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Characterization of confined hydrogen-air jet flame in a crossflow configuration using design of experiments
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Characterization of confined hydrogen-air jet flame in a crossflow configuration using design of experiments D.P. Mishra, Swarup Y. Jejurkar* Combustion Laboratory, Department of Aerospace Engineering, Indian Institute of Technology, Kanpur 208016, India
article info
abstract
Article history:
Hydrogen combustion has many industrial applications and development of new hydrogen
Received 8 December 2012
burners is required to fulfil new demands. A novel configuration of hydrogen burner uti-
Received in revised form
lizing crossflow injection of fuel jets into swirling combustion air is characterized empir-
13 February 2013
ically in this work. It is intended as a first step in the development of new burner
Accepted 16 February 2013
technologies having reduced emission levels and improved efficiency. Experiments were
Available online 13 March 2013
designed using the full factorial design method. Operating parameters were varied simultaneously and the NOX emissions from the flame stabilized on the burner were
Keywords:
measured. Statistical analysis of the experimental data showed that overall equivalence
Hydrogen combustion
ratio is the dominant factor and lower NOX emissions are observed at low equivalence
Crossflow
ratios, irrespective of the burner power level. The analysis yielded an empirical relation-
Full factorial design
ship among NOX emission, overall equivalence ratio, and power level that is useful in the
Emission
design activity for a future combustion system based on the proposed configuration.
Correlation
Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Economy of near future is likely to be based largely on hydrogen as fuel [1] rather than conventional hydrocarbons. Hydrogen combustion already has many existing and potential applications in domestic and industrial heating, cutting, and welding processes and hydrogen is a superior fuel than many conventional hydrocarbons. However, efficient mixing and operation, safety in handling, high turndown ratios, etc. need cognizance for design, development, and demonstration of hydrogen flame burners to harness the hydrogen power. Empirical studies on different research burners (including the coaxial tube) conducted in the past focused on flame characterization, stability, NOX emissions, and burner performance. Schefer et al. [2] evaluated stability characteristics of lean premixed hydrogen combustion. Nine channels were used to supply air. Hydrogen (or its blend with methane) was injected radially inward (i.e. in crossflow) through the orifices
located on either side of each channel. Mixing was thus achieved in a compact mixing zone before the exit from burner. Lean combustion was considered to reduce the NOX emission potential. Uniform mixing could be achieved for high momentum ratio of fuel and primary air. Since the maximization of coaxial air helps in shortening the flame length and reduction in NOX emission from nonpremixed jet flames [3], parametric studies are needed to find the optimal parameter combination that helps in NOX reduction. Shortening of the flame results in an overlap of flame and high velocity regions near the injectors. The residence time necessary for NOX formation is thus not available to hot gases. Experimental data of Feikema et al. [4] show that coaxial air and small enough velocity-to-diameter ratio of fuel jet result in a stable flame and reduced NOX emission. Swirl extends the blowout limit because it reduces the local velocities near the forward stagnation point of recirculation vortex where the flame is stabilized. Unlike hydrocarbon
* Corresponding author. Tel.: þ91 512 259 6086; fax: þ91 512 259 7626. E-mail addresses: [email protected], [email protected] (S.Y. Jejurkar). 0360-3199/$ e see front matter Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2013.02.085
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Nomenclature a b CI D Df e MS Nb Ncp Nnn Nrep
intercept in Eq. (1) model constants in Eq. (1) confidence interval diameter degree of freedom residual mean square number of blocks number of center points number of non-numeric factors number of replications
flames, prompt NOX formation mechanism is not active in hydrogen flames due to lack of any hydrocarbons and instead, temperature-sensitive thermal NOX mechanism is a dominant contributor. Chen and Driscoll [3] showed that thermal NOX in H2 flames (in terms of NOX emission index, EINOX) varied with the cube of flame length in the presence of coaxial air. However, too much coaxial air or premixing resulted in NOX increase per unit flame volume. Driscoll et al. [5] also found that weak radiation in hydrogen flame in comparison to methane was helpful in reducing NOX. In the absence of coaxial air, Damkohler number, (S2L/a)/(UF/dF), is the scaling parameter and EINOX scales as (UF/dF)1/2. UF is jet exit velocity, dF is jet diameter, SL is the maximum laminar burning velocity, and a is thermal diffusivity. Hwang et al. [6] varied turbulence intensity of annular air in the coaxial design to measure its effect on hydrogen jet flame. Their results verify that increased turbulence intensity enhances mixing and decreases flame length. As a side-effect of this strategy, flame temperature reduces due to high strain rate and conversion of NO to NO2 increases. Turbulence intensity is also beneficial for controlling NOX downstream of the flame as it promotes mixing and reduces pockets of high temperature where NOX formation rates can shoot up. Mixing of fuel and air external to the burner is preferable for operational ease and external fueleair contacting patterns allowing efficient mixing in a small enough zone as near to the injector as possible are consequently desirable. Evidently, swirling motion of air and/or fuel is the easiest route to enhance mixing efficiency in these burners. Swirling air also helps to reduce emission of harmful NOX. Mixing under fuellean conditions also helps in NOX reduction [3]. Further, due to its small quenching diameter, orifice diameters for hydrogen should be small enough to avoid flame stabilization very near the orifice or flashback in the worst case. In combination, these strategies could lead to a significant decrease
Fig. 1 e Crossflow injection scheme of fuel hydrogen into swirling combustion air.
Nr P SD SN SS x y y
total number of runs power level standard deviation swirl number sum of squares factors response sample mean
Greek symbols ε error term in Eq. (1) F equivalence ratio
in emissions, provided flame stability is not impaired in the process. Optimal set of operating conditions is required for a particular application and side-effects such as loss of heat due to high amount of coaxial air should be addressed. Different fueleair contacting patterns for external mixing are currently being evaluated in our laboratory on these lines as part of a program to obtain more efficient hydrogen burner for industrial applications. NOX emission is an important performance criterion in the program. In this paper, some empirical results on one such configuration are reported. Experiment protocols based on the concepts of design of experiments or DoE [7] are being implemented frequently by the fuel cell community, as evident from a number of studies published in this journal, but only sporadically by the combustion community [8,9]. Consequently, apart from evaluation of burner performance, our focus was also on the efficient experimentation strategy. As the systematic evaluation of multiple design configurations is a lengthy and expensive process, experiments were devised using the statistical concepts [7]. The objective of these experiments was to obtain an empirical relationship between NOX emission and the two operating parameters viz. global equivalence ratio between inlet H2 and air streams and the desired power level. In what follows, first the burner configuration in question is described. Next, the experimental program followed to arrive at the empirical relationship is discussed. Results of the experiments along with the diagnostics used for testing the validity of empirical correlation are then presented.
2.
Burner configuration
The crossflow configuration shown schematically in Fig. 1 is considered in the present paper. Hydrogen fuel is injected externally into the combustion air through three orifices arranged circumferentially on the lateral surface of the burner head. One centric orifice is also used in addition to the circumferential ones. Thus, division of fuel injection into additional streams in comparison to the conventional axial injection strategy is the major design change considered in the new configuration. The radial outflow of fuel jets is directly into the path of swirling combustion air arranged around the burner head. Radial fuel jets exit 2.5 mm downstream and centric fuel jet exits 5 mm downstream of the air
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Fig. 2 e Comparisons of NOX emissions from the axial fuel injection configuration (e-e) against the proposed crossflow configuration (e:e).
exit, respectively. It is expected that such an arrangement would result in fast mixing of fuel and air external to the burner head and flame stability envelope might be widened. NOX emissions from the proposed burner configuration are compared in Fig. 2 against the single orifice design in which only the centric orifice (D ¼ 4 mm) was retained and lateral orifices responsible for the crossflow were absent. Emission levels reduced with the use of crossflow design in the range of Fglobal of interest to this study.
