JOURNAL OF PROPULSION AND POWER
Improved Semiempirical Correlation to Predict Lean Blowout Limits for Gas Turbine Combustors Fa Xie,∗ Yong Huang,† Bin Hu,‡ and Fang Wang§ Beihang University, 100191 Beijing, People’s Republic of China DOI: 10.2514/1.B34296 Lean blowout limits play a critical role in the operational envelope of aircraft. Semiempirical correlations, a convenient and fast methodology to estimate the lean blowout limits for aircraft engine combustors, are extensively employed in the preliminary combustion design stage. Among the correlations, Lefebvre’s model is widely used. However, it is argued that the influences of the variations of combustor’s configurations upstream of dilution holes on lean blowout cannot be embodied in this model. Based on Lefebvre’s correlation, a new physical model is established and a flame volume concept is proposed according to the experimental observations. Then, an improved correlation (i.e., flame volume lean blowout model) is derived to consider the effects of the variations of dome geometry and primary zone configurations. The flame volume lean blowout model is verified by many fuel-lean visual experiments. In the experiments, three kinds of swirl-stabilized assemblies and two different primary hole arrangements have been employed. It is concluded that the flame volume lean blowout model shows better agreement with the corresponding experimental values of different designs than the Lefebvre model. The prediction uncertainties of the two models are about 15 and 45% in the present combustion chamber configurations, respectively.
Nomenclature A ar B d da dh dr Darvt Ddavt D0 f fc fPZ K _a m _ a;c m Nph ph ps
= constant determined by geometry and mixing characteristics of combustor = axial radial = width of passage of swirlers, m = distance from throat of venturi to exit plane of venturi, m = dual axial = dilution hole = dual radial = diameter of venturi’s throat in axial-radial swirl-stabilized assembly, m = diameter of venturi’s throat in dual-axial swirl-stabilized assembly, m = mean drop size relative to JP4 = fraction of airflow = fraction of combustion air = fraction of combustor primary zone air = universal constant determined by experiments for all combustors = inlet air mass flow rate, kg=s = air mass flow rate involved in combustion, kg=s = number of primary hole = primary hole = primary swirler
P3 qlbo qlbo;c ref S ss T3 Vc Vf
= = = = = = = = = =
T eff
= = = = =
inlet pressure, kPa overall lean blowout fuel/air ratio lean blowout fuel/air ratio of the combustion zone reference flow area, m2 secondary swirler inlet temperature, K combustor volume upstream dilution holes, m3 flame volume, m3 fraction of combustor dome airflow involved in combustion nondimensional flame volume temperature rise flare angle effective evaporation constant relative to JP4 lean blowout value of equivalence ratio
I. Introduction
I
N AEROENGINE applications, the lean blowout (LBO) limit plays a critical role in the operational envelope of the engine [1]. To improve engine thermodynamic performance and engine thrustto-weight ratio, many future aircraft turbine engines are expected to operate with high turbine inlet temperatures. The attainment of these increased turbine inlet temperatures requires combustors with higher temperature rise (T) than the typical engines of current technology [2]. A higher temperature rise implies a smaller fraction of dilution air. In other words, a consequence of higher temperature rise is that a larger fraction of the combustor airflow is delivered into the primary reaction zone. However, the increased airflow entering the primary zone will cause the LBO limit to be deteriorated at low power condition. On the other hand, from the viewpoint of environmental protection, aircraft and stationary gas turbines require lower and lower emissions to meet more stringent emission standards, especially for NOx emissions [3–5]. These requirements demand the combustors to operate at a rather low fuel/air ratio (FAR), which is very close to the LBO limits of combustors. Hence, the issue of how to predict LBO limits accurately in the combustion design process is of vital importance. Semiempirical correlations, a convenient and fast LBO limit prediction method, are extensively employed by designers to predict LBO limits of engine combustors in the preliminary combustion design stage. Until the early 1960s, these semiempirical correlations mainly focused on bluff body configurations, such as the perfect
Received 31 March 2011; revision received 22 June 2011; accepted for publication 29 June 2011. Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code and $10.00 in correspondence with the CCC. ∗ Ph.D. Candidate, National Key Laboratory of Science and Technology on Aero-Engines, School of Jet Propulsion, Department of Thermal Engineering;
