Burning velocity of 1, 1-diflurorethane (R-152a).

ABSTRACT

This paper presents measurements and numerical calculations of the burning velocity of 1,1-diflurorethane (R-152a, C[H.sub.3]-CH[F.sub.2]), compares the present results to others appearing in the literature, and discusses the influence of flame stretch and other experimental complications on the measured burning velocities. The measurements have been made in a Mache-Hebra nozzle burner over the range of equivalence ratios 0.9 [less than or equal to] [phi] [less than or equal to] 1.3. Corresponding numerical calculations for a steady, one-dimensional, planar flame have been made using a comprehensive chemical kinetic mechanism based on 783 reversible elementary reactions. The raw experimental data indicate a peak flame speed (based on the total area method) of 29.3 cm/s, while the numerical calculations predict a value of 27.6 cm/s, both near [phi] = 1.1. Stretch corrections for the conical Bunsen-type flame have been estimated and lower the experimentally measured values by about 20% for all [phi] < 1.05 but insignificantly for richer flames. Since flame stretch can significantly modify the laminar flame speed and also change the propensity of the flame to become turbulent (and have a much higher flame speed), it is suggested that it may be useful in future tests to use techniques that allow simultaneous determination of the unstretched laminar flame speed as well as the flame's response to stretch and preferential diffusion.

INTRODUCTION

Stratospheric ozone depletion has led to a phaseout of chlorofluorocarbons and hydrochlorofluorocarbons (HCFCs) in many industrial uses and their replacement by hydrofluorocarbons (HFCs). Some of the latter compounds, however, are flammable. The refrigeration industry needs a metric for comparing the relative flammability of alternative compounds, as well as an understanding of the relative ignition and fire hazards, overpressure potential from burning, and any explosion hazard for candidate working fluids. Various tests have traditionally been used to rank the flammability of gases and liquids, including heat of combustion, flammability limits, flash point temperature, quenching distance, and minimum ignition energy (Lewis and von Elbe 1961; Coward and Jones 1952; Zabetakis 1965). Many of these have recently been applied to understanding refrigerant flammability (Kondo et al. 2002a, 2002b, 2004). In addition, burning velocity is a fundamental measure of the flammability of a gaseous mixture and incorporates the effects of overall reaction rate, heat of combustion, and the transport rates for heat and mass. Consequently, burning velocity is both a traditional and active area of combustion research, and it has found wide application in the prediction of overpressure dynamics, and explosion and detonation hazards (Zalosh 1995). The present paper presents measurements and numerical calculations of the burning velocity of 1,1-diflurorethane (R-152a, C[H.sub.3]-CH[F.sub.2]), compares the present results to others appearing in the literature, and discusses the influence of flame stretch and other experimental complications on the measured burning velocities.

Background

Conceptually, the burning velocity is the rate of propagation of a one-dimensional, planar combustion wave into an unburned premixed gas containing fuel and oxidizer. There exist many experimental methods for measuring the burning velocity, and a good review appears in Andrews and Bradley (1972). Traditional methods include the tube method (Mallard and Le Chatelier 1883), the constant-volume bomb method (Fiock and Marvin 1937), the nozzle burner method (also sometimes called a Bunsen flame method, with variations based on the flame angle, total flame area, and particle tracking, and slot burners). Nonetheless, few of these measure a true adiabatic, one-dimensional, planar, burning velocity, and in addition, the importance of flame curvature and stretch on the measurement have been observed (Matalon and Matkowsky 1982; Law 1988). Although the idealized flame speed is based on a planar, infinite, steady flame with no heat losses, such flames do not exist in practice. Instead, they are typically curved, undergo aerodynamic straining (due to nonparallel streamlines), and are unsteady. The collective result of these effects is called flame stretch ([kappa]), which has the units of [s.sup.-1]. Flame stretch can modify the measured flame speed relative to unstretched conditions. A promising new method has been developed to measure the planar, adiabatic burning velocity directly (Bosschaart and de Goey 2004). Alternatively, other techniques aim to measure the burning velocity as a function of flame stretch, so that both the unstretched burning velocity and the flame response to stretch can be measured. These include the twin-flame premixed opposed-jet technique pioneered by Tsuji and Yamaoka (1982), Law and Wu (1984), and others (Vagelopoulos et al. 1994); the nozzle and slot burner methods (Echekki and Mungal 1990; Law et al. 1986; Mizomoto et al. 1984) with particle tracking; and the constant-volume spherical flame growth method with schlieren imaging of the flame (Tseng et al. 1993; Bradley et al. 1998; Aung et al. 2002; Johnston and Farrell 2005).

The buring velocities of R-152-air flames recently have been measured using both the flame tube method (Jabbour and Clodic 2004) and the spherical bomb technique, with both pressure rise and flame imaging used to extract the burning velocity (Takizawa et al. 2005). In other work, the flame speeds of mixtures of HFCs and methane have been determined using a nozzle burner (Linteris and Truett 1996; Linteris et al. 1998) and twin-flame opposed-jet burner (Saso et al. 1998). The present work extends the previous nozzle burner method for mixtures of HFCs and methane to pure R-152a-air flames and examines the flame structure to estimate the influence of stretch and preferential diffusion on the measured burning velocity.

