AIAA 2003-4634

ACOUSTIC WEAKENING OF METHANE-, ETHYLENE-, AND H2-AIR COUNTERFLOW DIFFUSION FLAMES, AND IMPLICATIONS FOR SCRAMJET FLAMEHOLDING

G.L. Pellett*, Beth Reid**, Clare McNamara†,

Rachel Johnson‡, Amy Kabaria§, Babita Panigrahi#, and L.G. Wilson≠

Abstract

This idealized study of the subject fuel-air systems used an Oscillatory-input Opposed Jet Burner (OOJB) system developed from a previous steady-state 7.2-mm Pyrex-nozzle OJB system. More than five-hundred dynamic-extinction “flame strength” measurements were obtained on unanchored (free-floating) laminar Counterflow Diffusion Flames (CFDFs), stabilized by steady flows and perturbed by superimposed in-phase sinusoidal velocity inputs. Dynamic flame strength is presently defined as the maximum average air input velocity (Uair, at nozzle exit) that a CFDF can sustain before it extinguishes due to increasing net heat loss, precipitous decline in temperature, and an oscillating input strain rate. Although Flame Strength may, in principle, be defined in terms of maximum steady (or dynamic) axial strain rate near the airside edge of a CFDF, the entire dynamic strain field varies complexly with frequency and magnitude of input velocity oscillations (e.g., pk/pk Uair) at the nozzle exits, which greatly increases the difficulties of measurement and analysis. The present magnitude of input velocity oscillations should also correspond to acoustic pressure (pk/pk P) oscillations (which represent a surrogate measurement) if the local acoustic impedance is properly accounted for.

Numerous steady state and dynamic CFDF extinction measurements were supplemented by 25-120 Hz Hot-Wire cold-input-flow, and 4-1600 Hz Probe Microphone acoustic-field calibrations at each nozzle exit. These enabled characterizations of the acoustic weakening of CFDFs at frequencies from 4 to 1600 Hz. For the ethylene-air system: At very low frequencies (< 8 Hz), a defined Normalized Flame Response appears effectively quasi-steady, where the maximum Uair attained determines flame extinction. At transition frequencies (~10 to 50 Hz), flames are also weakened by progressively increasing phase lags in diffusive transport, reaction rate, heat release and peak temperature (with respect to oscillating inputs).

* Senior Research Scientist, Hypersonic Airbreathing Propulsion Branch/AAAC, MS 197, NASA Langley Research Center, Hampton, VA 23681 e-mail: g.l.pellett@larc.nasa.gov

** NASA–VA Governor’s School; Virginia Polytechnic Institute and State University, Blacksburg, VA

† NASA–VA Governor’s School; Princeton University, Princeton, NJ

‡ NASA–VA Governor’s School; US Air Force Academy, Colorado Springs, CO

§ NASA–VA Governor’s School; Richlands High School, Richlands, VA

# NASA–VA Governor’s School; Ocean Lakes High School, Virginia Beach, VA

≠ Lockheed Martin Space Operations, Hampton, VA

This paper is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

Approved for public release; distribution is unlimited.

39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit20-23 July 2003, Huntsville, Alabama

AIAA 2003-4634

This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

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A flame-strengthening regime then commences after 50 Hz and extends to 200 Hz and beyond. Up to, say, 500 Hz, the ethylene-air flame becomes effectively insensitive to input oscillations, and thereafter the flame is (asymptotically) unaffected to 1600 Hz, the limit of this study. The dynamic methane–air system, however, is weakened to a much greater extent than ethylene, and it doesn’t recover strength until frequencies are considerably higher.

The fundamental results of this study may apply to airbreathing scramjet engines in which critical early stages of localized subsonic flameholding are associated with fuel injection processes that “feed” recirculation zones having “sufficient” residence-time distribution. Such incipient flames may be weakened or extinguished by acoustically driven strain-rate and frequency sensitive processes, such as H-atom diffusion in a “laminar-flamelet-like” reaction zone. Because such limitations may cause the loss of “robust” flameholding, and possibly generalized flameout, it appears important to characterize these dynamic effects and assess the potential for occurrence in scramjet designs.

Introduction

Turbulent non-premixed hydrocarbon-air flames are frequently exposed to strong acoustic fields in practical combustion devices, but research in characterizing the fundamentals of flame perturbation has been sporadic [1-5]. Although our applied objective is to understand key physical/chemical flameholding processes in hydrocarbon-fueled airbreathing scramjets (see [22] for discussion of flameholding and test effects), such engines represent but one of many different applications that may be affected. Despite the recent surge of interest in unsteady flames during the early 1990’s [3-15], much remains to be understood regarding specific physical/chemical effects of acoustic oscillations on the structure and extinction of even the simplest dynamically-strained diffusion flames. Most of the recently available knowledge stems from large-activation-energy asymptotic analyses [6,8,9] and numerical simulations [5,7,11,12]. The few known experimental studies have emphasized non-intrusive measurements of species, temperature, and velocity, and resultant axial strain rates in methane-air and propane-air systems at relatively low frequencies, up to 200 Hz [10,13-15].

This paper offers a unique idealized experimental study of the subject fuel-air systems, using an Oscillatory-input Opposed Jet Burner (OOJB) system that was developed based on earlier steady-state studies [15-21]. Extensive dynamic-extinction “flame strength” measurements were obtained on unanchored (free-floating) laminar Counterflow Diffusion Flames (CFDFs), stabilized by steady input flows and perturbed by superimposed in-phase sinusoidal velocity inputs. Note we define flame strength as the maximum average air input velocity (Uair, at nozzle exit) that a CFDF can sustain before it extinguishes suddenly, due to increasing net heat loss and precipitous decline in temperature [21]. Flame strength can also be defined more generally in terms of maximum axial strain rate near the airside edge of a CFDF [21]. Under dynamic conditions flame strength also varies complexly with the frequency and magnitude of applied input velocity oscillation (pk/pk Uair).

In this study, numerous steady state and dynamic CFDF extinction measurements, supplemented by Hot Wire and Probe Microphone cold-input-flow calibrations, enabled characterizations of acoustic weakening of the subject flames at frequencies up to 1600 Hz. For the ethylene-air system at very low frequencies (e.g., <10 Hz), the response should be effectively quasi-steady, where the maximum Uair

attained determines extinction. Otherwise, at transition frequencies, dynamic flame strength can be reduced significantly due to the effects of increasing phase lags in diffusive transport. And finally, at still higher frequencies, dynamic flame strength will eventually increase, until a flame is no longer affected.

Thus, analyses of these data and comparisons with published analytic and numerical results shouldoffer new insight and understanding of acoustic straining effects on quasi-steady combustion; the probable effects of diffusive-transport phase lags with increasing frequency, which can significantly weaken diffusion flames; and the eventual development of insensitivity to high-frequency oscillations caused by rate-limited molecular diffusion of reactive species.

