High-Repetition Rate Measurements of Temperature and Thermal Dissipation in a Nonpremixed Turbulent Jet Flame

Transcription

1 (To be Published in the Proceedings of the Combustion Institute, Vol. 30, 2004) High-Repetition Rate Measurements of Temperature and Thermal Dissipation in a Nonpremixed Turbulent Jet Flame G.H. Wang, N.T. Clemens* and P.L. Varghese Center for Aeromechanics Research Department of Aerospace Engineering and Engineering Mechanics The University of Texas at Austin Austin, Texas *Corresponding author: Center for Aeromechanics Research Department of Aerospace Engineering and Engineering Mechanics The University of Texas at Austin Austin TX , USA Fax: clemens@mail.utexas.edu. PID number: Running Title: PID29879 Time-Series Thermal Dissipation Measurement 1

2 ABSTRACT High-repetition rate laser Rayleigh scattering is used to study the temperature fluctuations, power spectra, gradients and thermal dissipation rate characteristics of a nonpremixed turbulent jet flame at a Reynolds number of 15,200. The radial temperature gradient is measured by a two-point technique, whereas the axial gradient is measured from the temperature time-series combined with Taylor s hypothesis. The temperature power spectra along the jet centerline exhibit only a small inertial subrange, probably because of the low local Reynolds number (Re δ 2000), although a larger inertial subrange is present in the spectra at off-centerline locations. Scaling the frequency by the estimated Batchelor frequency improves the collapse of the dissipation region of the spectra, but this collapse is not as good as is obtained in nonreacting jets. Probability density functions of the thermal dissipation are shown to deviate from lognormal in the low dissipation portion of the distribution when only one component of the gradient is used. In contrast, nearly lognormal distributions are obtained along the centerline when both axial and radial components are included, even for locations where the axial gradient is not resolved. The thermal dissipation PDFs measured off the centerline deviate from lognormal owing to large-scale intermittency. At one-half the visible flame length, the radial profile of the mean thermal dissipation exhibits a peak off the centerline, whereas farther downstream the peak dissipation occurs on the centerline. The mean thermal dissipation on centerline is observed to increase linearly with downstream distance, reach a peak at the location of maximum mean centerline temperature and then decrease for farther downstream locations. Many of these observed trends are not consistent with equivalent nonreacting turbulent jet 2

3 measurements, and thus indicate the importance of understanding how heat release modifies the turbulence structure of jet flames. KEYWORDS: TURBULENT FLAME, SCALAR DISSIPATION, RAYLEIGH SCATTERING 3

4 1. INTRODUCTION Detailed measurements of mean and fluctuating scalars, such as species mass fractions and temperature have been critical to developing an improved understanding of the physics of turbulent nonpremixed flames [1-4]. Of particular importance are the mixture fraction ξ and its gradients, because in flamelet theory the flame structure is fundamentally related to the value of ξ at stoichiometric conditions and the rate of scalar dissipation, χ 2D ( ξ ξ), where D is the diffusivity. The scalar dissipation rate, which is a measure of the mixing rate, limits the reaction rate under mixing limited conditions, and affects the degree of nonequilibrium under finite chemistry conditions. Because of its importance to combustion, measurements of χ in turbulent nonpremixed flames have received a lot of attention in recent years [5-7], but detailed statistical measurements of the type that exist for nonreacting flows are still relatively sparse. It can be argued that temperature does not play as fundamental a role as mixture fraction in determining the flame characteristics, but its fluctuations and gradients do provide important information about the underlying mixture fraction structure. This can be seen by considering the thermal dissipation rate χ Τ = 2α ( T T), where T is temperature and α is the thermal diffusivity, which is related to the rate of thermal mixing, or alternatively to the rate at which thermal inhomogeneities are removed by diffusion. Importantly, under the assumption of the state relationship T = T(ξ) and unity Lewis number, the scalar and thermal dissipation rates are related as χ Τ = χ (dτ/dξ) 2 [8]. As will be discussed in the results section, in some regions of the flame, dt/dξ is approximately constant, and so the thermal dissipation rate is proportional to the scalar dissipation rate. 4