EXPERIMENT

The nozzle burner is based on the design of Mache and Hebra (1941) with some modifications. The experimental system has been described in detail previously (Linteris and Truett 1996) and is shown in Figure 1. The burner consists of a quartz tube 27 cm long with an area contraction ratio of 4.7 (over a 3 cm length) and a final nozzle diameter of 1.02 [+ or -] 0.005 cm, which is placed in a square acrylic chimney 10 cm wide and 86 cm tall. There is co-flowing air at about 1 cm/s. A schlieren imaging system (Van Wonterghem and Van Tiggelen 1954) provides the flame area from which the average burning velocity of these Bunsen-type flames is determined using the total area method (Andrews and Bradley 1972). An optical system (a white-light source with a vertical slit at its exit, lenses, a vertical band, and filters) generates the schlieren image of the flame for capture by a 776 x 512 pixel Charged Injection Device (CID) array (Cidtec CID3710D).(1) The image is digitized by a 640 x 480 pixel frame-grabber board (Data Translation 3155) in a Pentium-II computer. The images are acquired and written to disk using the free University of Texas Health Science Center of San Antonio (UTHSCSA) Image-Tool program (UTHSCA 1996). The burner produces straight-sided, conical schlieren and visible images that are very closely parallel. For the present data, the visible flame height is maintained at constant value of 1.3 cm to provide similar rate of heat loss to the burner while preserving the desired equivalence ratio (the actual fuel-air ratio divided by the fuel-air ratio for stoichiometric combustion, both on a volumetric basis). The flame area is determined (assuming axial symmetry) using custom image-processing software, and the burning velocity is calculated by dividing the volumetric flow rate (corrected to 101 kPa and 298 K) by the flame area.

[FIGURE 1 OMITTED]

Gas flows are measured with digitally controlled mass flow controllers (Sierra Model 860) with a quoted repeatability (by the manufacturer) of 0.2% and accuracy of 1% of full-scale flow, which have been calibrated with piston (Bios Intl. DCL-20K) and dry (American Meter Co. DTM-200A) flow meters so that the expanded uncertainty of the indicated flow is 1.5%. House compressed air (filtered and dried) is used after it has been additionally cleaned by passing it through an 0.01 [micro]m filter, a carbon filter, and a desiccant bed to remove small aerosols, organic vapors, and water vapor. The resulting relative humidity of the added air is about 5%, as measured with a hygrometer (Extech Instr.). The R-152a is from Dupont.

The uncertainty analysis consists of calculation of individual uncertainty components and root mean square summation of components. All uncertainties are reported as expanded uncertainties: X [+ or -] U, where U is k[u.sub.c] and is determined from a combined standard uncertainty (estimated standard deviation) [u.sub.c] and a coverage factor k = 2 (level of confidence approximately 95%). Likewise, when reported, the relative uncertainty is U/X x 100%, or k[u.sub.c]/X x 100%. Uncertainty in the equivalence ratio is 2.0%, and uncertainty in the burning velocity is shown in the figures.

MODELING

The structures of the premixed R-152a-air flames are calculated using available techniques. The equations of mass, momentum, species, and energy conservation are solved, for the initial gas compositions of the experiments, using the Sandia PREMIX flame code with the Sandia chemical kinetics and transport interpreters (Kee et al. 1986, 1989, 1991). The solution assumes isobaric, steady, planar, one-dimensional, laminar flow and neglects radiation and the Dufour effect (concentration gradient-induced heat transfer) but includes thermal diffusion. The Bunsen flames are modeled as freely propagating flames, and the burning velocity is obtained as an eigenvalue of the energy equation. Molecular diffusion is modeled using mixture-averaged diffusion coefficients. The adopted boundary conditions are: inlet mass flux fractions, inlet temperature (298 K), and vanishing gradients downstream. The reaction pathway analyses are carried out using a graphical postprocessor (Burgess 1998). The spatial domain of the calculation is resolved so that the final solution has approximately 120 active grid points.

The calculations employ a chemical kinetic mechanism developed at NIST (Burgess et al. 1995a, 1995b) for fluorine inhibition of hydrocarbon flames. The hydrocarbon sub-mechanism uses GRI-Mech 1.2 (31 species, 177 reactions [Frenklach et al. 1995]), while the fluorocarbon sub-mechanism adds 46 species and 606 reactions of one- and two-carbon fluorinated species. The fluorinated-species thermochemistry is from the literature when available and is otherwise estimated using empirical methods. Fluorinated species reaction rates from the literature were used when available, and these were extended to wider temperature and pressure ranges using Rice-Ramsperger-Kassel-Marcus (RRKM) and Quantum-Rice-Ramsperger-Kassel (QRRK) methods. Where no rate data were available, rate constants were estimated by analogy with hydrocarbon reactions and using transition states from ab initio molecular orbital calculations with BAC corrections (Zachariah et al. 1995). The comprehensive full mechanism is used for the present calculations (available in a continuously updated form on the World Wide Web [Burgess 1999]). It should be emphasized that the mechanism adopted for the present calculations should be considered only as a starting point. Numerous changes to both the rates and the reactions incorporated may be made once a variety of experimental and theoretical data are available for testing the mechanism.

RESULTS

The burning velocity of R-152a with air was determined in the nozzle burner using the total area method based on the schlieren image of the flame. Images of the flame for fuel-air equivalence ratios [phi] of 0.9, 1.0, and 1.1 are shown in Figure 2. Note that in these images, the flame tip is occluded by the schlieren knife edge (which in this case was a 1 mm wide band, providing two knife edges, with the schlieren effect toward the left and right halves of the flame simultaneously). The flames were blue and steady in the range of 0.9 [less than or equal to] [phi] [less than or equal to] 1.3, while for richer conditions, 1.3 [less than or equal to] [phi] [less than or equal to] 1.5, flames were stabilized but were open-tipped. For 1.0 [less than or equal to] [phi] [less than or equal to] 1.1 the schlieren images were straight-sided over the entire flame, implying small effects of strain on the burning velocity. For other values of [phi], however, the flames showed curvature and, hence, variation of the burning velocity with radius; the effect was strong for flames at [phi] > 1.2, and at [phi] = 1.5, the flame became cellular and unstable on the upper half and had a faint yellow glow above the open tip, indicating fuel leakage and after-burning. Note that burning velocity data below are only presented for 0.9 [less than or equal to] [phi] [less than or equal to] 1.3 for which the flame was closed-tipped.

