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Cyclic modulation characteristics of pulse combustors
Twenty-Seventh Symposium (International) on Combustion/The Combustion Institute, 1998/pp. 3155–3162
CYCLIC MODULATION CHARACTERISTICS OF PULSE COMBUSTORS S. MARSANO, P. J. BOWEN and T. O’DOHERTY Cardiff School of Engineering Queen’s Buildings, The Parade P.O. Box 685 Cardiff CF2 3TA, Wales, UK
Pulse combustors have been recognized for some time as highly efficient combustors inducing high rates of heat transfer while producing relatively low levels of pollutants. However, the highly transient nature of the interaction between the fluid dynamic and combustion processes within the combustor means that adequately modeling such a system is a difficult proposition. In this paper, experimental results are presented for a 250-kW aerovalved pulse combustor that identify further complications to the problem. The phase difference between pressure and heat release oscillations is observed to modulate from cycle to cycle, and associated frequency variations are also identified. The characteristics of the inlet flow of reactants are also shown to exhibit periodic behavior, and it is postulated that this is responsible for the phase-shift modulations observed within the combustor. Several variations of a phenomenological spatially averaged model are introduced in an attempt to induce the cyclical modulations and hence substantiate the hypothesis. First, characteristics of a basic model with steady inlet flow are established and compared against mean values obtained from the experiments. A range of inlet flows for which continuous oscillations are induced is found, outside of which either flame extinction or steady combustion regimes prevail. Within the oscillatory regime, characteristics of pressure and temperature compare favorably with mean values measured. However, no phase modulation is predicted. Introduction of a sinusoidally varying flow of reactants induces modulations of the type observed in the experiments. Finally, coupling the frequency of the periodic flow of reactants with pressure oscillations within the combustor results in more chaotic oscillations, as observed in the experiments. There is no obvious similarity between pressure and heat release signatures for this model, but consistent with Rayleigh’s Criterion, excitation of the pressure oscillations occurs when the phase difference between pressure and heat release is at a minimum.
Introduction Flames are sensitive to excitation from sound waves, and their response depends upon the amplitude, frequency, and nature of wave impingement [1]. In pulse combustors (PCs), the response to this excitation can lead to increased combustion and thermal efficiencies, high rates of heat transfer, and reduced pollutant emissions, especially NOx. In these devices, the process of pulsating combustion involves the coupling of a three-dimensional transient flow field, generated by a transient energy release, with a resonant acoustic pressure wave. The Rayleigh criterion states the importance of the phase relationship between energy release and acoustic pressure wave in driving the pulsating combustion process [2]. The overall performance of a pulse combustor is a strong function of this phase relationship [3], so ignition delay is critical if a pulse combustor is to operate under optimum conditions. Changes in the ignition delay time cause changes in both oscillatory pressure amplitude and the frequency of operation [4,5]. The total ignition delay time is dependent upon three discrete processes [3]: first, the
mixing of fuel and air for non-premixed systems; second, the mixing between fresh reactants with the hot products of the previous cycle; and third, the chemical kinetics. In the present work, the ignition delay due to variation in the inlet flow of reactants has been investigated. A combustion model has been developed from one similar to that originally proposed by Richards et al. [6], which considered premixed conditions and a steady supply of fuel and air. This upgraded model has been appraised against results from a 250kW experimental PC [7,8]. The pure fuel and the open air inlets of this naturally aspirating PC generate a complicated unsteady flow of reactants, which in turn varies the phase shift between heat release and acoustic pressure wave—the Rayleigh phase. This results in irregularities in the oscillations such as amplitude modulation and cyclical frequency variations. The aim of this research is to explore the sensitivity of these modulations to inlet conditions comparing theoretical and experimental results. To adapt the model, it was essential to introduce a nonsteady
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Fig. 1. Geometry of the 250-kW pulse combustor used in the experiments.
the various model predictions are compared against new experimental data. Experiments
Fig. 2. The measured frequency of the temperature oscillations in the tailpipe. The approximative operational load is 120 kW of heat input. Due to the instability of the aerovalved-type combustor, instead of cycle averaging, a more realistic approach is not neglecting the fluctuations.
Fig. 3. Instantaneous experimental data of pressure and temperature in the combustion chamber at 0.025 m from the wall. Uncorrected temperature profiles have low amplitude and the peaks are delayed because of the response time of the thermocouple.
supply of premixed fuel and air. This induces the observed amplitude modulation of parameters such as pressure, temperature, and velocity. Theoretical results obtained with the steady and the unsteady inlet configurations are compared, and conclusions regarding the ignition delay are proposed. Results of
The 250-kW combustor used in the experiments consists of an inlet tube, combustor chamber, tailpipe, fuel inlet, and a resonance/tailpipe (Fig. 1). The spark plug and an initial airflow are needed only to initiate the oscillatory process that commences with an initial explosion, after which operation becomes self-sustaining. The operational load could be varied between about 60 and 260 kW of heat input using propane as the fuel. The pressure wave was measured using a fast response piezoelectric pressure transducer, and temperature was recorded with fine-wire thermocouples. The temperature measurements were corrected because of the slow response of the thermocouples compared to the cycle time. Velocity measurements were carried out using laser Doppler anemometry. The pulse combustor investigated is the aerovalved Helmholtz type. In these types of combustors, the cold air from the inlet restriction acts as a resistance for the gases attempting to exit the combustion chamber through the inlet. Still, in practice, a considerable amount of gas flows through the inlet during the high-pressure part of the cycle. This backflow complicates the process further still. The most important measurements to compare different operating conditions and burner configurations are simultaneous pressure and heat release measurements. These measurements indicate how closely Rayleigh’s criterion is satisfied. The evaluation of the frequency and the pressure amplitudes shows an important feature of the aerovalved-type combustor (Figs. 2 and 3). The frequency and amplitude of the pressure oscillations fluctuate considerably about their respective mean values. Moreover, the phase difference between pressure and temperature oscillations varies notably during operation. The results of measurements of the oscillating flows in inlet, outlet, fuel
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˙ is the heat transfer through the combustor wall. Q the instantaneous heat release per unit volume due to combustion. The mass balance in the combustion chamber is dq 4 Zi 1 Ze dt Combustion Submodel A bimolecular reaction rate law (C3H8 ` 5O2 → 3CO2 ` 4H2O) between the fuel (subscript f ) and ˙: the oxygen (subscript o) is employed to quantify Q Fig. 4. Cycle-averaged measurement of inlet and outlet velocities and fuel flow. Positive and negative values represent respectively flow in and flow out. The load is 120 kW of heat input.
