Pulse Combustion Characteristics of Various Gaseous Fuels


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Energy & Fuels 2008, 22, 915–924

915

Pulse Combustion Characteristics of Various Gaseous Fuels Wu Zhonghua* and Arun S. Mujumdar Engineering Science Program and Department of Mechanical Engineering, Mineral, Metal and Materials Technology Centre, National UniVersity of Singapore, 9 Engineering DriVe 1, 119260 Singapore ReceiVed July 19, 2007. ReVised Manuscript ReceiVed December 2, 2007

The combustion of a gas-fired pulse combustor was simulated using a computation fluid dynamic model to understand the flame structure, gas flow, and combustion characteristics in the burner and the resulting pulsation phenomenon. The specific impulse and thrust output to power input are computed and compared. Some typical gaseous fuels such as low molecular weight hydrocarbons, high molecular weight hydrocarbons, biofuels, and mixed fuels are tested via simulation of the pulse combustor, and their operation characteristics are summarized. It was found that the combustor can adjust itself automatically over a certain range of parameters and make it suitable for different gaseous fuels. Pulse combustion performance of fuels with low and high heating values is also compared.

1. Introduction Pulse combustion is recognized for its energy efficiency and reduced emission. It has several advantages such as ease of manufacture, high combustion intensity, lower NOx and CO pollutant emissions, improved heat and mass transfer, higher thermal efficiency, and its self-aspiration properties over steady combustion encountered in conventional burners.1–3 Because of these merits, pulse combustion has wide applications ranging from powering propulsion devices to incineration to drying. In pulse combustion drying, short drying time, high energy efficiency, improved product quality, and environmentally friendly operation are noted as the key advantages, and pulse combustion drying is regarded as the drying technology of the future.4–7 However, because of a lack of understanding of the pulse combustion mechanisms and the fact that pulse combustor * To whom correspondence should be addressed. Telephone: (65)-65157882. Fax: (65)-6779-1459. E-mail: [email protected] (1) Zinn, B. T. Mech. Eng. (Am. Soc. Mech. Eng.) 1985, 107, 36–41. (2) Putnam, A. A.; Belles, E.; Kentfield, J. A. C. Prog. Energy Combust. Sci. 1986, 12, 43–79. (3) Richards, G. A.; Morrs, G. J.; Shaw, D. W.; Keeler, S. A.; Welter, M. J. Combust. Sci. Technol. 1993, 94, 57–85. (4) Zinn, B. T. Pulse Combustion: Recent Applications and Research Issues. Proceedings of the 24th International Symposium on Combustion; The Combustion Institute: Pittsburgh, PA, 1992; pp 1297–1305. (5) Kudra, T.; Mujumdar, A. S. Handbook of Industrial Drying; Marcel Dekker: New York, 1995. (6) Kudra, T.; Mujumdar, A. S. AdVanced drying technologies; Marcel Dekker Inc.: New York, 2002. (7) Wu, Z. H. Mathematical Modeling of Pulse Combustion and its Applications to Innovative Thermal Drying Techniques. Ph.D. Thesis, National University of Singapore, Singapore, 2007. (8) Keller, J. O.; Hongo, I. Combust. Flame 1990, 80, 219–237. (9) Kentfield, J. A. C.; O’Blenes, M. J. J. Propul. Power 1990, 6, 214– 220. (10) Dec, J. E.; Keller, J. O.; Arpaci, V. S. Int. J. Heat Mass Transfer 1992, 35, 2311–2325. (11) Eibeck, P. A.; Keller, J. O.; Bramlette, T. T.; Sailor, D. J. Combust. Sci. Technol. 1993, 94, 147–165. (12) Neumeier, Y.; Zinn, B. T.; Jagoda, J. I. Combust. Sci. Technol. 1993, 94, 295–316. (13) Keller, J. O.; Bramlette, T. T.; Dec, J. E.; Westbrook, C. K. Combust. Flame 1989, 75, 33–44. (14) Benelli, G.; Michele de, G.; Cossalter, V.; Lio da, M.; Rossi, G. Proc. Combust. Inst. 1992, 24, 1307–1313. (15) Möller, S. I.; Lindholm, A. Combust. Sci. Technol. 1999, 149, 389– 406.

