N2

Combustion and Flame 161 (2014) 2890–2903

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Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e

Liftoff heights of turbulent non-premixed flames in co-flows diluted by CO2/N2 Yuzuru Nada a,⇑, Kazuo Matsumoto b, Susumu Noda b a b

Department of Energy System, The University of Tokushima, 2-1 Minami-Josanjima, Tokushima 770-8506, Japan Department of Mechanical Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku, Toyohashi 441-8580, Japan

a r t i c l e

i n f o

Article history: Received 25 October 2013 Received in revised form 31 January 2014 Accepted 12 May 2014 Available online 3 July 2014 Keywords: Turbulent lifted flame Dilution Entrainment Liftoff height Premixed model Large eddy model

a b s t r a c t The objective of this study was to propose a new model for the prediction of the liftoff heights of turbulent flames diluted by the entrainment of burned gases. In combustion furnaces with the internal recirculation of burned gases, mixtures of fuel and oxidizer are diluted with recirculated burned gases through entrainment into the gas jets. We focused on the effects which dilution resulting from entrainment has on the stabilization mechanism of lifted flames. In order to investigate the effects of dilution on liftoff height, we employed a concentric burner incorporating fuel, oxidizer and co-flow gas nozzles. The recirculated burned gas was simulated by co-flow air diluted with either N2 or CO2 gas. Liftoff heights were observed to increase with decreasing O2 concentrations in the co-flow gas when maintaining a constant O2 concentration in the oxidizer, due to dilution resulting from entrainment of the diluted co-flow gas. The liftoff heights obtained with co-flow gases diluted by CO2 were greater than those obtained when diluting with N2 due to both thermal and chemical dilution effects. The conventional premixed model was not able to predict the liftoff trends observed in this study and we therefore propose a modified premixed model which takes into account the dilution effect resulting from entrainment. In this model, the amount of entrained co-flow gas is evaluated according to the self-similarity law of a round jet. Non-dimensional liftoff heights based on this modified model exhibit excellent linear correlation with non-dimensional fuel gas velocities, even when various co-flow gases are used for dilution. The conventional large eddy model was also modified in the same manner and the results obtained from the modified model exhibit satisfactory correlation. Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction Combustion technologies based on dilution of the combustion mixture with recirculated burned gases are a useful means of reducing NOx and soot emissions from combustion furnaces. MILD combustion [1] is a representative reduction technology which is also sometimes referred to as high temperature air combustion [2] or flameless oxidation [3]. In MILD combustion furnaces, the fuel gas and oxidizer are generally supplied from separate nozzles into the furnace as high speed jets, after which each gas mixes with recirculated burned gas through entrainment by each jet until the bent fuel jet merges with the oxidizer jet [4,5]. Mixing with the recirculated burned gas dilutes both the fuel gas and the oxidizing gas while simultaneously raising the temperatures of the diluted gases, thus achieving a uniform temperature distribution throughout the furnace and allowing a low flame temperature, ⇑ Corresponding author. Fax: +81 886569124. E-mail address: [email protected] (Y. Nada).

which reduces NOx emissions through the Zel’dovich mechanism [6]. In general, there are three fundamental effects of dilution in terms of reducing NOx and soot emissions: the pure dilution, thermal and chemical effects [7,8]. The pure dilution effect is due to the reduction of reactant concentrations resulting from mixing with burned gases, while the thermal effect results from the greater specific heat of CO2 compared to that of air, since an increase in the specific heat reduces the flame temperature. The chemical effect is caused by modification of the equilibrium state in some chemical reactions; the addition of CO2 to the oxidizer, for example, increases the extent of the reaction CO2 + H ? CO + OH, thus decreasing combustion intensity. Additional NOx reduction technologies which are also based on dilution are still being developed [9,10]. Noda et al. [10] investigated the effects of burned gas dilution on NOx emissions from laboratory-scale cylindrical furnaces which incorporated a triple concentric burner supplying fuel and oxidizer at different initial velocities. In these furnaces, a concentric jet entrains the burned

http://dx.doi.org/10.1016/j.combustflame.2014.05.007 0010-2180/Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Y. Nada et al. / Combustion and Flame 161 (2014) 2890–2903

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Nomenclature A B d def H K Km l Lu M mi Re r rI SL ST Thr u u0 U x X

parameter used in Eq. (4) describing the decay of streamwise velocity parameter used in Eq. (5) describing the evolution of the jet half-width inner diameter of the nozzle effective diameter of the fuel nozzle mean liftoff height dilution ratio mixture dilution ratio (volume ratio of diluents to mixture) integral length scale jet half-width mass flow rate mass of gas i in a fluid Reynolds number radial coordinate radius of a cylindrical control volume laminar burning velocity turbulent burning velocity threshold value for binarization streamwise velocity root mean square fluctuation velocity bulk velocity axial coordinate volume fraction

gas as it is recirculated upstream by vortices formed in the lower section of the furnace. The reactants and the entrained burned gas are mixed with one another in the mixing layer of the jet and thus both the fuel and the oxidizer are diluted with the burned gas. The Noda study found that NOx emissions from the diluted flames can be correlated with the Reynolds number based on the furnace’s inner diameter, which is a measure of the quantity of entrained burned gas. This successful scaling of the NOx emissions demonstrates the importance of dilution through entrainment with regard to the NOx emissions characteristics of furnaces with recirculation vortices. The entrainment of hot recirculated burned gas stabilizes a flame due to the temperature rise of the diluted reactant gases [11] while simultaneously destabilizing the flame via dilution effects [12–14]. In the present study, we examine the effects of dilution resulting from entrainment on flame stability. Many researchers have previously investigated dilution effects on flame stability; Min and co-workers investigated dilution effects on flame lifting from a burner rim both experimentally [12] and theoretically [13], using different oxidizing gas mixtures containing CO2, N2 and Ar. This work demonstrated that dilution with CO2 has the greatest influence on flame lifting. Moreover, the contribution of the pure dilution effect to flame lifting was found to be the most significant, followed by the thermal effect, while the chemical effect is relatively small. Min and Baillot [14] also demonstrated that oxidizer dilution (which they term air-side dilution) with CO2 increases the liftoff height by reducing the flame propagation speed, indicating the significant influence of dilution on the stability of the lifted flame. Other researchers have investigated fuel dilution effects on liftoff height [15–19], and have demonstrated that fuel dilution increases liftoff height as well as the oxidizer dilution. Min and Baillot [14] also concluded that the influence of oxidizer dilution is greater than that of fuel dilution based on liftoff height scaling. Lock et al. [20] explained the differing effects of fuel

Yi Zi

a b

j m q h f

mass fraction of species i mixture fraction of gas i thermal diffusivity mass flow rate ratio of fuel gas to oxidizer (= MO/MF) density ratio of fuel gas to ambient gas viscosity density azimuthal coordinate distance from a virtual origin

Subscripts 0 jet axis C co-flow gas E gas flowing out from control volume EN entrained co-flow gas F fuel gas K diluted gas O oxidizer O2 oxygen st stoichiometric condition Superscript  relative value to co-flow gas

and oxidizer dilution on blowout characteristics in terms of deficient reactant quantities. In previous studies [12–20], dilution effects on liftoff heights were investigated using dual concentric burners in which either the fuel or the oxidizer is pre-diluted before being released. In contrast, combustion furnaces with burned gas recirculation dilute the fuel and oxidizer via entrainment by each jet. The amount of ambient gas entrained into a main jet is known to be proportional to the distance from the virtual origin of the jet [21], which indicates that the extent of dilution increases with increasing distance from the burner exit. The burned gas dilution responsible for increasing liftoff height occurs in the region from the nozzle exit to the flame base, and hence an increase in the liftoff height results in enhanced dilution, leading to a further increase in the liftoff height. In prior research [12–20], the effects of initial temperature and reactant concentrations on liftoff height were investigated. Even though these studies contributed significantly to the modeling of lifted flames, they were not aimed at elucidating the relationship between the liftoff height and the dilution level and thus did not do so. Predictions of liftoff heights and blowout limits have continued to be the main subjects of combustion research in recent years since flame stabilization is essential for safe combustion. A number of prediction models were proposed by previous studies [22,23], and can be roughly classified as the extinction, premixed and large eddy models [22]. Peters and Williams [24] applied the local extinction theory for laminar diffusion flame when studying the flame lifting mechanism. In their extinction model, liftoff height is deemed to be the length of the region in which flame extinction occurs due to pronounced flame stretch, and thus this height is expressed as a function of the critical scalar dissipation rate for local extinction of laminar flamelets. However, many results obtained from laser diagnostics (see, for example, Ref. [25]) support a different stabilization mechanism based on flame