line, and combustion chamber provide an indication of internal mixing conditions (Fig. 4). The pressure, temperature, fuel flow, and airflow data give an indication of the ignition delay time. The oscillation in the fuel line is fairly strong but always results in a positive supply of fuel to the combustion chamber. Models The model chosen takes the form of a thermal PC model in the sense that the process is characterized by the effect of heat transfer on the oscillations. The description of the physical process is simplified by integrating the general equations of motion over the PC volume. In this zero-dimensional system, effects of friction in the tailpipe and heat losses from the combustion zone are included. The friction force developed from the wall shear stress is introduced by way of a conventional friction coefficient, f [9]. Heat losses occur in the form of heat transfer between the gases and the combustor wall, where a convective heat transfer coefficient, h, is specified. The wall is presumed to be at a constant temperature, Tw. Solving the conservation equations for energy, mass and species in the combustion chamber, and momentum in the tail pipe induces the combustion and acoustic oscillations under appropriate conditions. Energy Balance Using the model previously outlined, the general equation of energy conservation is 1 dP 4 Cp[T0Zi 1 TZe] c 1 1 dt ˙ ` h (Tw 1 T) `Q Lc1
(1)
The last term on the right in equation 1 represents
˙ 4 DHf R˙ f Q
(2)
R˙ f 4 AT1/2q2Y0Yf e1c/T
(3)
Yf and Yo are determined from conservation of species. The model considers only stoichiometric conditions. Momentum and Mass Balance in the Tailpipe To determine the tailpipe velocity, the momentum conservation equation in the tailpipe is introduced:
1
2
du RTe f u3 4 (Pe 1 P0) 1 dt LtpPe 2Dtp |u|
(4)
The last term on the right of equation 4 represents frictional losses due to the wall shear stress [9]. Isentropic flow equations are used to relate pressures and temperatures in the combustion chamber to those in the tailpipe, thereby closing the system of equations. Initial Conditions The initial conditions are set as Ti 4 5 2 T0, Pi 4 P0, Yi 4 0.06, ui 4 0 m/s, which corresponds physically to filling the combustor with unburned fuel and air at ambient pressure, with no exiting flow, but at an absolute temperature of five times ambient temperature, high enough to initiate combustion. Inlet Mass Flow Two configurations for the flow of reactants have been considered; first a steady inlet flow, then a sinusoidal one. The experimental PC is fed with pure fuel and has an open air inlet (Fig. 1). Thus, the model with sinusoidal inlet flow allows better simulation of this PC. However, a theoretical comparison between the two inlet models has been conducted. The way the reactants are admitted in the combustor affects the ignition delay time and hence the phase shift between heat release and the acoustic wave [4,5]. Leaving the combustor model unchanged apart for the inlet conditions permits an investigation of the ignition delay time.
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Fig. 5. Predicted pressure (thick line) and temperature (thin line) obtained using Tw 4 1000 K, h 4 120 W/m2 K, f 4 0.03 with steady inlet of reactants of 0.055 kg/s. Close-up picture shows the phase between pressure and temperature.
Fig. 6. Predicted amplitude and frequency of oscillations as functions of the inlet flow of reactants. Tw 4 1000 K, h 4 120 W/m2 K, f 4 0.03. Combustor fed at constant loads.
Sinusoidal Inlet Flow As a first attempt to investigate the effect of the open air inlet configuration of the experimental combustor, a modified premixed PC has been considered: A nonsteady supply of reactants through a single inlet for both fuel and air is utilized, using a parametric expression for simplicity. Measurement of fuel flow and inlet velocity suggested that the inlet mass flow should be modeled as a sinusoidal function (Fig. 4): m ˙ i 4 C1 ` C2 sin(2qmt ` d)
(5)
Results and Discussion Steady Inlet Flow The predictions for pressure and temperature calculated for the “premixed” experimental combustor with steady inlet supply of fuel and air are shown in
Fig. 5. The simulation is presented for the first second of operational time. The rise in pressure and temperature occurring in the first millisecond of simulation are caused by the initial conditions and the sudden occurrence of reaction, but they should not affect the final solutions significantly. One-half second after start-up, the amplitude of the oscillations stabilizes. At this point, with an inlet mass flow of 0.055 kg/s, the predicted amplitudes of oscillations are approximately 60 kPa about a mean value of 110 kPa for pressure, and 410 K about a mean value of 1500 K for temperature. The mean amplitudes of the predicted oscillations are in reasonable agreement with those measured (Fig. 3). The predicted frequency of the oscillations is 69 Hz, and the average measured frequency was 75 Hz. This difference is considered to be primarily due to difficulties in estimating the effective length of the tailpipe because the shape of the exhaust is simplified in the model. As expected for a pulse combustor working under optimum conditions, the predicted phase shift between heat release and pressure wave, Dtp, is small (0.52 ms 4 12.88) and does not modulate between cycles. Thus, the Rayleigh criterion is satisfied, and stable combustion oscillations producing large pressure and temperature amplitudes are predicted. The oscillations of the predicted fuel mass fraction in the combustion chamber were compared with those for gas temperature, and as for Dtp, the phase shift between temperature and fuel mass fraction, DTYf , was found to be constant with time. The heat transfer process is prescribed by fixing the wall temperature at 1000 K, as measured, and setting the heat transfer coefficient at 120 W/m2 K. The friction factor in the tailpipe was set at 0.03. The inlet mass flow, which strongly affects the oscillations, was set at 0.055 kg/s. Large, stable oscillations, with constant Dtp, are observed when the inlet mass flow is set between 0.03 and 0.06 kg/s. Moreover, the amplitude of pressure oscillations is almost constant for these values of inlet flow (Fig. 6). The predicted amplitudes of temperature oscillations depend critically on the value of inlet mass flow, whereas the frequency of the oscillations does not. The frequency varies from 63 up to 69 Hz during stable oscillations. For inlet mass flows outside the range 0.015–0.065 kg/s either extinction or steady combustion conditions are predicted. When the inlet flow exceeds 0.06 kg/s, the predicted oscillation amplitudes rapidly decrease and steady combustion prevails. The occurrence of flame extinction is rather more complicated. For inlet flow less than 0.015 kg/s, the oscillations start to decrease quickly and become unstable as modulation effects develop. Low-temperature, fuel mass fraction at the stoichiometric inlet value and the pressure approaching atmospheric characterize flame extinction.
