- Email: [email protected]
Lifted flames in laminar jets of propane in coflow air
Combustion and Flame 135 (2003) 449 – 462
Lifted flames in laminar jets of propane in coflow air J. Lee, S. H. Won, S. H. Jin, S. H. Chung* School of Mechanical and Aerospace Engineering Seoul National University Seoul 151-742, Korea Received 20 July 2002; received in revised form 20 May 2003; accepted 16 July 2003
Abstract Characteristics of lifted flames in laminar axisymmetric jets of propane with coflowing air have been investigated experimentally. Approximate solutions for velocity and concentration accounting virtual origins have been proposed for coflow jets to analyze the behavior of liftoff height. From the measurement of Rayleigh scattering to probe the concentration field of propane, the validity of the approximate solutions was substantiated. From the images of OH PLIF and CH chemiluminescence and the Rayleigh concentration measurement, it has been shown that the positions of maximum luminosity in direct photographs of lifted tribrachial flames can reasonably be located along the stoichiometric contour. The liftoff height in coflow jets was found to increase highly nonlinearly with jet velocity and was sensitive to coflow velocity. The blowout and reattachment velocities decreased linearly with the increase in coflow velocity. These behaviors of liftoff height and the conditions at reattachment and blowout can be successfully predicted from the approximate solutions. © 2003 The Combustion Institute. All rights reserved.
1. Introduction Lifted flames in laminar jets have been studied extensively to identify the flame stabilization mechanism [1– 4]. The base of a laminar lifted flame exhibits a tribrachial (or triple) structure, consisting of a lean and a rich premixed flame wings and a trailing diffusion flame, all extending from a single location. The stabilization mechanism of laminar lifted flames has been explained based on the balance of the propagation speed of tribrachial flame and local flow velocity. This balance mechanism leads to an excellent correlation of liftoff height with jet velocity and nozzle diameter in free jets, demonstrating highly nonlinear dependency [1,2]. Various effects, including fuel dilution and fuel premixing with air, have been investigated [3,4]. Recently, lifted flame characteristics in coflow jets have been investigated. There are several advantages in adopting a coflow jet over a free jet. More stable flames can be obtained experimentally and the treatment of boundary condition is easier in numeri* Corresponding author. E-mail address: [email protected] (S.H. Chung).
cal approaches. In coflow jets, the detailed tribrachial flame structure at the lifted flame base has been revealed [5,6] and the buoyancy induced lifted flame oscillation has been investigated [7–9]. In these studies, typical nozzle diameters used were O (1 cm). The methane lifted flames have also been studied numerically and experimentally [10,11]. The present study focused on laminar lifted flames of propane jets in coflow air when a sub-millimeter size nozzle is adopted. Therefore, the lifted flames were stabilized in the far field region of the coflow jets. The similarity solutions for velocity and concentration enabled the prediction of lifted flame behavior in free jets [1– 4]. However, such explicit forms of similarity solutions are not available for coflow jets. In this regard, although there are several advantages in adopting coflow jets, the prediction of liftoff height is rather limited. Motivated by this, the present study investigated the liftoff height behavior experimentally and attempted to predict the liftoff height in terms of jet and coflow velocities. Approximate solutions for coflow jets were derived accounting the density difference between jet and coflow. The derivation was based on the experimental observations
0010-2180/03/$ – see front matter © 2003 The Combustion Institute. All rights reserved. doi:10.1016/S0010-2180(03)00182-2
450
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
Nomenclature A Function defined in Eq. (A9) C Constant d Nozzle diameter DF Diffusivity of Fuel F Function defined in Eq. (7) HL Liftoff height I Fuel mass flow rate of jet Imix Rayleigh scattering intensity I0 Incident laser power J Axial momentum of jet n Number density of scattering species q Relative intensity of coflow (⫽ VCO/um,0) r Radial coordinate r0 Nozzle radius r1/2 Half radius R Nondimensional radius (⫽ r/r0) Re Reynolds number 0 SL,st Stoichiometric laminar burning velocity Stri Propagation speed of tribrachial flame Sc Schmidt number of fuel t Time ˜t Dimensionless Lagrangian time u Axial velocity u0 Mean jet velocity at nozzle U Nondimensional axial velocity (⫽ u/um,0) VCO Coflow air velocity x axial coordinate X Nondimensional axial distance (⫽ (x/d)/Re) XC3H8 Propane mole fraction Xl Developing region length Xv Virtual origin
that the relative velocity, which is the difference between jet velocity and coflow velocity, is similar in coflow turbulent jets [12]. The validity of the solutions was tested from the concentration measurements using the Rayleigh scattering technique. From these solutions, various behaviors of lifted flames in coflow jets can be successfully predicted. 2. Experiment The apparatus consisted of a coflow burner and flow controllers, a concentration measurement sys-
YF
Fuel mass fraction Similarity variable defined in Eq. (15) Kinetic viscosity Density Rayleigh cross-section Subscripts BO Blowout F Fuel in Developing region L Lifted LO Liftoff m Centerline maximum out Far field RA Reattachment st Stoichiometric tri Tribrachial 0 Nozzle exit ⬁ Ambient Superscript * Anchoring position
tem, and a visualization setup. The coflow burner had a central fuel nozzle with d ⫽ 0.254 mm i.d. and 10 cm length for the flow inside to be fully developed. Coflow air was supplied to a coaxial nozzle with 152 mm i.d. through glass beads and a ceramic honeycomb to obtain uniform flow. The tip of the fuel nozzle protruded 15 mm above the honeycomb. The fuel was C.P. grade (⬎99%) propane. Mass flow controllers (MKS) were used for flow rate control of fuel and air. A Nd:YAG laser (Continuum, PL8000) was used for Rayleigh scattering measurements to probe fuel concentration. The pulse duration of the laser was 10 ns with a maximum power of 450 mJ at 532 nm. A sheet beam with 50 mm width was illuminated by using a set of cylindrical lenses. The Rayleigh scattering signal was captured by an intensified chargecoupled device (ICCD) camera (Princeton Instrument, ICCD-MAX) through a laser line interference filter of 532 nm (5 nm FWHM). At a specified condition, 1000 images were averaged to suppress noises in probing propane concentration. To minimize scatterings from the material surface of experimental setup, captured images were compensated with the Rayleigh scattering image by supplying helium to the jet and coflow nozzles, since helium has the Rayleigh cross section of 0.0136 times that of air. The intensity of Rayleigh scattering signal of mix-
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
451
ture Imix, depends on the incident laser power I0, the number density of scattering species n, fuel mole fraction XC3H8, and the Rayleigh scattering crosssections of propane C3H8 and air air [13]: I mix ⫽ CI 0n 关X C3H8 C3H8 ⫹ 共1 ⫺ X C3H8兲 air兴
(1)
where C is a system dependent constant. Then, the mole fraction of fuel can be determined from X C3 H8 ⫽
冉
冊冉
C3H8 I mix ⫺1 / ⫺1 I air air
冊
(2)
A planar laser-induced fluorescence (PLIF) system, consisting of a Nd:YAG laser (Continuum, PL8000), a dye laser (Continuum, ND 6000), and the ICCD camera, visualized OH radicals. The Q1(6) transition of A2⌺⫹ ⫺ X2II (1, 0) band for OH radical was excited with 282.95 nm. Pulse energy was approximately 7 mJ/p, which prevented the OH signal from local saturation. The fluorescence signal was captured at right angle through UG-11 and WG-305 optical filters. The chemiluminescence of CH* was taken by the ICCD camera through a narrow bandpass filter of 430 nm (10 nm FWHM). The ICCD camera was also used for direct photography of flames.
3. Results and discussion 3.1. Liftoff height in coflow The variation in liftoff height HL with jet velocity u0 at various coflow air velocities VCO for d ⫽ 0.254 mm and the fuel mass fraction of YF,0 ⫽ 1.0 is shown in Fig. 1. At a specified coflow velocity, the flame lifts off from a nozzle attached flame at a certain liftoff velocity. Then, the liftoff height increases highly nonlinearly with jet velocity and finally blowout occurs. The liftoff height behaviors are quite similar for both the free (VCO ⫽ 0) and coflow (VCO ⫽ 0) jets, except that the liftoff height increases with the coflow velocity. For both the free and coflow jets, the lifted flame base has a tribrachial structure; a diffusion flame, a lean and a rich premixed flames, all extending from a single location. This structure implies that the base is located along the stoichiometric contour and has propagation characteristics. The liftoff height in free jets has been correlated with jet velocity and nozzle diameter [1,2], based on the balance mechanism between the propagation speed of tribrachial flame Stri and local axial velocity along the stoichiometric contour. It has been found that HL/d2 ⬃ u0(2Sc⫺1)/(Sc⫺1) for a specified initial fuel mass fraction, where Sc is the Schmidt number of fuel. The experimental data in free jets are fitted
Fig. 1. Liftoff height variation with jet velocity at various coflow velocities (lines indicate best fits of data and arrows indicate the sensitivity of liftoff height to jet and coflow air velocities).
