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Characteristics of a Multi-jet Burner in Oxy-Liquefied Petroleum Gas (LPG) Flames Hyeon Jun Kim, Wonyoung Choi, Soo Ho Bae, 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 ReceiVed October 7, 2008. ReVised Manuscript ReceiVed December 17, 2008
In this study, a multi-jet burner with an extremely intense flame was designed for oxy-fuel combustion. The flame characteristics were experimentally and numerically investigated at a fixed overall flow rate of fuel and oxygen and at oxygen feeding ratios (OFRs) of 0.25, 0.5, and 0.75, which gives an overall equivalence ratio of 0.909. The measured temperature profiles were compared to values predicted by numerical simulations, and good agreement was observed. To determine the cause of differing flame height at various OFRs, the iso-surfaces of the fuel, oxygen mole fraction, and the mixture fraction in the physical space were investigated using the numerical data. These results can be understood through an analysis of the scalar dissipation rate, which signifies the mixing characteristics of the fuel with the oxygen and the destruction of scalar fluctuations by turbulent mixing. The flame height seen at an OFR of 0.25 was the lowest because the peak scalar dissipation rate was higher than at other flow conditions. This information is important to reduce the flame height for the control of an intense flame.
1. Introduction The combustion of hydrocarbon fuel with pure oxygen is used to create an intense flame because it offers high efficiency, low emission, and improved temperature stability. In particular, oxyfuel combustion affords near zero emissions and cleaner fossil fuel combustion because the exhaust is composed mainly of CO2 and H2O and most of the CO2 can be recovered by water condensation. The flame temperature produced by oxy-fuel combustion is much higher (∼3100 K) than that produced by air-fuel combustion, and therefore, careful design of the burner and furnace is required for the creation of a high-efficiency oxy-fuel flame. The Canadian Gas Research Institute (CGRI) designed ultralow NOx burners for furnaces to meet industry needs and to establish a high mixing pattern.1 The flow structures in a nonreacting multi-jet burner have already been analyzed in detail using laser Doppler velocimetry (LDV) by Heitor et al.2 In this type of burner, the mixing of fuel and oxidant is delayed until each stream has undergone substantial mixing with combustion products entrained from within the furnace. Fleck et al.1 numerically and experimentally investigated temperature distribution, velocity profiles, and the concentration of species in the CGRI burner, which consists of 14 fuel and air ports arranged in a circle around a central pilot flame. The velocity field in the furnace is dominated by high momentum air jets and furnace gases, which are entrained toward the burner axis and transport the fuel. Combustion close to the burner face is limited by delayed mixing because of the geometry of the multiple jets. Fleck et al.3 carried out a more detailed numerical simulation near the CGRI burner. A total of 14 jets form a ring * To whom correspondence should be addressed: 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. Telephone: 82-42-869-8821. Fax: 82-42-869-8820. E-mail:
[email protected]. (1) Fleck, B. A.; Sobiesiak, A.; Becker, H. A. Combust. Sci. Technol. 2000, 161, 89–112. (2) Heitor, M. V.; Moreira, A. L. N. Exp. Fluids 1992, 13, 179–189.