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Fig. 7. Predicted pressure and temperature with the combustor fed at unsteady load (sinusoidal). Load average value 0.05 kg/s, load amplitude 0.035 kg/s, load frequency 68 Hz (constant). Close-up pictures show phase shift between pressure and temperature at two different cycles (a and b). Tw 4 1000 K, h 4 120 W/m2 K, f 4 0.03.
However, steady flow inlet conditions do not predict some of the characteristics of the experimental PC. For instance, by comparison with experimental results, it is evident that such a model is not capable of simulating the amplitude and frequency modulations measured (Fig. 3). Hence, a first step to upgrade the model is to introduce a nonsteady supply of premixed fuel and air and investigate the effect on the oscillations. Sinusoidal Inlet Flow Using a sinusoidal inlet mass flow condition, amplitude modulations of pressure and temperature were predicted as well as frequency and phase shift changes from cycle to cycle (Fig. 7). The frequency and phase shift modulations from cycle to cycle represent a significant difference between the two models. The parameters of the sinusoidal inlet were chosen from the investigation conducted with the use of the basic model and from experimental data. Sensitive modulation effects are generated with values of the mean inlet mass flow C1 ranging from 0.035 up to 0.06 kg/s, the same range of inlet mass flow within which large and stable oscillations were predicted by the basic model. The experimental data show a clear reversed flow in the air inlet pipe (Fig. 4), and this high rate of reverse reactants flow is modeled with values of C2 ranging from 1.5 to twice the value of C1, corresponding to a maximum reverse flow of 0.03 kg/s. The frequency m of the inlet flow has initially been
set at the value predicted by the steady model for the internal flow. Although the inlet frequency is fixed, frequency changes are simulated for the internal flow. In reality, changes in the internal flow frequency would be coupled to the frequency of the inlet flow of reactants. The initial phase of the inlet mass flow of reactants, d, only weakly affects the simulated oscillation. It is mainly used to set appropriate initial conditions because on physical grounds, its value should guarantee a decreasing inlet flow following ignition. Adopting this sinusoidal inlet flow, the model predicts oscillations varying from 63 up to 89 kPa for pressure, and from 480 up to 550 K for temperature with the modulation in good agreement with that measured. Furthermore, the predicted phase shift between pressure and temperature decreases from a peak of 0.68 ms (16.98) down to 0.62 ms (14.68) during the highest amplitude cycles, indicating faster reaction and higher efficiency in agreement with Rayleigh’s criterion (Fig. 7). Similarly, the phase shift between temperature and fuel mass fraction decreases from 4.55 ms (113.78) down to 3.93 ms (92.68), and the frequency of the oscillations decreases from 70 down to 65 Hz during the highest amplitude cycles. Further improvements to the inlet flow model are now considered. Because the flow in the open inlet is driven by the internal flow, frequencies and amplitudes of these flows are coupled, so that frequency changes in one should influence the frequency of the other. A modification to the inlet flow is introduced
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Fig. 8. Predicted pressure and temperature at unsteady load, average load 0.05 kg/s, load amplitude 0.09 kg/s. In this simulation, the frequency of the inlet flow was related with a feedback mechanism to the frequency of the pressure oscillations in the combustion chamber.
Fig. 9. Instantaneous experimental data of pressure and temperature in the combustion chamber. Maximum temperature 1800 K, minimum 1350 K. Pressure in the range of 75–130 kPa. The load is 120 kW of heat input.
to account for this feedback effect, in that the frequency of the inlet flow is adjusted to the internal frequency of oscillation at each time step. Now the simulated oscillations of temperature and pressure are more irregular (Fig. 8), and the temperature curve in particular shows abrupt changes in both the amplitude and frequency of the oscillations. Temperature amplitude changes suddenly from 100 to 380 K with an irregular mean value while the frequency varies from 56 up to 74 Hz with no clear evidence of a relationship between frequency and the amplitude of the oscillations. The predicted pressure curve is rather irregular also, and the amplitudes of the oscillations vary from 41 to 82 kPa. The sensitivity of the model to parameters C1 and C2 is now not as strong as it was with the previous sinusoidal inlet. This updated model shows a more realistic behavior if compared with measurements over an extended operational time (Fig. 9). The temperature and pressure profiles are now less comparable than in Fig. 7. There is no obvious correspondence between the amplitudes of pressure and temperature oscillations; that is, the highest amplitude of pressure does not necessarily correspond
to the highest amplitude of temperature. This is a significant difference compared with the simulation conducted when a basic sinusoidal inlet flow was adopted. The phase shift between pressure and temperature ranges from a maximum of 1.88 ms (458) down to 1.22 ms (28.78) during the highest amplitude cycles of pressure. Hence, the updated model shows that the acoustic pressure oscillations are excited when the phase shift between heat released from combustion and the pressure oscillations reduces. Similarly, the pressure oscillations are weakened when the phase shift between temperature and pressure increases. The phase shift appears to be the parameter that most affects the evolution of the oscillations and is considerably more influential than the absolute amount of heat released during each cycle. It should also be noted that the mean temperature is generally higher during the cycles with highest amplitudes of pressure. Table 1 provides a summary of the main characteristics of the oscillations predicted with the different conditions utilized for inlet flow of reactants. Conclusions This paper presents several variations of a spatially averaged phenomenological model to provide predictions of trends recently observed in a 250-kW pulse combustor with aerovalved inlets. Recent measurements in this combustor are presented that identify instabilities in the combustion oscillations for the Helmholtz-type combustor through the following: comparing instantaneous measurements of pressure and temperature to identify a transient phase difference and analyzing frequency fluctuations of pressure and temperature at different locations in the combustion chamber and in the tailpipe. Not surprisingly, measurements of inlet flow characteristics also show harmonic variations, and it is proposed that these variations are the
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TABLE 1 Summary of main theoretical and experimental results Theoretical Results
Phase T-P Phase T-Y Frequency (Hz) Pressure amplitude (kPa) Temperature amplitude (K) Fuel mass fraction amplitude aThe
Steady Inlet
Simple Sinusoidal Inleta
Less Simplified Inletb
Experimental Results
12.88 1088 69 60 410 0.009
14.68/16.98 938/1148 65/70 89/63 550/480 0.013/0.012
28.78/458 768/1368 56/74 82/41 380 max
258/11108 71/100 42/28 270 max
inlet flow of reactants has fixed frequency, and the reverse flow is neglected. flow of reactants with frequency set cycle by cycle at the internal frequency of oscillations, reverse flow consid-
bInlet
ered.
