co-ordinate.

eral, but stays rather close to the stoichiometric velocity. Meanwhile, the mean velocity on the CH layer is bounded by the mean center-line velocity, as expected (see Fig. 13). On the top axis of Fig. 11, the ␰ co-ordinate suggested by Becker and Yamazaki [40] is indicated. ␰ is defined as:

␰⬅

冉 冊 gd* U 02

1/3

x d*

(18)

where d* is the equivalent-source diameter defined as: d* ⬅

2m ˙0 共 ␲␳ ⬁J 0兲 1/ 2

(19)

The equivalent-source diameter simplifies to the density-weighted diameter, d( ␳ 0 / ␳ ⬁ ) 1/ 2 , for a top-hatvelocity profile. If we model the jet as cone-shaped of width ␦, height x, and mean density ␳៮ , the ratio of the buoyancy that the entire flame-brush feels and the initial momentum of the jet can be written as:

B ⫽ I Fig. 11. The mean center-line velocity, U c , and the velocity on the CH layer, U Flame, for the cases of (a) Re d ⫽ 4600, (b) Re d ⫽ 9900, and (c) Re d ⫽ 19,900. The dashed lines indicate the stoichiometric velocity, U S .

U Flame, with the error bars representing the standard deviations. The black symbols represent the mean center-line velocity. The dashed lines in each image show the theoretical stoichiometric velocity, U S , computed from Eq. (10). The mean velocity on the CH layer increases slowly with axial position in gen-

共 ␳ ⬁ ⫺ ␳៮ 兲 g

␳ 0u 02

␲ 2x ␦ 4 3

␲ 2 d 4

(20)

Letting (␳⬁ ⫺ ␳៮ ) 3 ␳⬁ and ␦ ⬃ x, and applying a cube root to the entire expression, Eq. (18) is obtained. As the ␰ value increases, the relative effect of buoyancy grows. According to previous studies [40, 41], the jet is dominated by momentum for ␰ ⬍ 1, while the buoyancy is important for ␰ ⬎ 1. The buoyancy adds additional momentum to the jet and enhances the large-scale stirring, which results in the increase of the jet entrainment [40,41]. In Fig. 12, the U Flame/U c value is plotted in the x/L coordinate where L is the mean flame-length.

D. Han, M.G. Mungal / Combustion and Flame 132 (2003) 565–590

Fig. 13. Ratio of the velocity on the flame surface, U Flame, and the stoichiometric velocity, U S , for different Reynolds numbers in ␰ co-ordinate.

583

The U Flame/U c ratios for different Reynolds numbers are found to stay rather close, and it confirms the idea that the velocity on the flame surface is not randomly determined, but it is closely interacting with the flow field and bounded by the center-line velocity. One of the trends that can be observed in Fig. 11 is that U Flame deviates further from U S as ␰ increases. Fig. 13 shows the ratio of U Flame and U S versus the ␰ coordinate for all cases studied. Except for the upstream positions where the pilot flame has significant effect, U Flame/U S slowly increases with ␰. From this observation, it is thought that buoyancy is a factor influencing the systematic deviation of the mean axial velocity on the CH layer from the theoretical stoichiometric velocity.

Fig. 14. Mean profile of the axial velocity (solid line) and CH level (dotted line) at different axial locations with the stoichiometric velocity, U S , indicated by the dashed lines. (a) Re d ⫽ 4600, (b) Re d ⫽ 19,900.

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Fig. 15. RMS value of the radial velocity, 共ur2)1/2, on the CH layer at different axial positions.

3.2.2. Velocity and CH profile Fig. 14 shows the mean radial profile of the axial velocity and the mean CH profile at different axial positions. The mean CH profile becomes wider as it moves down-stream, however; it is not because the actual CH layer gets wider, but because the spatial distribution of the CH layer becomes broad as observed in instantaneous images. The peak of the CH profile is close to the stoichiometric-velocity positions of the mean axial-velocity profile, while it tends to stay slightly to the inside of the U S locations, except for the positions close to the nozzle. As noted by Pitsch and Steiner [42], the jet mixture-fraction field is influenced by the pilot flame, and it seems to cause a different trend near the nozzle exit compared to the other positions. If we assume the peak of the mean CH profile is close to the mean position of the stoichiometric mixture-fraction, Z S , the result of Fig. 14 suggests that the mean stoichiometric mixture-fraction-surface is close to or resides inside the mean stoichiometric velocity-surface. This observation is not consistent with experiments in non-reacting jets where the mean concentration and velocity profiles are measured [43, 44]. In non-reacting jets, the mean concentration profile is found to spread out wider than the mean velocity profile. If it were also true in the reacting cases, the mean stoichiometric mixture-fraction-surface should be outside the mean stoichiometric velocitysurface and therefore, the mean velocity on the stoichiometric surface should be lower than the stoichiometric velocity, U S . In Reynolds-averaged turbulent models of jets, the turbulent Schmidt number ␯ t / D t ⬃ 0.7 is used to achieve consistency with the non-reacting experimental results, where ␯ t and D t are the turbulent-eddy viscosity and the turbulenteddy diffusivity, respectively. However, present observations warn on the use of non-reacting-flow results for reacting flows, and thus, on the application