Figure 3 presents the experimental burning velocity data as a function of [phi], along with those of Jabbour and Clodic (2004) and Takizawa et al. (2005). (Stretch-corrected flame speeds for the present experiments are also given, as discussed below.) Two points from Takizawa et al. at [phi] = 0.76 and 1.0, which were obtained using a different combustion chamber and a schlieren image area to get the extent of reaction (rather than pressure rise), are also shown. Those data are about 10% lower than measurements using the pressure rise. The present experimental burning velocity data (stretched) are relatively constant in the range 1.0 [less than or equal to] [phi] [less than or equal to] 1.2, with a peak value of 29.3 cm/s. This peak burning velocity is about 21% and 28% higher than that given by Jabbour and Clodic and Takizawa et al., respectively, and the peak value is shifted very slightly to the richer flames. For comparison, the numerically calculated burning velocity data (for a planar, adiabatic, unstretched flame) is given by the solid curve marked ([S.sub.L,u Calc]), and the calculated final temperature is given by the solid curve marked [T.sub.calc](right scale). The calculated peak burning velocity is 27.6 cm/s, which is about 6% lower than the experimental value (stretched) for the present nozzle burner flame. The drop-off in the burning velocity away from the peak value is somewhat steeper in the present flames as compared to the results of the other researchers, more closely following that in the numerical prediction. The calculated peak temperature of the flame is 2226 K, which is very close to that for typical hydrocarbon-air flames (e.g., 2230 K for C[H.sub.4]-air). Since the present results, both numerical and experimental, deviate significantly from both each other and the experimental results of previous researchers, it is of interest to discuss possible reasons for the discrepancies.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

DISCUSSION

Differences Between Calculation and Experiment for Nozzle Burner

Differences between the physical characteristics of the experiment and the numerical calculation can cause discrepancies between their predicted flame speed for the R-152-air mixtures. The calculation is for a one-dimensional, planar, stretch-free, adiabatic flame with pure R-152 and air. Conversely, the experiment is a two-dimensional, axi-symmetric, conical burner-stabilized flame with some water vapor in the reactants. The effects of these differences on measured and predicted flame speeds are discussed below.

Water Vapor. The overall rate for the high-temperature reaction of HFCs with air is dependent upon the concentration of chain-carrying radicals (H, OH, and O); these, in turn, depend upon the amount of hydrogen and fluorine in the system. Since the unstretched laminar flame speed [S.sub.L,u.sup.0] is proportional to the square root of the product of the mixture thermal diffusivity [alpha] and the overall reaction rate [dot.[omega]], [S.sub.L,u.sup.0] [approximately equal to] [square root of ([alpha][dot.[omega]])], the flame speed may be affected by the amount of hydrogen in the system. This was noted by Takizawa et al. (2005), who plotted flame speed of HFCs vs. the H/F ratio in the fuel, and previously by Linteris and co-workers in research to predict HF formation from flames (Linteris 1995a) and studies of methane-air flames inhibited by one-carbon HFCs (Linteris 1995b). Since R-152a has an H/F ratio of 2, its high-temperature reaction will not be as starved for H radicals as other refrigerants; nonetheless, it could be sensitive to the water in the system. Since humidity in the air can be a significant source of hydrogen, we tested its effect by varying water vapor volume fraction in the reactants of the numerical calculations. At [phi] = 1.0, the calculated adiabatic flame temperature [T.sub.ad], and flame speed, with a relative humidity of 0%, 5%, and 50%, are 2226 K, 2225 K, and 2210 K, 26.65 cm/s, 26.61 cm/s, and 26.08 cm/s, respectively. That is, a volume fraction of water in the air of 1.5% (50% RH) slows the calculated flame speed by about 2%. Hence, water vapor at about 5% relative humidity is not expected to have a significant effect on the flame speed.

Heat Losses. Heat losses to the burner rim are typically believed to affect the flame temperature at the base (Andrews and Bradley 1972; Law et al. 1986). However, the present burner uses a thin quartz tube rather than a more typical stainless steel tube. The fused silica has a thermal conductivity 11 times lower than a typical stainless steel burner tube, so that the conductive losses down the tube will be much lower. The unimportance of the heat losses to the base are illustrated by the schlieren image for [phi] = 1.0 in Figure 2: if there were heat losses affecting the flame speed at the flame base, the schlieren image would be curved at the base, but no curvature is observed.

Hydrodynamic Strain. Hydrodynamic strain, or flame stretching caused by expansion or contraction of a flow stream tube (e.g., flame curvature), is known to affect the laminar flame speed. The stretched laminar flame speed [S.sub.L,u] can be significantly higher or lower than the unstretched laminar flame speed [S.sub.L,u.sup.0], depending upon the sign and magnitude of the stretch and other effects. For example, the flame speed in the tip of a Bunsen flame can be more than six times the unstretched value (Echekki and Mungal 1990)--of course the tip is only a fraction of the total cross-sectional area of the flame. Flame stretch is defined as the fractional area change in a Lagrangian surface element A with time: [kappa][equivalent to] 1/AdA/dt. For the present steady, conical, nozzle-burner flame, the stretch experienced on the cone surface by a flame element located at a radius [r.sub.f] has been derived (Matalon 1983) as

[kappa] = -[U.sub.jet]sin[theta]/[r.sub.f], (1)

in which [U.sub.jet] is the nozzle jet exit velocity, and [theta] is the cone apex half-angle. At the flame tip, [kappa] = -2[S.sub.L,u]/[r.sub.f]. Note that the flame stretch is defined as positive for flames convex to the unburned mixture, so that nozzle burner flames have negative stretch; i.e., they experience "compression." [U.sub.jet] is equal to [S.sub.L,u] [A.sub.cone]/[A.sub.jet]([A.sub.cone] and [A.sub.jet] are the areas of the flame cone and nozzle jet, respectively) so that

[kappa] = -[[S.sub.L,u]/[r.sub.f]][[A.sub.cone]/[A.sub.jet]]sin([theta]). (2)

The flame stretch can be nondimensionalized by [S.sub.L,u.sup.0] and [[delta].sub.u.sup.0], where [[delta].sub.u.sup.0] = [[alpha].sub.u]/[S.sub.L,u.sup.0], and [[alpha].sub.u] is the thermal diffusivity [[alpha].sub.u] = [[lambda].sub.u]/([[rho].sub.u][C.sub.p,u]), [lambda] = thermal conductivity, [C.sub.p] = the specific heat at constant pressure, and [rho] = the density, all evaluated with respect to the unburned gases (u). Hence, the nondimensionalized stretch [~.[kappa]]is given by