likely source of the modulation of phase difference between various diagnostics within the combustor. Several variations of the model for inlet flow of reactants to the combustor have been proposed and investigated. First, with a steady inlet flow of reactants, oscillatory combustion was predicted for a specific range of inlet mass flows. When the inlet mass flow was too low, flame extinction was predicted, and beyond the upper limit, stable combustion prevailed. Within the stable regime, reasonable agreement was found between the predicted mean values of the combustor diagnostics and the experimental data, but no variation in phase shift was predicted. Second, the inlet flow was modeled as a premixed sinusoidal supply of reactants, allowing reverse flow in the inlet, and adopting this variation induced the modulations identified experimentally between the primary variables. Finally, the frequency of the inlet supply was coupled to the frequency in the main combustor that, while generally retaining the feedback loop between the acoustic wave and heat release, induced a more stochastic oscillatory behavior showing less similarity between temperature and pressure signatures, again consistent with the experimental records. Acoustic pressure oscillations were repeatedly excited and diminished from cycle to cycle as the phase shift between heat released from combustion and pressure oscillations fluctuates.
Ltp Lc1 m ˙i P Pe P0 ˙ Q q R˙f T Te Tw T0 t u Yf Y0 Ze Zi DHf d, m c q
length of the tailpipe volume to surface area ratio of combustion chamber instantaneous mass inlet rate pressure in the combustion chamber pressure at the tailpipe entrance ambient pressure heat release per unit volume heat transfer rate through the combustor wall fuel reaction rate temperature in the combustion chamber temperature at the tailpipe entrance temperature of combustor wall ambient temperature time velocity of the gas in the tailpipe fuel mass fraction oxygen mass fraction exit mass flow per combustion chamber volume inlet mass flow per combustion chamber volume heat of reaction constants in sinusoidal inlet flow function ratio of specific heat density
REFERENCES
Nomenclature Cp C1 C2 Dtp f h Lf
specific heat at constant pressure average value of the inlet flow of reactants amplitude of the sinusoidal inlet flow of reactants diameter of the tailpipe frequency of oscillations in combustor convective heat transfer coefficient friction losses in tailpipe
1. Tyndall, J., Sound, D. Appleton & Co., New York, 1897. 2. Lord Rayleigh, Nature 18:319 (1878). 3. Keller, J. O., Bramlette, T. T., Dec, J. E., and Westbrook, C. K., “Pulse Combustion: The Importance of Characteristic Times,” Combust. Flame 75:33–44 (1989). 4. Tsujimoto, Y. and Machii N., in Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1986, pp. 539–546.
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5. Vishwanath, P. S. and Priem, R. J., Poster presentation at the Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1986. 6. Richards, G. A., Morris, G. J., Shaw, D. W., Keeley, S. A., and Welter, M. J., “Thermal Pulse Combustion,” Combust. Sci. Technol. 94:57–85 (1993). 7. Van Den Bos, B., “Experimental Studies in Pulse Combustion,” Division of Mechanical Engineering, Univer-
sity of Wales, Cardiff, Internal report 2157, August 1996. 8. Marsano, S., “A Phenomenological Model for Pulse Combustion,” Division of Mechanical Engineering, University of Wales, Cardiff, Internal report 2171, September 1996. 9. Schlichting, H., Boundary Layer Theory, McGraw-Hill, New York, ISBN 0-07-055334-3.
COMMENTS Joao A. Carvalho Jr., INPE, Brazil. What is done to account for the amplitude difference and phase lag in the measured temperature in relation to the real temperature? ● Jay Keller, Sandia National Laboratories, USA. Would you please describe the thermocouple correction you used to reduce your temperature measurements? Also, what is the radial location of the thermocouple? Author’s Reply. Both of the questions relate to how transient thermocouple measurements are compensated in terms of amplitude difference and the time lag (response) of measurements to actual temperatures. We acknowledge these sentiments behind the questions in that the use of thermocouples in this environment is not ideal. The experimental measurements presented have been compensated in terms of radiation and convection losses, consistent with established methodologies [1–3]. We have also developed a post processor to compensate for thermocouple phase lag.
The emphasis of the paper was to model heat-release/ pressure-phase modulation and to compare qualitatively with the experimental data. The question now arises of whether phase modulation is a real phenomenon or artifact for thermocouple response time. Since presenting this paper, we have confirmed phase modulation experimentally by using transient CH emission data to characterize heat release and also by using an improved methodology for thermocouple compensation. These data will be described in a forthcoming paper in preparation that models the combustor in a non-premixed manner.
REFERENCES 1. Keller, J. O. and Saito, K., CST 53:137–163 (1987). 2. Heitor, M. V. and Moreira, A. L. N., Prog. Energy Combust. Sci. 19:259–278 (1993). 3. Tagawa, M. and Ohta, Y., Combust. Flame 109:549–560 (1993).
