Abstract

An experimental study is conducted on bluff-body stabilized premixed flames in a curved, square cross section duct. High flow velocities coupled with a small radius of curvature of the duct induce high centrifugal acceleration normal to the flame sheet. A cylindrical flame holder spans the width of the square cross section and is positioned at the channel midheight. Flame shear layers are stabilized on the radially inward (upper) and outward (lower) edges of the flame holder. Side-view high-speed Schlieren images and high-speed pressure measurements are captured. Static stability, overall pressure loss, and statistics and velocimetry results from the Schlieren images are reported, and results are compared to a straight configuration with no centrifugal acceleration. Two bluff-body diameters are studied to show the effect of flame holder diameter on static stability. For the curved configuration, blowout velocities are higher for the smaller bluff-body diameter, likely due to flow acceleration effects. Blowout velocities are lower for the curved configuration compared to the straight configuration which may be due to the destabilizing Rayleigh–Taylor (RT) effect on the upper flame layer. Overall pressure loss is slightly higher for the curved configuration than the straight configuration. High-speed Schlieren results show centrifugal acceleration causes significant structural and velocimetric asymmetry in the bluff-body wake. In the curved configuration, the upper flame layer displays destabilizing RT instabilities, and the lower flame layer displays stabilizing RT effects. The upper flame shows vigorous RT instabilities which broaden the flame brush and sustain a flame leading edge independent of inlet Reynolds number or velocity. Conversely, the lower flame exhibits suppression of Kelvin–Helmholtz and flame-generated instabilities in the wake, which confines the flame brush and significantly reduces transverse flame velocities. The lower flame edge profile moves toward the channel centerline with increasing inlet Reynolds number. The upper flame in the curved configuration shows higher flame edge velocities than the straight configuration while the lower flame shows velocities closer to zero. The empirical constant to the power law relation for upper flame edge velocities agrees with RT-dominated flame growth theory for this experimental scale and agrees with other RT-dominated flame studies.

Introduction

The aviation gas turbine industry seeks new combustion technologies that reduce engine weight, increase space heating rates, and reduce thrust specific fuel consumption because of increasing performance requirements, volatile fuel prices, and increasingly stringent pollutant regulations. High centrifugal acceleration within a combusting flow field can increase turbulent mixing rates between the combustion reactants and products to increase space heating rate and reduce combustor size. This can be used to design more efficient main combustors and augmentors and even enable flight-weight interturbine burners.

A density gradient in a fluid domain with an imposed body force field generates a buoyant force on the fluid in an opposite direction to the body force that is proportional to the density gradient and the imposed body force field. In combustion studies, when the buoyant force results from a gravitational body force, it is only significant when flow velocities or pressure gradients are low and density gradients are high, such as the turbulent flame far downstream of a diffusion jet orifice or a candle flame. Body forces much greater than Earth's gravitational acceleration are possible via inertial (rectilinear or centrifugal) accelerations. The centrifugal acceleration is reported in multiples of Earth's gravity (g) as ac = utan2/r, where utan is the tangential flow velocity and r is the radius from the center of rotation.

The Rayleigh–Taylor (RT) instability arises via baroclinic torque across the interface between fluids of different density in this body force field [14]. RT instabilities have been heavily studied in the literature from the perspective of theoretical bubble merger models [57], experiments [812], and direct numerical simulations [7,1322]. As Atwood number At=(ρ1ρ2)/(ρ1+ρ2) approaches unity, where ρ1 is the higher density fluid and ρ2 is the lower density fluid, this instability interface is characterized by round-topped “bubbles” propagating into the heavy fluid and “spikes,” walls, or curtains propagating into the low density fluid [5]. The growth rates of these bubbles and spikes have been shown [810] to be quadratic with time
hi=αiAtact2
(1)

where i is either “b” for bubble or “s” for spike, α is an empirical constant, ac is the imposed body force, and t is the elapsed time.

It has been shown that nonreacting RT bubbles [15,2328] approach a maximum terminal velocity for a given bubble length scale where the buoyant forces and drag forces on the interface are equal. This steady-state velocity is typically represented in the form
sb=CacLB
(2)

where C is an empirical constant which is a function of the viscous effects and fluid properties, ac is the induced acceleration, L is a characteristic length, and B is the buoyancy term B=Δρ/ρ. Khokhlov et al. [29] showed that reacting RT bubbles trend toward this steady-state behavior when the laminar flame thickness is small relative to the turbulent integral length scale (δl/L1), diffusion effects are small relative to the fluid dynamic effects (large Péclet number), and laminar flame speed (sl) is much less than the RT characteristic speed (uRT=acL), or equivalently, for very small flame Froude number (FrL=sl/acL1).

There are fewer studies on the combined effects of deflagration flames and RT instabilities. Hicks and Rosner [3032] showed the turbulent flame speed is affected more by large-scale RT stretching than by small-scale turbulent wrinkling and that the formation of cusps along the flame regulates the growth of the RT instability but also increases the flame speed. Timmes and Woosley [33] showed the flame imposes a critical length scale called the fire-polishing wavelength below which any perturbations are washed out by reactions. Zingale et al. [34] showed via three-dimensional direct numerical simulation that RT flame turbulence follows a Kolmogorov spectrum and is highly anisotropic at large scales but becomes more isotropic at small scales. Bell et al. [35,36] presented evidence that Rayleigh–Taylor instabilities provided most of the acceleration of the deflagration wave compared to the Landau–Darrieus instability.