Fig. 16. The residence time on the CH layer, ␶ F , normalized by d/U b , assuming a constant thickness of the CH layer along axial position.

in reacting jets of the Reynolds-averaged turbulent models with the Sc t ⬃ 0.7 assumption. 3.2.3. Residence time in the flame surface The residence time in the flame surface is important in the formation and removal of pollutants [6,45]. Especially for NOx , formation and removal occur in a specific temperature window and stoichiometry condition [46 – 48], and thus, the correct residence time in the high-temperature-flame surface is crucial to predict the formation and removal of NOx . The residence time in the CH layer can be estimated from the characteristic radial velocity on the CH layer. Since the velocity on the left and right branch of the CH layer would have different signs on average, the characteristic radial velocity on the CH layer is estimated by the RMS value of the radial velocity, (ur2) 1/ 2 . By dividing the width of the CH layer, ␦ F , with the characteristic velocity on the CH layer, a characteristic residence time on the CH layer, ␶ F , could be estimated; i.e., the characteristic residence time can be expressed as:

␶F ⫽

␦F 共u r2兲 1/ 2

(21)

Fig. 15 shows the RMS value of the radial velocity, (ur2) 1/ 2 , measured at different axial positions. Except for the positions near the nozzle, which will be affected by the pilot flame, the (ur2) 1/ 2 value varies little with axial position and is proportional to the jet exit-velocity. The thickness of the CH layer is somewhat difficult to quantify owing to the following reasons. First, the CH line could be partially saturated, and therefore, the signal may not be directly proportional to the concentration. Second, the thickness of the CH layer fluctuates significantly especially for the high-

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585

Fig. 18. Comparison of various scalings for the mean compressive strain rate, ⫺S2, in (a) linear and (b) log scale. Red ⫽ 9900.

Fig. 17. Mean compressive strain rate (⫺S2) variation along axial positions in (a) linear scale and (b) log scale. The lines represent the least-squares fit of the data, which is S2 ⫽ ⫺2.1(U c,0 /d)( x/d) ⫺0.7 . In (c), ⫺S2 is normalized by (U c,0 /d) to show the good correlation for different Reynolds numbers.

Reynolds-number case. Third, three-dimensional distortion of the flame surface leads to the over-estimation of flame-surface thickness in two-dimensional imaging [4]. The thickness of the flame surface could be roughly estimated from Figs. 6 – 8 using the solid contour-lines. The thickness represented by the boundary in Figs. 6 – 8 ranges between 1 and ⬃2 mm. According to the measurement by Donbar et al. [4], the thickness of the CH layer increases slightly with axial position, but within a factor of 2. With all the uncertainties, the thickness of the CH layer in this study will be assumed to be constant, or ␦F ⬃ 1.5 mm.

Assuming a constant flame-surface thickness, a small variation of the (ur2) 1/ 2 value with axial position suggests a nearly constant ␶ F for each jet flame. Fig. 16 shows the ␶ F /(d/U b ) ratio versus axial position for all three cases, where d and U b are the nozzle exit-diameter and bulk nozzle-exit velocity. If a constant ␶ F is assumed, a simple relation can be obtained:

␶ F ⫽ 4.1

d Ub

(22)

In numerical value, ␶ F ranges from 0.3 to 1.4 ms. It is interesting to compare this value with the flamesheet residence time used by Broadwell and Lutz [6] in the two-stage Lagrangian model developed for the prediction of NOx formation. They used the same relation as Eq. (22), but the constant was 30 instead of 4.1. The high-temperature region as might be marked by OH is typically found to be 3 to 10 times thicker than the CH layer [4,49]. The NOx will peak on the lean side where O atoms are abundant, and OH tends to reside on the lean side of the flame, while CH

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Fig. 20. Comparison of stretching (S 1 ) and compressive (S 2 ) mean principal strain rates at different axial positions for Re d ⫽ 9900. Two-dimensional dilatation rate (ⵜ 2D 䡠 uជ ⫽ S 1 ⫹ S 2 ) is also shown for comparison.

