Detailed characterization of the dynamics of thermoacoustic pulsations in a lean premixed swirl flame

Combustion and Flame 150 (2007) 2–26 www.elsevier.com/locate/combustflame

Feature Article

Detailed characterization of the dynamics of thermoacoustic pulsations in a lean premixed swirl flame W. Meier ∗ , P. Weigand, X.R. Duan 1 , R. Giezendanner-Thoben 2 Institut für Verbrennungstechnik, Deutsches Zentrum für Luft- und Raumfahrt (DLR), Pfaffenwaldring 38, D-70569 Stuttgart, Germany Received 28 November 2006; received in revised form 2 April 2007; accepted 3 April 2007 Available online 23 May 2007

Abstract A nozzle configuration for technically premixed gas turbine flames was operated with CH4 and air at atmospheric pressure. The flames were confined by a combustion chamber with large quartz windows, allowing the application of optical and laser diagnostics. In a distinct range of operating conditions the flames exhibited strong self-excited thermoacoustic pulsations at a frequency around 290 Hz. A flame with P = 25 kW thermal power and an equivalence ratio of Φ = 0.7 was chosen as a target flame in order to analyze the dynamics and the feedback mechanism of the periodic instability in detail. The velocity field was measured by three-component laser Doppler velocimetry, the flame structures were measured by chemiluminescence imaging and planar laserinduced fluorescence of OH, and the joint probability density functions of major species concentrations, mixture fraction, and temperature were measured by laser Raman scattering. All measuring techniques were applied in a phase-locked mode with respect to the phase angle of the periodic pulsation. In addition to the pulsating flame, a nonpulsating flame with increased fuel flow rate (P = 30 kW, Φ = 0.83) was studied for comparison. The measurements revealed significant differences between the structures of the pulsating and the nonpulsating (or “quiet”) flame. Effects of finite-rate chemistry and unmixedness were observed in both flames but were more pronounced in the pulsating flame. The phase-locked measurements revealed large variations of all measured quantities during an oscillation cycle. This yielded a clear picture of the sequence of events and allowed the feedback mechanism of the instability to be identified and described quantitatively. The data set presents a very good basis for the verification of numerical combustion simulations because the boundary conditions of the experiment were well-defined and the most important quantities were measured with a high accuracy. © 2007 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Gas turbine combustion; Combustion oscillation; Swirl flame; Turbulence–chemistry interaction; Validation measurements

* Corresponding author. Fax: +49 711 6862 578.

E-mail address: [email protected] (W. Meier). 1 Current address: Southwestern Institute of Physics, P.O. Box 432, 610041 Chengdu Sichuan, People’s Republic of China. 2 Current address: Robert Bosch GmbH, Postfach 10 60 50, 70049 Stuttgart, Germany.

0010-2180/$ – see front matter © 2007 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2007.04.002

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

1. Introduction In stationary gas turbines (GT) the concept of lean premixed combustion is widely used in order to meet the stringent demands for low emissions of NOx . This concept also allows the achievement of a quite homogeneous temperature distribution at the turbine inlet and thus a lower thermal load. Unfortunately, lean premixed GT flames are susceptible to thermoacoustic instabilities driven by the combustion process and sustained by a resonant feedback mechanism coupling pressure and heat release [1–7]. These pulsations can lead to strong perturbations in the gas turbine and even to the destruction of system components. The physical and chemical mechanisms driving the instabilities are based on a complex interaction between combustor geometry, pressure, flow field, mixing, chemical reactions, and heat release and are not understood well enough yet. While active and passive control mechanisms have been developed to reduce or even eliminate instabilities in some industrial burners [8–12], the problem is not fundamentally solved. Major efforts are currently being made in the development of numerical simulation tools in order to predict unsteady combustion behavior so that improved GT combustors can be designed with their help [1–3, 13–17]. However, a deeper understanding of the complex interactions involved in combustion instabilities is now and in the near future based on experimental research using advanced measuring techniques with high temporal and spatial resolution. In order to investigate the phenomenon of combustion pulsations, the German Aerospace Center (DLR) has performed comprehensive measurements in an atmospheric pressure GT model combustor. The combustor was operated with premixed CH4 /air and exhibited a self-excited thermoacoustic instability. The burner nozzle was designed by Turbomeca S.A. [18,19]. In this configuration CH4 was mixed into the air flow within the radial swirler of the nozzle [18]. The flames were confined by a combustion chamber with an exhaust tube at the top. The flame investigated (equivalence ratio of Φ = 0.7, thermal power 25 kW) exhibited a strong self-excited thermoacoustic oscillation at a frequency of about 290 Hz. For comparison, a nonpulsating (or “quiet”) flame with Φ = 0.83 and thermal power 30 kW was also measured. The main goals of the investigations were a deeper understanding of the physical and chemical mechanisms driving the oscillation and the provision of a database of experimental results which shall be used for the comparison with numerical simulations. For the validation purposes, great care was taken to specify the experimental uncertainties and to characterize the boundary conditions.

3

The combustion chamber was equipped with large quartz windows in order to apply laser and optical diagnostic techniques. The measurements were performed with phase resolution, i.e., triggered with respect to the phase of the pressure pulsation measured by a microphone. The shape and position of the flame zone were determined by OH chemiluminescence measurements. These measurements also yielded a measure of the heat release rate [20,21]. The flow velocities were measured by LDV and the joint probability density functions of major species concentrations, temperature, and mixture fraction by laser Raman scattering. Due to its ability of multispecies detection, the single-shot Raman technique is of special value for the flame investigation because it yields information about mixing and finite-rate chemistry effects [22,23]. Previous investigations in nonpremixed and partially premixed swirl flames demonstrated that turbulence–chemistry interactions play an important role in those flames [24–26]. Furthermore, Raman measurements characterize the mixing process, e.g., mixing of burnt gas from the recirculation zones with fresh gas from the nozzle, which represents the main stabilization mechanism in strongly swirling flames. Another important parameter is the degree of unmixedness in industrial-type premixed flames, as this can have a significant influence on flame stabilization and NO formation [27]. It is also known that equivalence ratio fluctuations can be the source of combustor instabilities [28–32]. Thus, the measurement of the gas composition is of great importance for this investigation. In previous experiments at the DLR, another GT burner was employed to study the details of thermoacoustic instabilities using the same optical combustion chamber and the same measuring techniques [33, 34]. In that study, periodic variations of the mixing of exhaust gas from the recirculation zones with fresh gas were identified as the main source of the periodic changes of the heat release rate. In the burner examined in the present study, the feedback mechanism is of a different nature. In the current paper the combustor configuration is presented and results from phase-resolved measurements of OH* chemiluminescence, flow velocities, mixture fraction, temperature, and species concentrations are shown. Effects of mixing and turbulence–chemistry interactions are addressed and periodic variations of the gas flow rates at the inlet of the combustion chamber are discussed.

2. Combustor and target flames The gas turbine model combustor was derived from an industrial design by Turbomeca. In Fig. 1 a schematic of the nozzle design with the combus-

4

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

Fig. 1. Schematic of the injector with combustion chamber and photo of the flame.