3.
Experimental program
3.1.
Experimental design
The experimental design and subsequent analysis is performed using Design Expert [10], a specialized DoE and statistical analysis software. Experimental design is generated using the full factorial design method [7] and necessary information for this step is collected in Table 1. Two-level factorial designs assume that a linear model as in Eq. (1) can adequately explain the effects of factors. y¼aþ
n X i¼1
bi xi þ
n XX j
bji xi xj þ ε
Main effect is the effect of a factor when considered alone. Mathematically, it is the difference between the average responses at the two possible levels (extremes in the range of factor values) of a factor [7]. It is necessary that the chosen factors be mutually independent. However, in some cases, the difference in the response between the levels of one factor is not the same at all levels of the other factors. This situation indicates the presence of interaction among the factors. Interaction effect is simply the average difference in the main effects of a factor vis-a`-vis the other factor. Importance of interaction effects is judged by the magnitude of bji relative to bi in the linear model of Eq. (1). Consideration of these interaction effects augments the basic linear model and accounts for curvature in the response function, relevance of which in the present case is demonstrated subsequently in Section 4.5. However, when the third term cannot account for curvature adequately (higher order effects are also important), then it is necessary first to obtain an estimate of the error (ε) involved in using Eq. (1) and then to reduce the effects of second-order effects. Both these requirements are satisfied by the addition of center points to the basic design. Number of center points is equal to the number of replications for the combination of the centroids of factors (combination a0 b0 of Fig. 3a). Fig. 3b depicts the possible four combinations of the two factors according to the 22 factorial design. The actual number of runs is determined from Eq. (2) after adjusting for the number of replications and center points. Nr ¼ 2n Nrep þ Ncp Nb þ Ncp Nnn
(2)
Non-numeric factors are not present in the present case (Nnn ¼ 0) and the experiments were conducted sequentially in a single block (day) so that Nb ¼ 1. Operating parameters, global equivalence ratio _ f =m _ a Þ=ðm _ f =m _ a Þstoich Þ and desired power level (P), ðFglobal ¼ ðm are the factors, while NOX emission (in ppm) is the flame response to simultaneous changes in Fglobal and P. NOX emissions are known to depend upon a number of other factors [3e6], including intensity of swirling, O2 concentration in combustion air, and inlet air temperature. In this work, we fixed the swirl intensity of incoming atmospheric air and considered only Fglobal and P, in the interest of economy. Power level is treated as a combustor design requirement to be prescribed independently and the burner performance for the prescribed power level is then empirically modeled. In this arrangement, it is necessary to maintain fuel and air mass
(1)
i
Second term on the r.h.s. represents main effects xi of each of the factors, while the third term represents interaction effects xixj. b represents the model coefficients which can be dimensionless. The gain in efficiency by using the factorial design instead of the classical one factor-at-a-time approach is modest in the present case (relative efficiency of 1.5 in terms of the number of required factor combinations) because the number of factors is small. However, factorial design accommodates the interaction effects that are difficult to detect with the conventional approach [7]. This advantage will be revealed in the analysis of experimental data.
Table 1 e Preliminary data for the experimental design. Factors, n
2
Factor statistics
Numeric
2
Fglobal
P (kW)
Non-numeric, Nnn Response Replicates, Nrep Blocks, Nb Center Points (per block), Ncp Runs, Nr
0 1 3 1 4
0.2 0.6 0.4 0.17
5 10 7.5 2.17
16
Min. Max. Mean SD
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Fig. 3 e (a) Generic representation of full factorial designs with center points, (b) possible factor combinations, and (c) design space.
flow rates to confirm to the desired power level and equivalence ratio. Preliminary unplanned experiments identified the useful ranges of these operating conditions; Fglobal: 0.2e0.6 and P: 5e10 kW because a stable flame was observed in this range. The factors are chosen to represent the extremes of these ranges and such a choice automatically excludes the possibility of choosing the factors randomly from within the ranges. In other words, we apply the model proposed in Eq. (1) for the fixed effects [7]. Standard order in which experiments could be performed is obtained by arranging the test sequence such that only one factor is introduced at a time and the second factor is combined successively with the preceding ones [7] (i.e. a, b, and ab). This order is randomized and the resulting parameter combinations arrived at after randomization with respect to the run order are arranged in the order shown in Table 2. Experiments were performed sequentially in the order shown in column 2. Fig. 3c graphically establishes the design space, within which the resulting correlation is valid. Numbers near the design points indicate the number of replications for a given design point. Both factors were varied simultaneously for a run.
3.2.
Experimental setup
Experimental setup in Fig. 4a includes a hydrogen gas cylinder, pressure regulator, mass flow meter, and the insulated combustor. Air line consists of compressor, pressure
regulator, manometer, settling chamber, and the Swirler (swirl number, SN ¼ 0.67). Swirler was constructed from eight vanes (vane angle 45 , ID 30 mm, thickness 2.5 mm) and fitted concentrically to the fuel port. Flow rates of hydrogen were varied from 28 to 140 lpm corresponding to a power output of 5e10 kW. Air-flow rates were in the range 50e400 lpm for each
Table 2 e Experimental design for NOX emission. Standard order 5 1 14 6 15 9 2 7 3 11 12 13 16 10 4 6
Run order
Factor 1 (Fglobal)
Factor 2 (P, kW)
Response (NOX, ppm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.6 0.2 0.4 0.2 0.4 0.2 0.2 0.2 0.2 0.6 0.6 0.4 0.4 0.6 0.6 0.6
5 5 7.5 10 7.5 10 5 10 5 10 10 7.5 7.5 10 5 5
27 3 23 4 21 3 3 3.5 4 60 57 20 22 57 27 28
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Fig. 4 e (a) Experimental arrangement, (b) direct luminosity photographs of hydrogen-air swirling flames obtained with the crossflow configuration.
hydrogen flow rate. The combustor is made of stainless steel (SS304L) cylinder (ID 80 mm, OD 90 mm, height 430 mm). Fig. 4b shows the direct flame luminosity photographs at three Fglobal, from which some features can be extracted qualitatively. The swirling flame appears to have stabilized around the burner rim and three luminous regions corresponding to the radial orifices are visible. Flame is obscure at its periphery, possibly due to high burning velocity of hydrogen fuel and turbulence. It also touches the walls, especially near the injection points due to radial injection of fuel jets. The flameewall contact could significantly alter flow-field near the flame base, especially with respect to the formation of
Table 4 e List of ordered factor effects and sum of squares for the experimental design.
Table 3 e Statistics of the flame response. Response statistics Min. Max. Mean SD Max/min
secondary flow structures. Further, flame volume increases and its luminosity decreases with equivalence ratio. Quantitative analysis of post-combustion gases was performed using a hand-held analyzer (Kane-May, Model KM900) able to measure O2, CO, CO2, NO, total nitric oxides (NOX), and SO2 concentrations. The stainless steel sample probe is aligned with the flow at a height of 440 mm from the burner base. Tip of the probe is located on the cylinder axis. The sample probe is water-cooled to quench NO conversion reactions but condensation of water vapor present in the sample is avoided. Sampled gas mixture is
NOX (ppm) 3 60 22.6563 20.0871 20
Model term A (Fglobal) B (P) AB
Effecta
Sum of squares
% contribution
39.25 15.42 15.25
4621.69 713.02 697.69
76.36 11.78 11.53
a Standardized effect.
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Fig. 5 e Half-normal probability plot for the effects A, B, and AB. Selected effects are represented by highlighted - and error estimates are shown by :.
then passed in succession to in-line water trap, particle filter, and sensors.
