GT THERMOACOUSTIC MODELING OF A GAS TURBINE USING TRANSFER FUNCTIONS MEASURED AT FULL ENGINE PRESSURE

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1 Proceedings of ASME Turbo Expo 9: Power for Land, Sea and Air GT9 June 8-, 9, Orlando, USA GT THERMOACOUSTIC MODELING OF A GAS TURBINE USING TRANSFER FUNCTIONS MEASURED AT FULL ENGINE PRESSURE Bruno Schuermans, Felix Guethe, Douglas Pennel Alstom CH-545 Baden Switzerland Daniel Guyot, Christian Oliver Paschereit Technische Universität Berlin Germany ABSTRACT Thermoacoustic transfer functions have been measured of a full-scale gas turbine burner operating at full engine pressure. Excitation of the high-pressure test facility was done using a siren that modulated part of the combustion airflow. Pulsation probes have been used to record the acoustic response of the system to this excitation. In addition, the flame s luminescence response was measured by multiple photomultiplier tubes and a light spectrometer. Three techniques to obtain the thermoacoustic transfer function are proposed and employed: two combined acoustical-optical technique and a purely acoustic technique. The first acoustical-optical technique uses one single optical signal capturing the chemiluminescence intensity of the flame as a measure for the heat release in the flame. It only works, if heat release fluctuations in the flame have only one contribution, e.g. equivalence ratio or mass flow fluctuations. The second acoustic-optical acousticoptical technique makes use of the different response of the flame s luminescence at different optical wavelengths bands to acoustic excitation. It also works, if the heat release fluctuations have two contributions, e.g. equivalence ratio and mass flow fluctuation. For the purely acoustic technique, a new method was developed in order to obtain the flame transfer function, burner transfer function and flame source term from only three pressure transducer signals. The purely acoustic method could be validated by the results obtained from the acoustic-optical techniques. The acoustic and acoustic-optical methods have been compared and a discussion on the benefits and limitations of the methods is given. The measured transfer functions have been implemented into a non-linear, threedimensional, time domain network model of a gas turbine with an annular combustion chamber. The predicted pulsation behavior shows a good agreement with pulsation measurements on a field gas turbine. NOMENCLATURE A f flame area H f chemical enthalpy He Helmholtz number, He = ωl/(πc) I chemiluminesence intensity I BB spectral black body radiance Q heat release rate S f flame speed S xy estimate of the cross power spectral density T temperature T BB black body temperature c speed of sound c light speed of light h P Planck constant k B Boltzmann constant m mass flux through flame surface p pressure u velocity y fuel mass fraction γ ratio of specific heats Copyright c 9 by Alstom

2 λ optical wavelength ρ density ω angular frequency x steady component of x x (t) unsteady component of x, x (t) x(t) x ˆx(ω) Fourier coefficient of x (t) INTRODUCTION Thermoacoustic analysis is an integrated part in Alstoms gas turbine technology and product development process. Alstom s approach to thermoacoustic analysis is to use measured flame transfer functions and source terms in a non-linear, 3-dimensional, acoustic network model. The acoustic wave propagation through combustion chamber and plenum are represented in the model via a modal expansion. The required acoustic modes are obtained from a finite element calculation of the detailed geometry. This combined experimental and numerical approach to thermoacoustic modeling is discussed in detail in [] and []. A crucial aspect of this modeling approach is to obtain a correct representation of the interaction between the heat release and the acoustic field. Alstom s approach is to measure flame transfer functions in a single burner test facility and to fit models to this transfer function data. This approach has proven to give very good results in predicting stability behavior and pulsation spectra of multi-burner gas turbine combustion systems [3, 4]. The influence of pressure on transfer functions is particularly important for fuel flexibility (high hydrocarbon and hydrogen content, liquid fuels). In order to correctly predict thermoacoustic behaviors for cases where such fuels are used, transfer functions measured at elevated pressure are needed. This paper is about the measurement of flame transfer functions of a full scale swirl-stabilized EV-type burner at full engine pressure and about using these transfer functions to predict stability and pulsation spectra of a gas turbine with annular combustion chamber. Due to the limited access in an industrial high pressure test facility, new techniques had to be developed to obtain transfer functions from only three pulsation probes and optical sensors. Two different techniques have been used to measure the flame transfer function: the first technique uses pulsation probes and multiple chemiluminescence sensors, the second only uses pulsation probes. Using chemiluminescence signals to obtain transfer function is not very straight forward, because fluctuations of the fuel to air ratio may be present in this type of burner and hence the chemiluminescence intensity is not necessarily proportional to the heat release. To overcome this problem a technique has been used that uses chemiluminescence signals of different wavelengths bands. This method has been