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Finally, with particular application to airbreathing scramjet engines, we recognize that critical early stages of localized subsonic flameholding are generally associated with fuel injection processes that “feed” recirculation zones having “sufficient” residence-time distribution [22]. Such incipient flames may be weakened or extinguished by acoustically driven strain-rate and frequency sensitive processes, such as H-atom diffusion in a “laminar-flamelet-like” reaction zone. Because such limitations may cause the loss of “robust” flameholding, and possibly generalized flameout, it is important to characterize these dynamic effects and assess the potential for occurrence in scramjet designs.

Experimental Approach

The experimental approach builds upon previous extensive studies of steady-state CFDFs detailed in [21]. The primary dynamic-effects portion of this study includes three major sets of previously unpublished experimental results for the dynamic extinction of different fuel-air systems. These data, obtained as functions of applied pk/pk voltages to twin speaker-drivers, are respectively combined with Hot Wire and Probe Microphone dynamic flow calibration data obtained under identical conditions (except for cold-flow). Thus we express dynamic flame strength results in terms of axially applied sinusoidal velocity or pressure oscillations at the nozzle exits. The combined results enable analyses of some potentially important effects due to forced oscillations of fuel and air input velocities on the “flame strength” of the subject laminar counterflow diffusion flame (CFDF) systems.

The dynamic OOJB system shown in Fig. 1 consists of several subsystems (see [18-21]). First a mass flow-metered gas mixing system delivers a N2-diluted fuel mixture, containing methane (CH4), ethylene (C2H4), or H2, to the upper speaker-driver. The fuel mixture enters a shallow cone-shaped plenum (~ 6-cm high at the center), bounded at the top by a 20-cm diameter polypropylene-coated speaker-driver diaphragm, and below by a machined metal plate. The plate has a 2.5-cm diameter hole, centered on the speaker axis, which is O-ring sealed to a vertically-oriented 2.2-cm i.d. Pyrex tube that effectively extends 38.3-cm to the nozzle exit. Similarly, mass flow-metered air is delivered to an identical speaker-driver system at the bottom. Thus in each experiment, axisymmetric laminar nearly-uniform jets of fuel mixture and air are impinged through matched pairs of 7.2 mm convergent Pyrex nozzles to form a free-floating flame (after spark ignition); this flame is centered and moves vertically with any flow imbalance. The nozzle gap is fixed at two exit diameters. The nozzle area contraction ratio is ~9:1 with convergence over ~1 tube diameter, and each nozzle is slightly "recurved" near the exit. The resultant plug-flow velocity field, which exhibits a shallow dish-shaped central depression (consistent with numerical predictions), has been previously characterized using LDV and PIV measurements [18,19]. The Pyrex nozzles, insulated by blocks of silica foam insulation, are mounted in a rigid ceramic fiber box with three Pyrex windows and a porous top of sintered metal or ceramic fiber. Argon or N2 bath gas, dispersed radially via a jet near the bottom of the box, prevents/inhibits extraneous combustion outside the central impingement region, and thus minimizes adverse flame attachment, buoyancy, and visibility effects. Fuel and air component flows were hand-controlled using micrometer valves, and monitored by the mass flowmeters.

Steady State Flame Strength Measurements

To obtain steady-state extinction of a CFDF, the mass flows of fuel mixture and air are slowly increased simultaneously, so the disk flame, located primarily on the airside, is always centered and free-floating [16-21]. Manually controlled flame centering is monitored visually, and also through the CCD output display from a horizontally oriented focusing schlieren system [18]. Whenever N2-diluted fuels are used, the combustible component is fixed at a target rate and N2 is increased. Because metered fuel and diluent flows are blended in a small glass bead mixer, and then pass through a substantial “dead volume” up to the fuel nozzle, diluent flow is increased very slowly so the drift in mixture composition has sufficient time to reach the nozzle exit. After each extinction (blowoff), or rupture of the (very) flat disk-shaped-flame structure (monitored via focusing schlieren), a residual ring-shaped flame quickly establishes at a stable location centered on the stagnation point, where the degree of mixing is maximized. Mass flow rates of each component are then recorded for extinction.

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The global nozzle-area-average jet velocity used to evaluate flame strength at extinction, Uair, is

calculated from the mass flow of dry “service” air standardized at 273 oK and 1 atm, and measured nozzle exit diameters, 7.2 mm. The Ufuel is evaluated similarly from component mass flows. Corresponding Reynolds numbers are generally less than 1500, but are not so low that CFDFs are unacceptably thick or non one-dimensional.

To restore the ring-like “tribrachial” or “edge” flame to a disk flame, respective flows are gradually decreased, so the slowly shrinking ring approaches ~1 jet diameter on the stagnation surface. At flame restoration the ring suddenly propagates inward and shifts axially > 1 mm to the airside. After flame restoration, another set of extinction/restoration measurements is almost always obtained for replication purposes.

In previous studies of H2–air and HC–air systems, flame restoration was found independent of jet diameter, and a large hysteresis generally separated extinction and restoration [16-21]. It was concluded that flame restoration occurs as a velocity-limited piloted-reignition along a thin stagnated region containing inter-diffused jet flows, or, when the "stretched laminar burning velocity" finally exceeds the maximum outward radial velocity [21]. Recent very detailed numerical simulations [23,24] fully support our earlier simplified description. Note, for restoration, the radial strain rate in the central stagnation region must always be smaller than that required for extinction. Otherwise blowoff and restoration would occur at essentially the same flow rates -- which was observed for methane–air using (unnecessarily) small 2.7-mm tube-OJB’s [16].

Dynamic Flame Strength Measurements

Dynamic extinction measurements were obtained using the same basic flow technique as in the steady-state measurements, except the twin speakers were driven in-phase by a pre-selected applied voltage and frequency. Thus, a waveform generator was set to a desired frequency and sinusoidal output of 1.0 volt amplitude, which became input to a variable speaker-amplifier. Twin analog outputs from the amplifier powered the twin speakers. The amplifier was manually adjusted to pre-selected peak-to-peak (pk/pk) output voltages while viewing waveform displays on a LeCroy digital oscilloscope. Once the speaker-drivers were set, dynamic flame strength measurements were obtained using the same flow procedures as discussed above. If flow reversal in the nozzles appeared likely, based on previous hot-wire flow calibrations (described later) and/or the flame was too unstable, based on visual and focusing schlieren observations and also difficulties in maintaining a centered and unanchored flame, a lower pk/pk applied voltage was used.

During early stages of the study, dynamic extinction measurements were obtained for the subject fuel-air systems over a range of pk/pk speaker-driver voltages, at respective frequencies of 30, 60, 120 Hz, and 25, 50, 100 Hz. Thus three limited sets of dynamic flame strength data corresponded to known speaker-voltage waveforms. To analyze these data in terms of physically realistic input velocities and strain rates that effectively characterize extinction limits, independent nozzle exit velocity information was needed as a function of applied speaker voltage. (Note that limited, but more definitive measure-ments of dynamic axial strain rate at the airside flame edge have been reported by others [13-15].)