There are a few notable studies on the specific effect of centrifugal acceleration on flames. Sykes et al. [37] simulated turbulent premixed flames in a curved two-stream flow via large Eddy simulations and contrasted this with a configuration where centrifugal acceleration was artificially removed. He showed that RT-dominated flames increase fuel consumption rate and global turbulent flame speed and manifest a larger range of stretches and curvatures compared to the case without centrifugal acceleration. Lewis et al. [2426] rotated a closed tube filled with a gaseous fuel–air mixture about its center and ignited the mixture at one end of the tube in a constant volume reaction. He observed the flame propagation rate was directly proportional to the square root of centrifugal force and increased with increasing centrifugal acceleration to above 3000 g. Flame speed abruptly decreased prior to extinction taking place at about 5000 g for a propane–air mixture. Briones et al. [38] performed unsteady Reynolds-averaged Navier–Stokes reacting simulations on Lewis's rotating tube apparatus and found that the region of hot gas expanded while the flame sheet wrinkled, and flame surface area substantially increased. In addition, several combustion research efforts have attempted to take advantage of the potential increases in flame speed by utilizing a “high-g cavity” whereby high centrifugal accelerations are induced by flowing combustion reactants around the engine axis [3943].

Erdmann et al. [44] examined a backward-facing step (BFS) configuration in a curved duct that was previously studied by Lapsa and Dahm [45,46]. They reported large amplitude, low frequency velocity, and pressure fluctuations in the destabilizing BFS configuration due to a convective instability but revealed local RT flame growth and an average flame leading edge that was independent of inlet velocity. Lapsa and Dahm also studied a stabilizing BFS configuration and showed that RT effects suppress flame propagation in this mode. Erdmann et al. [44] examined a hot-surface-stabilized flame in a curved duct, which minimized Kelvin–Helmholtz (KH) instabilities in the flame front. They showed that destabilizing RT effects significantly increase turbulent flame brush thickness, flame turbulence, wrinkling, curvature, flame edge velocities, and overall pressure loss, and unsteady pressure fluctuations. Maximum flame edge velocities near 13 m/s were observed for induced local centrifugal accelerations near 3500 g.

Bluff-body stabilized flames have been heavily studied in the literature. Studies have investigated the effects of fuel, oxidizer, and flow conditions on flame holder stability and operability [4752]. DeZubay [50] conducted seminal experiments on disk-shaped flame holders and proposed the DeZubay parameter to describe flame holder stability. These efforts showed an increase in flame holder size was accompanied by an increase in blowout velocity. For large flame holder sizes, maximum blowout velocity was observed near stoichiometric equivalence ratio. For smaller flame holder sizes, maximum blowout velocity shifted toward richer equivalence ratios. Ozawa [53] also presented a review of bluff-body stabilized flames and identified pressure, temperature, velocity, geometry, fuel type, and heat loss as key parameters for bluff-body stability and blowout. Chaudhuri et al. [54] proposed that a partial or total extinction of the flame sheet along the shear layers is the major factor that determines the final blowoff event.

Zukoski [55] explored the static stability and flame structure characteristics of small cylindrical bluff-body stabilized flames, and those results will be compared to the data of the current study for bluff-body stabilized flames in a curved duct. He showed that the flame stabilization mechanism changes significantly at low Reynolds numbers as the flame shear layer is more prominently laminar near the bluff-body and transitions to a turbulent surface along the wake. He also observed the blowout velocity depends on the square root of flame holder characteristic dimension if the flame holder is a small fineness ratio. And Olson et al. [21] showed that as mean shear increases along an RT unstable interface, induced KH instabilities nonmonotonically decrease and then later increase RT growth rates. This competition between KH and RT instabilities will be explored in this study.

The purpose of the current study is to examine RT-dominated, premixed, turbulent, constant-pressure, propane–air flames at similar centrifugal accelerations, and Reynolds numbers as prior efforts [2426,4446] but on a bluff-body stabilized configuration where both RT stabilized and destabilized flame layers are present and interact. The objectives of this work are to assess the effect of high centrifugal acceleration on (1) unsteady, premixed, turbulent bluff-body stabilized flame dynamics, static stability, and overall pressure loss, (2) upper and lower flame and wake velocities, and (3) upper and lower flame edge profiles and growth rates.

Experimental Arrangement

Facility Setup.

A schematic of the facility setup is shown in Fig. 1. Air is supplied from a continuous 830 kPa, low dew point source. Propane fuel is supplied from a 45 kg bottle, and nitrogen is supplied from a continuous 1500 kPa source. The propane fuel and nitrogen purge circuits both enter the 1.0 cm inside diameter air stream at the same point at a crossflow injection point, which is at least 100 tube diameters upstream of the conditioning tube and test section. The air and propane flows are metered and controlled separately with Alicat mass flow controllers. A labview virtual instrument is used to control air and fuel flows.

Fig. 1
Schematics of the: (a) experimental setup surrounding the test section, (b) curved (5.715 cm mean line radius), (c) straight constant-area channel configurations, and (d) the side view cut through the middle of the bluff-body and the front (flow-normal) view of the bluff-body and igniter
Fig. 1
Schematics of the: (a) experimental setup surrounding the test section, (b) curved (5.715 cm mean line radius), (c) straight constant-area channel configurations, and (d) the side view cut through the middle of the bluff-body and the front (flow-normal) view of the bluff-body and igniter
Close modal

The premixed fuel–air mixture enters the inlet of the conditioning tube through a jet-diffuser into a 4.75 cm diameter tube. The flow passes through several 40 × 40 mesh screens and a set of 0.32 cm cell-size honeycomb sections, which break up large-scale turbulence and straighten the flow, respectively. At the exit of the conditioning tube, a sintered metal plate with an average pore size of 5.0 μm simultaneously chokes the flow and reduces the maximum turbulence length scale to the order of the pore size (O(10 μm) for the highest inlet velocity). The flow then passes through a circle-to-square transition nozzle where the cross-sectional area is reduced to the 1.27 cm × 1.27 cm test section channel cross-sectional area with an area reduction ratio of 10, further reducing transverse turbulence fluctuations. The premixed flow passes through 15.4 cm of the test section before flowing over the cylindrical bluff-body, which stabilizes the flame in the high-velocity flow. The stabilized flame then propagates downstream through the premixed mixture. The combustion products flow out through the exhaust into the ambient environment and are captured and vented in an exhaust hood.

