Measurements and statistics of mixture fraction and scalar dissipation rates in turbulent non-premixed jet flames

Combustion and Flame 160 (2013) 1767–1778

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Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e

Measurements and statistics of mixture fraction and scalar dissipation rates in turbulent non-premixed jet flames Jeffrey A. Sutton a,⇑, James F. Driscoll b a b

Department of Mechanical and Aerospace Engineering, Ohio State University, Columbus, OH 43210, United States Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, United States

a r t i c l e

i n f o

Article history: Received 20 May 2011 Received in revised form 14 March 2012 Accepted 6 March 2013 Available online 2 April 2013 Keywords: Mixture fraction Scalar dissipation rate Turbulent combustion Non-premixed flames Planar laser-induced fluorescence Local extinction

a b s t r a c t The present study adds to the limited database of mixture fraction and scalar dissipation rate measurements within turbulent flames. One noteworthy aspect is that the current measurements are two-dimensional images, which provide the physical structure of the scalar dissipation rate field. Two turbulent carbon monoxide flames are studied at two different jet-exit velocities, where the latter flame is near blowoff. The effects of increasing levels of local extinction (by increasing the jet velocities) on the structure and statistics of the mixture fraction fluctuation and scalar dissipation rate fields are investigated in detail. In general, the topology of the scalar dissipation rate layers is similar to that found previously in turbulent non-reacting flows, with some notable exceptions. For the lower jet-velocity case, the dissipation layers were somewhat smooth, isolated, and preferentially aligned in the axial direction, while for the higher jet-velocity case (near global extinction), the scalar dissipation rate field was characterized by an increased number of shorter, thinner, and highly wrinkled dissipation layers. It appears that as the flame nears blowoff, the scalar dissipation rate field exhibits an increasing level of isotropy, resembling turbulent non-reacting flows. In addition to providing new insights on the physical nature of the dissipation fields, the two-dimensional statistics of the mixture fraction and scalar dissipation rate are examined in detail, in the form of conditional averaging and through the construction of probability density functions. It is found, that although the two flames have apparent differences in physical structure, the corresponding statistical properties of the scalar dissipation rate were similar. Probability density functions (pdfs) of the scalar dissipation rate exhibited large departures from strict log-normality and the pdfs of the scalar dissipation rate were found to be significantly different if only the values of the scalar dissipation conditioned on the stoichiometric contour were considered compared to the entire flowfield. This has implications for modeling assumptions that seek to describe the entire turbulent flowfield by a single pdf. The nature of the scalar dissipation rate in the current lower-Reynolds number turbulent flames, as revealed through the statistics, is compared to previous, well-known data sets obtained in the Sandia series of piloted jet flames as well as other piloted non-premixed jet flames at higher Reynolds numbers. The present flame conditions are significantly different from previous work, yet the general structure, statistical trends, and general effects of increasing levels of local extinction agree favorably with the previous experimental data. Ó 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction For non-premixed and partially-premixed combustion systems, the rate of molecular mixing governs chemical reaction and is characterized by the scalar dissipation rate, v ¼ 2Dðrn  rnÞ, where D is the mass diffusivity and n is the mixture fraction. The scalar dissipation rate is a governing parameter that appears in a large number of turbulent combustion models including conditional moment closure (CMC) [e.g., 1–3] and laminar flamelet mod-

⇑ Corresponding author. Fax: +1-614-292-3163.

els [e.g., 4–7], where the turbulent flame structure can be uniquely related back to n and its derivatives. Because of the importance of n and v in turbulent non-premixed and partially-premixed combustion, a key focus of experimental combustion research for the past two decades has been measuring these quantities in reacting flows [e.g., 8–28]. Due to the difficulty of accurately measuring n and v in turbulent flames, the current data base of scalar dissipation rate measurements is rather limited. The most common approach of measuring n (and deducing v) has been to use simultaneous Raman/Rayleigh/LIF diagnostics to make multi-scalar measurements of temperature and major species concentrations in hydrogen

E-mail address: [email protected] (J.A. Sutton). 0010-2180/$ - see front matter Ó 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.combustflame.2013.03.006

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and hydrocarbon flames. This approach has been successfully applied in turbulent jet flames [e.g., 16,19–21], opposed-flow flames [e.g., 23,24], and laboratory-scale gas-turbine burners [e.g., 27]. While the measurement of the major species (and temperature) allows an accurate deduction of the mixture fraction, the measurements are limited to single point or 1D line imaging configurations. In this manner, the 1D measurements yield a 1D surrogate of the true scalar dissipation rate. There has been on-going work to develop methodologies for acquiring 2D images of the scalar dissipation rate field [e.g., 9,13,14,18,22,25,26], all with varying levels of success. In this regard, there still remains a vital need for additional two-dimensional data sets, which not only yield an additional component of the scalar dissipation rate, but allows investigation of the structure of the scalar dissipation rate field. The present work adds new two-dimensional measurements of dissipation rates in turbulent jet flames that allow the simultaneous investigation of the physical and statistical nature of the scalar dissipation rate in turbulent flames. It is noted that a different fuel (CO) is considered as compared to previous studies which have focused on methane and hydrogen fuels. This allows turbulence-chemistry investigations within a different chemical kinetic system. In addition, an alternative diagnostic approach based on simultaneous planar laser-induced fluorescence (PLIF) of a passive scalar tracer and Rayleigh scattering imaging was used to acquire the 2D n and v measurements [25,26]. The authors contend that the present data is complementary to the existing scalar dissipation rate data obtained through the 1D Raman/Rayleigh/LIF diagnostics; that is the current information allows for a more complete data base of information which includes investigating scalar dissipation structure and topology under reacting conditions, a different type of fuel and the associated chemical kinetics, and an independent measurement technique.