discussed in detail in [5] and was validated at atmospheric pressure conditions. At high-pressure the correct measurement of the flame chemiluminescence is more challenging than at atmospheric conditions, however. This is due to constrains regarding optical access to the flame, an overlapping of the wavelengths bands of flame luminescence and the combustor walls heat radiation, and the generally lower probability of the formation of the chemical species associated to the flame chemiluminescence under high pressures. Therefore, the error of the acoustical-optical technique was expected to be larger than under atmospheric conditions. For this reason a second new technique has been developed to obtain transfer functions from only three pulsation probes. A comparison of the acoustical and the combined acoustical-optical method for obtaining the transfer functions and source terms is given in this paper, together with an error analysis. Both methodologies have been used to obtain transfer functions and predict engine pulsation spectra for a wide range of operating conditions (varying flame temperature, burner exit velocity, pressure, air temperature, fuel type and fuel staging ratio) and hardware configurations. Due to limited length of this paper only a small part of the results will be discussed here. EXPERIMENTAL SET-UP High-Pressure Combustion Test Facility The process of Alstom burner development and improvement includes combustion tests under high-pressure conditions. The facility is shown in Fig.. It allows quick, cost-effective and therefore extensive testing of single AL- STOM machine burners. The test-rig consists of a plenum chamber upstream of the burner, two tubular pressure vessels and the rectangular chamber liner. The hot exhaust gases are quenched before the pressure reduction throttle and then discharged to the chimney. During the combustion tests the flow through the throttle was choked to minimize acoustic perturbations traveling in upstream direction through the throttle. The combustor liner is convectively cooled to prevent contamination of actual burner emissions by introducing additional film cooling air into the combustor and to avoid the introduction of unrelated acoustic damping effects. The test were performed on an Alstom EV-type test burner. Such a burner has the unique property of flame stabilization in free space near the burner outlet utilizing the sudden breakdown of a swirling flow, called vortex breakdown. Gaseous or liquid fuels are injected into the combustion air by means of fuel distribution tubes comprising Copyright c 9 by Alstom

3 pulsation probes fiber optic probe for flame chemiluminescence detection light spectrometer PMT : UV filter PMT : CW 37nm PMT 3: CW 43nm PMT 4: CW 45nm PMT 5: CW 55nm splitter siren actuator air vessel plenum burner exhaust motor air supply insulation siren actuator preheater air supply support preheater mass flow controller Figure. The siren actuator. Figure. Experimental set-up: High-pressure test facility equipped with siren, pulsation probes and optical access via an fiber optic probe. rows of small holes perpendicular to the inlet ports of the swirler. Complete mixing of fuel and air is obtained shortly after injection. given frequency range during one recording. The generated acoustic forcing amplitude was sufficiently high to limit the recording time per frequency step to seconds, while still achieving a good signal to noise ratio.in fact, the maximum acoustic forcing was not limited by the siren actuator, but rather by the mechanical integrity of the test facility. Acoustic Forcing At high-pressure conditions loudspeakers provide neither the required robustness nor sufficient acoustic forcing amplitudes for good transfer function measurements. Therefore, a siren actuator has been designed (Fig. ). The siren features an insulated air vessel to which preheated air is supplied. The pressurized air exits the air vessel through an orifice into the test-rig s plenum chamber. The orifice is periodically blocked by a rotating disc. This disc has eight holes. Hence, the orifice is opened and closed eight times during one revolution of the disc. The disc is driven by a 6. kw motor. The disc s rotational speed is measured by a trigger placed onto the motor axle, which generates one short pulse signal per disc revolution. The free cross section of the orifice was designed in a way that resulted in an almost sinusoidal modulation of the siren air flow with only minor response at higher harmonics. Acoustic excitation can thus be forced onto the combustion test-rig by feeding a fraction of the combustion air via the siren into the plenum chamber. The forcing amplitude can be adjusted by changing the siren air mass flow. The excitation frequency is controlled by defining the siren disc speed and can be varied between and 4 Hz. To perform transfer function measurements in a given frequency range the test-rig was generally consecutively excited at discrete frequencies (i.e., mono-frequent siren excitation). In most cases frequency steps of 5 to Hz were chosen. Alternatively, the siren can also sweep through a Measurement Set-up Pressure fluctuations in the test-rig are measured using three pulsation probes. One probe is situated in the plenum chamber and two in the combustion chamber. Their positions are indicated in Fig.. The light emitted by the flame is collected by a watercooled fiber optic probe equipped with a lens system situated in the downstream half of the combustion chamber. The optical detection is