tion chamber is shown. Dry air at ambient temperature is fed via a plenum ( = 78 mm) through 12 radial swirler vanes to the burner nozzle. The fuel gas (CH4 ) is injected into the air flow through small holes ( = 1 mm) within the radial swirler with high momentum to ensure good mixing before it enters the combustion chamber. The nozzle exit has a diameter of 27.85 mm. The air and fuel flows were each measured by two different mass-flow meters (Brooks Type 5853S for air and 5851S for CH4 and Danfoss Type 2100). The accuracy of the flow measurements was ±1.5%. The exit plane of the nozzle was defined as h = 0 for all measurements. The combustion chamber consists of large quartz windows of thickness 1.5 mm held by steel posts in the corners, thus creating a confinement with a square

section of 85 × 85 mm and a height of h = 114 mm. The exit of the upright combustion chamber is coneshaped, leading to a short central exhaust pipe with a diameter of 40 mm. The large windows on each side enable unobstructed optical access to nearly the whole flame zone and in particular close to the nozzle exit. In order to change the measuring location within the flames, the burner could be translated in axial and radial directions. The burner position was measured by photoelectric encoder systems. The measuring accuracy for the distance between the radial and axial measuring locations was estimated to be ±0.1 mm and the day-to-day reproducibility to be ±0.5 mm. Two different flames were investigated: (1) An unsteady, pulsating flame operated at 25 kW with an equivalence ratio of Φ = 0.70 that exhibited thermoacoustic pulsations at a frequency of f ≈ 290 Hz. For these operating conditions the Reynolds number at the exit of the nozzle, based on the cold flow and the exit diameter, is about 35,000 and the swirl number, derived from the velocity measurements at 1.5 mm above the exit, is approx. 0.6. (2a) A quiet flame with 30 kW and Φ = 0.83 (for the LDV measurements the flame was operated under slightly different conditions, i.e., 27 kW and Φ = 0.75, termed 2b). The flame parameters are summarized in Table 1. The Kolmogorov length scale was estimated to be on the order of 0.1 mm in the turbulent flame regions; the corresponding time scale is 35 µs. After a warm-up period of typically 30 min, the combustor would reach a constant temperature. Contact of the fuel/air mixtures with the higher temperature plenum and nozzle resulted in a slight preheating. The fuel/air mixtures were measured to reach temperatures between T ≈ 320 and 380 K prior to entering the combustion chamber. The pressure drop between the plenum and the combustion chamber was on the order of 8–9 mbar. Whereas the LDV measurements were performed at the DLR research facility in Berlin, the Raman, LIF, and chemiluminescence measurements were performed at the DLR facility in Stuttgart. The measurement campaigns were performed on different days, and the phase-resolved Raman measurements were performed over several days. The ambient pressure

Table 1 Investigated flames Air 1 2a 2b

CH4

Pth

sl/min

g/min

sl/min

g/min

(kW)

570 570 570

734.2 734.2 734.2

41.8 50.0 45.0

30 35.9 32.3

25.1 30.0 27.0

Φ

f

Tad(295 K) (K)

0.70 0.83 0.75

0.0391 0.0463 0.0418

1834 2037 1915

Note. sl/min means standard liters per minute (standard conditions are 0 ◦ C and 1013 mbar). f is mixture fraction corresponding to the equivalence ratio. Adiabatic flame temperature Tad was calculated for a fresh gas temperature of 295 K.

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

5

Fig. 2. Pressure signals and respective spectra from the plenum and the combustion chamber.

was 995 to 1030 mbar during the LDV measurements and 955 to 985 mbar during the Raman measurements. Because the air and fuel mass flows were kept constant (as stated in the table), the difference in ambient pressure resulted in a difference in flow velocity and density. It should be kept in mind that this might have a small influence on the flame behavior.

3. Pressure pulsations and phase angle assignment The pressure fluctuations were measured with two microphone probes (Brüel & Kjær 4939—1/4 ), one mounted flush with the inner wall of the plenum and the other connected to an air-cooled probe in one of the posts of the combustion chamber at the positions shown in Fig. 1. The pressure signals from the plenum and from the combustion chamber and their respective power density spectra are shown in Fig. 2. The figure shows that the trace of the signal from the plenum is smoother than that from the combustion chamber. As the frequency peaks in both spectra are very pronounced and no shift of the frequency occurs between the two positions, the signal from the plenum was taken as the reference for triggering the phase-locked measurements. The microphone signal was of sufficient magnitude and clarity that no filtering was necessary for accurate triggering. The maximum amplitude of the acoustic pressure in the combustion cham-

ber was determined to be on the order of 1.2 mbar. The acoustic pressure in the plenum was higher by a factor of about 1.4. The measurements further revealed that the pressure variation in the combustion chamber ran ahead of the pressure variation in the plenum by approximately 80◦ . Under the conditions prevailing in the plenum, f ≈ 290 Hz corresponds to a wavelength of λ ≈ 1.2 m; under the conditions in the combustion chamber to λ ≈ 2.8 m. These wavelengths are large compared to the dimensions of the plenum and combustion chamber and the phase differences within the plenum or combustion chamber are on the order of 10◦ –15◦ . In order to adapt the repetition rate of the ICCDcamera system (≈1 Hz) and the pulsed laser systems for Raman (≈5 Hz) and LIF (≈10 Hz) to the oscillation frequency of the flame (f ≈ 290 Hz), a triggering scheme with inhibition times was set up as follows. The negative-to-positive transition of the microphone signal from the plenum triggered a delay generator (SRS, DG535), which itself generated the trigger signal for the laser or the camera systems after a time delay dt1. The inhibition time dt1 was adjusted according to the repetition rate of the laser and camera systems. After the inhibition time had passed, the next negative-to-positive transition of the microphone signal initiated the trigger sequence. In order to carry out the measurements at different phase angles, a delay time dt2 (= 0 to 1/f ) was applied as indicated in Fig. 3 [33]. The delay time dt2 ( 1/f ≈ 3.4 ms) was

6

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

assignment. The minimum pressure in the plenum was arbitrarily assigned as ph1 = 0◦ . Accordingly, the minimum pressure in the combustion chamber was at −80◦ or 280◦ , close to ph7.

4. Measuring techniques 4.1. Laser Doppler velocimetry

Fig. 3. Pressure signal of the plenum with trigger scheme for the pulsed measurements.

Fig. 4. Pressure oscillation compared to a pure sine function; the black curve shows a sine function and the red curve displays the pressure signal of the plenum. The markers ph1–ph8 indicate the assigned phase angles at which measurements were performed. These were ph1 = 0◦ , ph2 = 50◦ , ph3 = 105◦ , ph4 = 150◦ , ph5 = 195◦ , ph6 = 230◦ , ph7 = 270◦ , and ph8 = 315◦ .

small compared to dt1 (≈100 ms) and thus permitted stable operation of the laser system. Measurements were performed at eight phase angles. The assignment of the phase angles was chosen taking the minimum, maximum, and medium pressure values as reference points ph1, ph3, ph5, and ph7, respectively. The additional phase angles, ph2 to ph8, were taken in the (temporal) middle between adjacent phase angles. It should be noted the pressure signal was not perfectly sinusoidal. The phase triggering and the pressure trace are shown in Fig. 4 in comparison to a pure sine wave. It can be seen that the pressure rise (maximum at 195◦ ) was slightly slower than the pressure drop. Due to a permanently present jitter of the frequency on the scale of approx. ±5 Hz (±1.7%), the reference points also jittered by ±1.7%, resulting in a corresponding uncertainty of the phase

The three velocity components were measured simultaneously by LDV using an Ar+ -laser (Coherent, Innova 90) and two orthogonally positioned DantecDISA optics (DISA 55X and DISA flow direction adapter). Commercial camera lenses were used to focus the signals in forward scattering onto three photomultiplier tubes. Signal recording and pretreatment were performed with Dantec BSA enhanced units (57N20 + 57N35). The seeding particles (TiO2 , d ≈ 0.8 µm) added to the air flow were small enough to follow the large-scale turbulence up to >1 kHz [35]. In order to link the velocity signals to the pressure fluctuations, the BSA units additionally recorded trigger events that were created by the positive zero crossing of the pressure signal from the plenum. In a postprocessing step, the velocity signals were assorted according to their arrival times into 72 phases (steps of 5◦ ) each covering a 10◦ window (±5◦ ). The measurements were performed in one vertical plane along radial profiles at the heights h = 1.5, 5, 15, 25, and 35 mm in order to capture the flow field, especially at the nozzle exit. The radial spacing was r = 1 mm at h = 1.5 mm and 2 mm at the other heights. At each position 100,000–200,000 velocity data were recorded. The resulting probe volumes were about 60 µm in diameter and 1.0 mm in length for axial (u) and radial (v) velocity components and 120 µm and 1.5 mm for the tangential (w) direction of the velocity. The sorted velocity data were selected according to the phase assignment (ph1–ph8) explained above (Fig. 4). The uncertainty of the velocity measurements for each phase is typically 1.5–2% for the mean value and 2–2.5% for the rms value. 4.2. OH* chemiluminescence detection OH* chemiluminescence was imaged using an intensified CCD camera (Roper Scientific) equipped with an achromatic UV lens (f = 100 mm, f/2, Halle Nachf.) and an interference filter with high transmission between 295 and 342 nm (Laser Components GmbH). The plane of focus of the system was located at the center of the combustion chamber. Although image sharpness decreased with increasing distance from this plane, lines separated by 1 mm could still be resolved at the forward and rear windows of the