4.
Results and discussion
4.1.
NOX emission data
Sequential experimental runs yielded the NOX emission for each combination of operating parameters. The complete dataset is collected in the last column of Table 2, while major statistical figures are summarized in Table 3. The NOX emissions ranged from 3 to 60 ppm and the ratio Max/Min indicates variation over the entire design space. It is useful to decide whether any transformation of the raw response data is needed. The decision to use response data without transformation was based on the observations that residuals are normally distributed (Fig. 8) and the difference between minimum and maximum values of response is not very large.
4.2.
Estimation of factor effects
Significant effects are identified first. Eq. (1) accounts for the effects x1 for A, x2 for B, and x1x2 (interaction of A and B). Quantitatively, an effect denotes the change in average flame response to the change in a factor from low to high level and can be estimated using the contrast constants [7]. In this work, it is estimated using the regression model and is calculated as the difference between marginal mean and overall mean. It is in fact the coefficient of the model term and is half the value calculated using Yates method [7]. Sum of squares (SS) is simply the sum of squares of the deviations of the responses due to a change in factor from its mean, while the % contribution is the normalized SS per term.
The resulting estimates are listed in Table 4. The importance of each of these effects is judged by plotting the absolute values of effect estimates against their half-normal probability (also called cumulative normal probability) shown in Fig. 5 considering only the positive half of the normal probability distribution. A standardized effect is obtained by transformation of data by subtracting each value from the mean and diving it by the standard deviation. Significant effects are away from the line as outliers while the normally distributed effects tend to have zero mean and cluster around the straight line [11]. This plot ensures correct selection of effects as it also guards against the possibility that one or more of the effects included in the model are not random. Similar information is also obtained from the % contribution column of Table 4. The line is drawn to fit all the error estimates indicated by : and passes through the origin indicated by C. This fit depends upon what effects are included in the final model. While the choice of statistically significant effects is also aided by other expedients like a Pareto chart, the important guiding principle is the prior knowledge of the system under consideration. Large effects appear on the top right side of the plot in Fig. 5 and relatively unimportant effects are located on the lower left. This demarcation is not distinct in this case as power level (B) and the interaction (AB) effects are located in the upper half towards the center of the plot. Nevertheless, the effect of Fglobal is more significant than the other two but the interaction effect (AB) is not negligible and needs closer inspection. Effects A, B, and AB are plotted in Fig. 6a, b and c, respectively. A represents the design points corresponding to different factor combinations. From Fig. 6a, NOX emissions could be reduced by operating the burner with low enough Fglobal. Same effect is obtained by operation at reduced powers (Fig. 6b), which however results in under-utilization. Such straightforward conclusions must be qualified in the presence of interaction between the factors. The effect of Fglobal at the low power level (P ¼ 5 kW) shown in Fig. 6c by the continuous black line is weaker than the effect when power level increases to 10 kW. This is indicated by increased NOX emission when Fglobal is increased from 0.2 to 0.6 at P ¼ 10 kW. Fig. 6c also reveals that reduction in NOX levels can still be attained at higher power level, if Fglobal is kept as low as possible.
4.3.
Analysis of variance and empirical model
As mentioned earlier, center points are added in the present experimental design to guard against second-order effects on curvature. Following the usage by Montgomery [7], we call the model including center points as the “full model” (also termed as unadjusted model [10]) and that excluding center points is called “reduced model” (or adjusted model [10]). Analysis of variance (ANOVA) is performed on both these models and Tables 5 and 6 summarize the ANOVA results. Among the statistics, F-value is the ratio of variances of model or curvature against the residual variance. Larger F-value is desirable for model and curvature since noise contributions to variances are small. On the other hand, lack of fit F-value indicates adequacy of fit and should be small. F-value for curvature (lack of fit) in adjusted (unadjusted) model is 6.11, which indicates that second-order effects are significant and additional runs
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Fig. 6 e (a) Main effect of factor A: Fglobal, (b) main effect of factor B: P, (c) interaction effect. A show the design points, - are the predicted outcomes, and the vertical bars at either ends of lines show the least significant difference at 95% CI.
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Table 5 e ANOVA table for the adjusted model. Sum of squares
Degree of freedom
Mean square
F-value
p-value
Remark
Fglobal (A) P (B) AB Model Curvature Pure error
4621.69 713.02 697.69 6032.40 7.13 12.83
1 1 1 3 1 11
4621.69 713.02 697.69 2010.8 7.13 1.17
3961.45 611.16 598.02 1723.54 6.11 e
<0.0001 <0.0001 <0.0001 <0.0001 0.031 e
e e e Statistically significant Significant e
Total
6052.36
15
e
e
e
e
are dimensional quantities (kW1, for both terms), they do not connote any physical significance in the present case. Empirical model in terms of coded factors (1 for low level and þ1 for high level) is as in Eq. (4).
Table 6 e ANOVA table for the unadjusted model. Sum of Degree Mean Fpsquares of square Value Value freedom Fglobal (A) P (B) AB Model Residual Lack of fit Pure error Total
Remark
y ¼ 22:66 þ 19:624global þ 7:71P þ 7:634global P
4621.69
1
4621.69 2778.08 <0.0001
e
713.02 697.69 6032.40
1 1 3
19.96 7.13
12 1
713.02 428.59 <0.0001 e 697.69 419.38 <0.0001 e 2010.8 1208.68 <0.0001 Statistically significant 1.66 e e 7.13 6.11 0.031 Significant
12.83
11
1.17
e
e
e
6052.36
15
e
e
e
e
might be necessary. Further, F-value for the unadjusted model (1208.68) is high enough for the model to be statistically significant. p-value (probability of seeing the observed F-value if the null hypothesis is true) indicates significance of model terms and it should be <0.05 [10]. Thus, Fglobal (A), P (B), and AB are the significant model terms. Ability to obtain an empirical model of the processes underlying the observations is an attractive feature of statistical design of experiments methodology because sample size is much smaller than the classical method and design space is searched comprehensively. The empirical model shown in Eq. (3) is obtained using regression analysis. y ¼ 6:03125 16:254global 3:01667P þ 15:254global P
(3)
y is the NOX emitted in ppm and P is in kW. Although, the regression coefficients for P and FglobalP as reported in Eq. (3)
(4)
Model coefficients in Eq. (4) are directly comparable with each other and each is estimated at same precision (standard error of 0.37). This comparison reveals that Fglobal is the important factor. It should be noted that all the data analysis reported herein is carried out in terms of coded factors. Mechanisms governing combustion, heat and mass transfer, and fluid flow are non-hierarchical as interactions of different processes (and thereby variables) are dominant and coupled non-linearly. Hence, even though the analysis software enforces model hierarchy (all lower order terms must be present in the model if a higher order term is to be included), we examine the effects of excluding the P and FglobalP terms using the comparison of the scale-invariant regression coefficients of Eq. (4). A non-hierarchical model results after removing the P term in Eq. (4). The predicted data are examined for the changes in the width of 95% confidence intervals, with and without the inclusion of P term and the interaction effect exemplified by FglobalP [12]. Table 7 summarizes the sample calculations done on one design point for which P ¼ 10 kW and Fglobal ¼ 0.6. Changes in the resulting empirical models in each case are reflected in the predictions vis-a`-vis the experimental data. Since the width of 5e95 confidence interval increases when FglobalP and/or P are excluded and predictions become worse, we conclude that FglobalP and P should be retained for ensuring the predictive reliability of the empirical model even though they are statistically less significant than Fglobal alone. Validity of the empirical model is easily established (albeit with less reliability) from Fig. 7, which shows a scatter plot of the predicted and empirical data for all the factor
Table 7 e Examination of the predictive reliability of empirical model in Eq. (4) in the absence of FglobalP and/or P (operating conditions: Fglobal [ 0.6 and P [ 10 kW). Included factor effects All All Only Fglobal Only Fglobal and P Only Fglobal and FglobalP
NOX (ppm)
SD
CIlow
CIhigh
Remarks
58 57.6 42.3 49.98 49.9
e 1.29 10.11 7.43 7.51
e 56.04 34.0 42.31 42.14
e 59.18 50.56 57.674 57.672
Mean of three replicates Full model No interaction effect No interaction effect Non-hierarchical model
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Fig. 7 e Parity plot for comparison of predictions of Eqs. (3) or (4) with the experimental data. Dashed lines represent the range of uncertainty.
combinations considered in the design. Predictions are based on the adjusted (reduced) model in which the center points are not included. The even split of points by the 45 line shows that no transformation is required for the raw data [10]. Further, the reliability of model predictions depends upon the outcome of diagnostic checks described further.