CYCLIC MODULATION CHARACTERISTICS OF PULSE COMBUSTORS S. MARSANO, P. J. BOWEN and T. O’DOHERTY Cardiff School of Engineering Queen’s Buildings, The Parade P.O. Box 685 Cardiff CF2 3TA, Wales, UK
Pulse combustors have been recognized for some time as highly efficient combustors inducing high rates of heat transfer while producing relatively low levels of pollutants. However, the highly transient nature of the interaction between the fluid dynamic and combustion processes within the combustor means that adequately modeling such a system is a difficult proposition. In this paper, experimental results are presented for a 250-kW aerovalved pulse combustor that identify further complications to the problem. The phase difference between pressure and heat release oscillations is observed to modulate from cycle to cycle, and associated frequency variations are also identified. The characteristics of the inlet flow of reactants are also shown to exhibit periodic behavior, and it is postulated that this is responsible for the phase-shift modulations observed within the combustor. Several variations of a phenomenological spatially averaged model are introduced in an attempt to induce the cyclical modulations and hence substantiate the hypothesis. First, characteristics of a basic model with steady inlet flow are established and compared against mean values obtained from the experiments. A range of inlet flows for which continuous oscillations are induced is found, outside of which either flame extinction or steady combustion regimes prevail. Within the oscillatory regime, characteristics of pressure and temperature compare favorably with mean values measured. However, no phase modulation is predicted. Introduction of a sinusoidally varying flow of reactants induces modulations of the type observed in the experiments. Finally, coupling the frequency of the periodic flow of reactants with pressure oscillations within the combustor results in more chaotic oscillations, as observed in the experiments. There is no obvious similarity between pressure and heat release signatures for this model, but consistent with Rayleigh’s Criterion, excitation of the pressure oscillations occurs when the phase difference between pressure and heat release is at a minimum.
Introduction Flames are sensitive to excitation from sound waves, and their response depends upon the amplitude, frequency, and nature of wave impingement [1]. In pulse combustors (PCs), the response to this excitation can lead to increased combustion and thermal efficiencies, high rates of heat transfer, and reduced pollutant emissions, especially NOx. In these devices, the process of pulsating combustion involves the coupling of a three-dimensional transient flow field, generated by a transient energy release, with a resonant acoustic pressure wave. The Rayleigh criterion states the importance of the phase relationship between energy release and acoustic pressure wave in driving the pulsating combustion process [2]. The overall performance of a pulse combustor is a strong function of this phase relationship [3], so ignition delay is critical if a pulse combustor is to operate under optimum conditions. Changes in the ignition delay time cause changes in both oscillatory pressure amplitude and the frequency of operation [4,5]. The total ignition delay time is dependent upon three discrete processes [3]: first, the
mixing of fuel and air for non-premixed systems; second, the mixing between fresh reactants with the hot products of the previous cycle; and third, the chemical kinetics. In the present work, the ignition delay due to variation in the inlet flow of reactants has been investigated. A combustion model has been developed from one similar to that originally proposed by Richards et al. [6], which considered premixed conditions and a steady supply of fuel and air. This upgraded model has been appraised against results from a 250kW experimental PC [7,8]. The pure fuel and the open air inlets of this naturally aspirating PC generate a complicated unsteady flow of reactants, which in turn varies the phase shift between heat release and acoustic pressure wave—the Rayleigh phase. This results in irregularities in the oscillations such as amplitude modulation and cyclical frequency variations. The aim of this research is to explore the sensitivity of these modulations to inlet conditions comparing theoretical and experimental results. To adapt the model, it was essential to introduce a nonsteady
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Fig. 1. Geometry of the 250-kW pulse combustor used in the experiments.
the various model predictions are compared against new experimental data. Experiments
Fig. 2. The measured frequency of the temperature oscillations in the tailpipe. The approximative operational load is 120 kW of heat input. Due to the instability of the aerovalved-type combustor, instead of cycle averaging, a more realistic approach is not neglecting the fluctuations.
Fig. 3. Instantaneous experimental data of pressure and temperature in the combustion chamber at 0.025 m from the wall. Uncorrected temperature profiles have low amplitude and the peaks are delayed because of the response time of the thermocouple.
supply of premixed fuel and air. This induces the observed amplitude modulation of parameters such as pressure, temperature, and velocity. Theoretical results obtained with the steady and the unsteady inlet configurations are compared, and conclusions regarding the ignition delay are proposed. Results of
The 250-kW combustor used in the experiments consists of an inlet tube, combustor chamber, tailpipe, fuel inlet, and a resonance/tailpipe (Fig. 1). The spark plug and an initial airflow are needed only to initiate the oscillatory process that commences with an initial explosion, after which operation becomes self-sustaining. The operational load could be varied between about 60 and 260 kW of heat input using propane as the fuel. The pressure wave was measured using a fast response piezoelectric pressure transducer, and temperature was recorded with fine-wire thermocouples. The temperature measurements were corrected because of the slow response of the thermocouples compared to the cycle time. Velocity measurements were carried out using laser Doppler anemometry. The pulse combustor investigated is the aerovalved Helmholtz type. In these types of combustors, the cold air from the inlet restriction acts as a resistance for the gases attempting to exit the combustion chamber through the inlet. Still, in practice, a considerable amount of gas flows through the inlet during the high-pressure part of the cycle. This backflow complicates the process further still. The most important measurements to compare different operating conditions and burner configurations are simultaneous pressure and heat release measurements. These measurements indicate how closely Rayleigh’s criterion is satisfied. The evaluation of the frequency and the pressure amplitudes shows an important feature of the aerovalved-type combustor (Figs. 2 and 3). The frequency and amplitude of the pressure oscillations fluctuate considerably about their respective mean values. Moreover, the phase difference between pressure and temperature oscillations varies notably during operation. The results of measurements of the oscillating flows in inlet, outlet, fuel
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˙ is the heat transfer through the combustor wall. Q the instantaneous heat release per unit volume due to combustion. The mass balance in the combustion chamber is dq 4 Zi 1 Ze dt Combustion Submodel A bimolecular reaction rate law (C3H8 ` 5O2 → 3CO2 ` 4H2O) between the fuel (subscript f ) and ˙: the oxygen (subscript o) is employed to quantify Q Fig. 4. Cycle-averaged measurement of inlet and outlet velocities and fuel flow. Positive and negative values represent respectively flow in and flow out. The load is 120 kW of heat input.