around the pilot flame and generate a unique flow field, in which fuel jets are quickly entrained with furnace gases and lead into a central core oriented along the burner axis. Sze et al.4 investigated a co-axial (CoA) jet burner and developed an inverse diffusion flame (IDF) burner with circumferentially arranged fuel ports (CAPs). The burners were tested in an unconfined condition. Furthermore, flame shape, temperature distribution, and NOx emissions were reported and compared. On the basis of a comparison of the intensities of air-fuel mixing at different air jet Reynolds numbers and fueling rates, it was concluded that there is more intense air-fuel mixing in the CAP flame than in the CoA flame. According to Sze et al.,4 the IDF is a combination of a premixed flame and a diffusion flame, has a larger flammability range than a premixed flame, and is cleaner than a diffusion flame. Therefore, the feasibility of applying IDFs to industrial and domestic heating processes warrants further investigation. The triple multi-jet burner used in this study was based on an IDF burner with a CAP similar to that of the burner studied by Sze et al.4 An additional CAP was designed for the strong mixing of fuel and oxygen. Consequently, a flame control factor was added to the burner. Oxy-fuel combustion presents many difficulties with regard to flow field and temperature measurement because of the high flame temperature. Therefore, a numerical method is a reasonable alternative because an abundance of information can be gathered, although the results should be validated by experimental data. At the high temperature of an oxy-fuel flame, chemical processes proceed very rapidly. This means that the Damko¨hler number, which is defined as the ratio of the characteristic time scale of turbulence to that of the reaction, is high because the characteristic chemical time scales in the oxyfuel combustion process are negligibly small compared to the (3) Fleck, B. A.; Matovic, M. D.; Grandmaiso, E. W.; Sobiesiak, A. IFRF Combust. J. 2003, 200306. (4) Sze, L. K.; Cheung, C. S.; Leung, C. W. Combust. Flame 2006, 144, 237–248.
10.1021/ef800854e CCC: $40.75 2009 American Chemical Society Published on Web 02/13/2009
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Figure 1. Experimental setup.
characteristic turbulent time scale. Therefore, it can be assumed that the effects of turbulent mixing are more important in oxyfuel flames than in air-fuel flames. The one-step mechanism of Westbrook and Dryer5 is unrealistic in an oxy-fuel flame, because its flame reaches a very high temperature (>5000 K) and there is no mechanism capable of accounting for the thermal dissociation of CO2 and H2O. In oxy-fuel flames, the level of thermal dissociation into radical species is significant. To study the detailed mechanism in a realistic manner is costly and complex; therefore, the study of a reduced mechanism is a reasonable alternative. Hedley et al.6 modeled an oxy-natural gas flame with a four-step mechanism capable of accounting for the thermal dissociation of CO2 and H2O. Reasonable agreement can be obtained for the gas temperature and species concentration. Another alternative is to use a chemical equilibrium assumption. This approach is generally considered to be a poor compromise but is a reasonable alternative from an engineering perspective because the chemical reaction process in oxy-fuel flames is faster than in air-fuel flames. Computational results were obtained using the probability density function (PDF) and eddy dissipation concept (EDC) and were compared to the experimental results of Brink et al.7 The advantage of the EDC is its relatively good agreement with experimental data on flow and temperature compared to the PDF model. However, the PDF model is more applicable to our work because the calculation costs are lower because of the threedimensional geometry of the multi-jet burner. Kim et al.8 numerically and experimentally investigated the flow patterns and flame mixing characteristics of a multi-jet burner. They reported only the two-dimensional cross-sectional distribution of the mole fraction, mixture fraction, and temperature including velocity vectors. However, it is difficult to quantitatively estimate the effect of mixing with these variables. Therefore, it is necessary to investigate the scalar dissipation rate, which (5) Westbrook, C. K.; Dryer, F. L. Prog. Energy Combust. Sci. 1984, 10, 1–57. (6) Hedley, J. T.; Pourkashanian, M.; Williams, A.; Yap, L. T. Combust. Sci. Technol. 1995, 108, 311–322. (7) Brink, A.; Hupa, M.; Breussin, F.; Lallemant, N.; Weber, R. J. Propul. Power 2000, 16 (4), 609–614. (8) Kim, H. J.; Choi, W.; Bae, S. H.; Shin, H. D. Proceedings of KSME Spring Annual Conference, 2007; pp 1-6.