accomplished by a non imaging system of quartz lenses focusing the light on one thick fiber of 5 m length. From this thick fiber the light is transmitted into 7 different fibers by an optical splitter. This setup assures that each fiber obtains the same light and avoids angle dependency. The lens has been optimized in order to minimize the flame position dependence of the intensity. This is important in order to avoid that flame movement is interpreted as intensity fluctuation. The opening angle of the system was chosen such that the entire heat release zone was covered. The geometrical extent and movement of the heat release zone are known from previous flame visualization studies. The light is then distributed to a system of filters and photomultiplier tubes (PMTs) as indicated in Fig.. This yields five separate signals for five different optical wavelength regions. The chemiluminescence signals are recorded simultaneously with the pulsation probe signals on the same data acquisition system. The optical setup incorporates five different band pass- 3 Copyright c 9 by Alstom

4 filters of about nm width at central wavelengths (CW) of 37 nm, 43 nm, 45 nm, 55 nm and one UV transparent broad band filter (DUGX, Schott). The transmission curves are shown in Fig. 3 together with the transmission of the fiber optic probe. As an example, Fig. 4 presents the light spectrum of the premixed natural gas flame of an EVtype burner at atmospheric conditions. Using this optical set-up the different channels can be attributed to the occurrence of chemiluminescence of mainly the species (OH, CH, C ) as indicated in [6, 7]. To monitor the broad emission (attributed to the CO + O CO chemiluminescence) which contributes as background in the spectrum [8] a filter with CW 45 nm is used. transmission (%) 5 Figure 3. Figure wavelength (nm) UV band CW 37 nm CW 43 nm CW 45 nm CW 55 nm optical probe Light transmission of the optical filters an the fiber optic probe. OH * CH * CO * C * Light spectrum of a premixed flame at atmospheric conditions. All channels are mainly detecting emission from different species probing a different part of the flame chemistry. Note that for the fiber optic probe only the relative transmission is presented. The maximum of the relative transmission is interpreted as % transmission. Each of these detection windows scale differently with the operating parameters burner velocity and flame temperature. With the calibration of at least three averaged steady operating points this ratio of the channels allows the interpretation as instantaneous measurements of these operating parameters. This reading can be interpreted as fluctuations of the governing heat release parameters (adiabatic flame temperature and mixture mass flow) as described in [9, ]. A further correlation of the signals to individual molecular emissions utilizing the spectra can be undertaken and would improve the quality of the interpretation. However, because it is not necessary for the approach described in this work this has been omitted here. The fiber optic probe in the combustion chamber does not only collect the light emitted by the flame, but also the heat radiation of the combustor walls. Therefore, an Ocean Optics QE65 high-sensitivity spectrometer measured the spectrum of the light captured by the fiber optic probe in the range of to 85 nm to allow for correction for the captured heat radiation in the data post-processing. TRANSFER FUNCTION MEASUREMENT USING ACOUSTIC SIGNALS The combustion system can conceptually be divided into six subsystems: the siren, the plenum, the burner, the flame, a noise source and the combustion chamber. A causal network representation of this system is given in figure 5. In this diagram the measured signals are represented by plain symbols. The unsteady pressure signals recorded by the pulsation sensors in the plenum and combustion chamber are represented by the symbols p, p and p 3. The light intensity of the different chemical species recorded by the photo multipliers are represented by the symbols I to I 5. The siren actuator provided a reference signal, which gave a pulse for each revolution of the siren. This signal is represented by r. The italic symbols in the diagram represent relevant signals that can not be measured directly. The velocity fluctuation imposed by the siren is represented by u siren. The flame is considered as a compact interface between the cold and hot products, represented by underscores c and h respectively. Because of the low Mach number, continuity of pressure is assumed across the flame sheet (p c = p h ). The velocity fluctuation just before and after the flame location are denoted as u c and u h. The relation between u c and u h is given by the flame transfer function H. The flame will also act as a source of sound independent of u c. The physical nature of this source is believed to be mainly due to turbulent unsteady heat release. Nevertheless, it can be represented by an equivalent velocity source term u s. The sum of the velocity fluctuations right after the flame and the source term is represented as u t. 4 Copyright c 9 by Alstom