3.3. Mean strain rate and the CH field As observed in Figs. 6 – 8, the CH distribution tends to align with the high-strain rate region. A quantitative knowledge of the strain rate and scalardissipation rate on the flame surface is essential for combustion modeling. In this section, the strain rate on the CH layer will be investigated, and the strain rate scaling will be assessed. 3.3.1. Mean strain rate on the CH layer The three components of strain rate that can be measured from the two velocity components of PIV are: S rr ⫽

Fig. 19. The probability-density function of the compressive strain rate, S 2 , at different axial positions for (a) Re d ⫽ 4600, (b) Re d ⫽ 9900, and (c) Re d ⫽ 19,900.

is found on the rich side. Therefore, the OH region will tend to over-lap with the NOx -formation region, and the difference between the value used in the modeling work of Broadwell and Lutz [6] and the present work can be rationalized. In addition, since the flame surface of the current example resides in a higher-velocity region compared to a pure methane flame owing to the high stoichiometric mixture-fraction, Z S , the residence time would have been shortened.

⭸u r ⭸r

S xx ⫽

⭸u x ⭸x

S rx ⫽

1 2

冉

冊

⭸u r ⭸u x ⫹ ⭸x ⭸r

The derivatives in these expressions are computed using the second-order accurate central-difference scheme. From these three components, two principal strain rates (S 1 and S 2 ) can be computed, which are illustrated in Fig. 9. Between the two principal strainrates, S 1 is defined to be greater than S 2 , or S 1 ⬎ S 2 . Since the shear-strain rate component, S rx , is dominant near the flame surface, S 1 is the positive-stretching component, while S 2 represents the negativecompressive component in general. In addition, the principal stretching of the fluid element will occur in a direction inclined to the axial direction as shown in Fig. 9. Fig. 17a shows the mean value of ⫺S 2 on the CH layer with different Reynolds numbers and axial positions. The physical meaning of ⫺ S2 is the mean magnitude of the compressive strain rate on the CH layer. For all cases, the ⫺ S2 value is found to de-

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587

Fig. 22. (a) Distribution of the flame-surface angle at different axial positions. (b) Distribution of the principal strain rate direction at different axial positions. Both distributions are for the Re d ⫽ 9900 case. Fig. 21. (a) Variation of the axi-symmetric flame-surface stretch rate, K r , along the axial positions for Re d ⫽ 9900. Both the mean value, Kr, and the RMS value, 共Kr2)1/2, are plotted. (b) Distribution of the axi-symmetric flame surface stretch rate, K r , at different axial positions.

crease with axial position, while its decrease rate is more gradual than expected from the scaling of nonreacting turbulent jets. The strain rate of a non-reacting jet is known to decay as ( x/d) ⫺2 due to the velocity decay (⬃x ⫺1 ) and growth of the jet (⬃x). Since the velocity and spreading rate of jet flames in co-flow are different from the non-reacting jet, another possible scaling relation would be S ⬃ U c / ␦ FWHM , where U c is the center-line velocity and ␦ FWHM is the jet width measured by the FWHM of the mean-velocity profile. However, these scalings are obtained from the center-line velocity and global width of the jet and thus, are not expected to represent the scaling of the strain rate on the CH layer.

3.3.2. Strain rate scaling In their discussion of the scalar-dissipation-rate scaling, Lin˜ a´ n and Williams [50] noted that the scalar-dissipation rate on the stoichiometric surface would scale as ␹ ⬃ ( x/d) ⫺m , where m ⫽ 2 or possibly less, depending upon the location of the stoichiometric surface. Since ␹ ⬃ S 2 , this suggests that the strain rate on the stoichiometric surface would scale as S ⬃ ( x/d) ⫺n with n ⱕ 1, which allows movement of the stoichiometric surface outside the center-line. As shown in Fig. 17a (linear scale) and b (log-log scale), least-squares fits of ⫺ S2 to all three cases show a good correlation to S ⬃ ( x/d) ⫺0.7 . Furthermore, if the strain rate is normalized by U c,0 /d, all three cases can be collapsed into a single line, which can be expressed as: S 2 ⫽ ⫺2.1