represents the effects of mixing fuel and oxidizer in a nonpremixed flame. This study focuses on understanding the mixing characteristics of a multi-jet burner using the scalar dissipation rate distribution for oxy-fuel combustion. Temperature distributions were measured experimentally by thermocouples and were compared to the temperature distribution obtained from numerical simulation. The scalar dissipation rate is an important parameter in nonpremixed combustion, and it is possible to predict the mixing effect between fuel and oxygen from the scalar dissipation rate distributions. The mole fraction distribution and mixture fraction of fuel and oxidizer were compared at various conditions to three-dimensional contour plots. The temperature and scalar dissipation rate distributions were investigated in detail. 2. Experimental Setup and Method Figure 1 shows a schematic diagram of the experimental system. We used a two-stage cylindrical furnace made of steel and fireresistant cement. Oxygen gas was supplied through an evaporator from a liquefied oxygen tank, and fuel (∼98% propane) was fed from liquefied petroleum gas (LPG) tanks. Both supplies were controlled by mass flow controllers (MFCs) with an error of less than 1%. Water was used to cool the burner. A total of 22 holes were drilled on the side of the furnace to measure the temperature distribution in the furnace and for the installation of sampling probes for gas analysis. The temperature was measured using R-type thermocouples, which were covered with a ceramic material to protect against oxidation of the thermocouple beads. The concentrations of the chemical species were obtained from dried samples passing through silica gel using a water-cooled stainless-steel probe connected to a gas analyzer (CO2, BEA715NDIR; others, PG-250A). A digital camera was used to obtain images of the flames through a quartz window. All measured data were collected after the thermal conditions inside the furnace reached a steady state. (9) Hwang, S. S.; Gore, J. P. Proc. Inst. Mech. Eng., Part A 2002, 216, 379–386. (10) Seo, J. I.; Guahk, Y. T.; Bae, S. H.; Hong, J. G.; Lee, U. D.; Shin, H. D. J. Korean Soc. Combust. 2005, 10, 26–34. (11) Fluent User’s Guide, Dec 2001. (12) Peters, N. Turbulent Combustion; Cambridge University Press: Cambridge, U.K., 2000. (13) Poinsot, T.; Veynante, D. Theoretical and Numerical Combustion; R.T. Edwards, Inc.: Philadelphia, PA, 2001.
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Figure 2. Schematics of the furnace and multi-jet burner.
The structure of the combustion chamber and the burner is illustrated in Figure 2. The height of the chamber was 1230 mm, with probe ports set at intervals of 50 mm, and the injection port of the burner was set at a height of 50 mm. The inner diameter of the furnace, which was made of fire-resistant cement, was 210 mm, and the height from the bottom of the furnace to the first flange was 30 mm. The height of the chamber was taken to be 955 mm in the computational domain because the temperature profile was nearly uniform above 900 mm. The multi-jet burner with circumferentially arranged ports based on the structure of a triple concentric burner was designed to enhance turbulent mixing between the fuel and oxygen.10 The burner consisted of one center port (CP) with a diameter of 6.0 mm for the oxygen and two groups of eight circumferentially arranged ports, which were the first CAPs and second CAPs. The fuel was supplied through the first CAPs, and the oxygen was supplied through the second CAPs. P1 was the axial location for data collection at a radius of 8 mm and azimuth angle of 22.5°; S1 was the axial surface at an azimuth angle of 45° for the contour plot; and S2 was the axial surface at an azimuth angle of 22.5° for the contour plot. The burner was surrounded by a water jacket that protected it from high temperatures. The position of the first CAPs and second CAPs were 11 and 21 mm from the center, respectively. The overall diameter of the multi-jet burner was 28 mm. Two kinds of diffusion flames can exist in this burner: inner flames between the CP and first CAPs and outer flames between the first CAPs and second CAPs. Unburned hydrocarbons passing through the inner flame region can be burned in the outer flame region, and complete combustion can thus be achieved. Numerical simulation of the multi-jet burner was performed using the commercial code FLUENT.11 The overall grid was a 16 × 60 × 681 non-uniform hexagonal grid, which was applied to finer grids placed near the injection ports of the burner to resolve the complex flow patterns in the furnace. To reduce computational costs, the furnace was cut at 45°, including the multi-jet burner, and this section was treated as the computational domain. Both surfaces of the furnace were assigned a periodic boundary condition. The overall height of the grids was 950 mm, and the diameter was 105 mm. The flow supply conditions are listed in Table 1. The operating conditions of the furnace were controlled by changing the oxygen feeding ratio (OFR) at a fixed overall flow rate of fuel. The excess oxygen ratio (EOR) was 1.1, which gave an overall equivalence ratio of 0.909. The OFR values were 0.25 (OFR_0.25), 0.5
Table 1. Experimental Conditions inlet conditions (lpm) cases
first CAPs (fuel ports)
CP (inner oxygen ports)
second CAPs (outer oxygen ports)
EOR
OFR
1 2 3
15.00 15.00 15.00
20.625 41.25 61.875
61.875 41.25 20.625
1.1 1.1 1.1
0.25 0.5 0.75
(OFR_0.5), and 0.75 (OFR_0.75). The EOR and OFR are defined in eqs 1 and 2.
