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Characteristics of the Pulsatile Flow in a Self-excited Pulse Combustor Tailpipe Zhai Ming* and Dong Peng School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, China, 150001
This paper designs and describes a self-excited pulse combustion system. The experimental result shows that combustion oscillations can be produced with a steady supply of fuel and air without mechanical or aerodynamic valves. A large decoupling chamber with an exhaust pipe is connected at the end of the tailpipe of the pulse combustor. The temperatures and pressures along the tailpipe are measured. Pulsatile flow in the self-excited pulse combustor tailpipe is numerically simulated by FLUENT. A study case based on the experimental measurement data is simulated with compressible flow equations. Numerical simulation results which are close to the experimental measurement data show that the main characteristics are the increase in velocity amplitude and the decrease in mean velocity along the tailpipe, and the profiles of velocity at the tailpipe exit behave more like laminar pulsatile flows, whereas the profiles of velocity far away from the tailpipe exit behave like turbulence pulsatile flows. The profile of mean temperature along the tailpipe is affected only within a short distance from the tailpipe exit, where the amplitude of mass flow rate oscillation significantly increases. The pressure amplitude gradient is greater near the tailpipe exit than upstream. The pulsatile flow in the tailpipe of the self-excited pulse combustor behaves like an acoustic resonance in a Schmidt pulse combustor. 1. Introduction Pulse combustion is a special oscillating process driven by combustion, coupled with resonant oscillation of the flow in a tailpipe. Pulse combustion is recognized for high combustion intensity, high heat transfer rates, and lower pollutant emission than steady combustion.1-6 At the present time, pulse combustion is emerging in many industrial applications including from powering propulsion to incineration to drying, and a large variety of possible uses of pulse combustors are in the developmental stage.7-20 There are three types of pulse combustors, such as Schmidt, Helmholtz, and Rijke tubes.15,21,22 The most commercially available pulse combustor is the Helmholtz type. Typically, the important components of a pulse combustor are the combustion chamber and one or some tailpipes attached at the end of the combustion chamber, and some pulse combustors also have a mix chamber attached at front of the combustion chamber or a decoupling chamber connected at the end of the tailpipes. In most practical Helmholtz pulse combustors, one-way supply valves are used for reactants. The reactants can be either premixed in a mixing chamber prior to entering the combustion chamber or separately fed to the combustion chamber. The pressure difference across the valve determines the one-way valve’s operation. Richards et al.23 developed a pulse combustor without any mechanical valves for pulse action. The pulsations can be selfsustained even with steady fuel and airflow rates at the inlet. In fact, this kind of pulse combustor can also be considered as the Helmholtz type. Daw et al.24 using the model of ref 23 demonstrated that with a laboratory-scale pulse combustor and a model combustor, a bifurcation can lead to chaos. They used residence time as the bifurcation parameter. In et al.25 maintained anticontrol chaos in the system to prevent the system from a * To whom correspondence should be addressed. Address: Room 422, Dongli Building, School of Energy Science and Engineering, Harbin Institute of Technology, 92# West Dazhi Street, Nangang District, Harbin, Heilongjiang Province, China, 150001. E-mail:
[email protected]. Mobile: +86 +0 +15045118090. Fax: +86 +451 +86413171.
transition to flame extinction. Rhode et al.26 used the model of ref 23 with friction factor as the control variable to demonstrate that controlling the chaos can extend the flammable range of flow time. Although there have been numerous studies about internal pulsatile flows, there are few studies on flows with similar characteristics in a pulse combustor tailpipe. Liewkongsataporn27 investigated the characteristics of pulsating flows in a Helmholtz pulse combustor tailpipe, which followed the experimental data from Sandia National Laboratories by Dec et al.3,5 However, since his simulation focused on the impingement heat transfer by a pulsating jet from a pulse combustor tailpipe, the boundary condition at the exit of the pulse combustor tailpipe (a decoupling tank with a bottom wall in axial direction and two large open ends at radial direction) was not for common practical use of a pulse combustor. In this paper, a self-excited pulse combustor which is similar to but more stable than that of Richards et al.23 was designed. A large decoupling chamber with an exhaust pipe was attached at the end of the tailpipe. The main objective of the paper is to study the characteristics of pulsatile flow in the tailpipe of the self-excited pulse combustor based on the specified combustion chamber pressure oscillation and frequency available from the experiment measurement. 2. Experimental Facility and Diagnostics 2.1. Experimental Facility. The basic combustor geometry is shown in Figures 1 and 2. The combustor consists of a mixing chamber, combustor chamber, and tailpipe. All the components are connected by flanges. The structure of this pulse combustor is similar to the one studied by Richards et al.,23 except that propane and air are separately forced through two groups of vertical orifices. The sizes of the orifices are determined by the flux value when the equivalence ratio of air and propane is approximately 1. Besides, the igniter is located at the front of the combustion chamber. This arrangement guarantees a steady flame without keeping the igniter on and avoiding the igniter firing effect on observed behavior. Two pieces of quartz glass
10.1021/ie901979a 2010 American Chemical Society Published on Web 02/02/2010
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Figure 1. Experimental setup of the self-excited pulse combustor.