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propagation as described below. In addition, Peters noted in a recent publication [26] that stabilization at the liftoff height occurs as the result of premixed flame propagation and not by diffusion flamelet quenching. Vanquickenborne and van Tiggelen [27] proposed a stabilization mechanism in which lifted flames are stabilized at the position where the turbulent burning velocity matches the local mean velocity of a main jet. Based on this mechanism, Kalghatgi [28] demonstrated a linear correlation between liftoff height and fuel velocity normalized by the laminar burning velocities of stoichiometric mixtures for three hydrocarbon flames with different fuel nozzle diameters. In the premixed model proposed by Kalghatgi [28], the ratio between turbulent and laminar burning velocities is assumed to be proportional to the square root of the turbulent Reynolds number based on the integral length scale. Peters [26] also proposed a premixed model in which turbulent burning velocity is a function of the turbulent Damköhler number. In the large eddy model proposed by Miake-Lye and Hammer [29], re-entrained burned gases into unburned gas mixtures stabilize the lifted flame through the mixing by large eddies in the mixing layer of the main jet. The liftoff height is predicted on the basis of the relationship between the critical strain rate and the chemical time scale. Many analyses meant to assess the viability of the above conventional models, in particular the premixed model and the large eddy model, have been reported for lifted flames with different types of fuel dilution [15–18] and oxidizer dilution [14]. In these studies, the conventional models were found to provide excellent correlations between non-dimensional liftoff heights and fuel velocities regardless of the dilution. These tests, however, were limited to lifted flames associated with pre-diluted fuel and oxidizer streams. In the case of lifted flames in furnaces with burned gas recirculation, the liftoff heights are not expected to show the same correlations, because the dilution level varies with the liftoff height. Therefore, in order to apply the conventional models to diluted flames produced through entrainment, some modifications are needed to take into account the variation of the dilution level. In addition, the conventional models do not include the dilution effects on turbulent burning velocity. Kobayashi et al. [30] found that the ratio of the turbulent to laminar burning velocities decreases with CO2 dilution under high pressure conditions. Tang et al. [31,32] demonstrated that N2 dilution enhances the effect of flame stretching on the laminar burning velocity of a propane/ air premixed flame. The objective of this study was to propose a new model for predicting liftoff heights of flames diluted through the entrainment of burned gases, focusing on the dilution effect rather than the temperature rise effect. In this work, the effect of dilution with co-flow air, which simulates the recirculated burned gases, on liftoff heights is demonstrated through experimental investigations. In addition, the burned gas dilution is evaluated according to the self-similarity of an isolated round jet. Finally, the conventional premixed model proposed by Kalghatgi [28] and the large eddy model of Miake-Lye and Hammer [29] are modified so as to predict the liftoff heights of flames diluted with the entrained gases.

2. Experimental methodology 2.1. Experimental apparatus The objective of this study was to develop a new method for predicting the liftoff heights of flames diluted with recirculated burned gases. While it is possible to use a combustion furnace with burned gas recirculation [9–11] to measure liftoff heights, this has a disadvantage in that the residual O2 concentration in the

(a)

(b) Fig. 1. Schematics of experimental apparatus, showing (a) side view of the apparatus and (b) cross-section of the co-flow burner.

recirculated burned gas cannot be controlled independently of the fuel gas velocity. This is because changes in fuel gas velocity vary the composition of the burned gases, since the residual O2 concentration depends on the mass flow rate of the fuel gas. In addition, it is difficult to distinguish between the dilution effect and the temperature rise effect when studying the effects of entrainment of the hot recirculated burned gas. In order to avoid these problems, we employed a co-flow burner instead of a combustion furnace for the experiment trials. Figure 1 shows schematics of the experimental apparatus used in this study. The co-flow burner consists of concentric fuel, oxidizer and co-flow nozzles. The co-flow nozzle surrounding both the fuel and oxidizer nozzles supplies various co-flow gases with low O2 concentrations which simulate the recirculated burned gas. It should be noted that the burner configuration employed in this study (fuel/oxidizer/co-flow gas) is not directly relevant to specific practical applications and experimental facilities. This burner however provides a reasonable approximation of a combustion furnace incorporating internal burned gas recirculation. In such furnaces, burned gases in the downstream region of the combustion flow are moved upstream via convection due to the reverse flows of the recirculation vortices and are then entrained by the combustion flow. In contrast, in the burner employed during this work, the main fuel jet entrains the surrounding oxidizer and co-flow gases which simulate the recirculated burned gas. In other words, the burner used here reproduces the entrainment of burned gases without the convection process induced by the reverse flow. This burner configuration therefore allows control over the O2 concentration in the entrained gas. Studies on combustion furnaces with internal burned gas recirculation are ongoing [9–11], the results of which should be useful with regard to improving the performance of small furnaces, including small boilers and radiant tube burners.

Y. Nada et al. / Combustion and Flame 161 (2014) 2890–2903

The central fuel nozzle of the burner is made of a stainless tube with an inner diameter of 2 mm and a rim thickness of 0.5 mm. To achieve fully developed velocity distributions at the nozzle exit, the nozzle length is set to 900 mm. The oxidizer nozzle coaxially surrounding the fuel nozzle is also a stainless tube with a 30 mm inner diameter, a 450 mm length and a 1.0 mm thickness. For flow uniformity, a 180 mm long honeycomb is installed into the nozzle at an upstream location 15 mm from the nozzle exit. The co-flow nozzle has a large inner diameter of 205 mm so as to prevent the intrusion of ambient air into the fuel gas jet. A 5 mm thick, sintered metal 40 lm filter is mounted on the exit of the co-flow nozzle to ensure uniform velocity distribution at the exit. In addition, the lower section of the co-flow nozzle is filled with ceramic beads. The volume flow rate of each gas is controlled with needle valves and calibrated rotameters. The burner is enclosed in a housing with a 500 mm  500 mm cross-section to minimize flow disturbances originating from external factors. The housing has a glass window on the lateral side to allow the capture of direct photographic images of the lifted flames formed above the burner. In this paper, a cylindrical coordinate system (x, r) is used which has its origin at the center of the fuel nozzle exit and in which the x-coordinate is measured vertically upward. 2.2. Experimental conditions for liftoff height measurements A mixture of 60% C3H8 and 40% N2 by volume was used as the fuel gas. When employing our experimental burner, the application of fuel without N2 dilution blew the flames out at lower liftoff heights, at which heights the dilution effect through the entrainment of co-flow gases is very weak. Thus we added N2 to the fuel in order to obtain sufficient liftoff heights and thus dilution by the entrainment of co-flow gases. The oxidizer and the co-flow gas were mixtures of a diluting gas (either N2 or CO2) and air supplied from a compressor. Table 1 summarizes the experimental conditions in terms of the compositions of oxidizers and co-flow gases. In this table, the LF1 flame is that which results from both an oxidizer and a co-flow gas such that the O2 concentration in the oxidizer (XO2,O) is equal to that in the co-flow gas (XO2,C). This situation essentially reduces the triple concentric co-flow burner used here to a dual concentric burner similar to that employed by other researchers [12–20]. The reductions in the O2 concentration in each gas with regard to LF1 flames are due to the addition of N2. The co-flow gases used for the LF2 and LF3 flames were diluted by either N2 or CO2, respectively, with air used as the oxidizer for both flames. Comparison between liftoff heights of the LF1 for XO2,O = 21% and LF1 for XO2,O 6 20% shows the effect of oxidizer dilution under the dual concentric burner configuration as reported by Min and Baillot [14]. The difference between the liftoff heights of the LF1 for XO2,O = 21% and LF2 flames results from the dilution effects through entrainment of the diluted co-flow gas, which is the main subject of this study. The influence of different additive gases for the purposes of dilution is seen in the difference

Table 1 Compositions of oxidizers and co-flow gases. Oxidizer

Co-flow

O2 (%) (= XO2,O)

N2 (%)

CO2 (%)

O2 (%) (= XO2,C)

N2 (%)

CO2 (%)