excess oxygen ratio )
total oxygen flow rate oxygen flow rate for stoichiometry (1)
oxygen feeding ratio )
inner oxygen flow rate total oxygen flow rate
(2)
3. Mathematical Models The Favre-averaged conservation equations for mass, momentum, energy, mean mixture fraction, and variance can be readily found in the literature.11-13 The standard k-ε turbulent model was used, and the PDF along with the equilibrium chemistry model was used for the reaction model. A detailed investigation of the chemical reaction that occurs during oxy-fuel combustion is very important because the thermal dissociation effect is dominant in oxy-fuel combustion. The rate equation and chemical equilibrium models can be used to describe the adiabatic flame temperature. The former is mainly used for calculating non-equilibrium chemical reactions. It is not applicable to oxy-fuel combustion because the calculation cost of solving ordinary differential equations (ODEs) is high. The latter, on the other hand, makes use of the concept that a chemical reaction is assumed to quickly reach an equilibrium state. In that case, only thermodynamic state quantities can be considered without complicated chemical reaction mechanisms. The chemical equilibrium calculation is easy because we can use the Gibbs free energy minimization technique.14 It is important to be able to predict the maximum temperature in an oxy-fuel flame. The predicted temperature will be high if the influence of radicals is neglected because most species exist
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Table 2. Species Applied for Equilibrium Calculation cases
considered species
4 species 5 species 6 species 7 species 9 species 17 species
C3H8, O2, H2O, CO2 C3H8, O2, H2O, CO2, CO C3H8, O2, H2O, CO2, CO, H2 C3H8, O2, H2O, CO2, CO, H2, OH C3H8, O2, H2O, CO2, CO, O, H, H2, OH C3H8, O2, CH2O, CH4, CO, CO2, H, H2, H2O, HCO, O, OH, H2O2, HO2, C2H6, C2H4, C
remarks a a a a
a Species that have a high concentration were selected from the calculation for a stoichiometric equivalence ratio with GRI 3.0 using EQUIL code.14
Figure 3. Adiabatic temperature from the chemical equilibrium calculation according to the number of species.