2. Experimental methods The methodology for obtaining mixture fraction, temperature, fuel consumption, and scalar dissipation rate measurements has been described in detail elsewhere [25,26]. Only a brief description of the experimental system, the measurement approach, and data analysis will be provided here. Previous work by the authors using the following experimental approach investigated the role of the interaction between strong scalar dissipation layers and the stoichiometric contour on local flame extinction [26]. This work demonstrated that the instantaneous value of the scalar dissipation rate at the stoichiometric contour plays an important and direct role in the local extinction process in turbulent non-premixed jet-flames. Direct visualization of the instantaneous scalar dissipation rate, temperature, and fuel consumption fields along with statistical analysis showed that a strong correlation exists between large values of v at the stoichiometric contour and a decrease in both the local temperature and the fuel consumption rate, which is indicative of local flame extinction. In 2006, the authors described the development and validation of an experimental technique in which a small quantity (<2000 ppm) of nitric oxide (NO) is seeded into a ‘‘dry’’ carbon monoxide (CO) fuel jet burning in ‘‘dry’’ air [25]. Special care was taken to ensure that that minimal hydrocarbons, hydrogen, and water vapor was present in the experiment (<0.1 ppm in the fuel and <1 ppm in the co-flowing air stream). Under these experimental conditions (no hydrogen-containing species), NO does not react and remains as a passive scalar. Extensive set of laminar flame calibration experiments and computations were presented that demonstrated that the seeded NO does not react in this flame

configuration and by measuring the local mass fraction of NO (YNO), the instantaneous mixture fraction can be determined as

n¼

Y NO Y NO;fuel

ð1Þ

where YNO,fuel is the mass fraction of NO seeded into the carbon monoxide fuel stream. The goal was to develop a method to image the mixture fraction (n) and scalar dissipation rate (v) fields with high signal-to-noise ratios (>200 in the fuel core), which is achievable using NO planar laser-induced fluorescence (PLIF). Although the technique is limited to a specific fuel (dry CO), the SNR of the 2D images exceeds those provided by previously proposed 2D diagnostics for measuring n and v [e.g., 9,13,14,18,22]. The local NO mass fraction was determined from a simultaneous NO PLIF and Rayleigh scattering thermometry imaging methodology. The experimental setup for these measurements is shown schematically in Fig. 1. As described below, PLIF measurements of NO yield a signal that is proportional to the NO number density and NO-specific spectroscopy quantities, which are temperature dependent. The NO PLIF measurements were performed using 226-nm laser light that was generated by frequency doubling the 452-nm output from an Nd:YAG-pumped dye laser. A second Nd:YAG operating at 355 nm was used for the Rayleigh scattering thermometry imaging. The 226 and 355 nm laser beams were formed into laser sheets (30  0.24 mm2 for 226 nm and 50  0.21 mm2 for 355 nm) through independent sheet-forming optics (plano-concave cylindrical lenses and plano-convex spherical lenses) and overlapped onto the same spatial volume via a dichroic beam splitter which was coated to reflect 226-nm laser light and transmit 355-nm laser light. The overlapped laser sheets were measured to be aligned to within ±10 lm at the measurement location. PLIF measurements of NO were made by exciting rotational lines of the A–X(0, 0) vibrational band near 226 nm. The linewidth of the 226-nm laser beam was measured to be 0.9 cm1, so the excitation included a main contribution from the Q1(14.5) transition, with minor contributions from the P1(23.5), P21(14.5), Q2(20.5), and R12(20.5) transitions. Each rotational transition and its overlap with the laser’s spectral distribution were taken into account in the conversion of fluorescence signal to absolute NO number density. Broadband, non-resonant detection of the fluorescence signal from the A–X(0, v00 > 0) bands in the region of 230–300 nm was collected by an ICCD camera (Roper Scientific PI Max 512) coupled to a UV-transparent Nikon 105-mm, f/4.5 camera lens and a combination of a UG-5 filter and a custom-made dichroic beam splitter (Lattice Electro Optics LWP-HT-230-335HR355-35). This filter combination not only provides high throughput of the NO A-X(0, v00 > 0) emission, but high rejection at 226 and 355 nm; thus any interference with Rayleigh scattering or errors associated with radiative trapping are negligible. Utilizing the low-irradiance solution of the fluorescence equation [29], the mixture fraction based on NO acting as a passive scalar (Eq. (1)) can be expressed as

hP

N i fB

n¼

CB12 A21 =Q

i

Sfl X NO;ref T W fuel h iref Sfl;ref X NO;fuel T ref W mix PN fB CB12 A21 =Q i

ð2Þ

which is similar to that shown in Ref. [25]. The low-irradiance form of the fluorescence equation is justified by the fact that the laser irradiance used under the present experimental conditions is 8  104 W/cm2/cm1, which is well below previously reported requirements for low-irradiance solutions to the fluorescence equations for NO [e.g., 30–32]. In Eq. (2), Sfl is the instantaneous fluorescence signal; T is the temperature; Wfuel is the molecular weight of the fluid issuing from the fuel tube; Wmix is the molecular weight of

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Fig. 1. Experimental setup for simultaneous NO PLIF and Rayleigh scattering measurements. CL – cylindrical lens, DC – doubling crystal, DB – dichroic beamsplitter, GF – glass flat, HB – Hencken burner, M – mirror, PD – photodiode, PMT photomultiplier tube, SL – spherical lens, T – telescope (Galilean or Keplerian), PB – Pellin-Broca crystal.

the mixture at any point in the flowfield; fB is the Boltzmann fraction, C is the dimensionless spectral overlap fraction defined by Partridge and Laurendeau [33], which accounts for the overlap between the laser spectral profile and the NO absorption transitions; A21 is the Einstein A coefficient, and Q is the electronic quenching rate. Quantities with a subscript ‘‘ref’’ denote values obtained at known reference condition (temperature, pressure, composition, and NO concentration). Finally, it is noted that Eq. (2) is written under the assumption that the laser system is described by the two laser-coupled states such that emission is only allowed from the upper to lower states (2 ? 1) and that A21  Q. The electronic quenching rate (or rate of collisional energy transfer) P is written as Q ¼ nv NO j X j ð1 þ mNO =mj Þrj [34], where n is the number density, vNO is the average molecular velocity of NO, Xj, mj, and rj are the mole fraction, molecular mass, and the electronic quenching cross-section of any colliding species j, respectively, and mNO is the molecular mass of NO. The quenching cross sections of the species present in the current ‘‘dry’’ CO–air system (N2, O2, CO, CO2, Ar, and NO) are taken from the literature [34–36]. It is noted that the quenching cross sections of the individual species are temperature-dependent. This coupled with the fact that the local gas temperature, T, appears directly in Eq. (2) necessitates the simultaneous Rayleigh scattering thermometry measurement in order to determine n. Temperature is determined from the expression, T ¼ T ref  Iref =IRAY  rmix =rref , where IRAY is the instantaneous Rayleigh scattering signal, rmix is the local mixture-averaged differential Rayleigh scattering cross-section, and Tref, Iref, rref are the temperature, measured Rayleigh scattering signal, and differential Rayleigh scattering cross section from a reference condition of known temperature and species concentration (air at room temperature). The final set of information needed to quantify the NO PLIF signal (and deduce n) is the local concentration of each individual species present in the flowfield. Both the electronic quenching rate and the Rayleigh scattering signal are species dependent. In Ref. [25], it was shown that because of the extremely simple chemistry of the dry CO–air combustion system, it is possible to develop a series of non-linear algebraic equations relating the measured