[email protected]. † Professor, National Key Laboratory of Science and Technology on AeroEngines, School of Jet Propulsion, Department of Thermal Engineering;
[email protected]. ‡ Ph.D. Candidate, National Key Laboratory of Science and Technology on Aero-Engines, School of Jet Propulsion, Department of Thermal Engineering;
[email protected]. § Associate Professor, National Key Laboratory of Science and Technology on Aero-Engines, School of Jet Propulsion, Department of Thermal Engineering;
[email protected]. 197
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stirred-reactor (PSR) model [6] and characteristic-time (CT) model [7]. However, they could not be used to estimate the LBO limits of swirl-stabilized combustors. Later, the PSR model and the CT model were improved by Ballal and Lefebvre [8,9] and Plee and Mellor [10], respectively, so that they could be used for swirl-stabilized combustors for LBO prediction. Among the two improved LBO models, the former model (i.e., the Lefebvre model) was employed rather extensively, and it had been verified by eight engine combustors before the 1980s. By verification, Lefebvre claimed that his model was universal because the value of (Afpz ) remained nearly constant for all the different combustors [11]. If 0.22 was used for (Afpz ) in his equation, one would determine a LBO limit within the uncertainty of approximately 30% [11]. However, it is argued that the effects of the variations of the combustor configurations upstream of the dilution holes on the LBO cannot be embodied in this model if the value of (Afpz ) remains constant. Later, some improved models, based on Lefebvre’s correlation, were proposed, such as a LBO hybrid model proposed by Rizk and Mongia [12–14], which was a combination of Lefebvre’s model and a three-dimensional code, an Ateshkadi model [1,15], and so on. In the study of Ateshkadi, a statistical analysis to the experimental data was employed to develop a new predictive model for LBO limits. This model explicitly related the mixer components (primary swirl vane, secondary swirl vane, Venturi, and co- and counterswirl) to the LBO limit. However, the two improved models did not take into account the actual physical process of fuel-lean combustion, so it is difficult for them to be applied extensively in the combustion design process. In addition, Mongia et al. [16] revealed that none of the existing LBO correlations could be used for predicting the LBO limits of modern turbopropulsion engine combustors, at least not to the degree of accuracy comparable with the experimental database. In a recent lecture [17], Mongia suggested that one should focus on the combustion volume [i.e., flame volume (FV)] rather than the combustor volume for improving Lefebvre’s model, but no specific work had been done from this viewpoint. So, the present study plans to develop a new LBO model for a swirl-stabilized combustor based on the FV concept.
II. General Idea To improve Lefebvre’s LBO correlation, a detailed analysis to the derivation of this model will first be conducted, and then comparisons will be made with the experimental observations of the LBO process. Fuel Turbulent flame zone
Diffuser
Liner
Casing
Air
A.
Physical model of Lefebvre’s LBO expression.
a) q = 0.00533 Fig. 2
Lefebvre Lean Blowout Model
The physical model of Lefebvre’s LBO expression is shown as Fig. 1 (the original figure can be found in [18]). It implied the following: 1) All inlet airflow was involved in fuel mixing and combustion at LBO. 2) The turbulent flame filled the whole combustor at LBO. According to the above physical model, first, a LBO correlation for predicting homogeneous mixtures is derived as follows: x _a m (1) qlbo / Vc Pn3 expT3 =b Based on Eq. (1), modifications are then made to account for the effects of atomization, vaporization, and the heating value of the fuel. Finally, according to the experimental verification, the order of Vc , _ a , and P3 are taken to be the values of 1, 1, and 1.3, respectively, and m b is taken to be the value of 300. Thus, the simplest form of the Lefebvre LBO model becomes [19] _a AfPZ m D20 (2) qlbo Vc P1:3 eff LHV 3 expT3 =300 where PZ denotes the primary zone, and LHV denotes the value of the lower calorific relative to JP4. The first term on the right-hand side of Eq. (2) is a function of combustor design. The second term represents the combustor operating condition, and the third term embodies the relevant fueldependent properties. However, it is clear that the effects of the variations of the combustor configurations upstream dilution holes on LBO cannot be embodied in this model if a constant is used for (Afpz ). B.
