Extinction of turbulent diffusion flames by Kolmogorov microscale turbulence

Extinction of Turbulent Diffusion Flames by Koimogorov Microscale Turbulence A. YOSHIDA,* T. IGARASHI, and Y. KOTANI Department of Mechanical Engineering, Tokyo Denki University, 2-2 Kanda-Nishikicho, Chiyoda-ku, Tokyo 101, Japan The effects of turbulent straining on the structure and response of cylindrical diffusion fames were studied experimentally by using the counterflow flame configuration formed in the forward stagnation region of a porous cylinder from which propane or methane was ejected. From the shadowgraphs, it was found that the turbulence caused large-scale distortions with small amplitude on a diffusion flame which had a locally laminar structure. The time-averaged flame thickness was three times as large as the laminar flame, qThe turbulent flow field was measured in detail by a hot-wire anemometer. The temperature profiles were determined as functions of the applied strain rate by using a fine-wire thermocouple the thermal inertia of which was compensated electrically. The total strain rate applied to the flame was decomposed into the bulk strain rate induced by the mean flow velocity gradient and the turbulent strain rate which was modelled, in the present study, the latter was modelled by the reciprocal of the Kolmogorov time scale. The total strain rate at which the turbulent diffusion flame was extinguished coincided with the critical velocity gradient at which the extinction of a laminar flame occurred. With the increase of the total strain rate, the turbulent diffusion flame became thinner, and the maximum mean temperature gradually decreased due to the decrease of the maximum temperature within the laminar flamelet. On the other hand, the maximum rms fluctuating temperature was rather insensitive to the total strain rate over a wide range of total strain rates. However, close to extinction, nonreactive holes appeared intermittently in the flame along the stagnation line established in the forward stagnation region of the porous cylinder. These holes led to an abrupt increase in the maximum rms fluctuating temperature and, also, a decrease in the maximum mean temperature very close to the state of extinction. © 1997 by The Combustion Institute

INTRODUCTION The extinction of turbulent flames is important from the engineering point of view and has received attention for a long time. Extinction of a diffusion flame can be caused when the reaction rates of fuel and oxidizer become slower than the rate at which reactants are supplied to the reaction zone by the diffusion process. In a turbulent flow, the steep velocity gradients and high strain rates cause an excess amount of mass and heat transfer which affects the extinction phenomena of diffusion flames. The extinction of a laminar premixed flame has been investigated in detail [1, 2], using the counterflow twin flame configuration (back-toback geometry), and the scalar structure of an aerodynamically strained planar laminar premixed flame is largely insensitive to strain rate variation, even near the state of extinction both for mixtures which are diffusionally neu-

* Corresponding author.

tral [1] and, also, for those which are diffusionally imbalanced [2]. In general, the extinction occurs when the characteristic residence time in the strained flame is reduced, and incomplete combustion occurs both for backto-back and fresh-counter-to-burnt geometries [3]. On the contrary, for the fresh-counter-toburnt geometry, Cant. et al. [4] predicted that strain alone could not induce extinction. A series of investigations [5-8] have been conducted to quantify the scalar structure of a steady-state, aerodynamically strained, adiabatic laminar diffusion flame by using the counterflow diffusion flame established in the forward stagnation region of a porous cylinder. Recently, the extinction of a laminar diffusion flame has been investigated in detail, using a nonintrusive laser-based technique [9]° The laminar diffusion flame, unlike the premixed flame, is sensitive to imposed strain rate variations and it becomes thinner with increasing strain. This leads to an increased amount of reactant leakage, progressive reduction in the flame temperature, and, eventually, extinction of the laminar diffusion flame.

COMBUSTION AND FLAME 109:669-681 (1997) © 1997 by The Combustion Institute Published by Elsevier Science Inc.