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

chamber. Sets of 100 images (exposure time 130 µs) were accumulated at each of the eight phase angles outlined above. OH* chemiluminescence intensities from lean premixed flames represent an indicator for the heat release rate [20,21], but the correlation between OH* chemiluminescence and heat release rate may be influenced by multiple parameters and is still subject to research [6,36]. Thus from these images only qualitative information can be deduced about the phase-dependent variations in heat release and the location and extension of the flame zone. Even though this technique is line-of-sight integrated, spatially resolved information can be gained by deconvolution, taking advantage of the rotational symmetry of the flame. This results in a quasi 2-D image of the center plane where the local distribution of the chemiluminescence can be identified more clearly than in the integral view. 4.3. Planar laser-induced fluorescence of OH PLIF of OH radicals was applied to visualize the flame structures. A pulsed Nd:YAG-pumped dye laser was used to supply pulsed laser radiation for the excitation of OH on the R2 (13) line of the A2 Σ + –X 2 Π (ν  = 1, ν  = 0) transition at λ = 282.6 nm. The beam was formed to a vertical sheet (h ≈ 55 mm) and directed into the combustion chamber intersecting the flame axis. The pulse energies at the measuring location were typically 1.5 mJ/pulse with a band width of about 0.45 cm−1 and a duration of 5 ns. The sheet thickness was approximately 0.8 mm in the imaged area. The resulting spectral laser intensities were on the order of 1.5 MW/cm2 cm−1 . Considering that the saturation intensity is around 1 MW/cm2 cm−1 , the applied laser intensities may have resulted in a small degree of saturation (which is mostly unimportant for the structural information gained from the PLIF images). The excited fluorescence signal was collected at 90◦ by an achromatic UV lens (f = 100 mm, f/2, Halle Nachf.) equipped with an interference filter (λ ≈ 295–342 nm) and detected by an intensified CCD camera (LaVision Flamestar II, 286 × 384 pixels). The temporal detection gate of the image intensifier was 50 ns. The spatial resolution of the measurement is mainly limited by the thickness of the laser sheet (0.8 mm). In the other two directions, i.e., in the image plane, the spatial resolution is on the order of 0.3 mm. 4.4. Laser Raman scattering For the pointwise quantitative measurement of the major species concentrations (O2 , N2 , CH4 , H2 , CO, CO2 , H2 O) and the temperature, laser Raman scattering was applied [37]. The radiation of a flashlamp-

7

pumped dye laser (Candela LFDL 20, wavelength λ = 489 nm, pulse energy Ep ≈ 3 J, pulse duration τp ≈ 3 µs) was focused into the combustion chamber and the Raman scattering emitted from the measuring volume (length ≈ 0.6 mm, diameter ≈ 0.6 mm) was collected by an achromatic lens (D = 80 mm, f = 160 mm) and relayed to the entrance slit of a spectrograph (SPEX 1802, f = 1 m, slit width 2 mm, dispersion ≈ 0.5 nm/mm). The dispersed and spatially separated signals from the different species were detected by individual photomultiplier tubes (PMTs) in the focal plane of the spectrograph and sampled using boxcar integrators. The species number densities were calculated from these signals using calibration measurements and the temperature was deduced from the total number density via the ideal gas law [37]. The simultaneous detection of all major species with each laser pulse also enabled the determination of the instantaneous mixture fraction [38]. In the data sets the mixture fraction defined by Bilger [39,40] is used. Due to restrictions of the optical access of the Raman setup, measurements could not be performed for h < 6 mm and r > 30 mm. In the pulsating flame, phase-resolved measurements were performed at h = 6, 15, 25, 35, and 60 mm over a scan pattern of 50 points altogether. The radial spacing was r = 2 mm at h = 6 mm, r = 3 mm at h = 15 mm, r = 4 mm at h = 25 and 35 mm, and r = 5 mm or 10 mm at h = 60 mm. At each point in the scan pattern 400 single-shot measurements were acquired. These data were used to compute joint probability density functions (PDF). At some locations, where turbulent or phase-dependent fluctuations were very small (especially in the outer region of the flame), less than 400 samples were recorded. In the pulsating flame, Raman measurements were also performed without phaselocking; i.e., the measuring system was triggered at random phase angle. In this case, measurements were performed at h = 6, 10, 15, 20, 30, 40, 60, and 80 mm, and 500 single-shots were taken at each location. In the quiet flame Raman measurements were performed at h = 6, 10, 15, 20, 30, 40, 60, and 80 mm (500 shots at each location). Signal interferences from C2 and PAHs were very low in the flames investigated and there was little need for correction procedures. Nonetheless, the signal background was recorded by additional PMTs in Raman-free spectral regions and the few samples with significant background were filtered out in the data reduction routine. Single-shot measurements with PMT saturation or unrealistic C/H or N/O ratios were also discarded during data evaluation. Thus, the final data sets do not always contain 400 (or 500) single-shot realizations. For the phase-resolved measurements in the pulsating flame the percentage of discarded sam-

8

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

Table 2 Summary of the measurement uncertainties (for details see text) Measured quantity

Systematic uncertainty

Statistical uncertainty

Measuring location h, relative Measuring location h, absolute Measuring location r, relative Measuring location r, absolute Velocity Temperature Mixture fraction H2 O mole fraction O2 mole fraction CO2 mole fraction CO mole fraction H2 mole fraction CH4 mole fraction

±0.1 mm ±0.5 mm ±0.1 mm ±0.5 mm <0.5% ±3–4% ±3–4% ±3–5% ±3–5% ±3–5% ±5–10% ±5–10% +5–9%

±1.5–2% ±2.5% ±1% ±3% (density-dependent) ±7% (density-dependent) ±7% (density-dependent) ±20–50% (density-dependent) ±10–30% (density-dependent) ±1–3% (density-dependent)

ples was 3.5% in the worst case (at h = 6 mm, r = 10 mm) and on average it was below 0.6%. For the measurements without phase resolution in the pulsating flame, the percentage of discarded samples was 4.8% in the worst case (at h = 6 mm, r = 6 mm) and on average it was below 1.2%. For the measurements in the stable flame the worst case was 4.4% (h = 6 mm, r = 10 mm) and the average percentage of discarded samples was smaller than 0.7%. A significant bias of the joint PDFs due to filtering was not observed. For example, in the worst case in the pulsating flame, the mean values of T , f , and the mole fractions of the major species changed by less than 0.5% due to filtering. With respect to measurement uncertainties, one must distinguish between systematic errors arising from, for example, uncertainties in the calibration procedure and statistical errors that are mainly caused by the statistics (shot noise) of the detected Raman photons NP in a single-shot measurement. Systematic uncertainties were typically ±3–4% for the temperature and mixture fraction, ±3–5% for the mole fractions of O2 , H2 O, and CO2 , and ±5–10% for H2 and CO. The systematic errors are largely independent of the mole fraction and temperature in the flame. In the measurements reported here, it turned out that the evaluated CH4 mole fractions were systematically too large by about 7%. In regions with significant amounts of CH4 the measured mixture fraction was therefore also biased to larger values (up to ≈7%). The statistical uncertainties were quantified by recording single-shot data sets in stable laminar flames. The rms fluctuations in these flames were, for example, 2.5% for T at T = 1916 K, 3.2% for H2 O at a mole fraction of X(H2 O) = 0.19, 7% for O2 at X(O2 ) = 0.06, 7.4% for CO2 at X(CO2 ) = 0.068, and 1% for the mixture fraction. In an electrically heated flow of pure CH4 the rms value was 1% at 850 K. To a good approximation the rms fluctuations

scale with NP−0.5 . Due to this dependence, the statistical uncertainties are quite large for CO and H2 . The cross talk correction for CO leads to an additional error source, so that the statistical error for CO is 20– 50%. The uncertainties are summarized in Table 2. The statistical uncertainty due to shot noise of detected signal photons is only relevant for single-shot measurements. For the mean value from a PDF comprising 500 single-shot measurements, shot noise is negligible because the number of signal photons for the complete PDF is 500 · NP . Systematic and statistical uncertainties are largely independent of each other. A further uncertainty concerns the number of single-shot measurements necessary to reproduce the true PDF. This question cannot be answered in general because the necessary number of samples depends on the shape of the true PDF. To estimate the uncertainty a measured PDF can be used, and the convergence of, e.g., the mean value with the number of samples can be considered. It turned out that in regions with strong turbulent fluctuations the final mean value is typically reached to within 2% after 300 samples. A number of 400 to 500 single shots at each location thus seems a good trade-off between measuring time and convergence.