with Sc ⫽ 1.366 for propane [2], as depicted in the solid line in Fig. 1. The liftoff height data in coflow jets are also fitted to the same form with Sc ⫽ 1.366. The results show that the jet velocity correlation can reasonably represent the liftoff height data for the coflow jets. The sensitivity of coflow velocity to liftoff height is also demonstrated in Fig. 1. For example, the liftoff height variation with the change in coflow velocity from VCO ⫽ 0 to 15.0 cm/s is 3.7 cm at u0 ⫽ 10 m/s. Note that the change of 15 cm/s in jet velocity u0 is minimal near u0 ⫽ 10 m/s, e.g., 0.3 cm/s. The coflow velocity also influences the liftoff and reattachment velocities appreciably, where the velocities are determined by increasing and decreasing jet velocity in the experiment. This point will be further elaborated later. The sensitivity of the coflow velocity to lifted flame behavior is investigated in the following. 3.2. Velocity and concentration fields To investigate the effect of coflow velocity on liftoff height, the information on velocity and concentration fields is needed. However, explicit forms of similarity solutions for coflow jets are not available, especially, accounting the density difference between jet and coflow. In this regard, approximate solutions will be derived based on the similarity solutions in free jets. The similarity solutions for the velocity and concentration in free jets have been successfully applied in deriving liftoff height correlations with jet veloc-
452
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
ity, nozzle diameter, and fuel dilution. This suggests that the velocity and concentration fields with different densities between jet and ambience can also be reasonably similar. In coflow jets, experimental observations in turbulent coflow jets showed that the relative velocity (u ⫺ VCO) is reasonably similar [12]. If the analogy can be applied to coflow laminar jets, the approximate solutions for velocity and concentration can be used in predicting the liftoff height behavior. The similarity solutions for the velocity and concentration in laminar cold free jets are as follows [1,3]: 3 J 1 8 x 共1 ⫹ 2/8兲 2 1 3 I YF ⫽ 8 x 共1 ⫹ 2/8兲 2Sc
and ambience, the axial momentum and fuel mass flow rate are represented by the density of fuel F. Then, the solutions for velocity and concentration in coflow jets are approximated as follows: 1 J 3 8 ⬁x ⬁ 共1 ⫹ 2/8兲 2 1 I 3 YF ⫽ 8 ⬁x ⬁ 共1 ⫹ 2/8兲 2Sc
u ⫺ V CO ⫽
where the subscript ⬁ indicates the ambient condition and the similarity variable , the axial momentum J and the fuel mass flow rate I are
u⫽
⫽
(3) J⫽
where u is the axial flow velocity, r, x are the radial and axial coordinates, respectively, J is the axial 2 momentum (um,0 d2/12), I is the fuel mass flow rate 2 (u0d /4), is the density, is the kinematic viscosity, is the similarity variable defined as ⫽ 冑1/32共um,0 d/兲 共r/x兲, and Sc is the Schmidt number of fuel defined as /DF, where DF is the diffusivity of fuel, and the subscripts m and 0 indicate the centerline maximum at a specified x and the jet nozzle exit, respectively. Based on the experimental observations [12], the relative velocity (u ⫺ VCO) is assumed similar, and the centerline relative velocity (um ⫺ VCO) is proportional to 1/x for the strong jet with (u0 ⫺ VCO) ⬎⬎ VCO. Considering the density difference between jet
u ⫺ V CO F ⫽ u m,0 ⫺ V CO ⬁
冉
3 ⬁ q 2 F 1⫺q
1⫺
冊
F 2Sc ⫹ 1 YF ⫽ ⬁ 64共X ⫹ X , F兲
I⫽
1⫹
F ⬁
冉
where q ⫽ VCO/um,0 is the relative intensity of coflow. The virtual origins for velocity and concentration have been derived assuming the potential core in which the radial diffusion dominates and the entrainment is negligible in case of parabolic velocity profile at the nozzle exit [14 –16]. Similar method has been applied to determine the virtual origins in coflow jets [Appendix, Eq. (A15)]. By using the values, the calculated dimensionless stoichiometric contour Rst and the dimensionless velocity along the stoichiometric contour Ust ⫽ ust /um,0
冕
冕
r0
冑
共u m ⫺ V CO兲 x r x
u共 Fu ⫺ ⬁V CO兲2 rdr
0
r0
F uY F,0 2 rdr ⫽
0
冕
r0
(5)
F u2 rdr
0
Since the similarity solutions become singular at the nozzle exit, the virtual origins are frequently introduced to improve the accuracy of the solutions. By introducing the Reynolds number based on um,0 as Re ⫽ um,0d/⬁ ⫽ 2u0d/⬁ for the Poiseuille flow at the nozzle exit, the dimensionless axial distance X ⫽ (x/d)/Re[14], the dimensionless radius R ⫽ r/r0, and the dimensionless relative velocity (u ⫺ VCO)/ (um,0 ⫺ VCO), the approximate solutions accounting the virtual origins X for velocity and X,F for concentration become
1 32共X ⫹ X 兲
再
(4)
1 F 1 R 3 ⬁ 1⫹ 1⫺ q ⬁ 2 F 32 X ⫹ X 1 2 2Sc 1 R 3 ⬁ 1⫺ q 2 F 32 X ⫹ X , F
再
冉 冊冉
冊冉
冊冎 2
2
(6)
冊冎
are plotted in Fig. 2 for propane fuel with Sc ⫽ 1.366. The axial velocity demonstrates qualitatively similar behavior for both the coflow and free jets; increases with X near the nozzle, having a maximum, and then decreases slowly. This non-monotonic behavior agrees qualitatively well with the previous numerical data [18]. However, The magnitude of axial velocity is sensitive to the coflow velocity. For example, ust is approximately 30% larger for q ⫽ 0.015 compared to that for q ⫽ 0. On the other hand, the stoichiometric contour Rst in the coflow jet is nearly unchanged from that of the free jet.
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
453
Fig. 2. Profiles of stoichiometric contour and axial velocities along stoichiometric contours.
3.3. Concentration measurement Experimental verification of the validity of the approximate velocity solution is rather difficult. One problem is due to particle seeding through very small nozzle with low flow rate of fuel and the other is to very low velocity of the coflow. Since the similarity of velocity field has been tested previously [12], we have indirectly test the approximate solutions by experimentally probing the propane concentration in coflow. The Rayleigh scattering technique has been adopted where the Rayleigh cross section for propane is 13.01 times that of air [19]. Figure 3 shows the Rayleigh signal in a cold jets (a) and with lifted flame (b), together with the direct photograph of the flame (c). The OH PLIF image and the Abel transformed image of CH chemiluminescence are superimposed on the Rayleigh image (b), which exhibits relatively large burnt gas region. From the Rayleigh scattering images, the mass fraction of propane is calculated by assuming the
binary mixture of propane and air. At specified axial distances X ⫽ 0.52 (x ⫽ 3.8 cm and 4.0 cm for u0 ⫽ 9.0 m/s and 9.5 m/s, respectively) and X ⫽ 0.67 (x ⫽ 4.9 cm and 5.2 cm for u0 ⫽ 9.0 m/s and 9.5 m/s, respectively), the radial profiles of propane concentrations are plotted in Fig. 4 for VCO ⫽ 4.0 cm/s. The mass fraction predicted from Eq. (6) is also represented. The experiment and prediction with Sc ⫽ 1.366 are in good agreement within the accuracy of about 10%. For comparison, the predicted profile with Sc ⫽ 1.0 at X ⫽ 0.67 is also plotted, demonstrating fast mass diffusion as compared to the case with Sc ⫽ 1.366. Note that the mass fractions at the stoichiometry, the lean and rich flammability limits are 0.06, 0.03, and 0.15 respectively. The propane mass fraction along the centerline YF,m is shown in Fig. 5 for u0 ⫽ 9.0 and 9.5 m/s, demonstrating satisfactory agreement with the prediction. Note that due to the noise from surface scattering near the nozzle region, the experimental data for X ⬍ 0.42 (x ⬇ 3.0 cm) were discarded.
454
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
Fig. 3. Images of (a) Rayleigh intensity for cold flow, (b) Rayleigh intensity, OH PLIF and CH* for lifted flame, and (c) direct photograph (u0 ⫽ 9.0 m/s, VCO ⫽ 4 cm/s).
Fig. 4. Radial profile of fuel mass fraction with dimensionless radius for VCO ⫽ 4.0 cm/s.
Fig. 5. Fuel mass fraction along the centerline with dimensionless axial distance.
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
Fig. 6. Radial concentration profiles demonstrating similarity in coflow jets with VCO ⫽ 4.0 cm/s.
The similarity of the concentration field is further tested by plotting the normalized propane concentration YF/YF,m with the normalized radius r/r1/2, where r1/2 is the half radius at YF ⫽ YF,m/2. As shown in Fig. 6 the concentration profiles are similar for the present coflow. The comparison of measured data with the prediction substantiates the validity of the approximate solutions in describing the flow characteristics of coflow jets. 3.4. Maximum luminosity and stoichiometric contour A tribrachial flame is composed of a rich and a lean premixed wings and a trailing diffusion flame. Due to the coexistence of these three different types of flames, a tribrachial point should be located along a stoichiometric contour. For the propagating tribrachial flames in methane free jets once ignited at a downstream location [20], it has been found that the tribrachial point travels along the stoichiometric contour, where the contour was calculated by assuming a cold jet. Since the lifted flame base propagated with relatively high speed, the gas expansion and subsequent buoyancy effects to upstream concentration field was expected to be not significant. However, for stationary lifted flames, the gas expansion and buoyancy effects could influence the concentration field since upstream flow field has sufficient time to adjust from the cold jet. Thus, it is needed to test the concentration field for stationary lifted flames. In addition, if the tribrachial point is located along the stoichiometric contour assuming a
455
cold jet, then the stoichiometric contour can be traced by measuring the loci of tribrachial points in jets. This could be a convenient experimental tool in estimating the stoichiometric contour, especially for unknown concentration fields. It has been shown previously in a tribrachial flame that OH LIF signal has maximum intensity along the diffusion flame and the chemiluminescences of OH* could represent the premixed flame [7]. Preliminary test reveals that the locations of the chemiluminescences of OH* and CH* signals are indistinguishable in representing the premixed flame wings in a lifted tribrachial flame. Thus, we have qualitatively represented the tribrachial flame based on OH LIF and CH*. Note that it is a somewhat difficult task to pinpoint the tribrachial point experimentally and even numerically. The superimposed image of the OH PLIF, CH*, and the Rayleigh intensity in Fig. 3b shows the branching of flames indicating the tribrachial flame structure for the stationary lifted flame. Here, the OH LIF indicates the trailing diffusion flame and CH* the premixed flame wings. Due to significant decrease in CH* intensity in lean premixed flames compared to rich premixed flames, the lean premixed flame wing is less obvious. As a consequence, the base of the tribrachial flame seems to be more slanted, as compared to the judgment based on the direct photograph. To further illustrate this behavior, the stoichiometric contours from the Rayleigh measurements in coflow jets and the corresponding jets with lifted flames are plotted in Fig. 7. From the average of 1000 images, the height-by-height measurements of stoichiometric radius are represented. The scattering of data can be attributed to the noise in the Rayleigh measurements, since the stoichiometric mole fraction of propane is very low, that is, 0.042. The standard deviations of Rayleigh signals from the respective best fit curves for u0 ⫽ 9.0 and 9.5 m/s are 0.089 and 0.095 mm, respectively, which are within the accuracy of measurement. Note that the rapid decrease in the Rayleigh intensity for the case with the lifted flame is due to the decrease in the Rayleigh cross-section by gas expansion in the preheat zone of the premixed flame wings of the lifted tribrachial flame. The predicted contours are represented by solid lines. The results demonstrate that the concentration field upstream region of the lifted flame is nearly identical with that of the cold flow, demonstrating that the effects of gas expansion and buoyancy by the lifted flame are not significant. The point of maximum luminosity after the Abel transformation from the direct photograph is marked as a closed circle. Note that this point is located reasonably along the stoichiometric contour, deter-
456
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
Fig. 7. Stoichiometric contour from Rayleigh measurements and maximum luminosity from direct photography for VCO ⫽ 4 cm/s; (a) u0 ⫽ 9.0 m/s and (b) 9.5 m/s.