[~.[kappa]] = [[S.sub.L,u]/[S.sub.L,u.sup.02]][[[alpha].sub.u]/[r.sub.f]][[A.sub.cone]/[A.sub.jet]]sin([theta]). (3)

As outlined in Echekki and Mungal (1990), it has been shown (Matalon and Matkowsky 1982; Clavin and Williams 1982) that, for small stretch,

[S.sub.L,u]/[S.sub.L,u.sup.O] [approximately equal to] 1 - [alpha][~.[kappa]], (4)

in which a is a constant that accounts for heat release and preferential diffusion. In the absence of preferential diffusion, the parameter a is given solely by the burned and unburned temperatures of the mixture:

a [approximately] [T.sub.b]/([T.sub.b] - [T.sub.u]) ln ([T.sub.b]/[T.sub.u]). (5)

Echekki and Mungal determined [alpha] to be 6.46 for the tip of two-dimensional slot burner flames, and half of that for the tip of axi-symmetric nozzle flames. Using [alpha] = 6.46 (or 3.23 at the tip), Equations (1-5) can be solved for the ratio of the stretched to unstretched laminar flame speed in terms of the flame radius.

[S.sub.L,u]/[S.sub.L,u.sup.0] = 1/[1 - a[[[A.sub.cone]sin([theta])]/[A.sub.jet]][[[alpha].sub.u]/[S.sub.L,u.sup.0][r.sub.f]]] (6)

Equation 6 can be solved for [S.sub.L,u.sup.0] based on the experimental values of [S.sub.L,u], [A.sub.cone], [A.sub.jet], [r.sub.f], and the property values that form [[alpha].sub.u]. Figure 4 (points with dotted line) shows the estimated effect of hydrodynamic strain on the ratio of the stretched to unstretched laminar flame speed, from Equation 6, as a function of the flame radius. As shown, stretch effects can raise the measured flame speed in a conical nozzle burner flame by factors of 1.1 to 1.55 above the unstretched values for the present conditions. Since the effect varies over the conical flame surface, the flow-averaged value for the entire flame is also calculated and is indicated by the horizontal bar. The results estimate that hydrodynamic strain (in the absence of preferential diffusion) causes the Bunsen flame to have an average burning velocity 1.2 times that of an unstretched flame.

[FIGURE 4 OMITTED]

Preferential Diffusion. The above results are valid for conditions without preferential diffusion. Nonetheless, the rates of diffusion of heat or species can differ from one another, with additional effects on the burning velocity. The Lewis number Le = [[alpha].sub.u]/[D.sub.u] describes the ratio of the diffusion of heat to that of the deficient reactant, both evaluated at the unburned gas condition. If there is flame curvature or stretch, non-unity Lewis numbers lead to focusing or de-focusing of heat and species, leading to local modifications to the flame speed. As described by Law et al. (1986), theoretical results (Matalon and Mtkowsky 1982; Clavin and Williams 1982; Chung and Law 1988) have shown that, for small stretch, deviation of the flame temperature from the adiabatic flame temperature is given by

([T.sub.f] - [T.sub.ad])/[T.sub.ad] = [~.[kappa]]([1/Le] - 1), (7)

in which [T.sub.ad] is the adiabatic flame temperature, and [T.sub.f] is the local flame temperature. Hence, non-unity Lewis numbers coupled with flame stretch can modify the local temperature and change the flame speed. In the case of Le [not equal to] 1, the nondimensionalized stretch [~.[kappa]] is calculated with the binary diffusion coefficient of the fuel [D.sub.u] in nitrogen, replacing the thermal diffusivity of the mixture [[alpha].sub.u] in Equation 3. The thermal diffusivity [[alpha].sub.u] of the premixed R-152a and air were calculated with REFPROP (Lemmon et al. 2002) and the diffusion coefficients of R-152a or oxygen in air [D.sub.u], using the CHEMKIN TRANFIT curve fits (Kee et al. 1986).

Values of the parameters necessary for the stretch corrections using Equations 6 and 7 are listed in Table 1. The first three rows were estimated as described above, and [T.sub.ad] was obtained from the numerical calculation (but equilibrium calculations could have been used as well). The last three rows, which provide [S.sub.L,u,exp,] [A.sub.cone], and [theta], are from the experimental data. The stretch and the nondimensionalized stretch for the present nozzle burner flames, as a function of flame radius, for various values of the equivalence ratio are given in Figure 5. As shown, the stretch varies from about 40 to 500 [s.sup.-1], while the nondimensional stretch varies from 0.01 to 0.2. Using Equation 7 above, one can calculate the effect of the stretch on the local temperature (as a function of radius), and these are presented in Figure 6. The local temperature near the tip can be increased above the adiabatic flame temperature by 120 K for lean flames or decreased by 14 K for rich flames. To estimate the effects of these temperature changes on the flame speed, we performed additional numerical calculations with more or less [N.sub.2] diluent in the airstream, at a given value of [phi], and fit an exponential curve to the plot of flame speed vs. peak flame temperature. These fits, together with the estimated deviations from the adiabatic flame temperature [T.sub.ad] in figure 6, permitted an estimation of the modification to the flame speed at each value of [r.sub.f]. As above, the effect was then flow averaged over the flame, and the result is plotted in Figure 7. As shown, it is estimated that preferential diffusion can increase the average flame speed determined with the nozzle burner technique by about 6% for [phi] = 0.9 and negligibly at other values of [phi]. These preferential diffusion effects on the flame speed are small (< 6%), which is a result of the narrow range of equivalence ratios (0.9 [less than or equal to] [phi] [less than or equal to] 1.2) considered in the present experiments. Nonetheless, as stretch increases, the local temperature and, hence, flame speed of lean flames is expected to increase. The flattening of the flame tip in the left schlieren image in Figure 2 is consistent with this predicted effect--the flame speed for the lean flames is higher at the tip, so the flame position becomes more normal to the flow direction. In contrast, rich flames should have a slower flame speed as the curvature and stretch increase at the tip, and the flame speed (which is proportional to the sine of the cone apex half angle) at the tip should be lower (as manifested in the pinched appearance of the tip in the right image of Figure 2). As mentioned above, the richest flames tested, 1.3 [less than or equal to] [phi] [less than or equal to] 1.5, had open tips; in this case, the flame temperature was lowered (due to preferential diffusion) enough so as to cause local flame extinction, again consistent with the direction of the corrections in Figure 7.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