The range of conditions investigated is shown in Table 1. Inlet pressure is 0.97 atm; inlet temperature is 294 K; and inlet velocities range from 4.0 m/s to 24 m/s. These correspond to inlet Mach numbers from 0.012 to 0.070, inlet Reynolds numbers based on channel height (1.27 cm) from Reh = 3300 to 20,100, flame Froude number based on channel width from 23.3 × 10−2 to 3.89 × 10−2, and global centrifugal acceleration at the mean-line radius (5.72 cm) from 29 to 1027 g. Area-averaged inlet turbulence intensity based on hot wire anemometer measurements at the exit of the 10:1 nozzle is less than 1% for all inlet velocities. The premixed propane–air equivalence ratio is 1.0 for the curved configuration and 1.2 for the straight configuration. Stoichiometric equivalence ratio was desired for both configurations; however, the straight configuration had issues maintaining flame stability for ϕ < 1.2. Laminar flame speed and adiabatic flame temperature have the greatest effect on RT characteristic speed and fire-polishing length scale, and these are only a few percent different for the two equivalence ratios studied.

Table 1

Operating conditions for both straight and curved configurations

Inlet pressurePi0.973 atmAtwood numberAt0.77
Inlet temperatureTi293 KRichardson no. (curved)Ri1.5
Equivalence ratioϕ1.0–1.2Laminar flame speedSl0.44 m/s (Ref. [56])
MixturePropane–airLaminar flame thicknessD1.2 mm (Ref. [56])
Inlet pressurePi0.973 atmAtwood numberAt0.77
Inlet temperatureTi293 KRichardson no. (curved)Ri1.5
Equivalence ratioϕ1.0–1.2Laminar flame speedSl0.44 m/s (Ref. [56])
MixturePropane–airLaminar flame thicknessD1.2 mm (Ref. [56])
Inlet Reynolds no.Rewc3.34 × 1036.68 × 10313.4 × 10320.1 × 103
Froude no. (curved)Frwc23.3 × 10−211.7 × 10−25.83 × 10−23.89 × 10−2
Inlet bulk velocityui4.0 m/s8.0 m/s16 m/s24 m/s
Dean no. (curved)De1.11 × 1032.23 × 1034.46 × 1036.68 × 103
Centrifugal acceleration (curved)ac/g28.51144571027
Inlet Mach no.Mi0.0120.0230.0470.070
Fire-polishing length scale (Ref. [33])λfp11.3 mm2.82 mm0.71 mm0.31 mm
Inlet Reynolds no.Rewc3.34 × 1036.68 × 10313.4 × 10320.1 × 103
Froude no. (curved)Frwc23.3 × 10−211.7 × 10−25.83 × 10−23.89 × 10−2
Inlet bulk velocityui4.0 m/s8.0 m/s16 m/s24 m/s
Dean no. (curved)De1.11 × 1032.23 × 1034.46 × 1036.68 × 103
Centrifugal acceleration (curved)ac/g28.51144571027
Inlet Mach no.Mi0.0120.0230.0470.070
Fire-polishing length scale (Ref. [33])λfp11.3 mm2.82 mm0.71 mm0.31 mm

The relevance of the buoyant forces relative to the inertial forces can be determined from the Richardson number Ricent=L/rΔρ/ρ2, which for the curved configuration with propane–air combustion at ambient conditions (Δρ/ρ6.7, At = 0.77) is Ricent = 1.5. Thus, the buoyant forces due to the centrifugal body force are significant relative to the inertial forces for all inlet velocities. For comparison, the Richardson number based on the gravitational body force for both the straight and curved configurations is greatest at the lowest inlet velocity of 4 m/s, which is Rigrav = 0.05. Thus, the impact of gravitational body force is neglected in this study. The Richardson number remains constant with inlet velocity, and Erdmann et al. [44] showed a fluid parcel under such conditions will tend to move along a quadratic spiraling arc toward the centroid.

Curvature can introduce unfavorable streamwise vortices within a turning duct such as Dean vortices, which have vortex diameters of the order of the duct height, and Görtler vortices, which have vortex diameters of the order of the boundary layer height. High Dean numbers in the current study (Table 1) suggest some isotropic turbulence generation may be present in the 135 deg curve upstream of the bluff-body. All conditions examined in the current study are at Görtler numbers much less than 1, which indicates widespread damping of boundary layer disturbances.

Straight and Curved Configurations.

The current study investigates two configurations of a square cross section channel with premixed propane–air combustion. The test section schematics are shown in Fig. 1. The intent of this study is to examine the impact of centrifugal acceleration on the flame characteristics; thus, the curved channel geometry is identical to the straight channel geometry with the only difference that the curved channel is wrapped along a constant meanline radius of 5.72 cm. The lower and upper (or inner radius and outer radius) walls are machined out of stainless steel, and the left and right walls (as seen from the front view) are 1.27 cm thick Schlieren-grade, quartz glass windows. The windows allow optical access to most of the test section length, except for the last 2.54 cm which are blocked by the window retainers.

Cylindrical Bluff-Body and Igniter.