LF1

21 20 19

79 80 81

0 0 0

21 20 19

79 80 81

0 0 0

LF2

21 21

79 79

0 0

20 19

80 81

0 0

LF3

21 21

79 79

0 0

20 19

75 72

5 9

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between liftoff heights of the LF2 and LF3 flames. Each gas was used at ambient temperature since we wished to focus on the dilution effects rather than the temperature rise effect. The bulk velocity of the fuel gas in the nozzle (UF) was increased at intervals of 1 m/s, up to the value at which blowout occurred. The bulk velocities of the oxidizer and the co-flow gas were maintained at 0.2 m/s during all the experimental trials, such that the fuel jet behaved as though weakly confined by the co-flow gases [22,33]. 2.3. Liftoff height measurements Liftoff heights were determined by the analysis of photographic images of the lifted flames taken with a digital camera (Nikon D90) through the glass window on the lateral side of the housing, as shown in Fig. 1(a), using a shutter speed of 1/125, an f-number of 3.5 and an ISO speed of 400. It should be noted that photographic images were captured directly, without the application of any optical band pass filters. Each photographic image captured by the digital camera contained R (red), G (green) and B (blue) components and the intensity value of each component was represented by 8 bit data. The spatial resolution of the resulting photographs was 0.2 mm/pixel. The focal point of the camera was set at a height of 80 mm from the fuel nozzle exit, and thus the camera looked down towards the flame base of the lifted flame. The error introduced into the measurements of liftoff heights by the focal point height was estimated to be less than 1 mm, based on the geometry between the positions of the observed flame base and the camera. The instantaneous liftoff height was defined as the height of the leading edge of a lifted flame, as calculated from an image binarized with an adequate threshold of blue component luminosity (= 70 in 8 bit data). The data processing procedure used during the calculation of instantaneous liftoff heights may be summarized as follows; (1) the intensity values of the blue components are extracted from a flame picture, (2) these intensities are binarized based on a designated threshold value in order to identify the flame region, and (3) a data processing program automatically detects the edge of the flame region by scanning the binarized image. The lowest position in the detected edge is deemed to be the leading flame edge. The instantaneous liftoff height is considered to be the vertical distance between the leading edge and the fuel nozzle exit. The mean liftoff height (H) was determined by time-averaging the instantaneous liftoff heights obtained from more than 200 photographs. The repeatability of replicate liftoff heights was within 2 mm. The optimized threshold value of 70 for the binarization of images was determined based on the threshold dependence of the mean liftoff height. Figure 2 shows the relationship between the threshold value (Thr) and the mean liftoff height under the experimental conditions of UF = 12 m/s and XO2,O = XO2,C = 21%. Error bars in this figure denote the standard deviations associated with the calculated instantaneous liftoff heights. In this figure, the mean liftoff height (= 25 mm) determined based on a threshold value of 70 is represented by a broken line. Figure 3(a) shows the intensity distribution of the blue component extracted from an image acquired under the same conditions as were used to acquire the data in Fig. 2. The high intensity region appearing in the lower sections of the images corresponds to a blue flame formed at the flame base, while the upper regions of each image correspond to luminous flames formed downstream. Figure 3(b–d) present binarized images of the flame produced under the above conditions when applying threshold values of 10, 70 and 170, respectively.

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Fig. 2. Relationship between threshold value (Thr) and mean liftoff height (H) under experimental conditions of UF = 12 m/s and XO2,O = XO2,C = 21%. The broken line denotes the value of liftoff height obtained when applying a threshold of 70. At Thr = 190, the standard deviation of liftoff height, as indicated by the error bar, is 41.6 mm and therefore exceeds the magnitude of the mean liftoff height.

The red dots shown in these figures denote the positions of the detected flame edge. When applying a threshold value of 10, the calculated mean liftoff height will be much lower than that obtained with a threshold value of 70, due to incorrect detection of the flame edge. As shown in Fig. 3(b), the majority of the detected flame edge at the bottom of the image coincides with the burner exit (indicated by the circle in this figure). The light emitted from the downstream luminous flame is scattered by the surface of the sintered filter mounted on the exit of the burner, which is responsible for the incorrect detection. When applying moderate threshold values (30 6 Thr 6 110), the flame height is almost constant at approximately 25 mm regardless of increases in the threshold value. At higher threshold values (130 6 Thr), however, this procedure cannot correctly detect the edge of the dense blue flame formed at the flame base. Within the threshold range 170 6 Thr, both mean liftoff height and the variance in height increase with increasing

threshold values, since these threshold values incorrectly locate the position of the downstream luminous flame (Fig. 3(d)). Under different experimental conditions, trends similar to that in Fig. 2 can be observed. Therefore, the optimal threshold value is in the range of 30 6 Thr 6 110. In this range, the liftoff height increases by 2 mm with increasing threshold values. We therefore selected a threshold value of 70 so as to eliminate the influence of scattered light and also to allow detection of the edge of the dense blue flame. We have confirmed that the above procedure successfully detects the flame edge in every image. It is well-known that variations in liftoff heights with fuel gas velocity show hysteresis characteristics [34]. We therefore initially lifted flames from the fuel nozzle tip with an arbitrarily high fuel gas velocity and then re-adjusted the velocity to a designated value. Accordingly, the fuel velocity at which the flame is formed on the burner corresponds to the reattachment velocity. In this study we used a commercial digital camera (a Nikon D90) without band-pass filters in order to measure the liftoff heights. Thus, the detectable wavelength range of chemiluminescent emission in our measurement system was dependent on the transmission characteristics of the window glass used in the hood, as well as the spectral sensitivity of the sensor mounted on the camera. The window was made of commercial silicate glass and so absorbed a significant amount of the ultraviolet component of the flame emission. Although we were unable to find any literature concerning the spectral sensitivity of the D90 camera, Sigernes et al. [35] reported the sensitivity of the Nikon D300, which is in the same series. They reported that the blue channel sensitivity of the D300 exhibits a peak at 460 nm, and the range over which the sensitivity is greater than 50% of the maximum value is from 420 to 500 nm. In addition, the sensitivity at wavelengths less than 400 nm is nearly equal to zero. Considering Sigernes’s results, we infer that the measurement system used in this study was not responsive to the ultraviolet components of the emission. It is well known that chemiluminescent emissions at wavelengths around 460 nm are attributed to excited OH, CH and C2 species in premixed propane/air flames (see, for example, Ref.

Fig. 3. Influence of threshold value on the flame edge detected under experimental conditions of UF = 12 m/s and XO2,O = XO2,C = 21%. The binarization is based on the intensity value of the blue component in the acquired flame picture. The red coloration applied to (b–d) denotes the detected flame edges. (a) shows the intensity distribution of the blue component extracted from a flame image, while (b–d) are the result of binarization based on the intensity distribution of (a) and threshold values of 10, 70 and 170, respectively. In (b), the red dots in the green circle result from incorrect detection of flame edges due to the scattering of light from a sintered air filter plate.

Y. Nada et al. / Combustion and Flame 161 (2014) 2890–2903

[36]). Assuming that the spectral sensitivity of the D90 is similar to that of the D300, our measurement system primarily detects the CH (0, 0) and C2 (1, 0) emission bands. The emission of CH (0, 0) is likely dominant since this emission has a particularly high intensity. Our measurement system based on the D90 is unable to detect emissions from excited OH since the associated wavelengths are in the ultraviolet, and this means that the acquired photographic images do not involve information about OH distribution. Therefore the lack of information about OH could possibly introduce some level of error during the calculation of the instantaneous liftoff heights. Kojima et al. [37] conducted numerical simulations of laminar premixed methane/air flames based on a kinetics mechanism including excited-state species. This analysis generated spatial profiles showing both mole fractions and emission intensities of excited OH, CH and C2. These profiles demonstrated that the peak value position of emission intensity for each excited species is located in the reaction layer of the premixed flame, and the difference between the positions for different species is within 0.2 mm. These results suggest that the possible liftoff height error introduced by a lack of ultraviolet sensitivity is on the order of 0.1 mm. This error is therefore likely less than that introduced by the selection of the threshold value during image processing.

2.4. Velocity and species concentration measurements The velocities and species concentration distributions of nonreactive jets were measured to evaluate the amount of entrained co-flow gas in the region from the fuel nozzle exit to the flame base. In these measurements, CO2 was used as an alternative to C3H8 for safety reasons. A previous study [38] has reported that the initial density ratio between the main jet and the ambient gas strongly affects the development of the jet. In the measurements of velocities and species concentrations of the non-reactive jets, the density ratio between the main jet gas and the co-flow gas can be maintained at the same value as that applied during the measurements of the reactive jets. The Reynolds number of the jet, however, decreases from 5800 to 3800 at UF = 20 m/s due to the increase in the viscosity of the main jet gas. The O2 concentration in the co-flow gas was set to 16% via the addition of N2 so as to improve the accuracy of the species concentration measurements. Although this oxygen concentration is at least 3% lower than the value applied during measurements of the reactive jets, the influence of this lower concentration on velocity measurements is negligible due to the small difference in density between the co-flow gases. The gas temperature affects the development of the jet by varying the density ratio between the main jet and the ambient gas. The temperatures of the gases used in the non-reactive jet trials were measured and found to equal ambient temperature ( 293 K) and therefore we believe that the effects of the gas temperature on our measurements will be minimal. Velocity measurements were made using an anemometer (KANOMAX model 1010) with a 1.5 mm long hot wire and a data logger with a 100 Hz sampling frequency. The mean velocity was obtained by averaging the measured instantaneous velocities over a span of 5 s. O2 and CO2 concentrations were measured with a flue gas analyzer (HORIBA MEXA-554J) and an L-shaped gas sampling probe with an inner diameter of 1 mm and an outer diameter of 2 mm. Gases sampled from the non-reactive jet were sent to the gas analyzer at a constant flow rate of 4 L/min. The measured concentrations were recorded using the data logger with a 100 Hz sampling frequency over a span of 5 s. The mean concentrations thus obtained were used to evaluate the distribution of the co-flow gas mixture fraction (Eqs. (13)–(15) and Fig. 12). The hot-wire probe and the L-shaped gas sampling probe were installed into