Figure 1. Schematic diagram of the simulated pulse combustor.

design relies on empirical knowledge, industrial application of pulse combustion in drying is still low. Much research has been carried out to investigate pulse combustion mechanisms.8–16 Among them, numerical methods play an important role. For example, Neumeier et al. analyzed a Helmholtz type combustor in the frequency domain creating the pulse combustor as a feedback system.12 Keller et al. investigated the pulse combustion numerically using the method of characteristic.13 In the above two methods, the combustion chamber was regarded as a well-stirred reactor with homogeneous thermal properties. Hence, these early mathematical models were simple and were used to analyze the general operational properties of pulse combustors. More advanced and comprehensive models were developed in recent years using the computational fluid dynamic (CFD) technique which has many applications in simulating the combustion process including pulse combustion.14,17,18 Benelli et al. used commercial CFD software to model the Helmholtz type pulse combustor with self-sustained acoustic oscillations.14 The inlet valves, when (16) Tarjiri, K.; Menon, S. LES of Combustion Dynamics in a Pulse Combustor. Presented at the 39th Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan 8–13, 2001. (17) Galletti, C.; Parente, A.; Tognotti, L. Combust. Flame 2007, 151, 649–664. (18) Norton, D. G.; Vlachos, D. G. Combust. Flame 2004, 138, 97– 107.

10.1021/ef7004207 CCC: $40.75  2008 American Chemical Society Published on Web 02/06/2008

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Figure 2. Computation mesh for the pulse combustor. Table 1. Homogeneous Reaction and the Kinetic Equations fuel

chemical reaction

methane propane butane methanol ethanol fuel oil

CH4 + 2O2 f CO2 + 2H2O C3H8 + 5O2 f 3CO2 + 4H2O C4H10 + 6.5O2 f 4CO2 + 5H2O CH3OH + 1.5O2 f CO2 + 2H2O C2H5OH + 3O2 f2CO2 + 3H2O C19H30 + 26.5O2 f 19CO2 + 15H2O

equation [kg mol/(m3 s)] R1 R2 R3 R4 R5 R6

) ) ) ) ) )

k1[CCH4]0.2[CO2]1.3 k2[CC3H8]0.1[CO2]1.65 k3[CC4H10]0.15[CO2]1.6 k4[CCH3OH]0.25[CO2]1.5 k5[CC2H5OH]0.15[CO2]1.6 k6[CC19H30]0.25[CO2]1.6

Table 2. Arrhenius Coefficients and Combustion Heat Related to R1-R6 reaction R1 R2 R3 R4 R5 R6

equation k3 k1 k3 k4 k5 k6

) ) ) ) ) )

2.119 4.836 4.161 1.799 8.439 2.587

× × × × × ×

1011 exp[2.027 × 108/T] 109 exp[1.256 × 108/T] 109 exp[1.256 × 108/T] 1010 exp[1.256 × 108/T] 109 exp[1.256 × 108/T] 109 exp[1.256 × 108/T]

low heating value 50.001 MJ/kg 46.362 MJ/kg 45.594 MJ/kg 21.102 MJ/kg 28.079 MJ/kg 40.531 MJ/kg

opened, were considered as orifices of a given cross section, and a characteristic pressure drop curve was used to define the relationship between the velocity and the pressure changes across the valves. Möller and Lindholm examined the effects of inlet geometry change using a large eddy simulation (LES) in a commercial CFD code, 15 and a similar model was applied by Tarjiri and Menon to investigate the combustion dynamics of a pulse combustor.16 The CFD models can provide detailed information inside the combustor including flame structure, gas dynamics, and so forth, which contribute to improving our understanding of pulse combustion. However, there are still many unknowns about the mechanisms of pulse combustion. For example, most combustors use methane, propane, natural gas, and liquefied petroleum gas (LPG) as fuels. Whether other gaseous fuels such as biofuels can be

used in pulse combustors is worth exploring. Biofuels are derived from biomass and renewable energy sources. As the demand of fossil fuels has increased worldwide, the development of renewable energy sources has become an attractive research area.19–23 For example, Lebedevas and Vaicekauskas used waste fats of animal and vegetable origin to produce biodiesel fuel and determine their motor characteristics and emissions of harmful components.19 Biofuels are important means of reducing greenhouse gas emissions and increasing energy security for nations by providing a viable alternative to increasingly expensive fossil fuels. Biofuels are also considered as potential fuels for pulse combustors and hence are examined in this work. Among biofuels, biogas is an important potential one produced by the anaerobic digestion or fermentation of organic matter such as municipal solid waste, biodegradable wastes from various industries, and so forth. Biogas is a clean gaseous fuel and does not cause air pollution as it does not contain sulfur.20 Another biofuel, ethanol, is a clean-burning, flammable, colorless, slightly toxic, high-octane fuel that can be produced from renewable sources. At its most basic level, ethanol is a grain alcohol, produced from crops such as corn. The largest single use of ethanol is as a motor fuel and fuel additive.21,22 Similar to ethanol, methanol is a light, volatile, colorless, flammable, poisonous fuel with a distinctive odor. Methanol is often called wood alcohol because it was once produced chiefly as a (19) Lebedevas, S.; Vaicekauskas, A. Energy Fuels 2006, 20, 2274– 2280. (20) Fan, Z. L.; Zhang, J.; Sheng, C. D.; Lin, X. F.; Xu, Y. Q. Energy Fuels 2006, 20, 579–582. (21) Abu-Zaid, M.; Badran, O.; Yamin, J. Energy Fuels 2004, 18, 312– 315. (22) Hou, Y. C.; Lu, X. C.; Zu, L. L.; Ji, L. B.; Huang, Z. Energy Fuels 2006, 20, 1425–1433. (23) Grammelis, P.; Kakaras, E. Energy Fuels 2005, 19, 292–297.