Figure 2. Combustor geometry.
are set at the end region of mixing chamber and the profile of the combustion chamber, respectively, for observing the flame in the combustion zone. Propane flows into the mixing chamber through two independent pipes from a standard gas cylinder. Air supplied by an air compressor also flows into the mixing chamber through two independence pipes. Propane and air are steadily supplied during the operation. The exit of the tailpipe is connected to a decoupling chamber, a large-diameter tank with an exhaust pipe. Around the tailpipe walls, cooling water is fed as in a counterflow heat exchanger. The decoupling
Figure 3. Positions of measuring points.
Figure 4. Pressure oscillation in the combustion chamber.
chamber geometry is shown in Figure 3. The decoupling chamber should be large enough for noise and pressure fluctuation reduction. In the experiment, the volume of the decoupling chamber is more than 80 times larger than that of the combustion chamber. The typical cycle of operation process of the self-excited pulse combustor is as follows: Initially, a heat source such as a pulse igniter is required to initiate the combustion when reactants initially flow into the combustion chamber. The reaction between propane and air leads to a sudden pressure increase in combustion chamber, which subsequently causes the flow to slow down into the combustion chamber. Flue gas from the reaction flows out of the combustion chamber and through the tailpipe. Then, the combustion chamber pressure decreases. If the pressure level is lower than supply pressure of reactants, fresh reactants will flow into the combustion chamber again. At the same time, hot flue gas in the tailpipe starts to slow down and eventually flows back toward the combustion chamber. This process repeats itself over and over again. The pressure oscillation parameters (amplitude and frequency) depend on several factors such as the geometry and the dimension of the pulse combustor, the operating power of the combustor, the equivalence ratio of the reactants, and so on. 2.2. Diagnostics. The diagnostics used in the experiment are flowmeters, thermocouples, pressure transducers, and a flue gas analyzer. Flowmeters are used to measure the volume flow rates of propane and air. Thermocouples are used to measure the temperatures of the tailpipe entrance and exit of the exhaust gas and the inner wall along the tailpipe. The positions of measuring points are shown in Figure 3. Thermocouples in the combustion chamber just before the inlet of the tailpipe and in the middle of decoupling chamber are placed in the center; others are placed near wall. Thermocouple connections are added to the exterior of the combustor body at the measuring points. Pressure transducers are used to measure the pressure
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Figure 6. Computational domain. Table 1. Number of Grid Cells
Figure 5. Power spectrum of pressure in the combustion chamber.