5 Thermal mixing is also important because it affects high-temperature chemical reaction processes and can be important in the development and validation of turbulent flame models [8]. For these reasons fluctuating temperature and thermal dissipation rates have been measured in a number of studies by using, e.g., dualthermocouple measurements [9, 10], two-point laser Rayleigh measurements [11, 12] and planar laser Rayleigh imaging [8]. An important issue with such measurements is that the requirement to obtain fully spatially- and temporallyresolved measurements of the finest scales of turbulence is very stringent and this makes dissipation measurements particularly challenging [13]. It is clear from careful study of the literature that the Batchelor scale is rarely resolved even in turbulent flame studies that explicitly seek to measure the dissipation rate. The objective in this study is to make high-quality, high-repetition rate (10 khz), two-point laser Rayleigh temperature measurements in a weakly co-flowing turbulent nonpremixed jet flame at a Reynolds number of 15,200, with high signalto-noise ratio ( 50 in room air) and where the finest scales of turbulence are spatially and temporally resolved. These two-point temperature data were used to obtain temperature power spectra and detailed statistics of the thermal dissipation rate. The flame studied here is similar to the TNF simple jet flame (DLR_A) which is used as a benchmark flame for the TNF Workshop [14-17]. 2. EXPERIMENTAL SETUP The flow studied was a weakly co-flowing jet flame. The coflow air was filtered to remove particles larger than 0.2 µm and then passed through a flow conditioning section. The coflow velocity was 0.45 m/s. The fuel issued from a long tube with inside diameter d = 7.75 mm. The test section had a 0.75 m 0.75 m cross section. The whole jet flow facility was mounted on a traverse that was driven by 5

6 stepper motors to provide positioning in the radial and axial directions. The fuel composition used in this study was 22.1% CH 4, 33.2% H 2, 44.7% N 2 (by volume), which gives a stoichiometric mixture fraction of The fuel gases were metered by pressure regulators and monitored by mass flow meters to an accuracy of ±1.0 SLPM for N 2 and ±0.5 SLPM for CH 4 and H 2. The Rayleigh cross-section of this fuel has been shown to vary by ±3% across the whole flame [15]. The source Reynolds number was Re d = U 0 d/ν 0 = 15,200 (where ν 0 is the kinematic viscosity of the fuel and U 0 is the mean jet exit velocity) and the measurements were taken at downstream locations from x/d = 40 to 80. Here, x and r are the axial and radial coordinates, respectively. The visible flame length was at about x/d = 84 and the stoichiometric flame length, estimated based on data in the TNF database, was at about x/d = 60. The laser Rayleigh system is based on a diode-pumped Nd:YAG laser operated at 71W average power at 532 nm and with a 10 khz repetition rate. The laser beam was focused into the test section by using a 300 mm focal length lens. The beam diameter was measured to be about 0.3 mm. An external photodiode was used to correct for variations in the laser pulse energy on a shot-by-shot basis. Rayleigh scattered light was collected using custom-designed optics that consisted of a pair of 150 mm diameter plano-convex lenses, one 50.8 mm diameter meniscus lens and one 50.8 mm diameter double-convex lens. The lens system was designed with ZEMAX and produced an aberration-limited blur-spot of less than 34 µm. The working f# was 2.4 and the magnification was Two-point measurements were made by imaging the scattered light onto a broadband hybrid cube beam splitter, which reflected and transmitted the split signal onto two different PMTs. Two 200 µm slits were placed in front of the PMTs to define the spatial resolution (i.e., 6