Flame Observations
To observe the size of the flame in the combustion process, visual experiments were then conducted, the introduction of which can be found in the literature [20]. Figures 2a–2d show the variations of the sizes of the flames with the decrease of the FAR in the combustion process. It can be seen from Fig. 2a that, when combustion FAR is large enough, the flame is long and fills the entire combustor. With the decrease of the FAR, the flame will become shorter and shorter and the size of the flame will become smaller and smaller, as shown in Figs. 2b and 2c. Near LBO, the size of the flame will become very small, as shown in Fig. 2d, but the width of the flame will remain almost unchanged in the whole combustion process. According to the experimental observation of the fuel-lean combustion process, it is concluded that the LBO limit (i.e., LBO FAR) may relate to the size of the flame (i.e., FV) for different combustors. C.
Dome
Fig. 1
Therefore, in the next section, Lefebvre’s LBO model will be briefly introduced.
Flame Volume Lean Blowout Model
According to the flame observation of the fuel-lean combustion process, new physical hypotheses are made as follows: 1) The fuel and air were well stirred in the combustion zone (turbulent flame zone) due to strong swirl.
b) q = 0.00516 c) q = 0.00495 d) q = 0.00475 Variations of the size of the flame with the decrease of FAR in the combustion process [20].
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The nondimensional FV is defined as follows:
2) The inlet airflow was divided into two parts: one part (i.e., the fraction of dome airflow and part of the liner airflow) was involved in combustion, and the other was involved in dilution downstream. 3) Except for the dome airflow, the remaining airflow entered the liner uniformly along the circumferential and axial directions, and the fraction of liner airflow involved in combustion was proportional to the size of the turbulent flame zone. The new physical model, based on the FV concept, is depicted in Fig. 3. According to hypotheses 1 and 2, combined with the above physical model, it is clear that the air involved in combustion is part of _ a and the size _ a;c instead of the whole inlet airflow m the inlet airflow m of combustion zone is the turbulent FV Vf instead of the whole combustor volume Vc . Thus, the combustion zone LBO FAR can be expressed as follows:
x _ a;c m Vf Pn3 expT3 =b
(3)
In the improved correlation, two key parameters, and , are included; they could embody the effects of the variations of dome components and primary zone configurations on LBO. To verify the validity of the proposed model, many LBO visual experiments were conducted, as will be introduced in the next section.
III. Model Verification All the verification experiments for the improved model were conducted at the fundamental combustion laboratory of Beihang University on a single-dome rectangular visualization model combustor with a dual swirl-stabilized assembly. In the experiments, three kinds of swirl-stabilized assemblies and two different primary hole arrangements were selected. The introduction of the whole experimental system can be seen in the literature [21,22]. The schematic of the single-dome rectangular model combustor, the different dual swirl-stabilized assemblies, and the primary hole arrangements are described, respectively, as follows. A.
Since fc denotes the faction of combustion air, the combustion air _ a;f can be expressed as follows: m _ a;c fc m _a m
(4)
Similarly, the relations between the overall LBO FAR qlbo and the combustion zone LBO FAR qlbo;c can be expressed as follows: qlbo fc qlbo;c
(5)
In addition, according to hypothesis 2, the fraction of combustion air fc comprises the fraction of dome airflow (i.e., ) and the fraction of liner airflow involved in combustion. According to hypothesis 3, the fraction of liner airflow involved in combustion is proportional to the size of turbulent flame zone; hence, the fraction of the liner airflow involved in combustion is 1 Vf =Vc . Finally, an equation for the fraction of combustion airfc is derived as follows: fc 1
Vf Vc
(9)
Substituting fc and from Eqs. (6) and (9) into Eq. (8) leads to the final FV LBO model: p 2 1 _a m qlbo K p 1 1:3 Vc P3 expT3 =300 2 D0 (10) eff LHV
Fig. 3 Physical model of FV LBO correlation.