冉冊

U c,0 x d d

⫺0.7

(23)

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where U c,0 is the center-line velocity at the nozzle exit (see Fig. 17c). This expression has a slow variation, especially near the flame tip, compared to the scalings of non-reacting turbulent jets introduced in the previous section. Fig. 18 shows the comparison of various strain rate scalings applied to the case of Re d ⫽ 9900 in both linear and log scale. Both S ⬃ ( x/d) ⫺2 and S ⬃ U c / ␦ FWHM do not predict such a slow variation of the strain rate on the CH layer and fail to match the data as well. It is expected from the current result that the scalar-dissipation rate on the flame surface, ␹ F , would also vary more slowly than that of the non-reacting jet, or ␹ F ⬃ ( x/d) ⫺m with m ⬍ 2, and most likely, m ⬃ 1.4. 3.3.3. Strain-rate distribution Fig. 19 shows the distribution of S 2 at different axial positions and jet Reynolds numbers. The distribution is wide at upstream positions, while it is reduced as it moves downstream for all three cases. However, it is interesting to observe that the peaks of the distribution (most probable strain rate) are closely located between 兩S 2 兩 ⫽ 500 and ⬃3000 s⫺1, regardless of the position and Reynolds’ number. In other words, it is a distribution skewed toward high strain rate that separates the mean values at different positions, but the most preferred strain rate does not change with position or jet Reynolds number. In the strain rate distributions shown in Fig. 19, strain rates that are four to five times larger than the mean value are observed. It is thought that these peak values are highly transient, and therefore, the reaction surface has not responded to the strain rate at that instant. If the flame surface is exposed to such high strain rates above the short transient limit, it is expected that the flame surface will be extinguished. This phenomenon is thought to cause the distribution skewed toward low strain rates as shown in Fig. 19. This observation also suggests that the strain rate scaling of non-reacting jets would not be appropriate to predict the strain rate on the flame surface, since it is not able to predict transient effects, such as extinction of the flame surface by excessive strain rate. 3.3.4. Dilatation Fig. 20 compares the mean stretching component of the principal strain rate, S1, with the mean compressive principal strain rate, ⫺S2, for the Re d ⫽ 9900 case. There exists little difference between these two values throughout the length of the flame. It also implies that the mean value of the two-dimensional dilatation (ⵜ 2D 䡠 uជ ⫽ S 1 ⫹ S 2 ) on the CH layer is negligible compared to the mean strain rate on CH. Mullin et al. [51] investigated the two-dimensional dilatation on the CH layer and reported that the mean two-dimensional dilatation on the CH layer is

on the order of 200 –300 s⫺1. However, since the error bound of the current experimental system on determining the derivative of velocity is on the order of 200 –300 s⫺1, it is difficult to confirm this result. In general, the correlation between the CH and twodimensional dilatation is weak in instantaneous images. This result is quite contrary to the PIV result of premixed flames by Mungal et al. [52] and Mueller and Driscoll [53], where they found a very good correlation between the two-dimensional dilatation and the reaction zone. 3.4. Flame surface stretch rate An interesting property that was investigated by Donbar et al. [17] is the flame-surface stretch rate defined as: K⫽

1 dA A dt

(24)

Since only two components of the velocity were available from the experiment, Donbar et al. [17] considered the axi-symmetric formulation of Eq. (24), which can be expressed as: K r ⫽ ⫺n rn x

冉

冊

⭸u r ⭸u x ⭸u r ⫹ ⫹ 共1 ⫺ n r2兲 ⭸x ⭸r ⭸r

⫹ 共1 ⫺ n x2兲

⭸u x u r ⫹ ⭸x r

(25)

They found that the mean value of the quantity shown in Eq. (25) stays constant or linearly increases along the axial position. For comparison, this quantity is computed from the current data, and both the variation of the mean and distribution along the axial position for the Re d ⫽ 9900 case are shown in Fig. 21. The mean value of the axi-symmetric flamesurface stretch rate, Kr, varies little near zero with axial position as shown in Fig. 21a. The distributions at different axial positions appear symmetric with the mean near zero, while the deviation from the mean decreases with downstream position, as observed in Fig. 21b. The RMS value of K r is found to decrease at a rate proportional to ( x/d) ⫺0.52 , which is somewhat slower than the decreasing rate of the mean principal strain rate discussed above. It is thought that the u r /r term in Eq. (25) contributes to the decreasing rate at downstream positions. Unlike premixed flames, the flame-surface stretch-rate does not appear to be as important in non-premixed flames, since the limiting process in non-premixed combustion is the mixing between the fuel and oxidizer. As illustrated in Fig. 9, the total strain rate will determine the mixing between the fuel and oxidizer and subsequently, the scalar dissipation rate. Principal strain rate could therefore be a good