as dissociated radicals at high temperatures and contribute to a decrease in temperature by absorbing energy. To investigate the thermal dissociation effect in the mixture fraction domain, the adiabatic flame temperature and species concentration were calculated with six different sets of species (Table 2) in the chemical equilibrium calculation. Calculation of the effects of thermal dissociation on oxyfuel and air-fuel combustion using the EQUIL code in the CHEMKIN packages14 can be found in the reports of Kim et al.15 They obtained adiabatic flame temperatures of about 2200 K for air-fuel combustion, and 3100 K for oxy-fuel combustion using species consisting of GRI 3.0. In air-fuel combustion, the choice of a one- or two-step reaction mechanism,5 including CO species for the non-equilibrium chemical reaction calculation, leads to reasonable simulation results. However, in oxyfuel combustion (Figure 3), the adiabatic flame temperature with four species at stoichiometry reached approximately 5070 K or more because the thermal dissociation effect was not considered at high temperatures. This value falls to 4200 K when five species are considered. Furthermore, this peak temperature reaches about 3100 K when H2, OH, H, and O species including five species are considered. This temperature is similar to that calculated in the 17 species case. Therefore, it is desirable to consider a minimum of nine species for the chemical equilibrium calculation. The non-equilibrium chemical reaction calculation with a one- or two-step reaction mechanism5 will not give reasonable results because the thermal dissociation effect in the oxy-fuel flame is dominant over the air-fuel flame. The presumed PDF combustion model is a well-known approach to the flamelet concept, which allows for the interaction between turbulence and combustion, and has been used in (14) Kee, R. J.; Rupley, M. F.; Miller, J. A.; Coltrin, M. E.; Grcar, J. F.; Meeks, E.; Moffat, H. K.; Lutz, A. E.; Dixon-Lewis, G.; Smooke, M. D.; Warnatz, J.; Evans, G. H.; Larson, R. S.; Mitchell, R. E.; Petzold, L. R.; Reynolds, W. C.; Caracotsios, M.; Stewart, W. E.; Glarborg, P.; Wang, C.; Adigun, O.; Houf, W. G.; Chou, C. P.; Miller, S. F. Chemkin Collection, Technical Report Release 3.7, Reaction Design, Inc., San Diego, CA, 2002. (15) Kim, H. J.; Choi, W.; Bae, S. H.; Shin, H. D. Trans. KSME 2008, 32 (10), 729–753.
numerous air-fuel combustion applications.16-21 Recently, this model was applied to oxy-natural gas combustion by Brink et al.7 and was used for oxy-LPG flames by Kim et al.8 The β function is the most popular presumed PDF function and depends upon the mean mixture fraction and the variance of the mixture fraction. The advantages of the presumed PDF model are that the method is computationally efficient, and it does not require the solution of a large number of species transport equations. Optical thickness was first considered for application of the radiation model. The optical thickness of gases is considered thick for aL > 1 and thin for aL < 1, where L is the mean beam length and a is the absorption coefficient, which is on the order of 0.3 m-1 for clean fuel combustion. The mean beam length was determined to be 0.5 from the equation L ) 3.6V/ A,22 where L is the mean beam length, V is the furnace volume, and A is the internal surface area of the furnace. In this study, the optical thickness was aL ) 0.15. This means that the gases in the furnace were optically thin. Therefore, the discrete ordinate method (DOM) for radiative heat transfer was a reasonable choice. The absorption coefficients for the radiative transfer equation (RTE) were modeled with the weighted sum of gray gases model (WSGGM), in which the polynomial coefficients were modified for T > 2400 K, according to the results of Coppalle et al.23 A second-order discretization scheme was used to solve all governing equations. The temperature measured at the furnace wall was applied to the wall boundary conditions in the computational domain. The emissivity values for cement and steel in the furnace wall were taken from Incropera and DeWitt.24 4. Results and Discussion 4.1. Comparison of Temperature Profiles between the Numerical and Experimental Results. The radial temperature profiles are illustrated for the locations z ) 180, 330, 480, and 730 mm in Figure 4. The profiles show that the predicted temperature distributions agree fairly well with the measured data. The near flame could not be measured by the R-type thermocouple because of its high temperature (above 2000 K) at the locations z ) 180 and 330 mm in the overall OFR range. Temperature profiles were nearly zero-gradient at the location z ) 730 mm, having a uniform temperature field because of the radiative heat-transfer effect in the overall OFR range. At z ) 180 mm near the burner exit, the maximum temperature was located at 10 mm in the radial direction from the axis and the temperature profile decreased with an increasing radial distance above 10 mm. The reason for the eccentric temperature profile is the eccentric location of the first CAPs. The maximum temperature was about 2800 K in OFR_0.25, 2600 K in OFR_0.5, and 2400 K in OFR_0.75. (16) Ishii, T.; Zhang, C.; Sugiyama, S. Trans. ASME 1998, 120, 275– 284. (17) Ishii, T.; Zhang, C.; Sugiyama, S. Trans. ASME 2000, 122, 224– 228. (18) Jiang, L. Y.; Campbell, I. J. Eng. Gas Turbines Power 2005, 127, 483–491. (19) Kim, J. G.; Huh, K. Y.; Kim, I. T. Numer. Heat Transfer, Part A 2000, 38, 589–609. (20) Liu, F.; Guo, H.; Smallwood, G. J.; Gulder, O. L.; Matovic, M. D. Int. J. Therm. Sci. 2002, 41, 763–772. (21) Albrecht, B. A.; Zahirovic, S.; Bastiaans, R. J. M.; Van Oijen, J. A.; De Goey, L. P. H. Energy Fuels 2008, 22 (3), 1570–1580. (22) Siegel, R.; Howell, J. R. Thermal Radiation Heat Transfer, 3rd ed.; McGraw-Hill, Inc.: New York, 1993. (23) Coppalle, A.; Vervish, P. Combust. Flame 1983, 49, 101–108. (24) Incropera, F. P.; DeWitt, D. P. Fundamentals of Heat and Mass Transfer, 5th ed.; John Wiley and Sons: New York, 2002.