quantities (Sfl and IRAY), the species concentrations, and the mixture fraction based on the conservation of C and O atoms. This procedure allows a unique solution for CO, O2, N2, CO2, Ar, and NO. The reader is referred to Ref. [25] for the specifics of the data processing that yield the local species concentrations as well as the individual uncertainties for temperature, mixture fraction, and the two-dimensional surrogate of the scalar dissipation rate measurements. Experiments were performed in two piloted non-premixed CO jet flames issuing into a low-speed (0.08 m/s) co-flowing stream of air. The stoichiometric mixture fraction for these flames is 0.29. The two flames correspond to Reynolds numbers of 7000 (flame CO_A) and 8300 (flame CO_B) based on cold jet exit conditions. The jet-exit velocity was 10.5 and 12.5 m/s for the two cases, respectively, and the jet-exit diameter (d) was 10.2 mm. All measurements reported are at an axial position of x/d = 17 and the images are centered at r/d = 1. This axial position corresponds to the region in which ‘‘blowoff’’ occurs. Since these flames utilize a pilot flame, the heat release maintains combustion for the first few diameters downstream of the pilot, so the blowoff condition is defined as the velocity (or Reynolds number) in which no flame exists downstream of the ‘‘extinction neck’’ near the burner exit. Flame CO_A has an exit velocity that was approximately 75% of the blowoff velocity and flame CO_B has an exit velocity that was approximately 90% of the blowoff velocity. For more details on the flames, including pilot composition and the flame facility, the reader is referred to Ref. [25]. Although the current studies focus on lower-Reynolds number turbulent flames (due to the limited robustness of the CO/air system), comparisons to results from higher-Reynolds number flames of previous studies are made throughout the manuscript to assess a more general Reynolds number effect on the characteristics of mixture fraction and scalar dissipation rate.

3. Results and discussion The present work reports results for the mixture fraction, mixture fraction variance, and two-dimensional scalar dissipation rate

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in turbulent non-premixed flames. In this work, the 2D scalar dissipation rate field is defined as v = 2D((@n/@x)2 + (@n/@r)2). Such measurements are important for understanding the rate of mixing in turbulent flames, the interaction between turbulent fluid mechanics and chemistry, and providing new information for comparison with other experiments and turbulent combustion models. One of the primary goals of the present work is to examine the effects of increasing jet velocity and increasing levels of extinction on the scalar dissipation rate. This is of particular importance in the context of combustion modeling development as turbulent flames with increasing levels of local flame extinction are the most challenging to predict. When possible, the current results are compared to previous experimental results in piloted flames at higher Reynolds numbers [13,19–21,37]. 3.1. Mixture fraction fluctuations The mixture fraction variance is a measure of the turbulent fluctuations in the mixture fraction field and is an important modeled quantity in turbulent non-premixed flames, with particular importance in pdf modeling. In this manuscript we report values of the f mixture fraction variance ( n002 ), where the double prime indicates that Favre (density-weighted) averaging has been performed. Figf ure 2a shows the calculated results for n002 conditioned on the ~ Favre-averaged mixture fraction (n) for both flame CO flames,

0.04

Flame CO_A

(a)

Flame CO_B

ξ

0.03

~

ξ

3.2. Scalar dissipation rate layer structure 0.02

0.01

0.00

0.04

(b)

Sandia D

ξ

Sandia E Sandia F

0.03

~

ξ

while Fig. 2b shows values of the mixture fraction variance for Sandia series of piloted partially-premixed jet flames, denoted flames D–F [37], at an axial position of x/d = 15. The variance results from Sandia flames D–F are shown for comparison with the current CO flame results. The mixture fraction variance values are shown for Favre-averaged mixture fraction values ranging from 0 to 0.6 to highlight the regions around the stoichiometric contour for each set of flames (ns = 0.29 for the CO flames and 0.35 for the Sandia flames). Overall, the mixture fraction variance results in the lower-Reynolds number CO flames exhibit a similar behavior as the higher002 Reynolds number Sandia series of flames; that is nf peaks at a mixture fraction value somewhat greater than ns and decreases through the stoichiometric mixture fraction to zero at ~ n¼0 f (regions of co-flowing air). In addition, the shape of the n002 curve as a function of ~ n for the CO flames is similar to the Sandia series of flames and the mixture fraction variance decreases as the flame approaches blowout. It is well established that increasing levels of local extinction are a result of finite rate chemistry effects and that the increased jet velocities (flame CO_B vs. CO_A) and the corresponding increased turbulence levels result in increased mixing (or lower values of the mixture fraction variance [38,39]). This is f observed in Fig. 2a, where n002 decreases from in CO_B with respect to flame CO_A. However, there are some differences between the two sets of flames shown in Fig. 2, namely the fact that for the f CO flames, there is an observable change in n002 over a small range of Reynolds numbers as compared to the Sandia series of flames, which are tightly grouped over much larger range of Reynolds numbers. It is not known if this is an artifact of the lower Reynolds number conditions of the CO flames or a result of flame CO_B being very close to blowout (note the difference between Sandia flames D and F, which represent cases where the jet exit velocity is 40% and 80% of the blowout velocity, respectively).

0.02

0.01

0.00 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Fig. 2. (a) Favre-averaged variance of the mixture fraction conditioned on the Favre-averaged mixture fraction for the current set of turbulent carbon monoxide (CO) flames. (b) Favre-averaged variance of the mixture fraction conditioned on the Favre-averaged mixture fraction for the Sandia D–F flames. Data is taken from Ref. [37].