D. Han, M.G. Mungal / Combustion and Flame 132 (2003) 565–590

representation of the total strain rate and thus, scalardissipation rate. Another interesting observation made in the course of computing the flame-surface stretch rate is the variation of the flame-surface direction along the axial position. Fig. 22a shows the distribution of the flame-surface tangential angle at three different axial positions. As we can expect from the instantaneous CH images of Figs. 6 – 8, the flame-surface tangential angle distribution deviates from nearly-vertical angles as it moves to downstream positions. For comparison, the distribution of the principal strain-rate direction is plotted versus the axial position in Fig. 22b. As observed by Rehm and Clemens [15], the peak distribution of the principal strain rate direction resides near ⫾45° with respect to the axial direction. The change of the flame-surface angle distribution with axial position shown in Fig. 22a would be induced by the slow response to the main stretching direction of the flow field and by large-scale structures enhanced by buoyancy.

4. Conclusions In this study, the velocity and strain rate on the CH layer for jet flames in coflow were investigated. The important findings of the present study can be summarized as follows: Y OPPDIF calculations show that CH is coincident with the highest-temperature zones for the fuel mixture used here, and hence, CH serves as an excellent flame marker. Y The velocity on the CH layer, U Flame, tends to stay close to the stoichiometric velocity, U S ⫽ Z S U 0 ⫹ (1 ⫺ Z S )U CF , both instantaneously and on average. This can be explained from the similarity of the momentum and mixture-fraction equations and also by the momentum mixing between the jet and the coflow fluid. As the effect of buoyancy grows, a systematic deviation of U Flame from U S is observed on average. Y The residence time in the CH layer is estimated by dividing the width of the CH layer by the characteristic radial velocity on the CH layer, 共ur2)1/2. The estimated residence time ␶ F does not vary significantly along the axial position and can be scaled as ␶ F ⬃ (d/U b ). In other words, the residence time in the CH layer can be described from the initial jet conditions. Y The CH layer is also found to align with the high-strain rate region. The strain rate on the flame surface tends to enhance the mixing between the fuel and oxidizer and thus, enhances the combustion if it does not exceed the ex-

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tinction limit. For the positions where the CH layer deviates from the stoichiometric velocity contour, it is often observed that the CH layer is aligned with the high-strain rate region in instantaneous images. Y The mean principal strain rate decays at a slower rate compared to the scalings of turbulent non-reacting jets using the center-line and global properties, such as ( x/d) ⫺2 or U c / ␦ . For all Reynolds numbers studied, the mean strain rate on the CH layer scales well with S ⬃ ( x/d) ⫺0.7 . In addition, the most probable strain rates on the CH layer stay close between 兩S兩 ⫽ 500 ⬃ 3000 s⫺1, regardless of the position and Reynolds number. Y Finally, the two-dimensional dilatation is found to be small and not a particularly good flame marker when compared to the strain rate. This is unlike the case for premixed flames, where dilatation coincides well with the flame location. From these observations, it is seen that there exist strong interactions between the flame surface and the surrounding turbulent flow. These interactions should be considered in predictions of non-premixed flame combustion processes using turbulent combustion models. Acknowledgment This work was sponsored by the Gas Research Institute (GRI), National Science Foundation (NSF), and Center for Turbulence Research (CTR). The authors gratefully acknowledge valuable discussions with Heinz Pitsch and James E. Broadwell. The authors also would like to thank Joongsoo Kim and Christophe Laux for their help with running the flame codes. D. Han acknowledges the support of the Stanford Graduate Fellowship (Mr. and Mrs. Benhamou Fellow). References ¨ ngu¨ t, P.H. Paul, R.K. Hanson, [1] J.M. Seitzman, A. U Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 637– 644. [2] D.A. Everest, J.F. Driscoll, W.J.A. Dahm, D.A. Feikema, Combust. Flame 101 (1995) 58 – 68. [3] J.M. Donbar, Reaction zone structure and velocity measurements in permanently blue nonpremixed jet flames, PhD thesis, University of Michigan, Department of Aerospace Engineering, 1998. [4] J.M. Donbar, J.F. Driscoll, C.D. Carter, Combust. Flame 122 (2000) 1–19.

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