5. Results 5.1. Time-averaged velocity distributions Fig. 5 shows plots of the combined mean u and v velocity components of the pulsating and quiet flames. For most of the measuring heights in the pulsating flame, data were taken only on one side of the flame axis, because of the assumption of axial symmetry. In Fig. 5 the profiles in the upper panel (pulsating flame) are mirrored to yield a better impression

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

9

Fig. 6. Radial profiles of the mean axial velocity of the pulsating and the quiet flame at h = 1.5 mm.

flame is subject not only to turbulent fluctuations but also to periodic variations of the flow field. This will be considered in the following section. Fig. 5. Vector plot of combined mean u and v velocity components of the pulsating and the quiet flame. Negative velocities are displayed in red.

of the flow field. Three different flow regions can be distinguished: (1) The inlet flow of fresh gases which is conically shaped; (2) an inner recirculation zone (irz); and (3) an outer recirculation zone (orz). It is seen that the inflow of the quiet flame is more widely opened and exhibits a broader irz in comparison to the pulsating flame. Slight deviations from axial symmetry are seen in the profiles of the quiet flame within the irz. Similar deviations can be found in the profiles of the other velocity components and of the rms fluctuations. These deviations are not explained by the measurement uncertainty and are probably real. However, the effects are small and are neglected in the further discussion. The velocities of the reverse flow are higher in the pulsating than in the quiet flame. This can be seen more clearly in the radial profiles of Fig. 6, displaying the mean axial velocities at h = 1.5 mm. The irz of the pulsating flame extends to r ≈ 4 mm at this height and reaches a mean axial velocity of u ≈ −24 m/s. The quiet flame has negative axial velocities of up to u ≈ −10 m/s and its irz extends to r ≈ 6 mm at h = 1.5 mm. The mean axial velocity of the inflow is on the order of 35 m/s for both flames, but the radial region of the inflow is broader for the pulsating flame. The outer recirculation zones are characterized by very low axial velocities and radial velocities that are directed to the flame axis. From Figs. 5 and 6 it is clear the mean flow fields of the two flames exhibit significant differences. However, it should be kept in mind that the pulsating

5.2. Phase-resolved velocity distributions The phase-dependent variations of the mean axial, radial, and tangential velocity components are displayed in Fig. 7 for the heights h = 1.5, 5, 25, and 35 mm. It is clearly seen that the flowfield varies drastically during an oscillation cycle. The profiles of umean near the nozzle (h = 1.5 and 5 mm) show that the irz changes strongly in radial expansion and velocity with a maximum expansion around ph5 and a minimum expansion around ph1. Accordingly, the radial extension of the inflow varies between r ≈ 9 mm (ph5–ph7) to r ≈ 14 mm (ph2). In the outer radial region the axial velocities are very small. At h = 5 mm the variations of umean are still prominent and at h = 25 mm they have become relatively small but at h = 35 mm differences again become apparent. The radial velocity component is significantly smaller than the axial component and the periodic variations of vmean are not generally in phase with umean . At h = 1.5 and 5 mm, vmean is positive (i.e., directed outward) out to r ≈ 15 mm and r ≈ 17 mm, respectively, and becomes negative further outside. The negative values of vmean characterize the outer recirculation zone. In contrast to umean , the variations of vmean become stronger further downstream, as can be seen in the radial profiles at h = 25 and 35 mm. At h = 25 mm the injected gases are rapidly moving outward at around ph2 (vmean > 25 m/s), but vmean becomes rather small around ph7. At 10 mm further downstream (h = 35 mm) the flowfield looks quite different: now vmean is very small at ph2 and the maximum occurs at ph4. Considering the variation of the flowfield near the nozzle, the fast radial movement at h = 25 mm is associated with a broad inflow and vice

10

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

Fig. 7. Phase-resolved radial velocity profiles of mean axial (u), radial (v), and tangential (w) velocity components at h = 1.5, 5, 25, and 35 mm. Note the different scales at the axis.

versa. The tangential velocity component w exhibits significant phase-dependent variations for all measuring heights. At h = 1.5 mm maximum values around 35 m/s and steep gradients of wmean are observed. With increasing height the profiles flatten and become broader. At h = 35 mm the maximum wmean is around 12 m/s. Near the nozzle (h = 1.5 and 5 mm), wmean and umean are quite well in phase with respect to radial extension and amplitude; however, wmean is quite low in the irz, independent of phase angle. The profiles of wmean reflect neither a solid body rotation near the axis (where w would linearly increase with r) nor a potential vortex further outside (where w would decrease as 1/r).

The pumping motion of the flowfield is of course related to the pressure variations in the combustion chamber and the plenum. However, the details of this relationship depend on the geometry of the nozzle, the acoustic behavior of the configuration, and the temperature distribution. In a very simplified approach, assuming the inflow is influenced only by the pressure variation in the combustion chamber (pchamber ) and that the pressure has a sinusoidal temporal variation, the axial velocity of the inflow would behave according to du/dt ∼ −pchamber . In this simplified approach one would expect the velocity to reach its maximum 90◦ after the pressure minimum in the combustion chamber. The pressure minimum in the

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

11

Fig. 8. Imaged chemiluminescence intensity distribution at eight different phase angles. Each image was averaged over 100 shots with an exposure time of 130 µs each. Scales are in mm.

combustion chamber is around ph7 (−80◦ or 260◦ ) and from the simplified approach one would then expect high inflow velocities in the nozzle around ph1, which is in qualitative agreement with the measurement. Naturally, the real situation is much more complex, but a quantitative analysis is beyond the scope of this work.

5.3. Phase-resolved OH* chemiluminescence Fig. 8 shows the mean OH* chemiluminescence field measured at each of the eight phase angles studied. Each field represents the ensemble average of 100 images and each image was acquired with a 130-µs exposure time. Fig. 8 clearly shows that the intensity

12

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

It should be noted that the very high intensities at the wall and also the large gradients are an artifact of the Abel inversion routine [41]. Due to the sharp cutoff at the wall, the gradient is overestimated by the program. However, for ph2–ph4, there are high chemiluminescence intensities at h ≈ 40–60 mm that represent the largest contribution to the integrated chemiluminescence (see Fig. 9). 5.4. Phase-resolved OH PLIF distributions

Fig. 9. Fig. 9: Normalized integrated OH chemiluminescence and normalized pressure variation in the combustion chamber.

varies significantly during an oscillation cycle, with a maximum close to ph3 and a minimum half a period later. The chemiluminescence distributions resemble, of course, the photo of the flame in Fig. 1. The dark regions near the nozzle are associated with the inflow of the fresh gases, but include also the orz. It can further be seen that combustion is already taking place at h = 0 for all phase angles and that the flame root extends to h < 0. At ph1 to ph4 the main region of heat release is at h ≈ 40–60 mm and r  20 mm. In these images it has to be considered that the chemiluminescence is integrated along the line of sight. More details of the structure will be discussed on the basis of the deconvoluted images below. The OH* chemiluminescence intensity integrated over the imaged area is displayed in Fig. 9 as a function of phase angle together with the pressure variation in the combustion chamber. It is seen that the integrated chemiluminescence varies between 16 and 100% and that this variation is quite well in phase with the pressure variations. Provided the integrated chemiluminescence represents the total heat release rate, the result demonstrates that the Rayleigh criterion for self-sustained combustion pulsations is fulfilled. The deconvoluted chemiluminescence distributions corresponding to the images in Fig. 8 are displayed in Fig. 10. These represent quasi-2D cuts through the flame provided that cylindrical symmetry is present. Here, the phase-dependent changes of the flame shape can be seen more clearly. The flame is anchored near the central bluff body at h  0 mm and for lower heights (h < 30 mm) combustion is only taking place in the central region where r < 20 mm. At the base of the flame the chemiluminescence intensity is highest around ph1–ph3, when the reverse flow increases strongly. Throughout most of the oscillation cycle the flame is hitting the wall (located at r = 42.5 mm) further downstream at h ≈ 30–70 mm.