Thus limited hot-wire velocimetry measurements of cold flows at the nozzle exits were obtained at three frequencies each, over two distinct time periods. In each case, pk/pk sinusoidal air and fuel cold-flow input velocities were measured at the nozzle exits corresponding to respective pk/pk speaker voltages, steady input mass flows, and applied frequency. The respective hot-wire velocity data sets were analyzed using three levels of empirical curve fits. Thus dynamic extinction data could be transformed and analyzed as functions of pk/pk sinusoidal air input velocities. The inputs were calculated as functions of pk/pk speaker voltage, mass flow rates of air and fuel, and frequency, using one of the independently-derived expressions that produced nearly identical results when compared with two of the others (obtained a year apart).

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Upon combining the dynamic-velocity and extinction data, it was found that for any given C2H4 mass flow, e.g. 3 SLPM, the measured flame strength, Uair, was a linear decreasing function of the pk/pk sinusoidal velocity inputs, pk/pk (Uair). The resultant negative slopes of these data were primarily a function of frequency only, and didn’t appear to vary greatly with the input mass flow rate of C2H4. (Later on, different input mass flows and steady-state flame strengths were accounted-for by normalizing the Flame Response data; see Results section.)

Errors in extinction limits stemmed from various sources; and some are compensated for internally. For example, according to the ideal gas law, jet velocities at constant mass flow vary linearly with input temperature. Because mass flowmeter measurements stem from internal measurements of temperature rise per unit of applied resistive-heating-power, resultant mass flow measurements are unaffected by variations in actual jet input temperature and mean velocity, via the ideal gas law. Thus potential data scatter due to temperature variations was significantly reduced, which is especially helpful when heated fuel jets are used. However, variations in atmospheric pressure do affect the data slightly, and these are not routinely accounted-for. Although the same OJB was used throughout this study, on an absolute basis the calculated jet exit velocities are sensitive to (measured) jet diameter squared, and strain rates are sensitive to diameter cubed. This can be important when results are compared from different-size OJBs.

Results

Steady State Flame Strength

Steady-state extinction results for C2H4/N2–air CFDFs, shown in Fig. 2, exhibit typically observed patterns of data reproducibility and variation of flame strength with input mole fraction for a simple hydrocarbon fuel. A minor extrapolation of the asymptotic data trend from a simple polynomial fit (well-established in earlier papers [16-21]) indicates a flame strength of 310 cm/s for 100% C2H4–air flames, at a standard input temperature of 273 K. This corresponds to an applied stress of 310/0.72 = 430 1/s, and a global axial strain rate at the airside edge of 2 x 430 = 860 1/s for an idealized 1-D CFDF with uniform axial velocity input. These measurements represent a chemical kinetic limiting rate for a CFDF that is unaffected by the diffusion rate and thermodynamic properties of the fuel diluent. The indicatedraw C2H4 inputs, in uncorrected Standard Liters per Minute (SLPM), do not contain a factor of 0.69 for ethylene mass flows (based on heat capacity) that is otherwise applied to all calculated quantities.

The steady-state flame strength for 100% C2H4–air can be compared with previous measurements for 100% CH4–air and 18% H2–air CFDFs obtained using the same 7.2 mm OJB, and 100% H2–air CFDFs that were characterized earlier using a series of scaled OJBs [21]. Based on the previously measured flame strength of 113.6 cm/s at 300 K for CH4–air, the C2H4–air flame is 2.73 times stronger than the CH4–air flame. And based on the extensive H2–air results in [21], the C2H4–air flame is 12.9 times weaker than the 100% H2–air CFDF.

Dynamic Flame Strength, and Transformation of Dynamic Flame Data, using Limited Hot-Wire Velocimetry of Cold Flows

Fig. 3 exemplifies a transformation of the dynamic extinction data using Hot Wire data to examine the effect of sinusoidal pk/pk exit velocity (rather than sinusoidal pk/pk voltage to speakers) on the flame strength of C2H4/N2–air CFDFs, for 3 SLPM (raw) C2H4 input flows. The abscissa is based on our empirical analysis of Hot Wire velocimetry data on nozzle exit flows, from 25-120 Hz, and an extrapolation of the empirical pk/pk exit velocity function to higher frequency. The data in Fig. 3 apply to a critical range of frequencies over which the weakening effects on flame strength appeared to grow, and then become negligible. The data at 100 and 200 Hz show the response of flame strength to projected pk/pk Uair is linear, even though the amplitudes of oscillation are substantial compared with the mean Uair. Checks at other flows and frequencies indicate similar linear responses, even under

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conditions where local flow reversal is believed to occur (which we generally avoid). The large transition in response of flame strength that occurs between 450 and 500 Hz appears to mark a so-called high frequency transition, where flame strength is no longer affected.

Thus the linear slopes, defined in Fig. 3 and in numerous similar plots, which are based on extrapolation of an empirical pk/pk exit velocity function to frequencies higher than 120Hz, are used to characterize the sensitivity of flame strength to projected pk/pk sinusoidal velocity inputs at various frequencies. This slope is defined as the “dynamic velocity response” of flame strength for a laminar CFDF, and it provides a possible measure of the dynamic response of idealized flameholding to imposed velocity oscillations as a function of frequency (shown in Fig. 5).

Fig. 4 shows a wide range of dynamic extinction results, representing ~ 200 C2H4/N2–air CFDF measurements. These were obtained using various sinusoidal speaker-voltage inputs that correspond to axial velocity inputs of differing pk/pk Uair and frequency. For certain mid-range frequencies, the data illustrate significant impacts of oscillatory velocity inputs on flame strength (up to a factor of 2) over a wide range of raw C2H4 inputs, and resultant C2H4/N2 mole fractions. At frequencies of 500 to 1600 Hz there is very little effect of oscillation on flame strength compared to 0 Hz (steady-state). At very low frequencies (e.g. 4 and 10 Hz) some minor “apparent” weakening is evident, but this occurred at very large amplitudes of oscillation which are additive to the imposed mean velocity (strain rate).