The cylindrical bluff-body is a 1.25 cm long, stainless steel tube positioned at the midheight of the 1.27 cm channel and supported by 0.5 mm Rene 41 wire as shown in Fig. 1. Two bluff-body diameters are used in this study. A 0.312 cm diameter bluff-body, roughly one-quarter the height of the channel, is utilized for most of this study comparing the straight and curved configurations. A 0.236 cm diameter bluff-body is also used to show the effect of bluff-body diameter on blowout characteristics. A 0.5 mm tungsten wire igniter lead is positioned underneath the bluff-body. A 10 Hz high voltage exciter box is connected to the tungsten wire lead, and the Rene 41 wire supports are connected to ground. Once the exciter box is energized, a spark is generated between the tungsten wire lead and the bluff-body, and the flame stabilizes on the leeward side of the bluff-body.

Diagnostics.

A schematic of the Schlieren setup is shown in Fig. 2. A green (532 nm), 10 W, 600 lumen light-emitting diode with continuous output is used as the light source for the Schlieren system. The collimated light passes through the quartz glass windows along the transverse direction of the test section, perpendicular to the straight or curved channel mean flow direction. The knife edge is oriented parallel to the channel exit flow to resolve the transverse density gradient, which is nearly perpendicular to the flame brush for both the straight and curved configurations. A 532±10 nm filter is positioned upstream of the high-frame-rate camera (Phantom). The camera settings are 20 kHz frame rate (50 μs frame-to-frame) and 3.91 μs exposure time. A 180 mm focal length lens with f-stop of 3.5 is attached to the camera. The image resolution is 85±0.7 μm per pixel. This is smaller than the fire-polishing length scale [33], which is the theoretical minimum turbulence length scale for Rayleigh–Taylor flames, for all conditions listed in Table 1. This indicates sufficient resolution to capture the smallest flame wrinkles.

Fig. 2
Schematic of the Schlieren system setup
Fig. 2
Schematic of the Schlieren system setup
Close modal

Inlet static temperature and pressure of the inlet channel flow are measured 8.9 cm downstream of the sintered metal plate (26.8 cm upstream of the exit) along the 35.7 cm total channel length as shown in Fig. 1. Static temperature is measured with a type K thermocouple (uncertainty σTs=±1°C); static pressure is measured with an Omega 206.8 kPa (30 psia) absolute pressure transducer (uncertainty σPs=±170Pa); and unsteady pressure is measured with a 50 kHz sample rate Kulite pressure transducer. The proximity of the Kulite pressure transducer to the pressure antinode of the longitudinal mode at the choked inlet enables high frequency response of the first several longitudinal modes. Unsteady pressure spectrograms are not presented in the current study, but results are similar to the same conditions reported in Ref. [44]. The most prominent peak is at ∼150 Hz with a secondary peak around 1.1 kHz, though both have low amplitudes less than 10 dB/Hz. These correspond to the quarter-wave longitudinal mode and the L4 (7/4 wave) longitudinal mode, respectively. Neither of these modes produces significant large-scale fluctuations in the high-speed Schlieren images.

Coherent Structure Velocimetry Analysis.

A two-dimensional cross-correlation, forward-marching coherent structure velocimetry code (matlab) is utilized. The interrogation window size is 9 pixels × 9 pixels with 50% overlap among windows, which is small enough to enable high velocimetry resolution and large enough to provide accurate resolution of the flame features in the flow. 20 kHz Schlieren images combined with the 85 μm per pixel resolution produces a velocimetry uncertainty of ±1.69 m/s per pixel between an image pair. A cubic spatial subpixel interpolation expansion is utilized to reduce uncertainties for both X and Y components and for lower inlet velocities; these uncertainties are reported in Fig. 3. The cross-correlation matrix is compiled using interrogation window shifting. The Schlieren intensities range from the lowest measured values in the lower flame shear layer (negative vertical density gradient) to the highest measured values in the upper flame shear layer (positive vertical density gradient). Therefore, the velocimetry tracks the flame wrinkles as shown in Fig. 3. The X and Y components of velocity are converted to circumferential and radial components about the centroid of curvature for the curved configuration. These components are presented as streamwise and transverse components, respectively, for consistency between the straight and curved configurations. One thousand image pairs are processed and averaged pixel-by-pixel only where the velocimetry produces a correlation coefficient of at least 0.5. The radial and circumferential velocity components from coherent structure velocimetry of the curved configuration at 24 m/s inlet velocity are shown in Fig. 3 for an image pair (a) and (b) and for the final averaged result (c) and (d).

Fig. 3
Sample results from velocimetry on the curved configuration with 24 m/s inlet velocity. Radial and circumferential velocities are reported for an image pair (a) and (b) including the Schlieren image shown (above) and after averaging all 1000 image pairs (c) and (d). Velocimetry uncertainties of the X and Y velocity components are shown at the upper right.
Fig. 3
Sample results from velocimetry on the curved configuration with 24 m/s inlet velocity. Radial and circumferential velocities are reported for an image pair (a) and (b) including the Schlieren image shown (above) and after averaging all 1000 image pairs (c) and (d). Velocimetry uncertainties of the X and Y velocity components are shown at the upper right.
Close modal

Rayleigh–Taylor Flame Growth Analysis.

To measure the growth rates of the Rayleigh–Taylor flame, the propagation distance of the flame brush across the channel must be identified. This distance is defined as the maximum transverse (vertical or radial) distance for which ϵA(xs,xt,t)t, where ϵ = 0.01 [14,16] and At is the ratio of the number of high-speed Schlieren image pairs used in the velocimetry analysis to the total number of image pairs (1000) is calculated at each pixel
A(xs,xt,t)t=NumberofImagePairsUsedTotalNumberofImagePairs=f(xs,xt)
(3)

The resultant leading edge curve is smoothed using a central moving average filter with shorter sample window width near the ends.