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
457
mined assuming the cold jet. Thus, the result suggests that the stoichiometric contour can be traced from the locus of maximum luminosities in lifted flames. The predicted result from Eq. (6) has satisfactory agreement with the experiment. The average deviation in the radial direction between the experiment and prediction was about ⌬r0 ⫽ 0.127 mm, which is within the accuracy of measurement. These results substantiate that the previous studies based on the cold jet theory [1– 4] could lead to successful correlations for the behavior of lifted flames in laminar free jets. 3.5. Prediction of liftoff height in coflow Having confirmed the validity of the approximate solutions from the Rayleigh measurement, the liftoff heights in coflow jets are analyzed. A tribrachial point is premixed in nature, having the propagation characteristics. Thus, at the flame anchoring position, the local axial velocity along a stoichiometric contour should balance with the propagation speed of tribrachial flame Stri for stationary lifted flames. If the propagation speed of tribrachial flame is available, the experimental liftoff height can be predicted by using the balance mechanism between the propagation speed of tribrachial flame and local axial velocity. Recently, the propagation speed of tribrachial flame of propane has been determined in terms of fuel mass fraction gradient under microgravity 0 condition as Stri/SL,st ⫽ 0.00344[dYF/dR|st ⫹ 0 ⫺1 0.00237] ⫹ 1.562 [21], where SL,st is the stoichiometric laminar burning velocity having chosen to be 0.40 m/s [22,23]. By using this, the liftoff height can be calculated from Eq. (6) based on the balance between the local axial velocity along the stoichiometric contour and Stri accounting the radial concentration gradient. Figure 8 exhibits the liftoff height variation with jet velocity for VCO ⫽ 0 and 15 cm/s, with the prediction represented in lines. The results demonstrate satisfactory agreement. Note that the closed and open symbols for the experimental data indicate the experiments conducted by increasing and decreasing jet velocity, respectively, to identify liftoff and reattachment conditions between nozzle attached and lifted flames. This difference will be elaborated later. The prediction substantiates that the approximate solutions can be applied in analyzing various behaviors of lifted flames in coflow jets. The relation among liftoff height, jet velocity, and coflow velocity can be derived from Eq. (6). The dimensionless anchoring position XL* can be derived in terms of the dimensionless velocity at the position (uL* ⫺ VCO)/(um,0 ⫺ VCO) as follows:
Fig. 8. Comparison of liftoff height with jet velocity between experiment and prediction (closed symbols are for experiment conducted with increasing jet velocity and open symbols with decreasing jet velocity).
X L* 兵共u L* ⫺ V CO兲 F 共X L* 兲其 Sc/(Sc⫺1)
冉
⫽ u m,0 ⫺
3 F V 2 ⬁ CO
冊
where F共X L* 兲 ⫽ ⫻
再冉
⬁ 32共X L* ⫹ X 兲 F X L*共Sc⫺1兲/Sc
Sc/(Sc⫺1)
(7)
冋 冉 1⫹
冊 冎册
X L* ⫹ X , F X L* ⫹ X
F 2Sc ⫹ 1 1 1 * ⬁ 64 X L ⫹ X , F Y F, st
冊
1/ 2Sc
2
2
⫺1
Here, the superscript* indicates the anchoring position, thus HL ⫽ xL* and uL* ⫽ Stri. For the strong jet with um,0 ⱖ VCO, the above relation results in HL v⬁ 0 d 2 S L, st
再 冉 冊
⫽ ⬀
再
F共X L* 兲
冎
S tri ⫺ V CO 0 S L, st
Sc/(Sc⫺1)
冎
u m, 0 ⫺ 共3/ 2兲 共 F/ ⬁兲 V CO 0 S L, st
u m, 0 0 S L, st
Sc/(Sc⫺1)
冉 冊 u m, 0 0 S L, st
共2Sc⫺1兲/共Sc⫺1兲
(8)
The experimental data are represented in terms of LHS and RHS of Eq. (8) in Fig. 9. The result demonstrates excellent linear correlation with the correlation coefficient of R ⫽ 0.979. This substantiates the validity of the approximate solutions and the functional dependence of jet velocity and coflow velocity on liftoff height.
458
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
Fig. 9. Correlation of liftoff height with jet velocity and coflow velocity with the units in [m, s].
The liftoff height is influenced by the jet velocity (2Sc⫺1)/(Sc⫺1) in terms of um,0 , which confirms the validity of the jet velocity dependence, as was demonstrated in Fig. 1. The dependency of coflow velocity is in two ways. One is from (Stri ⫺ VCO)Sc/(1⫺Sc) and the other from F(XL*), which exhibits the dependence of coflow velocity through the virtual origins. The effect of the virtual origins in F(XL*) is not significant when HL ⬎⬎ d. Thus, the dominant influence of coflow velocity on liftoff height is through (Stri ⫺ VCO)Sc/(1⫺Sc). This point will be further illustrated in the following. The anchoring position of a stationary tribrachial flame is located in the far field from the nozzle with the typical minimum height of 1.5 cm, which is at least 60 diameters away from the nozzle. Thus, regardless of the adoption of virtual origins, the overall characteristics of the axial velocity along the stoichiometric contour will be at least qualitatively similar in the far field region. Consequently, it is expected that the functional dependence of coflow velocity on liftoff heights is not influenced much by the adoption of the virtual origins. In this regard, it is assumed that X ⫽ X,F ⫽ 0, and the effects of jet velocity and coflow velocity on liftoff height are analyzed. Note that F(XL*) ⫽ const for this case. Then, the relation of liftoff height becomes HL 共2Sc⫺1兲/共Sc⫺1兲 共S ⫺ V CO兲 Sc/(Sc⫺1) ⫽ const ⫻ u m, 0 d 2 tri (9) The experimental liftoff data in Fig. 1 are correlated by using Eq. (9) including the effect of coflow velocity and the results are shown in Fig. 10. It
Fig. 10. Correlation of liftoff height with jet velocity and coflow velocity without considering virtual origins with the units in [m, s].
demonstrates satisfactory linear correlation with R ⫽ 0.982. Since the virtual origins are not accounted, the correlation does not pass through the origin. Note that the liftoff height HL is influenced by coflow velocity through the factor of (Stri ⫺ VCO)Sc/(1⫺Sc) and jet velocity with the factor of u(2Sc⫺1)/(Sc⫺1) . Since 0.7 m,0 ⱕ Stri ⱕ 0.85 m/s [21], 0 ⱕ VCO ⱕ 15 cm/s, and 7 ⬍ u0 ⬍ 13 m/s, (Stri ⫺ VCO) can be varied up to 20% and the effect is amplified by the exponent Sc/(Sc ⫺ 1) ⫽ 3.7322. This explains why the liftoff height is so sensitive to the coflow velocity, as was demonstrated in Fig. 1. 3.6. Reattachment and blowout Figure 8 showed the typical characteristics of lifted flame with the variation of jet velocity. For example, as u0 increases for VCO ⫽ 15 cm/s, a nozzle attached flame has a liftoff (LO) at uLO ⫽ 9.7 m/s and the liftoff height increases with u0 and finally blowout (BO) occurs at uBO ⫽ 11.0 m/s. As u0 decreases from a lifted flame, the lifted flame has a reattachment (RA) to the nozzle at uRA ⫽ 7.4 m/s. Therefore, there exists a hysterisis region of 7.4 ⬍ u0 ⬍ 9.7 m/s. Note that the hysterisis region is appreciably extended for the case with the coflow compared to the free jet (VCO ⫽ 0). Although the conditions of liftoff cannot be predicted from the present study due to complex nature of flow field and heat transfer near the nozzle region for attached flames, the reattachment and blowout can be predicted from the cold jet solutions since the liftoff height is far away from the nozzle at those moments. Therefore, the influence of
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
coflow velocity on reattachment and blowout are analyzed in the following. 3.6.1. Reattachment conditions Jet velocity and flame position at reattachment can be calculated from the balance of propagation speed and axial velocity. The axial velocity along the stoichiometric contour ust has a local maximum, as was shown in Fig. 2. In such a case, the reattachment condition can be identified [17], since the range of
S tri, RA ⫺ V CO F ⫽ 2u RA ⫺ V CO ⬁
⬇ const ⫻
冉
冉
3 ⬁ q 2 F 1⫺q
1⫺
3 ⬁ q 2 F 1⫺q
1⫺
冊
冊
冋 冉
459
increasing ust with x is unstable such that the balance between the propagation speed of a tribrachial flame and the local flow velocity cannot be maintained for u0 smaller than the reattachment velocity uRA. Rigorous explicit form is difficult to derive, however, since the variation of XRA is within 15% for the coflow velocity of 0 ⱕ VCO ⱕ 15 cm/s, XRA is assumed constant for simplicity. In such a case, the correlation between xRA, uRA and VCO can be derived as follows:
冊 再冉
X RA ⫹ X , F 1⫹ X RA ⫹ X
1 32共X RA ⫹ X 兲
F 2Sc ⫹ 1 1 1 ⬁ 64 X RA ⫹ X Y F,st
冊
1/ 2Sc
⫺1
冎册
2
(10)
Then, the functional relations for uRA and xRA ⫽ HL,RA with VCO becomes u RA ⫽ C 1 ⫺ C 2V CO,
C 1, C 2; constants
H L,RA ⫽ C 3 ⫺ C 4V CO,
(11)
C 3, C 4; constants
(12)
Here, the dependence of VCO on HL,RA is from the definition of XRA through the Reynolds number Re. 3.6.2. Blowout conditions It has been shown previously [1,3] that the condition of Rst ⫽ f(X;u0, VCO) ⫽ 0 can represent the blowout for propane having Sc ⬎ 1. From Eq. (6), the stoichiometric contour becomes R st ⫽
冋再 ⫻
F 2Sc ⫹ 1 1 ⬁ 64共X ⫹ X ,F兲 Y F,st 32共X ⫹ X ,F兲 F 3⬁ 1⫺ q ⬁ 2 F
再 冉
冊冎
冎
1/ 2Sc
⫺1
册
1/ 2
(13)
1/ 2
Then, the liftoff height at blowout XBO and the blowout velocity uBO, using the condition of Rst ⫽ 0, becomes
F 2Sc ⫹ 1 1 X BO ⫽ X , F ⫹ ⬁ 64 Y F, st S tri, BO ⫺ V CO F ⫽ 2u BO ⫺ V CO ⬁
冉
3 ⬁ q 2 F 1⫺q
1⫺
(15)
冊
1 1 32 X BO ⫹ X (16)
These lead to the following correlations for uBO and xBO ⫽ HL,BO with VCO for q ⬍⬍ 1.