7 length of the beam imaged). The slit width in the image plane corresponded to 300 µm in the object plane. These two slits were arranged such that the separation of probe volumes in the flow was 300 µm. The PMT and photodiode outputs were read by gated integrators operated with gate widths of 300 ns. The integrated signals were synchronously sampled by a 12-bit A/D converter at 10 khz. For constant Rayleigh cross section, the temperature is derived from the formula: T = I R, ref T ref / I R, where I R, ref is the reference Rayleigh scattering signal from air at room temperature (T ref ). The two-point instantaneous temperature signals were used to determine the instantaneous radial temperature gradient by using the approximation T/ r = T/ r, where T is the temperature difference of the two measurements and r = 300 µm is the probe separation distance. The axial gradient is estimated by the time-series and Taylor s hypothesis, T/ x = - (1/U) T/ t, where U is the local velocity obtained from [17]. The error in using Taylor s hypothesis is estimated to be about 10% at the jet centerline [11,18]. For convenience, we define the thermal dissipation based on single components of the gradient vector: χ Τ,r = 2α ( Τ/ r) 2, χ Τ,x = 2α U -2 ( Τ/ t) 2 and χ Τ,2D = χ Τ,r +χ Τ,x, where the thermal diffusivity is computed from the formula α = (T/300) 1.8 (m 2 /s) [11]. 3. RESOLUTION ESTIMATION The finest spatial structures in the scalar field are of order the Batchelor scale, which is defined as λ B = η Sc -1/2, where η = (ν 3 / <ε>) 1/4 is the Kolmogorov scale, ν is the kinematic viscosity, <ε> is the mean rate of kinetic energy dissipation and Sc = ν / D is the Schmidt number. Using measurements of <ε> in nonreacting round jets [19], the Batchelor scale can be shown to be equal to λ B = 2.3 δ Re -3/4 δ Sc -1/2, where Re δ is the local Reynolds number and is defined 7

8 as U C δ /ν, with U C the jet centerline velocity and δ the full width at half maximum of the velocity profile. In nonreacting jets Re d is approximately equal to Re δ but this is not true in jet flames [20]. For example, the local Reynolds numbers at the downstream stations studied are shown in Table 1. The kinematic viscosity was estimated to be that of the local fluid mixture at the measured centerline temperature per the formula ν = ν 0 (T C / T 0 ) 1.7. For time-series measurements, the highest frequency present in the flow is expected to be the convective Batchelor frequency f B = U/(2πλ B ), where U is the local mean velocity. Note that the Batchelor frequency can be quite large in jet flames and is not always resolved because signal-to-noise ratio considerations usually necessitate relatively low bandwidths. To estimate f B in this study, the velocities used were taken from [17]. The velocities and the estimated Batchelor scales and Batchelor frequencies are shown in Table 1 for various locations along the jet centerline. Off-centerline mean velocities were also taken from [17] and used for scaling the data where appropriate, but these values are not shown in the table. Table 1 shows that the current two-point spatial separation of 300 µm is equal to λ B at x/d = 40 and is about a factor of two smaller than λ B farther downstream. This suggests that the radial gradient measurement is fully spatially-resolved. The convective Batchelor frequency f B is about 2 times the frequency resolution at x/d = 40 and the errors in the axial dissipation are expected to be about 10%. The sampling frequency of this study is sufficient to resolve convective Batchelor frequency (and hence the Batchelor scale) along the centerline for x/d 60. The measurements were limited to stations of x/d = 40 and larger so that the resolution of the dissipation scales could be maintained, at least for the radial gradient. 8

9 4. RESULTS AND DISCUSSION Figure 1 shows measured mean and rms radial temperature profiles at three downstream stations (x/d = 40, 60, 80). For comparison, the temperature profiles from the TNF database [14] are also shown and it is seen that the current measurements agree very well with the database. Temperature power spectra are shown in Fig. 2. In Fig. 2a, spectra are shown along the centerline of the jet flame at the five axial stations with the range x/d= The frequency is normalized by the convective Batchelor frequency, and the power spectral density is normalized by T 2 rms /f B. The spectra have also been corrected to remove the contribution from shot-noise by using the procedure developed in [21]. This procedure requires that the measurement cut-off frequency is higher than the Batchelor frequency so that the power of the noise fluctuations can be determined. Since this was not the case for all of the measurement locations, the correction was not applied in all cases (see figure caption). All of the spectra exhibit a similar appearance in that they are relatively flat at low frequency, begin rolling off for f/f B > 10-2, and then roll-off more rapidly in the dissipation range (f/f B > 0.4). An inertial subrange, where the power scales as f -5/3, characterizes scalar spectra at high Reynolds numbers [22,23], and a line that follows this scaling is shown as reference. Figure 2a shows the spectra along the centerline exhibit only a small inertial subrange (if any), likely because the local Reynolds number at all locations is only about A large inertial-subrange is a well known signature of fully developed turbulence and measurements of mixture fraction fluctuations clearly show this range diminishing with decreasing Reynolds number [23]. The farthest upstream location seems to exhibit a more extended inertial subrange, but that spectrum is not corrected for noise and that seems to 9