A characteristic time for RT-dominated flows has typically [16] been reported as
τ=(HcAtac)1/2
(4)
For the curved configuration, Hc is the channel height, At is the Atwood number, and ac is the centrifugal acceleration. This will be used to normalize the time, t, from the center of the bluff-body to a point “p” along the flame leading edge, defined as
tp=xsusp
(5)
where us is the streamwise velocity. Thus, Eq. (1) can be rewritten
xtHc=C(tτ)2
(6)

The constant C replaces αb for the present work to limit confusion. The latter has been canonically used to describe bubble and spike growth rates in low-shear RT studies.

Results and Discussion

Blowout velocities are compared to the experimental results of Zukoski [55] and overall pressure loss data are shown. Statistics of high-frame-rate Schlieren images are presented. Velocimetry of the high-frame-rate Schlieren images are then reported. Finally, reacting Rayleigh–Taylor flame growth rates and velocities are presented.

Static Stability Characteristics.

Blowout velocities as a function of premixed propane–air equivalence ratio are shown in Fig. 4. Approach gas velocity, or inlet bulk velocity, is calculated based on measured inlet mass flow, density, and geometric cross-sectional area of the duct. Blowouts were performed by igniting the flame at low inlet bulk velocity and slowly increasing propane fuel and air mass flow rates to maintain equivalence ratio during the ramp. Bulk velocity was increased by 0.01 m/s every 2 s, and three blowouts at the same equivalence ratio were averaged for the final data. Most samples were within ±0.5% of the mean.

Fig. 4
Dependence of blowout velocity on equivalence ratio for cylindrical flame holders in premixed propane–air flow compared between the current study and Zukoski [55]
Fig. 4
Dependence of blowout velocity on equivalence ratio for cylindrical flame holders in premixed propane–air flow compared between the current study and Zukoski [55]
Close modal

Results for the curved and straight configuration are plotted with the results of Zukoski [55] who also studied blowout limits for small cylindrical bluff-bodies in a premixed propane–air flow. The test section dimensions for his study (10.2 cm height × 5.1 cm width and 5.1 cm flame holder length) are much larger than the present study (1.27 cm height × 1.27 cm width). Centrifugal acceleration taken at the midheight radius of 5.715 cm is shown at the right for the curved configurations. Zukoski's results show increasing maximum blowout velocity with bluff-body diameter around stoichiometric equivalence ratio. The maximum blowout velocity for the straight configuration in the present study is 33.7 m/s (111 ft/s) at an equivalence ratio of 1.2. This is significantly lower than Zukoski's results for a similar diameter cylinder (0.323 cm) with a maximum blowout velocity at 110 m/s (350 ft/s). This is likely due to the much smaller cross-sectional area for the present study, where wall effects such as corner vortex structures, cold wall flame extinction, and fluid acceleration due to the relatively large flame holder blockage may be reducing flame stability and recirculation strength. Minimum stable equivalence ratio for the straight configuration is 1.15 compared to 0.65 for Zukoski's 0.323 cm bluff-body.

Two bluff-body diameters of 0.312 cm and 0.236 cm were tested in the curved configuration. The maximum blowout velocity for the 0.312 cm bluff-body of 30 m/s (98 ft/s) and equivalence ratio of 1.2 is lower than the peak velocity for the straight configuration. This may be due to the more turbulent,RT-dominated upper flame layer in the curved configuration as shown in the Schlieren images in Fig. 2. This turbulence may introduce increased velocity fluctuation magnitude in the bluff-body wake, destabilizing the recirculation zone. Interestingly, the peak blowout velocity for the 0.236 cm bluff-body is slightly higher at 32 m/s (105 ft/s) and shifted to a lower equivalence ratio of 1.1. This again may be due to the aforementioned wall effects. A larger bluff-body in the small cross section will increase tip flow velocities on the flame holder due to flow acceleration. Indeed, the larger bluff-body should increase bulk flow velocity at the flame holder by 8% over the smaller bluff-body, and maximum blowout velocity for the larger bluff-body is 6.3% lower.

Overall pressure loss as a function of inlet Reynolds number is shown in Fig. 5. This is taken between a point 26.8 cm upstream of the exit and the ambient exhaust. Overall pressure loss increases with increasing inlet Rewc, with reactions, and for the centrifugally loaded, curved configuration over the straight configuration. There is only a minor pressure loss increase from the reacting straight to the reacting curved configuration indicating the centrifugal acceleration has a minimal effect on overall pressure losses for a bluff-body stabilized flame.

Fig. 5
Overall pressure loss from the inlet to the exhaust of the curved and straight test sections
Fig. 5
Overall pressure loss from the inlet to the exhaust of the curved and straight test sections
Close modal

Schlieren Statistics.

Instantaneous Schlieren images and computed standard deviations of 1001 Schlieren images are shown for the straight and curved configurations in Fig. 6. Data are reported for 3.34 × 103 < Rewc < 20.1 × 103 or inlet bulk velocities from 4 to 24 m/s.

Fig. 6
Instantaneous Schlieren images and the standard deviation of 1001 Schlieren images taken at 20 kHz for the straight and curved configurations for 3.34 × 103 < Rewc < 20.1 × 103
Fig. 6
Instantaneous Schlieren images and the standard deviation of 1001 Schlieren images taken at 20 kHz for the straight and curved configurations for 3.34 × 103 < Rewc < 20.1 × 103
Close modal

For the straight configuration, instantaneous Schlieren images show upper and lower flame shear layers are distinguished by the bright and dark features due to positive and negative vertical density gradients, respectively. The shear layers transition from steady and smooth to increasingly wrinkled structure with downstream distance. Also, the flames transition from smooth, broad features to wrinkled, turbulent flame structure with increasing inlet Reynolds number. The standard deviation images reveal increasing standard deviation magnitude with increasing inlet Reynolds number. The upper flame layer standard deviation is higher than the lower flame layer, which may be due to effect of the support and igniter on the lower flame. The angle of the upper and lower flame layers relative to the streamwise direction remains roughly constant with inlet Reynolds number.