Fig. 11. Liftoff height at reattachment, blowout, and liftoff conditions with coflow velocity (symbols: experiments, lines: best linear fits).
u BO ⫽ C 5 ⫺ C 6V CO, H L,BO ⫽ C 7 ⫺ C 8V CO,
C 5, C 6; constants C 7, C 8; constants
(17) (18)
3.6.3. Comparison with experiments It has been derived that the liftoff height and jet velocity at reattachment and blowout decrease linearly with coflow velocity. To confirm the correlations, the experimental data at reattachment and blowout are plotted in Figs. 11 and 12 for the liftoff height and jet velocity, respectively. The results
460
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
counting the effects of density difference between fuel and ambient air and the virtual origins. The validity of the solutions has been confirmed from the fuel concentration measurement using the Rayleigh scattering technique. By adopting OH PLIF, CH chemiluminescence, and direct photography, the positions of maximum luminosity from direct photography could represent the stoichiometric loci in axisymmetric jets. The liftoff height in coflow jets increases with u(2Sc-1)/(Sc-1) and the sensitivity of coflow velocity on 0 liftoff height has been successfully predicted through the effect of (Stri ⫺ VCO)Sc/(Sc-1). The influence of coflow velocity on the conditions of reattachment and blowout has been predicted, resulting in the linear decrease in liftoff height and jet velocity with coflow velocity and the experiments confirm the behavior.
Fig. 12. Jet velocity at reattachment, blowout, and liftoff conditions with coflow velocity (symbols: experiments, lines: best linear fits).
clearly demonstrate the linear dependencies of the liftoff height and jet velocities at reattachment and blowout with coflow velocity. As mentioned previously in Fig. 2, the local axial velocity along a stoichiometric contour increases with coflow velocity. Because the stoichiometric contour Rst, thereby the propagation speed of tribrachial flame, is insensitive to coflow, the increase in the local axial velocity with coflow velocity leads to the decrease in u0 with VCO at blowout and reattachment. The conditions at liftoff are also plotted in Figs. 11 and 12. Note that the jet velocity and liftoff height at the liftoff condition also decrease linearly with coflow velocity, except the case of the free jet (VCO ⫽ 0). The experimental data are significantly lower than the linearly extrapolated values for VCO 3 0. These behaviors cannot be clearly explained at present, however, it may be attributed to the near nozzle flow characteristics between free and coflow jets, for example, the recirculation zone near the nozzle tip can be significantly influenced by the existence of coflow.
Acknowledgments This work was supported by the Combustion Engineering Research Center. SHW and SHJ were supported by the BK-21 Program for Mechanical Engineering, Seoul National University.
Appendix Virtual origin for coflow jets By adopting the similar approach in deriving the virtual origins in free jets [14 –16], it is assumed that the entrainment can be negligibly small in the developing region near a nozzle such that the radial diffusion dominates over the axial convection and the Lagrangian description along the centerline could describe the axial convection. Then, the momentum and species equations and boundary and initial conditions in the near field are as follows: ⭸u v F ⭸ ⫽ ⭸t r ⭸r
冉 冊 冉 冊 再 冉 冊冎 r
⭸u ⭸r
⭸Y F v F 1 ⭸ ⫽ ⭸t Sc r ⭸r
r
⭸Y F ⭸r
t ⫽ 0; u ⫽ um,0 1 ⫺ 4. Concluding remarks Characteristics of lifted flames in axisymmetric laminar coflow jets of propane have been investigated experimentally. To analyze the behavior of lifted flames, the approximate solutions for velocity and concentration in coflow have been derived ac-
for 0 ⱕ r ⱕ r0 r ⫽ 0; r 3 ⬁;
(A1)
r r0
(A2)
2
, YF ⫽ YF,0 ⫽ 1
⭸Y F ⭸u ⫽ 0, ⫽0 ⭸r ⭸r u 3 V CO, Y F 3 0
(A3)
The formal solutions of these transient diffusion equations are
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
冕
u ⫺ V CO 1 2˜ 关2t˜e ⫺R t ⫽ u m,0 ⫺ V CO 1 ⫺ q
˜
Y F, m,in ⫽ 1 ⫺ e ⫺Sct
1
共1 ⫺ 兲 2
0
2˜ ⫻ e ⫺ tI 0共2 Rt˜ 兲d ⫺ q兴
冕
˜
Y F ⫽ 2Sct˜e ⫺R Sct 2
1
(A4)
˜
e ⫺ SctI 0共2 RSct˜ 兲d 2
461
(A5)
(A7)
where the subscript in indicates the solution in the near field developing region. Here, the velocity and concentration are expressed in terms of the Lagrangian time. By using the Lagrangian description of fluid particle along the centerline, the relation between the axial distance x and the time is
0
where ˜t is the dimensionless Lagrangian time scale, defined as ˜t ⫽ r02/(4vFt) and q ⫽ VCO /um,0. Then, the velocity and concentration along the centerline (r ⫽ 0) can be derived by substituting r ⫽ 0 into Eqs. (A4) and (A5) and integrating u m,in ⫺ V CO 1 1 ˜ ⫽1⫺ 共1 ⫺ e ⫺t兲 u m,0 ⫺ V CO 1 ⫺ q ˜t X⬅
(A6)
x x v⬁ 1 ⫽ ⫽ 共u m,0d/v ⬁兲d Re d v F 16
冋
冕
dx ⫽ u m共 x兲 dt
where um(x) is the centerline velocity [16]. By substituting Eqs. (A6) and (6) into Eq. (A8) in the velocity developing region and in the velocity developed region, and integrating, the following relations between the axial coordinate X and the Lagrangian time ˜t can be obtained
1/t˜
兵 1 ⫺ 共1 ⫺ e ⫺1/兲其d ,
册
0
1 1 v⬁ 1 A A ⫹ q共X ⫹ X v兲 ˜t ⫽ ˜t l ⫹ 16 v F q 共X ⫺ X l兲 ⫺ q 2 log A ⫹ q共X l ⫹ X v兲 , v⬁ 1 3⬁ A⫽ 1⫺ q v F 32 2 F
冉
冊
where ˜tl is the time to reach Xl, which is the length of the developing region. Thus, by substituting Eq. (A9) into Eqs. (A6) and (A7), the velocity and concentration can be expressed in terms of the axial coordinate X in the developing region. The developed region solutions for the velocity and concentration along the centerline are expressed as follow from the far field solution of Eq. (6)
u m,out ⫺ V CO F ⫽ u m,0 ⫺ V CO ⬁
冉
3 ⬁ 1⫺ q 2 F 1⫺q
冊
1 32共X ⫹ X v兲 (A10)
Y F,m,out ⫽
F 2Sc ⫹ 1 1 ⬁ 64 X ⫹ X v, F
(A11)
where the subscript out indicates the solution for the far field region. Then, the virtual origins Xv, Xv,F and the developing region lengths Xl, Xl,F for velocity and concentration, respectively, can be determined from the following matching conditions [14]. u m,in ⫽ u m,out,
⭸u m,in ⭸u m,out ⫽ , ⭸X ⭸X
(A8)
at X ⫽ X l (A12)
for 0 ⱕ X ⬍ X l
for X l ⱕ X ⱕ X l,F
Y F,m,in ⫽ Y F,m,out,
(A9)
⭸Y F,m,in ⭸Y F,m,out ⫽ , ⭸X ⭸X
at X ⫽ X l,F
(13)
With Sc ⫽ 1.366 for propane, the developing region length and the virtual origins for velocity and concentration can be derived as X l ⫽ 0.05017 ⫺ 0.12422q X l, F ⫽ 0.11343 ⫹ 0.07610q
(A14)
X v ⫽ 0.09575 ⫹ 0.05235q X v, F ⫽ 0.12745 ⫺ 0.02123q
(A15)
References [1] S.H. Chung, B.J. Lee, Combust. Flame 86 (1991) 62–72. [2] B.J. Lee, S.H. Chung, Combust Flame 109 (1997) 163–182. [3] B.J. Lee, M.S. Cha, S.H. Chung, Combust Sci. Technol. 127 (1997) 55–70. [4] B.J. Lee, J.S. Kim, S.H. Chung, Proc. Combust. Inst. 25 (1994) 1175–1181. [5] T. Plessing, P. Terhoeven, N. Peters, M.S. Mansour, Combust. Flame 115 (1995) 335–353. [6] M.D. Smooke, A. Ern, M.A. Tanoff, B.A. Valdati, R.K. Mohammed, D.F. Marran, M.B. Long, Proc. Combust. Inst. 26 (1996) 2161–2170. [7] S.H. Won, S.H. Chung, M.S. Cha, B.J. Lee, Proc. Combust. Inst. 28 (2000) 2093–2099. [8] S.H. Won, J. Kim, M.K. Shin, S.H. Chung, O. Fujita,
462
[9] [10] [11] [12] [13]
[14] [15]
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462 T. Mori, J.H. Choi, K. Ito, Proc. Combust. Inst. 29 (2002) 37– 44. J. Kim, S.H. Won, M.K. Shin, S.H. Chung, Proc. Combust. Inst. 29 (2002) 1589 –1595. I.K. Puri, S.K. Aggarwal, S. Ratti, R. Azzoni, Combust. Flame 124 (2001) 311–325. X. Qin, I.K. Puri, S.K. Aggarwal, Proc. Combust. Inst. 29 (2002) 1565–1572. N Rajaratnam, Turbulent Jets, Elsevier Scientific Publishing, Amsterdam, 1976. A.C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species. 2nd ed, Gordon and Breach, Amsterdam, 1996. G.W. Rankin, K. Sridhar, M. Arulraja, K.R. Kumar, J. Fluid Mech. 133 (1983) 217–231. G.W. Rankin, K. Sridhar, J. Fluids Engineering/Trans. ASME 100 (1978) 55–59.
[16] D.S. Lee, K.D. Kihm, S.H. Chung, J. Fluids Engineering/Trans. ASME 119 (1997) 716 –718. [17] J. Lee, S.H. Chung, Combust. Flame 127 (2001) 2194 –2204. [18] Y.-C. Chen, R.W. Bilger, Combust. Flame 122 (2000) 377–399. [19] A. Koch, H. Voges, P. Andresen, H. Schluter, D. Wolff, W. Hentschel, W. Oppermann, E. Rothe, Appl. Phys. B 56 (1993) 177–184. [20] Y.S. Ko, S.H. Chung, G.S. Kim, S.W. Kim, Combust. Flame 123 (2000) 430 – 433. [21] J. Lee, S.H. Won, S.H. Jin, S.H. Chung, O. Fujita, K. Ito, Combust. Flame (2003) 411– 420. [22] S.G. Davis, C.K. Law, Combust. Sci. Tech. 140 (1998) 427– 449. [23] M.I. Hassan, K.T. Aung, O.C. Kwon, G.M. Faeth, J. Propulsion Power 14 (1998) 479 – 488.