in the combustion chamber and along the tailpipe and to determine the combustor frequency. The flue gas analyzer is used to measure the components content of the flue gas such as O2, CO, and CO2 in the exit region of the tailpipe and to determine the total equivalence ratio. 3. Numerical Simulation The simulation in this paper is largely based on measurement data from the self-excited pulse combustor experiments. Several operating parameters, such as mass flow rate, equivalence ratio, and pressure in the decoupling chamber, are varied in the experiments. However, a case with relatively high oscillation amplitude of pressure is selected as a base case. The measurement data employed in this paper are based on this base case. The base case has an 1100 mm long tailpipe with a mean mass flow rate of 4.2 g/s (the value is determined by the flow rate of the reactants from the experiment data). Figure 4a shows the pressure oscillation signals in the combustion chamber. The highest oscillation amplitude of pressure from the signals is selected as shown in Figure 4b. The pressure amplitude in the combustion chamber is 10.345 kPa. Figure 5 is the power spectrum of pressure signals in combustion chamber. Therefore, the pattern of oscillation can be assumed to be sinusoidal. In the experiment, pure propane and air with an equivalence ratio of 0.8 are used as the reactants. The exhaust gas from the combustion is, assuming a complete reaction, 73.1% of nitrogen, 7.9% of water vapor, 4.4% of oxygen, and 14.6% of carbon dioxide, on a mass basis. The fluid for the flows in the simulations is assumed to be air, because the amount of nitrogen is 73.1% by mass of the exhaust gas, using air properties may not significantly affect the results. The scope of the study in the paper is limited to main flow variables such as velocity, temperature, and pressure. The study concentrates on time-averaged and bulk characteristics of flow variables so that the results can be compared with simplified one-dimensional solutions and the experimental measurement data. The fully compressible flow model (density is assumed to follow the ideal gas law) is applied in the simulation. 3.1. Computational Domain and Grid Generation. The numerical simulation in this paper is performed using the commercial software, FLUENT version 6.3. The grid cells in the computational domain are generated by the software GAMBIT version 2.3. In order to simulate the characteristics of the pulsatile flow in the tailpipe accurately, the computational domain and boundary conditions must be reasonable. In the self-excited pulse combustor, since the velocity profile at the tailpipe exit will be influenced by the boundary conditions outside the tailpipe during flow reversal, the computational domain has to extend large
zone
direction
number of cells
ratio
1 1, 2, 4 2, 3 3 4
axial radial axial radial axial
110 52 80 79 20
1 first length ) 0.001 1 first length ) 0.001 1
enough beyond the tailpipe exit. Therefore, the computational domain consists of a tailpipe and a large decoupling chamber with an exhaust pipe extending beyond the tailpipe exit as shown in Figure 6. In order to simplify the simulation, the pulsatile flow is assumed to be axisymmetric without swirl. For grid generation, the computational domain is divided into four zones as shown in Figure 6. The number of cells and the ratios and first lengths of each zone are shown in Table 1. 3.2. Governing Equations and Boundary Conditions. The governing equations consist of three basic conservation equations for a Newtonian fluid, a state equation, and a turbulence model. Flow variables in the following governing equations are written as averaged quantities in Reynolds-averaged NavierStokes (RANS) equations. Continuity equation ∂F + ∇ · (FV b) ) 0 ∂t
(1)
Momentum equation ∂ (FV b) + ∇ · (FV bb V ) ) -∇p + ∇ · (τ + τt) ∂t 2 VI τ ) µ (∇V b + ∇V bT) - ∇ · b 3
[
[
τt ) µt (∇V b + ∇V bT) -
]
(
(2) (3)
)]
2 Fk + ∇·b V I 3 µt
(4)
The boundary conditions for the momentum equations at the walls are the stationary and no-slip condition. The pressureinlet condition is selected at the entrance of the tailpipe, because it coincides with the actual condition in the self-excited pulse combustor, and the experimental data of pressure amplitude are available. The inlet boundary condition is total pressure oscillation with the amplitude from the experiment as shown in Figure 4b. The pressure oscillation in the combustion chamber can be assumed sinusoidal. Therefore, the pressure-inlet condition can be simply written as a mean value plus a sin oscillating part: p(t) ) pm + pA sin(ωt)
(5)
With this condition, at the “inlet” of the computational domain, the mean pressure value is 1430 Pa according to Figure 4, and the oscillation frequency is 63.1313 Hz according to Figure 5. At the “outlet” of the computational domain, the boundary condition for the momentum equations is constant ambient pressure.