5 Plenum Siren usiren p p p p 3 c = p h r Burner Flame u c u h u t I :5 u s Source Combustion Chamber (F =, thus u c = u h ) the burner transfer function (B) is obtained as: B(ω) = ˆp,ε ˆp,ε û h (3) The flame transfer function H = ûh ûc test case with combustion from: is obtained from a Figure 5. Thermoacoustic network representation of the test facility. The aim of the present system identification is to obtain the flame transfer function H and the source term u s from the measured quantities. It is evident from figure 5 that the system has two input signals: the naturally occurring source term u s and the externally impose excitation by the siren: u siren. Thus all measured quantities are a superposition of the response to the siren and to the source term. For system identification it is crucial to separate these two contributions of the signal. This can be done via a correlation analysis with the excitation signal. However, the excitation is not measured. This is why an artificial excitation signal ε(t) is constructed from the reference signal r provided by the siren. This is done by constructing a series of sine waves such that exactly eight periods (the siren disc has eight holes) fit between every two consecutive trigger pulses. The response of the microphone signal i to the siren excitation will be denoted as p i,ε. An estimate of the Fourier transform of p i,ε is given by: H(ω) = ûh,ε u h,ε = û c,ε B( ˆp,ε ˆp,ε ), (4) where û h,ε is obtained from ˆp and ˆp 3 using the two microphone method, and B was already obtained from the test case without combustion. The response of a pressure signal to the combustion source term u s is obtained from a separate test case where there was combustion, but where the siren is switched off. The noise driven response is then obtained from the cross power spectral density between pressure signal i and the reference microphone. p i,s = The source term is then obtained as: S p p i Sp p. (5) u s = u t,s H u c,s = u t,s H B( ˆp,s ˆp,s ), (6) p i,ε = S ε p i Sεε, () where S xy is the estimate of the cross power spectral density, which is the Fourier transform of the cross correlation. Using the two microphone method [, ], the velocity fluctuations û h can be calculated from the pressure signals ˆp and ˆp 3 : where H and B where obtained from the previous test cases, and u t,s is obtained by applying the two microphone method to ˆp,s and ˆp 3,s. Thus, the burner transfer function, the flame transfer function and the source term are calculated from three pressure signals using three test cases (no combustion with forcing, combustion without forcing and combustion with forcing). û h = i ρ cos(k ) p cos(k 3 ) p 3, () sin(k k 3 ) where k n ωx n c, and x n denotes the axial position of the n th pressure transducer. The acoustic velocity at the exit of the burner is assumed to be a function of the unsteady pressure drop over the burner and the burner transfer function: û c = B(ω)( ˆp,ε ˆp,ε ). From a test case without combustion TRANSFER FUNCTION MEASUREMENT USING OPTI- CAL SIGNALS The heat release flux of the flame is given by the following expression: Q = m f H f = myh f (7) where m f and m are the instantaneous values of the mass fluxes of fuel and mixture entering the reaction zone,y the 5 Copyright c 9 by Alstom

6 mass fraction of fuel (y = m f /m), the chemical enthalpy of the fuel is represented as H f. The mass flux of the mixture through the flame front fulfills the following equality: m = ρsda = ρs f A f. Please note that in the following, all relevant quantities are considered as averages of the quantity over the flame surface (hence assuming homogeneity of the time-averaged quantities and linearity of the perturbations). Flame chemiluminescence intensity has frequently been reported to depend linearly on the mass flux and exponentially on the fuel mass fraction of the mixture entering the flame (see e.g. Higgins et al. [9]). Therefore, the recorded chemiluminescence intensity for the n th optical signal is assumed to have the following dependency of mass flux and fuel mass fraction: I n = k n my α n, (8) where k n and α n are constants for the n th optical signal. It is assumed here that the Mach number is sufficiently small, see [5] for a more elaborate discussion on this topic. The present work deals with acoustic phenomena. That is why only small perturbation of the flow conditions are considered, which justifies a linearization of Eqns. 7 and 8 : Q Q = m m + y ȳ I n Īn = m m + α n y ȳ (9) () These relations show that in case of α n = or y = the chemiluminescence is proportional to the heat release. However, as pointed out in [5], typically α n so, the chemiluminescence intensity is not proportional to the heat release if equivalence ratio fluctuations are present. The method used here overcomes this problem by using chemiluminescence of at least two species as input and calculates the heat release from these signals via an inverse operation. Thus, measurement of the intensity of N species would result in N relations like equation, which is written in matrix form as: I Ī. I N ĪN = α.. α N [ m m y ȳ ] [ ] m = C m α y, () ȳ with α C α.... () α N If α i α j, then the system can be inverted in least squares sense, in order to calculated m m and y ȳ from measured I n Īn. The flame transfer function can be obtained if the acoustic velocity fluctuation in front of the flame is measured. In case of a negligible effect of the influence of pressure on the heat release fluctuation, the transfer function is then obtained as: F(ω) = ˆQ û ū Q = ( ˆm m + ŷ ȳ )ū û. (3) The optical method proposed here has the advantage that it does not only provide quantitative heat release fluctuations, but it also quantifies the underlying physical mechanisms that cause the heat release fluctuations: it shows what part of the heat release is caused by equivalence ratio fluctuations and what part by flame front dynamics. The relation by the transfer function F and H is found by making use of the Rankine-Hugoniot relations for low Mach number flows: û h = û c + ( T h T c )ū c ˆQ Q = û c ( + ( T h T c )F) (4) H = + ( T h T c )F (5) Note that in case of the negligible equivalence ratio fluctuations (y = ), the flame chemiluminescence is proportional to the heat release and Eqn. 3 can by simplified to F(ω) = ˆQ ū û Q = (În I )ū, (6) n û where I n denotes one of the recorded chemiluminescence signals. Optical signal correction for wall radiation The fiber optic probe in the combustion chamber does not only collect the light emitted by the flame, but also the heat radiation of the combustor wall. 6 Copyright c 9 by Alstom