For the curved configuration, instantaneous Schlieren images also show increasing flame wrinkling with increasing Reynolds number, and the flame appears to be much more wrinkled at all conditions when compared to the images for the straight configuration. Also, rounded Rayleigh–Taylor bubblelike features are more prominent along the upper flame front in the curved configuration for all conditions when compared to the straight configuration due to destabilizing RT effects. Conversely, the lower flame front for the curved configuration appears more contiguous, confined, and less turbulent than the lower flame front for the straight configuration due to stabilizing RT effects. The standard deviation images reveal much higher variance in Schlieren intensity at higher Rewc and a much broader flame brush for the upper flame front while the standard deviation of the lower flame front only increases marginally, and flame brush thickness remains constant. The shape of the standard deviation leading edge of the upper flame front is static across all Rewc conditions, which agrees with theoretical predictions that destabilizing centrifugal Rayleigh–Taylor flame growth should travel along a quadratic spiral arc independent of inlet velocity [44]. Conversely, the leading edge of the lower flame front in the curved standard deviation images initially touches the outer radius wall at low velocities but proceeds to lift off the outer wall surface at higher Rewc. This also agrees with theoretical predictions that stabilizing centrifugal Rayleigh–Taylor flame growth will trend toward a constant radius arc with increasing velocity as RT effects inhibit flame growth.

Velocimetry of Schlieren Images.

Velocimetry analysis of high-frame-rate Schlieren images of the straight and curved configurations are shown in Fig. 7. Horizontal and vertical components of velocity are reported for the straight configuration, and circumferential and radial velocity components are reported for the curved configuration. The circumferential velocity is positive in the counterclockwise direction and the radial velocity is positive toward the centroid of curvature. The streamwise (horizontal and circumferential) plots show similar velocity distributions at the same Rewc. Streamwise velocity increases slightly along the channel length indicating flow acceleration due to thermal expansion from the flame.

Fig. 7
Velocimetry results from 1001 Schlieren images taken at 20 kHz for the straight and curved configurations
Fig. 7
Velocimetry results from 1001 Schlieren images taken at 20 kHz for the straight and curved configurations
Close modal

The transverse (vertical and radial) velocity distributions reveal markedly different behavior between the straight and curved configurations. The maximum vertical velocities along the upper and lower flame leading edge for the straight configuration increase with Rewc to a maximum near +3 m/s for the upper flame front and −3 m/s for the lower flame front. In contrast, the maximum radial velocities along the upper flame front for the curved configuration increase with Rewc to a maximum of roughly 6 m/s, and the radial velocities for the lower flame front approach −2 m/s. Thus, the centrifugal RT effects accelerate upper flame front velocities and suppress lower flame front velocities. The angle of the flame leading edge relative to the streamwise direction for the straight configuration stays roughly constant with increasing Rewc indicating that Kelvin–Helmholtz instabilities drive the turbulent flame speed. Conversely, the shape of the upper flame front in the curved configuration—a nearly quadratic spiral—remains roughly constant with increasing Rewc, and the lower curved flame front trends toward a constant radius arc. This aligns with theoretical expectations for RT-dominated flame growth.

Reacting Rayleigh–Taylor Flame Growth Rates and Velocities.

Flame leading edge curves of the straight and curved configurations are shown in Fig. 8. These are calculated with Eq. (3). Both upper and lower flame fronts are shown with the lower flame fronts plotted on an inverse negative scale, and they follow similar trajectories. The lower flame profiles for both configurations initiate slightly further away from center, possibly affected by the supports and igniter. The leading edge of the upper and lower flames in the straight configuration remains roughly constant for higher inlet Reynolds number, corresponding to the same trends shown in Figs. 6 and 7. Turbulent flame speed in the straight configuration is dominated by Kelvin–Helmholtz turbulence from the bluff-body and flame leading edge angle for the upper and lower flames is αflame7.1deg.

Fig. 8
Flame front transverse propagation distance (xt/Hc) as a function of streamwise length (xs/Hc) for the straight (left) and curved (right) configurations. Upper (blue or dark gray) and lower (red or light gray) flame fronts are shown for each. Lower flame fronts are plotted on an inverse negative scale. Theoretical RT-dominated terminal velocity is shown for the curved configuration.
Fig. 8
Flame front transverse propagation distance (xt/Hc) as a function of streamwise length (xs/Hc) for the straight (left) and curved (right) configurations. Upper (blue or dark gray) and lower (red or light gray) flame fronts are shown for each. Lower flame fronts are plotted on an inverse negative scale. Theoretical RT-dominated terminal velocity is shown for the curved configuration.
Close modal

The upper and lower flame fronts in the curved configuration show much different behavior. The upper flame front grows at an overall faster rate toward the upper (inner radius) wall than the straight configuration, and the upper flame front profile remains largely independent of inlet Reynolds number. The lower flame front grows at an overall slower rate when compared to the straight configuration, and it grows at a slower rate with increasing inlet Reynolds number. At the highest Reynolds number, upper flame angle is about 10 deg, and the lower flame angle is about 4.1 deg. These trends for the upper and lower curved flame fronts agree with predicted destabilizing and stabilizing centrifugal RT-dominated growth. For reference, a slope indicator shows the theoretical terminal RT-dominated growth velocity Eq. (2) for the upper flame front in the curved configuration, sb/ui0.22 or a flame leading edge angle of αflame12deg. As Rewc increases, the upper flame leading edge maximum slope increases slightly toward this terminal velocity, indicating that destabilizing centrifugal RT effects dominate the flame behavior. For the lower flame front, stabilizing RT effects act to suppress Kelvin–Helmholtz and flame-generated instabilities toward the laminar flame speed (sl0.44m/s). This is illustrated in Fig. 8, where lower flame front growth rates outpace the laminar flame speed at all inlet Reynolds numbers, showing a complex effect of Kelvin– Helmholtz instabilities on flame growth.