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the main jet through an open section on the lateral side of the housing. 3. Results 3.1. Effects of dilution with entrained co-flow gas on liftoff height Figure 4 shows the variations in the liftoff heights of the LF1 flames with the fuel gas velocity. The upper abscissa in this figure provides the Reynolds number based on the inner diameter of the fuel nozzle and the fuel gas velocity and the error bars represent standard deviations of measured instantaneous liftoff heights. The overall behavior observed for the LF1 flame for XO2,O = 21%, which is the base flame without dilution through entrainment, is consistent with that reported by previous studies [28,39,40]. A laminar lifted flame is formed above the fuel nozzle exit at UF = 5 m/s, whereas flames at UF 6 4 m/s reattach to the nozzle exit. The higher liftoff height of the laminar lifted flame observed at UF = 5 m/s is due to the high sensitivity of the liftoff height to the fuel jet velocity, as reported by Lee and Chung [39]. As the fuel gas velocity increases, the flame front at the flame base begins to wrinkle and the position of the flame base is subsequently reduced to a height of 20 mm at UF = 8 m/s. This is attributed to a decrease in the breakup height with increasing fuel gas velocity [40]. A further increase in the fuel gas velocity induces transition from a laminar flame to a turbulent flame. At UF > 13 m/s, the liftoff height increases linearly with the fuel gas velocity, in agreement with the results reported by Kalghatgi [28]. The liftoff heights of the LF1 flames are seen to increase with decreasing values of both XO2,O and XO2,C over the entire range of fuel gas velocity, which is the same as the trend reported by Min and Baillot [14]. This trend can be easily explained in view of the premixed model [28]: the propagation speed of the premixed flames formed at the flame base decreases with decreasing O2 concentration and hence the flame base recedes from the burner exit. The specific heats of the oxidizers diluted with N2 are comparable to that of air and, moreover, the use of N2 ensures that the additive gas does not participate in the combustion reaction. The decrease in the propagation speed is therefore exclusively due to the pure dilution effect. Figure 5 shows the liftoff heights of LF2 and LF3 flames. In these data, the effect of dilution through the entrainment of the co-flow gas is evident in the liftoff height behavior. As expected, the liftoff heights of LF2 flames measured at UF > 12 m/s increase as the O2 concentration in the co-flow gas decreases, even though the O2 concentration in the oxidizer is maintained at a constant 21%. This is due to dilution effects through the entrainment of the co-flow

Fig. 4. Effects of the oxidizer and co-flow gas O2 concentrations on liftoff height.

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Fig. 5. Effects of dilution with different co-flow gases on liftoff heights at constant O2 concentration in the oxidizer (XO2,O = 21%).

gas. Flammable mixtures formed in the vicinity of the flame base are diluted with the entrained co-flow gas and the liftoff heights therefore increase with decreasing values of XO2,C. In contrast, the increase in the liftoff heights at UF < 9 m/s is negligibly small. This is attributed to the low Reynolds numbers of the fuel gas jets. The Reynolds numbers associated with the jets at UF < 9 m/s have a maximum of 2600, which indicates that the jets at UF < 9 m/s are not fully turbulent. The amount of entrained co-flow gas is therefore small and hence the dilution effect is reduced. The liftoff heights of the LF3 flames are greater than those of the LF2 flames. The variation in the LF2 flame liftoff heights is mainly due to the pure dilution effect, in the same manner as observed with the LF1 flames. The LF3 flames, however, are subjected to additional thermal and chemical dilution effects, which lead to a further decrease in burning velocity and are responsible for the higher liftoff heights of the LF3 flames. Liu et al. [8] investigated the chemical effect of CO2 dilution on soot and NOx emissions through the analysis of elementary reaction pathways and found that CO2 addition on the oxidizer side enhances the reactions CO2 + H ? CO + OH and CO2 + CH ? CO + HCO. The HCO produced through the second reaction is consumed by the subsequent reaction HCO + H + M ? CH2O + M. Enhancement of these reactions via CO2 dilution leads to a decrease in the H radical concentration. Liu et al. [41] also reported that these reactions compete with the most important chain branching reaction, H + O2 ? O + OH, which leads to significant reduction of the laminar burning velocity. Liu also presents numerical simulations involving the fictitious species FCO2 which demonstrate that the contribution of the thermal effect to the burning velocity is probably greater than that of the chemical effect. It is also observed that the liftoff heights of both LF2 and LF3 flames rapidly increase with increases in the fuel velocity around H = 40 mm. After this initial rapid increase, further dilution with co-flow gas increases the liftoff height. These behaviors can be explained in terms of the mixing layer thickness of the fuel jet; large eddies in the mixing layer can entrain the co-flow gas outside the oxidizer flow when the mixing layer thickness is larger than that of the oxidizer flow. The entrainment thus causes a rapid increase in the liftoff heights through dilution with the co-flow gas. Based on the results shown in Fig. 5, the region with a mixing layer thick enough to entrain the co-flow gas appears to be downstream at a location more than 40 mm from the nozzle exit. It should be noted that minimal dilution of the co-flow gas induces a significant increase in liftoff height. In the case of the LF3 flames, a decrease in the O2 concentration of the co-flow gas of only 1.0%, from XO2,C = 21% to 20%, increases the liftoff height

twofold. This high sensitivity to the dilution effect indicates that so-called air-side dilution [14] occurs in the cold jet region between the nozzle exit and the flame base. The entrained co-flow gas does not mix with the fuel gas but rather mixes with the oxidizer and hence the dilution occurs on the oxidizer side. In a previous study concerning a stagnation point reverse flow (SPRF) combustor under non-premixed flame conditions [11] a similar mixing mode was observed such that fuel gas issued from a central nozzle was shielded from recirculated burned gas by annular air while the annular air and the recirculated burned gas mixed with one another in the shear layer between the streams. Lock et al. [20] conducted numerical simulations of laminar lifted flames with pre-diluted fuel and air in order to examine the effectiveness of fuel-side and air-side dilution. According to their proposed mechanism, if the stoichiometric mixture fraction between the diluted air and fuel is less than 0.5, indicating a flame formed on the air side, air-side dilution significantly increases liftoff height because oxygen is the deficient reactant in this flame. Under all the experimental conditions applied in the present study, the mixture fraction between fuel and oxidizer is less than 0.1 and therefore air-side dilution significantly increases the liftoff height, as shown in Fig. 5. Consequently, the LF2 and LF3 flames can be regarded as flames with air-side dilution through entrainment, which simplifies calculations of the extent of dilution, as described below. The conventional premixed model [28] was employed to generalize the liftoff heights of the flames diluted with various co-flow gases. The applicability of the prevailing model to flames with diluted oxidizers [14], diluted fuel gases [15,16] and hot co-flow gases [17,18] was examined, which showed good linear correlations between liftoff heights and fuel velocities under different conditions. In previous studies [42,43], the authors have concluded that the premixed flame correlation is adequate for lifted flames with liftoff heights more than 20 times the inner diameter of the fuel nozzle. As shown in Fig. 5, most of the measured liftoff heights of the turbulent lifted flames are above 40 mm, which is 20 times the inner diameter, and therefore this model should be applicable to the analysis of lifted flames in this study. In the premixed model proposed by Kalghatgi [28], the relationship between liftoff height and fuel gas velocity can be expressed as a linear function of nondimensional liftoff height (HSL/mF) and non-dimensional fuel gas velocity (j1.5UF/SL).

HSL

mF

/ j1:5

UF : SL

ð1Þ

Here, j is the density ratio between the fuel and ambient gases. In order to examine the applicability of the conventional model to lifted flames diluted with entrained co-flow gases, we applied the premixed model without any modifications to the diluted flame data. Table 2 shows the values of laminar burning velocities used in the premixed model, where SL,O denotes the laminar burning velocity based on a stoichiometric mixture of fuel gas and oxidizer, and SL,C denotes the velocity based on co-flow gas. These velocities are obtained from the numerical simulation of a 1D premixed flame using the CHEMKIN PREMIX code [44] along with a detailed kinetic mechanism for propane [45]. Figure 6 presents a comparison between the calculated and measured [31,46,47] laminar burning velocities. Here Km is the mixture dilution ratio, defined as the ratio of diluent gas volume to mixture volume. The mixture dilution ratio was also used to represent the dilution level in some previous studies [31,47]. In contrast, Akram et al. [46] used a different definition based on the ratio of diluent gas volume to the total volume of fuel and diluent gases. While several data sets for propane/air mixtures highly diluted with N2 are available in literature [31,46,47], we unfortunately were unable to find any data for such mixtures diluted with both N2 and CO2. It should be noted that the stoichiometric mixtures formed in the LF3 flames

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Y. Nada et al. / Combustion and Flame 161 (2014) 2890–2903 Table 2 Laminar burning velocities of stoichiometric mixtures. XO2,O (%)

XO2,C (%)

SL,O (m/s)

SL,C (m/s)

LF1

21 20 19

21 20 19

0.37 0.33 0.28

0.37 0.33 0.28

LF2

21 21

20 19

0.37 0.37

0.33 0.28

LF3

21 21

20 19

0.37 0.37

0.27 0.19

(a)

Fig. 6. Effect of mixture dilution ratio on laminar burning velocity.