Fig. 5 summarizes the resultant “dynamic velocity response” of flame strength for C2H4/N2–air CFDFs obtained from ~ 200 measurements, and based on velocity fluctuations derived from empirically-projections of Hot Wire data. Because the respective data sets for 3, 5, and 8 SLPM C2H4 exhibit very similar trends and slightly more scatter, data averaging is used to define the effect of frequency more clearly. The 4 Hz, and possibly 10 Hz, data are essentially quasi-steady, so that limiting molecular flame radical transport and reaction processes are fast enough to follow the oscillations in input strain rate. In such cases, flame extinction occurs near peak input velocity, which equals Uair + (pk/pk Uair)/2. At higher frequencies, however, the dynamic velocity response of flame strength grows more negative until, just beyond 250 Hz, it decreases steeply by a factor of four. Shortly after this fall-off, a very steep recovery occurs between 450 and 500 Hz, which appears to define a highly weakened “notch” region terminated by a steep high-frequency cut-off limit. The reproducibility of the extinction data is remarkably good (typically + 3%), even at highly-sensitive frequencies, e.g. 475 Hz. At frequencies above 500 Hz, the CFDFs are minimally responsive, and tend asymptotically to become totally unresponsive with respect to extinction.

The possible influence of significant acoustic resonance effects became a major question. The small waviness in the spline fits of Fig. 5 suggested minor resonance phenomena over some regions. But more importantly, the large and abrupt changes in dynamic velocity response around the “notch” region suggested that significant resonance phenomena might be occurring. In this case the 38-cm length of Pyrex tube to each nozzle exit, plus ~ 6-cm of dead space between the tube and the speaker diaphragm in the plenum region, coincides with one-half wavelength at 395 Hz (= (348/0.44)/2), which would promote constructive interference with the speaker systems. Although obvious changes in sound intensity were not heard when frequency was changed at fixed applied voltage, it was nevertheless considered important to conduct a sound measurement survey.

Probe Microphone Measurements

A calibrated Probe Microphone system was used to characterize the localized sound pressure field at the air nozzle exit without flow (note fuel speaker was powered identically), and thus characterize possible resonance phenomena. The results, in Fig. 6, show substantial effects of acoustic resonance equivalent to 1/2, 1, 3/2, and 2 wavelengths. Presently it is assumed that the Euler equation can be solved to obtain the corresponding oscillating velocity field in a confined environment, where acoustic impedance is important, but this is to be determined. Meanwhile, the dynamic extinction results are analyzed in a similar manner as before, using the sound pressure data as follows.

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Transformation of Dynamic Data using Probe Microphone Measurements

Fig. 7 shows the same dynamic extinction data as in Fig. 3, except the new abscissa is measured pk/pk sinusoidal acoustic pressure at the air nozzle exit. The data trends are similarly linear, and thus slopes denoted as “dynamic-pressure flame-response” are defined. All the dynamic extinction data are analyzed as before, and no significant non-linearity is apparent in the complete data set. Although corresponding pk/pk sinusoidal input velocities are preferable, to allow a more physically meaningful analysis of the results, this requires a solution of the Euler equation, which is presently unavailable.

Finally, the resultant “dynamic-pressure-response” slopes (for the same dynamic extinction data as in Fig. 5) are plotted in Fig. 8 as a function of frequency. The most striking feature of this plot is that the former “notch” in dynamic-velocity-response data has effectively disappeared as a result of normalizing the flame strength data with measured sound pressures. Second, a different (and more accurate) mid-frequency transition, and a “high-frequency” cutoff limit near 200 Hz, are apparent, and these are followed by an asymptotic approach to “complete insensitivity” at frequencies up to 1600 Hz, the limit of this study.

Refinement of the Flame Response Function for the C2H4/N2–Air System

The results in Fig. 8, which provisionally defined the Flame Response of the C2H4/N2–air system at an earlier stage of the study (11/02), were then supplemented by additional Flame Strength data to refine the Flame Response function, and to attempt further normalization of the results.

Thus the resultant cumulative set of Flame strength data were reanalyzed to obtain linear slopes as a function of pk/pk pressure, as shown earlier in Fig. 7, and to determine a more comprehensive Flame Response function, shown in Fig. 9. A comparison of the respective “Smooth fits” of averaged Flame Responses, for different ethylene flow rates, shows surprisingly little difference, and exemplifies the reproducibility of the results. However, inspection of Fig. 9 shows a tendency for increased flame weakening with increased ethylene flow rate, especially in the 8 to 50 Hz data. This suggests that the data in Fig. 9 can be normalized by, e.g., steady-state Flame Strength to reduce the apparent data scatter.

After the data in Fig. 9 are normalized by steady-state Flame Strengths for the respective ethylene flows of 3, 5, and 8 SLPM (Uair,ss = 210.8, 256.4, and 289.6 cm/s), and also multiplied by 100 to define the percent change in Flame Strength per unit of pk/pk pressure (Pa), the resultant Normalized Flame Response data are shown in Fig. 10. Note the “weakened-flame data” in the 8 to 100 Hz range were most affected, with a substantial reduction of scatter for the 3 to 8 SLPM range of ethylene mass flows. Note also that this represents a respectably large range of steady state Flame Strengths and corresponding mole fractions of ethylene.

Further analyses of the Figure 10 Normalized Flame Response Data

Significant effort was given to empirically analyze the data, to define simple relationships that help characterize and generalize the data set. First, to facilitate subsequent power-law and log plot analyses, the negative-signed data were made positive, as shown in Fig. 11. Second, some trial plots quickly reinforced the observation that an apparently fundamental change occurred near 50 Hz, which, in fact, required separate analyses of the data about the 50 Hz data point.

First the the “higher” frequency, 50 to 1600 Hz, data of Fig. 11 were analyzed to determine functional relationships that characterize “flame strengthening” from the turn-around point, and throughout the asymptotic approach towards zero Flame Response. Fig. 12 shows a power-law fit that exhibits a nearly unity inverse relationship to imposed frequency. Despite the appearance of a reasonable fit, there is a considerable (and deceptive) lack of good fit at low frequencies, which is less evident due to the curve’s steepness. By plotting the Fig. 12 data as a function of inverse frequency, a fairly good fit is obtained in Fig. 13, which shows departure from a horizontal line that would otherwise characterize a perfect inverse relationship. Figure 14 represents a semi-log approach that incorporates Flame

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Response per unit frequency as the ordinate. This empiricism correlates all the data very well out to 1600 Hz (although the plot terminates at 600 Hz).

Next the “low frequency” portion of the data in Fig. 11 were analyzed. First, multiplication of the (negative) Normalized Flame Response ordinate by frequency produced the unusual result in Fig. 15, where the entire data set was included. Obviously, the 8 to 50 Hz data conform to a smooth relationship that differs drastically when compared with the “previously well behaved“ 50 to 1600 Hz data trends. Of course, with increasing frequency, multiplication of increasingly small Flame Responses by increasingly large frequencies tends to magnify the effect. Clearly, however, this result strongly emphasizes the fact that a major transition occurred in the vicinity of 50 Hz. Finally, Figure 16 is a simple linear plot of the 8 to 50 Hz data of Fig. 15, which provides a good correlation of the data, and also an indication of the projected intercept for quasi-steady behavior.