line, and combustion chamber provide an indication of internal mixing conditions (Fig. 4). The pressure, temperature, fuel flow, and airflow data give an indication of the ignition delay time. The oscillation in the fuel line is fairly strong but always results in a positive supply of fuel to the combustion chamber. Models The model chosen takes the form of a thermal PC model in the sense that the process is characterized by the effect of heat transfer on the oscillations. The description of the physical process is simplified by integrating the general equations of motion over the PC volume. In this zero-dimensional system, effects of friction in the tailpipe and heat losses from the combustion zone are included. The friction force developed from the wall shear stress is introduced by way of a conventional friction coefficient, f [9]. Heat losses occur in the form of heat transfer between the gases and the combustor wall, where a convective heat transfer coefficient, h, is specified. The wall is presumed to be at a constant temperature, Tw. Solving the conservation equations for energy, mass and species in the combustion chamber, and momentum in the tail pipe induces the combustion and acoustic oscillations under appropriate conditions. Energy Balance Using the model previously outlined, the general equation of energy conservation is 1 dP 4 Cp[T0Zi 1 TZe] c 1 1 dt ˙ ` h (Tw 1 T) `Q Lc1
(1)
The last term on the right in equation 1 represents
˙ 4 DHf R˙ f Q
(2)
R˙ f 4 AT1/2q2Y0Yf e1c/T
(3)
Yf and Yo are determined from conservation of species. The model considers only stoichiometric conditions. Momentum and Mass Balance in the Tailpipe To determine the tailpipe velocity, the momentum conservation equation in the tailpipe is introduced:
1
2
du RTe f u3 4 (Pe 1 P0) 1 dt LtpPe 2Dtp |u|
(4)
The last term on the right of equation 4 represents frictional losses due to the wall shear stress [9]. Isentropic flow equations are used to relate pressures and temperatures in the combustion chamber to those in the tailpipe, thereby closing the system of equations. Initial Conditions The initial conditions are set as Ti 4 5 2 T0, Pi 4 P0, Yi 4 0.06, ui 4 0 m/s, which corresponds physically to filling the combustor with unburned fuel and air at ambient pressure, with no exiting flow, but at an absolute temperature of five times ambient temperature, high enough to initiate combustion. Inlet Mass Flow Two configurations for the flow of reactants have been considered; first a steady inlet flow, then a sinusoidal one. The experimental PC is fed with pure fuel and has an open air inlet (Fig. 1). Thus, the model with sinusoidal inlet flow allows better simulation of this PC. However, a theoretical comparison between the two inlet models has been conducted. The way the reactants are admitted in the combustor affects the ignition delay time and hence the phase shift between heat release and the acoustic wave [4,5]. Leaving the combustor model unchanged apart for the inlet conditions permits an investigation of the ignition delay time.
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Fig. 5. Predicted pressure (thick line) and temperature (thin line) obtained using Tw 4 1000 K, h 4 120 W/m2 K, f 4 0.03 with steady inlet of reactants of 0.055 kg/s. Close-up picture shows the phase between pressure and temperature.
Fig. 6. Predicted amplitude and frequency of oscillations as functions of the inlet flow of reactants. Tw 4 1000 K, h 4 120 W/m2 K, f 4 0.03. Combustor fed at constant loads.
Sinusoidal Inlet Flow As a first attempt to investigate the effect of the open air inlet configuration of the experimental combustor, a modified premixed PC has been considered: A nonsteady supply of reactants through a single inlet for both fuel and air is utilized, using a parametric expression for simplicity. Measurement of fuel flow and inlet velocity suggested that the inlet mass flow should be modeled as a sinusoidal function (Fig. 4): m ˙ i 4 C1 ` C2 sin(2qmt ` d)
(5)
Results and Discussion Steady Inlet Flow The predictions for pressure and temperature calculated for the “premixed” experimental combustor with steady inlet supply of fuel and air are shown in
Fig. 5. The simulation is presented for the first second of operational time. The rise in pressure and temperature occurring in the first millisecond of simulation are caused by the initial conditions and the sudden occurrence of reaction, but they should not affect the final solutions significantly. One-half second after start-up, the amplitude of the oscillations stabilizes. At this point, with an inlet mass flow of 0.055 kg/s, the predicted amplitudes of oscillations are approximately 60 kPa about a mean value of 110 kPa for pressure, and 410 K about a mean value of 1500 K for temperature. The mean amplitudes of the predicted oscillations are in reasonable agreement with those measured (Fig. 3). The predicted frequency of the oscillations is 69 Hz, and the average measured frequency was 75 Hz. This difference is considered to be primarily due to difficulties in estimating the effective length of the tailpipe because the shape of the exhaust is simplified in the model. As expected for a pulse combustor working under optimum conditions, the predicted phase shift between heat release and pressure wave, Dtp, is small (0.52 ms 4 12.88) and does not modulate between cycles. Thus, the Rayleigh criterion is satisfied, and stable combustion oscillations producing large pressure and temperature amplitudes are predicted. The oscillations of the predicted fuel mass fraction in the combustion chamber were compared with those for gas temperature, and as for Dtp, the phase shift between temperature and fuel mass fraction, DTYf , was found to be constant with time. The heat transfer process is prescribed by fixing the wall temperature at 1000 K, as measured, and setting the heat transfer coefficient at 120 W/m2 K. The friction factor in the tailpipe was set at 0.03. The inlet mass flow, which strongly affects the oscillations, was set at 0.055 kg/s. Large, stable oscillations, with constant Dtp, are observed when the inlet mass flow is set between 0.03 and 0.06 kg/s. Moreover, the amplitude of pressure oscillations is almost constant for these values of inlet flow (Fig. 6). The predicted amplitudes of temperature oscillations depend critically on the value of inlet mass flow, whereas the frequency of the oscillations does not. The frequency varies from 63 up to 69 Hz during stable oscillations. For inlet mass flows outside the range 0.015–0.065 kg/s either extinction or steady combustion conditions are predicted. When the inlet flow exceeds 0.06 kg/s, the predicted oscillation amplitudes rapidly decrease and steady combustion prevails. The occurrence of flame extinction is rather more complicated. For inlet flow less than 0.015 kg/s, the oscillations start to decrease quickly and become unstable as modulation effects develop. Low-temperature, fuel mass fraction at the stoichiometric inlet value and the pressure approaching atmospheric characterize flame extinction.
