Energy Fuels 2010, 24, 324–332 Published on Web 10/20/2009
: DOI:10.1021/ef900805v
Investigation of the Structures of Attached and Lifted Flames with Various Ignition Positions over a Triple Concentric Burner in the Hysteresis Regime Hyeon Jun Kim,† Jinhoon Choe,‡ and Hyun Dong Shin*,† † School of Mechanical, Aerospace and Systems Engineering, Korea Advanced Institute of Science and Technology, 373-1, Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea, and ‡Corporate R&D Institute, Doosan Heavy Industries & Construction, 463-1, Jeonmin-dong, Yuseong-gu, Daejeon 305-811, Republic of Korea
Received July 29, 2009. Revised Manuscript Received October 6, 2009
This study focuses on the turbulent nonpremixed flame characteristics in a triple concentric burner with the ignition positions “on the burner” (upstream position) and “above the burner” (downstream position). The flames were attached and lifted when the ignition positions were upstream and downstream, respectively. Numerical simulations were performed for cold flow, attached, and lifted flames. The calculated lift-off height and velocity profiles were in good agreement with the experimental results. In both the attached and lifted flame cases, the flame was situated along the stoichiometric mixture fraction line and in the region where the Damk€ ohler number (Da) was >1. The stoichiometric mixture fraction curve below the lifted flame was on the same line as the stoichiometric equivalence ratio curve of the cold jet. Furthermore, it was found that the two flames exist at the crossover point of the triple curves, which are comprised of the stoichiometric mixture fraction curves of two flames, the Da = 1 curves of the two flames, and the stoichiometric equivalence ratio curve of the cold jet. It was inferred that cold jet fields may dominantly affect the characteristics of a turbulent nonpremixed flame. That is, the ignition position in the cold jet determines the bifurcation of the attached and lifted flames.
well as the relationship between the lift-off height and gas velocity.1-16 Many studies have reported hysteresis phenomena of nonpremixed combustion,17-26 and recent progress was discussed to understand the stabilization mechanisms of lifted turbulent flames.27 It has generally been observed that reattachment phenomena of the flame occur with a reduction of gas velocity to one below the velocity at which the flame was lifted. Therefore, the velocity of reattachment is different from that of liftoff. In addition, the lift-off heights are also different from each other. This phenomenon, which is known as hysteresis, is
1. Introduction Nonpremixed combustion technology is mainly used in industrial burners because of safety issues. The flame often is lifted above the burner exit and remains as a stabilizing flame. Lifted flames are generally dangerous in industrial combustors, because, when coupled with acoustics, they can become unstable and blowout may occur. Therefore, lift-off, reattachment, and hysteresis have been the main research topics in the area of nonpremixed combustion. Many researchers have investigated the structure of lifted flames to understand the mechanisms responsible for the lift-off phenomenon, as
(12) Wu, Z.; Masri, A. R.; Bilger, R. W. Flow, Turbul. Combust. 2006, 76, 61–81. (13) Prasad, A.; Gundavelli, S.; Gollahalli, S. R. J. Propuls. Technol. 1991, 7, 5. (14) Røkke, N. A.; Hustad, J. E.; Sønju, O. K. Combust. Flame 1994, 97, 88–106. (15) Pitts, W. M. Combust. Flame 1989, 76, 197–212. (16) Ferraris, S. A.; Wen, J. X. Combust. Flame 2007, 150, 320–339. (17) Shekarchi, S.; Savas, O.; Gollahalli, S. R. Combust. Flame 1998, 73, 221–232. (18) Chen, Y.-C.; Chang, C.-C.; Pan, K.-L.; Yang, J.-T. Combust. Flame 1998, 115, 51–65. (19) Scholefield, D. A.; Garside, J. E. In Twentieth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1949. € Gollahalli, S. R. J. Fluid Mech. 1986, 165, 297–318. (20) Savas-, O.; € Gollahalli, S. R. AIAA J. 1986, 24 (7), 1137–1140. (21) Savas-, O.; € Huang, R. F.; Azara, J. L. R. In (22) Gollahalli, S. R.; Savas-, O.; Twenty-First Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA; 1988; pp 1463-1471. (23) Terry, S. D.; Lyons, K. M. J. Energy Resour. Technol. 2006, 128, 319–324. (24) Lin, C. K.; Jeng, M. S.; Chao, Y. C. Exp. Fluids 1993, 14, 353– 365. (25) Mu niz, L.; Mungal, M. G. Combust. Flame 1997, 111, 16–31. (26) Terry, S. D.; Lyons, K. M. Combust. Sci. Technol. 2005, 177, 2091–2112. (27) Lyons, K. M. Prog. Energy Combust. Sci. 2007, 33, 211–231.