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Figure 4. Measured and predicted radial temperature profiles at z ) 180, 330, 480, and 730 mm for (a) OFR_0.25, (b) OFR_0.5, and (c) OFR_0.75.
Figure 5. Measured and predicted temperature contour: (a) OFR_0.25, (b) OFR_0.5, and (c) OFR_0.75.
Figure 5 shows the measured and predicted temperature contours at various OFRs. The flame was located in the first stage of the furnace in all cases. The blank region near the flame in the measured temperature contour is the space where the temperature could not be measured by the R-type thermocouple because of the high temperature of the oxy-fuel flame. The isolevel of the temperature moved downstream as the OFR increased. The calculated temperature contours were also in good agreement with the measured temperatures. 4.2. Characteristics of Multi-jet Burners. Figure 6 shows the effects of increasing OFR values on the appearance of the flames and the temperature contour. The concentration of CO emission was nearly zero, and that of CO2 emission was about 90%, which corresponds to the values at equilibrium measured by gas analyzers. The region where the measured temperature was above 1800 K was replaced in the flame picture because of the R-type thermocouple limitation. The maximum temperature was located near the flame in the overall OFR. The iso-level of the high-temperature contour broadened toward the outlet as the OFR increased and the temperature distributions became more uniform. The visualized flame height was about 150 mm at OFR_0.25, 300
Figure 6. Temperature contours and flame pictures of the furnace with respect to various OFR: (a) OFR_0.25, (b) OFR_0.5, and (c) OFR_0.75.25
mm at OFR_0.5, and 350 mm at OFR_0.75. The flame height tended to decrease, and the flame was highly luminous at OFR_0.25. The temperature decreased with an increasing flame height because the flame surface area was enlarged. The jet structures of the oxidizer are visualized by arbitrary iso-surfaces of the mole fraction of oxygen in Figure 7. The iso-surface where the mole fraction was 0.75 for OFR_0.25 was located at a height of 0.15 m, and the iso-surfaces at a mole fraction of 0.75 for OFR_0.5 and OFR_0.75 were at a height of about 0.2 m in the region between the CP and first CAPs. The iso-surface for a mole fraction of 0.25 near the second CAPs broadened in the radial direction with decreasing OFR because the flow rate of oxygen through the second CAPs increased with decreasing OFR at an overall fixed flow rate of fuel and oxygen. (25) Choi, W.; Kim, H. J.; Park, J. H.; Shin, H. D. Proceedings of KSME Spring Annual Conference, 2007; pp 1-6.
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Figure 7. Mole fraction iso-surface of oxygen: (a) OFR_0.25, (b) OFR_0.5, and (c) OFR_0.75.
Figure 8. Mole fraction iso-surface of propane: (a) OFR_0.25, (b) OFR_0.5, and (c) OFR_0.75.
Figure 9. Mean mixture fraction iso-surface: (a) OFR_0.25, (b) OFR_0.5, and (c) OFR_0.75.