0010-2180/97/'$17.00 PII S0010-2180(97)00053-9

670

A. YOSHIDA, T. IGARASHI, AND Y. KOTANI

Turbulence provides additional ways to transport mass and energy in the flow and an extra strain rate through eddy motion. A turbulent premixed flame can be assumed to be an ensemble of laminar flamelets, and the stretch experienced by the flamelet surface has been shown by the transport equation of the surface density to be decomposed into the aerodynamic straining and the stretch due to propagation of a curved flame [10]. In addition, the former consists of the strain due to the mean flow field and the turbulent strain acting in the flame tangent plane. In the counterflow geometry, the bulk flow strain rate can be estimated by the velocity gradient of the mean flow. Kostiuk et al. [11] modelled the turbulent strain rate by the inverse of the Kolmogorov time scale and showed that the extinction of turbulent premixed flames occurs when the sum of bulk flow strain rate and small-scale strain rate exceeds a critical value [12]. Also, for partially premixed and nonpremixed turbulent flames, extinction limits have been found to be correlated with the sum of the bulk flow strain rate and smallscale strain rate [13, 14]. Total strain rates, when the extinction occurred, were found to follow a single curve as a function of air volume fraction in the fuel [14]. Recently, a systematic investigation [15] has been conducted to quantify the role of turbulence in the extinction of a strained, adiabatic turbulent premixed flame, with emphasis on the effect of the small eddies of the Kolmogorov microscale. Of significance is the finding that the extinction of the turbulent premixed flame occurs when the sum of the bulk and turbulent strain rates coincides with the critical velocity gradient at which the extinction of the laminar flame occurs. However, Poinsot et al. [16] suggested, by using the results of the direct numerical simulations, that vortices of the order of the Kolmogorov microscale are too small and decay too quickly to interact with the flame. For diffusion flames in an axisymmetric turbulent shear layer, extinction occurs when a large-scale aerodynamic time scale is small compared with the chemical reaction time scale [17]. It may seem natural that the extinction of such a flame should be affected by large eddies

rather than by small dissipative eddies, because the flame is at first subjected to shear-generated large eddies which break down to smallscale eddies downstream through the turbulent energy cascade. Even for fully developed turbulent flow, it has been suggested that largescale eddies play an important role in the lifting off and blowing out of the jet diffusion flame [18]. On the other hand, the importance of the Kolmogorov-scale eddies has been suggested in [19], where extinction was assumed to occur when the mixing rate in Kolmogorov-scale eddies was faster than the chemical reaction rate. Based on the small-scale straining of laminar diffusion flamelets, a critical value of the mean scalar dissipation rate, X, has been introduced to predict the lift-off heights of jet diffusion flames [20]. It should be noted that X may be nondimensionalised by a chemical time and viewed as the reciprocal of a Damkohler number. Recently, for the premixed flames, the average mass of products created per unit volume of reactants during a flamelet crossing was measured experimentally, which is directly correlated with the scalar dissipation rate [21]. Also, for diffusion flames, the scalar dissipation rate has been measured [22, 23]. The role of the small-scale straining by eddies of Kolmogorov microscale in the flame extinction is still controversial. The mean scalar dissipation rate, X may also be also modelled as a function of the mean turbulent strain rate, a, which is the inverse of a turbulent time scale defined by the turbulent kinetic energy and its dissipation rate [24]. In our previous study, we showed directly that the total strain rate at which extinction of the turbulent flame occurs coincides with the critical velocity gradient at which the laminar diffusion flame is extinguished [25]. In the present study, we have extended the range of the turbulence conditions, and the temperature measurements have been made by using a fine-wire thermocouple the thermal inertia of which is compensated electrically. As in the previous study [25], we adopted the counterflow geometry established in the forward stagnation region of a porous cylinder, from which fuel gas is ejected uniformly into the counterflowing air stream. However, the turbulent

EXTINCTION OF TURBULENT DIFFUSION FLAMES Reynolds number was relatively low. The specific objectives of this study are to measure the extinction limits at high turbulent Reynolds number as a function of bulk flow and turbulent strain rates, and to determine which scale of turbulence plays a crucial role in extinguishing the laminar diffusion flamelets. For this purpose, a new turbulence generator was designed. At the same time, the extinction mechanism is discussed using the results of temperature measurements.