7 An Ocean Optics QE65 high-sensitivity spectrometer measured the spectrum of the light captured by the fiber optic probe in the range of to 85 nm. As an example, a typical light spectrum recorded at high pressure is shown in Fig. 6. Note that the light spectrum has already been corrected for the spectrometer sensitivity and the transmission of the optical probe. As evident from the figure, the recorded spectra features increasingly high light emission above approximately 5 nm. This increase is believed to be due to heat radiation of the combustor walls within the field of view of the optical probe. By fitting a black body radiation spectrum to the recorded spectrum an average combustor wall temperature can be estimated. For this fit the black body radiation is assumed to follow Planck s law: I BB (λ,t BB ) = h Pc light λ 5 ( h P c light e λk B T BB ), (7) where I BB is the spectral black body radiation, λ the optical wavelength, T BB the black body temperature, c light the speed of light, h P the Planck constant, and k B the Boltzmann constant. The estimated combustor wall temperatures are within the range of temperatures measured by several thermocouples distributed along the liner walls, thus giving confidence to the interpretation of the recorded spectra. light intensity (arb.) Figure 6. recorded light spectrum black body fit (T BB = 85 K) estimated flame luminescence wavelength (nm) Optical spectrum measured inside the combustion chamber and fit of the black body radiation. By subtracting the contribution of the combustor wall radiation from the recorded spectra an estimation of the flame luminescence spectra is obtained, as indicated in Fig. 6. Four main observation can be made: ) The estimated flame spectrum features a broad background, which is believed to correspond to CO. ) The estimated flame spectrum also feature the CH peak at 43 nm, although it is less pronounced compared to the atmospheric flame. (Note that generally a pressure increase results in weaker chemiluminescence emission as the excited radicals are more likely to dissipate their energy in collisions with other molecules or atoms.) 3) No C peak can be observed. 4) At 39 nm the high-pressure light spectra do not feature the expected peak corresponding to OH formation in the flame front, but instead a distinct dip in the spectral intensity. This effect is attributed to the presents of OH radicals in the exhaust between flame and fiber optic probe. While the excited OH radicals in the flame front emit light at 39 nm, the unexcited OH radicals in the exhaust absorb light at exactly this wavelength. From the filter transmission and the light spectrometer results for each burner operating condition the offset in the photomultiplier signals due to wall radiation is estimated and accounted for in the further evaluation. NETWORK MODELING The in-house acoustic network modeling tool Ta 3 has been used to predict stability characteristics and pulsation amplitudes of a gas turbine combustion chamber. In order to obtain dynamic models of such systems, a hybrid approach is used: numerical, experimental and analytical techniques are combined to describe the system. The system is modeled as a modular network, where the input output relation of the modules can be based on analytic models, experimental data or numerical analysis. The modules are represented as state-space realizations. A modal expansion technique is used to obtain a state-space representation of the acoustic propagation through complex 3-dimensional geometries. The modal expansion can be based on an analytic model (for relatively simple volumes), or on a finite element analysis (for geometries of any complexity). The flame transfer functions and source terms are incorporated by fitting state space models to the measured data. The method is not restricted to symmetries of any kind: configurations with geometrically or operationally different burners are simulated. The state-space network approach allows either for time domain simulations, including non-linearities. Alternatively an eigenvalue analysis can be performed which is very straightforward due to the state-space formulation. Frequency spectra can either be obtained directly from a 7 Copyright c 9 by Alstom