4.4.
Diagnostic checks
Since the hypothesis of no difference in treatment means is not satisfied in practice [7], ANOVA results are backed up by checking whether the residuals ðeij ¼ yij yi Þ are normally distributed. The residuals indicate the number of standard deviations separating the actual and predicted response. A number of graphical tests in Figs. 8e10 indicate the adequacy of model as suggested by Montgomery [7]. Fig. 8 is the normal probability plot of residuals that approximates a straight line and hence indicates that the error is normally distributed. Internally Studentized residuals (calculated by dividing the residual with its estimated standard deviation) are used. Outlier points can be detected using standardized residuals pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (defined as eij = SSerror =N a). For normally distributed errors, standardized residuals have zero mean and unity variance, and the point for which residual is larger than 3 or 4 standard deviations from the mean is considered as outlier [7]. In fact, the half-normal probability plot of effects drawn in Fig. 5 can also give an indication of the presence of an outlier data point if the straight line fitting the error estimates (:) does not pass through the origin [13]. Based on this criterion, it is evident that outlier point/s are not present in the dataset. Further, variation of these residuals with run order (Fig. 9) is a measure of correlation between them. Random scatter among the residuals in Fig. 9 shows that randomization has worked and the effects of unaccounted variables are minimal. Correctness of model is further checked by plotting the residuals against model predictions in Fig. 10. Lack of a pattern indicates that
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Fig. 8 e Normal probability plot for residuals eij (experimental data of Table 2). Black - show values of NOX near the lower limit of 3 ppm, fainter ones near the 60 ppm limit, and the grey denotes values in the middle of the range 3e60 ppm.
the model is correct and its assumptions are valid. Variance should not depend upon the magnitude of the response. Note that measuring instruments are used extensively in combustion experiments, and above statement is generally not true in our case. An outward conical pattern from left to right (small residual for small response magnitude and large for large responses) in the residual-prediction plot similar to Fig. 10 indicates such a situation. The examination of data in this respect is inconclusive. It might be necessary to force the variance to a constant by performing transformations on the collected responses and conducting ANOVA again [10]. Finally, residual-factor plots in Fig. 11 check whether the variance not accounted for by the model is different for
Fig. 9 e Residual variation with the run order.
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Fig. 10 e Plot of residuals against model predictions (Eq. (3) or (4)) to check for the model correctness.
Fig. 12 e Flame response surface in the form of (a) contour map of NOX emission and (b) as a three-dimensional surface. Color code shows variation in the range 3e60 ppm and design points are overlaid in the shape of A.
different levels of a factor. The plot should exhibit a random scatter. Pronounced curvature may indicate a systematic contribution of the independent factor not accounted for by the model.
4.5.
Interpretations
We set out to physically interpret the results with the help of contour plot shown in Fig. 12a, which is a two-dimensional map of flame response over the design space. The response surface is continuous over this space. A less user friendly, but more detailed representation is the 3D surface of Fig. 12b and a is the 2D projection of this surface on the FeP plane. Following observations can be made based on these maps. Fig. 11 e Residual plots for checking against any unaccounted effects (a) residual against Fglobal and (b) residual against P.
NOX emissions remain low at low power level and global equivalence ratios.
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At any power level, NOX emission increases with equivalence ratio. However, at a fixed equivalence ratio, the increase in NOX levels is very slow comparatively as the power level is increased. Lowest emission occurs for the leanest flame (Fglobal < 0.3), while the highest NOX emission occurs for comparatively fuel-rich flame operating with high power levels. This corresponds to region near the top right corner of Fig. 12a. Finally, it will be recalled from earlier discussion (cf. Fig. 6c) that the effect of equivalence ratio is small at the low power level and significant at high power level. Best results (minimum NOX) are obtained at low enough equivalence ratios, irrespective of the power level at which the combustor operates. The contour map of Fig. 12a is a convenient representation of these interaction effects. Best operating conditions are located in the left hand region of Fig. 12a. At a more fundamental level, low power flames produce comparatively low temperatures. Since, NOX formation and destruction is a highly temperatureesensitive reaction and its formation rate increases with temperature [11], we can see why the combinations of low factor levels produce lower NOX. It can also be easily seen that high NOX levels at the other extreme are explained on this basis.
5.
Concluding remarks
In this work, a novel hydrogen burner was characterized in terms of its emission potential using experiments designed by applying the full factorial design method. The arrangement of lateral orifices in addition to the centric orifice of some conventional configurations significantly reduces NOX emissions in hydrogen combustion. This is achieved by improved mixing in the crossflow arrangement and elimination of hot gas pockets in the flame zone. The full factorial design method was instrumental in establishing an empirical correlation of NOX emission with the global equivalence ratio and desired power level, viz. y ¼ 22:66 þ 19:624global þ 7:71P þ 7:634global P. The regression coefficients are dimensionless. Only a small number of experimental runs were needed to arrive at the relationship and operating parameters were varied simultaneously, unlike the traditional method in which only one operating parameter is varied at a time. This correlation could be useful in evaluating the performance of burner in a future design activity. Global equivalence ratio is the dominant factor in determining emission level, although the combined effects of power level and global equivalence ratio are on the same
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order as the power level. Finally, a useful operating region for this kind of burners is in the range of low enough global equivalence ratios irrespective of the power level since the emissions are reduced in this range.
Acknowledgments Experiments reported in this paper were performed as part of a research project funded by the Ministry of New and Renewable Energy, Government of India and its support is gratefully acknowledged. Mr. Ashish Tiwari and the personnel of Combustion Laboratory provided assistance in the experiments described in this paper.
references
[1] Marban G, ValdeseSolis T. Towards the hydrogen economy? Int J Hydrogen Energy 2007;32:1625e37. [2] Schefer RW, Smith TD, Marek CJ. Evaluation of NASA lean premixed hydrogen burner. SAND2002-8609. [3] Chen ReH, Driscoll JF. Nitric oxide levels of jet diffusion flames: effects of coaxial air and other mixing parameters. Symp (Int) Combust 1990;23:281e8. [4] Feikema D, Chen ReH, Driscoll JF. Blowout of nonpremixed flames: maximum coaxial air velocities achievable, with and without swirl. Combust Flame 1991;86:347e58. [5] Driscoll JF, Chen ReH, Yoon Y. Nitric oxide levels of turbulent jet diffusion flames: effects of residence time and Damkohler number. Combust Flame 1992;83:37e49. [6] Hwang CeH, Lee S, Lee CeE. The effect of turbulence intensity of ambient air flow on NOX emissions in H2/air nonpremixed jet flames. Int J Hydrogen Energy 2008;33:832e41. [7] Montgomery DC. In: Design and analysis of experiments. 7th ed. New York: John Wiley and Sons; 2009. [8] Ma F, Wang J, Wang Y, Wang Y, Zhong Z, Ding S, et al. An investigation of optimum control of a spark ignition engine fueled by NG and hydrogen mixtures. Int J Hydrogen Energy 2008;33:7592e606. [9] Ateshkadi A, McDonnel VG, Samuelsen GS. Lean blowout model for a spray-fired swirl-stabilized combustor. Proc Combust Inst 2000;28:1281e8. [10] Design Expert. Available from: http://www.statease.com/ dx8descr.html [accessed 27.11.12]. [11] Miller JA, Bowman CT. Mechanism and modeling of nitrogen chemistry in combustion. Prog Energy Combust Sci 1989;15:287e338. [12] Montgomery DC, Myers RH, Carter Jr WH, Vining GG. The hierarchy principle in designed industrial experiments. Qual Reliab Eng Int 2005;21:197e201. [13] Daniel C. Use of half-normal plots in interpreting factorial two level experiements. Technometrics 1959;1:311e42.