One of the main advantages of the present experimental technique is the ability to image the two-dimensional scalar dissipation rate (v) field in turbulent flames. Not only do the measurements provide conditional measurements and statistical assessment of scalar dissipation as described below, but the 2D images provide visualization of the structure, topology, and orientation of the regions of intense mixing rates. Figure 3 shows example scalar dissipation rate and temperature fluctuation images from both flame CO_A and CO_B. The natural logarithm of the scalar dissipation rate field is shown to reveal the underlying structure of the dissipation rate layers at both large and small values of v. The dissipation images are normalized by D(hni/kB)2, similar to previous approaches applied in non-reacting flows [e.g., 40–44], where D is the mixture-averaged mass diffusivity, which is a function of the local temperature and species concentrations, hni is the local mean value of the mixture fraction, and kB is the Batchelor scale which 3=4 was defined as kB ¼ 2:3dRed Sc1=2 [45,46], where d is the local outer length scale (jet width) which is defined as 0.44x [47], Red is the Reynolds number based on the local outer length scale, and Sc = m/D is the Schmidt number, which is calculated locally in each image from the deduction of the species concentrations and temperature and is typically 0.7. The temperature fluctuation field is computed by subtracting the mean temperature field, hTi, from each instantaneous temperature field. The temperature fluctuation field is reported to highlight local regions of suppressed temperature possibly due to local flame extinction. As described previously in Ref. [25], the majority of the scalar dissipation in the CO flames is confined to thin ‘‘sheet-like’’ layers; that is the dissipation layers maintain their orientation over distances that are much larger than their local thickness. These results

J.A. Sutton, J.F. Driscoll / Combustion and Flame 160 (2013) 1767–1778

CO_A χ

1771

CO_B T’

T’ = T- 500

-500 -7

ln

χ

0

2

D(<ξ>/λB)

CL Fig. 3. (Left) Instantaneous photograph of the turbulent carbon monoxide flame, CO_A. Red box indicates the location and field-of-view of the 2D measurements. (Right) Instantaneous examples of the scalar dissipation rate and temperature fluctuation fields at x/d = 17 for flames CO_A and CO_B. The natural logarithm of the scalar dissipation rate (v) is shown and normalized by D(hni/kB)2. The field-of-view of the images is 23.5  23.5 mm and the jet centerline is located 2.5 mm from the left edge of each image as indicated by the arrow. The stoichiometric contour (white line; ns = 0.29) is superimposed on each image. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

are consistent with the non-reacting flow studies of Dahm and co-workers [e.g., 40–42] and Su and Clemens [e.g., 43,44] and previous studies in higher-Reynolds number reacting flows [e.g., 13,22,48]. In previous non-reacting flow studies, the scalar dissipation layers were found to be both isolated and interacting with other dissipation layers, while recent measurements of the thermal dissipation rate in higher-Reynolds number jet flames [e.g., 49–51] found that the thermal dissipation layers are observed over the majority of the measurement region and exhibit varying levels of morphology and convolution depending on the axial and radial position. While both isolated and interacting scalar dissipation layers are noted in flames CO_A and CO_B, the majority of the dissipation rate layers in flame CO_A are isolated, while many more the dissipation layers in flame B interact with one another. This is noted throughout the entire image set (>500 images) and not just in the selected images. In some cases (as shown in the third column of Fig. 3), the scalar dissipation rate layers of flame CO_B coalesce in very small regions. This is consistent with the higher level of flame wrinkling (not shown) in flame CO_B than in flame CO_A. Overall, the scalar dissipation is confined to a smaller region of the flowfield than previous scalar dissipation rate measurements in non-reacting flows [e.g., 40–44] and thermal dissipation rate measurements in non-premixed flames [e.g., 49–51]. The lower level of scalar dissipation layer interaction and convolution may be a result

of the lower Reynolds number and turbulence levels in the current flames. When comparing the mixture fraction image sets between flame CO_A and CO_B, it was found that flame CO_A was characterized by having smoother stoichiometric contours (reaction zone) along the field-of-views, where the stoichiometric contour was typically aligned in the axial direction. In contrast, flame CO_B (which exhibits higher levels of local extinction) was characterized by higher levels of contortion due to higher levels of smaller-scale turbulence (e.g., higher Reynolds number and lower temperatures/ viscosity) and possible vortex entrainment of pockets of products and air. Both of these processes are amplified by increasing levels of local flame extinction. These features are captured in the example scalar dissipation layers (and corresponding temperature fluctuation images) shown in Fig. 3. For flame CO_A, the dissipation layers are largely aligned in the axial direction, while the dissipation layers in flame CO_B show an increasing level of isotropy in their orientation. Higher turbulence levels increase the wrinkling of dissipation structures at increasingly smaller length scales and vortex entrainment of products and air act to both wrinkle the stoichiometric contour and to dilute the fuel core, thus mixing regions previously characterized by pure fuel, pure products, and pure air. Both processes can be expected to occur at many different spatial locations, changing the composition rapidly from fuel to air and

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creating an increasing number of scalar gradients that are close to each other. As the turbulence level intensifies, the regions of high scalar dissipation can coalesce and/or interact, thus changing the orientation of the regions of high scalar mixing. The result that the higher Reynolds number flame exhibits lower levels of anisotropy is consistent with the thermal dissipation results from Frank and Kaiser [50]. In lower Reynolds number cases, where turbulence levels can still be considered low and vortex entrainment is not expected to occur as frequently, there are on average only a few well-defined boundaries between fuel and air, which produces fewer dissipation layers that will tend to be more isolated. While the dissipation layers in flame CO_A are characterized by long layers with minimal distortion, the dissipation layers in flame CO_B are characterized by a larger number of much shorter and contorted segments. The dissipation layer topology of flame CO_B appears to be more consistent with the observations of the layer topology found in the dissipation rate layers downstream in nonreacting flows [e.g., 40–44]. It is worth noting that flame CO_A and CO_B differ in Reynolds number by <20%, so this change in topology may occur only when the flame is on the verge of blowoff or experiencing high levels of local flame extinction for these lower-Reynolds number cases. This is supported by the recent thermal dissipation results of Frank and Kaiser [50] that showed that the impact of the flame on the turbulence is reduced in extinguished regions. One final feature in the structure of the dissipation layers is that the layers are thinner in flame CO_B compared to flame CO_A, although it is noted that a rigorous processing of quantitative values as demonstrated in Refs. [49,50] has not been performed as of yet. Keeping in mind that the scalar dissipation rate layers shown in Fig. 3 have been properly normalized by D(hni/kB)2, which should account for any local length-scale or temperature effects between the two flames; the normalized dissipation layers in the higher jet-velocity (or Reynolds number for constant nozzle diameter) case are still thinner, indicating that the topology of the intense mixing regions has a Reynolds number dependence. This aspect was noted in the non-reacting jet studies of Su and Clemens [44], which confirmed that the average dissipation layer thicknesses followed the Re3=4 scaling of Batchelor and Kolmogorov. d 3.3. Conditional values of scalar dissipation While there have been a number of carefully executed experiments detailing the relationship between a passive scalar and its dissipation rate in non-reacting, turbulent flows [e.g., 52,53], the correlation between the mixture fraction and its scalar dissipation rate have been limited in reacting flows [e.g., 10,13,21]. The current measurements, although at lower Reynolds number than previous studies, add to the existing database detailing the relationship between instantaneous values of the scalar dissipation rate, the mean scalar dissipation rate and the RMS fluctuation of the scalar dissipation rate, conditioned on the mixture fraction. A scatter plot of the scalar dissipation rate conditioned on the mixture fraction is shown in Fig. 4 for flame CO_A. The original image set consists of 300 instantaneous images, corresponding to >4  106 data points. The scatter plot shown in Fig. 4 was constructed from 5000 random data points from the image set. Also shown on the image is the mean value of the scalar dissipation rate conditioned on the mixture fraction. This scatter plot is reported to show that v has large departures from the mean value of v (this is noted in both flames). Fluctuations in v yield instantaneous values of v as large as 450 s1, which is approximately 30 times the mean peak value for flame CO_A. A similar level of fluctuation is noted for flame CO_B. The conditional mean of the scalar dissipation rate is shown for both flame CO_A and CO_B in Fig. 5a. The conditioning interval is