*Author to whom correspondence should be addressed. Tel.: 82-42869-8821. Fax: 82-42-869-8820. E-mail:
[email protected]. (1) Demare, D.; Baillot, F. Phys. Fluids 2001, 13 (9), 2662–2670. (2) Lyons, K. M.; Watson, K. A. J. Energy Resour. Technol. 2001, 123, 221–227. (3) Montgomery, C. J.; Kaplan, C. R.; Oran, E. S. In Twenty-Seventh Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1998; pp 1175-1182. (4) Marley, S. K.; Lyons, K. M.; Watson, K. A. Flow, Turbul. Combust. 2004, 72, 29–47. (5) Vanquickenborne, L.; van Tiggelen, A. Combust. Flame 1966, 10, 59–69. (6) Takahashi, F.; Schmoll, W. J. In Twenty-Third Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1990; pp 677-683. (7) Takahashi, F.; Mizomoto, M.; Ikai, S.; Futaki, N. In Twentieth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1984; pp 295-302. (8) Eickhoff, H.; Lenze, B.; Leuckel, W. In Twentieth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1984; pp 311-318. (9) Janicka, J.; Peters, N. In Nineteenth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1984; pp 367-374. (10) Peters, N. In Twentieth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1984; pp 353-360. (11) Brown, C. D.; Watson, K. A.; Lyons, K. M. Flow, Turbul. Combust. 1999, 62, 249–273. r 2009 American Chemical Society
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always present in jet flames and has been investigated in nonpremixed turbulent combustion since Scholefield and Garside in 1949.11,19 They hypothesized that hysteresis occurs because of a sudden decrease in height generated by turbulence at a particular flow, which implies that the transition to turbulence is a prerequisite for the stabilization of a lifted flame in the downstream. However, in 1986, Savas- and Gollahalli showed that a jet flame is lifted and stabilized downstream for laminar flames.20 It was shown that the exact solution of the concentration field of a round laminar jet is explicitly dependent on the Schmidt number. Also in 1986, Savas- and Gollahalli21 reported a big difference in the flow structures of attached and lifted flames . They concluded that combustion cannot exist in coherent structures and that the flame suppresses the development and coalescence of these structures. In 1988, Gollahalli et al.22 reported that the flow structure is related to flame stability. The formation and development of flow structure is similar in cold jets and in nonburning parts of the lifted flame. The difference in flow structure between attached and lifted flames accounts for the hysteresis, because reattachment and lift-off processes are controlled by the organized structure in the vicinity of the burner. In 2005, Terry and Lyons26 investigated the lift-off heights and hysteresis reattachment velocities using methane and ethylene fuels under low-Reynolds-number (low-Re) turbulence. They found that the lift-off height at the reattachment point is proportional to the nozzle size and is inversely proportional to the cube of the laminar burning velocity. Furthermore, in 2006, they examined flames of a co-flow of methane and ethylene fuels under laminar and turbulent conditions in 2006.23 Among their conclusions, they reported that the reattachment velocity and lift-off height vary linearly with co-flow, and that reattachment velocity is a function of the type of fuel. They observed that the lift-off height was dependent on the co-flow velocity, the nozzle diameter, and the type of fuel. As the co-flow velocity increases, the lift-off height increases and the fuel velocity at the initial lift-off and reattachment velocity decrease. In 1993, Lin et al.24 reported that the most probable flame base location in the hysteresis regime is located at the vortex roll-up and paring locations. They emphasized that the flame base can be viewed as propagating along a thin premixed layer when the gas velocity is smaller than the flame speed. They also indicated that entrained air during vortex rollup and pairing pointed upward, which inhibits the flame propagation and causes the hysteresis phenomenon. As mentioned by Terry and Lyons,23 for low-fuel applications, an understanding of flame behavior in the hysteresis regime is needed, because burner designers want to know the necessary conditions for a stable flame with maximum efficiency, even though they are interested in turbulent flow with a high velocity flow field. Most industrial burners have more than three nozzles, as opposed to the one or two nozzles usually used in academic experiments. Therefore, study of the hysteresis or lift-off phenomena in a triple concentric burner, which is the basic structure of a multijet burner, is needed to understand the fundamental phenomena of nonpremixed combustion. For numerical simulation, although lifted turbulent flames have been investigated with direct numerical simulation