10 contribute to the apparent power law dependence. Figure 2a also shows that the spectra collapse relatively well in the dissipation range near f/f B = 1. This is significant because it suggests that the estimate of the Batchelor scale is largely correct, and that the dissipation range is apparently resolved. Note, however, that no dissipation range is observed at x/d = 40 because the sampling frequency was not high enough to resolve it. This conclusion is consistent with Table 1. We also note that when scaled by the integral-scale frequency ( U/δ), the spectra exhibit a rolloff at a non-dimensional frequency of about 10, which is consistent with measurements of mixture fraction fluctuations in non-reacting jets [23]. However, in agreement with nonreacting jet studies, the dissipation range could not be collapsed with this outer-scale normalization of the frequency. This latter result is different from that of [21], whose OH fluctuation spectra could be collapsed over the entire frequency range with integral-scale normalization. Figure 2b shows the power spectra at the same downstream locations but along the ray where r/δ = 0.4, which is close to the region of maximum shear. The convective Batchelor frequency used in the normalization of the frequency was scaled by the local velocity. Figure 2b shows that, in contrast to the centerline locations, the spectra seem to exhibit an extended inertial-subrange. This observation of a larger power-law region for increasing radial location is similar to what has been seen in non-reacting jet scalar dissipation measurements [24], and is likely related to the proximity to the peak shear region. This similarity with nonreacting jets is somewhat surprising at the x/d = 40 location, because the r/δ = 0.4 location is near the reaction zone and so substantial turbulence damping by the increased viscosity is expected. 10

11 Figure 2c shows normalized temperature power spectra as a function of radial location at the x/d = 80 station, which is fully resolved. Note that this station is past the stoichiometric flame length and point of maximum centerline temperature. Although not entirely apparent from the figure, the spectra exhibit an increasing inertial-subrange with increasing radial location, and they collapse relatively well in the dissipation range. Since this location is downstream of the stoichiometric flame tip it represents an effectively nonreacting flow, and so its characteristics should be similar to those of a low Reynolds number, nonreacting, low-density jet. Figure 3 shows PDFs of the normalized temperature gradients in the radial direction at the jet centerline. At x/d = 60, 70 and 80, the semi-log plot shows that the PDFs are similar, which indicates the similarity of the gradients when normalized by the T C /λ B. All the distributions appear to exhibit approximately exponential scaling of the tails (which should appear as a straight line in the semilog plot). Exponential scaling is well documented in nonreacting turbulent flows and is a result of the intermittent nature of the scalar dissipation fluctuations [25]. Figure 3 also shows the gradient PDFs at the x/d = 40 and 50 stations. One can see that the shapes of the radial components are similar to those for x/d > 60, but the normalized values are much smaller. The dissipation scale should be resolved for x/d > 40 (and well resolved at 60) and so it seems unlikely that inadequate resolution is the cause of the difference. Instead, the difference in the distributions may result from a difference in the nature of the gradient fluctuations or possibly the estimate of the Batchelor scale is not correct for the upstream stations. PDFs of the normalized thermal dissipation rate, which were computed from measurements made along the jet centerline and at three axial stations, are shown in 11