For the present R-152a-air flames over a range of 0.9 [less than or equal to] [phi] [less than or equal to] 1.25, the hydrodynamic strain in the Bunsen-type nozzle burner flame is predicted to modify the flame speed from the planar one-dimensional value more than the preferential diffusion effects. This may not necessarily be the case for other fuels or flame configurations. The estimated stretch-corrected laminar flame speed [S.sub.L,u.sup.0] for the present experiments is given by the solid triangles in Figure 3. After corrections for stretch, the data are within the uncertainty of those of other researchers except for [phi] > 1.1. Alternatively, the slope of the stretch-corrected flame speed matches that of the numerical calculation, but the location of the peak flame speed is shifted to the richer conditions by about 0.08. That is, if the peak in the flame speed has been shifted to the richer conditions due to preferential diffusion effects, correcting for those effects would yield excellent agreement between calculation and experiment. Although not estimated here, the preferential diffusion of the [O.sub.2] over R-152a (or preferential diffusion of other crucial intermediate species in the reaction mechanism) can modify the value of [phi] for which the maximum flame speed occurs (Mizomoto et al. 1984). For example, the magnitude of the shift in [phi] for the peak flame speed in Figure 3 is consistent with the shift in [phi] for the calculated and measured peak temperature of propane-air Bunsen flames as measured by Mizomoto et al. (1984), although the direction is opposite.

[FIGURE 7 OMITTED]

It is important to stress that the stretch corrections are relatively imprecise and are an active area of research; consequently, most researchers have moved in the direction of measuring directly the response of the flame speed to stretch (Kim et al. 2002). Although the peak flame speed for the present stretch-corrected flames in Figure 3 is not exactly clear, from the present results (since measurements and corrections out to larger [phi] would be required), it appears that the peak stretch-corrected flame speed matches that in the numerical calculations, which are both about 15% to 20% higher than the peak measured by previous researchers. Flame speed measurements that can quantify any stretch corrections should be able to resolve most of these discrepancies.

Possible Sources of Error in Other Burning Velocity Measurements

The effects of stretch could influence the previous flame speed measurements of other researchers (Tseng et al. 1993). As described above, flame stretch is defined as positive for flames convex to the unburned mixture. Unlike the nozzle burner that has negative stretch, both the expanding spherical flames and the flame propagating in a tube have positive stretch. For steady (not expanding) spherical flames, the stretch K is given by [kappa] = 2/[y.sub.f][d.sub.yf]/[d.sub.t], and for a flame propagating in a tube [kappa] = 2[S.sub.L,u]/[y.sub.f]. Hence, both of the previous measurements will have steady hydrodynamic strain corrections that are in the opposite direction (i.e., tending to raise the measured flame speed rather than lower it as in the present work). The radii of the previous experiments, however, are larger than in the present work, so the magnitude of the corrections should be smaller. On the other hand, the flame speed of R-152a is relatively high; for other refrigerants with lower flame speeds, as the flame thickness increases, the effects of curvature and stretch are more pronounced.

Other complications can affect data interpretation in bomb experiments. The expanding spherical flame measurements require consideration of nonstationarity to the stretch (Frankel and Sivashinsky 1983), i.e., a time-varying flow field when viewed from a Lagrangian element on the flame surface (Tseng et al. 1993; Clavin 1985; Ronney and Sivashinsky 1989). Measurements at the largest radii are the closest to the laminar unstretched planar one-dimensional flame speed; however, as the flame grows, wrinkling and cellular structure can occur, increasing the flame speed. The tendency toward flame wrinkling and cellular structure are greater at higher pressure (Bradley et al. 1998), and these, if they occur, can influence the extrapolations to T = 298 K, p = 101 kPa conditions. Takizawa et al. (2005) reported that in their measurements, wrinkling was not observed for any conditions. It is not clear, however, if they recorded and inspected images for all times and all stoichiometries; the presence of only two data points (at [phi] = 0.76 and 1.0) from that experimental system (see Figure 3) implies that they did not collect data for rich conditions (for which the wrinkling is likely to be more severe (Bradley et al. 1998). Also, their schlieren images were recorded in a different chamber than that used for the determination of flame speed by the pressure rise. Since acoustic waves in the chamber have been implicated as contributing to the growth of flame instability (Bradley et al. 1998), different chambers might modify the growth of flame wrinkling.

For the flames propagating in a tube, there also exist complications that might affect the measured flame speed. The flames are quenched near the wall, and corrections are necessary to account for the wall heat losses (Andrews and Bradley 1972), particularly for slower burning flames. The reactant gases upstream of the flame, and into which the flame propagates, are assumed to be quiescent. Any movement in those gases, such as those induced by buoyancy effects, could affect the measured flame speed.