Lifted flames in laminar jets of propane in coflow air J. Lee, S. H. Won, S. H. Jin, S. H. Chung* School of Mechanical and Aerospace Engineering Seoul National University Seoul 151-742, Korea Received 20 July 2002; received in revised form 20 May 2003; accepted 16 July 2003
Abstract Characteristics of lifted flames in laminar axisymmetric jets of propane with coflowing air have been investigated experimentally. Approximate solutions for velocity and concentration accounting virtual origins have been proposed for coflow jets to analyze the behavior of liftoff height. From the measurement of Rayleigh scattering to probe the concentration field of propane, the validity of the approximate solutions was substantiated. From the images of OH PLIF and CH chemiluminescence and the Rayleigh concentration measurement, it has been shown that the positions of maximum luminosity in direct photographs of lifted tribrachial flames can reasonably be located along the stoichiometric contour. The liftoff height in coflow jets was found to increase highly nonlinearly with jet velocity and was sensitive to coflow velocity. The blowout and reattachment velocities decreased linearly with the increase in coflow velocity. These behaviors of liftoff height and the conditions at reattachment and blowout can be successfully predicted from the approximate solutions. © 2003 The Combustion Institute. All rights reserved.
1. Introduction Lifted flames in laminar jets have been studied extensively to identify the flame stabilization mechanism [1– 4]. The base of a laminar lifted flame exhibits a tribrachial (or triple) structure, consisting of a lean and a rich premixed flame wings and a trailing diffusion flame, all extending from a single location. The stabilization mechanism of laminar lifted flames has been explained based on the balance of the propagation speed of tribrachial flame and local flow velocity. This balance mechanism leads to an excellent correlation of liftoff height with jet velocity and nozzle diameter in free jets, demonstrating highly nonlinear dependency [1,2]. Various effects, including fuel dilution and fuel premixing with air, have been investigated [3,4]. Recently, lifted flame characteristics in coflow jets have been investigated. There are several advantages in adopting a coflow jet over a free jet. More stable flames can be obtained experimentally and the treatment of boundary condition is easier in numeri* Corresponding author. E-mail address: [email protected] (S.H. Chung).
cal approaches. In coflow jets, the detailed tribrachial flame structure at the lifted flame base has been revealed [5,6] and the buoyancy induced lifted flame oscillation has been investigated [7–9]. In these studies, typical nozzle diameters used were O (1 cm). The methane lifted flames have also been studied numerically and experimentally [10,11]. The present study focused on laminar lifted flames of propane jets in coflow air when a sub-millimeter size nozzle is adopted. Therefore, the lifted flames were stabilized in the far field region of the coflow jets. The similarity solutions for velocity and concentration enabled the prediction of lifted flame behavior in free jets [1– 4]. However, such explicit forms of similarity solutions are not available for coflow jets. In this regard, although there are several advantages in adopting coflow jets, the prediction of liftoff height is rather limited. Motivated by this, the present study investigated the liftoff height behavior experimentally and attempted to predict the liftoff height in terms of jet and coflow velocities. Approximate solutions for coflow jets were derived accounting the density difference between jet and coflow. The derivation was based on the experimental observations
0010-2180/03/$ – see front matter © 2003 The Combustion Institute. All rights reserved. doi:10.1016/S0010-2180(03)00182-2
450
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
Nomenclature A Function defined in Eq. (A9) C Constant d Nozzle diameter DF Diffusivity of Fuel F Function defined in Eq. (7) HL Liftoff height I Fuel mass flow rate of jet Imix Rayleigh scattering intensity I0 Incident laser power J Axial momentum of jet n Number density of scattering species q Relative intensity of coflow (⫽ VCO/um,0) r Radial coordinate r0 Nozzle radius r1/2 Half radius R Nondimensional radius (⫽ r/r0) Re Reynolds number 0 SL,st Stoichiometric laminar burning velocity Stri Propagation speed of tribrachial flame Sc Schmidt number of fuel t Time ˜t Dimensionless Lagrangian time u Axial velocity u0 Mean jet velocity at nozzle U Nondimensional axial velocity (⫽ u/um,0) VCO Coflow air velocity x axial coordinate X Nondimensional axial distance (⫽ (x/d)/Re) XC3H8 Propane mole fraction Xl Developing region length Xv Virtual origin
that the relative velocity, which is the difference between jet velocity and coflow velocity, is similar in coflow turbulent jets [12]. The validity of the solutions was tested from the concentration measurements using the Rayleigh scattering technique. From these solutions, various behaviors of lifted flames in coflow jets can be successfully predicted. 2. Experiment The apparatus consisted of a coflow burner and flow controllers, a concentration measurement sys-
YF
Fuel mass fraction Similarity variable defined in Eq. (15) Kinetic viscosity Density Rayleigh cross-section Subscripts BO Blowout F Fuel in Developing region L Lifted LO Liftoff m Centerline maximum out Far field RA Reattachment st Stoichiometric tri Tribrachial 0 Nozzle exit ⬁ Ambient Superscript * Anchoring position
tem, and a visualization setup. The coflow burner had a central fuel nozzle with d ⫽ 0.254 mm i.d. and 10 cm length for the flow inside to be fully developed. Coflow air was supplied to a coaxial nozzle with 152 mm i.d. through glass beads and a ceramic honeycomb to obtain uniform flow. The tip of the fuel nozzle protruded 15 mm above the honeycomb. The fuel was C.P. grade (⬎99%) propane. Mass flow controllers (MKS) were used for flow rate control of fuel and air. A Nd:YAG laser (Continuum, PL8000) was used for Rayleigh scattering measurements to probe fuel concentration. The pulse duration of the laser was 10 ns with a maximum power of 450 mJ at 532 nm. A sheet beam with 50 mm width was illuminated by using a set of cylindrical lenses. The Rayleigh scattering signal was captured by an intensified chargecoupled device (ICCD) camera (Princeton Instrument, ICCD-MAX) through a laser line interference filter of 532 nm (5 nm FWHM). At a specified condition, 1000 images were averaged to suppress noises in probing propane concentration. To minimize scatterings from the material surface of experimental setup, captured images were compensated with the Rayleigh scattering image by supplying helium to the jet and coflow nozzles, since helium has the Rayleigh cross section of 0.0136 times that of air. The intensity of Rayleigh scattering signal of mix-
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
451
ture Imix, depends on the incident laser power I0, the number density of scattering species n, fuel mole fraction XC3H8, and the Rayleigh scattering crosssections of propane C3H8 and air air [13]: I mix ⫽ CI 0n 关X C3H8 C3H8 ⫹ 共1 ⫺ X C3H8兲 air兴
(1)
where C is a system dependent constant. Then, the mole fraction of fuel can be determined from X C3 H8 ⫽
冉
冊冉
C3H8 I mix ⫺1 / ⫺1 I air air
冊
(2)
A planar laser-induced fluorescence (PLIF) system, consisting of a Nd:YAG laser (Continuum, PL8000), a dye laser (Continuum, ND 6000), and the ICCD camera, visualized OH radicals. The Q1(6) transition of A2⌺⫹ ⫺ X2II (1, 0) band for OH radical was excited with 282.95 nm. Pulse energy was approximately 7 mJ/p, which prevented the OH signal from local saturation. The fluorescence signal was captured at right angle through UG-11 and WG-305 optical filters. The chemiluminescence of CH* was taken by the ICCD camera through a narrow bandpass filter of 430 nm (10 nm FWHM). The ICCD camera was also used for direct photography of flames.
3. Results and discussion 3.1. Liftoff height in coflow The variation in liftoff height HL with jet velocity u0 at various coflow air velocities VCO for d ⫽ 0.254 mm and the fuel mass fraction of YF,0 ⫽ 1.0 is shown in Fig. 1. At a specified coflow velocity, the flame lifts off from a nozzle attached flame at a certain liftoff velocity. Then, the liftoff height increases highly nonlinearly with jet velocity and finally blowout occurs. The liftoff height behaviors are quite similar for both the free (VCO ⫽ 0) and coflow (VCO ⫽ 0) jets, except that the liftoff height increases with the coflow velocity. For both the free and coflow jets, the lifted flame base has a tribrachial structure; a diffusion flame, a lean and a rich premixed flames, all extending from a single location. This structure implies that the base is located along the stoichiometric contour and has propagation characteristics. The liftoff height in free jets has been correlated with jet velocity and nozzle diameter [1,2], based on the balance mechanism between the propagation speed of tribrachial flame Stri and local axial velocity along the stoichiometric contour. It has been found that HL/d2 ⬃ u0(2Sc⫺1)/(Sc⫺1) for a specified initial fuel mass fraction, where Sc is the Schmidt number of fuel. The experimental data in free jets are fitted
Fig. 1. Liftoff height variation with jet velocity at various coflow velocities (lines indicate best fits of data and arrows indicate the sensitivity of liftoff height to jet and coflow air velocities).