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Characterization of confined hydrogen-air jet flame in a crossflow configuration using design of experiments D.P. Mishra, Swarup Y. Jejurkar* Combustion Laboratory, Department of Aerospace Engineering, Indian Institute of Technology, Kanpur 208016, India
article info
abstract
Article history:
Hydrogen combustion has many industrial applications and development of new hydrogen
Received 8 December 2012
burners is required to fulfil new demands. A novel configuration of hydrogen burner uti-
Received in revised form
lizing crossflow injection of fuel jets into swirling combustion air is characterized empir-
13 February 2013
ically in this work. It is intended as a first step in the development of new burner
Accepted 16 February 2013
technologies having reduced emission levels and improved efficiency. Experiments were
Available online 13 March 2013
designed using the full factorial design method. Operating parameters were varied simultaneously and the NOX emissions from the flame stabilized on the burner were
Keywords:
measured. Statistical analysis of the experimental data showed that overall equivalence
Hydrogen combustion
ratio is the dominant factor and lower NOX emissions are observed at low equivalence
Crossflow
ratios, irrespective of the burner power level. The analysis yielded an empirical relation-
Full factorial design
ship among NOX emission, overall equivalence ratio, and power level that is useful in the
Emission
design activity for a future combustion system based on the proposed configuration.
Correlation
Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Economy of near future is likely to be based largely on hydrogen as fuel [1] rather than conventional hydrocarbons. Hydrogen combustion already has many existing and potential applications in domestic and industrial heating, cutting, and welding processes and hydrogen is a superior fuel than many conventional hydrocarbons. However, efficient mixing and operation, safety in handling, high turndown ratios, etc. need cognizance for design, development, and demonstration of hydrogen flame burners to harness the hydrogen power. Empirical studies on different research burners (including the coaxial tube) conducted in the past focused on flame characterization, stability, NOX emissions, and burner performance. Schefer et al. [2] evaluated stability characteristics of lean premixed hydrogen combustion. Nine channels were used to supply air. Hydrogen (or its blend with methane) was injected radially inward (i.e. in crossflow) through the orifices
located on either side of each channel. Mixing was thus achieved in a compact mixing zone before the exit from burner. Lean combustion was considered to reduce the NOX emission potential. Uniform mixing could be achieved for high momentum ratio of fuel and primary air. Since the maximization of coaxial air helps in shortening the flame length and reduction in NOX emission from nonpremixed jet flames [3], parametric studies are needed to find the optimal parameter combination that helps in NOX reduction. Shortening of the flame results in an overlap of flame and high velocity regions near the injectors. The residence time necessary for NOX formation is thus not available to hot gases. Experimental data of Feikema et al. [4] show that coaxial air and small enough velocity-to-diameter ratio of fuel jet result in a stable flame and reduced NOX emission. Swirl extends the blowout limit because it reduces the local velocities near the forward stagnation point of recirculation vortex where the flame is stabilized. Unlike hydrocarbon
* Corresponding author. Tel.: þ91 512 259 6086; fax: þ91 512 259 7626. E-mail addresses: [email protected], [email protected] (S.Y. Jejurkar). 0360-3199/$ e see front matter Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2013.02.085
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Nomenclature a b CI D Df e MS Nb Ncp Nnn Nrep
intercept in Eq. (1) model constants in Eq. (1) confidence interval diameter degree of freedom residual mean square number of blocks number of center points number of non-numeric factors number of replications
flames, prompt NOX formation mechanism is not active in hydrogen flames due to lack of any hydrocarbons and instead, temperature-sensitive thermal NOX mechanism is a dominant contributor. Chen and Driscoll [3] showed that thermal NOX in H2 flames (in terms of NOX emission index, EINOX) varied with the cube of flame length in the presence of coaxial air. However, too much coaxial air or premixing resulted in NOX increase per unit flame volume. Driscoll et al. [5] also found that weak radiation in hydrogen flame in comparison to methane was helpful in reducing NOX. In the absence of coaxial air, Damkohler number, (S2L/a)/(UF/dF), is the scaling parameter and EINOX scales as (UF/dF)1/2. UF is jet exit velocity, dF is jet diameter, SL is the maximum laminar burning velocity, and a is thermal diffusivity. Hwang et al. [6] varied turbulence intensity of annular air in the coaxial design to measure its effect on hydrogen jet flame. Their results verify that increased turbulence intensity enhances mixing and decreases flame length. As a side-effect of this strategy, flame temperature reduces due to high strain rate and conversion of NO to NO2 increases. Turbulence intensity is also beneficial for controlling NOX downstream of the flame as it promotes mixing and reduces pockets of high temperature where NOX formation rates can shoot up. Mixing of fuel and air external to the burner is preferable for operational ease and external fueleair contacting patterns allowing efficient mixing in a small enough zone as near to the injector as possible are consequently desirable. Evidently, swirling motion of air and/or fuel is the easiest route to enhance mixing efficiency in these burners. Swirling air also helps to reduce emission of harmful NOX. Mixing under fuellean conditions also helps in NOX reduction [3]. Further, due to its small quenching diameter, orifice diameters for hydrogen should be small enough to avoid flame stabilization very near the orifice or flashback in the worst case. In combination, these strategies could lead to a significant decrease
Fig. 1 e Crossflow injection scheme of fuel hydrogen into swirling combustion air.
Nr P SD SN SS x y y
total number of runs power level standard deviation swirl number sum of squares factors response sample mean
Greek symbols ε error term in Eq. (1) F equivalence ratio
in emissions, provided flame stability is not impaired in the process. Optimal set of operating conditions is required for a particular application and side-effects such as loss of heat due to high amount of coaxial air should be addressed. Different fueleair contacting patterns for external mixing are currently being evaluated in our laboratory on these lines as part of a program to obtain more efficient hydrogen burner for industrial applications. NOX emission is an important performance criterion in the program. In this paper, some empirical results on one such configuration are reported. Experiment protocols based on the concepts of design of experiments or DoE [7] are being implemented frequently by the fuel cell community, as evident from a number of studies published in this journal, but only sporadically by the combustion community [8,9]. Consequently, apart from evaluation of burner performance, our focus was also on the efficient experimentation strategy. As the systematic evaluation of multiple design configurations is a lengthy and expensive process, experiments were devised using the statistical concepts [7]. The objective of these experiments was to obtain an empirical relationship between NOX emission and the two operating parameters viz. global equivalence ratio between inlet H2 and air streams and the desired power level. In what follows, first the burner configuration in question is described. Next, the experimental program followed to arrive at the empirical relationship is discussed. Results of the experiments along with the diagnostics used for testing the validity of empirical correlation are then presented.
2.