EXPERIMENTAL APPARATUS The experiments were performed using a rectangular chamber of 30 mm × 120 mm crosssection and an uncooled porous cylinder 30 mm in diameter and 30 mm long, as shown in Fig. 1. The air stream at the exit of the converging nozzle had a uniform velocity profile and was of low turbulence level. A turbulenceproducing grid was installed at the nozzle exit. A constant area extension duct 100 mm in length was placed behind the turbulence-producing grid to ensure the establishment of a fully-developed isotropic turbulent flow. In the present study, three kinds of perforated plates (P1-P3) and a specially designed turbulence generator (D]) were used to vary the turbulence characteristics. Illustrated in Fig. 1 is the D] turbulence generator which produces a high turbulent Reynolds number to ensure isotropy

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of small scale eddies [26]. This consists of 18 by 4, a total of 72, closed-end tubes, each of which has four 1.5 mm holes equally spaced around it. The jets impinge on each other and produce intense turbulence. This is a modification of a design developed by Videto and Santavicca [27]. When estimating the velocity gradient, we used the value of the mean velocity, 11, at the center of the extension duct exit, 55 mm upstream from the cylinder surface. Table 1 shows the characteristics of turbulence at the center of the extension duct exit for V = 2.0 m/s. Here, v' is the turbulence intensity (nns fluctuating velocity), L the integral scale of turbulence, and R L, the turbulence Reynolds number based on the integral scale. In this table, r K is the Kolmogorov time scale which will be explained later. The flow field was measured under isothermal flow condition by a hot wire anemometer. Figure 2 shows the temperature measurement system. Temperature was measured with a thermocouple of 50 /zm diameter wire. The thermocouple signal was amplified, linearized and compensated for its thermal inertia, and then the high frequency noise was cut off by a low-pass filter the cut-off frequency of which is 3 kHz. The temperature signal was finally analyzed by an FFT analyzer. This time, we used an analogue compensation system with a fixed time constant for compensation. The time constant was determined by using the characteristic values for air at room temperature. Therefore, the instantaneous value of the compensated temperature signal is slightly in error quantitatively, but the mean values are correct and the instantaneous values provide physical insight into the extinction mechanism of the turbulent diffusion flame.

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RESULTS AND DISCUSSION Flow Field Characteristics

Figure 3 shows the lateral profiles of mean and fluctuating velocities at y = 55 mm for the D 1 grid with V - 2.8 m / s , where P is the mean velocity averaged over the nozzle cross-section. Mean and fluctuating velocities are uniform across the exit cross-section except near the boundaries. Therefore, the fuel flow ejected from the porous cylinder was subjected to a uniform turbulent air stream. Figure 4 shows the mean velocity profiles for V = 2.8 m / s along the stagnation streamline, the origin being placed on the cylinder surface. This graph includes the laminar case for comparison. The solid line shows the velocity profile based on the potential flow theory of uniform stream impinging a solid cylinder. When the fuel is ,

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ejected from the cylinder, the stagnation point moves outward and the flame is stabilized just outside the stagnation point (air side). At the state of extinction, the flame zone is located at about 2 mm from the cylinder surface. As a result, the prediction of the bulk strain rate using the cylinder radius leads to an underestimation of about 10%. It is clear that the mean velocity profile along the stagnation streamline is independent of the turbulence characteristics, and coincides with the laminar and theoretical profiles. On the other hand, the turbulence intensity is fairly constant along the stagnation streamline even near the cylinder surface as shown in Fig. 5 for = 2.8 m/s. In general, the turbulence should decay with the distance from the turbulenceproducing grid. Therefore, the turbulence intensity should decrease with the decrease of y, 0.8

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EXTINCTION OF TURBULENT DIFFUSION FLAMES because the distance from the turbulence-producing grid increases with the decrease of y. Nevertheless, Fig. 5 shows that the turbulence intensity is constant independent of y. This fact means that turbulence is produced in the deceleration region due to the strain of the mean flow. Figure 6 shows the characteristics of turbulence for P = 2.8 m / s with the D~ grid. The open circles show the turbulence intensity, v', the open squares show the integral scale, L, and the solid circles show the Kolmogorov microscale length, r/K. These turbulence characteristics are fairly constant along the stagnation streamline. This is also due to the turbulence production resulting from the strain of the mean flow. The independence of the mean flow from the turbulence suggested in Figs. 4, 5 and 6 implies that the mean and the turbulent fields can be described independently. Figure 7 shows the power spectra of turbulence at difference locations along the stagnation streamline for P = 2 m / s and the D1 grid. Even though the mean velocity decreases with the decrease of y, the power spectra expressed as functions of the wave number k are similar to each other, even very close to the stagnation point. These spectra are characteristic of isotropic turbulence, with an inertial subrange where the slope of the spectra is - 5 / 3 . Although the inertial subrange does not even last a decade in these plots, it has been found that the spectral separation between the large eddies and the small dissipative eddies is sufficient for the vortex stretching process to ensure isotropy of the small 1.0