were diluted by both N2 originating from the fuel gas and CO2 from the co-flow gas. Results previously reported by Tang et al. [31] and Zhao et al. [47] are represented by approximated lines over the range of Km < 0.3. It can be seen that there is a large difference between measured velocities which may be due to differences in experimental methodology. Tang et al. [31] employed a spherically propagating flame in a combustion vessel while Akram et al. [46] used a planar flame propagating through a diverging channel. In addition, Zhao et al. [47] employed a single jet-wall stagnation flame. The numerical results of our study exhibit good agreement with the line approximating Zhao’s data. The burning velocities of mixtures diluted with both CO2 and N2, which correspond to the mixtures in the LF3 flames, are lower than those diluted solely with N2, due to both chemical and thermal effects. The non-dimensional liftoff heights and fuel gas velocities based on Eq. (1) are plotted in Fig. 7(a) with the laminar burning velocity of a stoichiometric mixture consisting of the fuel gas and the corresponding oxidizer (SL,O) shown in Table 2. Accordingly, the dilution effects through the entrainment of co-flow gas are not considered in this model. The density ratio j in Eq. (1) was derived based on the densities of the fuel gas and the oxidizer. The results shown in this figure are those for the turbulent lifted flames in the range of UF P 12 m/s. However, this figure contains the results for LF3 flames for which XO2,C = 19% at UF = 10 m/s and UF = 11 m/s for comparison purposes. The results for the LF1 flames at XO2,O = XO2,C = 21% and at XO2,O = XO2,C = 20% converge into a single line with a slope of 51, which is close to the value of 50 reported by Kalghatgi [28]. As discussed above, dilution through the entrainment of co-flow gas can be regarded as air-side dilution. In the case of these data, dilution does not reduce the O2 concentration in the oxidizer because XO2,O = XO2,C. The use of the O2 concentration in the corresponding oxidizer is therefore valid when evaluating the laminar burning velocity. Nevertheless, the data for the LF1 flame with XO2,O = XO2,C = 19% deviate slightly from the correlation line. A similar trend was

(b) Fig. 7. Liftoff height correlations between HSL/mF and j1.5UF/SL. Laminar burning velocities are evaluated based on (a) XO2,O and (b) XO2,C.

observed for highly diluted lifted flames in a previous study [14] in which the authors used the density ratio of fuel gas to air rather than the diluted oxidizer to obtain a linear correlation. As the O2 concentration in the co-flow gas is decreased, the slope of HSL/mF vs. j1.5UF/SL for the LF2 flames becomes large, such that the liftoff height values begin to deviate from the linear correlation. These deviations are caused by over-predictions of the laminar burning velocities. The laminar burning velocities used in this model are higher than those of the actual mixtures formed in the vicinity of the flame base because this model does not take into account dilution with the entrained co-flow gas. Note that the deviations for the flames with lower liftoff heights (HSL/ vF < 2000) are smaller than those for the data associated with higher heights (HSL/vF > 3000). According to the similarity law for jets [21], the amount of entrained co-flow gas in the mixture increases with the liftoff height, and thus the influence of the dilution is weak in lifted flames with lower liftoff heights. Therefore, as shown in Fig. 7(a), the deviation from the correlation line becomes small in the case of flames with HSL/vF < 2000. The non-dimensional liftoff heights of the LF3 flames do not agree with those of the LF2 flames even at the same O2 concentrations. The thermal and the chemical effects of CO2 addition cause a significant reduction in burning velocity which leads to further over-prediction of the velocity. Consequently, the non-dimensional liftoff heights of the LF3 flames are higher than those of the LF2 flames. A plot of the LF3 flame with XO2,C = 19% at UF = 10 m/s deviates from the correlation line even though the non-dimensional liftoff height associated with this flame is much lower (1500). This occurs because the fuel jet at UF = 10 m/s is not fully turbulent. Figure 7(b) presents the correlations between non-dimensional liftoff height and non-dimensional fuel gas velocity, normalized by

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burning velocities based on the O2 concentration in the corresponding co-flow gas. j in Eq. (1) is also based on the density of the co-flow gas. The incorporation of the properties of the co-flow gas requires that the oxidizer is assumed to be perfectly mixed with all the co-flow gas issuing from the burner since the amount of co-flow gas is large compared to that of the oxidizer. In contrast to this assumption, the oxidizer is actually mixed only with co-flow gas entrained into the jet, the amount of which is much less than the entire quantity of the co-flow gas. The use of co-flow gas properties, especially the O2 concentration in the co-flow gas, therefore results in under-prediction of the laminar burning velocity and, as a result, the plots of HSL/mF vs. j1.5UF/SL for LF2 flames shift to the lower right in this figure with decreasing values of XO2,C. These plots do, however, tend to approach the correlation line with increasing non-dimensional liftoff height. This is due to the increase in the amount of entrained co-flow gas at greater liftoff heights. The plots obtained from the LF3 flames do not agree with those from the LF2 flames. In previous studies involving scaling of liftoff height [14,16,18] the authors modified the conventional models so as to obtain a linear correlation between normalized liftoff height and fuel velocity. Choi and Chung [18] proposed a modified normalized fuel velocity (= j1.5UF/SL/YF) to allow for the effect of fuel dilution, while Wu et al. [16] changed the order of j in Eq. (1) from 1.5 to 1.0 to obtain linear correlations for hydrogen flames diluted with several gases. Min and Baillot [14] employed the air density instead of the diluted oxidizer density when estimating j in order to extend Kalghatgi’s correlation to air-side dilution configurations. We applied these modifications to the conventional premixed model, but could not obtain satisfactory correlations for diluted flames obtained through entrainment. These failures indicate that the generalization of the liftoff heights of the diluted flames with various co-flow gases requires an accurate estimation of the amount of entrained co-flow gas. 3.2. Evaluations of similarity constants for mean velocity and the amount of entrained co-flow gas In order to obtain a single linear correlation between the liftoff heights and the fuel velocities, we evaluated the amount of entrained co-flow gas on the basis of a mass balance between the fuel gas, oxidizer and co-flow gas. Figure 8(a) shows a schematic of the mass balance in a cylindrical control volume with a radius (rI) large enough to enclose the fuel gas jet. In this figure, the square described by broken lines denotes the control volume. The top of this region coincides with the base of the lifted flame while the lower limit is located at the burner exit. Solid lines represent the outline of the fuel gas jet. The fuel gas, oxidizer and coflow gas flow into the volume from the bottom at mass flow rates of MF, MO and MC, respectively. It should be noted that MC is the mass flow rate of the co-flow gas directly issued from the burner exit in the region where r 6 rI. Another co-flow gas stream also enters into the volume from the lateral side at the same rate as that of the entrained co-flow gas, corresponding to MEN. The mixture of the fuel gas, oxidizer and co-flow gas exits from the top of this region at mass flow rate ME. Figure 8(b) provides a schematic showing the radial distribution of the streamwise velocity at the top of the control volume. In this figure, the velocity distribution splits into two regions with a boundary located at u = UC, where UC is the bulk velocity of the co-flow gas issuing from the burner exit. The mass flow rate corresponding to the upper region (ME1) is that of the main jet entraining the co-flow gas. The mass balance in the control volume is therefore described by the following simple relation.

M E ¼ M E1 þ ME2 ¼ MF þ MO þ M C þ M EN :

ð2Þ

(a)

(b) Fig. 8. Evaluation of the mass flow rate of entrained co-flow gas, showing (a) the mass balance in a cylindrical control volume with a radius much larger than that of the fuel gas jet and (b) streamwise velocity distribution at the upper limit of the control volume.

Self-similarity of streamwise velocity distributions can be found even in variable density turbulent jets [38]. According to the similarity law, the velocity distribution of the jet can be represented by the Gaussian function of excess velocities relative to the co-flow velocity, as in Eq. (3):

u ¼ u0 exp½ðr=Lu Þ2 lnð2Þ; 

ð3Þ

u0

where u = u  UC and is the excess velocity along the jet axis. The jet half-width (Lu) in the right hand side of Eq. (3) is defined as the radius at which u/u0 = 0.5. The inverse of the excess velocity along the jet axis (1/u0) is well-known to be linearly related to the distance from the virtual origin n [22,38] as in Eq. (4):

U F =u0 ¼ 2An=def ;

ð4Þ

where the effective diameter of the fuel nozzle (def) is defined as (qF/qE)0.5dF, in which qE is a reference density. The jet half-width is also reported to be a linear function of n [38], as in Eq. (5).

Lu ¼ Bn:

ð5Þ

Integration of Eq. (3) in both the radial and azimuthal directions with the reference density qE gives the mass flow rate ME,1, defined as in Eq. (6).

ME;1 ¼

Z 2p Z 0

0

rI

qu rdrdh ¼ 8pqE U F def n=C 1 :

ð6Þ

C1 in Eq. (6) is a function of parameters characterizing the decay of the central velocity and the evolution of the jet half width, as shown below.

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C1 ¼

16A B2

lnð2Þ:

ð7Þ

The mass flow rate (ME,2) corresponding to the strip area in Fig. 8(b) may be obtained from the following simple equation when the integral radius rI is much larger than the jet half-width.

M E;2 ¼

Z 2p Z 0

0

rI

p qU C rdrdh ¼ qF U C d2F þ MO þ MC : 4

ð8Þ

The mass flow rate of the entrained co-flow gas (MEN) is then derived from Eqs. (2), (6), and (8), as in Eq. (9).

M EN ¼

  32 n MF  M F : C 1 def

ð9Þ

Here, MF = qFUFpdF2/4. The term MF in Eq. (9) can subsequently be replaced with MF when UF  UC, to give Eq. (10).

M EN

  32 n MF  MF : ¼ C 1 def

Fig. 10. Evolution of the streamwise velocity half-width.