16
(DNS) and large eddy simulation (LES) techniques, some researchers have used the eddy dissipation concept (EDC) model and the probability density function (PDF) model with the Reynolds-averaged Navier-Stokes (RANS) technique to investigate lift-off phenomena for the combustion model.28-43 The former is the model that accounts for turbulent mixing; however, the latter implements statistical mixing in a nonpremixed flame. This EDC model, in particular, accounts for the assumption of premixed combustion at the flame base of the lifted flame. In other words, when the turbulent time scale in the fine structure balances the chemical time scale, the flame base is stabilized at the lift-off height.14 This study has focused on finding the causes of the two flame shapes of the attached and lifted flames in the hysteresis regime at fixed flow rates for the fuel and the oxidizer. Three jets of a triple concentric burner exit into quiescent air, followed by ignition in the downstream and upstream fields by a pilot flame. After that, a lifted flame appeared for the downstream ignition and an attached flame existed for upstream ignition, coinciding with numerical predictions. For numerical simulation, the EDC model, which is a reactor model that accounts for the interaction between turbulence and chemical reaction, was used with a reduced reaction mechanism. Two types of ignition sources were used in the computational domain. Two different flames were experimentally and numerically observed and verified, and they were numerically analyzed in detail. The existence of attached and lifted flames can be determined with the flow field of the cold jet and ignition position. 2. Experimental Setup The structure of the triple concentric burner is shown in Figure 1. Air flows into the center pipe of the inner air port (IAP), which has an outer diameter of 12 mm and an inner diameter of 8 mm. The fuel flows into a second fuel port (FP) pipe, which has an outer diameter of 18 mm and an inner diameter of 14 mm. Air also flows through a third outer air port (OAP) pipe, which has an outer diameter of 36 mm and an inner diameter of 24 mm. It is easy to make a grid, because of the axisymmetric structure of the burner. The normal diffusion flame and inverse (29) Gran, I. R.; Bjorn F, M. Combust. Sci. Technol. 1996, 119 (1), 191–217. (30) Morvan, D.; Porterie, B.; Larini, M.; Loraud, J. C. Combust. Sci. Technol. 1998, 140 (1), 93–122. (31) Jessee, J. P.; Gansman, F. F.; Fiveland, W. A. Combust. Sci. Technol. 1997, 129 (1), 113–140. (32) Kj€aldman, L.; Brink, A.; Hupa, M. Combust. Sci. Technol. 2000, 129 (1), 113–140. (33) Habibi, A.; Merci, B.; Heynderickx, G. J. AIChE J. 2007, 53 (9), 2384–2398. (34) Magel, H. C.; Schnell, U.; Hein, K. R. G. In Twenty-Sxith Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA; 1996; pp 67-74. (35) Cuoci, A.; Frassoldati, A.; Ferraris, G. B.; Faravelli, T.; Ranzi, E. Int. J. Hydrogen Energy 2007, 32, 3486–3500. (36) Habib, M. A.; Ben-Mansour, R.; Antar, M. A. Heat Mass Transfer 2005, 41, 909–920. (37) Myhrvold, T.; Ertesva˚g, I. S.; Gran, I. R.; Cabra, R.; Chen, J. Y. Combust. Sci. Technol. 2006, 178 (6), 1001–1030. (38) Stefanidis, G. D.; Merci, B.; Heynderickx, G. J.; Marin, G. B. Comput. Chem. Eng. 2006, 30, 635–649. (39) Benim, A. C.; Syed, K. J. Appl. Math. Model. 1998, 22, 113–136. (40) Cabra, R.; Myhrvold, T.; Chen, J. Y.; Dibble, R. W.; Karpetis, A. N.; Barlow, R. S. Proc. Combust. Inst. 2002 29, 1881-1888. (41) Merci, B.; Naud, B.; Poekaerts, D. Flow, Turbul. Combust. 2005, 74, 239–272. (42) Masri, A. R.; Cao, R.; Pope, S. B.; Goldin, G. M. Combust. Theory Model. 2003, 8 (1), 1–22. (43) Gordon, R. L.; Masri, A. R.; Pope, S. B.; Goldin, G. M. Combust. Flame 2007, 151, 495–511.
(28) Wang, Z.; Fan, J.; Zhou, J.; Cen, K. Chin. Sci. Bull. 2007, 52 (15), 2147–2156.