400

300

χ (s-1)

200

100

χ 0 0.0

0.2

0.4

ξ

0.6

0.8

1.0

Fig. 4. Scatterplot of scalar dissipation rate (v) conditioned on mixture-fraction for flame CO_A. Also shown (in red) is the mean scalar dissipation rate (peak value 15.6 s1). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Dn = 0.02 and the conditional averages are based the full image set (>4  106 data points). The full radial profile from the images is used to compute the conditional mean. For comparison, the conditional mean of the scalar dissipation rate is shown for the Sandia flames D and E [21] in Fig. 5b and for a series of H2/CO2 flames with increasing Reynolds numbers from the study of Kelman and Masri [13] in Fig. 5c. The data presented in Fig. 5b and c provide additional scalar dissipation rate measurements (conditioned on n) for other piloted flames with similar stoichiometric mixture fractions (ns = 0.29 for the current flames; ns = 0.35 for the Sandia flames; and ns = 0.37 for the H2/CO2 flames). For the CO flames presented in this manuscript, the peak scalar dissipation rate values occur on the rich side of the stoichiometric contour at n = 0.45 for flame CO_A and n = 0.50 for flame CO_B. A rich side maximum in the scalar dissipation rate is consistent with the results from the Sandia flames and the H2/CO2 flames shown in Fig. 5b and c, in addition to other experimental studies in non-premixed flames [e.g., 10] and large-eddy simulation (LES) results [e.g., 54]. The most prominent feature of Fig. 5a is the decrease in the mean value of the scalar dissipation rate as Reynolds number increases (hviCO_A > hviCO_B). The increase in jet velocity from flame CO_A to flame CO_B corresponds to an increase in global strain rate and an expected increase in the scalar dissipation rate. However, as shown in Fig. 5a, there is a 20% decrease in the peak value of the mean scalar dissipation rate even though there is a 20% increase in exit velocity. Similar phenomena have been observed in turbulent flames as the Reynolds number is increased towards extinction by previous groups [e.g., 13,14,21], including the piloted flame studies shown in Fig. 5b and c. It should be noted that while there is only a modest decrease in the radial component of the scalar dissipation rate from Sandia flames D to E (Fig. 5b); flame E corresponds to a jet-exit velocity that is 33% higher than flame D. The fact that there is little difference in the mean scalar dissipation rate between flames D and E, despite the fact that the velocity is increased by 33% is of interest and unexpected. It should also be noted that Sandia flame E has an exit velocity that only is approximately 60% of the blowoff velocity. A more interesting comparison would be to compare Sandia flames E and F (which is very close to blowoff). In contrast to the Sandia flames, the H2/CO2 flames of Kelman and Masri [13] show an extreme decrease in the mean scalar dissipation rate as the exit velocity is increased towards blowoff. As shown in Fig. 5c, the peak value of the mean scalar

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20

(a)

Flame CO_A Flame CO_B

ξ

15

<χ|ξ> (s-1)

10

5

0 60

(b)

Sandia D

ξ

Sandia E

45

<χ r|ξ> (s-1)

30

15

0 50

(c)

H2/CO2 Flames

ξ

Uf/Ub = 0.50 Uf/Ub = 0.85 Uf/Ub = 0.95

40

30

<χ|ξ> (s-1) 20

rate measurements in non-reacting and reacting flows [55,56]. As detailed in Ref. [25], the spatial resolution of the current measurements (as limited by the laser-sheet thickness) was less than the Batchelor scale, thus it is expected that the majority of the scalar gradients are well resolved and noise effects are much more important [56] for the conditional scalar dissipation rate measurements shown in Fig. 5. Using results from [56] (at conditions with similar resolution, scalar variance, signal-to-noise, and dissipation values) we estimate the uncertainty of the peak mean conditional scalar dissipation rate to be less than 10%. In addition, it is noted from [56] that the noise contribution is not constant and depends of mixture fraction. However, as shown in Fig. 5, the conditional scalar dissipation rate also depends on mixture fraction and for the values of hv|ni away from the peak, both the mixture fraction gradients and the scalar variance (see Fig. 2) are reduced. In this manner, the noise contributions decrease away from the peak value of hv|ni and we further estimate that the maximum uncertainty in the conditional scalar dissipation rate measurements is <10%. Previous studies have speculated that the reduction in scalar dissipation rate as exit velocity is increased is most likely due to a decrease in temperature due to increased local extinction, causing a decrease in the mass diffusivity [e.g., 13,20]. Increased levels of localized extinction create pockets of unburned fluid which act to dilute the local mixture of combustion products, decreasing the temperature, and in turn reducing the mass diffusivity and the scalar dissipation rate. In a similar manner, increasing the exit velocity and the levels of local extinction may lead to fewer separate homogenous regions of fuel, products, and air (and the corresponding well-defined boundaries and large scalar gradients) due to aforementioned dilution effect. If the (square of the) scalar gradients are reduced, as a consequence, the scalar dissipation rate is reduced. For the current set of flames, each of these mechanisms are investigated in Fig. 6 by examining the ratio of the conditionally-averaged temperature, diffusivity, and squares of axial and radial mixture fraction gradients [(@n/@x)2; (@n/@r)2] for flame CO_B and flame CO_A. As expected the temperature (and hence the mass diffusivity) is lower in flame CO_B compared to flame CO_A. However, there are some interesting observations concerning the square of the mixture fraction gradients as the exit velocity is increased. For rich regions (0.8 < n < 0.4), there is an increase in h(@n/@x)2|ni for flame CO_B compared to flame CO_A, consistent with the increase in the