The Effects of Input Phase on Dynamic Flame Response

It was considered important, from both theoretical and practical standpoints, to determine the possible effects of fuel input phase on Flame Response, with respect to the phase of sinusoidal air inputs. Note that the previous single waveform preamplifier and twin output amplifier were replaced by a system of twin preamplifiers, and an amplifier with a settable phase lag. In all cases the respective voltage waveforms applied to the twin speakers were monitored using a digital oscilloscope (LeCroy) system. Fig. 17, which shows the results obtained at 150 Hz, indicates there is a mild phase effect over the very large range investigated. Each data point represents at least duplicate determinations, and at zero phase the data point represents an average of determinations throughout the study.

Fig. 18 shows all the phase-effect data obtained, which included frequencies of 50, 75, 100, 150 and 200 Hz. Although the data trends for the two higher frequencies are nearly flat (including the 150 Hz data discussed above), the average trends for the lower three frequencies trend upward and show increasing scatter, especially the 75 and 50 Hz results. The apparent upward trends between zero phase and 180 degrees can be rationalized on the basis that, e.g., a 180 degree shift at 50 Hz represents a “push-pull” oscillation that is effectively 100 Hz. Despite the scatter, these “independently-derived” zero-phase intercepts agree very well with the corresponding averaged values in the previously evaluated zero-phase data shown in Fig. 9 (and 10).

The Normalized Dynamic Flame Response of Methane-Air CFDF’s

Figure 19 shows normalized Flame Response results, recently obtained for pure methane fuel, plotted for comparison with the entire set of ethylene results from Fig. 10. Clearly, the Flame Response data demonstrate that methane flames are weakened to a much greater extent than ethylene flames, and the “progressive strengthening” at higher frequencies (notably after 30 to 50 Hz) is displaced towards significantly higher frequencies with respect to ethylene. Because all the data are normalized with respect to steady-state flame strengths (for recent methane-air results, Uair,ss = 100.4 cm/s at 273 K), the absolute differences in Flame Response between ethylene and methane are somewhat smaller.

Although data for 18 mole % H2/N2–Air were obtained and analyzed, there was some systematic uncertainty in the speaker voltages that were recorded. Nevertheless, because hydrogen data were obtained in 1998 along with methane–air data using the same OOJB system, we found that Flame (weakening) Responses for hydrogen were considerably smaller than for methane. Based on considerations of the data, and also the molecular diffusion and reactivity of H2, we project that 18 % hydrogen/N2 is probably weakened somewhat less than ethylene.

Implications for Scramjet Combustors

Possible implications of the dynamic results for scramjet combustion are certainly varied and difficult to determine, considering the known complexity of flameholding processes, reviewed in [22]. One relatively obvious approach is to consider fundamental resonant frequencies in cavity pressure oscillations caused by ducted supersonic flows, and resultant turbulent shear layer flows, over both

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open and closed cavities [25]. For example, application of a “modified Rossiter” expression, reviewed in [25], predicts a fundamental frequency of 2960 Hz for a typical free stream air velocity of 1500 m/s over an open cavity of 10-cm. length. Because this frequency is considerably beyond the present high-responsivity range for ethylene-air combustion-extinction, such induced oscillations may not directly affect open-cavity-based flameholding in this idealized case. However, it seems prudent that acoustic measurements and more detailed analyses of flameholding in various cavities, subsonic wake flows, and in the vicinity of possibly-oscillating fuel jets are needed to fully assess the potential for flame weakening effects in both test engines and flight vehicles.

Findings and Concluding Remarks

This paper offers a unique idealized experimental study of the subject fuel-air systems using an Oscillatory-input Opposed Jet Burner (OOJB) system. Extensive dynamic-extinction “flame strength” measurements were obtained on unanchored (free-floating) laminar Counterflow Diffusion Flames (CFDFs), stabilized by steady input flows and perturbed by superimposed in-phase sinusoidal velocity inputs at both the fuel and air nozzle exits. Both limited Hot-Wire measurements of velocity fluctuations at the nozzle exits, and much more extensive and accurate Probe Microphone measurements of acoustic pressure, were obtained with cold flows, and used to analyze the dynamic flame strength data.

The numerous steady state and dynamic CFDF extinction measurements in this study, coupled with the two independent dynamic cold-flow nozzle-input calibrations, have led to the following findings and provisional conclusions:

1. The experimental ethylene-air extinction results are unique, but are fundamentally consistent with limited published results on the structure and extinction of forced unsteady counterflow diffusion flames (CFDFs). This consistency applies to overall projected effects of increased oscillatory strain and imposed frequency, based on analytic asymptotic studies, numerical simulations of unsteady methane-air flames, and simulations of the structure and extinction of hydrogen-air flames.

2. Available numerical simulations and limited experimental results indicate that finite-rate diffusive responses of key species (e.g. H-atom) control phase lags (relative to input flow oscillations) in concentration and temperature profiles of dynamically perturbed flames, which leads to flame weakening. At high frequencies, rate-limited diffusive responses ultimately cause flame insensitivity.

3. Dynamic Flame Strength (Uair at extinction) measures flame weakening, and is linearly proportional to pk/pk Velocity (HW), and also pk/pk Pressure (PM).

4. Probe Microphone response measurements effectively normalized-out substantial acoustic resonance effects in dynamic Flame Strength data obtained from the OOJB system.

5. Flame Response was successfully normalized by steady state Flame Strength. Normalized Flame Response is defined as a percentage change in Flame Strength per unit Pascal of peak-to-peak pressure oscillation, namely, FR = 100 d(Uair / Uair,ss) / d (pkpk P).

6. Acoustic weakening is significant for the ethylene-air system. A “fundamental transition” in ethylene Flame Response occurs at ~ 50 Hz, which presently cannot be adequately explained.

7. For the ethylene-air system at very low frequencies (<10 Hz), the dynamic Flame Strength, or Flame Response, is effectively quasi-steady, in which the maximum Uair (and hence strain rate) attained determines extinction. At higher frequencies (e.g. to 50 Hz), the Flame Response is most likely affected by increasing internal phase lags in diffusive transport. (Note that numerical results for methane–Air CFDF [Ref.11] indicate that internal phase lags for Tmax and heat release rate begin at 10 Hz; and extend to 5000 Hz!) Although moderate flame weakening occurs for ethylene between 10 and 50 Hz, major flame strengthening begins after the “fundamental transition,” up to 200 Hz and higher. A

10

practical high-frequency limit for dynamic ethylene flame sensitivity is effectively ~ 200 Hz. However, asymptotic strengthening continues to 1600 Hz (limit of study).

8. Systematic Fuel-Air input phase effects were measured, especially for 50 Hz (for example), but the relative changes in Flame Response appear relatively small.

9. Acoustic Weakening of methane flames is much greater than for ethylene flames, up to nearly 300 Hz; and the flame strength of methane flames is 2.7 x smaller than for ethylene.