Pulse Combustion Characteristics of Gaseous Fuels

Energy & Fuels, Vol. 22, No. 2, 2008 917

tively, while fuel oil no. 6 is a heavy residual oil that requires preheating to burn properly. Heavy fuel oils and diesel fuels are similar and consist of hydrocarbons with more than 16 carbon atoms per molecule.24 It is also interesting to test some fuels with a high carbon number in a pulse combustor and examine how their combustion characteristics differ from fuels with a low carbon number. The aim of this paper is to predict via simulation the combustion characteristics of different gaseous fuels in pulse combustors. First, a CFD model was developed, and a baseline case was carried out to simulate the pulse combustion process of methane in a gas-fired combustor. The simulation results are compared with experimental data to validate the model. Flame structure and gas dynamics in the combustor are described on the basis of the numerical results. Parametric studies were carried out for different gaseous fuels, and their combustion characteristics are compared. The prime motivation for this study was the potential of utilization of pulse combustion using biofuels for the development of novel drying techniques for liquids, particles, and continuous sheets such as papers. Prior work in this area has been limited to experimental studies at laboratory and pilot scales for spray drying of suspensions of heat sensitive materials by injecting them into the exhaust of a pulse combustor tailpipe.25,26 2. Mathematical Model

Figure 3. Time sequence of gas temperature (K) contours.

byproduct of the destructive distillation of wood. Here, these biofuels are considered for use in pulse combustors. Fuel oil consists of crude oil fractions that boil in the 340–420 °C range. Six grades of fuel oil have been established covering the requirements of atomization and heat release of various burner fuels. For example, fuel oils no. 1 and no. 2 are light and medium domestic fuel oils, respec-

2.1. Combustor Geometry. Figure 1 presents a schematic view of the combustor system simulated in this study. The combustor geometry is nearly identical to the one used in earlier experiments and simulations by Möller and Lindholm.15 This pulse combustor is a Helmholtz type device fitted with a flapper valve. Fuel and air are premixed before they enter the combustion chamber. A spark plug positioned at the combustion chamber sidewall is used to initiate the combustion process. Hot product gases exit the combustor through the tailpipe. The chamber has a 45.2 mm radius and is 150 mm long. It is connected to a tailpipe with an inner radius of 18 mm that is 1430 mm long. A flame holder (12.5 mm radius) is mounted onto a 2.5 mm radius rod and is placed on the symmetric axis of the combustor. The inner radius of the inlet tube to the combustion chamber is 10.25 mm. The computation domain is limited to the pulse combustor including the combustion chamber and tailpipe. Because of its axisymmetric geometry and operating conditions, the computation domain is a two-dimensional (2D)-axisymmetric one. Because the pulsation is primarily driven by the longitudinal acoustic mode in the tailpipe, the axisymmetric formulation is sufficient to capture the expected dynamics in the pulse combustor. Figure 2 shows a typical mesh design for the pulse combustor. In the combustion chamber zone, the gas temperature varies markedly as a result of the release of the heat of combustion. Thus, a fine mesh is applied in this zone, especially near the inlet part where the flapper valve opens and closes alternately. A relatively coarse mesh is used in the tailpipe region. The grid independence of the solution was tested by the doubling of the axial and radial nodes. 2.2. Governing Equations. The unsteady state continuity, momentum, energy, and species concentrations equations used to describe the pulse combustion process are written as follows. (24) Keating, E. L. Applied Combustion; Marcel Dekker: New York, 1993. (25) Wu, Z. H.; Liu, X. D. Drying Technol. 2002, 20, 1097–1117. (26) Wu, Z. H.; Liu, X. D. Drying Technol. 2006, 24, 751–761.