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Figure 1. Schematic of the experimental method. Figure 3. Grid system used for numerical simulation of the burner (measurement units are millimeters).
Direct color photographs were taken with a camcorder at a film speed of 25 frames per second. The average height of the lifted flame was determined from 25 frames over the course of 60 s. The phase-averaged velocity in the nonpremixed flame was measured by a one-component laser doppler velocimeter (LDV, DANTEC Co., Ltd.) with an argon-ion beam source using only the split wavelength of 514.5 nm. For each condition, ∼2000 velocity data samples were acquired at a sampling rate of 2000 Hz. The jet fluid was seeded with 0.05 μm Al2O3 for the LDV measurements. Numerical simulation of the triple concentric burner was performed using the commercial code FLUENT.44 Figure 3 shows the grid system used in this study, in which finer grids were applied near the injection ports of the burner to resolve the complex flow patterns in the furnace and enhance the convergence of the combustion calculations. This burner structure is axisymmetric, with respect to the axial direction (X-axis) and the radial direction (Y-axis). The computational domain extended 800 mm downstream and 36 mm upstream, based on the burner exit. The radial diameter of the computation domain was 108 mm. Pressure boundary conditions were applied to all boundary conditions, except for the inlet and wall conditions. Adiabatic wall conditions were applied to the surface of the burner. A pressure boundary condition was set to the surrounding burner. The inlet conditions used included a turbulent intensity of 10% and a hydraulic diameter for each inlet to generate the turbulent kinetic energy and dissipation rate. The second-order upwind scheme was used to guarantee stable and accurate convergence of the solutions. The Semi-Implicit Method for Pressure-Linked Equations (SIMPLE ) algorithm44,45 was applied to describe the coupling between pressure and velocity. The flow supply conditions used are listed in Table 1. Lifted and attached flames were simulated for the upstream and downstream ignition positions, respectively. Without an ignition source, the fuel and air flows were set at the inlet conditions to investigate the equivalence ratio and velocity field in a nonreacting flow field. The burner was located in a draft-free environment, and, consequently, air for combustion was supplied from the quiescent atmosphere. It is very dangerous to inject fuel and oxidizer directly in a nonreacting flow field to measure velocity profiles. The choice of CO2, whose molecular weight is similar to that of propane (∼44 g/mol), was therefore guaranteed to be safe and
Figure 2. Schematic of the triple concentric burner.
diffusion flame may appear simultaneously, but the normal diffusion flame type does not persist, because of flame extinction that is caused by excess flow. Figure 2 shows a schematic of the experimental method. Liquefied petroleum gas (LPG) fuel (∼98% propane) was used as the jet fluid at a supplied fixed fuel flow rate of 5 L/min and a fixed air flow rate of 10 L/min, as set by the MFC (mass flow controller). A pilot flame was used for the ignition source in a stainless steel pipe with an outer diameter of 4 mm and an inner diameter of 2.5 mm. Stationary flow was first established with fixed fuel and oxidizer flow rates and a nonreacting flow field. When ignited in the upstream field, an attached flame appeared, and when ignited in the downstream field, the flame propagated toward the upstream field and then a lifted flame was formed. All experiments were performed in quiescent air.
(44) Fluent User’s Guide; December 2001. (45) Versteeg, H. K.; Malalasekera, W. An Introduction to Computational Fluid Dynamics: The Finite Volume Method; Longman: Harlow, Essex, U.K., 1995.
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where the asterisk (*) denotes fine-scale quantities, ν is the kinematic viscosity, and Cξ is the volume fraction constant (Cξ = 2.1377). The species were assumed to react in the fine structures over a time scale τ*, and the source term Ri in the governing equation for species i was modeled as follows: 1=2 ν ð5Þ τ ¼ Cτ ε
Table 1. Experimental and Numerical Simulation Conditions Inlet Conditions (Lpm) FP IAP OAP case (fuel ports) (inner air) (outer air) 1 2 3
5 5 5
10 10 10
10 10 10
ignition position
remarks
upstream attached flame downstream lifted flame cold jet
accurate for the measurement of species concentration instead of LPG, because the mixing characteristics are controlled by the momentum of flow, rather than by molecular diffusion.