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Energy equation: ∂ (FE) + ∇ · [V b(FE + p)] ) ∇ · (keff∇T) ∂t V2 p E)h- + F 2
The turbulence model uses the standard k-ε equations:
(6)
keff
∫
T c Tref p
dT
cpµt )k+ Prt
(8)
(9)
The eddy viscosity (µt) in the Reynolds stress tensor term (τt) and in the effective thermal conductivity (keff) is calculated according to the turbulence model being used. The fluid properties: dynamic viscosity (µ), specific heat (cp), and thermal conductivity (k) are given by temperature-dependent functions in FLUENT. For the boundary conditions of the energy equation at the tailpipe wall, the temperature is assumed to be uniform and constant for simplification. The tailpipe wall temperature is set to 500 K based on the average value of experimental measurement data. At the other walls, the boundary conditions for are zero heat flux. The temperature at the “inlet” is also set to be uniform, and the value is 1533 K according to the average value of experimental measurement data. The backflow temperature in this simulation is regarded as the ambient temperature, which is 300 K. Equation of state for ideal gases p RgT
R Rg ) M
µ+
j - Cε2Fε Cε1 ′P ∂ + ∇· (Fε) + ∇ · (FεV b) ) ∂t j T
where Tref ) 298.15 K and Prt ) 0.85.
F)
[(
)]
µt ∇k σk
(7)
where sensible enthalpy h is defined by h)
∂ j - Fε + ∇ · (Fk) + ∇ · (FkV b) ) P ∂t
(10)
Because the density depends on both temperature and pressure, the pulsatile flow behaves as a fully compressible flow. For turbulence models, there are several options in FLUENT such as k-ε and k-ω families. For complex and strongly separated flows, an appropriate choice is the υ2-f or V2F model. This model is similar to the standard k-ε model, but incorporates near-wall turbulence anisotropy and nonlocal pressurestrain effects. The distinguishing feature of this model is its use of the velocity scale, Vj2, instead of the turbulent kinetic energy, k, for evaluating the eddy viscosity. The term Vj2, which can be thought of as the velocity fluctuation normal to the streamlines, has shown to provide the right scaling in representing the damping of turbulent transport close to the wall, a feature that k does not provide. It has been shown that this model is accurate for complex separated flows and heat transfer.28 The reason for selecting the V2F model is that strong separation may occur in pulsatile flows in the self-excited pulse combustor tailpipe during flow reversal. The following equations are the V2F model in FLUENT.
µ+
)]
µt ∇ε σε (13)
The Vj2 transport equation is ∂ ε (FV2) + ∇ · (FV2b V ) ) Fkf - 6FV2 + ∇ · ∂t k
[(
µ+
) ]
µt ∇V2 σk (14)
The term kf, the source of Vj2, represents the redistribution of turbulent intensity from the streamwise component. Nonlocality is represented mathematically by an elliptic relaxation equation for f V2 V2 2 5 j 3 k P k + C2 + f - L2∇2f ) (C1 - 1) jT jT Fk
(15)
In FLUENT, the elliptic relaxation function (f) is assumed zero-gradient at inlet boundaries. At outlet boundaries where the flow is going out, turbulence parameters are assumed zerogradient. For boundary conditions at walls, k and ν2 are zero and ε ) 2ν(k/y2), f ) (-20ν2/ε)(Vj2/y4), where y is the wall normal distance. The rate of turbulent energy production is j ) 2µtS2 P
(16)
where S2 ) Sc:Sc, Sc ) (1/2)(∇b V + ∇b VT). The time and length scales appearing in the model equations are
(
k3/2 j ) min T', R T √3 V¯2C √2S2
(11)
[(
(12)
µ
)
[ ()]
L ) CL max L', Cη
V3 ε
(17)
1/4
(18)
where T′ ) max((k/ε), 6(V/ε)1/2), L′ ) min[(k3/2/ε), (1/3)(k3/2/ (Vj2Cµ(2S2)1/2)]. The eddy viscosity is given by j µt ) FCµV2T
(19)
The constants of the model are R ) 0.6, C1 ) 1.4, C2 ) 0.3, Cε1 ) 1.4, Cε2 ) 1.9, Cη ) 70, Cµ ) 0.22, CL ) 0.23, σk ) 1, σε ) 1.3, Cε1 ′ ) Cε1(1 + 0.045√k/V2)
(20)
In this simulation, turbulence intensity and hydraulic diameter are selected to determine boundary conditions of turbulence parameters. The “inlet” boundary conditions are 10% for the turbulence intensity and 26 mm for the hydraulic diameter. As for the ambient air, the turbulence level is assumed to be low, the “outlet” boundary conditions are set to be 0.1% for the turbulence intensity and 26 mm for the hydraulic diameter.
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Table 2. Mean and Amplitude of Bulk Velocity (m/s)
Figure 7. Inlet mass flow rate (10 cycles).