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ξ Fig. 5. (a) Mean value of the scalar dissipation rate conditioned on mixture fraction n for flames CO_A and CO_B. The conditioning interval is Dn = 0.02. The units of hv|ni are s1. The stoichiometric mixture fraction (ns = 0.29) is shown as the vertical dotted line. (b) Conditional mean of the radial component of the scalar dissipation rate for Sandia flames D and E [21]. The stoichiometric mixture fraction (ns = 0.35) is shown as the vertical dotted line. (c) Conditional mean of the scalar dissipation rate for a series of H2/CO2 flames from Kelman and Masri [13]. The stoichiometric mixture fraction (ns = 0.37) is shown as the vertical dotted line.

dissipation rate decreased by more than 500% as the exit velocity is increased from 50% of the blowoff value to 95% of the blowoff value The decrease of the mean conditional scalar dissipation rate (from flames CO_A to CO_B) has to be taken in the context of the uncertainty of the conditional scalar dissipation rate measurements. Recently, there have been methods presented to assess the noise and resolution effects of the conditional scalar dissipation

(dξ/dx)2 (dξ/dr)2

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overall strain rate of the higher Reynolds number flame. For mixture fraction values near ns, h(@n/@x)2|ni is equivalent for both flames. However, the square of the radial component of the mixture fraction gradient, h(@n/@r)2|ni, shows a similar trend as the temperature for n P ns; that is there is a systematic decrease in h(@n/@r)2|ni for flame CO_B compared to flame CO_A for decreasing mixture fraction, with a minimum near the stoichiometric mixture fraction. This implies that while the decreased diffusivity (due to decreased temperature) is important in reducing the scalar dissipation rate (as the jet-exit velocity increases toward blowoff conditions), the reduction of the radial component of the mixture fraction gradient plays an important role as well. The reduction of h(@n/@r)2|ni is most likely due to a combination of effects, namely (i) the possibility of an increased number of ‘‘non-burning’’ regions (either due to flame extinction or lack of ignition) in flame CO_B compared to flame CO_A, which acts to mix previously isolated regions of fuel, air, or products. Such a process would give rise to an increased number of dissipation layers, but with gradient magnitudes that are less than the few strong gradient regions found under lower Reynolds number conditions. This is consistent with the scalar dissipation rate field images shown in Fig. 3, where flame CO_A is characterized by fewer strong dissipation layers and flame CO_B is characterized by an increased number of dissipation layers, where many exhibit magnitudes less than those characteristic of flame CO_A. (ii) Second, the reduction of h(@n/@r)2|ni would be consistent with the results of Kelman and Masri [13] who suggested that as turbulence levels are increased, the reaction zone is broadened (by turbulence) and the resultant radial scalar gradients are smoothed. Kelman and Masri [13] also pointed out that as turbulence levels are increased, this ‘‘broadening’’ of the reaction zone would be responsible for an effective shift of the peak scalar dissipation rate away from the stoichiometric contour. This phenomenon is observed in Fig. 5a as well. (iii) Finally, the reduction of h(@n/@r)2|ni may be due to a change in the distribution of the orientation of the dissipation layers from flame CO_A to flame CO_B. This would imply for a given scalar gradient magnitude (in any arbitrary direction) that as h(@n/@r)2|ni decreases, h(@n/@x)2|ni would increase to compensate. What is observed in Fig. 6 is that the trends of h(@n/@r)2|ni and h(@n/@x)2|ni track one another; that is, as h(@n/@r)2|ni decreases as a function of n, h(@n/@x)2|ni decreases as well. While this may suggest that a change in the distribution of the orientation of the dissipation layers from flame CO_A to flame CO_B is not occurring, it is noted that there is a region on the rich side (0.4 < n < 0.8), where h(@n/@x)2|ni is greater in flame CO_B as compared to CO_A and h(@n/@r)2|ni is less in flame CO_B as compared to CO_A. Such observations could be the result of differences in orientation statistics. Further analysis of the results are needed to fully understand the governing mechanisms behind the decrease in h(@n/@r)2|ni from flame CO_A to flame CO_B. One final interesting note concerning the data shown in Fig. 6, is the large decrease in ratio of the temperature (and diffusivity) and increase in the ratios of the square of the mixture fraction gradients around n = 0.15. While it is known that this mixture fraction value corresponds to the lean flammability limit of CO–air flames, the reason(s) for the abrupt change in flame CO_B compared to flame CO_A currently is unknown. However, it should be pointed out the increases in the ratio of mixture fraction gradients are cancelled by the decreased diffusivity, resulting in scalar dissipation rates that are nearly identical for flames CO_A and CO_B under very lean conditions (n < 0.15; Fig. 5a). The conditional standard deviation of the scalar dissipation rate, (v|n)rms, is shown for both flames CO_A and CO_B in Fig. 7. Similar to the conditional mean values shown in Fig. 5a, (v|n)rms peaks on the rich side for the two flames, exhibits the same ‘‘rich shift’’ and decrease in peak value for flame CO_B as compared to flame CO_A. However, if the ratio of the conditional standard deviation to the

conditional mean is examined for both flames as shown in Fig. 7, it is noted that (v|n)rms/hv|ni is largely independent of n and equivalent for both flames. This result shows that, at least for the current flames, there may not be a jet-velocity (or overall strain)-dependence on level of scalar dissipation rate fluctuation when normalized by the mean value. Furthermore, it is noted that the RMS fluctuation is roughly twice the mean value for the current flames. This large RMS fluctuation level demonstrates the spatially-intermittent nature of the scalar dissipation rate. An identical level is determined when considering the Favre-averaged and Favre-RMS quantities in the same flames (not shown). This level of fluctuation (and its n-independence) has been noted by previous experimental studies [e.g., 13,19], including the Sandia series of flames, characterized in Fig. 5b. While this RMS fluctuation level may not be universal, when considering experimental studies of laboratory-scale jet flames with many different fuels, Reynolds number, velocities, and levels of extinction, it is found that the RMS fluctuation of v tends to be approximately twice the mean. A comparison of the mean axial component of the scalar dissipation rate (denoted vx) and the mean radial component of the scalar dissipation rate (denoted vr) for flames CO_A and CO_B is shown in Fig. 8a–c. Little change in the axial component of the scalar dissipation rate when operating flame CO_B compared to flame CO_A is seen. As noted in Fig. 6, there was a small increase in the square of the axial component of the mixture fraction gradient, (@n/@x)2, as the mixture fraction decreased from 1 (pure fuel) to ns, but this is offset by a decrease in diffusivity due to the lower temperatures found in flame CO_B. Thus, the rate of mixing along the axial direction remains constant between flames CO_A and CO_B. In contrast, the decrease in the square of the radial component of the mixture fraction gradient, (@n/@r)2 (as noted in Fig. 6), combined with a decrease in diffusivity for flame CO_B as compared to flame CO_A results in a smaller mean radial component of the scalar dissipation rate for flame CO_B. Since hvxi is largely unaffected by the increase in the jet-exit velocity, it is the reduction of hvri that accounts for the reduction of hvi seen in Fig. 5a. Figure 8c shows that hvri is equivalent to hvxi for large mixture fraction values (presumably on centerline) for both flames CO_A and CO_B. For flame CO_A, hvri/hvxi then increased to a value of approximately 2 from 0.4 < n < 0.2, which occurs in the shear layer of the jet-flame. This anisotropy has been documented