10. Scramjet subsonic flameholding may be affected up to 300 Hz. Mechanisms may include acoustic resonance in cavity flameholders and fuel-injector wakes; near-field coupling with subsonic vortex shedding; and dynamic coupling with unsteady fuel injection systems.

11. Measurements of acoustic fields are needed to assess possible effects of localized acoustic fields on critical flameholding in ground-based and flight tests of scramjet engine configurations.

References

1. Clarke, J.F., and Stegen, G.R., “Some Unsteady Motions of a Diffusion Flame Sheet,” J. Fluid Mech., 34: part 2, 1968, pp. 343-358.

2. Saitoh, T., and Otsuks, Y., “Unsteady Behavior of Diffusion Flames and Premixed Flames for Counter Flow Geometry,” Comb. Sci. Tech. 12: 1976, pp. 135-146.

3. Stahl, G., and Warnatz, J., “Numerical Investigation of Time-Dependent Properties and Extinction of Strained Methane- and Propane-Air Flamelets,” Combust. Flame, 85: 1991, pp. 285-299.

4. Ghoniem, A.F., Soteriou, M.C., and Knio, O.M., “Effect of Steady and Periodic Strain on Unsteady Flamelet Combustion,” Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute,1992, pp. 223-230.

5. Darabiha, N., “Transient Behavior of Laminar Counterflow Hydrogen-Air Diffusion Flames with Complex Chemistry,” Comb. Sci. Tech., 86: 163-181 (1992).

6. Kim, J.S. and Williams, F.A., “Contribution of Strained Diffusion Flames to Acoustic Pressure Response,” Combust. Flame, 98: 1994, pp. 279-299.

7. Egolfopoulos, F.N., “Dynamics and Structure of Unsteady, Strained, Laminar Premixed Flames, Twenty-Fifth Symposium (International) on Combustion, The Combustion Institute,1994, pp. 1365-1373.

8. Im, H.G, Bechtold, J.K. and Law, C.K., “Counterflow Diffusion Flames with Unsteady Strain Rates,” AIAA Paper 95-0128, Jan., 1995, 9 pp.

9. Im, H.G., Law, C.K., Kim, J.S. and Williams, F.A., “Response of Counterflow Diffusion Flames to Oscillating Strain Rates,” Combust. Flame, 100: 21-30 (1995).

10. Brown, T.M., and Pitz, R.W., “Experimental Investigation of Counterflow Diffusion Flames with Oscillatory Stretch,” AIAA Paper 96-0124, Jan. 1996.

11. Egolfopoulos, F. and Campbell, C.S., “Unsteady Counterflowing Strained Diffusion Flames: Diffusion-Limited Frequency Response,” J. Fluid Mech. 318: 1996, pp. 1-29.

11

12. Kistler, J.S., Sung, C.J., Kreutz, T.G., Law, C.K., Nishioka, M., “Extinction of Counterflow Diffusion Flames Under Velocity Oscillations,” Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, 1996, pp. 113-120.

13. Brown, T.M., Pitz, R.W., and Sung, C.J., “Oscillatory Stretch Effects on the Structure and Extinction of Counterflow Diffusion Flames,” Twenty-Seventh Symposium (International) on Combustion, The Combustion Institute, 1998, pp. 703-710.

14. Decroix, M.E., and Roberts, W.L., “Study of Transient Effects on the Extinction Limits of an Unsteady Counterflow Diffusion Flame,” Combust. Sci and Tech.146: 1999, pp. 57-84.

15. Welle, E.J., Roberts, W.L., Donbar, J.M., Carter, C.D., DeCroix, M.E., “Simultaneous PIV and OH-PLIF Measurements in an Unsteady Counterflow Propane-Air Diffusion Flame,” Proceedings of the Combustion Institute, 28, 2001, pp. 2021-2027.

16. Pellett, G.L., Northam, G.B., Wilson, L.G., "Counterflow Diffusion Flames of Hydrogen, and Hydrogen Plus Methane, Ethylene, Propane, and Silane, vs. Air: Strain Rates at Extinction," AIAA Paper 91-0370, Jan., 1991, 17 pp.

17. Pellett, G.L., Northam, G.B., Wilson, L.G., "Strain-Induced Extinction of Hydrogen–Air Counterflow Diffusion Flames: Effects of Steam, CO2, N2 , and O2 Additives to Air," AIAA Paper 92-0877, Jan., 1992, 15 pp.

18. Pellett, G. L., Roberts, W. L., Wilson, L. G., Humphreys, W. M., Jr., Bartram, S. M., Weinstein, L. M., and Isaac, K. M., "Structure of Hydrogen–Air Counterflow Diffusion Flames Obtained by Focusing Schlieren, Shadowgraph, PIV, Thermometry, and Computation,” AIAA Paper 94-2300, June 1994, 23 pp.

19. Pellett, G. L., Wilson, L. G., Humphreys, W. M.,Jr., Bartram, S. M., Gartrell, L. R., and Isaac, K. M., Roberts, W. L., IV, and Northam, G. B., "Velocity Fields of Axisymmetric Hydrogen-Air Counterflow Diffusion Flames from LDV, PIV, and Numerical Computation," AIAA paper 95-3112, July 1995, 23 pp.

20. Isaac, K. M., Ho, Y. H., Zhao, J., Pellett, G. L., and Northam, G. B., "Global Characteristics and Structure of Hydrogen-Air Counterflow Diffusion Flames: A One-Dimensional Model," AIAA Paper 94-0680, Jan.,1994. Also, Zhao, J., Isaac, K. M., and Pellett, G. L., J. Propul. Power 12, No. 3: 534-542 (1996).

21. Pellett, G.L., Isaac, K.M., Humphreys, W.M., Jr., Gartrell, L.R., Roberts, W.L., Dancey, C.L., and Northam, G.B., "Velocity and Thermal Structure, and Strain-Induced Extinction of 14 to 100% Hydrogen-Air Counterflow Diffusion Flames," Combust. Flame 112, No. 4, 1998, pp. 575-592.

22. Pellett, G.L., Bruno, C., and Chinitz, W., “Review of Air Vitiation Effects on Scramjet Ignition and Flameholding Combustion Processes,” AIAA Paper 2002-3880, July, 2002, 37 pp.

23. Frouzakis, C.E., Lee, J., Tomboulides, A.G., and Boulouchos, K., “Two-Dimensional Direct Numerical Simulation of Opposed-Jet Hydrogen-Air Diffusion Flame,” Twenty-Seventh Symposium (International) on Combustion, The Combustion Institute, 1998, pp. 571-577.

24. Lee, J., Frouzakis, C.E., and Boulouchos, K., “Two-Dimensional Direct Numerical Simulation of Opposed-Jet Hydrogen-Air Diffusion Flames: Transition from a Diffusion to an Edge Flame,” Proceedings of the Combustion Institute, 28, 2000, pp. 801-806.