3.3. Numerical Schemes. The second-order schemes are used in both space and time domain. For the case in this paper, the segregated solver is used. The physical time step is 110 µs. And the maximum number of iterations allowed in each physical time step is 500. The pressure-velocity coupling method is SIMPLEC and PISO for steady and unsteady flows, respectively. Other parameters are default values in FLUENT. A user-defined function or UDF source code file is used to define the pressureinlet boundary condition for unsteady flows. 4. Results and Discussion The simulation with the mean pressure has to be run for many cycles until the oscillation becomes stable before the mean mass flow rate and other parameters could be evaluated. Figure 7 shows 10 stable cycles of mass flow rate at the inlet. The timeaveraged mass flow rate is 4.2 g/s. For comparison, velocity and temperature oscillation of the bulk flow are considered. The bulk velocity and bulk temperature are mass-weighted average, defined by ub )
Tb )
∫ Fu dA ∫ F dA
(21)
∫ TF|u dA| ∫ F|u dA|
(22)
Axial and bulk velocity oscillations at five positions along the tailpipe are plotted in Figure 8. Compared to the oscillation
Figure 8. Axial and bulk velocity oscillations.
axial position
inlet
250 mm
550 mm
850 mm
exit
mean amplitude
32.91 50.07
27.95 54.07
22.94 57.02
19.16 60.46
15.50 66.42
of velocity at the center of the tailpipe in Figure 8a, bulk velocity oscillation in Figure 8b shows more evident characteristics. The values of mean and amplitude of bulk velocities are listed in Table 2. Since the pattern of the oscillations is assumed sinusoidal, the amplitude of the oscillations of flow variables in this paper is equal to (maximum value - minimum value)/ 2. The amplitudes values increase but the mean values decrease along the tailpipe. Figure 9 shows instantaneous axial velocity and temperature profiles with normalized cycle time across the tailpipe at x ) 550 mm (the middle of the tailpipe) and at the tailpipe exit. From Figure 9a and b, it can be seen that both the unsteady parts of the velocity boundary layer and thermal boundary layer are limited to within 2-3 mm from the wall. The profiles of velocity and temperature are relatively flat from the wall to the axis of the tailpipe, which behave turbulence pulsatile flows. However, at the tailpipe exit of the tailpipe, there are overshoot velocities in the boundary layer as shown in Figure 9c, which behave more like laminar pulsatile flows. The reason for this is that the large decoupling chamber attached at the tailpipe exit reduces dissipation of turbulence. The profiles of temperature in Figure 9d indicate the effect of flow reversal on temperature at the tailpipe exit is very significant. Axial and bulk temperature oscillations are plotted in Figure 10. In Figure 10a, the temperature reaches a minimum value when the velocity is about to change from negative to positive. Because when the flow velocity is negative, the cooler fluid outside the tailpipe exit flows back to the tailpipe until the flow changes direction again. When the flow velocity is positive, the fluid continuously flows from upstream to downstream and the hot fluid from further inside the tailpipe is driven out of the tailpipe until the flow changes direction again; therefore, the temperature reaches a local maximum due to higher-temperature fluid upstream. The heat loss along the wall results in the timeaveraged temperature decrease along the tailpipe. The oscillation of bulk temperature, as shown in Figure 10b, appears to be significantly different from the temperature oscillation at the axis in Figure 10a. There are sudden drops in temperature when the bulk flow changes direction. When the bulk velocity approaches zero, the fluid near the wall has phase-lead velocity which is larger than that of the fluid away from the wall. Since the temperature is much lower near the wall than away from the wall, the density near the wall is much higher. Thus, mass fluxes near the wall are much greater than that away from the
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Figure 9. Instantaneous axial velocity and temperature profiles.