Fig. 11 shows examples of single-shot OH PLIF images recorded in the pulsating flame at four different phase angles. Before the results are discussed, a few explanations about OH concentrations in flames should be given. At chemical equilibrium, the OH concentration increases exponentially with temperature. The increase is, however, different for fuellean and fuel-rich mixtures [42]. In fuel-lean mixtures, OH concentrations are detectable above T ≈ 1400–1500 K, while in fuel-rich mixtures, the OH equilibrium concentrations are significantly lower and barely detectable by LIF below 1900 K. However, in reaction zones, OH is formed in superequilibrium concentrations, which in turbulent flames are typically several times higher than at equilibrium. The lifetime of this superequilibrium OH is several milliseconds at atmospheric pressure. Thus, the highest OH concentrations within a PLIF image stem probably from superequilibrium OH, i.e., “young” OH that has just been formed in a reaction zone. Medium OH concentration levels are typical of high-temperature regions with “old” OH at chemical equilibrium. The R2 (13) line was used for excitation because two-line OH PLIF thermometry measurements were also conducted within this experiment (not reported here). The second excitation line for those measurements was the P1 (2) line [43]. For the R2 (13) line the Boltzmann fraction fB of the initial state changes significantly with T ; for example, it increases by about 72% between 1500 and 2200 K. However, the quenching rate also increases with T , and a calculation using LASKIN [44] showed that the fluorescence quantum efficiency QE decreases by ≈37% from 1500 to 2200 K for an exhaust gas composition from stoichiometric combustion. Without taking variations of the gas composition into account, the net effect from changes in fB and QE yields a variation of about 30% over the temperature range considered. Within this limit, the displayed OH LIF signals are representative of the OH density. The single-shot images in Fig. 11 are dominated by turbulent fluctuations and do not well reflect the phase-dependent variations which are identified in the ensemble-average images (discussed below). In the image recorded at ph1, the region around the flame

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

13

Fig. 10. Abel-transformed OH chemiluminescence images corresponding to the distribution of Fig. 8.

axis shows medium OH LIF intensities (blue color) which most probably reflect “old” OH at rather high temperatures. On each side of this region there are high OH LIF intensities (yellow and red) from h = 0 to 20 mm. These stem presumably from “young” OH, i.e., from reaction zones and burnt gases next to the reaction zones. The low intensity regions farther outside

(black) have to be interpreted as fresh gas or mixtures of fresh gas with some exhaust gas at temperatures below 1400 K. In the outer recirculation zones the LIF intensities are quite low (violet) probably reflecting “old” OH at intermediate temperatures. The OH LIF distribution and the interpretation given are consistent with the deconvoluted chemiluminescence

14

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

Fig. 11. Examples of single-shot OH PLIF images at four different phase angles. Scales at axes are in mm; color bar is given in arbitrary units.

images displayed in Fig. 10, which show a flame region in the area where high OH LIF intensities are present. The single-shot image at ph5 shows high OH LIF intensities on the flame axis, again in agreement with the deconvoluted chemiluminescence image. At ph7, the OH LIF distribution shows quite nicely the inflow of the fresh gases (dark area). Considering the structures within the single-shot samples, one can see the wrinkled and convoluted boundary layer between the different regions of the flow field, for example between the irz and the inflow of fresh gases. The ensemble averaged OH PLIF distributions are presented in Fig. 12 for the eight phase angles studied. It is seen that the highest mean OH LIF intensities are found in the irz, especially below h ≈ 30 mm, and that this region is surrounded by a low-intensity layer, indicative of the inflow of fresh gases. Also, at ph3 and ph4, high intensities occur near the combustor wall at h > 20 mm. In these averaged images the contribution from superequilibrium OH and “old” OH can hardly be distinguished. Only with the additional information from the deconvoluted chemiluminescence images can it be stated that the high LIF intensities are well correlated with the flame zones. Noticeable phase-dependent differences are clearly seen in the shapes of the irz (high OH LIF levels) and the inflow (very low LIF intensities). Around ph8, the inflow exhibits a curved shape (resembling bullhorns) with a bow around h = 30 mm. This bow is very prominent at ph1 (at h ≈ 30 mm) and collapses

during the transition to ph2. The drastic change of the radial velocity component between h = 25 and 35 mm at these phase angles also underlines the significant phase-dependent change of the flame at this location. 5.5. Correlation between temperature and mixture fraction at random phase From the simultaneous measurement of the temperature and the species concentrations by laser Raman scattering, the correlations between different quantities can be derived which contain the information about the thermochemical state of the flame. The scatterplots in Fig. 13 show the correlation between temperature and mixture fraction for the quiet and pulsating flame, measured without phase correlation. Each symbol represents the result from a single-shot measurement recorded at various radial locations at h = 6 mm. The different colors help to identify different radial regions of the flame. The solid line is the result of a strained laminar flame calculation for a counterflow diffusion geometry with a strain rate of a = 1 s−1 [45,46], which represents a state close to chemical equilibrium. The scatter in mixture fraction demonstrates that the premixing is not perfect and that there are variations between f ≈ 0.03 and 0.07 for the quiet flame and between f ≈ 0.015 and 0.08 for the pulsating flame (it should be kept in mind that f is biased by about +7% for cold samples).

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

15

Fig. 12. Phase-resolved averaged OH PLIF distributions at eight phase angles. Notice the slightly different color bar compared to Fig. 11. Images are averaged over 200 single shots.

There are a lot of samples at room temperature that have not reacted yet, mainly from the radial region r ≈ 12–16 mm. In the inner recirculation zone the gas is close to equilibrium with high temperatures. The samples from the outer recirculation zone exhibit only a low scatter in mixture fraction around fglob. and their temperatures lie below the calculated curve.

This temperature reduction is probably due to heat loss to the burner plate. In addition the scatterplots contain many samples with intermediate temperatures (i.e., between room temperature and flame temperature). These partially reacted gas mixtures stem either from local flame extinction events or from the mixing of cold and hot gases that have not reacted yet

16

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

Fig. 13. Correlation between temperature and mixture fraction for the quiet flame (left) and pulsating flame (right). Symbols represent single-shot Raman measurements; the line shows a calculated curve for a near-equilibrium state. The global mixture fractions of the flames are indicated by the vertical lines; the stoichiometric mixture fraction is f = 0.055.

due to ignition delay [26]. Comparing the two scatterplots, the major difference lies in the degree of unmixedness of fuel and air. The phase-resolved Raman measurements will be considered further below to determine whether the poorer mixing of the pulsating flame stems from the thermoacoustic pulsations. Fig. 14 illustrates the development of the scatterplots for the two flames with increasing downstream position. As expected, the mixing and reaction progress increases with downstream position, but partially reacted mixtures are still present at h = 30 mm. The reaction progress is slightly faster for the quiet flame. This may be caused by the higher equivalence ratio of this flame and hence the higher temperature. Burnout is complete in the quiet flame at h ≈ 40 mm and in the pulsating flame at h ≈ 60 mm (not displayed). It is further seen that unmixedness persists longer for the pulsating flame, so that near-stoichiometric mixtures are still present at h = 30 mm. Finally, at h = 80 mm, mixing and reaction are complete and the thermochemical state of the flames is very close to equilibrium. The samples displayed in the scatterplot of the quiet flame correspond to a standard deviation of the mixture fraction of 3.3% and of the temperature of 3.5%, which is largely caused by the inherent uncertainty of the measurement. 5.6. Mean temperature and mixture fraction distributions at random phase In order to compare the mean (Reynolds-averaged) mixture fraction distributions of the quiet and pulsating flames, Fig. 15 displays 2D charts of f . Here, the mean values measured at the different locations were interpolated using the program “Origin” to yield quasi two-dimensional distributions. The scales for f are not chosen to be identical because the global mixture fractions are not identical. However, both scales reach