ð10Þ

As shown in Eqs. (7) and (10), the evaluation of MEN requires the similarity constants for mean velocity, A and B, characterizing the development of the fuel gas jet. Figure 9 shows the decay of streamwise velocities measured along the jet axis. It should be noted that the jets used for the velocity and species concentrations measurements are non-reactive. The use of CO2 as an alternative to C3H8 reduces the Reynolds numbers of the main jet associated with various values of fuel velocity. To simplify calculations, the reference density used in the effective diameter is assumed to be the co-flow gas density. Selecting a suitable position for the virtual origin of each jet allows the streamwise velocities to conform to a single line with an A value of 0.077 in Eq. (4). The selected virtual origin exists at a different position for each jet and the positions of the virtual origins for Re = 3800 and 4750 are x = 0.04 and 1.87 mm, respectively, whereas the origin for Re = 2850 is located further downstream at x = 11.12 mm. This is due to extension of the potential core, indicating that the jet for Re = 2850 is not fully turbulent. The evolutions of the streamwise velocity half-widths are shown in Fig. 10. The jet half-width is reported to be more sensitive to the Reynolds number than to the density ratio between the fuel and co-flow gases [38]. Accordingly, Fig. 10 does not include the results obtained for the low Reynolds number jet with Re = 2850. The slope of the approximated line shown in Fig. 10, which corresponds to the value of B in Eq. (5), is 0.091 while the value of C1 resulting from Eq. (7) is 103. Lawn [22] reported values of A and B in his review, in which the similarity constants A and B were represented by aU (= 1/A) and bU (= ln(2)/B2), respectively. Values of A are reported to be in the range from 0.085 to 0.1,

corresponding to values of aU ranging from 10 to 11.8, indicating that the value of A measured in this study, 0.077, is slightly lower than previously published values. In contrast, the value of B determined in this study, 0.091, is in good agreement with previously published values which range from 0.086 to 0.094, corresponding to the bU values from 78.4 to 93.7. In addition, the values of A and B measured in this study agree with the relationship between the similarity constants aU and bU derived from the momentum equation for the self-similar region of a free jet [22], such that the value of aU2/2bU based on our derived values of A and B is unity. These results demonstrate the high level of accuracy of the velocity measurements obtained in this study. Figure 11 shows the radial distributions of streamwise velocity in the similarity form for the jets with higher Reynolds numbers. Each virtual origin is assumed to be at the fuel nozzle exit. The streamwise velocities in the region defined by 25 mm 6 x 6 105 mm essentially coincide with the similarity distribution obtained from Eq. (3) for both jets. The measured heights in the x direction surpass the range of liftoff height values measured for turbulent lifted flames, as shown in Figs. 4 and 5, demonstrating that Eq. (3), in conjunction with appropriate values of A and of B, can reproduce the radial distribution of the streamwise velocity of a cold jet in the region from the nozzle exit to the flame base. As expected, however, the velocity distribution of the low Reynolds number jet (Re = 2850) does not exhibit obvious selfsimilarity (data not shown here). To examine the accuracy of Eq. (10) when predicting the mass flow rate of entrained co-flow gas, we evaluated the mass flow rate based on the measured velocities and species distributions, using the following equation:

MEN ¼

Z 2p Z 0

rI



qZ C urdrdh  MC ;

ð11Þ

0

where ZC is the mixture fraction of the co-flow gas. The mixture fraction of each gas is defined as:

Z i ¼ mi =ðmF þ mO þ mC Þ;

Fig. 9. Decay of streamwise velocities along the jet axis.

ð12Þ

where m denotes the mass of the fluid and the subscript i differentiates between gases. The integration of the co-flow gas mass flux (qZcu) on the right hand side of Eq. (11) can also be expressed as ME  MF  MO. The evaluation of MEN through Eq. (11) requires the values of the velocity, density and mixture fraction. The timeaveraged velocity as shown in Fig. 11 was used as u in Eq. (11) while the density value was estimated based on measured CO2 and O2 concentrations using a state equation at a constant pressure of 0.1 MPa and a temperature of 300 K. Measured species concentrations in the non-reactive jet are conserved scalar, and therefore

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Y. Nada et al. / Combustion and Flame 161 (2014) 2890–2903

(a)

Fig. 12. Radial distributions of the co-flow gas mixture fraction for Re = 3800 at typical heights from x = 25 to 105 mm.

(b) Fig. 11. Streamwise velocity distributions in similarity form for (a) Re = 3800 and (b) Re = 4750.

the mixture fraction of the co-flow gas can be evaluated through the following equations.

Z F þ Z O þ Z C ¼ 1;

ð13Þ

Z F ¼ Y CO2 =Y CO2;F ;

ð14Þ

and

Y O2 ¼ Y O2;O Z O þ Y O2;C Z C :

ð15Þ

Figure 12 presents the radial distribution of the mixture fraction of the co-flow gas (ZC) determined using Eqs. (13)–(15) for a jet with Re = 3800. The high speed CO2 jet issuing from the central nozzle accelerates the slower surrounding oxidizer stream and generates a pressure gradient around the jet which induces radial streams toward the main jet. The co-flow gas is convected toward the center by the induced radial streams, resulting in an elevated co-flow gas mixture fraction in the region of r < 15 mm at a height of 25 mm. Note that the region r < 15 mm is above the fuel and oxidizer nozzles. Eddies subsequently develop in the shear layer of the fuel jet and mix the fuel gas, oxidizer and co-flow gases. At a height of 5 mm, the velocity distribution does not coincide with the similarity form due to the influence of the potential core (not shown here), meaning that there is no entrainment in the early stage of the shear layer. The entrainment process through the vortices, which is described in Eq. (10), is established at a distance from the nozzle exit. It is also evident from this plot that the mixture fraction at the center (r = 0 mm) increases with increasing distance from the fuel nozzle exit, indicating increased dilution due to entrainment of the co-flow gas with distance. The mixture fraction

of co-flow gas approaches unity with radial distance in the measured region corresponding to 25 mm 6 x 6 105 mm, showing that external air does not intrude into the jet. Figure 13 plots the mass flow rates of the entrained co-flow gas as calculated using Eq. (11). The solid line in this figure represents the evolution of the predicted mass flow rate obtained using Eq. (10), applying a C1 value of 103. The virtual origin of each jet is assumed to be at the fuel nozzle exit and therefore n = x in Eq. (10). A linear increase in the mass flow rate with x can be observed in these plots. Because the conventional premixed model does not include the influence of the linear increase in the amount of entrained co-flow gas on liftoff height, the significant deviations evident in Fig. 7(a) appear, especially in the case of flames with higher liftoff heights. The predicted mass flow rate indicated by the solid line in Fig. 13 shows good agreement with the measured values, meaning that Eq. (10), when used with suitable input values for its variables, is able to predict the mass flow rate of entrained co-flow gas with a suitable degree of accuracy. 3.3. Modeling of liftoff heights of diluted flames resulting from entrainment In this section, we modify the conventional models so as to predict liftoff heights of flames diluted with entrained co-flow gases. As pointed out by Min and Baillot [14], the laminar burning velocity which characterizes the leading edge dynamics is a key element in the modeling of liftoff heights. The dilution effect must therefore take into account the laminar burning velocity used in the equations of the conventional models for evaluating turbulent burning

Fig. 13. Evolution of the mass flow rate of the entrained co-flow gas.

Y. Nada et al. / Combustion and Flame 161 (2014) 2890–2903

2901

velocity [28] and chemical reaction time scales [29]. In order to simplify our analysis of the dilution effect on the laminar burning velocity, we assumed that air-side dilution occurs through the entrainment of the co-flow gas, such that the oxidizer is diluted with the entrained co-flow gas while the fuel gas is not. This assumption results from the discussion of the sensitivity of liftoff height to dilution in Section 3.1. In order to evaluate the magnitude of dilution, we introduce an oxidizer dilution ratio (KO) defined as below.

KO ¼

M EN : MO þ M EN

ð16Þ

Substituting Eq. (10) into Eq. (16) gives

KO ¼

KF ; bð1  K F Þ þ K F

ð17Þ

and

  C 1 def : KF ¼ 1  32 x

Fig. 14. Liftoff height correlations based on the modified premixed model for flames diluted with various co-flow gases.

ð18Þ

The mass fraction of species i in the diluted oxidizer (Yi,O,K) is expressed as the weighted average of the mass fractions in the oxidizer (Yi,O) and the co-flow gas (Yi,C) with the dilution ratio, as in Eq. (19).

Y i;O;K ¼ ð1  K O ÞY i;O þ K O Y i;C :

ð19Þ

The mass fraction of species i in a stoichiometric mixture consisting of the fuel gas and the diluted oxidizer (Yi,K,st) is given by the following equation.