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scale eddies, when Rx > 100 [26]. The Taylor's hypothesis used to obtain the length scales is not well satisfied in terms of the relative turbulence intensity being greater than 0.1 [28]. Therefore, Taylor's hypothesis is not valid near the stagnation point. For the present study, as shown by the power spectra, Fig. 7, Taylor's hypothesis is valid even at y = 3 mm. However, with close inspection, we can see that the contribution of high wave number components increases for the spectra of y = 5 mm and 3 ram. This fact is attributed to turbulence production by vortex stretching [28]. Flame Configuration

Having completed the measurements of the characteristics of the nonreactive flow field, we now proceed to study the effect of turbulence on the flame shape stabilized in the forward stagnation region of the porous cylinder. Figures 8(a) and (b) show direct photographs of laminar and turbulent propane diffusion flames, respectively, for the mean velocity, V = 1.0 m/s, and the fuel ejection velocity, v w = 0.22 m/s. The exposure time was eight sec. The D 1 grid was used for the turbulence generator and the turbulence intensity, v', was 0.2 m/s. The diameter of the cylinder was 30 mm. When the air flow is laminar, a thin laminar flame is stabilized at some distance from the cylinder surface. If turbulence is given to the

674

A. YOSHIDA, T. IGARASHI, AND Y. KOTANI

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Fig. 9. Side view of turbulent flame. Conditions are same as Fig. 8. (a) Direct photograph with long exposure time. (b) Instantaneous shadowgraph.

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air flow, the flame becomes turbulent and the mean flame thickness becomes three times larger than that of the laminar flame for these conditions. The mean flame thickness depends on the strain rate which acts on the flame surface. Figure 9 shows a side view of the turbulent flame under the same conditions. Figure 9 (a) is a direct photograph, and (b) is an instantaneous shadowgraph of the same flame. The exposure time was 4 sec and 25 ~sec, respectively. From Fig. 9 (b), it can be seen that large scale distortions with small amplitude were generated on the apparently laminar diffusion flame. The increase of the mean flame thickness is attributable to these distortions, which move rather rapidly in space and time. From these visual observations, the local structure of this curved flame apparently seems the same as that of the unstrained laminar diffusion flame. So, it may seem that only large-scale eddies play a dominant role in flame distortion

and, also, in extinction. The large-scale eddies contain a large amount of turbulent kinetic energy. However, the estimated strain rate based on these large eddies is too small to explain the extinction by turbulence, as will be shown later. With increasing bulk strain rate, the turbulent flame becomes thinner and the flame extinction occurs locally and intermittently somewhere close to the stagnation line established parallel to the cylinder axis. This intermittency is a typical feature of extinction due to turbulence. When the strain rate is increased slightly, the global extinction occurs. Total Strain Rates at Extinction

When the air flow is laminar, the flow field can be solved analytically by potential theory, and the lateral strain rate at the stagnation point is expressed by: a b = 2V/R,

EXTINCTION OF T U R B U L E N T DIFFUSION FLAMES where V is the uniform velocity of the approach flow and R is the cylinder radius. Figure 10 shows the extinction limits of laminar propane and methane diffusion flames as a function of the fuel ejection velocity, vw, and the stagnation velocity gradient, 2 V / R . Two types of extinction limits appear. The extinction at small value of the ejection velocity is mainly due to thermal quenching of the flame near the cylinder surface. On the other hand, the extinction at the critical velocity gradient is due to chemical limitations on the reaction rate in the flame zone. It is clear that the critical stagnation velocity gradient has the dimension of the so-called reaction frequency (time -1) and, thus, the critical stagnation velocity gradient may be thought to represent a measure of the over-all reaction rate or the flame strength for each combination of reactants [7]. With increasing strain rate, a b, the diffusion flame structure becomes narrower, with its thermal thickness approximately inversely proportional to ~ 0 [9]. This leads to an increased amount of reactant leakage, progressive reduction in the flame temperature, and, eventually, extinction of the flame. The critical velocity gradients at the laminar flame extinction are 430 1/s and 550 1/s for methane and propane, respectively. For the methane case, the agreement with the previous data obtained experimentally and numerically is excellent [29]. When the air flow becomes turbulent, the mean flow field does not change from the laminar one as shown in Fig. 4. Therefore, the 0.3