8 Globals u p p Sysnoi se Figure 7. pi ui u Causal network interconnection of the elements of the combustion chamber click to plot system poles pj uj u p Flame u3 p3 Source u4 Modal Analysis Spectral Analysis u p p4 Sysnoi se frequency domain analysis or by applying a Fourier analysis of the time traces in a post-processing step. The method is very computational efficient: all results shown in this work have been calculated in only a few seconds of computation time. This modeling approach relies on the assumption that the transfer function of a burner in single burner and multi burner configurations are similar. This assumption has been validated experimentally on down-scaled but very realistic geometry in [3]. For the analysis shown in this work, the elements of the gas turbine combustion chamber are interconnected in a Matlab/Simulink block diagram a shown in figure 7. The modeling approaches for the different blocks are detailed below. Modeling 3-D wave propagation A key aspect of this modeling approach is that the wave propagation through a volume of any complexity is represented by a transfer matrix between m velocity inputs and n pressure outputs: where Ψ is a N K matrix which K columns contain ψ k(x n ) Λ k, the diagonal matrix A contains the area corresponding to the m th velocity inputs. The K K diagonal matrix Ω contains the eigenfrequencies of the solid walled geometry, I and are the K K unit matrix and zero matrix respectively. The vectors η, p and u, contain the modal amplitudes, the input velocities u m and the output pressures p n. In the limit case of K approaching infinity, the system of equations 9 is an exact solution of the wave equation. However the solution converges rapidly, so in practice only a limited number of modes K is required in the modal expansion. Note that although the modal expansion is based on a set of orthonormal modes of the solid walled geometry, this representation remains exact even in the case when (complex, frequency dependent) boundary conditions are applied to Equ. 9 or if the geometry represented by Equ. 9 takes part in a more complex network interconnection. Clearly in such a case, the modes of the final, interconnected systems will generally not be orthogonal anymore. However in this methodology no assumption of orthogonality of the resulting modes has been made. Time domain transfer function and source models The flame model has been incorporated in the model by fitting a state space model to the measured transfer function data. The fitting routine minimizes the magnitude squared difference between the measured frequency response data and the frequency response of the state space system under the constraint that the fitted system must be stable. The source term is modeled in a similar way: a state space system is fitted to the measured source term. This state space model is then used to filter a normally distributed random sequence (white noise). The phase of the source term is undefined. However, in order to obtain the filter transfer function, a phase needs to be generated. This was done here by using the so-called complex cepstrum algorithm. ˆp n û m = ρc A m ψ k (x n )ψ k (x m ) Λ k (s + ω k ) (8) where ψ k (x n ) is the value of the k th mode at location x n on the boundary and Λ k = ψ k (x)dx is a normalization factor for the modes. This equation can be expressed in statespace form as: [ ] [ η I = t η Ω ][ η η p ρc = c[,ψ][ η η ] [ ] + Ψ T u (9) A ], () Burner transfer function The burner geometry was incorporated in the FEM analysis of the plenum geometry and was hence included in the plenum state space representation. However, this representation does not take into account the damping in the burner and the length correction at the exit of the burner. These have been modeled separately by using a so-called L Zeta model. The L-zeta models relates the acoustic velocity at an area discontinuity to the pressure drop over the discontinuity: ˆp ˆp uˆ = iωlρ + ū ρζ. () 8 Copyright c 9 by Alstom

9 The value of L has been obtained by a fit to the finite element model results of the entire combustion system (including plenum, burner and combustion chamber), the value of ζ has been obtained from the measured mean flow conditions: ζ = p p. ρū OPTICAL VS. ACOUSTICAL TRANSFER FUNCTION RESULTS For two burner configurations (A and B) the transfer function H was measured. Figures 8 and 9 present a comparison of this transfer function obtained from the acoustical approach (Eqn. 4) and the combined acoustical / optical approach (Eqn. 4). The purely acoustical results are labeled acoustical. For the combined approach results obtained from multiple chemiluminescence signals according to Eqn. 3 are labeled optical, while results obtained from one single chemiluminescence signal according to Eqn. 6 are labeled with the center wavelength of corresponding filter (e.g. CW39nm). For the multi-signal optical method the matrix C α, which contains the coefficients α i and links the intensity fluctuations to mass flow and fuel mass fraction fluctuation (see Eq. ), was determined in a calibration measurement. This calibration was permormed for each burner configuration individually. Note, that although the two optical methods provide interesting additional insights into to combustion process, their main purpose in this work was to validate the purely acoustic transfer function results. For this validation it has to be considered that the reliability of the two acousticoptical methods depends on the cause of heat release fluctuations in the flame, i.e., equivalence ratio fluctuations and/or mass flow fluctuations. In case only one of these two contributions to heat release fluctuations is present, the acoustic-optical method based on only one optical signal is expected to work well according to Eqn. 6. The multi-signal optical technique on the other hand also works, if the heat release fluctuations have two contributions, e.g. equivalence ratio and mass flow fluctuations. However, this method relies on the difference in the response of the flame chemiluminescence at different wavelength regions to these fluctuations. These differences in response are