12 Figure 4. The PDFs were computed by using the radial term only, and the radial and axial terms. PDFs of the 2-D scalar [26] and thermal [8] dissipation have been shown to be approximately log-normal, and some evidence suggests the 1-D dissipation PDF is also log-normal [9, 11]. It is seen from Fig. 4a that the PDFs that used the radial term only, do not exhibit a log-normal distribution, which would appear as an inverted parabola on a log-log plot. This observation is consistent for all three axial stations. The high dissipation values are apparently log-normally distributed but not the low dissipation values. However, when the axial component is included, the PDFs approach the lognormal distribution. These observations are consistent with previous measurements of scalar dissipation in nonreacting jets [22] and mixture fraction dissipation in jet flames [7]. In nonreacting flows the 1-D dissipation exhibits a slope of ½ in the low-dissipation portion of the PDF when plotted in log-log coordinates, which is similar to what is seen in Fig. 4a. The power law dependence of the low-dissipation portion of the PDF is a direct result of the 1-D gradient overestimating the total gradient vector magnitude [23]. It is interesting that including the axial gradient term improves the log-normality of the PDF as well as it does, considering that the axial term is not fully resolved at the upstream stations. It is likely that the low-dissipation end of the distribution is in fact better resolved because the associated structures are much larger than the Batchelor scale. Figure 4b shows a linear-log plot of the PDFs of thermal dissipation computed from the two-component data at several radial locations at x/d = 80. This figure shows that the PDFs exhibit essentially log-normal behavior on centerline and near the outside edge of the jet, but not at intermediate locations. For example, at r/δ = 1.0, the profile is almost bimodal, suggesting that the dissipation is either 12

13 high or low at that location. The PDF at r/δ = 1.0 at the x/d = 40 station is similarly not log-normal and the shape suggests a double-hump structure. The bimodal structure results from the intermittent edge of the jet, which alternatively brings turbulent fluid or co-flow air into the probe volume. The radial distribution of the mean thermal dissipation, computed from the radial temperature gradient only is shown in Fig. 5. The dissipation rates, shown at three axial stations, have been scaled by (T C /λ B ) 2. Figure 5 shows that at x/d = 40, the mean dissipation exhibits a peak away from the centerline. The off-centerline maximum is similar to what was measured in [8], but they found the peak mean dissipation to be approximately five times the centerline value, as compared to a factor of two in the current study. The reason for this difference is probably because their measurements were made farther upstream (relative to the flame length) than in the current study. Furthermore, radial profiles similar to the current x/d = 40 case were obtained with dual-thermocouples in the near field of a lifted propane flame [9]. They showed that the peak values were about a factor of 2-3 larger than the centerline values, but these results should be viewed with some caution because the measurements significantly under-resolved the Batchelor scale. Figure 5 further shows that at x/d = 60, the profile may exhibit a weak local maximum off-centerline, but at x/d = 80, the mean dissipation is clearly at a maximum on centerline. Note that measurements made in the far-field of non-reacting jets seem to show somewhat contradictory trends for the radial variation of the mean scalar dissipation. For example, models suggest that the mean scalar dissipation should peak off-centerline near the region of maximum shear and hence maximum turbulence intensity. Indeed, the measurements of [24], taken at a single axial station, seem to validate this. However, other measurements [26-28] show the far- 13

14 field mean dissipation reaching a maximum on the centerline, similar to the thermal dissipation profiles in Fig. 5. It is not entirely clear therefore, whether the jet flame exhibits different mixing characteristics than a non-reacting jet, but at the very least it can be stated that the jet flame apparently does not exhibit self-similar behavior in terms of the mean dissipation. Because the off-centerline peak in the thermal dissipation is only present at the upstream location, this suggests that it is related to the presence of the reaction zone, rather than the region of maximum shear. The reaction zone is a source of temperature fluctuations, and so perhaps the local maximum is not surprising, but this issue is worth looking at in more detail. According to [8], the thermal dissipation differs from the scalar dissipation (based on mixture fraction fluctuations) only by the factor (dt/dξ) 2. The relationship between T and ξ for this flame is known [14-17], and it is similar to a piecewise linear function that peaks near the stoichiometric mixture fraction and is zero at ξ = 0 and 1. This means that on each side of the stoichiometric mixture fraction, dt/dξ is approximately constant, and hence the thermal dissipation should be proportional to the mixture fraction dissipation. Near stoichiometric, dt/dξ should decrease, and so the thermal dissipation should be smaller than the mixture fraction dissipation. This argument suggests that if the underlying mean scalar dissipation peaks on centerline, and decreases with increasing radius, then the thermal dissipation would not exhibit a local maximum off-centerline, but in fact would exhibit a local minimum at the reaction zone. Since this is not the behavior we see, it suggests that the underlying scalar dissipation indeed exhibits an off-centerline peak. Of course, this does not explain why the downstream profiles exhibit a centerline peak but it may have to do with variations in the function dt/dξ near stoichiometric. As a final point regarding 14