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[(

) ]

µt ∂ (FY ) + ∇·(Fυ bYi) ) ∇· FDi,m + ∇Yi + Ri ∂t i Sct

(2)

where Ri represents the species change due to the combustion reaction. Sct is the turbulent Schmidt number Sct ) µt/(FDt) , where µt is the turbulent viscosity and Dt is the turbulent diffusivity. Here, Sct ) 0.7. For 2D axial-symmetric geometries, the axial and radial momentum conservation equations are given by Axial and radial momentum equations ∂ 1 ∂ 1 ∂ ∂p (Fυ ) + (rFυxυx) + (rFυrυx) ) - + ∂t x r ∂x r ∂r ∂x

[(

)]

∂υx 2 1 ∂ - (∇·υ rµ 2 b) + r ∂x ∂x 3 ∂υx ∂υr 1 ∂ + rµ 2 r ∂r ∂r ∂x

[(

)]

+ Fgx (3)

and 1 ∂ 1 ∂ ∂p ∂ (Fυ ) + (rFυxυr) + (rFυrυr) ) + ∂t r r ∂x r ∂r ∂r

[(

∂υx ∂υr 1 ∂ + rµ r ∂x ∂r ∂x

)]

+

[(

)]

∂υx 2 1 ∂ - (∇·υ rµ 2 b) r ∂r ∂r 3 υr 2 µ (∇·υ b) + Fgr (4) 2µ 2 + 3r r

where

∇·υ b)

∂Vx ∂Vr Vr + + ∂x ∂r r

(5)

Turbulence predictions of the gas flow are obtained from the standard k-ε turbulence model expressed by equations 6 and 7.

[( ) ] [( ) ]

µt ∂k ∂ ∂ ∂ ∂ (Fk) + (rFkVx) + (rFkVr) ) r µ+ + ∂t r∂x r∂r r∂x σk ∂x µt ∂k ∂ r µ+ + Gk - Fε (6) r∂r σk ∂r and

[( ) ]

µt ∂ε ∂ ∂ ∂ ∂ (Fε) + (rFεVx) + (rFεVr) ) r µ+ + ∂t r∂x r∂r r∂x σk ∂x

[( ) ]

µt ∂ε ε ∂ ε2 r µ+ + C1ε Gk - C2εF (7) r∂r σk ∂r k k

Figure 4. Time sequence of the reaction rate (kmol/(m3 s)) contours.

Energy equation Continuity equation ∂F + ∇·(Fυ b) ) 0 ∂t Species equation

∂ ∂ ∂T ∂ ∂ (Fh) + (rFhυx) + (rFhυr) ) rk + ∂t r∂x r∂r r ∂ x ∂x

( )

(1)

(

)

(

)

∂hiYi ∂hiYi ∂ ∂T ∂ ∂ rk + rFDi + rFDi + Sh (8) r ∂ r ∂r r∂x ∂x r∂r ∂r

( )

Pulse Combustion Characteristics of Gaseous Fuels

Energy & Fuels, Vol. 22, No. 2, 2008 919

Figure 5. Time trace of the oscillating pressure, temperature, and mass fraction of methane in the combustion chamber (ξ ) 25, methane-air mixture).

Figure 6. Peak-to-peak amplitude of gas pressure and velocity along combustor (chamber length, 0.15 m; tailpipe length, 1.43 m; ξ ) 25).

where Sh describes the heat release of gas fuel species’ combustion Sh ) -

∑ i

(

h0i + Mi



T c Tref,i p,i

)

dT Ri

(9)

In this work, as a first attempt, one-step propane combustion chemistry is assumed to model combustion. Multistep combustion chemistry will yield more detailed information about the combustion process, but that needs a much longer computation

time and memory. Because of the limitations of the computational resources, only one-step combustion chemistry was considered in this study. CH4 + 2O2 f CO2 + 2H2O Consequently, five species, namely, CH4, O2, N2, CO2, and H2O, were modeled with corresponding conservation equations. The reaction rate was computed considering both the Arrhenius law and the Magnussen-Hjertager model taking account of the slower kinetics of this model. This approach was adopted

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Figure 7. Predicted methane inlet flow rate and instantaneous flue velocity and thrust generated by the combustor during a pulse cycle. Table 3. Selected Thrust and Specific Impulse of Modern Engines aircraft

engine

thrust (kN)

specific impulse (N · s/kg)

Concorde F15 Sukhoi 27

Olympus 593 F-100-PW Saturn/Lyulka

4 × 170 2 × 64 2 × 122.6

29700 52000 14000

because it was felt that there might be regions within the flow field where the chemical kinetics are slower than the turbulent reaction rate. The form for the Arrhenius law used is the one proposed by Westbrook and Dryer,28 R1 ) 2.119 × 1011 ×

[

exp -

]

2.027 × 108 J/(kg mol) [CCH4]0.2[CO2]1.3 (10) RT

The concentrations of reactants are in units of kg mol/(m3 s). In this work, several gaseous fuels were tested, and Tables 1 and 2 list their Arrhenius kinetic chemical reaction equations and the combustion heat released. The form of the turbulent reaction rate is