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bulk strain rate, a b, induced by the mean velocity gradient, can be estimated by 2 V / R , where V is the mean velocity of the uniform approach flow. We can expect that extinction will occur at a smaller velocity gradient than in the laminar flame, because additional strain is imposed by turbulence. Figure 11 shows the extinction limits of turbulent propane and methane diffusion flames. At a bulk strain rate slightly lower than that for extinction of the entire flame, extinguished holes appeared intermittently along the stagnation line established in the forward stagnation region of the porous cylinder. The extinction limits of laminar diffusion flames are also shown for comparison. In general, we can see that the mean velocity gradient at which extinction occurs shifts toward smaller values with increasing turbulence intensity. The critical velocity gradient at which the turbulent flame is extinguished decreases (for the extreme cases of D 1) to 110 1/s and 180 1/s for methane and propane, respectively. Such large differences are presumably caused by the turbulent strain acting in the flame tangent plane, which should be modelled. As mentioned earlier, for the premixed flame, it has been shown that the total strain rate can be decomposed into the turbulent strain rate acting in the flame tangent plane and the strain rate due to the mean flow field [11]. Recently, a general transport equation for a surface density function was derived for turbulent premixed [30] and diffusion flames [31], and it was shown that the diffusion flame experiences a stretch equal to the strain rate which can be decomposed into the turbulent strain rate and the mean velocity gradient. Peters [32] related the turbulent strain rate to the dissipation rate of the turbulent kinetic energy per unit mass, e, and the kinematic viscosity, u, by a t = ( e / t , ) 1/2,

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sured experimentally. This turbulent strain rate is the reciprocal of the Kolmogorov time scale. Then, the total strain rate, at , is expressed by:

lence, coincide with the critical velocity gradient at extinction of laminar diffusion flame. The mean turbulent flame zone becomes thinner with increase of strain rate, leading to a decrease of the instantaneous flame curvature. Near the state of extinction, the distortions of the flame surface seemingly almost disappear due to the strong lateral stretch. As compared to methane, the extinction of propane flame occurs at higher bulk strain rate, and the turbulent flame becomes almost smooth at the state of extinction. Therefore, the effect of flame curvature on extinction can be neglected. However, for the methane flame, small distortions remained even at the state of extinction and the effect of flame curvature should be taken into account into the total stretch rate to reduce the deviation from the critical velocity gradient of the laminar flame.

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We applied the total strain rate to the previous data shown in Fig. 11. Figures 12 (a) and (b) show the extinction limits of propane and methane turbulent diffusion flames as a function of total strain rate, a t , and fuel ejection velocity, vw. In these figures, the extinction limits of laminar diffusion flames are also shown by solid lines for comparison. Although there remains a small scatter, especially for methane compared with propane, the total strain rates at extinction estimated by using the turbulent strain rate of small-scale turbu-

EXTINCTION OF T U R B U L E N T DIFFUSION FLAMES For the present case, the smallest scale of turbulence which can exist in viscous fluids is much larger than the molecular scale at which combustion reaction takes place. Therefore, the overall reaction rate of the laminar flamelet under turbulent conditions should not be affected by the small-scale turbulence. As a result, the total strain rate at which the extinction of the turbulent flame occurs, coincides with the critical velocity gradient of the laminar flame. In the coherent flame model [33], the turbulent strain rate, a,, is modelled by the reciprocal of the integral time scale of the turbulence field. We also estimated a t based on the integral scale. However, the strain rate thus obtained is smaller than those defined by the inverse of the Kolmogorov time scale by one order of magnitude. As a result, the total strain rate at the extinction is much smaller than the critical velocity gradient of the laminar flame. Therefore, the role of the small eddies of Kolmogorov microscale is predominant in the extinction of the turbulent diffusion flame. It should be noted that the extinction mechanism of the turbulent diffusion flame is the same as that of the laminar flame. The local flamelet thickness decreases due to the total strain rate (the sum of the bulk strain rate and the turbulent strain rate), which leads to leakage of the reactants. Temperature Measurements Figure 13 shows the distributions of the mean temperature and the rms temperature fluctuation along the stagnation streamline. For this case, the fuel ejection velocity, uw, was kept constant at 0.14 m / s . The notation, 85% ( a r ) c, means that the velocity gradient was 85% of the critical velocity gradient. Therefore, this condition is relatively close to extinction. On the other hand, for the case of 70%(aT)c, the velocity gradient corresponds to 70% of the critical velocity gradient and, therefore, the flame is quite stable. The thickness of the flame zone was determined by direct photography and is shown by a rectangular bar in this figure. On approaching the state of extinction, namely with an increase in the mean air velocity, the mean flame thickness decreases, and