Figure 8 shows the spatial distribution of propane near the burner. The distribution of the iso-surface where the mole fraction was 0.01 broadened as the OFR increased. The gradients of 0.01 iso-surfaces between the CP and first CAPs (REGION 1) were similar regardless of the OFR because the increased oxygen flow rate in the CP did not strongly affect their slope variation. The shape of the 0.01 iso-surface between the first and second CAPs (REGION 2) changed at various OFRs, because the oxygen flow rate produced low-momentum jets through each port of the second CAPs. Figure 9 shows the distribution of the mean mixture fraction at various OFR values. The iso-surface of the mean mixture fraction varied with changing OFRs. The distribution of the iso-surface where the mean mixture fraction was 0.23, representing the stoichiometric value, broadened as the OFR increased. It is likely that the low-momentum fuel jets were not directly entrained into the high-momentum oxygen jet of the CP, and the surface on which the fuel in the first CAPs and the oxygen in the second CAPs met
was broad in the upstream region of OFR_0.25. The flame features between the first and second CAPs were thus enhanced by the mixing pattern of the overall flow field. The mixing of scalars in a turbulent flow is a very interesting problem because it provides fundamental information on the basic processes involved in non-premixed combustion. According to Sanders and Gokalp,26 scalar dissipation indicates “the destruction of turbulent scalar fluctuations which is associated with their mixing at the smallest scales of turbulence and plays an important role in turbulent combustion models”. The inverse scalar dissipation rate used in turbulent combustion models can therefore be interpreted as a characteristic turbulent diffusion or mixing time. A detailed description provided by Pitsch and Steiner27 states that “in non-premixed combustion, chemical reactions occur only if fuel and oxidizer are mixed at the (26) Sanders, J. P. H.; Gokalp, I. Phys. Fluids 1998, 10 (4), 938–948. (27) Pitsch, H.; Steiner, H. Proc. Combust. Inst. 2000, 28, 41–49.
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Figure 10. Scalar dissipation rate iso-surface: (a) OFR_0.25, (b) OFR_0.5, and (c) OFR_0.75.
Figure 11. Scalar dissipation rate contours at the cross-sectional surface of (a) S1 and (b) S2: (a1 and b1) OFR_0.25, (a2 and b2) OFR_0.5, and (a3 and b3) OFR_0.75 (length unit: m).
molecular level”. The scalar dissipation rate contributes to the mixing of the molecular scalars indirectly and increases with the scalar variance. Molecular scalar mixing occurs with the disappearance of the scalar variance because of viscosity, and its rate is equivalent to the scalar dissipation rate, which is the most important property describing the mixing of scalars in nonpremixed combustion. The scalar dissipation rate used in the present study is a function of the inverse turbulent time scale and the mean mixture fraction variance as follows: χc ) Cd(ε/k)f˜ ′2
(1a)
Here, k is the turbulent kinetic energy, ε is the turbulent kinetic energy dissipation rate, ˜f ′2 is the mean mixture fraction variance, and Cd is the coefficient of 2.0. The physical dimension of the scalar dissipation rate is inverse time; therefore, it can be interpreted as a characteristic turbulent diffusion or mixing time scale, as mentioned above by Sanders and Gokalp.26 Chemical reactions in non-premixed combustion are controlled by the turbulent time scale, which is generally inversely proportional to the scalar dissipation rate. Figure 10 shows the distribution of the scalar dissipation rate in the vicinity of the burner nozzle. At OFR_0.25, the iso-surface
where the scalar dissipation rate is four existed at the top of the iso-surface at approximately 0.15 m and broadened toward the radius, while it existed at the top of the iso-surface at about 0.2 m and narrowed toward the radius at OFR_0.75. Because the scalar dissipation rate represents the molecular scalar mixing, its rapid reduction along the z axis for OFR_0.25 indicates that the chemical reaction proceeded rapidly because of turbulence. Figure 11 shows the distribution of the scalar dissipation rate contours at the cross-sectional surfaces, S1 (a) and S2 (b) in Figure 2. The fuel inlet in Figure 11b is not included because of the position of S2, while that in Figure 11a appears because of the periodic boundary through the center of the fuel inlet port. The distributions of the maximum scalar dissipation rates at the two regions appeared near the CP and second CAPs in Figure 11b. The distributions of the scalar dissipation rates near the CP became large with increasing OFR, whereas those near the second CAPs became small with increasing OFR because the flow rate of oxygen between the CP and second CAPs varied with changing OFRs. The distribution of the scalar dissipation rate was broader at OFR_0.75 than at OFR_0.25. These results indicate that the mixing effect was stronger at OFR_0.25 than
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Figure 12. Temperature contours at the cross-sectional surface of (a) S1 and (b) S2: (a1 and b1) OFR_0.25, (a2 and b2) OFR_0.5, and (a3 and b3) OFR_0.75 (length unit: m).