qlbo;c /
Vf Vc
Experimental Setup
Figure 4 shows the schematic of the single dome rectangular visualization model combustor (1=18th of the annular combustor) with a dual swirl-stabilized assembly. It consists of a fuel injector, a dual swirl-stabilized assembly, visualization window, primary holes, and dilution holes. The height of the model combustor dome is 92 mm. The length between the dome and the combustion liner exit is 226 mm. The combustor reference velocity is about 20 m=s in the design point, but in the fuel-lean operation (i.e., offdesign point), the combustor reference velocity is about 9 m=s, and the cold flow residence time is about 0.025 s. To achieve good atomization at a low fuel flow, a duplex pressure atomizer was employed in the experiment. Only the pilot was operated in the experiments because only a low fuel flow could meet the present fuel-lean operating conditions. The visualization window was designed in both the liner and the casing. The thickness of the quartz glass installed on the liner was 3 mm, and the casing quartz glass was 20 mm. Three primary holes and two dilution holes were designed on both inner and outer liners. Three kinds of swirl-stabilized designs were selected, i.e., dual-radial swirl-stabilized assembly, dual-axial swirl-stabilized
(6)
_ a;c from Eqs. (4) and (5) into Eq. (3) leads Substituting qlbo;c and m
Spark ignitor
to
Dilution hole
qlbo / fc
_a fc m Vf Pn3 expT3 =b
x (7) Dual swirl-stabilized assembly
Similarly, for heterogeneous fuel/air mixtures, the effects of atomization and vaporization are considered. Besides, the effect of the heating value of the fuel is also considered. Thus, the final form of Eq. (7) can be expressed as qlbo K
fc2 Vf
_a m P1:3 expT 3 =300 3
D20 eff LHV
Fuel injector
Primary hole
(8)
Visualization window
Fig. 4 Schematic of the single-dome rectangular visualization model combustor with a dual swirl-stabilized assembly.
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Bdr,ps Secondary swirler
Venturi
Flare
Bdr,ss Primary swirler
Fig. 5
Sketch of dual-radial swirl-stabilized assembly.
Primary swirler
Flare
Dda,ss
Ddavt
Dda,ps
θ FA
a) b) Fig. 8 Schematic of the variations of flow area of the primary holes.
Two different primary hole arrangements were designed in the experiments. One arrangement varied the flow area of primary holes and kept the number of primary holes unchanged, as shown in Figs. 8a and 8b. Figure 8a shows the primary hole reference configuration. Figure 8b shows the primary hole half-blocked configuration. The other changed the number of primary holes and kept the total flow area of primary holes unchanged, as shown in Figs. 9a–9c. The number of primary holes in Figs. 9a–9c are 3, 2, and 4, respectively. B.
Secondary swirler Venturi d da
Fig. 6 Sketch of dual-axial swirl-stabilized assembly.
assembly, and axial-radial swirl-stabilized assembly. The dual-radial swirl-stabilized assembly consisted of a primary radial swirler, a secondary radial counter-rotating swirler, a venturi that was fixed on the primary swirler, and a flare that was fixed on the secondary swirler, as shown in Fig. 5. The dual-axial swirl-stabilized assembly consisted of a primary axial swirler, a secondary axial counterrotating swirler, a venturi, and a flare, as shown in Fig. 6. The venturi was fixed on the primary axial swirler, and the primary axial swirler was fixed on the secondary axial swirler. The flare was fixed on the secondary axial swirler. The axial-radial swirl-stabilized assembly consisted of a primary axial swirler, a secondary radial counterrotating swirler, a venturi, and a flare, as shown in Fig. 7. The venturi was fixed on the primary axial swirler, and the flare was fixed on the secondary radial swirler.
Test Plan
To verify the improved correlation, a total of 25 swirl-stabilized combustors were used in the experiments. In the dual-radial swirl-stabilized combustors, five configurations were employed. The differences among them were the variations of flow area of the primary swirler, the secondary swirlers, and the primary holes. The variations of flow area of the primary and secondary swirlers were obtained by changing Bdr;ps and Bdr;ss , which denoted the widths of the passage of the primary and secondary swirlers, respectively, as shown in Fig. 5. Different primary holes were designed, as shown in Fig. 8. The variations of parameters of different dual-radial swirl-stabilized combustors are shown in Table 1. In the dual-axial swirl-stabilized combustors, 11 configurations were employed in the experiments. The differences among these configurations were the primary axial swirler, the secondary axial swirlers, the venturi, the flare, and the primary holes. The different configurations of the primary axial and the secondary axial swirlers were obtained by changing the parameters of Dda;ps and Dda;ps , respectively. The variations of the venturi were the diameter of the venturi throat and the distance from the throat to the exit plane, which were denoted by Ddavt and dda , respectively. The different flare designs were obtained by varying the flare angle, as shown in Fig. 6.