Figure 9 shows the propagation of the upper and lower centrifugal RT-dominated flames in the curved configuration as a function of normalized time. The characteristic time, τ, and time coordinate, t, are defined by Eqs. (4) and (5). The bluff-body trailing edge is at t/τ=0.05. The upper flame leading edge downstream of the bluff-body then accelerates due to Rayleigh–Taylor instabilities toward a theoretical quadratic growth rate (n =2) as shown in Eq. (1). The lower flame front also accelerates, though more slowly than the upper flame. A power law model is fitted to the flame leading edge profiles, and the power law exponents are plotted in Fig. 9. Most upper flame profiles approach a maximum growth rate exponent of 0.6. Growth rate decay occurs after t/τ0.6 and xt/Hc0.4 as the flame approaches the inner radius wall. The overall profiles of power law exponent for the upper flame front are very similar showing remarkable independence with inlet Rewc as predicted. The lower flame front approaches a maximum growth rate of about 0.5 but at increasingly later t/τ as inlet Rewc increases. Note that these are time-averaged profiles of the highly turbulent flame leading edge, not the trajectory of a single RT flame bubble. While the overall upper flame front profiles do not exhibit quadratic growth, this is possible for individual flame bubbles. Indeed, tracking of individual bubbles along the upper flame leading edge reveals quadratic growth at the local scale.

Fig. 9
Flame transverse distance (xt/Hc) (left) and power law exponent of the flame growth rates “n” (right) as functions of normalized time (t/τ) for the curved configuration
Fig. 9
Flame transverse distance (xt/Hc) (left) and power law exponent of the flame growth rates “n” (right) as functions of normalized time (t/τ) for the curved configuration
Close modal

Instantaneous flame leading edge velocities obtained from the velocimetry analysis near the maximum growth rates (xt/Hc ∼ 0.4) in Fig. 9 are reported for the straight and curved configurations in Fig. 10. Both upper (blue or dark gray) and lower (red or light gray) flame front data are shown, and lower flame velocities are plotted on an inverse negative scale. The upper flame edge for the curved configuration exhibits the highest transverse velocities, and the lower flame edge in the curved configuration shows the transverse velocities closest to zero. The upper and lower flame edges for the straight configuration show comparable velocity magnitudes in the positive and negative direction. The maximum flame edge velocities observed in the curved configuration are up to roughly 7.5 m/s at a local streamwise velocity of 33 m/s. The transverse flame velocities for the curved configuration become increasingly scattered with increasing streamwise velocity due to the highly turbulent flame leading edge. This clearly represents the effect of centrifugal RT instabilities to increase flame edge velocity in a destabilizing mode and drive flame velocity to zero in a stabilizing mode.

Fig. 10
Flame leading edge transverse (vertical or radial) flame velocity for the straight (open symbols) and curved (filled symbols) configurations as a function of streamwise bulk velocity. Upper (blue or dark gray) and lower (red or light gray) flame front data are shown. Points are taken from velocimetry analysis along bubble leading edge around xt/Hc ∼ 0.4.
Fig. 10
Flame leading edge transverse (vertical or radial) flame velocity for the straight (open symbols) and curved (filled symbols) configurations as a function of streamwise bulk velocity. Upper (blue or dark gray) and lower (red or light gray) flame front data are shown. Points are taken from velocimetry analysis along bubble leading edge around xt/Hc ∼ 0.4.
Close modal

The transverse velocities for the curved configuration follow a linear trend with streamwise velocity, and thus, a square root trend with centrifugal acceleration in g's (ut,curved=0.179ac[gs]). For reference, Lewis' et al. [2426] calculated bubble velocity curve for a propane–air mixture at Φ=1.0 is shown. The RT-dominated bubble theoretical terminal velocity Eq. (2) for the curved configuration is also shown. The reported flame edge velocities in the curved configuration trend very closely to the RT-dominated terminal velocity curve. Since the average flame edge velocities closely follow the theoretical RT-dominated curve, it appears that the RT-dominated flame in the curved configuration reaches local steady-state growth. The RT-dominated flame terminal velocity is a function of the domain characteristic length; thus, we expect and observe Lewis' reported flame velocities to be greater by a factor of the square root of the ratio of Lewis' tube inside diameter (6.7 cm) and the width of the curved channel (1.27 cm) of ∼2.3. Indeed, the ratio between the curve fit constants 0.381/0.179 ≈ 2.1.

Equivalently, the constant C from Eq. (2) can be calculated from the power law velocity correlations and compared. Induced centrifugal acceleration and reacting mixture were similar between the two studies. The constant C, which has been predicted to be C 0.5 [29], is calculated as C =0.504 for Lewis' study, C =0.540 for the hot surface study by Erdmann et al. [44], and C =0.543 for the present study showing good agreement in RT-dominated flame growth across experimental length scales.

Summary and Conclusions

This study is motivated by the previous studies by Erdmann et al. [44] which demonstrated the effects of centrifugal acceleration on hot-surface-stabilized flames. The purpose of the present study is to extend the examination of Rayleigh–Taylor-dominated flames to a bluff-body stabilized configuration.