( kε )

Ri ) AFm/

{( )

where m/ ) min

mi ViMi

, reactants

B



products

( )} mk VkMk

(11)

where Vi and Mi are the stoichiometric coefficients and the molecular weights of species i. The terms k and ε are the kinetic energy of turbulence and the dissipation rate, respectively. The coefficient A is a constant with a value of 4.0, and the coefficient B takes the value of 0.5.29 (27) Nijaguna, B. T. Biogas Technology; New Age International (P) Limited: New Delhi, 2002. (28) Westbrook, C. K.; Dryer, F. L. Combust. Sci. Technol. 1979, 20, 125–140. (29) Magnussen, B. F.; Hjertager, B. H. Proc. Combust. Inst. 1976, 16, 719–729.

2.3. Boundary Conditions. The symmetry boundary condition is applied along the centerline of the combustor. At the exit of the tailpipe, the pressure is atmospheric and the remaining variables are calculated assuming far-field conditions, that is, zero diffusive flux of species or energy normal to the exit. Nonslip conditions are prescribed on the walls. For the thermal wall condition, the heat loss through wall is calculated by considering the convective heat transfer between the ambient air and the hot wall, qwi ) h(Twi - Ta), where qwi is the heat flux from the ith wall cell of the grid, h is the whole convective heat-transfer coefficient, Twi is the temperature at the wall surface of the cell, and Ta is the ambient temperature, which is assumed to be 300 K. Here, we set h ) 120 W/(m2 K) 30. 2.3.1. Inlet Boundary Condition. The flapper valves open and close alternatively during the pulse combustion process depending on the pressure difference across the flapper. The valve closes when the pressure at the head end of the combustor, Pc, is greater than the pressure upstream of the valves (Pin), taken in this study to be 1 atm. In this condition, no fuel/air mixture enters the combustion chamber. u ) 0 when ∆P ) Pin - Pc e 0

(12)

When the pressure at the head end drops below the pressure upstream of the valve, the flapper valve opens and fresh fuel/ air mixture is drawn into the combustion chamber. Here, a simple relationship between the inlet velocity and the pressure difference across the valve of the following form is used: 1 ∆P ) ξFu2 2



u)

 2∆P Fξ

(13)

This expression has been used previously in pulse combustor studies by Tarjiri and Menon.16 Expressing the boundary condition in the form of eq 13 introduces another parameter into the system, namely, ξ, which physically represents the “willingness” of the valves to admit mass into the system. For (30) Liu, X. D.; Cao, C. W.; Lang, Z. H. Drying Technol. 2001, 19, 1939–1948.

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Energy & Fuels, Vol. 22, No. 2, 2008 921

Table 4. Frequency and Power Input Obtained in Möller’s Experiment and This Simulation Case frequency (Hz) power input (kW) methane flow rate (kg/s) mixture flow rate (kg/s)

experiment15

case ξ ) 25

case ξ ) 50

case ξ ) 75

103 11 0.22 × 10-3 5.05 × 10-3

106 8.72 0.1744 × 10-3 4.217 × 10-3

97 7.771 0.1554 × 10-3 3.758 × 10-3

79 6.686 0.1337 × 10-3 3.233 × 10-3

example, a larger value of ξ (relative to some reference ξ) translates into a lower inlet velocity, hence less mass injected into the combustor for a given pressure difference, whereas a smaller value of ξ allows for larger inflow velocities. The implications of this behavior will be discussed later in Section 3.1.3. The advantage of this method is that the mass flow is not set a priori and can now adjust itself accordingly depending on the operating conditions. The mass flow rate of the fuel/air mixture is calculated as m ˙ ) FmixAinletu

(14)