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Fig. 7. Predicted pressure and temperature with the combustor fed at unsteady load (sinusoidal). Load average value 0.05 kg/s, load amplitude 0.035 kg/s, load frequency 68 Hz (constant). Close-up pictures show phase shift between pressure and temperature at two different cycles (a and b). Tw 4 1000 K, h 4 120 W/m2 K, f 4 0.03.
However, steady flow inlet conditions do not predict some of the characteristics of the experimental PC. For instance, by comparison with experimental results, it is evident that such a model is not capable of simulating the amplitude and frequency modulations measured (Fig. 3). Hence, a first step to upgrade the model is to introduce a nonsteady supply of premixed fuel and air and investigate the effect on the oscillations. Sinusoidal Inlet Flow Using a sinusoidal inlet mass flow condition, amplitude modulations of pressure and temperature were predicted as well as frequency and phase shift changes from cycle to cycle (Fig. 7). The frequency and phase shift modulations from cycle to cycle represent a significant difference between the two models. The parameters of the sinusoidal inlet were chosen from the investigation conducted with the use of the basic model and from experimental data. Sensitive modulation effects are generated with values of the mean inlet mass flow C1 ranging from 0.035 up to 0.06 kg/s, the same range of inlet mass flow within which large and stable oscillations were predicted by the basic model. The experimental data show a clear reversed flow in the air inlet pipe (Fig. 4), and this high rate of reverse reactants flow is modeled with values of C2 ranging from 1.5 to twice the value of C1, corresponding to a maximum reverse flow of 0.03 kg/s. The frequency m of the inlet flow has initially been
set at the value predicted by the steady model for the internal flow. Although the inlet frequency is fixed, frequency changes are simulated for the internal flow. In reality, changes in the internal flow frequency would be coupled to the frequency of the inlet flow of reactants. The initial phase of the inlet mass flow of reactants, d, only weakly affects the simulated oscillation. It is mainly used to set appropriate initial conditions because on physical grounds, its value should guarantee a decreasing inlet flow following ignition. Adopting this sinusoidal inlet flow, the model predicts oscillations varying from 63 up to 89 kPa for pressure, and from 480 up to 550 K for temperature with the modulation in good agreement with that measured. Furthermore, the predicted phase shift between pressure and temperature decreases from a peak of 0.68 ms (16.98) down to 0.62 ms (14.68) during the highest amplitude cycles, indicating faster reaction and higher efficiency in agreement with Rayleigh’s criterion (Fig. 7). Similarly, the phase shift between temperature and fuel mass fraction decreases from 4.55 ms (113.78) down to 3.93 ms (92.68), and the frequency of the oscillations decreases from 70 down to 65 Hz during the highest amplitude cycles. Further improvements to the inlet flow model are now considered. Because the flow in the open inlet is driven by the internal flow, frequencies and amplitudes of these flows are coupled, so that frequency changes in one should influence the frequency of the other. A modification to the inlet flow is introduced
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Fig. 8. Predicted pressure and temperature at unsteady load, average load 0.05 kg/s, load amplitude 0.09 kg/s. In this simulation, the frequency of the inlet flow was related with a feedback mechanism to the frequency of the pressure oscillations in the combustion chamber.
Fig. 9. Instantaneous experimental data of pressure and temperature in the combustion chamber. Maximum temperature 1800 K, minimum 1350 K. Pressure in the range of 75–130 kPa. The load is 120 kW of heat input.
to account for this feedback effect, in that the frequency of the inlet flow is adjusted to the internal frequency of oscillation at each time step. Now the simulated oscillations of temperature and pressure are more irregular (Fig. 8), and the temperature curve in particular shows abrupt changes in both the amplitude and frequency of the oscillations. Temperature amplitude changes suddenly from 100 to 380 K with an irregular mean value while the frequency varies from 56 up to 74 Hz with no clear evidence of a relationship between frequency and the amplitude of the oscillations. The predicted pressure curve is rather irregular also, and the amplitudes of the oscillations vary from 41 to 82 kPa. The sensitivity of the model to parameters C1 and C2 is now not as strong as it was with the previous sinusoidal inlet. This updated model shows a more realistic behavior if compared with measurements over an extended operational time (Fig. 9). The temperature and pressure profiles are now less comparable than in Fig. 7. There is no obvious correspondence between the amplitudes of pressure and temperature oscillations; that is, the highest amplitude of pressure does not necessarily correspond
to the highest amplitude of temperature. This is a significant difference compared with the simulation conducted when a basic sinusoidal inlet flow was adopted. The phase shift between pressure and temperature ranges from a maximum of 1.88 ms (458) down to 1.22 ms (28.78) during the highest amplitude cycles of pressure. Hence, the updated model shows that the acoustic pressure oscillations are excited when the phase shift between heat released from combustion and the pressure oscillations reduces. Similarly, the pressure oscillations are weakened when the phase shift between temperature and pressure increases. The phase shift appears to be the parameter that most affects the evolution of the oscillations and is considerably more influential than the absolute amount of heat released during each cycle. It should also be noted that the mean temperature is generally higher during the cycles with highest amplitudes of pressure. Table 1 provides a summary of the main characteristics of the oscillations predicted with the different conditions utilized for inlet flow of reactants. Conclusions This paper presents several variations of a spatially averaged phenomenological model to provide predictions of trends recently observed in a 250-kW pulse combustor with aerovalved inlets. Recent measurements in this combustor are presented that identify instabilities in the combustion oscillations for the Helmholtz-type combustor through the following: comparing instantaneous measurements of pressure and temperature to identify a transient phase difference and analyzing frequency fluctuations of pressure and temperature at different locations in the combustion chamber and in the tailpipe. Not surprisingly, measurements of inlet flow characteristics also show harmonic variations, and it is proposed that these variations are the
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TABLE 1 Summary of main theoretical and experimental results Theoretical Results
Phase T-P Phase T-Y Frequency (Hz) Pressure amplitude (kPa) Temperature amplitude (K) Fuel mass fraction amplitude aThe
Steady Inlet
Simple Sinusoidal Inleta
Less Simplified Inletb
Experimental Results
12.88 1088 69 60 410 0.009
14.68/16.98 938/1148 65/70 89/63 550/480 0.013/0.012
28.78/458 768/1368 56/74 82/41 380 max
258/11108 71/100 42/28 270 max
inlet flow of reactants has fixed frequency, and the reverse flow is neglected. flow of reactants with frequency set cycle by cycle at the internal frequency of oscillations, reverse flow consid-
bInlet
ered.