15 Fig. 5, the dissipation was computed with the radial gradient only, and laminarization by the reaction zone may render this the dominant component of the dissipation, in contrast to the centerline where the gradients are likely to be more isotropic. It is therefore possible that the total dissipation does indeed peak at the centerline, even though the radial dissipation does not. This would be true for the upstream locations where the reaction zone is well off the centerline, but not for locations past the stoichiometric flame tip, such as at x/d = 80. The variation of the centerline mean thermal dissipation is shown in Fig. 6. The mean thermal dissipation is seen to increase approximately linearly from x/d = 40 to 60, reach a maximum at x/d = 60, and then decrease linearly for x/d > 60. In Ref. [29] it is argued that in nonreacting round jets the mean scalar dissipation rate should scale as <χ> (<ξ> / λ B ) 2, and since <ξ> x -1 in round jets and λ B δ Re -3/4 δ x (since δ x and Re δ is constant), then we have <χ> x -4. Although the measurements are not all consistent, the highly resolved dissipation data of [22] seem to validate this scaling law in nonreacting jets. The results in Fig. 6 clearly do not follow this scaling law, which was also proposed to apply to jet flames [29]. This means that either the underlying scalar dissipation decay is different in jet flames or the thermal dissipation does not reflect the underlying scalar dissipation. Once again, however, since we are using only the radial component to compute the dissipation (because it is resolved over a wider range), we cannot rule out the possibility that non-isotropy of the dissipation scales could account for the trend seen in Fig. 6. This seems unlikely however, because any laminarization that would occur near the stoichiometric flame tip should favor the axial temperature gradient and thus reduce the dissipation based only on the radialgradient. 15

16 One thing to note is that from the jet exit to a location somewhat upstream of the stoichiometric flame length (near x/d = 60), the factor dt/dξ should be approximately constant, and so the thermal dissipation should exhibit the (x/d) -4 scaling if the scalar dissipation does. We can explore this further by considering the scaling of the thermal dissipation. As above, it can be argued that the thermal dissipation rate along the jet flame centerline will scale as <χ T > α (<T C > / λ B ) 2. Table 1 shows that the Reynolds number is approximately constant from x/d = 40 to 60, and so the Batchelor scale should scale the same as in a nonreacting jet, i.e., λ B δ Re -3/4 δ x. If we make the approximation that <T C > x (which is really only true for locations upstream of the point of maximum temperature), and we make the further approximation that α <T C > 1.8 x 1.8, then we find <χ T > x 1.8. The current data suggest a somewhat weaker dependence on x (<χ T > x ) upstream of the location of maximum temperature on centerline. One reason for the difference between the theoretical and measured scalings may be that the assumption that <T C > x is not valid from x/d = 40 to 60 because the temperature peaks near x/d = 60 and so is rolling off above x/d = 40; therefore, the mean temperature will exhibit a weaker dependence on x and this will lead to a weaker scaling of <χ T >. Another possibility is that the assumed state relationship, T = T(ξ), may not hold in all regions of the flame or may be different from that assumed. More measurements and additional analyses are clearly warranted to clarify these issues. 5. CONCLUSIONS High-repetition rate laser Rayleigh scattering was used to study the temperature fluctuations, gradients and thermal dissipation rate characteristics in a nonpremixed turbulent jet flame at a Reynolds number of 15,200. The flame studied was similar to the TNF Workshop DLR_A simple jet flame. The radial 16