where Fmix is the density of mixture and Ainlet is the inlet port area of the flapper valve. The mixture had an initial temperature of 300 K and an excess air ratio of 1.22. 2.4. Solution Procedure. The conservation equations were solved implicitly with a 2D unsteady-state segregated solver using an under-relaxation method. The pressure-velocity coupling is discretized using the “SIMPLE” method. The momentum, species, and energy equations are discretized using a second-order upwind approximation. When discretizing the momentum equation, the pressure field and face mass fluxes are not known a priori, and the “standard” pressure interpolation scheme31 was used here to compute the face values of the pressure from the cell values. In this work, the time-step size of 1 × 10-6 s was selected for this simulation. To achieve convergence as well as to test the grid independence of the results, a volume-averaged pressure in the combustion chamber is defined and traced during the computation process. Figure 5 shows the convergence history of the chamber volume-averaged pressure. The pressure initially fluctuated significantly and then achieved a “cyclical steady” amplitude oscillation shown in Figure 5. The criterion to judge when the computation can be stopped is when the pressure amplitudes in the following cycles are the same (cyclical steady state).The calculation time for each case varied between one day and several days, depending on the complexity of the problem and the initial guess. 3. Results and Discussion 3.1. Baseline Case. A baseline run was first carried out for methane fuel, subject to the following boundary conditions: an inlet methane/air mixture gage pressure of 0 Pa (relative to ambient pressure) and an excess air ratio of 1.22. In addition, account is taken of the heat loss. 3.1.1. Self-Breathing Combustion Process. Figures 3 and 4 show the reaction rate contours and the corresponding gas temperature contours in the combustion chamber, respectively, using the color maps to depict the contour values. The reaction rate contours show that the flame (a body of burning gas) is a narrow band surrounding the reactant mixture. During the inflow (Figure 3a-e), the hot remnant gases from the previous cycle ignited the fresh fuel-air mixture as it entered the combustors, and the mixture gas deflected to the side wall. It is seen that the flame was anchored at two locations: the stagnation plate and the side wall near the inlet port. When the inlet port closes (Figure 3f-i), combustion continued but the flame structure (31) Rhie, C. M.; Chow, W. L. AIAA J. 1983, 21, 1525–1532.

collapsed slowly to a region near the inlet. Most of the gaseous fuel was completed before the inlet port reopened. There was still some unburnt mixture near the inlet that maintains the flame until the next cycle begins anew. Figure 5 shows the time evolution of the volume-averaged gas pressure, temperature, and mass fraction of methane in the combustion chamber. The computed gage pressure varies from -6400 to 8800 Pa (relative to atmospheric pressure) with a peak-to-peak value of 15.2 kPa, and its oscillation mode shape is nearly a cosine wave. In Figure 5, similar oscillation modes are found for the gas temperature and the fuel concentration. The pressure oscillation mode is consistent with those measured in practical pulse combustors,1,2 indicating that the predicted combustion process is a really periodic one (pulse combustion). Figure 5 also shows the phase relations between the instantaneous pressure, temperature, and mass fraction of fuel in the combustion chamber. The temperature oscillation is ahead of the pressure oscillation by 30° and is out of phase with the instantaneous mass fraction of propane. That is, the gas temperature reaches a peak when the mass fraction of methane reaches its minimum, indicating a phase delay between the heat release and the pressure wave. The predicted phase delay is consistent with the phase relation described by the Rayleigh criterion for combustion-driven instability.32 From Figure 5, the pulse frequency is calculated to be about 106 Hz. 3.1.2. Gas Characteristics in the Pulse Combustor. Figure 6 shows the distribution of the peak-to-peak amplitude for the gas pressure and the velocity along the axial distance from the inlet. The pressure amplitude decreases from 15.4 kPa initially to 0 kPa at the exit of the tailpipe while the velocity amplitude increases from 2 to 84 m/s. In the combustion chamber (axial distance < 0.15 m), both pressure and velocity amplitudes keep almost constant at different axial distances, indicating that the chamber can be regarded as a well-stirred reactor and its thermal properties are homogeneous. At the inlet of tailpipe, the velocity amplitude reaches its minimum while the pressure amplitude reaches the maximum. Opposite phenomena happen at the outlet. The pressure mode shown in Figure 6 has a quarter-wave shape, which corresponds to the fundamental acoustic mode of a closed-open duct.2 The above phenomena have also been observed in many actual pulse combustors.1–3 The mass flow rate of methane during a pulse cycle is plotted in Figure 7. It can be seen that the fuel is drawn into the chamber in only half of the pulse cycle. By integrating the area under the fuel influx curve shown in Figure 7, the average inflow rate of methane is calculated to be 0.1744 g/s. Taking the low heating value of methane as 50.01 MJ/kg, the power input of the pulse combustor is calculated to be 8.72 kW. Figure 7 also shows that during a pulse cycle, the exhaust gas velocity varies from -27 to 54 m/s with a mean velocity of 16.81 m/s. The phenomenon that a negative flue velocity exists during a pulse cycle was verified by pulse combustion impingement heating experiments where the instantaneous flue velocity was mea(32) Rayleigh, J. W. S. Theory of Sound; Dover Publications: New York, 1945.