from minimum to maximum f -values in each distribution. For the quiet flame the mean mixture fraction varies by f = 0.0048 between fmean = 0.0465 and fmean = 0.0513, and for the pulsating flame by f = 0.0114 between fmean = 0.0361 and fmean = 0.0475. This demonstrates again the different degrees of unmixedness of the two flames. In the quiet flame, high f -values are seen in the region of the inflow, and the irz and orz are relatively lean. Here it must be considered that according to the systematic measurement error of approx. +7% for CH4 the evaluated mixture fraction is also biased to higher values, especially in low-temperature regions. With increasing temperature the CH4 mole fraction and the bias of f decrease. In the pulsating flame, the mean f distribution reveals a separation of relatively rich and lean gases within the inflow with the lean gases appearing at the outer side of the inflow. In order to understand this behavior, the phase-dependent variations of f must be taken into account. This will be done further below. For both flames the measured f -values were slightly higher than expected from the fuel and air flow rates. For example, at h = 60 mm in the quiet flame, the measurements resulted in an average value of f ≈ 0.0473 in comparison to fglob. = 0.0463 and at h = 60 mm in the pulsating flame, the measured average was f ≈ 0.041 in comparison to fglob. = 0.0391. This deviation might be caused by an error of the flowmeters, possibly together with a systematic deviation of the Raman measurement. One must also consider that the cross section of the combustion chamber covered by the Raman measurements (r = 0–30 mm) is only 39% of the total cross section (85 × 85 mm), so the average gas composition deduced from the Raman measurements does not necessarily reflect the volume-averaged value. The corresponding temperature distributions are displayed in Fig. 16. The lowest temperatures are, of course, measured in the inflow of the fresh gases

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

17

Fig. 14. Scatterplots of temperature versus mixture fraction for the quiet and pulsating flames at h = 15, 30, and 80 mm.

and thus these distributions also visualize the average shape of the inflow. It can be seen that the quiet flame exhibits a larger opening angle than the pulsating flame, consistent with the velocity distributions shown in Fig. 5. The temperature level in the quiet flame is, as expected, higher than that in the pulsating flame, primarily due to the different equivalence ratios. The mean temperature gradients are steeper in the quiet flame and this flame reaches a homogeneous temperature distribution at lower heights than the pulsating flame does. From the mean mixture fraction and temperature distributions one gets the impression that the structures in the pulsating flame are more smeared out than in the quiet flame. This might be attributed to the periodic movement of the flowfield.

5.7. Correlation between temperature and mixture fraction at different phase angles Fig. 17 displays T –f scatterplots at h = 6 mm. Again, each symbol represents the result of a singleshot measurement and the solid curve shows adiabatic equilibrium. Colors are used to distinguish between different zones, i.e., the irz, the shear layer between the irz, and the inflow of fresh gases, the inlet flow, and the orz. Because these regions cannot be separated sharply, the colors serve more as a guide. It can be seen that the cyclic variations in the irz (r  4–6 mm) and the orz (r  16 mm) are relatively small and that these samples reflect reacted hot exhaust gas. Within the inflow and the neighboring

18

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

Fig. 15. Distributions of mean mixture fraction (Reynolds-averaged) constructed from interpolations of the Raman point measurements. The results from the pulsating flame (right-hand side) have been recorded without phase triggering.

Fig. 16. Distributions of mean temperature constructed from interpolations of the Raman point measurements. The results from the pulsating flame (right-hand side) have been recorded without phase triggering.

shear layers, large changes of temperature and mixture fraction are observed. The majority of the samples from this region have not reacted (T ≈ 300 K), a significant number have partially reacted, and some have completely reacted. Astonishing are the large cyclic variation and the scatter of f , reaching from f ≈ 0.015 (ph2–ph3) to f ≈ 0.1 (ph7–ph8). These results indicate that the periodically changing pressure in the combustion chamber has different impacts on the fuel and air supply lines in such a way that more fuel (or less air) enters the combustion chamber around phases 7 and 8. The variations of f dimin-

ish with increasing height but are still observable at h = 35 mm. 5.8. Mean temperature and species distributions at different phase-angles The phase-dependent variations of the mean values of f , T , and the mole fractions of CH4 and O2 at h = 6 mm are displayed in Fig. 18. A striking feature is the dramatic cyclic change of the mean mixture fraction within the inflow. From ph1 to ph6 the shapes of the radial profiles are quite similar, with a shallow

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

Fig. 17. Phase-resolved scatterplots of temperature versus mixture fraction at h = 6 mm.

19

20

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

Fig. 18. Radial profiles of the mean values (Reynolds averaged) of the mixture fraction, temperature, and mole fractions of CH4 and O2 at h = 6 mm at different phase angles.

bump at r ≈ 5–10 mm and a dip at r ≈ 16 mm. At ph7 and ph8, the profiles exhibit a completely different shape, resembling a burst in comparison to the other profiles, and fmean exceeds even the stoichiometric mixture fraction (fstoich. = 0.055). The corresponding profiles of the CH4 mole fraction reveal that at these phase angles high concentrations of CH4 are injected into the combustion chamber. The maximum mean CH4 mole fraction, measured at r = 15 mm at ph8, is 0.116 (taking into account the measurement bias of 7%, it would be 0.108). In comparison, at Φ = 0.7 the mole fraction of CH4 in the unburned premixed gas would be 0.0685. The lowest CH4 concentrations were measured at ph4 and ph5, where maximum mole fractions were about 0.05. The profiles of O2 are quite different from those of CH4 : the maximum value of the profiles does not change much with phase angle and lies between 0.18 and 0.196. However, the width of the O2 -profile changes significantly during the oscillation cycle with a maximum around ph7 and ph8 (halfwidth r ≈ 9 mm) and a minimum around ph3 and ph4 (r ≈ 4 mm). The profiles of f show a qualitative correspondence with the CH4 profile but not with the O2 profile, so it can be concluded that the mixture fraction is mainly influenced by the fuel flow variations. The corresponding

temperature profiles reveal large periodic variations of T between r ≈ 7 mm and 15 mm. In the orz no changes are observed and in the irz, for r  5 mm, the changes are small. These profiles correspond well with the profiles of O2 : at low temperatures the O2 mole fractions are large and they decrease with increasing T , as expected. 5.9. Estimation of phase-dependent gas flow rates into the combustion chamber From the results considered so far, it is clear the velocities, temperature, and species concentrations vary with phase angle. Now an estimation is presented for the phase-dependent variations of the fuel and air flows into the combustion chamber. Therefore the molecular fluxes (number of molecules flowing through an area per time) of CH4 and O2 are considered. The instantaneous molecular flux Si of a species i through the nozzle is the product u · ni integrated over the area of the nozzle, where ni is the molecular number density of the species i and u is the axial velocity of the gas. These quantities change with time and location and in order to determine Si , all quantities must be measured simultaneously over the entire area at h = 0. As this was not possible, the

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

21

Fig. 19. Approximated molecular fluxes of CH4 and O2 into the combustion chamber and simplified pressure traces as a function of phase angle.

following approximation was made: For each measuring location and phase angle, the mean values of ni (ni,mean ) and u (umean ) were used, with ni taken from the Raman measurements at h = 6 mm and u from the LDV measurements at h = 5 mm. Cylindrical symmetry was also assumed for the flow. Then Si,mean (r) was integrated over the area of the inflow (from r = 6 to 16 mm) for each phase angle by multiplying ni (r) · u(r) at each measuring location r with the area of an annulus around r with inner radius ri = r − 1 mm and outer radius ro = r + 1 mm. Finally, the total flux Si was determined by summing over all annuli. Of course, there are some crude simplifications in this calculation that must be considered: (1) The assumption of cylindrical symmetry of the flame was confirmed by taking images of the flame from various directions with respect to the square combustion chamber. The images did not reveal a difference in flame diameter, so that the assumption of cylindrical symmetry appears justified. (2) There were differences in height between the Raman measurements (h = 6 mm) and the LDV measurements (h = 5 mm). From the mean flow field it was estimated that the flow expands by less than 0.5 mm from h = 5 to h = 6 mm in the radial direction and that the changes in axial velocity are negligible. Therefore the error from this approximation is also quite small. (3) Using the mean values of n and u for the calculation of S instead of the instantaneous ones is only correct if n and u were statistically independent. This is certainly not generally the case in this flame. However, within the inflow u is not expected to depend significantly on gas composition, at least with respect to the ratio CH4 /O2 , which will be considered here. As an error analysis is unfeasible in this case, the results concerning the fluxes should be considered only an approximation. With this in mind, some important trends can