17 temperature gradients are measured by two-point detection, whereas the axial gradient is measured from the temperature time-series combined with Taylor s hypothesis. These two-point temperature data were used to obtain temperature power spectra and detailed statistics of the thermal dissipation rate. The temperature power spectra exhibit good collapse in the dissipation range when scaled by the convective Batchelor frequency. The off-centerline spectra (near the location of maximum shear) exhibit an inertial subrange, but little or no inertial subrange is observed on centerline. The latter observation likely results from the low local Reynolds number (Re δ 2000) of the jet flame. Probability density functions of the thermal dissipation are shown to deviate from lognormal in the low dissipation portion of the distribution when only one component of the gradient is used to compute the thermal dissipation. In contrast, nearly lognormal distributions are obtained along the centerline when both axial and radial components are included. Interestingly, this is true even for axial locations where the axial gradient is not resolved. It was also shown that the thermal dissipation PDFs off centerline deviate from lognormal. This is probably due to large-scale intermittency, which biases the PDFs with the low dissipation values associated with the co-flow air. The radial profile of the mean thermal dissipation at one-half the visible flame length exhibits a peak off centerline, whereas further downstream the peak dissipation occurs on centerline. The mean thermal dissipation on centerline is observed to scale approximately linearly with x from x/d = 40 to 60, reach a peak at x/d = 60, and then decrease linearly from x/d = 60 to 80. This scaling of the thermal dissipation is not consistent with expected scaling laws for the scalar dissipation in nonreacting jets. A scaling law is derived for the thermal dissipation rate that accounts for heat release effects 17

18 and predicts <χ T > x 1.8, which stronger than the measured scaling law, likely because the assumed mean temperature dependence is not correct over the measurement range. Taken as a whole, these results show that the time- and spacevarying temperature field of the flame exhibits strong similarities but also clear differences with the conserved scalar field in nonreacting jets. The reasons for the observed differences are not known at this time, but they do indicate that heat release has a strong influence on the nature of the turbulent fluctuations. ACKNOWLEDGEMENTS This work was funded by the National Science Foundation under grant CTS- REFERENCES [1]. N. Peters, Prog. Energy Combust. Sci., 10, (1984) [2]. R.W. Bilger, Proc. Comb. Institute 22 (1988) [3]. R.W. Dibble, A.R. Masri, R.W. Bilger, Combust. Flame, 67 (1987) [4]. A.R. Masri, R.W. Dibble, R.S. Barlow, Prog. Energy Combust. Sci., 22 (1996) [5]. S.P., Nandula, T.M., Brown, R.W., Pitz, Combust. Flame, 99 (1994) [6]. J. Fielding, A.M. Schaffer, M.B. Long, Proc. Comb. Institute 27 (1998) [7]. A.N. Karpetis, R.S. Barlow, Proc. Comb. Institute 29 (2002) [8]. D.A. Everest, J.F. Driscoll, W.J.A. Dahm, D.A. Feikema, Combust. Flame 101 (1995) [9]. L. Boyer, M. Queiroz, Combst. Sci. and Tech., 79 (1991) [10]. A. Caldeira-Pires, M.V. Heitor, Exp. Fluids 24: (1998). [11]. E. Effelsberg, N. Peters, Proc. Combust. Inst., Vol. 22, pp ,