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Fig. 13. Distributions of mean and fluctuating temperatures along stagnation streamline for vw = 0.14 m/s. the turbulent flame zone is pushed inward to the cylinder. The mean temperature profiles have finite gradients at the cylinder surface and the flame zone is not adiabatic. However, if the fuel ejection velocity, v w , is increased to 0.20 m / s , the temperature gradient at the cylinder surface becomes negligible as shown in Fig. 14. For this case, the velocity gradient is 85% of the critical velocity gradient. At the same time, the thickness of the turbulent diffusion flame zone increases with the fuel ejection velocity. Figure 15 shows the probability density functions of the temperature signal for the stable turbulent flame for 70%(aT) c. At both air and fuel sides, the PDFs can be assumed essentially as a delta function centered at the room temperature, although each case has a range of 200 K due to the signal noise. From the air side, the mean temperature increases and reaches a maximum at the center of the turbulent flame zone. It then decreases to room temperature again at the fuel side. Within the turbulent diffusion flame zone, the temperature fluctuation increases. It should be noted that almost all the PDF profiles can be assumed to be Gaussian, although some PDF profiles are slightly skewed. No probability of room temperature appeared in the turbulent flame zone. Therefore, there existed no holes due to extinguished regions. In addition, the thermocouple was not exposed to pure air nor to pure fuel, because even if the laminar reaction zone is thin, the surrounding diffusive layer is relatively broad and the amplitude of the fluctuation is small. From the air side to

678

A. YOSHIDA, T. IGARASHI, AND Y. KOTANI temperature, decreases from 1900 K for 70% of the critical velocity gradient to 1800 K for 85% of the critical velocity gradient. The decrease of the maximum temperature reflects the fact that, with increasing the strain rate, the temperature of the reaction zone decreases. Figure 17 shows the power spectra of the temperature fluctuation for 70% and 85% of the critical velocity gradients measured at positions of maximum mean temperature. For the 85%(aT)c case, the effect of the fuel ejection velocity, Vw, cannot be observed. However, the effect of the strain rate on the spectrum profile is clear. The spectra for 85%(aT)c include higher frequency components than those for the 70%(aT) ~ case. Even though the large-scale fluctuation seems predominant in the turbulent diffusion flame, as observed by the shadowgraph as shown in Fig. 9 (b), the diffusive layer which surrounds the thin reaction zone contains small-scale high frequency temperature fluctuations. Anyway, there should exist high frequency temperature fluctuations and the mean velocity at the position where the turbulent flame zone is stabilized is several tens of centimeters per second. Therefore, the smallest length scale measured is of the order of 0.1 mm, which is much smaller than the scale of distortions observed by the shadowgraphs.

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the fuel side, the amplitude of the temperature fluctuation decreases gradually because the turbulence is given only to the air side. Even when the velocity gradient is increased to 85% of the critical velocity gradient, the characteristic features do not change as shown in Fig. 16. Again, no probability of room temperature appears in the flame zone under these conditions relatively close to the state of extinction. Therefore, no holes appear due to intermittently extinguished regions. The extinguished holes appear at the total strain rate of about 97% of the critical velocity gradient. The amplitude of fluctuation also does not change. However, the maximum temperature of the PDF, which corresponds to the reaction zone