5

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J.A. Sutton, J.F. Driscoll / Combustion and Flame 160 (2013) 1767–1778

12

(a)

from approximately 1 at high mixture fraction values (i.e., the centerline) to approximately 1.5 for 0.4 < n < 0.2 (the shear layer) for flame CO_B. This is a decrease in the ratio of hvri/hvxi as compared to flame CO_A. This implies that the increasing jet-exit velocity (and corresponding levels of local extinction) act to impart an increasing level of isotropy to the flow.

Flame CO_A

ξ

Flame CO_B

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3.4. Scalar dissipation rate statistics

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Fig. 8. Comparison of the conditionally-averaged axial and radial components of scalar dissipation rate in flames CO_A and CO_B. The stoichiometric mixture fraction (ns = 0.29) is shown as the vertical dotted line.

in air-diluted methane and hydrogen flames by Starner et al. [14], air-diluted methane flames by Starner et al. [9], and in methane and H2/CO2 flames by Kelman and Masri [13]. Starner et al. [14] found that hvri/hvxi varied from approximately 0.9 on the centerline axis to 2 in the shear layer for the air-diluted methane flames and from 0.8 on axis to 2 in the shear layer for air-diluted hydrogen flames. At x/d = 10, Kelman and Masri [13] reported values of hvri/hvxi ranging from 1 on the centerline to 3 in the shear layer for pure methane flames and 1 on the centerline and 2 in the shear layer for the H2/CO2 flames. Referring back to Fig. 8c for the present experiment (at x/d = 17), the ratio of hvri/hvxi varies

Figure 9a and b shows the probability density function (pdf) for the scalar dissipation rate for both flames CO_A and CO_B. To clearly see differences between the two flame conditions, the natural logarithm of v is computed and properly scaled by the local diffusivity (D), the mean mixture fraction (hni), and the Batchelor scale (kB). This is the same normalization frequently used within non-reacting scalar dissipation rate studies [e.g., 40–44] with the exception that kB replaces the previously-used dissipative length scale, kD, which is proportional to, but somewhat h ilarger than kB. v using a linear Figure 9a presents the unconditioned pdf ln Dðhni=k 2 BÞ y-axis and Fig. 9b presents the pdf using logarithmic y-axis in order to examine the lower probability values. Also shown in Fig. 9a and b is a Gaussian distribution having the same first and second moments as flame CO_A. Experiments in non-reacting flows have found that that the distribution of the scalar dissipation rate is nearly lognormal [e.g., 41,42] or displays a mild level of asymmetry [e.g., 43,44,57]. Conversely many reacting flow experiments have found different shapes, that is, that the scalar dissipation distribution exhibits notable negative skewness (varying amounts depending on the study) and that the tails of the PDF are exponential functions [e.g., 10,14]. In the linear axes (Fig. 9a), the v distribution appears close to log-normal for large values of v, but definitely exhibits asymmetry for small values of v. However, the deviation from a log-normal distribution and the profound negative skewness is easily seen in Fig. 9b, which has a logarithmic y-axis. The right side of the pdf exhibits very fast decay, while the left side of the pdf exhibits very slow decay which is far from log-normal and also does not appear to be governed by simple exponential scaling. Previous 1-D measurements have considered the deviation from log-normality for the smaller values of v as an artifact of the 1-D measurement [e.g., 21]. However, this negative skewness is still apparent in the two-dimensional measurements presented in this manuscript. However, it musth be considered that the resulti v ing form of the unconditioned pdf ln Dðhni=k at low values of v 2 Þ B (small @n/@x and @n/@r) may not be accurate due to the finite uncertainty in the mixture fraction measurements. The shape (and skewness) of the pdf does not appear to be a strong function of Reynolds number (or increased levels of local extinction) when the flames are nearing blowoff as the scalar dissipation rate distribution is approximately the same for both flame CO_A and CO_B. Flame CO_B is characterized by a slight shift in the pdf in comparison with flame CO_A (noticeable in Fig. 9a), corresponding to an increased number of lower scalar dissipation rate values. The similar statistical properties between flame CO_A and flame CO_B is somewhat surprising considering the instantaneous scalar dissipation rate images within the flames showed different physical structure (Fig. 3). The pdf of the scalar dissipation rate conditioned on the stoichiometric contour, v|ns, is important for both theory and computational modeling of turbulent reacting flows. Figure 10 presents the pdf of v|ns, again reported as the natural logarithm of v|ns and normalized by the local diffusivity (D), the mean mixture fraction (hni), and theh Batchelor i scale (kB). Figure 10a vjnS using a linear y-axis presents the conditioned pdf ln Dðhni=k 2 BÞ and Fig. 10b presents the pdf using a logarithmic y-axis for examining the low values of the scalar dissipation rate. Because

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Fig. 9. Probability density function (pdf) of the natural logarithm of the scalar dissipation rate (v) for both flame CO_A and CO_B. The scalar dissipation rate is normalized by D(hni/kB)2. (a) Shown with a linear y-axis (b) Shown with a logarithmic y-axis. Also shown is a Gaussian distribution with same first and second moments as flame CO_A. Note the v distribution for all values of n shows a strong negative skewness.

of the large number of samples available with two-dimensional imaging, a small bin around the stoichiometric region is possible, while still maintaining sufficient statistical accuracy. Data with the range of 0.27 < n < 0.31 is used to form the pdf. For values of v conditioned on the stoichiometric mixture fraction, the difference between flame CO_A and flame CO_B is more significant that the difference between the two flames when all values of v are considered as reported in Fig. 9. This suggests that flame CO_A has larger values of v at and near the stoichiometric contour than flame CO_B and flame CO_B has larger values of v away from the stoichiometric region than flame CO_A. This, again, is consistent with the idea that as the turbulence levels are increased, the reaction zone is broadened and the fact that flame CO_B is characterized by an increased number of dissipation layers which exhibit magnitudes less than the fewer number of strong dissipation layers in flame CO_A. Figure 10b shows that v|ns is governed by exponential scaling for small values of v. The low scalar dissipation rate values conditioned on the stoichiometric mixture fraction exhibit a different distribution than the low scalar dissipation rate values for all values of v (any n value).