Numerical Model

As shown in Figure 3, the present nozzle burner experimental results, after estimations of the corrections due to stretch and preferential diffusion, are still 5% to 15% lower than those predicted by the numerical calculation (for all conditions except the richest flames, [phi] = 1.15 and [phi] = 1.2). Similarly, the measurements of previous researchers (Kondo et al. 2004; Jabbour and Clodic 2004), without stretch corrections, are also about 15%, 25%, and 33% lower than the numerical predictions for 0.75 [less than or equal to] [phi] [less than or equal to] 1.3, [phi] = 0.7, and [phi] = 0.63, respectively). While the stretch corrections applied to the present flames are only estimates, and other experimental complications in the measurements of other researchers may modify their results (as discussed above), there also are likely to be shortcomings in the numerical predictions. The PREMIX model used to predict the unstretched, planar, laminar flame speed is comprehensive, based on numerical solution of the conservation equations for species, mass, momentum, and energy, and is well established and validated. On the other hand, the detailed reaction mechanism with 783 reversible elementary reactions is comprehensive but is still in early stages of development. Many of the thermodynamic and transport properties of the fluorinated species are estimates, as are many of the elementary reaction rates. There has been some work aimed at experimental validation of the mechanism. These include flame structure comparisons for intermediate species (Hynes et al. 1998; Williams et al. 2000) and burning velocity comparisons (Linteris and Turett 1996; Linteris et al. 1998; Linteris 1996; Dlugogorski et al. 1998), one with corrections for stretch (Saso et al. 1998). All of these are for methane-air burner-stabilized flames inhibited by HFCs; the only comparisons involving pure HFC-air mixtures are the recent experiments for R-32 (C[H.sub.2][F.sub.2]), which have been compared to previous numerical predictions (Womeldorf and Grosshandler 1999) and are in agreement. Nonetheless, while the numerical calculations are immensely useful for understanding the general behavior of the reaction of HFCs, more validation of the NIST HFC mechanism is required before it can be considered to have a quantitative predictive capability for flame speeds.

Appropriate Burning Rate Measurements for Ranking Refrigerant Flammability

All of the flame speed measurement techniques are plagued by phenomena that affect either the measured experimental flame speed itself, the extraction of a stretch-free value, or both. Great efforts are made in the experiments to constrain them to conditions for which various instabilities are minimized so that a laminar flame speed can be observed. In applications, however, it is a flame's response to such disturbances that will most affect its becoming turbulent and having much higher flame speeds (Poinsot et al. 1992). Changes in flame conditions that reduce H radicals in the reaction zone also make the flames more unstable with respect to preferential diffusion instabilities (Kim et al. 2002). Since the HFCs lower H-atom concentration in the reaction zone (Linteris and Truett 1996), flames of pure HFCs will be more susceptible to preferential diffusion instabilities. Accurate determination of a fuel's propensity to cause turbulent flame propagation is essential for understanding its flammability risk. In explosion venting, for example, quantifying or predicting the modification of the laminar flame speed due to turbulence is an important, and particularly difficult part of the problem (Zalosh 1995).

Rather than trying to find conditions that avoid the influence of these instabilities, it may be more useful to try to characterize them. Methods currently exist that can simultaneously determine both the stretch-free laminar flame speed and the flame's response to stretch. These include (1) Bunsen flames with particle tracking velocimetry so that the flame speed, particularly at the tip, can be obtained directly; (2) the twin premixed counterflow flame technique, which again requires a velocity measurement such as laser Doppler velocimetry LDV (Law and Wu 1984); or (3) a combustion bomb of large enough volume so the pressure rise is negligible, coupled with high-speed video imaging (schlieren) of the flame (Tseng et al 1993; Bradley et al. 1998; Johnston and Farrell 2005). The latter of these would use far less of the flammable material and not require particle seeding or an LDV gas velocity measurement. It is very similar to the experiment already constructed by Takizawa et al. (2005), with slightly different data collection and reduction.

CONCLUSIONS

Experimental measurements of the average flame speed of R-152-air flames have been made in a Mache-Hebra nozzle burner, over a range of 0.9 [less than or equal to] [phi] [less than or equal to] 1.3 and indicate a peak value, near [phi] = 1.1, of 29.3 cm/s. Numerical calculations predict a peak flame speed of 27.6 cm/s and a peak flame temperature near 2226 K. The raw flame speed measurements are about 20% higher than previous measurements by other researchers in different flame systems. The presence of up to 0.15% [H.sub.2]O in the airstream is predicted to be negligible, as are heat losses to the burner rim. Estimations of the influence of hydrodynamic strain and preferential diffusion indicate that these effects are important for the present flames, such that unstretched flames with 0.9 [less than or equal to] [phi] [less than or equal to] 1.0 would have a burning velocity about 12% to 20% lower, while for 1.05 [less than or equal to] [phi] [less than or equal to] 1.2, the burning velocity would be 10% to 6% lower. Hence, after applying stretch corrections, the rich flame speeds are somewhat higher than previous measurements, but the lean flames are about the same. There is evidence to suggest that the present stretch-corrected values of the burning velocity are in good agreement with the predictions of the numerical calculations if preferential diffusion effects have caused the peak burning velocity to occur at a value of [phi] shifted 0.08 to the richer flames. It is suggested that since the flame response to stretch both modifies the flame speed and also changes the transition to a turbulent flame, it would be useful in future experiments to use techniques that allow determination of the unstretched laminar flame speed as well as the flame's response to stretch.

REFERENCES

Andrews, G.E., and D. Bradley. 1972. Determination of burning velocities: A critical review. Combustion and Flame 18:133.

Aung, K.T., M.I. Hassan, S. Kwon, L.K. Tseng, O.C. Kwon, and G.M. Faeth. 2002. Flame/stretch interactions in laminar and turbulent premixed flames. Combustion Science and Technology 174(1):61-99.

Bosschaart, K.J., and L.P.H. De Goey. 2004. The laminar burning velocity of flames propagating in mixtures of hydrocarbons and air measured with the heat flux method. Combustion and Flame 136(3):261-69.

Bradley, D., R.A. Hicks, M. Lawes, C.G.W. Sheppard, and R. Woolley. 1998. The measurement of laminar burning velocities and Markstein numbers for iso-octane-air and iso-octane-n-heptane-air mixtures at elevated temperatures and pressures in an explosion bomb. Combustion and Flame 115:126-44.

Burgess, D.R., Jr. 1999. CKMech NIST Mechanisms. http:// www.nist.gov/cstl/div836/ckmech/. National Institute of Standards and Technology.

Burgess, D.R., Jr. 1998. NIST XSenkplot; An interactive, graphics postprocessor for numerical simulations of chemical kinetics. http://www.nist.gov/cstl/div836/ xsenkplot, National Institute of Standards and Technology.