25. Ben-Yakar and Hanson, R.K., “Cavity Flameholders for Ignition and Flame Stabilization in Scramjets: Review and Experimental Study,” AIAA Paper 98-3122, July 1998, 17 pp.

12

Fig. 1. Schematic of Oscillatory Opposed Jet Burner (OOJB) system with twin 20-cm speaker-drivers. Diode laser system is passive in this study.

Focussing Schlieren Systemused here to visualize flows and disk-shaped flame structure, in horizontal direction. (Details in Pellett et al., AIAA-94-2300, and also AIAA-95-3112)

13

0

100

200

300

400

0 0.2 0.4 0.6 0.8 1

Uai

r, F

lam

e S

tren

gth

, cm

/s

Mole Fraction Ethylene in Nitrogen-diluted Fuel Mix

SLPM C 2 H 4 (raw) = 3

2

1

5

8109

76

4

1.5

U air = uniform air velocity at nozzle exit [= Flame Strength]

--- 310 cm/s[2.7 x methane,but 13 x smallerthan hydrogen]

Asymptote

Flame

No Flame

0

100

200

300

0 100 200 300 400 500 600

100 Hz

200

300

400

450

500

Uai

r,

Fla

me

Str

eng

th, c

m/s

Empirically-Extrapolated pk/pk Exit Velocity, cm/s

3 SLPM C 2 H 4 (raw)

U air = uniform air velocity at nozzle exit [= Flame Strength]

AppliedFrequency

Fig. 2. Flame Strength at steady-state extinction of C2H4/N2–Air Counter-flow Diffusion Flames (CFDFs), using 7.2 mm Pyrex Nozzle OOJB.

Fig. 3. Dynamic extinction of C2H4/N2–Air CFDFs using 7.2 mm Pyrex nozzle OOJB, with axially-applied sinusoidal velocity inputs for 3 SLPM (raw) C2H4

flows. Abscissa is based on an empirical analysis of Hot-Wire Velocimetry data (versus voltage applied to speakers) on nozzle-exit cold-air flows from 25-120 Hz; and an extrapolation of the same empirical pk/pk exit-velocity expression to higher frequencies.

14

0

100

200

300

400

0 0.2 0.4 0.6 0.8 1

4 Hz10

25501002002503003504004504755006008001000120016000 (ss)

Uai

r, F

lam

e S

tren

gth

, cm

/s

Mole Fraction Ethylene in Nitrogen-diluted Fuel Mix

SLPM C 2 H 4 (raw) = 3

2

1

5

8109

76

4

1.5

U air = uniform air velocity at nozzle exit [= Flame Strength]

AppliedFrequency

Increasing Osc. Amplitude

No Flame

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

10 100 1000

Dyn

amic

Vel

oci

ty R

esp

on

se, D

imen

sio

nle

ss

Imposed Frequency of Sinusoidal Velocity Inputs, Hz

Dynamic Velocity Response = d U air / d (pkpk U air )

Data averaged for3, 5, 8 SLPM ethylene

Spline Fit

Hot Wire Calibration Range

SiFig. 4. Steady-state and dynamic extinction of C2H4/N2–Air CFDFs, using 7.2 mm Nozzle OOJB with 1- 10 SLPM C2H4 flows, and axially-applied in-phase sinusoidal velocity inputs of C2H4/N2 and air at varied amplitude and frequency. Early data up to 11/02 are included here.

Fig. 5. Dynamic Velocity Response for extinction of C2H4/N2–Air CFDFs, using 7.2 mm Pyrex nozzle OOJB with 3, 5, 8 SLPM C2H4

flows, and axial sinusoidal velocity inputs. Dynamic Velocity Response is based on pk/pk nozzle exit air velocities that were originally derived from Hot Wire measurements on cold air and N2

flows at 25-120 Hz, and then empirically projected at higher frequencies.

15

0

20

40

60

80

100

0 500 1000 1500 2000

pk/

pk

Pre

ssu

re, P

asca

l

Applied Frequency, Hz

For zero flows of Air and Fuel (N 2).

Probe tip located in nozzle exit plane, at

2/3 radius out, tilted 25 o from exit plane.

0

100

200

300

0 10 20 30 40 50

100 Hz

200

300

400

450

500

Uai

r,

Fla

me

Str

eng

th, c

m/s

pk/pk Sinusoidal Pressure at Nozzle Exit, Pa

3 SLPM C 2 H 4 (raw)

U air = uniform air velocity at nozzle exit [= Flame Strength]

Applied Frequency

Fig. 6. Probe Microphone response of sinusoidal speaker-driver sound pressure at 7.2 mm Pyrex nozzle exit without flow, using calibrated Probe Microphone with both 50 and 100 mm probe tubes. The pk/pk voltage applied to the speaker-drivers was fixed at 1.0 volt in this calibration.

Fig. 7. Dynamic Extinction of C2H4–Air CFDFs using 7.2 mm Nozzle OOJB, with axially-applied sinusoidal velocity inputs (same data as analyzed in Fig. 3). The abscissa is now based on (surrogate) Probe Microphone pressure measurements of sound at nozzle exit without flow, shown in Fig. 6.

16

-20

-15

-10

-5

0

5

10 100 1000

Ave of 3,5,8 SLPM C 2 H4

Fla

me

Res

po

nse

, cm

/s-P

a

Imposed Frequency of Sinusoidal Velocity Inputs, Hz

Flame Response = d U air / d (pkpk P), cm/s-Pa

Smooth FitEarly Data (to 11/02)

FlameWeakening

-20

-15

-10

-5

0

5

10 100 1000

3 SLPM C 2 H458Ave of 3,5,8F

lam

e R

esp

on

se, c

m/s

-Pa

Imposed Frequency of Sinusoidal Velocity Inputs, Hz

Flame Response = d U air / d (pkpk P), cm/s-Pa

Smooth Fit

All 8-1600 Hz data

FlameWeakening

Fig. 8. Dynamic Pressure Response for extinction of C2H4/N2–Air CFDFs using 7.2 mm Pyrex Nozzle OOJB with 3, 5, 8 SLPM C2H4

flows, and axially-applied sinusoidal velocity Inputs. Dynamic-Pressure Flame-Response is based directly on calibrated Probe Microphone measurements of sound at air nozzle exit without flow, shown in Fig. 6.

Fig. 9. Complete set of Flame Response data for dynamic extinction of C2H4–Air CFDFs using 7.2 mm Pyrex Nozzle OOJB with 3, 5, 8 SLPM C2H4 flows, and axially applied sinusoidal velocity inputs probed by microphone.