Bar,ss
Secondary swirler
Fig. 7
Flare
dar
Darvt
Dar,ps
Primary swirler
Venturi
Sketch of axial-radial swirl-stabilized assembly.
a) Fig. 9
b) c) Schematic of the variations of the number of primary holes.
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Table 1 Combustor Sdr;ps , m2 1 2 3 4 5
Sdr;ps 0:5Sdr;ps Sdr;ps 0:5Sdr;ps 0:5Sdr;ps
Sdr;ss , m2
Sdr;ph , m2
Sdr;ss Sdr;ss 0:5Sdr;ss 0:5Sdr;ss Sdr;ss
Sdr;ph Sdr;ph Sdr;ph 0:5Sdr;ph 0:5Sdr;ph
Table 2 Combustor Sda;ps , m2 6 7 8 9 10 11 12 13 14 15 16
Sda;ps 1:2Sda;ps 0:8Sda;ps Sda;ps Sda;ps Sda;ps Sda;ps Sda;ps Sda;ps Sda;ps Sda;ps
Parameters of different dual-radial swirl-stabilized combustors fdr;ps , % fdr;ss , & 7.6 3.9 8.0 4.9 4.6
fdr;ph , % fdr;dh , % fc;dome , %
9.8 10.2 5.2 6.3 11.9
27.4 28.5 28.8 17.6 16.6
19.6 20.4 20.6 25.3 23.8
5.5 5.7 5.8 7.1 6.6
fc;liner , % 30.1 31.3 31.7 38.8 36.5
Parameters of different dual-axial swirl-stabilized combustors
Sda;ss , m2
Ddavt , m
dda , m
FA , 0
Nph
fda;ps , %
Sda;ss Sda;ss Sda;ss 1:2Sda;ss 0:8Sda;ss Sda;ss Sda;ss Sda;ss Sda;ss Sda;ss Sda;ss
Ddavt;ref , Ddavt;ref , Ddavt;ref , Ddavt;ref , Ddavt;ref , 0:9Ddavt;ref , Ddavt;ref , Ddavt;ref , Ddavt;ref , Ddavt;ref , Ddavt;ref ,
dda;ref dda;ref dda;ref dda;ref dda;ref dda;ref 1:8dda;ref dda;ref dda;ref dda;ref dda;ref
45 45 45 45 45 45 45 35 55 45 45
3 3 3 3 3 3 3 3 3 2 4
7.6 9.1 5.9 7.5 7.8 7.6 7.6 7.6 7.6 7.6 7.6
fda;ss , % fda;ph , % 9.6 9.5 9.8 11.3 7.9 9.6 9.6 9.6 9.6 9.6 9.6
fda;dh , % fc;dome , % fc;liner , %
27.4 27.0 28.0 26.9 28.0 27.4 27.4 27.4 27.4 27.4 27.4
19.6 19.3 20.0 19.3 20.0 19.6 19.6 19.6 19.6 19.6 19.6
5.5 5.4 5.6 5.4 5.6 5.5 5.5 5.5 5.5 5.5 5.5
30.2 29.7 30.8 29.6 30.8 30.2 30.2 30.2 30.2 30.2 30.2
Table 3 Parameters of different axial-radial swirl-stabilized combustors 2
Combustor Sar;ps , m 17 18 19 20 21 22 23 24 25
Sar;ps 1:2Sar;ps 0:8Sar;ps Sar;ps Sar;ps Sar;ps Sar;ps Sar;ps Sar;ps
Sar;ss , m2
Darvt , m
dar , m
Nph
Sar;ss Sar;ss Sar;ss 1:2Sar;ss 0:8Sar;ss Sar;ss Sar;ss Sar;ss Sar;ss
Darvt;ref Darvt;ref Darvt;ref Darvt;ref Darvt;ref 0:9Darvt;ref Darvt;ref Darvt;ref Darvt;ref
dar;ref dar;ref dar;ref dar;ref dar;ref dar;ref 1:5dar;ref dar;ref dar;ref
3 3 3 3 3 3 3 2 4
The different designs of the primary holes were shown in Fig. 9. The variations of the primary holes were the number of the primary hole, while the total flow area of the primary holes was kept unchanged. The variations of parameters of different dual-axial swirl-stabilized combustors are shown in Table 2. In the axial-radial swirl-stabilized combustors, nine configurations were used in the experiments. The differences among these configurations were the primary axial swirler, the secondary radial swirlers, the venturi, and the number of primary holes. The different configurations of the primary axial and the secondary radial swirlers were obtained by changing the parameters of Dar;ps and Bar;ss , respectively. The variations of the venturi were the diameter of the venturi throat and the distance from the throat to the exit plane, which were denoted by Darvt and dar , respectively, as shown in Fig. 7. The different designs of the primary holes used in the dual-axial swirlstabilized combustors are shown in Fig. 9. The variations of the primary holes were the number of the primary hole, while the total flow area of the primary holes kept unchanged. The variations of parameters of different axial-radial swirl-stabilized combustors are shown in Table 3. In Tables 1–3, the airflow splits among the dual swirlers, the primary jet, the dilution jet, the cooling air for the dome, and the liners are based on calculated flow areas. All the experiments were conducted under fuel-lean conditions. In the experiment, the LBO limits were determined in this way: stable combustion was established at a fixed air mass flow rate, and the fuel flow was varied until extinction occurred. When extinction was achieved, the final fuel flow rate was recorded. The flame images were recorded from the onset of ignition to the end.