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EXTINCTION OF TURBULENT DIFFUSION FLAMES

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Figure 18 shows the effect of total strain rate on the maximum mean and maximum fluctuating temperatures. The maximum mean temperature decreases gradually with the total strain rate. This decrease may be caused by the decrease of the maximum temperature which corresponds to the thin strained reaction zone as shown in Figs. 15 and 16. The maximum mean temperature decreases sharply very close to the critical velocity gradient of the laminar diffusion flame. On the other hand, the maximum fluctuating temperature is rather insensitive to the total strain rate and increases abruptly very close to the critical velocity gra-

dient. Close to the critical velocity gradient, locally-extinguished holes appear intermittently on the strained diffusion flame surface along the stagnation line produced in the forward stagnation region of the cylinder. Therefore, the maximum mean temperature decreases and the maximum fluctuating temperature increases sharply. In the turbulent flow field, the small volume of strongly-correlated, highly-localized, vortex tubes of the diameter of the order of Kolmogorov microscale and of the length of the order of Taylor microscale, are embedded in a weakly-correlated random background field [34]. Vorticity is concentrated in the vortex tubes, and the largest principal turbulent strain

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680

A. YOSHIDA, T. IGARASHI, AND Y. KOTANI

rate tends to align perpendicular to them. It can be therefore concluded that the high strain rates in the vicinity of the strong vortex tubes caused local intermittent extinction of the famelets. A slight increase of the total strain rate induces extinction of the entire flame. Scalar Dissipation Rate at Extinction

In the present study, it was found that the extinction of the turbulent diffusion flame occurs when the total strain rate coincides with the critical velocity gradient of the laminar diffusion flame. This fact suggests that the wrinkled laminar diffusion flamelets constitute the turbulent diffusion flame zone. The local quenching of the laminar diffusion flamelet occurs, if the scalar dissipation rate, X, exceeds a critical value, Xq [351. For the counterflow geometry, the scalar dissipation rate at the location where the mixture is stoichiometric may be approximated by: 1

2

)(st- 4aZst[erfc- (2Zst)], where a is the velocity gradient and Zst the stoichiometric mixture fraction [20]. For the methane case, the critical velocity gradient of the laminar flame a c = 430 1/s and Zst = 0.055. Therefore, one obtains Xq = 6.6 1/s. The order of magnitude of this value agrees well with those obtained in the jet diffusion flame [36] and the opposed jet diffusion flame [141. On the other hand, for propane flame, a c = 550 1/s and Zst = 0.062, which lead to X q = 10.0 1/s. Unfortunately, although there have been no published data to be compared, X q of propane is scaled approximately with that of methane by the ratio of the critical velocity gradients of laminar flames. CONCLUSIONS In the present study, methane or propane was ejected from a porous cylinder in a counterflowing turbulent air stream, and the extinction process due to turbulence was investigated, using classical methodology of shadowgraph, hot-wire anemometry and thermocouple. Con-

clusions of the present study are summarized as follows. 1. The air stream turbulence causes large-scale distortions with small amplitude on the apparently laminar diffusion fame, and the time-averaged flame thickness depends on the bulk stretch rate. 2. Even if the air stream becomes turbulent, there exists, over a wide range of the turbulent Reynolds number, a critical stagnation mean velocity gradient beyond which the flame can never be stabilized. This critical mean velocity gradient decreases with the increase of the turbulence intensity. 3. The total strain rate was decomposed into the bulk strain rate induced by the mean flow, and the turbulence strain rate induced by eddies of Kolmogorov microscale. The total strain rate at which the turbulent flame is extinguished coincides with the critical velocity gradient at which the laminar flame extinction occurs. This is true even at the turbulent Reynolds number as low as 50. 4. The maximum mean temperature decreases gradually with the increase of the total strain rate due to the decrease of the maximum temperature of the reaction zone and falls sharply near the state of extinction due to the fact that extinguished holes appear locally and intermittently due to the high strain rate of the localized vortex tubes of the order of the Kolmogorov microscale. The maximum fluctuating temperature is rather insensitive to the total strain rate and increases abruptly near the state of extinction due to the local intermittent extinction. 5. From visual observation, the large-scale distortion appears to be predominant. However, the power spectra of the temperature fluctuation reveal the important role of the high frequency component of the fluctuation, which dominates the extinction of the turbulent diffusion flame. 6. Scalar dissipation rates at extinction, estimated from the critical velocity gradients, agree well with the previously published data and are scaled approximately by the ratio of the critical velocity gradients of laminar flames.

EXTINCTION OF T U R B U L E N T DIFFUSION FLAMES

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