Ri ¼
3.1. Mathematical Models. The standard k-ε turbulent model was used to simulate reacting and nonreacting flows. It was assumed that the turbulent structure became more isotropic in the combustion field and the flow became fully turbulent in the derivation of this model. This turbulent model employed the Boussinesq hypothesis to relate the Reynolds stresses to the mean flow velocity gradients.44 The turbulent viscosity (μt) was computed using the following equation: ! k2 μt ¼ FCμ ð1Þ ε where Cμ is a constant (Cμ = 0.09) and F is the density. In the standard k-ε turbulent model, the transport equations for the turbulent kinetic energy (k) (see eq 2) and the dissipation rate (ε) (see eq 3) are solved. " # dFui k D μt Dk -Gk -Fε ¼ μþ ð2Þ dxi Dxi σk Dxi "
dðIðrF , sF ÞÞ ¼ -ða þ σs ÞIðrF , sF Þ þ aIb ds Z σs 4π F F0 0 þ Iðr , s ÞΦðsF , sF Þ dΩ0 4π 0
! # μt Dε ε ε2 Gk -C2ε F þ C1ε μþ k σk Dxi k
Here, μ is the molecular viscosity, ui is the velocity vector, and C1ε and C2ε are constants (C1ε = 1.44 and C2ε = 1.92). Gk is a turbulence generation term (Gk = μtS2), and S is the modulus of p theffiffiffiffiffiffiffiffiffiffiffiffiffi mean rate-of-strain tensor, which is defined as S 2Sij Sij where the mean strain rate Duj Dxi
þ
Dui Dxj
ð7Þ
where a is the absorption coefficient, σs the scattering 0 coefficient, ΦðsF , sF Þ is the scattering phase function for 0 radiation from the direction vector sF to the scattered direction vector sF , and Ω0 is the solid angle. I is the radiation intensity, which is dependent on the position ðrF Þ and the direction vector, and Ib is the radiation intensity in the blackbody. The first term in this equation denotes the attenuation, which consists of absorption and outscattering of the radiative energy, and the second term represents augmentation of the radiative energy, which means blackbody gas emission; the third term represents inscattering. In this study, the scattering coefficient was set at zero by assuming clean combustion. The polar and azimuthal angles were divided by Nθ (which has two angular components) and Nj (which has three angular components). The absorption coefficients for the radiative transfer equation were modeled using the Weighted Sum of Gray Gases Model (WSGGM).44
ð3Þ
is Sij ¼ 12
ð6Þ
The mass fractions in the fine structures were unknown. The fine structures were modeled as ideal reactors to calculate and close the equations. This combustion model can easily be found in some literature.33,44,46 In this study, to account for nonequilibrium chemistry effects and simultaneously reduce calculation costs, a four-step reaction mechanism that consists of six species was used with the EDC.47 3.3. The Radiation Model. The temperature is high in the vicinity of the reaction zone in nonpremixed combustion. The radiation model must be used because radiation effects will be dominant in this zone. The discrete ordinate method (DOM) was adopted to model the radiative heat transfer. The DOM is usually used for engineering computations.48-51 This model solves the following radiative transfer equation (RTE) for radiation intensities.44
3. Numerical Method
d D ðFεui Þ ¼ dxi Dxi
FðξÞ2 ðYi -Yi Þ τ½1 -ðξÞ3
. The turbulent Prandtl numbers σk
and σε are 1.0 and 1.3, respectively. The wall function was used against the wall boundary of the burner. 3.2. The Eddy Dissipation Concept (EDC). The eddy dissipation concept (EDC) is an extension of the eddy breakup model (EBM). The EDC takes into account the interactions of turbulence and chemical reactions, whereas the eddy dissipation model (EDM) is limited to irreversible chemistry when used in conjunction with the kinetic chemistry model.44 The EDC is a reactor concept that represents a reaction zone in the fine structures of turbulence where chemical reactions occur. The fine structures are characterized using the length scale and time scale from the turbulent model. The characteristic length and time scales defined in this structure are closely related to the Kolmogorov scales. It is assumed that reactions occur on the small turbulent scale, which is denoted by the term “fine scales”. The volume fraction of the fine scales is modeled as 3=4 νε ð4Þ ξ ¼ Cξ 2 k
4. Results and Discussion 4.1. Comparison of the Predicted and Measured Results. Three different regions were found in the nonpremixed flame, as illustrated in Figure 4: Regime I is the attached (46) Christo, F. C.; Dally, B. B. Combust. Flame 2005, 142, 117–129. (47) Jones, W. P.; Lindstedt, R. P. Combust. Flame 1998, 73, 233–249. (48) Byun, D.; Baek, S. W. Int. J. Heat Mass Transfer 2007, 50, 412– 422. (49) Kim, H. S.; Baek, S. W.; Yu, M. J. Int. J. Heat Mass Transfer 2003, 46, 2993–3008. (50) Baek, S. W.; Kim, H. S.; Yu, M. J.; Kang, S. J.; Kim, M. Y. Combust. Sci. Technol. 2002, 174 (7), 37–70. (51) Kim, J. G.; Huh, K. Y.; Kim, I. T. Numer. Heat Transfer, Part A 2000, 38 (6), 589–609.