19 [12]. P.G. Gladnick, J.C. LaRue, G.S. Samuelsen, Heat Transfer in Combustion Systems HTD, 142, ASME, New York, 1990, p. 33 [13]. J. Mi, G.J. Nathan, Exp. Fluids, 34, (2003) [14]. TNF workshop [15]. V. Bergmann, W. Meier, D. Wolff, W. Stricker, Appl. Phys. B 66 (1998) [16]. W. Meier, R.S. Barlow, Y.-L. Chen, J.-Y. Chen, Combust. Flame, 123 (2000) [17]. Ch. Schneider, A. Dreizler, J. Janicka, E.P. Hassel, Combust. Flame, 135 (2003) [18]. W.J.A. Dahm, K.B. Southerland, Phy. Fluids A 9(7) (1997) [19]. C.A. Friehe, C.W. Van Atta, C.H. Gibson, AGARD Turb. Shear Flows,CP- 93 (1971) [20]. L. Muniz, M.G. Mungal, Combust. Flame, 126 (2001) [21]. M.W. Renfro, J.P. Gore, G.B. King, N.M. Laurendeau, AIAA J. 38(7) (2000) [22]. D.R. Dowling, Phys. Fluids A 3(9) (1991) [23]. D.R. Dowling, P. Dimotakis, J Fluid Mech. 218 (1990) [24]. F.C. Lockwood, H.A. Moneib, Comb. Sci. Tech. 22 (1980) [25]. A.S. Gurvich, A.M. Yaglom, Phys. Fluids 10 (Suppl.) pt. II (1967) S59-S65. [26]. M. Namazian, R.W. Schefer, J. Kelly, Combust. Flame 74, (1988) [27]. R.W. Dibble, W. Kollmann, R.W. Schefer, Proc. Combust. Inst., 20 (1984) [28]. R.A. Antonia and J. Mi, J. Fluid Mech. 250 (1993) [29]. N. Peters, F.A. Williams, AIAA J. 21(3) (1983)

20 FIGURE CAPTIONS Figure 1. Radial profiles of (a) mean and (b) rms temperature at three different axial stations (x/d=40, 60, 80). Data from TNF workshop data base [14] are shown for comparison. Figure 2. Fluctuating temperature power spectra. (a) spectra at the jet flame centerline (corrected except at x/d = 40 and 50); (b) along ray r/δ=0.4 (corrected except at x/d =40); (c) at x/d=80 and different radial locations, all corrected. Figure3. Probability density functions of the normalized radial temperature gradients along the jet centerline. Figure 4. Probability density functions of temperature dissipation. (a) log-log plot showing effect of using radial and axial components to compute dissipation, (b) variation with radial location at x/d=80, (c) variation with radial location at x/d=40. Figure 5. Radial profiles of the normalized mean thermal dissipation (radial component only). Measurements were made at three downstream locations: x/d=40, 60, 80. Figure 6. Variation of the mean thermal dissipation (radial component only) along the jet flame centerline. 20

21 T (K) (a) Re d = 15,200 TNF: x/d = 40 TNF: x/d = 60 TNF: x/d = 80 x/d = 40 x/d = 60 x/d = PDF (a) χ T,r χ T,2D x/d = 40 x/d = 40 x/d = 60 x/d = 60 x/d = 80 x/d = 80 Lognormal fit x/d = 40 x/d = 60 x/d = 80 Slope = 1/2 Figure (b) r/d T rms χ T /(T C /λ B ) 2 (b) x/d = 80 r/δ = 0 r/δ = 0.4 r/δ = 0.8 r/δ = 1.0 r/δ = 1.6 PSD/(T 2 rms / f B ) Figure (a) Centerline x/d = 40 x/d = 50 x/d = 60 x/d = 70 x/d = 80 (b) r/δ = 0.4 x/d = 40 x/d = 60 x/d = 80 (c) x/d = 80 r/δ = 0 r/δ = 0.4 r/δ = 0.8 r/δ = 1.0-5/ f/f B x/d = 80 x/d = 70 x/d = 60 x/d = 50 x/d = PDF 0.0 Figure 4. χ T,r / (T C /λ B ) 2 (c) x/d = x x x x10-6 Figure 5. χ T /(T C /λ B ) 2 x/d = 40 x/d = 60 x/d = r/δ PDF ( T/ r)/(t C /λ B ) Figure 3. 21

22 3x10 8 2x10 8 χ T,r 1x x/d Figure 6. Table 1 Jet flame conditions and estimates of resolution requirements. (Velocity data from [17], U C0 = 51.6 m/s is the mean jet exit centerline velocity which is different from the mean jet exit velocity U 0 ; temperature data from TNF database [14]). x/d T C (K) U C /U C0 δ/d Re δ λ B (mm) f B (khz)