with Sc ⫽ 1.366 for propane [2], as depicted in the solid line in Fig. 1. The liftoff height data in coflow jets are also fitted to the same form with Sc ⫽ 1.366. The results show that the jet velocity correlation can reasonably represent the liftoff height data for the coflow jets. The sensitivity of coflow velocity to liftoff height is also demonstrated in Fig. 1. For example, the liftoff height variation with the change in coflow velocity from VCO ⫽ 0 to 15.0 cm/s is 3.7 cm at u0 ⫽ 10 m/s. Note that the change of 15 cm/s in jet velocity u0 is minimal near u0 ⫽ 10 m/s, e.g., 0.3 cm/s. The coflow velocity also influences the liftoff and reattachment velocities appreciably, where the velocities are determined by increasing and decreasing jet velocity in the experiment. This point will be further elaborated later. The sensitivity of the coflow velocity to lifted flame behavior is investigated in the following. 3.2. Velocity and concentration fields To investigate the effect of coflow velocity on liftoff height, the information on velocity and concentration fields is needed. However, explicit forms of similarity solutions for coflow jets are not available, especially, accounting the density difference between jet and coflow. In this regard, approximate solutions will be derived based on the similarity solutions in free jets. The similarity solutions for the velocity and concentration in free jets have been successfully applied in deriving liftoff height correlations with jet veloc-
452
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
ity, nozzle diameter, and fuel dilution. This suggests that the velocity and concentration fields with different densities between jet and ambience can also be reasonably similar. In coflow jets, experimental observations in turbulent coflow jets showed that the relative velocity (u ⫺ VCO) is reasonably similar [12]. If the analogy can be applied to coflow laminar jets, the approximate solutions for velocity and concentration can be used in predicting the liftoff height behavior. The similarity solutions for the velocity and concentration in laminar cold free jets are as follows [1,3]: 3 J 1 8 x 共1 ⫹ 2/8兲 2 1 3 I YF ⫽ 8 x 共1 ⫹ 2/8兲 2Sc
and ambience, the axial momentum and fuel mass flow rate are represented by the density of fuel F. Then, the solutions for velocity and concentration in coflow jets are approximated as follows: 1 J 3 8 ⬁x ⬁ 共1 ⫹ 2/8兲 2 1 I 3 YF ⫽ 8 ⬁x ⬁ 共1 ⫹ 2/8兲 2Sc
u ⫺ V CO ⫽
where the subscript ⬁ indicates the ambient condition and the similarity variable , the axial momentum J and the fuel mass flow rate I are
u⫽
⫽
(3) J⫽
where u is the axial flow velocity, r, x are the radial and axial coordinates, respectively, J is the axial 2 momentum (um,0 d2/12), I is the fuel mass flow rate 2 (u0d /4), is the density, is the kinematic viscosity, is the similarity variable defined as ⫽ 冑1/32共um,0 d/兲 共r/x兲, and Sc is the Schmidt number of fuel defined as /DF, where DF is the diffusivity of fuel, and the subscripts m and 0 indicate the centerline maximum at a specified x and the jet nozzle exit, respectively. Based on the experimental observations [12], the relative velocity (u ⫺ VCO) is assumed similar, and the centerline relative velocity (um ⫺ VCO) is proportional to 1/x for the strong jet with (u0 ⫺ VCO) ⬎⬎ VCO. Considering the density difference between jet
u ⫺ V CO F ⫽ u m,0 ⫺ V CO ⬁
冉
3 ⬁ q 2 F 1⫺q
1⫺
冊
F 2Sc ⫹ 1 YF ⫽ ⬁ 64共X ⫹ X , F兲
I⫽
1⫹
F ⬁
冉
where q ⫽ VCO/um,0 is the relative intensity of coflow. The virtual origins for velocity and concentration have been derived assuming the potential core in which the radial diffusion dominates and the entrainment is negligible in case of parabolic velocity profile at the nozzle exit [14 –16]. Similar method has been applied to determine the virtual origins in coflow jets [Appendix, Eq. (A15)]. By using the values, the calculated dimensionless stoichiometric contour Rst and the dimensionless velocity along the stoichiometric contour Ust ⫽ ust /um,0
冕
冕
r0
冑
共u m ⫺ V CO兲 x r x
u共 Fu ⫺ ⬁V CO兲2 rdr
0
r0
F uY F,0 2 rdr ⫽
0
冕
r0
(5)
F u2 rdr
0
Since the similarity solutions become singular at the nozzle exit, the virtual origins are frequently introduced to improve the accuracy of the solutions. By introducing the Reynolds number based on um,0 as Re ⫽ um,0d/⬁ ⫽ 2u0d/⬁ for the Poiseuille flow at the nozzle exit, the dimensionless axial distance X ⫽ (x/d)/Re[14], the dimensionless radius R ⫽ r/r0, and the dimensionless relative velocity (u ⫺ VCO)/ (um,0 ⫺ VCO), the approximate solutions accounting the virtual origins X for velocity and X,F for concentration become
1 32共X ⫹ X 兲
再
(4)
1 F 1 R 3 ⬁ 1⫹ 1⫺ q ⬁ 2 F 32 X ⫹ X 1 2 2Sc 1 R 3 ⬁ 1⫺ q 2 F 32 X ⫹ X , F
再
冉 冊冉
冊冉
冊冎 2
2
(6)
冊冎
are plotted in Fig. 2 for propane fuel with Sc ⫽ 1.366. The axial velocity demonstrates qualitatively similar behavior for both the coflow and free jets; increases with X near the nozzle, having a maximum, and then decreases slowly. This non-monotonic behavior agrees qualitatively well with the previous numerical data [18]. However, The magnitude of axial velocity is sensitive to the coflow velocity. For example, ust is approximately 30% larger for q ⫽ 0.015 compared to that for q ⫽ 0. On the other hand, the stoichiometric contour Rst in the coflow jet is nearly unchanged from that of the free jet.
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
453
Fig. 2. Profiles of stoichiometric contour and axial velocities along stoichiometric contours.
3.3. Concentration measurement Experimental verification of the validity of the approximate velocity solution is rather difficult. One problem is due to particle seeding through very small nozzle with low flow rate of fuel and the other is to very low velocity of the coflow. Since the similarity of velocity field has been tested previously [12], we have indirectly test the approximate solutions by experimentally probing the propane concentration in coflow. The Rayleigh scattering technique has been adopted where the Rayleigh cross section for propane is 13.01 times that of air [19]. Figure 3 shows the Rayleigh signal in a cold jets (a) and with lifted flame (b), together with the direct photograph of the flame (c). The OH PLIF image and the Abel transformed image of CH chemiluminescence are superimposed on the Rayleigh image (b), which exhibits relatively large burnt gas region. From the Rayleigh scattering images, the mass fraction of propane is calculated by assuming the
binary mixture of propane and air. At specified axial distances X ⫽ 0.52 (x ⫽ 3.8 cm and 4.0 cm for u0 ⫽ 9.0 m/s and 9.5 m/s, respectively) and X ⫽ 0.67 (x ⫽ 4.9 cm and 5.2 cm for u0 ⫽ 9.0 m/s and 9.5 m/s, respectively), the radial profiles of propane concentrations are plotted in Fig. 4 for VCO ⫽ 4.0 cm/s. The mass fraction predicted from Eq. (6) is also represented. The experiment and prediction with Sc ⫽ 1.366 are in good agreement within the accuracy of about 10%. For comparison, the predicted profile with Sc ⫽ 1.0 at X ⫽ 0.67 is also plotted, demonstrating fast mass diffusion as compared to the case with Sc ⫽ 1.366. Note that the mass fractions at the stoichiometry, the lean and rich flammability limits are 0.06, 0.03, and 0.15 respectively. The propane mass fraction along the centerline YF,m is shown in Fig. 5 for u0 ⫽ 9.0 and 9.5 m/s, demonstrating satisfactory agreement with the prediction. Note that due to the noise from surface scattering near the nozzle region, the experimental data for X ⬍ 0.42 (x ⬇ 3.0 cm) were discarded.
454
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
Fig. 3. Images of (a) Rayleigh intensity for cold flow, (b) Rayleigh intensity, OH PLIF and CH* for lifted flame, and (c) direct photograph (u0 ⫽ 9.0 m/s, VCO ⫽ 4 cm/s).
Fig. 4. Radial profile of fuel mass fraction with dimensionless radius for VCO ⫽ 4.0 cm/s.
Fig. 5. Fuel mass fraction along the centerline with dimensionless axial distance.
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
Fig. 6. Radial concentration profiles demonstrating similarity in coflow jets with VCO ⫽ 4.0 cm/s.
The similarity of the concentration field is further tested by plotting the normalized propane concentration YF/YF,m with the normalized radius r/r1/2, where r1/2 is the half radius at YF ⫽ YF,m/2. As shown in Fig. 6 the concentration profiles are similar for the present coflow. The comparison of measured data with the prediction substantiates the validity of the approximate solutions in describing the flow characteristics of coflow jets. 3.4. Maximum luminosity and stoichiometric contour A tribrachial flame is composed of a rich and a lean premixed wings and a trailing diffusion flame. Due to the coexistence of these three different types of flames, a tribrachial point should be located along a stoichiometric contour. For the propagating tribrachial flames in methane free jets once ignited at a downstream location [20], it has been found that the tribrachial point travels along the stoichiometric contour, where the contour was calculated by assuming a cold jet. Since the lifted flame base propagated with relatively high speed, the gas expansion and subsequent buoyancy effects to upstream concentration field was expected to be not significant. However, for stationary lifted flames, the gas expansion and buoyancy effects could influence the concentration field since upstream flow field has sufficient time to adjust from the cold jet. Thus, it is needed to test the concentration field for stationary lifted flames. In addition, if the tribrachial point is located along the stoichiometric contour assuming a
455
cold jet, then the stoichiometric contour can be traced by measuring the loci of tribrachial points in jets. This could be a convenient experimental tool in estimating the stoichiometric contour, especially for unknown concentration fields. It has been shown previously in a tribrachial flame that OH LIF signal has maximum intensity along the diffusion flame and the chemiluminescences of OH* could represent the premixed flame [7]. Preliminary test reveals that the locations of the chemiluminescences of OH* and CH* signals are indistinguishable in representing the premixed flame wings in a lifted tribrachial flame. Thus, we have qualitatively represented the tribrachial flame based on OH LIF and CH*. Note that it is a somewhat difficult task to pinpoint the tribrachial point experimentally and even numerically. The superimposed image of the OH PLIF, CH*, and the Rayleigh intensity in Fig. 3b shows the branching of flames indicating the tribrachial flame structure for the stationary lifted flame. Here, the OH LIF indicates the trailing diffusion flame and CH* the premixed flame wings. Due to significant decrease in CH* intensity in lean premixed flames compared to rich premixed flames, the lean premixed flame wing is less obvious. As a consequence, the base of the tribrachial flame seems to be more slanted, as compared to the judgment based on the direct photograph. To further illustrate this behavior, the stoichiometric contours from the Rayleigh measurements in coflow jets and the corresponding jets with lifted flames are plotted in Fig. 7. From the average of 1000 images, the height-by-height measurements of stoichiometric radius are represented. The scattering of data can be attributed to the noise in the Rayleigh measurements, since the stoichiometric mole fraction of propane is very low, that is, 0.042. The standard deviations of Rayleigh signals from the respective best fit curves for u0 ⫽ 9.0 and 9.5 m/s are 0.089 and 0.095 mm, respectively, which are within the accuracy of measurement. Note that the rapid decrease in the Rayleigh intensity for the case with the lifted flame is due to the decrease in the Rayleigh cross-section by gas expansion in the preheat zone of the premixed flame wings of the lifted tribrachial flame. The predicted contours are represented by solid lines. The results demonstrate that the concentration field upstream region of the lifted flame is nearly identical with that of the cold flow, demonstrating that the effects of gas expansion and buoyancy by the lifted flame are not significant. The point of maximum luminosity after the Abel transformation from the direct photograph is marked as a closed circle. Note that this point is located reasonably along the stoichiometric contour, deter-
456
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
Fig. 7. Stoichiometric contour from Rayleigh measurements and maximum luminosity from direct photography for VCO ⫽ 4 cm/s; (a) u0 ⫽ 9.0 m/s and (b) 9.5 m/s.