Burner configuration
The crossflow configuration shown schematically in Fig. 1 is considered in the present paper. Hydrogen fuel is injected externally into the combustion air through three orifices arranged circumferentially on the lateral surface of the burner head. One centric orifice is also used in addition to the circumferential ones. Thus, division of fuel injection into additional streams in comparison to the conventional axial injection strategy is the major design change considered in the new configuration. The radial outflow of fuel jets is directly into the path of swirling combustion air arranged around the burner head. Radial fuel jets exit 2.5 mm downstream and centric fuel jet exits 5 mm downstream of the air
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Fig. 2 e Comparisons of NOX emissions from the axial fuel injection configuration (e-e) against the proposed crossflow configuration (e:e).
exit, respectively. It is expected that such an arrangement would result in fast mixing of fuel and air external to the burner head and flame stability envelope might be widened. NOX emissions from the proposed burner configuration are compared in Fig. 2 against the single orifice design in which only the centric orifice (D ¼ 4 mm) was retained and lateral orifices responsible for the crossflow were absent. Emission levels reduced with the use of crossflow design in the range of Fglobal of interest to this study.
3.
Experimental program
3.1.
Experimental design
The experimental design and subsequent analysis is performed using Design Expert [10], a specialized DoE and statistical analysis software. Experimental design is generated using the full factorial design method [7] and necessary information for this step is collected in Table 1. Two-level factorial designs assume that a linear model as in Eq. (1) can adequately explain the effects of factors. y¼aþ
n X i¼1
bi xi þ
n XX j
bji xi xj þ ε
Main effect is the effect of a factor when considered alone. Mathematically, it is the difference between the average responses at the two possible levels (extremes in the range of factor values) of a factor [7]. It is necessary that the chosen factors be mutually independent. However, in some cases, the difference in the response between the levels of one factor is not the same at all levels of the other factors. This situation indicates the presence of interaction among the factors. Interaction effect is simply the average difference in the main effects of a factor vis-a`-vis the other factor. Importance of interaction effects is judged by the magnitude of bji relative to bi in the linear model of Eq. (1). Consideration of these interaction effects augments the basic linear model and accounts for curvature in the response function, relevance of which in the present case is demonstrated subsequently in Section 4.5. However, when the third term cannot account for curvature adequately (higher order effects are also important), then it is necessary first to obtain an estimate of the error (ε) involved in using Eq. (1) and then to reduce the effects of second-order effects. Both these requirements are satisfied by the addition of center points to the basic design. Number of center points is equal to the number of replications for the combination of the centroids of factors (combination a0 b0 of Fig. 3a). Fig. 3b depicts the possible four combinations of the two factors according to the 22 factorial design. The actual number of runs is determined from Eq. (2) after adjusting for the number of replications and center points. Nr ¼ 2n Nrep þ Ncp Nb þ Ncp Nnn
(2)
Non-numeric factors are not present in the present case (Nnn ¼ 0) and the experiments were conducted sequentially in a single block (day) so that Nb ¼ 1. Operating parameters, global equivalence ratio _ f =m _ a Þ=ðm _ f =m _ a Þstoich Þ and desired power level (P), ðFglobal ¼ ðm are the factors, while NOX emission (in ppm) is the flame response to simultaneous changes in Fglobal and P. NOX emissions are known to depend upon a number of other factors [3e6], including intensity of swirling, O2 concentration in combustion air, and inlet air temperature. In this work, we fixed the swirl intensity of incoming atmospheric air and considered only Fglobal and P, in the interest of economy. Power level is treated as a combustor design requirement to be prescribed independently and the burner performance for the prescribed power level is then empirically modeled. In this arrangement, it is necessary to maintain fuel and air mass
(1)
i
Second term on the r.h.s. represents main effects xi of each of the factors, while the third term represents interaction effects xixj. b represents the model coefficients which can be dimensionless. The gain in efficiency by using the factorial design instead of the classical one factor-at-a-time approach is modest in the present case (relative efficiency of 1.5 in terms of the number of required factor combinations) because the number of factors is small. However, factorial design accommodates the interaction effects that are difficult to detect with the conventional approach [7]. This advantage will be revealed in the analysis of experimental data.
Table 1 e Preliminary data for the experimental design. Factors, n
2
Factor statistics
Numeric
2
Fglobal
P (kW)
Non-numeric, Nnn Response Replicates, Nrep Blocks, Nb Center Points (per block), Ncp Runs, Nr
0 1 3 1 4
0.2 0.6 0.4 0.17
5 10 7.5 2.17
16
Min. Max. Mean SD
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Fig. 3 e (a) Generic representation of full factorial designs with center points, (b) possible factor combinations, and (c) design space.
flow rates to confirm to the desired power level and equivalence ratio. Preliminary unplanned experiments identified the useful ranges of these operating conditions; Fglobal: 0.2e0.6 and P: 5e10 kW because a stable flame was observed in this range. The factors are chosen to represent the extremes of these ranges and such a choice automatically excludes the possibility of choosing the factors randomly from within the ranges. In other words, we apply the model proposed in Eq. (1) for the fixed effects [7]. Standard order in which experiments could be performed is obtained by arranging the test sequence such that only one factor is introduced at a time and the second factor is combined successively with the preceding ones [7] (i.e. a, b, and ab). This order is randomized and the resulting parameter combinations arrived at after randomization with respect to the run order are arranged in the order shown in Table 2. Experiments were performed sequentially in the order shown in column 2. Fig. 3c graphically establishes the design space, within which the resulting correlation is valid. Numbers near the design points indicate the number of replications for a given design point. Both factors were varied simultaneously for a run.
3.2.
Experimental setup
Experimental setup in Fig. 4a includes a hydrogen gas cylinder, pressure regulator, mass flow meter, and the insulated combustor. Air line consists of compressor, pressure
regulator, manometer, settling chamber, and the Swirler (swirl number, SN ¼ 0.67). Swirler was constructed from eight vanes (vane angle 45 , ID 30 mm, thickness 2.5 mm) and fitted concentrically to the fuel port. Flow rates of hydrogen were varied from 28 to 140 lpm corresponding to a power output of 5e10 kW. Air-flow rates were in the range 50e400 lpm for each
Table 2 e Experimental design for NOX emission. Standard order 5 1 14 6 15 9 2 7 3 11 12 13 16 10 4 6
Run order
Factor 1 (Fglobal)
Factor 2 (P, kW)
Response (NOX, ppm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.6 0.2 0.4 0.2 0.4 0.2 0.2 0.2 0.2 0.6 0.6 0.4 0.4 0.6 0.6 0.6
5 5 7.5 10 7.5 10 5 10 5 10 10 7.5 7.5 10 5 5
27 3 23 4 21 3 3 3.5 4 60 57 20 22 57 27 28
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Fig. 4 e (a) Experimental arrangement, (b) direct luminosity photographs of hydrogen-air swirling flames obtained with the crossflow configuration.
hydrogen flow rate. The combustor is made of stainless steel (SS304L) cylinder (ID 80 mm, OD 90 mm, height 430 mm). Fig. 4b shows the direct flame luminosity photographs at three Fglobal, from which some features can be extracted qualitatively. The swirling flame appears to have stabilized around the burner rim and three luminous regions corresponding to the radial orifices are visible. Flame is obscure at its periphery, possibly due to high burning velocity of hydrogen fuel and turbulence. It also touches the walls, especially near the injection points due to radial injection of fuel jets. The flameewall contact could significantly alter flow-field near the flame base, especially with respect to the formation of
Table 4 e List of ordered factor effects and sum of squares for the experimental design.