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Figure 4. Plot showing the hysteresis effect, as measured from photographs.
Figure 6. Profiles of the axial velocities in the radial direction for (a) case 1, (b) case 2, and (c) case 3 at axial locations of 20 and 100 mm.
Figure 5. Temperature contours and instantaneous pictures, with respect to ignition position: (a) calculated temperature contour for case 1, (b) direct color photograph for case 1, (c) calculated temperature contour for case 2, and (d) direct color photograph for case 2.
can be inferred that (i) the hysteresis regime may be a region to allow two different solutions and (ii) the factor that determines these solutions may be the ignition position. Figure 6 shows the radial profiles of the axial velocity at axial distances of 20 and 100 mm, providing a comparison of the predicted data with the measured values of the two flames and the cold jet. The axial velocity profiles are in good agreement with the experimental data for the two flames and the cold jet in the upstream field, and the trend and magnitude are fairly captured for the two flames in the downstream field, although the isotropic turbulent model was used and deviations can be found in the upstream field. Overall, these figures show that the predicted radial profiles of the axial velocity coincide well with the experimental data. The fairly good agreements between the numerical results and experimental data indicate that the k-ε turbulent model is capable of predicting momentum mixing between two air jets and a fuel jet. 4.2. Temperature Distribution and Flow Structure. Figure 7a shows the temperature contours and flow paths obtained from the EDC combustion model for the attached flame. The contour plot provides a complete picture of the inter-relationship between the temperature and flow streamlines. As mentioned previously, the inverse diffusion flame between the IAP and the FP was extinguished by a strong central momentum flow and only the normal diffusion flame between the FP and the OAP exists along the flow stream pattern. There was a further small recirculation zone between the FP and OAP. This recirculation zone was
flame, Regime II is the hysteresis regime, and Regime III is the lifted flame. The ignited flame remains attached to the burner until it reaches the boundary between Regimes II and III when increasing the outer air flow rate. The lifted flame appeared at an outer air flow of ∼30 Lpm, while the lift-off height decreased from Regime III with a decreasing outer air flow rate. However, the lifted flame could not be attached until the outer air flow rate reached the boundary between Regimes I and II. The hysteresis term was used to describe Regime II in Figure 4, where the attached and lifted flames coexist. In this study, characteristics of the flames generated from different ignition positions were investigated in detail with fixed air and fuel flow rates for Regime II in Figure 4. The instantaneous photographs and the temperature distribution determined by numerical simulation are shown in Figure 5. It is impossible to compare numerical results and photographs directly, because these numerical results signify the time-averaged solutions (Figures 5a and 5c) but these photographs represent the instantaneous pictures (Figures 5b and 5d). However, it is clearly seen that the two different flames (lifted and attached) experimentally and numerically exist near the burner. This situation was previously reported in the hysteresis regime of jet flames.23 Furthermore, it means that two different solutions can numerically coexist in the hysteresis regime, because two different flames are observed, with respect to various ignitions, under the same initial conditions. Therefore, it 328
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: DOI:10.1021/ef900805v
Kim et al.
Figure 7. Temperature distributions and streamlines in the vicinity of the burner for (a) case 1 and (b) case 2 (length values are given in meters).