Burgess, D.R., M.R. Zachariah, W. Tsang, and P.R. Westmoreland. 1995a. Thermochemical and chemical kinetic data for fluorinated hydrocarbons, NIST TN 1412.

Burgess, D.R., M.R. Zachariah, W. Tsang, and P.R. Westmoreland. 1995b. Thermochemical and chemical kinetic data for fluorinated hydrocarbons. Progress in Energy and Combustion Science 21(6):453-529.

Chung, S.H., and C.K. Law. 1988. An integral analysis of the structure and propagation of stretched premixed flames. Combustion and Flame 72(3):325-36.

Clavin, P. 1985. Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Progress in Energy and Combustion Science 11(1):1-59.

Clavin, P., and F.A. Williams. 1982. Effects of molecular-diffusion and of thermal-expansion on the structure and dynamics of premixed flames in turbulent flows of large-scale and low intensity. Journal of Fluid Mechanics 116:251-82.

Coward, H.F., and G.W. Jones. 1952. Limits of Flammability of Gases and Vapors. US Bureau of Mines, Bulletin 503.

Dlugogorski, B.Z., R.K. Hichens, E.M. Kennedy, and J.W. Bozzelli. 1998. Propagation of laminar flames in wet premixed natural gas-air mixtures. Process Safety and Environmental Protection 76(B2):81-89.

Echekki, T., and M.G. Mungal. 1990. Flame speed measurements at the tip of a slot burner: Effect of flame curvature and hydrodynamic stretch. Proceedings of the Combustion Institute 23:455.

Fiock, E.F., and C.F. Marvin. 1937. Chem. Rev. 21:367.

Frankel, M.L., and G.I. Sivashinsky. 1983. On effects due to thermal-expansion and Lewis number in spherical flame propagation. Combustion Science and Technology 31:131-38.

Frenklach, M., H. Wang, C.-L. Yu, M. Goldenberg, C.T. Bowman, R.K. Hanson, D.F. Davidson, E.J. Chang, G.P. Smith, D.M. Golden, W.C. Gardiner, and V. Lissianski. 1995. GRI-Mech: An optimized detailed ASHRAE Transactions 457 chemical reaction mechanism for methane combustion. Gas Research Institute Topical Report, No. GRI-95/ 0058, http://www.me.berkeley.edu/gri_mech.

Hynes, R.G., J.C. Mackie, and A.R. Masri. 1998. Inhibition of premixed hydrogen-air flames by 2-hheptafluoropropane. Combustion and Flame 113(4):554-65.

Jabbour, T., and D. Clodic. 2004. Refrigerant flammability and other properties--Burning velocity and refrigerant flammability classification. ASHRAE Transactions 110(2):522-33.

Johnston, R.J., and J.T. Farrell. 2005. Laminar burning velocities and Markstein lengths of aromatics at elevated temperature and pressure. Proceedings of the Combustion Institute 30:217.

Kee, R.J., J.F. Grcar, M.D. Smooke, and J.A. Miller. 1991. A Fortran computer program for modeling steady laminar one-dimensional premixed flames. Sandia National Laboratories Report, SAND85-8240.

Kee, R.J., F.M. Rupley, and J.A. Miller. 1989. CHEMKIN-II: A Fortran chemical kinetics package for the analysis of gas phase chemical kinetics. Sandia National Laboratory, SAND89-8009B.

Kee, R.J., G. Dixon-Lewis, J. Warnatz, R.E. Coltrin, and J. Miller. 1986. A Fortran computer package for the evaluation of gas-phase, multicomponent transport properties. Sandia National Laboratory, SAND86-8246.

Kim, C.H., O.C. Kwon, and G.M. Faeth. 2002. Effects of halons and halon replacements on hydrogen-fueled laminar premixed flames. Journal of Propulsion and Power 18(5):1059-67.

Kondo, S., A. Takahashi, and K. Tokuhashi. 2002a. Theoretical calculation of heat of formation and heat of combustion for several flammable gases. Journal of Hazardous Materials 94(1):37-45.

Kondo, S., A. Takahashi, K. Tokuhashi, A. Sekiya, Y. Yamada, and K. Saito. 2002b. Theoretical calculation of heat of formation for a number of moderate sized fluorinated compounds. Journal of Fluorine Chemistry 117(1):47-53.

Kondo, S., K. Takizawa, A. Takahashi, and K. Tokuhashi. 2004. Measurement and numerical analysis of flammability limits of halogenated hydrocarbons. Journal of Hazardous Materials 109:13-21.

Law, C.K. 1988. Dynamics of stretched flames. Proceedings of the Combustion Institute 22:1381.

Law, C.K., and C.K. Wu. 1984. On the determination of laminar flame speeds from stretched flames. Proceedings of the Combustion Institute 20:1941.

Law, C.K., P. Cho, M. Mizomoto, and H. Yoshida. 1986. Flame curvature and preferential diffusion in the burning intensity of Bunsen flames. Proceedings of the Combustion Institute 21:1803.

Lemmon, E.W., M.O. McLinden, and M.L. Huber. 2002. NIST reference fluid thermodynamic and transport properties--REFPROP 7.0. Gaithersburg, MD: National Institute of Standards and Technology.

Lewis, B., and B. von Elbe. 1961. Combustion, Flames, and Explosions of Gases. New York: Academic Press.

Linteris, G.T. 1995a. Acid gas production in propane-air diffusion inhibited flames. In A. Miziolek and W. Tsang, eds., Halon Replacements, pp. 225-242. Washington, DC: ACS Symposium Series 611, American Chemical Society.

Linteris, G.T. 1995b. Effect of inhibitor concentration on the inhibition mechanism of fluoromethanes in premixed methane-air flames. In A.W. Miziolek and W. Tsang, eds., Halon Replacements, pp. 260-274. Washington, DC: ACS Symposium Series 611, American Chemical Society.