fda;ps , % fda;ss , % 7.5 8.7 5.9 7.3 7.7 7.5 7.5 7.5 7.5
9.8 9.7 10.0 11.3 7.5 9.8 9.8 9.8 9.8
fda;ph , % fda;dh , % fc;dome , % fc;liner , % 27.4 27.0 27.9 27.0 28.1 27.4 27.4 27.4 27.4
19.6 19.4 19.9 19.3 20.1 19.6 19.6 19.6 19.6
5.5 5.4 5.6 5.4 5.6 5.5 5.5 5.5 5.5
30.2 29.8 30.7 29.7 30.9 30.2 30.2 30.2 30.2
The fuel employed in the experiment was RP-3 kerosene. The air mass flow rate was about 0:6 kg=s, and the inlet air total temperature was 298 K. The pressure in the combustor was kept 220 KPa under each operating condition. C.
Uncertainty
The experimental uncertainties mainly come from the following aspects: 1) instruments, 2) manual adjustment, 3) signals acquisition, 4) calibration, and so on. Since the LBO limits are defined as the ratio of the fuel flow and the airflow at LBO, the relative uncertainty of the qlbo comprises the relative uncertainty of fuel flow and the relative uncertainty of airflow. The airflow’s uncertainty consists of the calibrated uncertainty of the airflow meter, instrument uncertainty, and manual adjustment uncertainty. The fuel flow’s uncertainty consists of the calibrated uncertainty of the fuel injector, the instrument uncertainty, the manual adjustment uncertainty, and so on. Therefore, the relative uncertainty of the LBO limits are obtained by the sum of the above relative uncertainties. The results show that the measurement uncertainty of the LBO limits are within 4%.
IV. A.
Results and Discussions
Experimental Observations
The variations of the size of the flame for combustors with different dual swirl-stabilized assemblies and primary hole arrangements are illustrated in Fig. 10. It is revealed that the size of the flame is different for different combustor configurations; that is,
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Fig. 10 Experimental observations near LBO for different dual-radial swirl-stabilized combustors.
B. Comparison Between Measured and Predicted Lean Blowout Limits
Table 4 shows the values of and for different combustors. Variable is the fraction of the combustor dome airflow involved in combustion. Variable is defined as the ratio of FV near LBO to combustor volume. The FV Vf is approximately determined by rotating the flame contour (in optical image) along the centerline. The value of K is selected as a constant of 43 for all the present research combustors. Figures 11–13 show the comparison of the measured and predicted LBO limits for combustors with different dual swirlstabilized assemblies and primary hole arrangements, respectively. In the figures, the abscissa denotes different combustor configurations, while the ordinate denotes LBO limits. It is found that the predicted value of LBO limits of the FV LBO model shows good agreement with the corresponding experimental values of LBO limits. The possible explanation is that the improved correlation is derived based on the practical flame images near LBO condition and includes two key parameters, i.e., and . They embody the effects of dome components and primary zone configurations at the LBO condition. C.