Table 3 e Statistics of the flame response. Response statistics Min. Max. Mean SD Max/min
secondary flow structures. Further, flame volume increases and its luminosity decreases with equivalence ratio. Quantitative analysis of post-combustion gases was performed using a hand-held analyzer (Kane-May, Model KM900) able to measure O2, CO, CO2, NO, total nitric oxides (NOX), and SO2 concentrations. The stainless steel sample probe is aligned with the flow at a height of 440 mm from the burner base. Tip of the probe is located on the cylinder axis. The sample probe is water-cooled to quench NO conversion reactions but condensation of water vapor present in the sample is avoided. Sampled gas mixture is
NOX (ppm) 3 60 22.6563 20.0871 20
Model term A (Fglobal) B (P) AB
Effecta
Sum of squares
% contribution
39.25 15.42 15.25
4621.69 713.02 697.69
76.36 11.78 11.53
a Standardized effect.
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Fig. 5 e Half-normal probability plot for the effects A, B, and AB. Selected effects are represented by highlighted - and error estimates are shown by :.
then passed in succession to in-line water trap, particle filter, and sensors.
4.
Results and discussion
4.1.
NOX emission data
Sequential experimental runs yielded the NOX emission for each combination of operating parameters. The complete dataset is collected in the last column of Table 2, while major statistical figures are summarized in Table 3. The NOX emissions ranged from 3 to 60 ppm and the ratio Max/Min indicates variation over the entire design space. It is useful to decide whether any transformation of the raw response data is needed. The decision to use response data without transformation was based on the observations that residuals are normally distributed (Fig. 8) and the difference between minimum and maximum values of response is not very large.
4.2.
Estimation of factor effects
Significant effects are identified first. Eq. (1) accounts for the effects x1 for A, x2 for B, and x1x2 (interaction of A and B). Quantitatively, an effect denotes the change in average flame response to the change in a factor from low to high level and can be estimated using the contrast constants [7]. In this work, it is estimated using the regression model and is calculated as the difference between marginal mean and overall mean. It is in fact the coefficient of the model term and is half the value calculated using Yates method [7]. Sum of squares (SS) is simply the sum of squares of the deviations of the responses due to a change in factor from its mean, while the % contribution is the normalized SS per term.
The resulting estimates are listed in Table 4. The importance of each of these effects is judged by plotting the absolute values of effect estimates against their half-normal probability (also called cumulative normal probability) shown in Fig. 5 considering only the positive half of the normal probability distribution. A standardized effect is obtained by transformation of data by subtracting each value from the mean and diving it by the standard deviation. Significant effects are away from the line as outliers while the normally distributed effects tend to have zero mean and cluster around the straight line [11]. This plot ensures correct selection of effects as it also guards against the possibility that one or more of the effects included in the model are not random. Similar information is also obtained from the % contribution column of Table 4. The line is drawn to fit all the error estimates indicated by : and passes through the origin indicated by C. This fit depends upon what effects are included in the final model. While the choice of statistically significant effects is also aided by other expedients like a Pareto chart, the important guiding principle is the prior knowledge of the system under consideration. Large effects appear on the top right side of the plot in Fig. 5 and relatively unimportant effects are located on the lower left. This demarcation is not distinct in this case as power level (B) and the interaction (AB) effects are located in the upper half towards the center of the plot. Nevertheless, the effect of Fglobal is more significant than the other two but the interaction effect (AB) is not negligible and needs closer inspection. Effects A, B, and AB are plotted in Fig. 6a, b and c, respectively. A represents the design points corresponding to different factor combinations. From Fig. 6a, NOX emissions could be reduced by operating the burner with low enough Fglobal. Same effect is obtained by operation at reduced powers (Fig. 6b), which however results in under-utilization. Such straightforward conclusions must be qualified in the presence of interaction between the factors. The effect of Fglobal at the low power level (P ¼ 5 kW) shown in Fig. 6c by the continuous black line is weaker than the effect when power level increases to 10 kW. This is indicated by increased NOX emission when Fglobal is increased from 0.2 to 0.6 at P ¼ 10 kW. Fig. 6c also reveals that reduction in NOX levels can still be attained at higher power level, if Fglobal is kept as low as possible.
4.3.
Analysis of variance and empirical model
As mentioned earlier, center points are added in the present experimental design to guard against second-order effects on curvature. Following the usage by Montgomery [7], we call the model including center points as the “full model” (also termed as unadjusted model [10]) and that excluding center points is called “reduced model” (or adjusted model [10]). Analysis of variance (ANOVA) is performed on both these models and Tables 5 and 6 summarize the ANOVA results. Among the statistics, F-value is the ratio of variances of model or curvature against the residual variance. Larger F-value is desirable for model and curvature since noise contributions to variances are small. On the other hand, lack of fit F-value indicates adequacy of fit and should be small. F-value for curvature (lack of fit) in adjusted (unadjusted) model is 6.11, which indicates that second-order effects are significant and additional runs
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Fig. 6 e (a) Main effect of factor A: Fglobal, (b) main effect of factor B: P, (c) interaction effect. A show the design points, - are the predicted outcomes, and the vertical bars at either ends of lines show the least significant difference at 95% CI.
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Table 5 e ANOVA table for the adjusted model. Sum of squares
Degree of freedom
Mean square
F-value
p-value
Remark
Fglobal (A) P (B) AB Model Curvature Pure error
4621.69 713.02 697.69 6032.40 7.13 12.83
1 1 1 3 1 11
4621.69 713.02 697.69 2010.8 7.13 1.17
3961.45 611.16 598.02 1723.54 6.11 e
<0.0001 <0.0001 <0.0001 <0.0001 0.031 e
e e e Statistically significant Significant e
Total
6052.36
15
e
e
e
e
are dimensional quantities (kW1, for both terms), they do not connote any physical significance in the present case. Empirical model in terms of coded factors (1 for low level and þ1 for high level) is as in Eq. (4).
Table 6 e ANOVA table for the unadjusted model. Sum of Degree Mean Fpsquares of square Value Value freedom Fglobal (A) P (B) AB Model Residual Lack of fit Pure error Total
Remark
y ¼ 22:66 þ 19:624global þ 7:71P þ 7:634global P
4621.69
1
4621.69 2778.08 <0.0001
e
713.02 697.69 6032.40
1 1 3
19.96 7.13
12 1
713.02 428.59 <0.0001 e 697.69 419.38 <0.0001 e 2010.8 1208.68 <0.0001 Statistically significant 1.66 e e 7.13 6.11 0.031 Significant
12.83
11
1.17
e
e
e
6052.36
15
e
e
e
e
might be necessary. Further, F-value for the unadjusted model (1208.68) is high enough for the model to be statistically significant. p-value (probability of seeing the observed F-value if the null hypothesis is true) indicates significance of model terms and it should be <0.05 [10]. Thus, Fglobal (A), P (B), and AB are the significant model terms. Ability to obtain an empirical model of the processes underlying the observations is an attractive feature of statistical design of experiments methodology because sample size is much smaller than the classical method and design space is searched comprehensively. The empirical model shown in Eq. (3) is obtained using regression analysis. y ¼ 6:03125 16:254global 3:01667P þ 15:254global P
(3)
y is the NOX emitted in ppm and P is in kW. Although, the regression coefficients for P and FglobalP as reported in Eq. (3)
(4)
Model coefficients in Eq. (4) are directly comparable with each other and each is estimated at same precision (standard error of 0.37). This comparison reveals that Fglobal is the important factor. It should be noted that all the data analysis reported herein is carried out in terms of coded factors. Mechanisms governing combustion, heat and mass transfer, and fluid flow are non-hierarchical as interactions of different processes (and thereby variables) are dominant and coupled non-linearly. Hence, even though the analysis software enforces model hierarchy (all lower order terms must be present in the model if a higher order term is to be included), we examine the effects of excluding the P and FglobalP terms using the comparison of the scale-invariant regression coefficients of Eq. (4). A non-hierarchical model results after removing the P term in Eq. (4). The predicted data are examined for the changes in the width of 95% confidence intervals, with and without the inclusion of P term and the interaction effect exemplified by FglobalP [12]. Table 7 summarizes the sample calculations done on one design point for which P ¼ 10 kW and Fglobal ¼ 0.6. Changes in the resulting empirical models in each case are reflected in the predictions vis-a`-vis the experimental data. Since the width of 5e95 confidence interval increases when FglobalP and/or P are excluded and predictions become worse, we conclude that FglobalP and P should be retained for ensuring the predictive reliability of the empirical model even though they are statistically less significant than Fglobal alone. Validity of the empirical model is easily established (albeit with less reliability) from Fig. 7, which shows a scatter plot of the predicted and empirical data for all the factor
Table 7 e Examination of the predictive reliability of empirical model in Eq. (4) in the absence of FglobalP and/or P (operating conditions: Fglobal [ 0.6 and P [ 10 kW). Included factor effects All All Only Fglobal Only Fglobal and P Only Fglobal and FglobalP
NOX (ppm)
SD
CIlow
CIhigh
Remarks
58 57.6 42.3 49.98 49.9
e 1.29 10.11 7.43 7.51
e 56.04 34.0 42.31 42.14
e 59.18 50.56 57.674 57.672
Mean of three replicates Full model No interaction effect No interaction effect Non-hierarchical model
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 8 ( 2 0 1 3 ) 5 1 6 5 e5 1 7 5
Fig. 7 e Parity plot for comparison of predictions of Eqs. (3) or (4) with the experimental data. Dashed lines represent the range of uncertainty.