commonly very small. Therefore, even small measurement errors in the intensity signals can have a significant impact on m y m and ȳ obtained from Eq., and hence the transfer function H. Additionally, errors in the determination of C α will also effect the accuracy of H. Especially large errors in H have to be expected, if C α is badly conditioned. This is the case, if the coefficients α i are very similar. Figure 8 shows the transfer function H for burner configuration A. The optical results based on multiple chemiluminescence signals are in good agreement with the acoustical results in terms of absolute values and phase. The results obtained from only one chemiluminescence signal show an increasing difference in absolute value for St >.3 and do not capture the falling slope of the phase obtained from the other two methods. This deviation validates the expectation that equivalence ratio fluctuations are present in the flame of this burner, and that therefore heat release oscillations can not be captures accurately from only one chemiluminescence signal. However, from the results of the multi-signal optical method it was still found that the main driver of heat release fluctuations are flame dynamics rather then equivalence ratio fluctuations. For burner configuration B the results are presented in Fig. 9. The figure shows a good agreement between the acoustical and the one-signal optical method, which indicates a negligible impact of equivalence ratio fluctuations on the heat release of the flame. The multi-signal optical method captures the main trends in absolute value, but with some deviations in amplitude, and features significant phase deviations for St <.5. abs(h) phs(h) UV band CW 37 nm CW 43 nm CW 45 nm optical acoustical Figure 8. Flame transfer function of burner configuration A. In order to identify the reason for these deviations an error analysis has been performed. In this error analysis it was found that for burner configuration B the condition of C α was significantly worse compared to burner configuration A due to very similar coefficients α i, which will cause larger errors in H for burner configration B. To visualize the sensitivity of the transfer function H to measurement errors 5% relative noise was artificially added to the Fourier coef- 9 Copyright c 9 by Alstom

10 abs(h) phs(h) UV band CW 37 nm CW 43 nm CW 45 nm optical acoustical Figure 9. Flame transfer function of burner configuration B. ficients ÎĪ (obtained from the measured chemiluminescence intensity time traces) and the determined α i, respectively. Then, the transfer function H was determined based on the contaminated values. This procedure was repeated times to obtain statistically meaningful results. Figures and shows the obtained results for burner configuration A and B, respectively. The original results obtained from the measured data are indicated by black crosses. The results obtained with 5% artificial relative noise in the intensity signals are plotted in blue, the results obtained with 5% artificial relative noise in the coefficients α i are plotted in red. The red and blue solid lines indicate the median absolute value and phase based on the repetitions, while the dotted lines represent the upper and lower quartil as a measure of the relative error. As evident from Figs. and the impact of artificial noise on the transfer function H is much stronger in case of burner configuration B, indicating that the results obtained for this burner configuration are likely to be less reliable then for burner configuration A. abs(h) phs(h) abs(h) phs(h).3 data as measurement 5% noise on optical signals 5% noise on coeff. α Figure. burner configuration A. abs(h) phs(h) Error sensitivity analysis for flame transfer function H of NETWORK MODELING RESULTS The detailed geometry of an annular gas turbine plenum, burner and combustion chamber was modeled in a finite element package to obtain the mode shapes and eigenfrequencies required for modal expansion. The measured transfer functions and source terms were then incorporated into this network in order to calculate eigenvalues and pulsation spectra of the engine. The investigated burner configuration allows for local enrichment of the fuel-air-mixture by fuel staging. Increasing the fuel stage ratio commonly has a stabilizing effect on combustion pulsations. As a typ- Figure. Error sensitivity analysis for flame transfer function H of burner configuration B. (Legend identical to Fig..) ical example, the influence of the fuel staging ratio on the flame transfer function, source term, eigenvalues and spectra will be shown. A comparison with spectra measured in the engine is given. The acoustic transfer functions used for this analysis are shown in Fig.. The normalize fuel staging ratio varied from to., where the nominal value was. The effect Copyright c 9 by Alstom