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
457
mined assuming the cold jet. Thus, the result suggests that the stoichiometric contour can be traced from the locus of maximum luminosities in lifted flames. The predicted result from Eq. (6) has satisfactory agreement with the experiment. The average deviation in the radial direction between the experiment and prediction was about ⌬r0 ⫽ 0.127 mm, which is within the accuracy of measurement. These results substantiate that the previous studies based on the cold jet theory [1– 4] could lead to successful correlations for the behavior of lifted flames in laminar free jets. 3.5. Prediction of liftoff height in coflow Having confirmed the validity of the approximate solutions from the Rayleigh measurement, the liftoff heights in coflow jets are analyzed. A tribrachial point is premixed in nature, having the propagation characteristics. Thus, at the flame anchoring position, the local axial velocity along a stoichiometric contour should balance with the propagation speed of tribrachial flame Stri for stationary lifted flames. If the propagation speed of tribrachial flame is available, the experimental liftoff height can be predicted by using the balance mechanism between the propagation speed of tribrachial flame and local axial velocity. Recently, the propagation speed of tribrachial flame of propane has been determined in terms of fuel mass fraction gradient under microgravity 0 condition as Stri/SL,st ⫽ 0.00344[dYF/dR|st ⫹ 0 ⫺1 0.00237] ⫹ 1.562 [21], where SL,st is the stoichiometric laminar burning velocity having chosen to be 0.40 m/s [22,23]. By using this, the liftoff height can be calculated from Eq. (6) based on the balance between the local axial velocity along the stoichiometric contour and Stri accounting the radial concentration gradient. Figure 8 exhibits the liftoff height variation with jet velocity for VCO ⫽ 0 and 15 cm/s, with the prediction represented in lines. The results demonstrate satisfactory agreement. Note that the closed and open symbols for the experimental data indicate the experiments conducted by increasing and decreasing jet velocity, respectively, to identify liftoff and reattachment conditions between nozzle attached and lifted flames. This difference will be elaborated later. The prediction substantiates that the approximate solutions can be applied in analyzing various behaviors of lifted flames in coflow jets. The relation among liftoff height, jet velocity, and coflow velocity can be derived from Eq. (6). The dimensionless anchoring position XL* can be derived in terms of the dimensionless velocity at the position (uL* ⫺ VCO)/(um,0 ⫺ VCO) as follows:
Fig. 8. Comparison of liftoff height with jet velocity between experiment and prediction (closed symbols are for experiment conducted with increasing jet velocity and open symbols with decreasing jet velocity).
X L* 兵共u L* ⫺ V CO兲 F 共X L* 兲其 Sc/(Sc⫺1)
冉
⫽ u m,0 ⫺
3 F V 2 ⬁ CO
冊
where F共X L* 兲 ⫽ ⫻
再冉
⬁ 32共X L* ⫹ X 兲 F X L*共Sc⫺1兲/Sc
Sc/(Sc⫺1)
(7)
冋 冉 1⫹
冊 冎册
X L* ⫹ X , F X L* ⫹ X
F 2Sc ⫹ 1 1 1 * ⬁ 64 X L ⫹ X , F Y F, st
冊
1/ 2Sc
2
2
⫺1
Here, the superscript* indicates the anchoring position, thus HL ⫽ xL* and uL* ⫽ Stri. For the strong jet with um,0 ⱖ VCO, the above relation results in HL v⬁ 0 d 2 S L, st
再 冉 冊
⫽ ⬀
再
F共X L* 兲
冎
S tri ⫺ V CO 0 S L, st
Sc/(Sc⫺1)
冎
u m, 0 ⫺ 共3/ 2兲 共 F/ ⬁兲 V CO 0 S L, st
u m, 0 0 S L, st
Sc/(Sc⫺1)
冉 冊 u m, 0 0 S L, st
共2Sc⫺1兲/共Sc⫺1兲
(8)
The experimental data are represented in terms of LHS and RHS of Eq. (8) in Fig. 9. The result demonstrates excellent linear correlation with the correlation coefficient of R ⫽ 0.979. This substantiates the validity of the approximate solutions and the functional dependence of jet velocity and coflow velocity on liftoff height.
458
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
Fig. 9. Correlation of liftoff height with jet velocity and coflow velocity with the units in [m, s].
The liftoff height is influenced by the jet velocity (2Sc⫺1)/(Sc⫺1) in terms of um,0 , which confirms the validity of the jet velocity dependence, as was demonstrated in Fig. 1. The dependency of coflow velocity is in two ways. One is from (Stri ⫺ VCO)Sc/(1⫺Sc) and the other from F(XL*), which exhibits the dependence of coflow velocity through the virtual origins. The effect of the virtual origins in F(XL*) is not significant when HL ⬎⬎ d. Thus, the dominant influence of coflow velocity on liftoff height is through (Stri ⫺ VCO)Sc/(1⫺Sc). This point will be further illustrated in the following. The anchoring position of a stationary tribrachial flame is located in the far field from the nozzle with the typical minimum height of 1.5 cm, which is at least 60 diameters away from the nozzle. Thus, regardless of the adoption of virtual origins, the overall characteristics of the axial velocity along the stoichiometric contour will be at least qualitatively similar in the far field region. Consequently, it is expected that the functional dependence of coflow velocity on liftoff heights is not influenced much by the adoption of the virtual origins. In this regard, it is assumed that X ⫽ X,F ⫽ 0, and the effects of jet velocity and coflow velocity on liftoff height are analyzed. Note that F(XL*) ⫽ const for this case. Then, the relation of liftoff height becomes HL 共2Sc⫺1兲/共Sc⫺1兲 共S ⫺ V CO兲 Sc/(Sc⫺1) ⫽ const ⫻ u m, 0 d 2 tri (9) The experimental liftoff data in Fig. 1 are correlated by using Eq. (9) including the effect of coflow velocity and the results are shown in Fig. 10. It
Fig. 10. Correlation of liftoff height with jet velocity and coflow velocity without considering virtual origins with the units in [m, s].
demonstrates satisfactory linear correlation with R ⫽ 0.982. Since the virtual origins are not accounted, the correlation does not pass through the origin. Note that the liftoff height HL is influenced by coflow velocity through the factor of (Stri ⫺ VCO)Sc/(1⫺Sc) and jet velocity with the factor of u(2Sc⫺1)/(Sc⫺1) . Since 0.7 m,0 ⱕ Stri ⱕ 0.85 m/s [21], 0 ⱕ VCO ⱕ 15 cm/s, and 7 ⬍ u0 ⬍ 13 m/s, (Stri ⫺ VCO) can be varied up to 20% and the effect is amplified by the exponent Sc/(Sc ⫺ 1) ⫽ 3.7322. This explains why the liftoff height is so sensitive to the coflow velocity, as was demonstrated in Fig. 1. 3.6. Reattachment and blowout Figure 8 showed the typical characteristics of lifted flame with the variation of jet velocity. For example, as u0 increases for VCO ⫽ 15 cm/s, a nozzle attached flame has a liftoff (LO) at uLO ⫽ 9.7 m/s and the liftoff height increases with u0 and finally blowout (BO) occurs at uBO ⫽ 11.0 m/s. As u0 decreases from a lifted flame, the lifted flame has a reattachment (RA) to the nozzle at uRA ⫽ 7.4 m/s. Therefore, there exists a hysterisis region of 7.4 ⬍ u0 ⬍ 9.7 m/s. Note that the hysterisis region is appreciably extended for the case with the coflow compared to the free jet (VCO ⫽ 0). Although the conditions of liftoff cannot be predicted from the present study due to complex nature of flow field and heat transfer near the nozzle region for attached flames, the reattachment and blowout can be predicted from the cold jet solutions since the liftoff height is far away from the nozzle at those moments. Therefore, the influence of
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
coflow velocity on reattachment and blowout are analyzed in the following. 3.6.1. Reattachment conditions Jet velocity and flame position at reattachment can be calculated from the balance of propagation speed and axial velocity. The axial velocity along the stoichiometric contour ust has a local maximum, as was shown in Fig. 2. In such a case, the reattachment condition can be identified [17], since the range of
S tri, RA ⫺ V CO F ⫽ 2u RA ⫺ V CO ⬁
⬇ const ⫻
冉
冉
3 ⬁ q 2 F 1⫺q
1⫺
3 ⬁ q 2 F 1⫺q
1⫺
冊
冊
冋 冉
459
increasing ust with x is unstable such that the balance between the propagation speed of a tribrachial flame and the local flow velocity cannot be maintained for u0 smaller than the reattachment velocity uRA. Rigorous explicit form is difficult to derive, however, since the variation of XRA is within 15% for the coflow velocity of 0 ⱕ VCO ⱕ 15 cm/s, XRA is assumed constant for simplicity. In such a case, the correlation between xRA, uRA and VCO can be derived as follows:
冊 再冉
X RA ⫹ X , F 1⫹ X RA ⫹ X
1 32共X RA ⫹ X 兲
F 2Sc ⫹ 1 1 1 ⬁ 64 X RA ⫹ X Y F,st
冊
1/ 2Sc
⫺1
冎册
2
(10)
Then, the functional relations for uRA and xRA ⫽ HL,RA with VCO becomes u RA ⫽ C 1 ⫺ C 2V CO,
C 1, C 2; constants
H L,RA ⫽ C 3 ⫺ C 4V CO,
(11)
C 3, C 4; constants
(12)
Here, the dependence of VCO on HL,RA is from the definition of XRA through the Reynolds number Re. 3.6.2. Blowout conditions It has been shown previously [1,3] that the condition of Rst ⫽ f(X;u0, VCO) ⫽ 0 can represent the blowout for propane having Sc ⬎ 1. From Eq. (6), the stoichiometric contour becomes R st ⫽
冋再 ⫻
F 2Sc ⫹ 1 1 ⬁ 64共X ⫹ X ,F兲 Y F,st 32共X ⫹ X ,F兲 F 3⬁ 1⫺ q ⬁ 2 F
再 冉
冊冎
冎
1/ 2Sc
⫺1
册
1/ 2
(13)
1/ 2
Then, the liftoff height at blowout XBO and the blowout velocity uBO, using the condition of Rst ⫽ 0, becomes
F 2Sc ⫹ 1 1 X BO ⫽ X , F ⫹ ⬁ 64 Y F, st S tri, BO ⫺ V CO F ⫽ 2u BO ⫺ V CO ⬁
冉
3 ⬁ q 2 F 1⫺q
1⫺
(15)
冊
1 1 32 X BO ⫹ X (16)
These lead to the following correlations for uBO and xBO ⫽ HL,BO with VCO for q ⬍⬍ 1.