Figure 10. Axial and bulk temperature oscillations.
wall, which causes a sudden drop in bulk temperature at the point when bulk flow velocity changes direction. The difference between oscillation of bulk temperature and temperature oscillation at the axis can be also explained by the definition of bulk temperature (eq 22). The axial velocity profiles across the tailpipe are relatively flat (see Figure 9a), and the velocity away from the wall is almost the same. When velocity away from the wall approaches zero, only the temperatures near wall contribute to bulk temperature according to eq 22. Since the temperature is much lower near the wall than away from the wall, there is a sudden drop in bulk temperature when velocity changes direction. However, it is not the case for the temperature oscillation at the tailpipe axis. At the beginning of flow reversal, part of the exiting fluid of the previous cycle is drawn back into the tailpipe. Thus, the temperature is decreasing but still high. Then the exiting fluid is cut off, and the ambient air starts to enter the tailpipe. The temperature remains low as ambient air continues to flow in. When the flow starts to change direction again, the part of ambient air that last enters the tailpipe is the first part to flow out of the tailpipe, and the temperature starts to increase. Finally, fresh hot fluid from upstream flow is driven out of the tailpipe, and the temperature reaches a maximum value. At the exit of the tailpipe, the temperature stays low at about the ambient level (300 K) longer than half of a cycle. Keller et al.29 explained this phenomenon. Over one cycle, it
Figure 11. Bulk velocity and bulk temperature profiles.
takes some time to drive out the fluid which is drawn into the tailpipe during flow reversal. Figure 11 shows the profiles of time-averaged and amplitude of bulk velocities and time-averaged bulk temperatures along the tailpipe. The amplitude of bulk velocities increases along the tailpipe and the time-averaged velocity decreases along the tailpipe, which behaves more like an acoustic resonance in a Schmidt pulse combustor. At the inlet of the tailpipe, the velocity amplitude is not zero, because the diameter and volume of combustion chamber are larger than that of the tailpipe. The
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5. Conclusions and Recommendations
Figure 12. Mean and amplitude profiles of mass flow rate.
Figure 13. Area-averaged mean and amplitude profiles of pressure.
temperature at the exit was approximately 445 K. The effect of cooler ambient air is limited only to a region near the tailpipe exit. The results confirm that the pulsatile flow in a self-excited pulse combustor tailpipe behaves compressible flow characteristics, and the effect of cooler ambient air on the temperature within the tailpipe is limited only to a short distance (about 20% of the length of the tailpipe) from the tailpipe exit. Figure 12 shows the mean and amplitude profiles of the mass flow rate along the tailpipe. The time-averaged mass flow rate over one cycle is the same everywhere, but the amplitude of the mass flow rate oscillation which is determined by the velocity and the density during the oscillation increases along the tailpipe. Near the tailpipe exit, the amplitude of the mass flow rate oscillation increases much more rapidly than upstream and reaches a maximum value at the tailpipe exit. The oscillating part of velocity contributes to the amplitude of mass flow rate which corresponds to maximum density due to the lowest temperature at the tailpipe exit. The mean velocity contributes to the mean mass flow rate that corresponds to the density of fresh hot fluid from upstream. Figure 13 shows the profiles of time-averaged and amplitude of pressure along the tailpipe. Both CFD results and experimental measurement data are presented in Figure 13. The pressure amplitude gradient is greater near the tailpipe exit than upstream. This indicates that the pulsatile flow in the tailpipe of the self-excited pulse combustor behaves like an acoustic resonance in a Schmidt pulse combustor (the maximum amplitude of pressure is at the inlet of the tailpipe then decreases sinusoidally to ambient pressure at the exit). Since the simulation results are close to the experimental measurement data, the methods and process of the simulation in this paper are reasonable.