17

-8

-6

-4

-2

0

2

10 100 1000

3 SLPM C 2 H4

5

8

Ave of 3,5,8

No

rmal

ized

Fla

me

Res

po

nse

, 1/P

a

Imposed Frequency of Sinusoidal Velocity Inputs, Hz

Flame Response (Normalized by U air,ss )

= 100 d (U air /U air,ss ) / d (pkpk P), 1/Pa

Smooth Fit

All 8 - 1600 Hz Data

FlameWeakening

-2

0

2

4

6

8

10 100 1000

3 SLPM C 2 H4

5

8

Ave of 3, 5, 8

- N

orm

aliz

ed F

lam

e R

esp

on

se, 1

/Pa

Imposed Frequency of Sinusoidal Velocity Inputs, Hz

Flame Response (Normalized by U air,ss )

= 100 d (U air /U air,ss )/ d (pkpk P), 1/Pa

All 8 - 1600 Hz Data

FlameWeakening

Fig. 10. Complete set of Fig. 9 Flame Response data normalized by steady-state Flame Strength, for dynamic extinction of C2H4–Air CFDFs using 7.2 mm Pyrex Nozzle OOJB with 3, 5, 8 SLPM C2H4 flows, and axially applied sinusoidal velocity inputs probed by microphone.

Fig. 11. Negative of Fig. 10 Normalized Flame Response data, for dynamic extinction of C2H4–Air CFDFs using 7.2 mm Pyrex Nozzle OOJB with 3, 5, 8 SLPM C2H4 flows, and axially-applied sinusoidal velocity inputs probed by microphone.

18

-2

0

2

4

6

8

0 500 1000 1500 2000

3 SLPM C 2 H4

5

8

Ave. of 3, 5, 8

y = 194.66 * x^(-0.99676) R= 0.97867

- N

orm

aliz

ed F

lam

e R

esp

on

se, 1

/Pa

Imposed Frequency of Sinusoidal Velocity Inputs, Hz

(U air,ss –Normalized) Flame Response

= 100 (dU air /U air,ss )/ d (pkpk P), 1/Pa

Data Used: 50 - 1600 Hz

-2

0

2

4

6

8

0 5 10 15 20

3 SLPM C 2 H4

5

8

Ave of 3,5,8

y = -0.19522 + 0.25599x R= 0.97888

- N

orm

aliz

ed F

lam

e R

esp

on

se, 1

/Pa

1000/(Frequency of Sinusoidal Inputs), ks

(U air,ss –Normalized) Flame Response

= 100 (dU air /U air,ss )/ d (pkpk P), 1/Pa

Data Used: 50 - 1600 HZ

Fig. 12. Power-Law analysis of 50 – 1600 Hz Normalized Flame Response data in Fig. 11, which shows an approximate relationship with inverse frequency for 50 Hz and above.

Fig. 13. Inverse-frequency plot of 50 – 1600 Hz Normalized Flame Response data in Figs. 11 and 12, which shows that linear relationship with inverse frequency is actually better for 50 Hz and above.

19

0.0001

0.001

0.01

0.1

0 100 200 300 400 500 600

Ave of 3,5,8 SLPM C 2 H4

y = 194.66 * x^(-1.9968) R= 0.99704

- N

orm

aliz

ed F

lam

e R

esp

on

se/f

, s/P

a

Imposed Frequency of Sinusoidal Velocity Inputs, Hz

(U air,ss –Normalized) Flame Response/f

= (100/f) (d U air /U air,ss )/ d (pkpk P), s/Pa

Data Used: 50 - 1600 HZ

0

100

200

300

400

500

10 100 1000

3 SLPM C 2 H4

58

Ave of 3, 5, 8

- N

orm

aliz

ed (

Fla

me

Res

po

nse

)*f,

1/P

a-s

Imposed Frequency of Sinusoidal Velocity Inputs, Hz

Flame Response (Normalized by U air,ss )

= 100 d (U air /U air,ss )/ d (pkpk P), 1/Pa

All 8 - 1600 Hz Data

FlameWeakening

Fig. 14. Normalized Flame Response per unit frequency for 50 – 1600 Hz Normalized data in Fig. 11. This power law relationship fits all the data quite well for 50 Hz and higher.

Fig. 15. Analysis of 8 – 50 Hz Normalized Flame Response data in Fig. 11 multiplied by frequency shows that 8 to 50 Hz data follow a highly-reproducible increasing function that loses validity beyond 50 Hz. These results clearly suggest a fundamental transition occurs near 50 Hz.

20

0

100

200

300

400

500

0 20 40 60 80 100

3 SLPM C 2 H4

5

8

Ave of 3,5,8

y = -22.275 + 5.426x R= 0.98814

- N

orm

aliz

ed (

Fla

me

Res

po

nse

)*f,

1/P

a-s

Imposed Frequency of Sinusoidal Velocity Inputs, Hz

(U air,ss –Normalized) Flame Response

= 100 d (U air /U air,ss )/ d (pkpk P), 1/Pa

Data Used: 8 - 50 Hz

-10

-5

0

5

-200 -150 -100 -50 0 50 100 150 200(Uai

r -

Uai

r,ss

)/(p

kpk

P),

cm

/s-P

a

Fuel Input Phase (Air = 0)

Fig. 16. Linear analysis of 8 – 50 Hz Normalized Flame Response data (multiplied by frequency) on left side of Fig. 15, which demonstrates a simple linear relationship for the frequency-multiplied 8 to 50 Hz Flame Response data.

Fig. 17. Effect of Fuel-Air Phase difference on dynamic extinction Flame Response (not normalized) of C2H4–Air CFDFs, using 7.2 mm Pyrex Nozzle OOJB with 3 SLPM C2H4 flows, and 150 Hz axially applied sinusoidal velocity inputs probed by Microphone.

21

-20

-15

-10

-5

0

5

-200 -150 -100 -50 0 50 100 150 200

200 Hz

150

100

75

50

(Uai

r -

Uai

r,ss

)/(p

kpk

P),

cm

/s-P

a

Fuel Input Phase (Air = 0)

AppliedFrequency

-25

-20

-15

-10

-5

0

5

10 100 1000

3 SLPM C 2 H 4

58Ave of 3,5,8

CH 4

No

rmal

ized

Fla

me

Res

po

nse

, 1/P

a

Imposed Frequency of Sinusoidal Velocity Inputs, Hz

Flame Response (Normalized by U air,ss )

= 100 d (U air /U air,ss ) / d (pkpk P), Pa

Smooth Fit

FlameWeakening

Wt'd (45%)

Fig. 18. Effect of Fuel-Air Phase difference on dynamic extinction Flame Responses (not normalized) of C2H4–Air CFDFs at four key frequencies, using 7.2 mm Pyrex Nozzle OOJB with 3 SLPM C2H4 flows, and axially-applied sinusoidal velocity Inputs probed by Microphone

Fig. 19. Normalized Flame Response for dynamic extinction of C2H4 and CH4 vs Air CFDFs, using 7.2 mm Pyrex Nozzle OOJB and axially-applied sinusoidal velocity inputs probed by Microphone. Note large differences with methane fuel.