axial temperature profile at OFR_0.25 was higher than that at OFR_0.75, as can be seen on the left side of Figure 13. As a consequence, chemical equilibrium can occur in the downstream field with a low scalar dissipation rate, while quenching phenomena may occur in the upstream field with a high scalar dissipation rate. Note that the quenching phenomena do not appear in the equilibrium chemistry model. 5. Conclusion
Figure 13. Axial temperature and scalar dissipation rate profiles at P1 in Figure 2.
at OFR_0.75, and thus, the flame height might be lower at OFR_0.25 than at OFR_0.75. As the stoichiometric mixture fraction iso-surface of 0.23 representing the flame location in Figure 9 moved upstream, the maximum temperature at OFR_0.25 became higher than that at OFR_0.75, as indicated in Figure 12. The temperature contour near the second CAPs appeared with decreasing OFR, and the hightemperature region broadened near the burner. As a consequence, a high-temperature zone (above 2482 K) existed in the upstream field and the maximum temperature then increased as the OFR decreased because the area of the flame decreased and the local heat release per unit volume increased. Therefore, the height of the visualized flame in Figure 6 decreased with decreasing OFR, and the luminosity of the flame became more intense. To observe this mixing effect in more detail, the axial temperature and scalar dissipation rate profiles at P1 in Figure 2, where the outer flame exists, were investigated (Figure 13). For all flow conditions, the scalar dissipation rates tended to start out relatively high in the upstream field near the burner exit and then decayed because of viscous dissipation in the downstream field, as shown on the right side of Figure 13. The
The characteristics of a non-premixed oxy-fuel flame in a combustion furnace with a multi-jet burner were numerically and experimentally investigated. The following results were obtained: (1) The temperature distributions found in the numerical simulation and the experimental measurements were in good agreement for the oxy-fuel flame, except for the case of a high-temperature flame. (2) In the near-field region of the jet exit, which is characterized by an OFR with first CAPs and second CAPs, the temperature profiles were complicated but followed the regular near-field pattern of the burner, while in the far-field region, the profiles were uniform because of heat transfer by radiation. (3) The visualized flame height at OFR_0.25 was lower than those at OFR_0.5 and OFR_0.75. The mean mixture fraction iso-surfaces were widely distributed as the OFR increased, and the scalar dissipation rate profiles from the numerical simulation were higher at OFR_0.25 than at OFR_0.5 and OFR_0.75. The flame height at OFR_0.25 may be the lowest for the enhanced mixing of the scalars. That is, the condition of OFR_0.25 in the multi-jet burner can enhance molecular mixing by turbulent flow to yield a low flame height. Acknowledgment. This research was initiated and supported by the Combustion Engineering Research Center (CERC) through KOSEF. This work was also supported by the Brain Korea 21 (BK21) program, Ministry of Education, Science, and Technology. The authors thank Dr. C. Y. Lee for his helpful comments. Finally, the authors also thank Prof. C. Park at KAIST for sharing his knowledge about the chemical equilibrium concept. EF800854E