attributed to continuous ignition by the fresh gases meeting the high temperature product gases. It was observed that the flame base moved downstream and formed the lifted flame shown in Figure 7b. This clearly showed that two different flames appeared, depending on the different ignition positions between the upstream and downstream fields. The lifted flame formed only at the region of the normal diffusion flame controlled by the FP and OAP jets, because of the extinction of the inverse diffusion flame. The flow path stiffly changed near the flame surface in the lifted and attached flames. It is inferred that the flame-generated vorticity front affects the deflection of the velocity field and the streamline in turbulent combustion from Choi’s results,52 which are from a laminar flow field. The two flames have a hightemperature zone along the center of the flame, where the fuel and the oxidizer meet. Figure 8 shows the velocity distribution and streamlines of the two flames and the cold jet. The streamlines in Figures 8a and 8b are the same as those in Figures 7a and 7b. The flow structure of the lifted flame clearly is different from that of the attached flame. The streamline pattern in the nonreacting part of Figure 8b, below the flame base, is similar to that in Figure 8c. However, above the flame base, the flow structure was distorted, and that of the lifted flame shows large differences from that of the cold jets. This result has already been reported through Schlieren pictures by Gollahalli et al.22 Thus, it was inferred that the lift-off height of the lifted flame was dependent on the flow structure of the cold jets. It is necessary to know how the mixture fraction is spatially distributed, because the existence of a flame is dependent on the stoichiometric mixture fraction in nonpremixed combustion. A formula to calculate the mixture fraction from the spatial distribution of species has been reported by Bilger and Starner:53 2ðZC =WC Þ þ ð1=2ÞðZH =WH Þ þ ½ðZO, 2 -ZO Þ=WO ξ ¼ ð9Þ 2ðZC, 1 =WC Þ þ ð1=2ÞðZH, 1 =WH Þ þ ðZO, 2 =WO Þ
streams, respectively. This definition has the advantage that the spatial distribution of the mixture faction can be easily determined from general solutions. The stoichiometric mixture fraction has a value of 0.059 in the case of a propane-air flame in nonpremixed combustion. Figure 9 shows the mixture fraction distribution and stoichiometric mixture fraction value. The stoichiometric value curve can be observed along the flow direction in Figure 9a, while it existed along the flow stream from the burner exit to the lift-off height in the situation illustrated in Figure 9b and changed to along the base of the lifted flame. The mixture fraction in Figure 9b is further distributed more broadly than that in Figure 9a, because of radial expansion of the lifted flame. The Damk€ ohler number (Da) is the ratio of the flow time scale (τf) to the chemical time scale (τc). The flow time scale is defined as the time scale under turbulent flow. The reaction that represents the combustion field must be defined to determine the chemical time scale. In this study, it was assumed that the reaction mechanism of H2þ 0.5O2 T H2O determined the overall chemical time scale. The value of the chemical time scale can be easily obtained because the rate coefficient of an Arrhenius-type nonequilibrium formula has the physical dimension of inverse time. The Da number is spatially presented with the turbulent and chemical time scales in Figure 10. The Da number is a nondimensional parameter that is defined in premixed combustion. In the case of Da > 1, the chemical time scale is less than the turbulent time scale, which means that turbulence can affect the flame structure. However, in the case of Da < 1, the chemical time scale is larger than the turbulent time scale, which means that the overall reaction rate is dominated by the chemical time scale. Flame extinctions occurs for low Da numbers.54 In this research, this concept of the Da number, which was originally used in premixed combustion, was applied to the nonpremixed flame. It is possible for this concept to be applied for nonpremixed flames when using the combustion model to describe the mixing characteristics for turbulence and the reactor concept for chemical reaction. The chemical time scale should be the same as the turbulent time scale to define the flame surface based on a value of Da = 1. The chemical reaction is active in the region of
Here, ξ is the mixture fraction; Zj and Wj are the respective elemental mass fractions and atomic masses for the elements of carbon (C), hydrogen (H), and oxygen (O), respectively; and the subscripts 1 and 2 refer to values in the fuel and air (52) Choi, B. I.; Shin, H. D. Combust. Sci. Technol. 2000, 159 (1), 87–107. (53) Bilger, R. W.; Starner, S. H. Combust. Flame 1990, 80, 135–149.
(54) Poinsot, T.; Veynante, D. Theoretical and Numerical Combustion; R. T. Edwards: Philadelphia, PA, 2001.
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Figure 8. Velocity magnitude contours and streamlines in the vicinity of the burner for (a) case 1, (b) case 2, and (c) case 3 (length values are given in meters).
Figure 9. Mixture fraction distributions and stoichiometric mixture fraction lines in the vicinity of the burner for (a) case 1 and (b) case 2 (length values are given in meters).