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Figure 8. Gas pressure oscillations in the combustion chamber for different fuel species (propane, butane, methanol, ethanol, and fuel oil). Table 5. Operational Characteristics of the Pulse Combustor Using Different Fuels items

propane

butane

methanol

ethanol

fuel oil

frequencies (Hz) peak-to-peak pressure amplitude (Pa) average temperature in chamber (K) average flue velocity (m/s) fuel flow rate (g/s) combustion heat (MJ/kg) power input (kW) average thrust (N) specific impulse (N · s/kg) thrust output /power input (N/kW)

116 -5082 to 6035 2094 16.55 0.1929 46.361 8.95 0.4244 2200 4.74 × 10-2

113.8 -5676 to 6998 2090 17.15 0.1983 45.752 9.07 0.4453 2250 4.91 × 10-2

114.1 -5195 to 6176 2075 21.30 0.4789 21.102 10.11 0.5754 1200 5.69 × 10-2

120 -6351 to 6800 2106 15.69 0.3077 28.079 8.64 0.4018 1310 4.65 × 10-2

112 -5283 to 6404 2070 17.67 0.2162 40.531 8.76 0.4595 2130 5.24 × 10-2

Table 6. Composition of Biogas27 components

%

methane, CH4 carbon dioxide, CO2 nitrogen, N2 hydrogen, H2 hydrogen sulfide, H2S oxygen, O2

55–75 25–45 0–0.3 1–5 0–3 0.1–0.5

sured.10,11,33 In these experiments, the negative part of the flue velocity was reported to decrease the thermal efficiency. The instantaneous thrust generated by this combustor is also plotted in Figure 7. Here, the instantaneous thrust is defined as Tthrust ) ∫Aexit FVx2 dA where Aexit is the cross-area of the tailpipe exit plane. In Figure 7, the instantaneous thrust oscillates from -0.38 to 2.55 N with a cycle-averaged thrust of 0.5496 N. Thus, the thrust output-to-power input is calculated to be 6.30 × 10-2 N/kW. Another parameter is defined to evaluate how much thrust can be generated by unit fuel, that is, the specific impulse. In this case, the specific impulse is calculated to be 3150 N · s/kg. Compared with the modern aircraft engines listed in Table 3, the specific impulse of the simulated pulse combustor is rather low. (33) Liewkongsataporn, W.; Patterson, T.; Ahrens, F.; Loughran, J. Impingment Drying Enhance Using a Pulsating Jet. Presented at 15th International Drying Symposium (IDS 2006), Budapest, Hungary, August 20–23, 2006.

3.1.3. Comparison with Experiments. During the pulse combustion process, the inlet valves open and close alternately depending on the pressure difference across the valves. Simulation of the behavior of inlet valves and the resulting mass flow rate of fuel is a major challenge for mathematical models of pulse combustion. As discussed in Section 2.3.1, in this case, we use a parameter ξ to physically represent the “willingness” of the valves to admit mass into the system. The advantage of this method is that the mass flow rate of fuel is not set a priori and can adjust itself depending on the operating conditions; the disadvantage is that we need to find the proper ξ value by trial and error. On the basis of the combustor configuration described earlier,15 we tested a series of ξ values. Table 4 shows the comparison of experimental and simulation results. From Table 4, it can be seen that the case of ξ ) 25 is closest to the experimental data. The predicted pulse frequency (106 Hz) matches well with the experimental one (103 Hz). The difference of the power input between simulation and experiment is about 21%, which is the lowest one among the selected cases. Also, from Sections 3.1.1 and 3.1.2, the key physics of pulse combustion is captured for ξ ) 25. Thus, ξ ) 25 was used in this simulation work. 3.2. Pulse Combustion Using Various Gaseous Fuels. Parametric studies were carried out to determine how various gaseous fuels perform in pulse combustors. The gaseous fuels selected were propane, butane, methanol, ethanol, and fuel oil. Methane, propane, and butane represent low molecular weight

Pulse Combustion Characteristics of Gaseous Fuels

Energy & Fuels, Vol. 22, No. 2, 2008 923

Figure 9. Gas pressure oscillations in the combustion chamber for biogas with different methane/carbon oxide ratios (100:0, 70:30, 60:40, 40:60). Table 7. Operational Characteristics of the Pulse Combustor Using the Biogas methane/CO2 ratio frequencies (Hz) peak-to-peak pressure amplitude (Pa) average temperature in chamber (K) average flue velocity (m/s) methane flow rate (g/s) biogas flow rate (g/s) power input (kW) average thrust (N) thrust/methane influx (N · s/kg) specific impulse (N · s/kg) thrust output/power input (N/kW)