The motivation of this paper is the potential application of using a pulse combustor for enhancing the heat transfer. A selfexcited pulse combustor experimental system was designed. The temperatures and pressures along the tailpipe were measured. The experimental measurement data were used for the initialization of the numerical simulation. The objective of this paper is to evaluate the solutions of the numerical simulation of pulsatile tailpipe flows with available experimental data. The CFD software package, FLUENT, was used to simulate the case which was run with the ideal-gas law for density function. The computational grid was generated. The flow was assumed axisymmetric. The computational domain began at the entrance of the tailpipe as the “inlet” of the domain. The exit of the tailpipe is connected with a large decoupling chamber with an exhaust pipe. The computational domain ended at the exit of the exhaust pipe as the “outlet” of the domain. The inlet boundary condition was pressure-inlet with an amplitude value from the experimental measurement data. The outlet boundary condition was ambient pressure with backflow temperatures as ambient temperature. The turbulence model used in the simulation is the V2F model. The simulation results were compared with the experimental measurement data. The main characteristics of the pulsatile flow in the selfexcited pulse combustor tailpipe are the increase in velocity amplitude and the decrease in mean velocity along the tailpipe, and the profiles of velocity at the tailpipe exit of the tailpipe behave more like laminar pulsatile flows, whereas the profiles of velocity far away from the tailpipe exit behave like turbulence pulsatile flows. The profile of mean temperature along the tailpipe is affected only within a short distance (about 20% of the length of the tailpipe) from the tailpipe exit, where the amplitude of mass flow rate oscillation significantly increases. The pressure amplitude gradient is greater near the tailpipe exit than upstream. The pulsatile flow in the tailpipe of the selfexcited pulse combustor behaves like an acoustic resonance in a Schmidt pulse combustor. The recommendation for future study is to change the pressure in the decoupling chamber for investigating the influence of ambient pressure outside the tailpipe on the characteristics of the pulsatile flow. Also, using other turbulence models for simulation and comparing the results with the results in this paper may be helpful for understanding the validation and accuracy of each model. Nomenclature Letter Symbols cp ) constant pressure specific heat E ) specific total energy f ) frequency h ) sensible enthalpy I ) unit tensor k ) thermal conductivity L ) tailpipe length M ) molecular weight p ) static pressure Pr ) Prandtl number r ) radial position Rg ) gas constant R ) universal gas constant t ) time T ) temperature u ) axial velocity
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b V ) velocity vector x ) axial distance along the tailpipe Greek Symbols µ ) dynamic viscosity ν ) kinematic viscosity F ) density τ ) stress tensor ω ) radian frequency Subscripts A ) amplitude b ) bulk-flow averaged m ) mean or time-averaged
Literature Cited (1) Zinn, B. T. Pulse combustion: recent applications and research issues. Symp. (Int.) Combust. 1992, 24 (1), 1297–1305. (2) Dold, J. W.; Short, M.; Clarke, J. F.; Nikiforakis, N. Accumulating Sequence of Ignitions from a Propagating Pulse. 25th International Symposium on Combustion, Irvine, Ca, Jul 31-Aug 05, 1994; Elsevier Science Publ Co Inc: Irvine, Ca, 1994; pp 465-473. (3) Dec, J. E.; Keller, J. O.; Hongo, I. Time-resolved velocities and turbulence in the oscillating flow of a pulse combustor tail pipe. Combust. Flame 1991, 83 (3-4), 271–292. (4) Dec, J. E.; Keller, J. O.; Arpaci, V. S. Heat transfer enhancement in the oscillating turbulent flow of a pulse combustor tail pipe. Int. J. Heat Mass Transf. 1992, 35 (9), 2311–2325. (5) Dec, J. E.; Keller, J. O. Time-resolved gas temperatures in the oscillating turbulent flow of a pulse combustor tail pipe. Combust. Flame 1990, 80 (3-4), 358–370. (6) Dec, J. E.; Keller, J. O. Pulse combustor tail-pipe heat-transfer dependence on frequency, amplitude, and mean flow rate. Combust. Flame 1989, 77 (3-4), 359–374. (7) Pulse-Combustion Drying Puts Heat on Slurries. Chem. Eng. 1994, 101, (2), 155-155. (8) Zbicinski, I.; Grad, J.; Strumillo, C.; Smucerowicz, I. Application of pulse combustion to drying process. 10th International Drying Symposium (IDS96). Krakow, Poland, Jul 30-Aug 02; Strumillo, C. P. Z., Ed.; Drukarnia Papaj: Krakow, Poland, 1996; pp 631-637. (9) Zbicinski, I.; Strumillo, C.; Kwapinska, M.; Smucerowicz, I. Calculations of the pulse combustion drying system. 2nd International Conference on Advanced Energy Conversion Systems and Related Technologies (RAN98). Nagoya, Japan, Dec 01-03; Pergamon-Elsevier Science Ltd: Nagoya, Japan, 1998; pp 1909-1918. (10) Strumillo, C.; Zbicinski, I.; Smucerowicz, I.; Crowe, C. An analysis of a pulse combustion drying system. Chem. Eng. Process. 1999, 38 (46), 593–600. (11) Kuts, P. S.; Akulich, P. V.; Grinchik, N. N.; Strumillo, C.; Zbicinski, I.; Nogotov, E. F. Modeling of gas dynamics in a pulse combustion chamber to predict initial drying process parameters. 12th International Drying Symposium (IDS2000). Noordwijkerhout, Netherlands, Aug 28-31; Elsevier Science Sa: Noordwijkerhout, Netherlands, 2000; pp 25-31.