be identified. The fluxes of O2 and CH4 calculated in this way are shown in Fig. 19 together with simplified pressure traces from the combustion chamber and the plenum. It is clearly seen that the approximated molecular flux into the combustion chamber changes significantly over an oscillation cycle and that CH4 and O2 vary in phase with one another. Both reach a pronounced maximum at phase 8 (315◦ ). The calculated CH4 flux varies by a factor of 5.0 and the O2 flux by 2.42. For comparison, the integrated chemiluminescence intensity varied by a factor of 6.25. This is mentioned because there are grounds for supposing that the chemiluminescence intensity and the fuel supply rate are correlated. The pressures in the plenum and the combustion chamber are out of phase by ≈80◦ , as explained earlier, and it is clear that the average pressure in the plenum is higher than that in the combustion chamber (by about 8 mbar). However, the traces shown in Fig. 19 and the displayed pressure difference (p = pplenum − pcombustion chamber ) are simplified in this graph. Comparing p and the fluxes, it is seen that the maximum flux is reached about 100◦ after the maximum of p. This value is close to 90◦ , which would be expected at the nozzle exit for a sinusoidal pressure variation in a configuration where only the pressure difference determines the inflow. The ratio (O2 flux/CH4 flux) is related to the equivalence ratio Φ and would be a direct measure for Φ if no combustion occurred below h = 6 mm. For Φ = 0.7 the ratio would be 2.86, which occurs in Fig. 19 around the phase angles 10◦ and 220◦ . The fact that the ratio changes between 1.84 (phase 8) and 4.02 (phase 3) is evidence of a different response of the air and fuel supply lines to the pressure variations in the combustion chamber and plenum. From the observed variation of the O2 flux it becomes apparent that the air flow is subject to similar variations within

22

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

the swirl generator and nozzle. If the CH4 injection within the swirler varied with the same relative amplitude as the air flow, the measured ratio O2 flux/CH4 flux would be constant over the period of oscillation. This is inconsistent with the experimental result. However, considering that CH4 is injected with high momentum into the air within the swirler, it can be assumed that the fuel line is less sensitive to the pressure variations than was the air supply. With this assumption, the qualitative explanation for the varying equivalence ratio is as follows: When the flow velocity of the air in the swirler is small due to a small p (around ph2), relatively large amounts of CH4 accumulate in the slowly flowing air. When p rises, this fuel-rich mixture is accelerated and enters the combustion chamber, leading to increased flow rates of air and CH4 at h = 6 mm. This represents the first step of the feedback loop known as oscillating fuel supply combined with a convective time delay [29, 47,48]. 5.10. Distributions of f , CH4 , and T at different phase-angles Fig. 20 shows the mixture fraction distribution for the eight phase angles studied. Again, the mean values of f measured at the different locations were interpolated using the program “Origin” to yield quasitwo-dimensional distributions. As the measurements were performed at h = 6, 15, 25, 35, and 60 mm, the interpolation is quite coarse in the upper part of the plots. It can be clearly seen that at ph7 and ph8 fuelrich mixtures are injected and that these are convected downstream as the oscillation proceeds. Assuming an average axial velocity of u ≈ 30 m/s, the gas is convected about 104 mm during the oscillation period of 3.45 ms, or 13 mm within 45◦ . This is in qualitative agreement with the observed development of the fuelrich region between ph7 and ph2. The next question to be addressed is where the CH4 is consumed. Fig. 21 displays the 2D distributions of CH4 corresponding to the distributions of f from the previous figure. The plot shows that the increase of CH4 mole fraction near the nozzle begins at ph5 and continues until ph8. The CH4 plume also increases in size, is convected downstream, and reaches its largest size around ph2. The region with r > 30 mm is not captured by the Raman measurements, but there are certainly significant CH4 concentrations beyond this radial position. From ph2 on, the CH4 concentrations are drastically reduced, i.e., CH4 is burnt. This observation is in good agreement with the OH chemiluminescence measurement, which exhibits a maximum around ph3. The corresponding pressure increase in the combustion chamber decelerates the inflow into the combustion chamber and

Fig. 20. Interpolated 2D distributions of the mixture fraction for eight phase angles from Raman measurements at h = 6, 15, 25, 35, and 60 mm.

initiates the creation of the next fuel-rich gas pocket in the swirler. The phase-dependent changes of the temperature distribution are displayed in Fig. 22. The temperature

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

Fig. 21. Interpolated 2D distributions of the CH4 mole fraction for eight phase angles.

distribution is closely related to the CH4 distribution in such a way that high concentrations of CH4 correspond to low temperatures and vice versa, as expected. The depletion of CH4 beginning at ph2 goes along with an increase in temperature. The tempera-

23

Fig. 22. Interpolated 2D distributions of the temperature for eight phase angles.

ture distributions show further that the orz exhibits a significant lower temperature than the irz for all phase angles. With respect to the low temperatures reflecting the inflow, it is seen that this region undergoes a significant change in shape from a cone with a rather small opening angle at ph1 to one with a large opening

24

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

angle at ph6. From this movement it becomes clear that the time-averaged temperature distribution from Fig. 16 appears smeared out in comparison to the nonpulsating flame. 5.11. The feedback loop of the self-sustained pulsations In the following, the sequence of events and the feedback loop are briefly summarized, beginning with phase 3, where the integrated chemiluminescence intensity Ichem. (and probably also the heat release rate) is at a maximum. ph3: Ichem. and also the pressure in the combustion chamber are at a maximum. The flow rate into the combustion chamber is low, and CH4 is accumulated in and slightly downstream of the swirler. ph4–ph5: Ichem. decreases together with pcomb. chamb. ; the CH4 concentration in the combustion chamber drops because the inflow rate of CH4 is still low. ph6–ph7: Ichem. and pcomb. chamb. approach a minimum. CH4 is largely burnt in the region of the main flame zone (h ≈ 40–60 mm). The pressure difference p has become large, the flow rates increase, and a new CH4 plume appears at the nozzle exit. ph8: The flow rate into combustion chamber (at h = 6 mm) reaches a maximum. ph1–ph3: the CH4 plume is convected to the main flame zone, leading to enhanced combustion; Ichem. and pcomb. chamb. increase. Thus, an oscillating fuel supply is the source of the varying combustion intensity, which in turn triggers the pressure oscillation. The oscillating pressure generates a modulation of the fuel and air supply rates in the swirler. This modulation of the CH4 flow (and equivalence ratio) is convected to the main flame zone. For an estimate of the convective time delay the residence time of the gas in the nozzle, τnozzle , is approximated using the flow rates and dimensions of the nozzle. The distance from the fuel injection within the swirler to the nozzle exit (h = 0) is about 4 cm. The mean cross section of the nozzle is approximately 6.2 cm2 . The flow rate of 612 slpm (see Table 1) corresponds to 785 lpm at the measured nozzle exit temperature of T ≈ 350 K. This yields a mean velocity of unozzle ≈ 21 m/s within the nozzle and a residence time of τnozzle ≈ 1.9 ms. For the convection of the gas from h = 0 to the main flame zone at h ≈ 50 mm a mean axial velocity of umean ≈ 30 m/s can be assumed (see Fig. 7), resulting in a time of flight of τchamber ≈ 1.67 ms. The total convective time delay is thus estimated to be τ ≈ 3.57 ms. This is in good agreement with the oscillation period of 3.45 ms and thus a further confirmation of the proposed feedback mechanism.