100:0

70:30

60:40

40:60

106 -6425 to 8865 2001 16.81 0.1744 0.1744 8.722 0.5496 3151 3151 6.30 × 10-2

102 -6959 to 8975 1915 18.21 0.1775 0.3867 8.777 0.5929 3341 1533 6.76 × 10-2

102 -7133 to 9111 1879.4 19.83 0.1806 0.5117 9.039 0.6593 3650 1289 7.29 × 10-2

95 -9236 to 12091 1738 22.77 0.2081 1.0665 10.415 0.8863 4259 831 8.51 × 10-2

hydrocarbon while fuel oil represents the high molecular weight one. Methanol and ethanol typically represent biofuels which are increasing in importance. Figure 8 shows the predicted gas pressure oscillation in the combustion chamber for these fuels. From Figure 8, it can be seen that the gas pressures vary periodically in the range of -6 to 7 kPa and that their oscillation mode shapes follow a cosine wave, indicating that these combustion processes are periodic ones. Thus, all these fuels can be used to drive a pulse combustor. Table 5 summarizes the predicted operational characteristics of the pulse combustor using different fuels. No major differences can be seen in most of the operational parameters: pulse frequency, peak-to-peak gas pressure amplitude, average gas temperature in the chamber, average flue gas velocity, and power input and thrust output to power input, indicating that these fuels achieve almost the same pulse combustion performance. The only major differences are in the specific impulse and fuel flow rate between fuels with low heating values (methanol, ethanol) and the ones with high heating values (propane, butane, fuel oil). Because of their low heating values, low specific impulse values are expected for methanol and ethanol. From Table 5, it seems that in this case of fuels with low heating values, pulse

combustors will draw in more fuel mass to sustain their performance. For example, the mass flow rate into the combustor using methanol is 0.4789 g/s, about 2.5 times the propane flow rate. From this point of view, as a result of its self-breathing function, pulse combustors can adjust fuel intake automatically at least over a certain range, which makes them suitable for different gaseous fuels. Thus, a given pulse combustor can switch fuel as needed with minor change in its performance. 3.3. Pulse Combustion Using the Mixed Fuels (Biogas). In view of the increasing interest in renewable fuels, it is interesting to investigate pulse combustion performance of mixed fuels. Here, we take biogas as an example. Table 6 lists the composition of the biogas tested, which is mainly composed of 55-75% methane and 25-45% carbon oxide.15 To simplify the simulation, the biogas was assumed to comprise only methane and carbon oxide. Three methane/carbon oxide ratios (70:30, 60:40, 40:60) were selected to study the combustion performance of biogas and to compare it with the one of pure methane. Note that here we have a mixture of a combustible and an inert gas. Figure 9 shows the predicted gas pressure oscillation in the combustion chamber for biogas at different methane/carbon

924 Energy & Fuels, Vol. 22, No. 2, 2008

oxide ratios. Similarly, these periodic pressure waves indicate that pulse combustion is achieved for these fuels. When the methane/carbon oxide ratio decreases from 100:0 to 40:60, the peak-to-peak pressure amplitude increases from 15 to 20 kPa, indicating that the pulse combustion process is indeed intensified at the lower ratio. Table 7 summarizes the predicted operational characteristics of the pulse combustor using biogas. From Table 7, it can be seen that, with a decrease of the methane/carbon oxide ratio, the heating value of the biogas decreases resulting in more fuel being drawn into the combustion chamber. For example, the biogas flow rate is 1.0665 g/s in the case of a 40:60 methane/carbon oxide mixture, about 10 times the flow rate if pure methane is used as the fuel. Thus, large quantities of the fuel/air mixture were drawn into the chamber causing a significant increase of the flue gas velocity, and hence the pulse combustor had enhanced thrust as shown in Table 7. This is an interesting observation of special interest in industrial drying. From Tables 5 and 7, we can conclude that when pulse combustors operate on fuels of low heating value, the following phenomena take place: (1) The combustor draws more fuel mass in to sustain combustion and even intensify its performance in terms of the thrust generated, for example, the increased peakto-peak pressure amplitude in the case of biogas with a 40:60

Zhonghua and Mujumdar

methane/carbon oxide mixture. (2) The combustor has a lower specific impulse. (3) The burner has a higher thrust output-topower inlet. In the case of fuels of low heating value, the gas temperature in the combustion chamber is lower (see Table 7). In this condition, a major fraction of the combustion heat released from the fuel combustion is converted into kinetic energy of the flue gas rather than into increased flue gas temperature. 4. Conclusions The combustion process of a gas-fired pulse combustor was simulated using a CFD model to understand the flame structure, the gas characteristics in the burner, and the resulting pulsations. The numerical results satisfactorily compare with the available experimental data. Selected gaseous fuels such as low molecular weight hydrocarbons, high molecular weight hydrocarbons, biofuels, and mixed fuels are tested for pulse combustion, and their operational properties are presented and compared. It is observed that the combustor can self-adjust automatically at least over a certain range of parameters which makes it suitable for different gaseous fuels. EF7004207