In the figure, the abscissa denotes the nondimensional FV, which is extracted from flame images near LBO. The ordinate denotes the LBO equivalence ratio. It can be seen from Eq. (3) that the Lefebvre model is correlated to the size of combustor volume instead of the size of FV. Therefore, the predicted values of the Lefebvre model remain unchanged when varying some parameters (dome components and primary hole arrangements) of combustors upstream of the dilution holes, as shown in Fig. 14. But the effects of the size of the FVand combustor 0.008
0.231 0.251 0.300 0.348 0.406 0.738 0.446 0.829 0.347 0.673 1.000 0.514 0.722 0.514 0.654 0.620 0.310 0.355 0.247 0.328 0.283 0.242 0.242 0.333 0.279
0.481 0.501 0.548 0.590 0.638 0.859 0.668 0.911 0.589 0.820 1.000 0.717 0.849 0.717 0.809 0.787 0.557 0.596 0.497 0.573 0.532 0.492 0.492 0.577 0.528
0.004
1
2
3
4
5
Combustor configuration Fig. 11 Comparison of measured and predicted LBO limits for different dual-radial swirl-stabilized combustors.
LBO limit
0.012 0.011 0.01 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 6
Measurement Prediction
7
8
9
10
11
12 13
14 15
16
Combustor configuration Fig. 12 Comparison of measured and predicted LBO limits for different dual-axial swirl-stabilized combustors.
0.008
Measurement Prediction
0.007
LBO limit
0.174 0.142 0.131 0.112 0.165 0.173 0.186 0.157 0.188 0.157 0.173 0.173 0.173 0.173 0.173 0.173 0.173 0.184 0.160 0.187 0.152 0.173 0.173 0.173 0.173
0.005
0.002
Comparison Between Flame Volume and Lefebvre Models
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
0.006
0.003
The predicted LBO equivalence ratios by the FV and Lefebvre model compared with the experimental values are shown in Fig. 14. Table 4 Values of and for different combustors p Combustor
Measurement Prediction
0.007
LBO limit
the variations of the size of the flame can embody the effects of dome components and primary hole arrangements on LBO. Besides, the size of the flame is small near LBO.
0.006 0.005 0.004 0.003 0.002 17
18
19
20
21
22
23
24
25
Combustor configuration Fig. 13 Comparison of measured and predicted LBO limits for different axial-radial swirl-stabilized combustors.
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0.18 0.16 0.14
Φ (Experimental) Φ (Lefebvre model) Φ (FV model)
Φ
0.12 0.1 0.08 0.06 0.04 0.02 0 0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
β Fig. 14 Comparison of the predicted values of different LBO models with the measured values.
volume can be embodied by the parameter of in the FV model. The uncertainty between the measured value and calculated value by the Lefebvre LBO expression of qlbo is about 45%, and the uncertainty between the measured value and the calculated value by the FV expression of qlbo is about 15%. The results reveal that the prediction accuracy of the FV model is much higher than Lefebvre model.
V.
Conclusions
To improve the prediction accuracy of the existing LBO semiempirical correlation, a new LBO model was developed and lots of LBO visual experiments for model verification were conducted. Some conclusions are obtained as follows: 1) A new physical model is established, and the FV concept is proposed by the visualization experimental observations. 2) Based on the new physical model, an improved correlation (i.e., FV LBO model) is obtained in the present study. 3) In the improved correlation, two key parameters, and , are included; they could embody the effects of the variations of dome components and primary zone configurations on LBO. 4) It is concluded that the FV LBO model shows better agreement with the corresponding experimental values of different designs than the Lefebvre model. The prediction uncertainties of the two models are about 15 and 45% in the present combustor configurations, respectively. It is known that the flame only exists in a suitable range of FAR. In other words, the FV is mainly embodied by the concentration contour in a given combustor configuration. Since the fuel concentration contour surfaces could be determined by numerical simulations, the possible method to predict FV is to determine the critical contour surface of fuel concentration after numerical simulations. It is planned to try different ways such as iteration and characteristic point methods to determine the critical concentration contour. Once the FV is determined, the air involved in the FV could be obtained easily by numerical simulations.
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G. Richards Associate Editor