combinations considered in the design. Predictions are based on the adjusted (reduced) model in which the center points are not included. The even split of points by the 45 line shows that no transformation is required for the raw data [10]. Further, the reliability of model predictions depends upon the outcome of diagnostic checks described further.
4.4.
Diagnostic checks
Since the hypothesis of no difference in treatment means is not satisfied in practice [7], ANOVA results are backed up by checking whether the residuals ðeij ¼ yij yi Þ are normally distributed. The residuals indicate the number of standard deviations separating the actual and predicted response. A number of graphical tests in Figs. 8e10 indicate the adequacy of model as suggested by Montgomery [7]. Fig. 8 is the normal probability plot of residuals that approximates a straight line and hence indicates that the error is normally distributed. Internally Studentized residuals (calculated by dividing the residual with its estimated standard deviation) are used. Outlier points can be detected using standardized residuals pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (defined as eij = SSerror =N a). For normally distributed errors, standardized residuals have zero mean and unity variance, and the point for which residual is larger than 3 or 4 standard deviations from the mean is considered as outlier [7]. In fact, the half-normal probability plot of effects drawn in Fig. 5 can also give an indication of the presence of an outlier data point if the straight line fitting the error estimates (:) does not pass through the origin [13]. Based on this criterion, it is evident that outlier point/s are not present in the dataset. Further, variation of these residuals with run order (Fig. 9) is a measure of correlation between them. Random scatter among the residuals in Fig. 9 shows that randomization has worked and the effects of unaccounted variables are minimal. Correctness of model is further checked by plotting the residuals against model predictions in Fig. 10. Lack of a pattern indicates that
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Fig. 8 e Normal probability plot for residuals eij (experimental data of Table 2). Black - show values of NOX near the lower limit of 3 ppm, fainter ones near the 60 ppm limit, and the grey denotes values in the middle of the range 3e60 ppm.
the model is correct and its assumptions are valid. Variance should not depend upon the magnitude of the response. Note that measuring instruments are used extensively in combustion experiments, and above statement is generally not true in our case. An outward conical pattern from left to right (small residual for small response magnitude and large for large responses) in the residual-prediction plot similar to Fig. 10 indicates such a situation. The examination of data in this respect is inconclusive. It might be necessary to force the variance to a constant by performing transformations on the collected responses and conducting ANOVA again [10]. Finally, residual-factor plots in Fig. 11 check whether the variance not accounted for by the model is different for
Fig. 9 e Residual variation with the run order.
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 8 ( 2 0 1 3 ) 5 1 6 5 e5 1 7 5
Fig. 10 e Plot of residuals against model predictions (Eq. (3) or (4)) to check for the model correctness.
Fig. 12 e Flame response surface in the form of (a) contour map of NOX emission and (b) as a three-dimensional surface. Color code shows variation in the range 3e60 ppm and design points are overlaid in the shape of A.
different levels of a factor. The plot should exhibit a random scatter. Pronounced curvature may indicate a systematic contribution of the independent factor not accounted for by the model.
4.5.
Interpretations
We set out to physically interpret the results with the help of contour plot shown in Fig. 12a, which is a two-dimensional map of flame response over the design space. The response surface is continuous over this space. A less user friendly, but more detailed representation is the 3D surface of Fig. 12b and a is the 2D projection of this surface on the FeP plane. Following observations can be made based on these maps. Fig. 11 e Residual plots for checking against any unaccounted effects (a) residual against Fglobal and (b) residual against P.
NOX emissions remain low at low power level and global equivalence ratios.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 8 ( 2 0 1 3 ) 5 1 6 5 e5 1 7 5
At any power level, NOX emission increases with equivalence ratio. However, at a fixed equivalence ratio, the increase in NOX levels is very slow comparatively as the power level is increased. Lowest emission occurs for the leanest flame (Fglobal < 0.3), while the highest NOX emission occurs for comparatively fuel-rich flame operating with high power levels. This corresponds to region near the top right corner of Fig. 12a. Finally, it will be recalled from earlier discussion (cf. Fig. 6c) that the effect of equivalence ratio is small at the low power level and significant at high power level. Best results (minimum NOX) are obtained at low enough equivalence ratios, irrespective of the power level at which the combustor operates. The contour map of Fig. 12a is a convenient representation of these interaction effects. Best operating conditions are located in the left hand region of Fig. 12a. At a more fundamental level, low power flames produce comparatively low temperatures. Since, NOX formation and destruction is a highly temperatureesensitive reaction and its formation rate increases with temperature [11], we can see why the combinations of low factor levels produce lower NOX. It can also be easily seen that high NOX levels at the other extreme are explained on this basis.
5.
Concluding remarks
In this work, a novel hydrogen burner was characterized in terms of its emission potential using experiments designed by applying the full factorial design method. The arrangement of lateral orifices in addition to the centric orifice of some conventional configurations significantly reduces NOX emissions in hydrogen combustion. This is achieved by improved mixing in the crossflow arrangement and elimination of hot gas pockets in the flame zone. The full factorial design method was instrumental in establishing an empirical correlation of NOX emission with the global equivalence ratio and desired power level, viz. y ¼ 22:66 þ 19:624global þ 7:71P þ 7:634global P. The regression coefficients are dimensionless. Only a small number of experimental runs were needed to arrive at the relationship and operating parameters were varied simultaneously, unlike the traditional method in which only one operating parameter is varied at a time. This correlation could be useful in evaluating the performance of burner in a future design activity. Global equivalence ratio is the dominant factor in determining emission level, although the combined effects of power level and global equivalence ratio are on the same
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order as the power level. Finally, a useful operating region for this kind of burners is in the range of low enough global equivalence ratios irrespective of the power level since the emissions are reduced in this range.
Acknowledgments Experiments reported in this paper were performed as part of a research project funded by the Ministry of New and Renewable Energy, Government of India and its support is gratefully acknowledged. Mr. Ashish Tiwari and the personnel of Combustion Laboratory provided assistance in the experiments described in this paper.
references
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