6. Summary and conclusions A gas turbine burner for premixed flames has been equipped with an optical combustion chamber in order to perform investigations at atmospheric pressure with optical and laser measuring techniques. Two flames were studied, one with Φ = 0.7 exhibiting pronounced thermoacoustic pulsations at f ≈ 290 Hz and a second, quiet flame with Φ = 0.83. The measurements include pressure fluctuation registration, OH* chemiluminescence detection as an indicator for the heat release rate, laser Doppler velocimetry, planar laser-induced fluorescence of OH, and laser Raman scattering for the simultaneous detection of the major species concentration and the temperature. For characterization of the phase-dependent variations, phase-locked measurements were performed. The flow field could be divided into three different regimes: the inflow of fresh gases and an inner and an outer recirculation zone. The flames were anchored below the nozzle exit plane close to the irz, but the main flame zone appeared at h ≈ 40–60 mm and r  20 mm. Although CH4 and air were premixed in a manner typical of practical GT burners, a significant level of unmixedness was revealed by the Raman measurements. These measurements also identified pronounced effects of finite-rate chemistry in both flames. Significant differences were observed between the pulsating and quiet flames with respect to flame shape, flow field, mixing, and the reaction progress. In the pulsating flame, all measured quantities varied with the frequency of the pulsation. The total OH* chemiluminescence intensity, which is, within certain limits, representative of the heat release rate varied between 16 and 100% over the oscillation cycle. These variations were in phase with the pressure variation in the combustion chamber. The phasedependent changes of the flow velocities were most prominent near the nozzle. Here, the lower part of the irz moved up and down during an oscillation cycle, thereby changing the width of the inflowing gas stream. From the phase-resolved measurements of mean axial velocity and the molecular number densities, the molecular fluxes within the inflow were approximated. The molecular fluxes of CH4 and O2 varied in phase, but by different amounts, leading to a periodic variation of the equivalence ratio. These variations were in qualitative agreement with the pressure variations in the plenum and combustion chamber. The convection of the mixtures with high or low CH4 concentrations to the main flame zone triggered the heat release rate, which in turn caused the pressure variations. The feedback loop for this flame is thus an oscillating fuel supply combined with a convective time delay. The reason for the oscillating fuel supply

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

lies most probably in the different impedances of the fuel and air supply lines of the combustor. However, this was not explicitly determined in the investigations. The current work yielded phase-resolved quantitative data on the flow velocities, the major species concentrations, mixture fraction, and temperature, which are well suited for a comparison with results from numerical simulations. In the results presented here, mole fractions and time-averaged mean values were used. However, the data archive also contains mass fractions and Favre-averaged mean values. Finally, it should be noted that the experimental data are available on request for validation of numerical codes.

Acknowledgments The work presented was mainly performed in the frame of the project “PRECCINSTA,” funded by the European Union, and as part of the DLR project NACOS. The financial support of these projects is gratefully acknowledged. We furthermore thank C. Berat for delivering the burner nozzle, B. Lehmann for the execution of the LDV measurements, and M. Aigner, L. Hernandez and K. Syed for fruitful discussions.

References [1] J.J. Keller, AIAA J. 33 (1995) 2280–2287. [2] E.C. Fernandes, M.V. Heitor, in: F. Culick, M.V. Heitor, J.H. Whitelaw (Eds.), Unsteady Combustion, Kluwer Academic, Dordrecht, 1996, p. 1. [3] C.O. Paschereit, E. Gutmark, W. Weisenstein, Combust. Sci. Technol. 138 (1998) 213–232. [4] A.H. Lefebvre, Gas Turbine Combustion, Taylor & Francis, Philadelphia, 1999. [5] S. Candel, Proc. Combust. Inst. 29 (2002) 1–28. [6] J.G. Lee, D.A. Santavicca, J. Propulsion Power 19 (2003) 735–750. [7] N. Syred, Prog. Energy Combust. Sci. 32 (2006) 93– 161. [8] N. Docquier, S. Candel, Prog. Energy Combust. Sci. 28 (2002) 107–150. [9] I. Emiris, J.H. Whitelaw, Combust. Sci. Technol. 175 (2003) 157–184. [10] G.A. Richards, D.L. Straub, E.H. Robey, J. Propulsion Power 19 (2003) 795–810. [11] H.C. Mongia, T.J. Held, G.C. Hsiao, R.P. Pandalai, J. Propulsion Power 19 (2003) 822–829. [12] B.T. Zinn, in: Proceedings ASME Turbo Expo 2005, GT2005-69138. [13] A.P. Dowling, S. Hubbard, Proc. Inst. Mech. Engrs. 214 (2000) 317–332. [14] C. Stone, S. Menon, Proc. Combust. Inst. 29 (2002) 155–160. [15] D.J. Cook, H. Pitsch, N. Peters, in: Proceedings ASME Turbo Expo 2003, GT2003-38558.

25

[16] T. Lieuwen, J. Propulsion Power 19 (2003) 765–781. [17] S. Roux, G. Latigue, T. Poinsot, U. Meier, C. Berat, Combust. Flame 141 (2005) 40–54. [18] G. Lartigue, U. Meier, C. Bérat, Appl. Therm. Eng. 24 (2004) 1583–1592. [19] G. Kelsall, C. Troger, Appl. Therm. Eng. 24 (2004) 1571–1582. [20] L.C. Haber, U. Vandsburger, Combust. Sci. Technol. 175 (2003) 1859–1891. [21] Y. Hardalupas, M. Orain, Combust. Flame 139 (2004) 188–207. [22] A.R. Masri, R.W. Dibble, R.S. Barlow, Prog. Energy Combust. Sci. 22 (1996) 307–362. [23] R.S. Barlow, C.D. Carter, R.W. Pitz, in: K. KohseHöinghaus, J. Jeffries (Eds.), Applied Combustion Diagnostics, Taylor & Francis, New York, 2002, p. 384. [24] A.R. Masri, P.A.M. Kalt, R.S. Barlow, Combust. Flame 137 (2004) 1–37. [25] W. Meier, X.R. Duan, P. Weigand, Proc. Combust. Inst. 30 (2005) 835–842. [26] W. Meier, X.R. Duan, P. Weigand, Combust. Flame 144 (2006) 225–236. [27] K.J. Syed, E. Buchanan, in: Proceedings ASME Turbo Expo 2005, GT-2005-68070. [28] T. Lieuwen, H. Torres, C. Johnson, B.T. Zinn, Trans. ASME 123 (2001) 182–189. [29] Th. Sattelmayer, J. Eng. Gas Turbines Power 125 (2003) 11–19. [30] C.J. Lawn, S. Evesque, W. Polifke, Combust. Sci. Technol. 176 (2004) 1331–1358. [31] T.M. Muruganandam, B.-H. Kim, M.R. Moreell, V. Nori, M. Patel, B.W. Romig, J.M. Seitzman, Proc. Combust. Inst. 30 (2005) 1601–1609. [32] K.-U. Schildmacher, R. Koch, H.-J. Bauer, Flow Turb. Combust. 76 (2006) 177–197. [33] X.R. Duan, W. Meier, P. Weigand, B. Lehmann, Appl. Phys. B 80 (2005) 389–396. [34] P. Weigand, W. Meier, X.R. Duan, R. GiezendannerThoben, U. Meier, Flow Turb. Combust. 75 (2005) 275–292. [35] H.E. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques, Springer, Heidelberg, 2002. [36] B.O. Ayoola, R. Balachandran, J.H. Frank, E. Mastorakos, C.F. Kaminski, Combust. Flame 144 (2005) 1–16. [37] O. Keck, W. Meier, W. Stricker, M. Aigner, Combust. Sci. Technol. 174 (2002) 117–151. [38] V. Bergmann, W. Meier, D. Wolff, W. Stricker, Appl. Phys. B 66 (1998) 489–502. [39] R.W. Bilger, S.H. Starner, R.J. Kee, Combust. Flame 80 (1990) 135–149. [40] http://www.dlr.de/vt/forschung/datenarchiv/tnf/jet_ flames/contents. [41] J.C. Dasch, Appl. Opt. 31 (1992) 1146–1152. [42] http://gaseq.co.uk. [43] R. Giezendanner-Thoben, U. Meier, W. Meier, J. Heinze, M. Aigner, Appl. Opt. 44 (2005) 6565–6577. [44] U. Rahmann, A. Bütler, U. Lenhard, R. Düsing, D. Markus, A. Brockhinke, K. Kohse-Höinghaus, LASKIN—A simulation program for time-resolved

26

W. Meier et al. / Combustion and Flame 150 (2007) 2–26

LIF-spectra, International Report, University of Bielefeld, Faculty of Chemistry, Physical Chemistry I, http:// pc1.uni-bielefeld.de/laskin, V.5.0. [45] J.H. Miller, R.J. Kee, M.D. Smooke, J.F. Grcar, in: Western State Section of the Combust. Inst., Spring Meeting, 1984, Paper WSS/CI 84-10.

[46] J.Y. Chen, UC Berkeley, personal communication. [47] M. Zhu, A.P. Dowling, K.N.C. Bray, J. Eng. Gas Turbines Power 124 (2002) 20–30. [48] T. Lieuwen, Turbomachinery Int. 44 (2003) 16– 19.