Fig. 11. Liftoff height at reattachment, blowout, and liftoff conditions with coflow velocity (symbols: experiments, lines: best linear fits).
u BO ⫽ C 5 ⫺ C 6V CO, H L,BO ⫽ C 7 ⫺ C 8V CO,
C 5, C 6; constants C 7, C 8; constants
(17) (18)
3.6.3. Comparison with experiments It has been derived that the liftoff height and jet velocity at reattachment and blowout decrease linearly with coflow velocity. To confirm the correlations, the experimental data at reattachment and blowout are plotted in Figs. 11 and 12 for the liftoff height and jet velocity, respectively. The results
460
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
counting the effects of density difference between fuel and ambient air and the virtual origins. The validity of the solutions has been confirmed from the fuel concentration measurement using the Rayleigh scattering technique. By adopting OH PLIF, CH chemiluminescence, and direct photography, the positions of maximum luminosity from direct photography could represent the stoichiometric loci in axisymmetric jets. The liftoff height in coflow jets increases with u(2Sc-1)/(Sc-1) and the sensitivity of coflow velocity on 0 liftoff height has been successfully predicted through the effect of (Stri ⫺ VCO)Sc/(Sc-1). The influence of coflow velocity on the conditions of reattachment and blowout has been predicted, resulting in the linear decrease in liftoff height and jet velocity with coflow velocity and the experiments confirm the behavior.
Fig. 12. Jet velocity at reattachment, blowout, and liftoff conditions with coflow velocity (symbols: experiments, lines: best linear fits).
clearly demonstrate the linear dependencies of the liftoff height and jet velocities at reattachment and blowout with coflow velocity. As mentioned previously in Fig. 2, the local axial velocity along a stoichiometric contour increases with coflow velocity. Because the stoichiometric contour Rst, thereby the propagation speed of tribrachial flame, is insensitive to coflow, the increase in the local axial velocity with coflow velocity leads to the decrease in u0 with VCO at blowout and reattachment. The conditions at liftoff are also plotted in Figs. 11 and 12. Note that the jet velocity and liftoff height at the liftoff condition also decrease linearly with coflow velocity, except the case of the free jet (VCO ⫽ 0). The experimental data are significantly lower than the linearly extrapolated values for VCO 3 0. These behaviors cannot be clearly explained at present, however, it may be attributed to the near nozzle flow characteristics between free and coflow jets, for example, the recirculation zone near the nozzle tip can be significantly influenced by the existence of coflow.
Acknowledgments This work was supported by the Combustion Engineering Research Center. SHW and SHJ were supported by the BK-21 Program for Mechanical Engineering, Seoul National University.
Appendix Virtual origin for coflow jets By adopting the similar approach in deriving the virtual origins in free jets [14 –16], it is assumed that the entrainment can be negligibly small in the developing region near a nozzle such that the radial diffusion dominates over the axial convection and the Lagrangian description along the centerline could describe the axial convection. Then, the momentum and species equations and boundary and initial conditions in the near field are as follows: ⭸u v F ⭸ ⫽ ⭸t r ⭸r
冉 冊 冉 冊 再 冉 冊冎 r
⭸u ⭸r
⭸Y F v F 1 ⭸ ⫽ ⭸t Sc r ⭸r
r
⭸Y F ⭸r
t ⫽ 0; u ⫽ um,0 1 ⫺ 4. Concluding remarks Characteristics of lifted flames in axisymmetric laminar coflow jets of propane have been investigated experimentally. To analyze the behavior of lifted flames, the approximate solutions for velocity and concentration in coflow have been derived ac-
for 0 ⱕ r ⱕ r0 r ⫽ 0; r 3 ⬁;
(A1)
r r0
(A2)
2
, YF ⫽ YF,0 ⫽ 1
⭸Y F ⭸u ⫽ 0, ⫽0 ⭸r ⭸r u 3 V CO, Y F 3 0
(A3)
The formal solutions of these transient diffusion equations are
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462
冕
u ⫺ V CO 1 2˜ 关2t˜e ⫺R t ⫽ u m,0 ⫺ V CO 1 ⫺ q
˜
Y F, m,in ⫽ 1 ⫺ e ⫺Sct
1
共1 ⫺ 兲 2
0
2˜ ⫻ e ⫺ tI 0共2 Rt˜ 兲d ⫺ q兴
冕
˜
Y F ⫽ 2Sct˜e ⫺R Sct 2
1
(A4)
˜
e ⫺ SctI 0共2 RSct˜ 兲d 2
461
(A5)
(A7)
where the subscript in indicates the solution in the near field developing region. Here, the velocity and concentration are expressed in terms of the Lagrangian time. By using the Lagrangian description of fluid particle along the centerline, the relation between the axial distance x and the time is
0
where ˜t is the dimensionless Lagrangian time scale, defined as ˜t ⫽ r02/(4vFt) and q ⫽ VCO /um,0. Then, the velocity and concentration along the centerline (r ⫽ 0) can be derived by substituting r ⫽ 0 into Eqs. (A4) and (A5) and integrating u m,in ⫺ V CO 1 1 ˜ ⫽1⫺ 共1 ⫺ e ⫺t兲 u m,0 ⫺ V CO 1 ⫺ q ˜t X⬅
(A6)
x x v⬁ 1 ⫽ ⫽ 共u m,0d/v ⬁兲d Re d v F 16
冋
冕
dx ⫽ u m共 x兲 dt
where um(x) is the centerline velocity [16]. By substituting Eqs. (A6) and (6) into Eq. (A8) in the velocity developing region and in the velocity developed region, and integrating, the following relations between the axial coordinate X and the Lagrangian time ˜t can be obtained
1/t˜
兵 1 ⫺ 共1 ⫺ e ⫺1/兲其d ,
册
0
1 1 v⬁ 1 A A ⫹ q共X ⫹ X v兲 ˜t ⫽ ˜t l ⫹ 16 v F q 共X ⫺ X l兲 ⫺ q 2 log A ⫹ q共X l ⫹ X v兲 , v⬁ 1 3⬁ A⫽ 1⫺ q v F 32 2 F
冉
冊
where ˜tl is the time to reach Xl, which is the length of the developing region. Thus, by substituting Eq. (A9) into Eqs. (A6) and (A7), the velocity and concentration can be expressed in terms of the axial coordinate X in the developing region. The developed region solutions for the velocity and concentration along the centerline are expressed as follow from the far field solution of Eq. (6)
u m,out ⫺ V CO F ⫽ u m,0 ⫺ V CO ⬁
冉
3 ⬁ 1⫺ q 2 F 1⫺q
冊
1 32共X ⫹ X v兲 (A10)
Y F,m,out ⫽
F 2Sc ⫹ 1 1 ⬁ 64 X ⫹ X v, F
(A11)
where the subscript out indicates the solution for the far field region. Then, the virtual origins Xv, Xv,F and the developing region lengths Xl, Xl,F for velocity and concentration, respectively, can be determined from the following matching conditions [14]. u m,in ⫽ u m,out,
⭸u m,in ⭸u m,out ⫽ , ⭸X ⭸X
(A8)
at X ⫽ X l (A12)
for 0 ⱕ X ⬍ X l
for X l ⱕ X ⱕ X l,F
Y F,m,in ⫽ Y F,m,out,
(A9)
⭸Y F,m,in ⭸Y F,m,out ⫽ , ⭸X ⭸X
at X ⫽ X l,F
(13)
With Sc ⫽ 1.366 for propane, the developing region length and the virtual origins for velocity and concentration can be derived as X l ⫽ 0.05017 ⫺ 0.12422q X l, F ⫽ 0.11343 ⫹ 0.07610q
(A14)
X v ⫽ 0.09575 ⫹ 0.05235q X v, F ⫽ 0.12745 ⫺ 0.02123q
(A15)
References [1] S.H. Chung, B.J. Lee, Combust. Flame 86 (1991) 62–72. [2] B.J. Lee, S.H. Chung, Combust Flame 109 (1997) 163–182. [3] B.J. Lee, M.S. Cha, S.H. Chung, Combust Sci. Technol. 127 (1997) 55–70. [4] B.J. Lee, J.S. Kim, S.H. Chung, Proc. Combust. Inst. 25 (1994) 1175–1181. [5] T. Plessing, P. Terhoeven, N. Peters, M.S. Mansour, Combust. Flame 115 (1995) 335–353. [6] M.D. Smooke, A. Ern, M.A. Tanoff, B.A. Valdati, R.K. Mohammed, D.F. Marran, M.B. Long, Proc. Combust. Inst. 26 (1996) 2161–2170. [7] S.H. Won, S.H. Chung, M.S. Cha, B.J. Lee, Proc. Combust. Inst. 28 (2000) 2093–2099. [8] S.H. Won, J. Kim, M.K. Shin, S.H. Chung, O. Fujita,
462
[9] [10] [11] [12] [13]
[14] [15]
J. Lee et al. / Combustion and Flame 135 (2003) 449 – 462 T. Mori, J.H. Choi, K. Ito, Proc. Combust. Inst. 29 (2002) 37– 44. J. Kim, S.H. Won, M.K. Shin, S.H. Chung, Proc. Combust. Inst. 29 (2002) 1589 –1595. I.K. Puri, S.K. Aggarwal, S. Ratti, R. Azzoni, Combust. Flame 124 (2001) 311–325. X. Qin, I.K. Puri, S.K. Aggarwal, Proc. Combust. Inst. 29 (2002) 1565–1572. N Rajaratnam, Turbulent Jets, Elsevier Scientific Publishing, Amsterdam, 1976. A.C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species. 2nd ed, Gordon and Breach, Amsterdam, 1996. G.W. Rankin, K. Sridhar, M. Arulraja, K.R. Kumar, J. Fluid Mech. 133 (1983) 217–231. G.W. Rankin, K. Sridhar, J. Fluids Engineering/Trans. ASME 100 (1978) 55–59.
[16] D.S. Lee, K.D. Kihm, S.H. Chung, J. Fluids Engineering/Trans. ASME 119 (1997) 716 –718. [17] J. Lee, S.H. Chung, Combust. Flame 127 (2001) 2194 –2204. [18] Y.-C. Chen, R.W. Bilger, Combust. Flame 122 (2000) 377–399. [19] A. Koch, H. Voges, P. Andresen, H. Schluter, D. Wolff, W. Hentschel, W. Oppermann, E. Rothe, Appl. Phys. B 56 (1993) 177–184. [20] Y.S. Ko, S.H. Chung, G.S. Kim, S.W. Kim, Combust. Flame 123 (2000) 430 – 433. [21] J. Lee, S.H. Won, S.H. Jin, S.H. Chung, O. Fujita, K. Ito, Combust. Flame (2003) 411– 420. [22] S.G. Davis, C.K. Law, Combust. Sci. Tech. 140 (1998) 427– 449. [23] M.I. Hassan, K.T. Aung, O.C. Kwon, G.M. Faeth, J. Propulsion Power 14 (1998) 479 – 488.