Y i;K;st ¼ ð1  Z st ÞY i;O;K þ Z st Y i;F :

ð20Þ

Here, the stoichiometric mixture fraction Zst is also a function of the dilution ratio KO and Yi,F is the mass fraction of species i in the fuel gas (C3H8 or N2). The mass fraction of species i in the mixture near the flame base can be predicted using Eq. (20) at x = H. The laminar burning velocity is estimated using the predicted mass fractions and a laminar burning velocity table, which is a multi-function of the various species of interest (C3H8, O2, N2 and CO2) and is constructed with the results of 1D simulations using the CHEMKIN PREMIX code [44]. Fortunately, under the present experimental conditions, the laminar burning velocity can be estimated with only two parameters: the particular diluent species for the co-flow gas (N2 or CO2) and the O2 concentration of the stoichiometric mixture (from Eq. (20)), since the co-flow gas is air diluted with N2 or CO2. In this study, the laminar burning velocity (SL,K) at each liftoff height was estimated with results obtained from the CHEMKIN simulations shown in Fig. 6. Lastly, we obtain a modified premixed model that includes the dilution effect and is summarized by the equations below.

HSL;K ðHÞ

mF

/ j1:5

UF : SL;K ðHÞ

ð21Þ

The laminar burning velocity used in this model is a function of liftoff height. Figure 14 shows the correlation between non-dimensional liftoff height and non-dimensional fuel gas velocity based on the modified premixed model. j in Eq. (21) is the density ratio of the fuel gas to the corresponding oxidizer. The correlations based on the modified model show good agreement with the linear correlation (the solid line in this figure) obtained from the results for the LF1 flame with XO2,O = 21% and 20%, which demonstrates the validity of the above modification. As shown in Fig. 5, most of lifted flames are stabilized in the far-field, and hence the stabilization mechanism must be based on flame propagation and therefore reflects the influence of dilution on the laminar burning velocity

which characterizes the propagation speed. Some differences remain between the correlation line and the plots for the LF1 flames with XO2,O = 19%, since the modification for evaluating the mass of entrained co-flow gas does not affect the results for LF1 flames because XO2,O = XO,C. The deviations observed with highly diluted flames are discussed in the next section. Although the results for the LF3 flames with XO2,C = 19% are situated near the correlation line the accuracy of the predicted results is not certain. In such cases, the mass flow rates of the entrained co-flow gas are only approximated since the velocity distributions of the low Reynolds number jet do not show an obvious similarity. The above modification can also be applied to the large eddy model, which is superior to the premixed model when describing the stabilization mechanism of lifted flames in the near-field. It is, however, difficult to confirm the advantage of a modified large eddy model because the effect of dilution through entrainment is not obvious in the near-field. Nevertheless, it is worth examining the accuracy of the modified large eddy model in terms of the applicability of the modification to other models. By replacing the laminar burning velocity (SL) with the velocity of the diluted mixture (SL,K), we can obtain a modified large eddy model as follows,

HSL;K ðHÞ

a

/

U F Y F;st : SL;K ðHÞ Y F

ð22Þ

Here, YF is the mass fraction of fuel at the fuel nozzle exit and YF,st is the fuel mass fraction in a stoichiometric undiluted mixture. Kim et al. [17] recommended that thermal diffusivity at the fuel nozzle exit be used as a in Eq. (22) rather than the diffusivity in the burned gas, a modification which essentially reduces the large eddy model to the premixed model. We, however, employed the thermal diffusivities in the burned gases originating from stoichiometric mixtures of the fuel gas and oxidizers in order to reproduce the reentrainment effect of the burned gas. The diffusivity values were obtained from equilibrium calculations based on the detailed kinetics mechanism [45]. Figure 15 shows the correlations resulting from the modified large eddy model. The line in this figure denotes a linear correlation among the plots for all the flames, with a slope of 8.9. Although this slope is lower than the value of 14 proposed by Miake-Lye and Hammer [29], most of the plots converge into a single line just as well as in the modified premixed model. The good linear correlation observed in this work demonstrates the general applicability of the modification in cases where a dilution effect resulting from entrainment must be considered. However, deviations from the correlation line in the case of highly diluted flames

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Fig. 15. Liftoff height correlations based on the modified large eddy model.

(LF1 with XO2,O = 19%) remain, just as in the modified premixed model. 4. Discussion As shown in Figs. 14 and 15, modification of the laminar burning velocity improves the accuracy of the liftoff height predictions under the triple feed configuration. However, deviations still remain between the plots of the LF1 flames with XO2,O = 19% and the correlation lines obtained from the modified premixed and large scale models. LF1 flames are regarded as flames obtained from dual concentric burner configurations and a similar deviation can be observed in Min’s results [14] for highly diluted flames using a dual concentric burner. These results indicate that the conventional models require further refinement with regard to predicting the liftoff heights of highly diluted flames. Under the present experimental conditions, the stoichiometric mixtures formed in the LF1 flames with XO2,O = 19% have a mixture dilution ratio of 11%. It should be noted that the plots of data obtained from highly diluted flames in both the Min study and the present work are situated at the upper regions of each correlation line. This result suggests that either the laminar or the turbulent burning velocity of the stoichiometric mixture near the flame base is over-predicted. Because the liftoff heights measured in this study are 20 times greater than the inner diameter of the fuel nozzle, the stabilization mechanism of the lifted flames within the range of the applied experimental conditions is based on the propagation mechanism. Therefore, the following discussion is also based on flame propagation. The premixed model proposed by Kalghatgi [28] employs the Reynolds number based on the integral length scale Rel to predict the turbulent burning velocity, as follows.

 2 ST u0 l / Rel ¼ ; SL m

ð23Þ

Here, ST is the turbulent burning velocity, u0 is the root mean square fluctuation velocity and l is the integral length scale. Turbulence effects on the premixed flame, however, including the flame stretch and flame wrinkling, will vary with the extent of dilution. Kobayashi et al. [30] investigated the effects of CO2 dilution on the turbulent burning velocity of a methane/air premixed flame under high pressure conditions and found that the ratio of turbulent burning velocity to laminar burning velocity of the non-stretched flame (ST/SL0) decreases with increasing levels of CO2 dilution. This is attributed to the relationship between dilution and Markstein length; dilution increases the Markstein length through increases

in flame thickness, which leads to further decreases in the laminar burning velocity of the stretched flame. Kobayashi concluded that the decrease in the laminar burning velocity lowers the value of ST and accordingly decreases the ratio ST/SL0, where SL0 is the velocity of the non-stretched flame. Tang et al. [31,32] demonstrated that the Markstein length of a stretched propane/air premixed flame increases with increasing amounts of N2 dilution, resulting in decreases in the laminar burning velocity. These results indicate that dilution enhances the loss of laminar burning velocity associated with flame stretching. This effect, however, is not incorporated into the premixed model proposed by Kalghatgi [28], which might be one cause of the deviations observed in the case of highly diluted flames. In the large eddy model of Miake-Lye and Hammer [29], the decrease in the laminar burning velocities of diluted and stretched flames is likely best interpreted as an increase in the chemical time scale. Dilution increases the flame thickness while simultaneously decreasing the laminar burning velocity. Shim et al. [48] investigated the fractal characteristics of turbulent premixed flames obtained from direct numerical simulations, and compared their results with those from other studies. Based on this comparison, they reported that the inner-cutoff scale of the flame front is approximated by an exponential function of the ratio of the turbulence eddy diameter to the flame thickness. This approximated function describes a tendency whereby an increase in the flame thickness increases the inner-cutoff scale, which suggests that increases in flame thickness due to dilution decrease the flame surface area, leading to reductions in turbulent burning velocity. However, Cohé et al. [49] showed that the flame surface density remains constant even with dilution. In light of these reports, the possibility exists that the deviations observed in highly diluted flames in Figs. 14 and 15 are caused by decreases in the local burning velocity due to increases in the Markstein length. It therefore appears that, in the future, the premixed model should be amended to include the stretching effect. In order to apply the modified model to other furnace or burner systems, it is helpful to consider the applicable range of the modification, which is associated with estimation of the mass flow rate of the entrained gas. Amielh et al. [38] showed that the axial velocity decays of different density jets conform to a single line when using the effective diameter. In addition, they demonstrated that the radial distributions of the mean streamwise velocities of different density jets coincide with a distribution in similarity form when applying suitable constants. These results imply that the mass flow rate of entrained gas can be predicted for various lifted flames using the effective diameter and similarity constants. There are, however, significant variations in the values suggested for the similarity constants A and B in the literature [22]. This scatter is due to differences in the turbulent characteristics and the inherent difficulty of calibration during velocity measurements [22]. The range of the scatter corresponds to a range of C1 (Eq. (7)) from 108 to 133, and results in an error of 25% when predicting the mass flow rate of the entrained gas. Therefore, users of the modified model should confirm the similarity constants of their own jet before applying the modified model. As noted in Section 1, mixing with the recirculated burned gases has the effect of raising the temperature of the reactant mixture. Choi et al. [50] revealed that laminar lifted flames with preheated air can be categorized as non-auto-ignited conventional lifted flames, auto-ignited lifted flames with tri-branchial edges and auto-ignited lifted flames with MILD combustion. When the temperature of the diluted mixture is lower than the auto-ignition temperature, the non-auto-ignited lifted flame is expected to be formed, with a stabilized mechanism based on flame propagation. The laminar burning velocity of the diluted mixture increases with increasing mixture temperature, which can likely be predicted