11 abs(h) phs(h).5 - Figure. staging staging. staging Measured transfer functions for different values of the normalized fuel staging ratio. abs(source) Figure 3. fuel staging ratio. staging staging. staging Measured source terms for different values of the normalized of increasing fuel staging show as expected that the absolute value of the transfer function is significantly reduced. The slope of the phase decreases for increasing fuel staging, which is also expected because staging will cause the flame to stabilize closer to the burner exit. The dependence on the source term on fuel staging ratio is less distinct, as can be seen in Fig. 3. The eigen analysis of the system clearly shows the stabilizing effect of the fuel staging on the stability of the system. In Fig. 4 the real part of the eigenvalue is plotted versus the imaginary part. Positive real parts of the eigenvalues indicate instability. The dominant eigenvalues close to normalized frequency of.35 are clearly stabilized by increasing the fuel staging. A simulation in the time domain has been performed to obtain time traces of pulsation in the combustion cham- growth rate (-) Figure 4. pulsation amplitude (-).8.6 x -3 staging staging. staging frequency (-).4. Figure 5. Calculated pulsation spectra of the annular engine configuration. Calculated eigenvalues of the annular engine configuration. staging staging. staging frequency (-) ber. The pulsation spectra shown in Fig. 5. These results reflect the general behavior already seen in the eigen analysis: the dominant pulsation peak is reduced by increased fuel staging. In Fig. 6 the measured pulsation spectra of the pulsations in the actual engine are shown. The qualitative agreement is very good: all dominant pulsation modes are correctly predicted. The predicted reduction of the main pulsation peak with increasing fuel staging is clearly observed in the measurements as well. CONCLUSION Three different methods have been used to measure source terms, flame and burner transfer functions in a fullscale high pressure test facility. A purely acoustical method has been compared with two optical methods. In the simplest optical method, the relative heat release fluctuation is assumed to be equal to the relative chemiluminescence intensity fluctuation. This is correct for cases where contribution of equivalence ratio fluctuations can assumed to Copyright c 9 by Alstom

12 pulsation amplitude (-) staging.5 staging. staging.5 staging frequency (-) Figure 6. Measured pulsation spectra of the engine. be negligible, which has been demonstrated experimentally. In case the equivalence ratio fluctuations do have an influence, only meaningful results can be obtained by using the method that uses multiple chemical species. This could be demonstrated by comparing the two methods with transfer functions that were obtained from acoustic data only. The measured transfer functions and source terms have been incorporated in an acoustic network model of a gas turbine. As a typical example the stabilizing influence of fuel staging on pulsation behavior is shown. The model with measured transfer functions proved to accurately reproduce the measured pulsation spectra. Being able to measure transfer functions at high pressure conditions on full scale burners opens up the possibility to predict thermoacoustic behavior of gas turbines using fuels whose combustion properties depend on pressure such a natural gases with higher hydrocarbon content, syngases and liquid fuels. ACKNOWLEDGMENT This work has been conducted in the framework of AG Turbo / COOREFF-T with support from the German Federal Ministry of Economics and Technology. REFERENCES [] Schuermans, B. Modeling and control of thermoacoustic instabilities. PhD Thesis nr. 8 (3), EPFL Lausanne, Switzerland. [] Schuermans, B., Bellucci, V., and Paschereit, C., 3. Thermoacoustic modeling and control of multi burner combustion systems. ASME 3-GT-38688, Proc. ASME Turbo Expo 3, Atlanta, June 6-9. [3] Bellucci, V., Schuermans, B., Nowak, D., Flohr, P., and Paschereit, O., 3. Thermoacoustic modeling of a gas turbine combustor equipped with acoustic dampers. ASME GT , Proc. ASME Turbo Expo 4, Vienna, June 4-7. [4] Bellucci, V., Nowak, D., Geng, W., and Steinbach, C., 7. Thermoacoustic modeling and control of multi burner combustion systems. ASME GT7-739, Proc. ASME Turbo Expo 7, Montreal, June 4-7. [5] Schuermans, B., Guethe, F., and Mohr, W., 8. Transfer function measurements for technically premixed flames using a novel optical method. ASME GT8-55, Proc. ASME Turbo Expo 8, Berlin, June 9-3. [6] Hardalupas, Y., and Orain, M., 4. Local measurements of the time-dependent heat release rate and equivalence ratio using chemiluminescent emission from a flame. Combustion and Flame 39, (4) 887. [7] Kojima, J., Ikeda, Y., and Nakajima, T.,. Detailed distributions of oh*, ch* and c* chemiluminescence in the reaction zone of laminar methane/air premixed flames. 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit () AIAA [8] Nori, V., and Seitzman, J., 7. Detailed distributions of oh*, ch* and c* chemiluminescence in the reaction zone of laminar methane/air premixed flames. AIAA at the 45th Aerospace Sciences Meeting, Reno, NV, Jan 8-, 7. [9] Higgins, B., McQuay, M., Lacas, F., Rolon, J., Darabiha, N., and Candel, S.,. Systematic measurements of oh chemiluminescence for fuel-lean highpressure, premixed, laminar flames. FUEL 8,, PP [] Higgins, B., McQuay, M., Lacas, F., and Candel, S.,. An experimantal study of pressure and strain rate on ch chemiluminescence on premixed fuel-lean methans /air flames. FUEL 8,, PP [] Cremer, L., 97. The treatment of fans as black boxes. Journal of Sound and Vibration, 6(), -5. [] Schuermans, B., Bellucci, B., Guethe, F., and Meili, F., 3. A detailed analysis of thermoacoustic interaction mechanisms in a turbulent premixed flame. ASME GT , Proc. ASME Turbo Expo 4, Vienna, June 4-7. [3] Fanaca, D., Alemela, P. R., Ettner, F., Hirsch, C., Sattelmayer, T., and Schuermans, B., 8. Determination and comparison of the dynamic characteristics of a perfectly premixed flame in both single and annular combustion chambers. ASME GT8-578, Proc. ASME Turbo Expo 8, Berlin, June 9-3. Copyright c 9 by Alstom