(12) Zbicinski, I. Equipment, technology, perspectives and modeling of pulse combustion drying. 12th International Drying Symposium (IDS2000). Noordwijkerhout, Netherlands, Aug 28-31; Elsevier Science Sa: Noordwijkerhout, Netherlands, 2000; pp 33-46. (13) Zbicinski, I.; Smucerowicz, I.; Strumillo, C.; Crowe, C. Application of pulse combustion technology in spray drying process. Braz. J. Chem. Eng. 2000, 17 (4-7), 441–450. (14) Zbicinski, I.; Benali, M.; Kudra, T. Pulse combustion: An advanced technology for efficient drying. Chem. Eng. Technol. 2002, 25 (7), 687– 691. (15) Kudra, T.; Benali, M.; Zbicinski, I. Pulse combustion drying: Aerodynamics, heat transfer, and drying kinetics. Dry. Technol. 2003, 21 (4), 629–655. (16) Wu, Z. H.; Mujumdar, A. S. R&D needs and opportunities in pulse combustion and pulse combustion drying. Dry. Technol. 2006, 24 (11), 1521–1523. (17) Wang, L.; Cui, F. D.; Sunada, H. Improvement of the dissolution rate of nitrendipine using a new pulse combustion drying method. Chem. Pharm. Bull. 2007, 55 (8), 1119–1125. (18) Wu, Z. H. Thesis summary: Mathematical modeling of pulse combustion and its applications to innovative thermal drying techniques. Dry. Technol. 2007, 25 (4-6), 941–942. (19) Xu, L.; Li, S. M.; Sunada, H. Preparation and evaluation of ibuprofen solid dispersion systems with Kollidon particles using a pulse combustion dryer system. Chem. Pharm. Bull. 2007, 55 (11), 1545–1550. (20) Putnam, A. A.; Belles, F. E.; Kentfield, J. A. C. Pulse combustion. Prog. Energy Combust. Sci. 1986, 12 (1), 43–79. (21) Kudra, T.; Mujumdar, A. S. Handbook of Industrial Drying; Marcel Dekker: New York, 1995. (22) Kudra, T.; Mujumdar, A. S. AdVanced drying technologies; Marcel Dekker: New York, 2002. (23) Richards, G. A.; Morris, G. J.; Shaw, D. W.; Keeley, S. A.; Welter, M. J. Thermal Pulse Combustion. Combust. Sci. Technol. 1993, 94 (1-6), 57–85. (24) Daw, C. S.; Thomas, J. F.; Richards, G. A.; Narayanaswami, L. L. Chaos in thermal pulse combustion. Chaos 1995, 5 (4), 662–670. (25) In, V.; Spano, M. L.; Neff, J. D.; Ditto, W. L.; Daw, C. S.; Edwards, K. D.; Nguyen, K. Maintenance of chaos in a computational model of a thermal pulse combustor. Chaos 1997, 7 (4), 605–613. (26) Rhode, M. A.; Rollins, R. W.; Markworth, A. J.; Edwards, K. D.; Nguyen, K.; Daw, C. S.; Thomas, J. F. Controlling Chaos in a Model of Thermal Pulse Combustion. J. Appl. Phys. 1995, 78 (4), 2224–2232. (27) Liewkongsataporn, W. Characteristics of Pulsating Flows in a Pulse Combustor. Master Thesis, Georgia Institute of Technology, Atlanta, 2006. (28) Durbin, P. A. Separated Flow Computations with the K-EpsilonUpsilon(2) Model. Aiaa J. 1995, 33 (4), 659–664. (29) Keller, J. O.; Eibeck, P. A.; Bramlette, T. T.; Barr, P. K. Pulse CombustionsTailpipe Exit Jet Characteristics. Combust. Sci. Technol. 1993, 94 (1-6), 167–192.
ReceiVed for reView October 20, 2009 ReVised manuscript receiVed January 13, 2010 Accepted January 15, 2010 IE901979A