Y. Nada et al. / Combustion and Flame 161 (2014) 2890–2903

using relationships similar to those in Eqs. (19) and (20). Therefore, the modified models proposed in this study should predict the liftoff height of non-auto-ignited conventional flames diluted with high temperature burned gases. When the mixture temperature is higher than the auto-ignition temperature, the flame will be stabilized by the auto-ignition of the diluted mixture. Choi et al. [50] also found that the liftoff height of a flame categorized as an auto-ignited lifted flame is correlated to the corresponding ignition delay time under adiabatic conditions. In the case of auto-ignited flames including MILD combustion, the temperature and species concentrations obtained from Eqs. (19) and (20) would be useful for predicting the liftoff heights, since the ignition delay time should be affected by the dilution and temperature rise effects of the recirculated burned gas. However, it is difficult to evaluate the accuracy of the modified model when applied to MILD combustion while using the present measurement system based on capturing images by camera, since the spectral sensitivity of this imaging system is limited to the visible wavelength region. The MILD combustion flame has quite weak chemiluminescent emissions in the visible wavelength range, and hence the present measurement system may fail to detect the flame edge. Thus there are requirements for future work to predict the liftoff height during MILD combustion by using an improved measurement system. 5. Conclusions The objective of this study was to propose a new method for predicting the liftoff heights of lifted flames diluted with entrained burned gases. In order to investigate dilution effects on the liftoff heights, a burner with three concentric nozzles was employed. The co-flow gas issued from the outermost nozzle of the burner and simulated the recirculated burned gases in an actual furnace. In this scenario, the fuel gas jet entrains both the oxidizer and the diluted co-flow gas in the region extending from the burner exit to the flame base. The oxidizer is diluted with the co-flow gas, which reduces the flame front propagation speed at the flame base. Consequently, the liftoff height of the turbulent flame increases as the O2 concentration in the co-flow gas decreases, even with a constant O2 concentration in the oxidizer. The liftoff heights of flames diluted with co-flow gas containing CO2 are higher than those by N2 due to thermal and chemical dilution effects. The conventional premixed model cannot reproduce these trends because the magnitude of the dilution increases with liftoff height equivalent to the length of the dilution region. In the modified premixed model proposed in this study, the laminar burning velocity of the diluted mixture, which characterizes the propagation speed of the flame front, is estimated based on the amount of entrained co-flow gas calculated according to the similarity law of a jet in still ambient air. The modified premixed model results in a satisfactory linear correlation between non-dimensional liftoff height and non-dimensional fuel gas velocity even when dilution occurs with different co-flow gases. The large eddy model was modified using the same procedure applied during modification of the premixed model and the new large eddy model was also found to give satisfactory correlations. However, there remain slight deviations from the linear correlations in the case of highly diluted flames, which can most likely be attributed to the turbulent combustion aspect of the conventional models. In the future, we intend to work towards improving the prediction accuracy associated with highly diluted flames.

2903

Acknowledgment This work was supported by a Grant for Young Researchers from the JGC-S Scholarship Foundation. References [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] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44]

[45] [46] [47] [48] [49] [50]

A. Cavaliere, M. de Joannon, Prog. Energy Combust. Sci. 30 (2004) 329–366. M. Katsuki, T. Hasegawa, Proc. Combust. Inst. 27 (1998) 3135–3146. J.A. Wünning, J.G. Wünning, Prog. Energy Combust. Sci. 23 (1997) 81–94. G.G. Szegö, B.B. Dally, G.J. Nathan, Combust. Flame 156 (2009) 429–438. M. Mancini, P. Schwöppe, R. Weber, S. Orsino, Combust. Flame 150 (2007) 54– 59. G.G. Szegö, B.B. Dally, G.J. Nathan, Combust. Flame 154 (2008) 281–295. D.X. Du, R.L. Axelbaum, C.K. Law, Proc. Combust. Inst. 23 (1991) 1501–1507. F. Liu, H. Guo, G.J. Smallwood, Ö.L. Gülder, Combust. Flame 125 (2001) 778– 787. K. Shinomori, K. Katou, D. Shimokuri, S. Ishizuka, Proc. Combust. Inst. 33 (2011) 2735–2742. S. Noda, J. Inohae, Z.S. Saldi, Proc. Combust. Inst. 31 (2007) 1625–1632. P. Gopalakrishnan, M.K. Bobba, J.M. Seitzman, Proc. Combust. Inst. 31 (2007) 3401–3408. J. Min, F. Baillot, A. Wyzgolik, E. Domingues, M. Talbaut, B. Patte-Rouland, C. Galizzi, Combust. Sci. Technol. 182 (2010) 1782–1804. H. Guo, J. Min, C. Galizzi, D. Escudié, F. Baillot, Combust. Sci. Technol. 182 (2010) 1549–1563. J. Min, F. Baillot, Combust. Flame 159 (2012) 3502–3517. Y. Wu, I.S. Al-Rahbi, Y. Lu, G.T. Kalghatgi, Fuel 86 (2007) 1840–1848. Y. Wu, Y. Lu, I.S. Al-Rahbi, G.T. Kalghatgi, Int. J. Hydrogen Energy 34 (2009) 5940–5945. K.N. Kim, S.H. Won, S.H. Chung, Proc. Combust. Inst. 31 (2007) 1591–1598. B.C. Choi, S.H. Chung, Fuel 103 (2013) 956–962. J. Oh, Q.S. Khan, Y. Yoon, Fuel 89 (2010) 1492–1498. A. Lock, A.M. Briones, S.K. Aggarwal, I.K. Puri, U. Hegde, Combust. Flame 149 (2007) 340–352. H. Schlichting, Boundary Layer Theory, sixth ed., McGraw-Hill, New York, 1968. C.J. Lawn, Prog. Energy Combust. Sci. 35 (2009) 1–30. K.M. Lyons, Prog. Energy Combust. Sci. 33 (2007) 211–231. N. Peters, F.A. Williams, AIAA J. 21 (1983) 423–429. A. Joedicke, N. Peters, M. Mansour, Proc. Combust. Inst. 30 (2005) 901–909. N. Peters, Turbulent Combustion, Cambridge University Press, U.K., 2000. L. Vanquickenborne, A. van Tiggelen, Combust. Flame 10 (1966) 59–69. G.T. Kalghatgi, Combust. Sci. Technol. 41 (1984) 17–29. R.C. Miake-Lye, J.A. Hammer, Proc. Combust. Inst. 22 (1988) 817–824. H. Kobayashi, H. Hagiwara, H. Kaneko, Y. Ogami, Proc. Combust. Inst. 31 (2007) 1451–1458. C. Tang, J. Zheng, Z. Huang, J. Wang, Energy Convers. Manage. 51 (2010) 288– 295. C. Tang, Z. Huang, J. He, C. Jin, X. Wang, H. Miao, Energy Fuels 23 (2009) 151– 156. A. Wyzgolik, F. Baillot, Proc. Combust. Inst. 31 (2007) 1583–1590. J. Lee, S.H. Chung, Combust. Flame 127 (2001) 2194–2204. F. Sigernes, M. Dyrland, N. Peters, D.A. Lorentzen, T. Svenøe, K. Heia, S. Chernouss, C.S. Deehr, M. Kosch, Opt. Express 17 (2009) 20211–20220. Y. Ikeda, J. Kojima, T. Nakajima, F. Akamatsu, M. Katsuki, Proc. Combust. Inst. 28 (2000) 343–350. J. Kojima, Y. Ikeda, T. Nakajima, Combust. Flame 140 (2005) 34–45. M. Amielh, T. Djeridane, F. Anselmet, L. Fulachier, Int. J. Heat. Mass Transfer 39 (1996) 2149–2164. B.J. Lee, S.H. Chung, Combust. Flame 109 (1997) 163–172. B.J. Lee, J.S. Kim, S.H. Chung, Proc. Combust. Inst. 25 (1994) 1175–1181. F. Liu, H. Guo, G.J. Smallwood, Combust. Flame 133 (2003) 495–497. C.D. Brown, K.A. Watson, K.M. Lyons, Flow Turbul. Combust. 62 (1999) 249– 273. C.P. Burgess, C.J. Lawn, Combust. Flame 119 (1999) 95–108. R.J. Kee, J.F. Grcar, M.D. Smooke, J.A. Miller, E. Meeks, PREMIX: A Fortran Program for Modeling Steady Laminar One-Dimensional Premixed Flame, in: Report No. SAND85-8240, Sandia National Laboratories, 1985. S.G. Davis, C.K. Law, H. Wang, Combust. Flame 119 (1999) 375–399. M. Akram, V.R. Kishore, S. Kumar, Energy Fuels 26 (2012) 5509–5518. Z. Zhao, A. Kazakov, J. Li, F.L. Dryer, Combust. Sci. Technol. 176 (2004) 1705– 1723. Y. Shim, S. Tanaka, M. Tanahashi, T. Miyauchi, Proc. Combust. Inst. 33 (2011) 1455–1462. C. Cohé, C. Chauveau, I. Gökalp, D.F. Kurtulusß, Proc. Combust. Inst. 32 (2009) 1803–1810. B.C. Choi, K.N. Kim, S.H. Chung, Combust. Flame 156 (2009) 396–404.