0.40

h i v Figures 11 and 12h compareithe unconditioned pdf ln Dðhni=k to Þ2 B vjnS for flames CO_A and CO_B, respecthe conditioned pdf ln Dðhni=k 2 Þ B tively. It is seen that for both flames, the peak value of the conditioned pdf is larger and the width of the conditioned pdf is smaller than the unconditioned pdf. The differences in the conditioned and unconditioned pdfs have a significant implication, that is, the pdf of the scalar dissipation rate distribution is different for different values of n. It may not be surprising that the pdf of v|ns should be biased toward higher values due to the elimination of samples that are on average subject to low scalar dissipation rates such as region of pure fuel or air. However, the difference between the unconditioned and conditioned pdfs has implications for common modeling assumptions. It is evident that multiple shapes of the pdf of the scalar dissipation rate need to be considered to accurately represent the mixing rate at all locations within the flowfield. It is also noted that unconditioned and conditioned pdfs agree more closely in flame CO_B than in flame CO_A. This is due to the fact that the average mixture fraction in the flowfield of flame CO_B is lower than flame CO_A and is closer to ns than flame CO_A. This is a consequence of the increased level of local extinction and the corresponding dilution effects. 0

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Fig. 10. Probability density function (pdf) of the natural logarithm of the scalar dissipation rate (v) for both flame CO_A and CO_B, conditioned on the stoichiometric mixture fraction ns. The scalar dissipation rate is normalized by D(hni/kB)2. (a) Shown with a linear y-axis. (b) Shown with a logarithmic y-axis. Data within the range of 0.27 < n < 0.31 is used to form the pdfs. Note the scalar dissipation rate exhibits negative skewness when conditioned on the stoichiometric contour.

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Fig. 11. Comparison between the unconditioned pdf of the scalar dissipation rate (for all values of mixture fraction) with the conditioned pdf of the scalar dissipation rate (conditioned on the stoichiometric contour) for flame CO_A. The scalar dissipation rate is normalized by D(hni/kB)2. (a) Shown with a linear y-axis (b) Shown with a logarithmic y-axis.

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Fig. 12. Comparison between the unconditioend pdf of the scalar dissipation rate (for all values of mixture fraction) with the conditioned pdf of the scalar dissipation rate (conditioned on the stoichiometric contour) for flame CO_B. The scalar dissipation rate is normalized by D(hni/kB)2. (a) Shown with a linear y-axis (b) Shown with a logarithmic y-axis.

4. Conclusions Two-dimensional images of the mixture fraction and scalar dissipation rate fields, based on simultaneous planar laser-induced fluorescence (PLIF) of a passive scalar seed and Rayleigh scattering, were reported for turbulent carbon monoxide non-premixed, jet flames (flames CO_A and CO_B). One of the primary goals of the present work was to investigate the effects of increasing jet-exit velocity, and in particular, increasing levels of local flame extinction, on the mixture fraction and scalar dissipation rate fields in a series of turbulent non-premixed jet flames. In addition, the present measurements were compared to existing measurements of mixture fraction and scalar dissipation rate in other piloted, turbulent flames at higher Reynolds numbers. As the jet-exit velocity was increased towards blowoff, several interesting phenomena were identified. First, measurements of the Favre-averaged mixture fraction variance decreased in flame CO_B as compared to flame CO_A. Since flame CO_B has a higher jet-exit velocity and it is closer to blowoff, the results are consistent with the fact that increasing levels of turbulence enhance mixing and changes in flame structure and increasing levels of local flame extinction

are due to finite-rate kinetic effects. These features have been suggested in previous experiments and are further confirmed in the present study. The two-dimensional measurements of the scalar dissipation rate in the present study provide visualization of the structure, topology, and orientation of the regions of intense mixing rates. Similar to previous results in non-reacting and reacting flows, the scalar dissipation is found to be confined to long, thin ‘‘sheet-like’’ layers. The dissipation layers in flame CO_A typically are isolated, smooth, and aligned in the axial direction, while for the higher Reynolds number case, flame CO_B; the dissipation layers showed a higher degree of wrinkling, interaction with adjacent layers, and layer coalescence, possibly due to an increased level of vortex entrainment. Flame CO_A was characterized by fewer long, continuous scalar dissipation rate layers, while the increase in exit velocity (and local flame extinction) resulted in an increased number of shorter and contorted dissipation layers. In addition, there appears to be a Reynolds number dependence on the thickness of the dissipation layer as the layers in flame CO_B were thinner than those in flame CO_A. Such results are consistent with previous non-reacting results and Kolmogorov/Batchelor scaling.

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For the current set of flames, the mean scalar dissipation rate was found to decrease as the overall global strain rate was increased by increasing the jet-exit velocity. The cause was determined to be primarily due to a decreased diffusivity due to the lower temperatures found in flame CO_B as compared to flame CO_A and a reduction in the square of the radial component of the mixture fraction gradient, (@n/@r)2. The reduction of (@n/@r)2 as the jet-exit velocity increased (and nears blowoff) was most likely due to a combination of effects which include an increased number of dissipation layers with lower gradient magnitudes (due to increased levels of local flame extinction or non-ignition) and the broadening of the reaction zone by increased levels of turbulence which act to ‘‘smooth’’ the scalar gradients. Although the instantaneous images of mixture fraction and scalar dissipation rate in flame CO_A displayed a different structure than flame CO_B, the corresponding statistical properties of the scalar dissipation rate were similar. Probability density functions (pdfs) of the scalar dissipation rate exhibited significant and consistent departures from strict log-normality. The pdfs of the scalar dissipation rate were found to be significantly different if only the values conditioned on the stoichiometric contour were considered compared to the entire flow-field. This has implications for computational models that seek to describe the entire flow-field by only a single pdf.

[10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37]

Acknowledgments This work was supported by the Space Vehicle Technology Institute Grant NCC3-989, which was jointly funded by NASA and DOD within the NASA Constellation Universities Project. Claudia Meyer served as the project manager. References [1] [2] [3] [4] [5] [6] [7] [8]

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