Da > 1. Figure 10a shows the Da number distribution and the stoichiometric mixture fraction curve together for the attached flame. The stoichiometric mixture fraction curve was along the center of the flame. The chemical reaction, on the other hand, does not occur below the flame base and, therefore, the flame does not exist in the region of Da < 1 in Figure 10b, because the chemical time scale is less than the
turbulent time scale. The stoichiometric mixture fraction curve also intersects the curve of Da = 1 at the flame base in the situation represented by Figure 10b. The stoichiometric mixture fraction curve passes through the center of the flame in the lifted and attached flames after the EDC model, which is based on the turbulent mixing concept of fuel and oxidizer, has been applied. These results 330
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: DOI:10.1021/ef900805v
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Figure 10. Damk€ ohler number distributions and stoichiometric mixture fraction isosurfaces for (a) case 1 and (b) case 2 (length values are given in meters).
lifted flame, as in the results obtained by Gollahalli et al.22 These curves are separated from the curve of the cold jet at a height of 0.025 m below the flame base, because the streamlines of the lifted flame were stiffly changed at the flame surface and the curve of the lifted flame passed through the center of the flame. In addition, these curves of the lifted flame and the cold jet are different from the curve of the attached flame below the lifted flame base. The curves of the lifted and attached flames crossed each other at a height of ∼0.03 m, at which the height was higher than the height of the flame base for the lifted flame with Da = 1. Both the lifted and attached flames were at almost the same spatial position along the flow direction above the height of the lifted flame, as shown in Figure 11, although the curves of the lifted flame and cold jet are slightly different from the curve of the attached flame below the flame base of the lifted flame. For the attached flame, the location of the three curve intersection, which includes the stoichiometric mixture fraction curve, the stoichiometric equivalence ratio curve, and the curve of Da = 1, is observed at the burner exit. The lifted flame intersects with these three curves near the flame base of the lifted flame. From these results, it can be inferred that the characteristics of the two flames can be determined from the flow field of the cold jet. It is significant that the shapes of the two flames are determined from the two different ignition positions (the upstream and downstream fields) in the hysteresis regime.
Figure 11. Damk€ ohler numbers and stoichiometric mixture fraction curves in the vicinity of the burner for cases 1 and 2 (length values are given in meters).
coincide with the theory of the nonpremixed combustion model, which is based on the mixture fraction and the variance.54 Furthermore, Upatnieks et al.55 and Ferraris et al.16 defined the stabilization point as the location with the maximum premixed heat release that remained at a quasi-stable height, although the lift-off change was attributed to velocity fluctuations induced by large eddies. This means that the good simulation results for nonpremixed combustion were obtained because the stoichiometric mixture fraction curve went through the center of the two flames. Therefore, the simulation with the EDC combustion model gave reasonable results in predicting the lift-off height, because the EDC model assumed a local premixed flow field. 4.3. Comparison of Lifted and Attached Flames. Figure 11 shows Figure 10a superimposed only on the flame part of Figure 10b after removing the blue color region and adding the curve of the stoichiometric mixture fraction, the line of Da = 1, and the curve of the stoichiometric equivalence ratio for the cold jet. The stoichiometric mixture fraction curves in the lifted flame and cold jet were on the same line below the height of the lifted flame. As mentioned previously, the flow field is along the cold jet field below the flame base of the
5. Conclusion The predicted velocity profiles of the attached flame, lifted flame, and cold jet were compared through measurements, and the characteristics of the two flames were numerically investigated in detail. The major findings of this study are as follows: (1) The two flames, attached and lifted, were observed numerically and experimentally, with respect to the ignition position. The attached flame seemed to have an upstream ignition and the lifted flame had a downstream ignition. (2) It was shown that the attached flame may be continuously maintained by the recirculation of burnt gases. The liftoff height of the lifted flame was well-predicted by numerical simulation, using the eddy dissipation concept (EDC) combustion model.
(55) Upatnieks, A.; Driscoll, J. F.; Rasmussen, C. C.; Ceccio, S. L. Combust. Flame 2004, 138, 259–272.
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(3) It was understood that (i) the hysteresis regime might be a region to numerically allow two different solutions and (ii) its control factor might be the ignition position. (4) The stoichiometric mixture fraction curve passed through the centers of the two flames. The numerical simulation using theoretical mixture fraction modeling gave reasonable results for nonpremixed combustion. (5) It was found that the two flames exist at their intersection points with the stoichiometric mixture fraction curve, the curve of Da = 1 (where Da is the Damk€ ohler number), and the stoichiometric equivalence ratio curve of the cold jet.
From this result, the mixing field of the cold jet may be used to determine the position of the flame, with respect to the ignition position (upstream or downstream). Acknowledgment. This research was primarily performed as part of the New Combustion System Controlling Oxidizer Project at the Combustion Engineering Research Center (CERC) in the Korea Advanced Institute of Science and Technology (KAIST). This work was also supported by the Brain Korea 21 (BK21) program, Ministry of Education, Science and Technology.
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