Linteris, G.T. 1996. Numerically predicted structure and burning velocity of premixed CO-Ar-[O.sub.2]-[H.sub.2] flames inhibited by C[F.sub.3]H. Combustion and Flame 107:72-84.

Linteris, G.T., and L. Truett. 1996. Inhibition of premixed methane-air flames by fluoromethanes. Combustion and Flame 105:15-27.

Linteris, G.T., D.R. Burgess, V. Babushok, M. Zachariah, W. Tsang, and P. Westmoreland. 1998. Inhibition of premixed methane-air flames by fluoroethanes and fluoropropanes. Combustion and Flame 113:164-180.

Mache, H., and A. Hebra. 1941. Sitzungsber. Osterreich. Akad. Wiss. IIa(150):157.

Mallard, E., and H.L. Le Chatelier. 1883. Ann. Mines. Sec. IV 8:274.

Matalon, M. 1983. On flame stretch. Combustion Science and Technology 31:169-81.

Matalon, M., and B.J. Matkowsky. 1982. Flames as gas-dynamic discontinuities. Journal of Fluid Mechanics 124:239-59.

Mizomoto, M., Y. Asaka, S. Ikai, and C.K. Law. 1984. Effects of preferential diffusion on the burning intensity of curved flames. Proceedings of the Combustion Institute 20:1933.

Poinsot, T., T. Echekki, and M.G. Mungal. 1992. A study of the laminar flame tip and implications for premixed turbulent combustion. Combustion Science and Technology 81:45-73.

Ronney, P.D., and G.I. Sivashinsky. 1989. A theoretical-study of propagation and extinction of nonsteady spherical flame fronts. SIAM Journal on Applied Mathematics 49(4):1029-46.

Saso, Y., D.L. Zhu, H. Wang, C.K. Law, and N. Saito. 1998. Laminar burning velocities of trifluoromethane-methane mixtures: Experiment and numerical simulation. Combustion and Flame 114:457-68.

Takizawa, K., A. Takahashi, K. Tokuhashi, S. Kondo, and A. Sekiya. 2005. Burning velocity measurement of fluorinated compounds by the spherical-vessel method. Combustion and Flame 141(3):298-307.

Tseng, L.K., M.A. Ismail, and G.M. Faeth. 1993. Laminar burning velocities and Markstein numbers of hydrocarbon/air flames. Combustion and Flame 95(4):410-426.

Tsuji, H., and I. Yamaoka. 1982. Structure and extinction of near-limit flames in a stagnation flow. Proceedings of the Combustion Institute 19:1533.

UTHSCA. 1996. ImageTool, V2.00. Image Tool is a free Windows95-based program developed at the University of Texas Health Science Center at San Antonio, Texas, and available from the Internet by anonymous FTP from ftp://maxrad6.uthscsa.edu or http://ddsdx.uthscsa.edu.

Vagelopoulos, C.M., F.N. Egolfopoulos, and C.K. Law. 1994. Further considerations on the determination of laminar flame speeds with the counterflow twin-flame technique. Proceedings of the Combustion Institute 25:1341.

Van Wonterghem, J., and A. Van Tiggelen. 1954. L'epaisseur et la vitesse de propagation du front de flamme. Bulletin des Societes Chimiques Belges 63:235.

Williams, B.A., D.M. L'esperance, and J.W. Fleming. 2000. Intermediate species profiles in low-pressure methane/ oxygen flames inhibited by 2-H heptafluoropropane: Comparison of experimental data with kinetic modeling. Combustion and Flame 120:160-72.

Womeldorf, C., and W. Grosshandler. 1999. Flame extinction limits in C[H.sub.2][F.sub.2]/air mixtures. Combustion and Flame 118:25-36.

Zabetakis, M.G. 1965. Flammability Characteristics of Gases and Vapors. US Bureau of Mines, Bulletin 627.

Zachariah, M.R., W. Tsang, P.R. Westmoreland, and D.R.F. Burgess. 1995. Theoretical prediction of the thermochemistry and kinetics of reactions of CF2O with hydrogen-atom and water. Journal of Physical Chemistry 99(33):12512-19.

Zalosh, R.G. 1995. Explosion protection. In SFPE Handbook of Fire Protection Engineering, pp. 3-312-3-329. Boston: Society of Fire Protection Engineers.

Gregory T. Linteris PhD

Gregory T. Linteris is a senior researcher in the Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD. This paper is an official contribution of NIST, not subject to copyright in the United States.

(1). Certain commercial equipment, instruments, or materials are identified in this paper for adequately specifying the procedure. Such identification does not imply recommendation or endorsement by NIST or ASHRAE, nor does it imply that the materials or equipment are necessarily the best available for the intended use.

Table 1. Mixture Properties Estimated for R-152a Air Flames for Use in
Estimates of Stretch Effects on Burning Velocity

                                Equivalence Ratio
                    0.6       0.9       0.95      1         1.05

[[alpha].sub.[nu]]     0.201     0.193     0.192     0.191     0.19
  ([cm.sup.2]/s)
[D.sub.ab,u]           0.107     0.107     0.107  -            0.203
  ([cm.sup.2]/s)
Le                     1.88      1.80      1.79      1.00      0.94
[T.sub.ad,calc]     1702      2154      2190      2228      2221
  (K)
[S.sub.L,u exp]     -           25.3      26.8      29.1      29.1
  (cm/s)
[A.sub.cone]        -            1.95      2.25      2.15      2.13
  ([cm.sup.2])
[theta](deg)        -           27.5      22.2      20.2      20.3

                                Equivalence Ratio
                    1.1       1.2        1.3

[[alpha].sub.[nu]]     0.189     0.1865     0.184
  ([cm.sup.2]/s)
[D.sub.ab,u]           0.203     0.203      0.203
  ([cm.sup.2]/s)
Le                     0.93      0.92       0.91
[T.sub.ad,calc]     2190      2125       2028
  (K)
[S.sub.L,u exp]       28.2      29.3       29.0
  (cm/s)
[A.sub.cone]           2.13      1.80    -
  ([cm.sup.2])
[theta](deg)          20.3      16.4     -