High centrifugal acceleration is induced within a steady, constant-pressure combustion, premixed, and propane–air plug flow reactor via high flow velocities through a curved channel. The flame is stabilized on a small cylindrical bluff-body located at the channel midheight. Due to the centrifugal acceleration on the flow field, high-density reactants near the inner radius are driven radially outward via the Rayleigh–Taylor instability and low-density combustion products near the outer radius are driven inward, generating highly turbulent flame structures. Experimental data are compared for two geometries—a straight channel without centrifugal acceleration and a curved channel with high centrifugal acceleration. Bulk inlet velocity up to 32 m/s, bulk centrifugal acceleration up to 1900 g's, Reynolds number up to 26.7 × 103, and Dean number up to 8.9 × 103 are explored. High-frequency Schlieren images are used to resolve the reacting flame edge.

The results indicate that centrifugal acceleration has numerous effects on bluff-body stabilized, premixed flames in a constant radius, curved duct, plug flow reactor. RT effects cause significant structural and velocimetric asymmetry in the bluff-body wake. In the curved configuration, the upper flame exhibits destabilizing RT effects due to an opposed centrifugal acceleration and density gradient. This drives vigorous RT instabilities which broaden the flame brush and sustain a flame leading edge independent of inlet Reynolds number or velocity. Conversely, the lower flame exhibits stabilizing RT effects, which suppress Kelvin–Helmholtz and flame-generated instabilities in the wake. This confines the flame brush and significantly reduces transverse flame velocities.

To the authors' knowledge, this is the first published study on the effect of centrifugal acceleration and Rayleigh–Taylor instabilities on bluff-body stabilized premixed flames in a curved channel. This is also the first bluff-body stabilized flame experiment to demonstrate predicted Rayleigh–Taylor flame edge terminal velocities. These stability, pressure loss, and velocimetry results add valuable insights for the combustion community on the effect of high centrifugal acceleration on flames. Major conclusions are summarized below.

  1. Maximum blowout velocities for the straight and curved configurations were significantly lower than comparable bluff-body stabilized flame studies by Zukoski [55] likely due to significant wall and flow acceleration effects from a much smaller cross section duct. Blowout velocities for the curved configuration are lower than the straight configuration which is likely caused by the destabilizing RT effect of the upper flame layer.

  2. Two bluff-body diameters were evaluated for the curved configuration. Blowout velocities are higher for the smaller bluff-body diameter, likely due to flow acceleration effects from the relatively large flame holder height-to-channel height ratio.

  3. Flame wrinkling, turbulence, overall pressure loss, and Schlieren standard deviation increase with increasing inlet velocity, and these are higher for the curved configuration than the straight configuration.

  4. In the curved configuration, the upper flame leading edge profile is largely independent of inlet Reynolds number due to RT-destabilizing effects whereas the lower flame profile moves downstream with increasing inlet Reynolds number due to RT-stabilizing effects. This matches theoretical expectations for RT-dominated flames. Maximum growth rate exponents for the upper flame in the curved configuration are about 0.6, but quadratic growth (n = 2) occurs in local flame bubbles.

  5. Velocimetry of the Schlieren images shows a significant increase in the upper flame edge velocities for the curved configuration up to about 7.5 m/s and a minor increase in the lower flame edge velocities to about −2 m/s, while the maximum flame edge velocities for the upper and lower flames in the straight configuration are about 3 and −3 m/s, respectively.

  6. Power-law relations are calculated for the maximum observed flame edges velocities for the upper and lower flames in the curved configuration. The relation for the upper flame shows remarkable agreement to theoretical expectations for flame terminal velocity in this configuration. The lower flame edge velocities are closer to zero than the velocities of the straight configuration.

  7. The empirical constant for terminal flame velocity for the curved configuration (C ≈ 0.543) shows good agreement to studies by Khokhlov et al. [29] (C ≈ 0.5), Lewis et al. [2426] (C ≈ 0.504), and Erdmann et al. [44] (C ≈ 0.540).

Acknowledgment

The authors express their gratitude to Jacob Diemer (formerly ISSI) and Benjamin Davis (ISSI/Purdue) for Labview data acquisition software programming, Hannah Mackin Schenck (ISSI/Purdue) for Schlieren diagnostics expertise, Jeff Monfort (UDRI) for unsteady pressure diagnostics expertise, Jack Yoder (ISSI) for CAD support, Harold Day (formerly ISSI) and Ryan Garwood (ISSI) for facility technical assistance, and Dave Burrus (formerly ISSI), Kyle Brady (formerly ISSI), Josh Sykes (ISSI), and Brent Rankin (AFRL) for technical advice. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of U.S. Air Force Research Laboratory or the U.S. Government.

Funding Data

  • Air Force Research Laboratory (Contract No. FA8650-14-D-2414; Funder ID: 10.13039/100006602).

Nomenclature

a =

acceleration

A =

area

At =

Atwood number

B =

buoyancy term (=Δρ/ρ)

BFS =

backward-facing step

D =

diameter

De =

Dean number

Fr = 

Froude number (=sl/acL )

g =

earth's gravitational acceleration at sea level ≈ 9.81 m/s2

H or h =

height

I =

intensity

KH =

Kelvin–Helmholtz

L =

length

M =

Mach number

m˙ =

mass flow

p =

pressure

r =

radius

Re =

Reynolds number

Ri =

Richardson number

RT =

Rayleigh–Taylor

s =

flame velocity

t =

time

T =

temperature

u =

velocity

x =

distance

Greek Symbols
α =

spike or bubble growth rate constant

δ =

flame thickness

ρ =

density

τ =

Rayleigh–Taylor time constant

ϕ =

equivalence ratio

Subscripts
B or b =

buoyant

c or cent =

centrifugal

g or grav =

gravitational

s =

streamwise

t =

transverse

tan =

tangential

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