likely source of the modulation of phase difference between various diagnostics within the combustor. Several variations of the model for inlet flow of reactants to the combustor have been proposed and investigated. First, with a steady inlet flow of reactants, oscillatory combustion was predicted for a specific range of inlet mass flows. When the inlet mass flow was too low, flame extinction was predicted, and beyond the upper limit, stable combustion prevailed. Within the stable regime, reasonable agreement was found between the predicted mean values of the combustor diagnostics and the experimental data, but no variation in phase shift was predicted. Second, the inlet flow was modeled as a premixed sinusoidal supply of reactants, allowing reverse flow in the inlet, and adopting this variation induced the modulations identified experimentally between the primary variables. Finally, the frequency of the inlet supply was coupled to the frequency in the main combustor that, while generally retaining the feedback loop between the acoustic wave and heat release, induced a more stochastic oscillatory behavior showing less similarity between temperature and pressure signatures, again consistent with the experimental records. Acoustic pressure oscillations were repeatedly excited and diminished from cycle to cycle as the phase shift between heat released from combustion and pressure oscillations fluctuates.
Ltp Lc1 m ˙i P Pe P0 ˙ Q q R˙f T Te Tw T0 t u Yf Y0 Ze Zi DHf d, m c q
length of the tailpipe volume to surface area ratio of combustion chamber instantaneous mass inlet rate pressure in the combustion chamber pressure at the tailpipe entrance ambient pressure heat release per unit volume heat transfer rate through the combustor wall fuel reaction rate temperature in the combustion chamber temperature at the tailpipe entrance temperature of combustor wall ambient temperature time velocity of the gas in the tailpipe fuel mass fraction oxygen mass fraction exit mass flow per combustion chamber volume inlet mass flow per combustion chamber volume heat of reaction constants in sinusoidal inlet flow function ratio of specific heat density
REFERENCES
Nomenclature Cp C1 C2 Dtp f h Lf
specific heat at constant pressure average value of the inlet flow of reactants amplitude of the sinusoidal inlet flow of reactants diameter of the tailpipe frequency of oscillations in combustor convective heat transfer coefficient friction losses in tailpipe
1. Tyndall, J., Sound, D. Appleton & Co., New York, 1897. 2. Lord Rayleigh, Nature 18:319 (1878). 3. Keller, J. O., Bramlette, T. T., Dec, J. E., and Westbrook, C. K., “Pulse Combustion: The Importance of Characteristic Times,” Combust. Flame 75:33–44 (1989). 4. Tsujimoto, Y. and Machii N., in Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1986, pp. 539–546.
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5. Vishwanath, P. S. and Priem, R. J., Poster presentation at the Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1986. 6. Richards, G. A., Morris, G. J., Shaw, D. W., Keeley, S. A., and Welter, M. J., “Thermal Pulse Combustion,” Combust. Sci. Technol. 94:57–85 (1993). 7. Van Den Bos, B., “Experimental Studies in Pulse Combustion,” Division of Mechanical Engineering, Univer-
sity of Wales, Cardiff, Internal report 2157, August 1996. 8. Marsano, S., “A Phenomenological Model for Pulse Combustion,” Division of Mechanical Engineering, University of Wales, Cardiff, Internal report 2171, September 1996. 9. Schlichting, H., Boundary Layer Theory, McGraw-Hill, New York, ISBN 0-07-055334-3.
COMMENTS Joao A. Carvalho Jr., INPE, Brazil. What is done to account for the amplitude difference and phase lag in the measured temperature in relation to the real temperature? ● Jay Keller, Sandia National Laboratories, USA. Would you please describe the thermocouple correction you used to reduce your temperature measurements? Also, what is the radial location of the thermocouple? Author’s Reply. Both of the questions relate to how transient thermocouple measurements are compensated in terms of amplitude difference and the time lag (response) of measurements to actual temperatures. We acknowledge these sentiments behind the questions in that the use of thermocouples in this environment is not ideal. The experimental measurements presented have been compensated in terms of radiation and convection losses, consistent with established methodologies [1–3]. We have also developed a post processor to compensate for thermocouple phase lag.
The emphasis of the paper was to model heat-release/ pressure-phase modulation and to compare qualitatively with the experimental data. The question now arises of whether phase modulation is a real phenomenon or artifact for thermocouple response time. Since presenting this paper, we have confirmed phase modulation experimentally by using transient CH emission data to characterize heat release and also by using an improved methodology for thermocouple compensation. These data will be described in a forthcoming paper in preparation that models the combustor in a non-premixed manner.
REFERENCES 1. Keller, J. O. and Saito, K., CST 53:137–163 (1987). 2. Heitor, M. V. and Moreira, A. L. N., Prog. Energy Combust. Sci. 19:259–278 (1993). 3. Tagawa, M. and Ohta, Y., Combust. Flame 109:549–560 (1993).