Cavity-based flameholding for chemically-reacting supersonic flows

Progress in Aerospace Sciences 76 (2015) 24–41

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Progress in Aerospace Sciences journal homepage: www.elsevier.com/locate/paerosci

Cavity-based flameholding for chemically-reacting supersonic flows Frank W. Barnes n, Corin Segal Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, United States

art ic l e i nf o

a b s t r a c t

Article history: Received 11 March 2015 Accepted 22 April 2015 Available online 20 May 2015

Recesses in the walls of supersonic combustion chambers – cavities – have emerged as a preferred flameholding device since they are non-intrusive, hence resulting in reduced drag, lower total pressure losses and minimal aerodynamic heating when compared with other means of piloting core combustion such as, for example, struts. The flowfield within and in the vicinity of a cavity is complex involving a strong coupling between hydrodynamics and acoustics. When employed as a flameholding device both fuel injection and heat release – which is closely coupled to local mixing processes – alter the flowfield and further complicate the interaction between the cavity and the core supersonic flow. The complexity of this flowfield makes the identification of the dominant flameholding mechanisms and prediction of flame stability limits substantially more difficult than in the case of premixed systems. The following sections review the current knowledge of the mechanics of cavity-based flameholding in supersonic flows. Aspects of the non-reacting and reacting cavity flowfield are discussed with particular emphasis on the impact of fuel injection location relative to the flameholder. Results obtained to date in the attempt to describe the operability of cavity flameholders in terms of experimentally determined flame stability limits are also presented. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Hypersonics Scramjet Cavity Flameholding Supersonic combustion Unsteady flows

Contents 1. 2.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Non-reacting flowfield. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.1. Cavities in external flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.1.1. Cavity oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2. Effect of cavity geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2.1. Effect of cavity geometry on the shear layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2.2. Effect of cavity geometry on the recirculation zone flowfield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2.3. Effect of cavity geometry on residence time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3. Fuel injection and mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.1. Upstream Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2. Floor injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.3. Parallel Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4. Reacting flowfield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.1. Upstream injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.2. Floor injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.3. Parallel Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 5. Flame stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.1. Cavity blowout limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.2. Unsteady Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 6. Concluding remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

n

Corresponding author.

http://dx.doi.org/10.1016/j.paerosci.2015.04.002 0376-0421/& 2015 Elsevier Ltd. All rights reserved.

F.W. Barnes, C. Segal / Progress in Aerospace Sciences 76 (2015) 24–41

Nomenclature

a∞ acav Cδ D Da DaNP fD fm* fs H K L LRZ M∞ Mc1 m ṁ ṁ A ṁ exchange ṁ F m* n P r rs rT S0 St SP s T∞ T0∞ TAD Tcav TF U∞ Uc uSL V W X x

freestream speed of sound, m/s cavity fluid speed of sound, m/s compressible shear layer growth rate proportionality constant cavity depth, mm Damköhler number non-premixed combustion Damköhler number flameholder shape factor oscillation frequency, Hz stoichiometric mixture fraction characteristic flameholder length scale, mm ratio of shed vortex velocity to freestream axial velocity cavity length, mm recirculation zone length, mm freestream Mach number convective Mach number, defined with respect highspeed stream cavity fluid mass, kg mass flow rate, kg/s characteristic air mass flow rate, kg/s cavity-freestream mass exchange rate, kg/s fuel mass flow rate, kg/s oscillation frequency mode number empirical constant static pressure, kPa shear layer velocity ratio stoichiometric fuel–air ratio temperature recovery factor laminar flame speed at 300 K, 1 atm Strouhal number flameholder scaling/stability parameter shear layer density ratio freestream static temperature, K freestream stagnation temperature, K adiabatic flame temperature, K cavity fluid static temperature, K fuel temperature, K freestream axial velocity, m/s shed vortex axial velocity, m/s shear layer axial velocity, m/s recirculation zone volume, mm3 cavity width, mm mole fraction streamwise distance, mm

1. Introduction The high speeds that must be accommodated as a consequence of allowing the ramjet combustor flowpath to remain supersonic pose a significant challenge for efficient conversion of fuel chemical energy into useful flow enthalpy within a reasonable combustor length. Unless provided with a means to extend the residence time and/or accelerate reaction rates, the range of Damköhler numbers to be encountered by supersonic combustors will be close to or less than unity. As a result, heat-releasing recombination reactions are unlikely to complete within the available combustor length. The problem is further exacerbated when accounting for the longer time scales associated with the prerequisite physical processes of fuel injection, molecular mixing, and atomization and vaporization in the case liquid fuels [80].

y Z

25

transverse distance, mm acoustic impedance, kg/m2 s

Greek symbols

α α0 β1 − 4 γ δ δm δp ε η θ κ λ ρ∞ ρcav σ

τc τNP τr ϕ ϕ0

shed vortex-acoustic radiation phase lag fuel–air mixture thermal diffusivity at 300 K, 1 atm empirical constants ratio of specific heats shear layer thickness, upstream boundary layer thickness molecularly mixed layer thickness product layer thickness empirical constant empirical constant cavity closeout angle empirical constant empirical constant freestream density cavity fluid density compressible shear layer growth rate proportionality constant characteristic chemical time scale non-premixed flame characteristic chemical time scale mean residence time global equivalence ratio characteristic equivalence ratio

Abbreviations DI DN FL FR FW IFP LE MS (p) PSR RW SCH SI TR UP

direct imaging of the flame/reaction zone fuel injection downstream of the flameholder fuel injection from the cavity floor fuel ramping fuel injection from the cavity front wall in-flow probing cavity leading edge mass spectrometry pilot fuel injection location perfectly-stirred reactor analysis fuel injection from the cavity rear wall Schlieren imaging shearing interferometry temperature ramping fuel injection upstream of the flameholder

At high flight Mach numbers M410 and/or with sufficient intake compression the combustor entrance temperature may be high enough to ensure autoignition within a reasonable distance downstream of the fuel injection sites. Yet, for combustor entrance conditions where deflagration is the dominant mode of combustion, typically occurring during dual-mode operation at low-tomoderate hypersonic freestream Mach numbers 5o Mo8, the problem of flame stabilization becomes pertinent. With flame propagation speeds orders of magnitude lower than combustor flow speeds it is obvious that a mechanism is required to stabilize and enable combustion. An array of fuel injection/flameholding schemes have been proposed including wall injection, steps, cavities, struts, pylons, ramps, etc., typically relying on the generation of low-speed, kinetically-favorable separated flow regions to anchor the reaction

26

F.W. Barnes, C. Segal / Progress in Aerospace Sciences 76 (2015) 24–41

Fig. 1. HIFiRE 2 flight test experiment payload. The scramjet payload was accelerated from Mach 5.5 to over Mach 8 by a three-stage sounding rocket while data was collected to examine ram-scram transition and supersonic combustion. The scramjet combustor flowpath consisted of parallel cavity flameholders. Fuel – a gaseous mixture of ethylene (64% by volume) and methane (36% by volume), used to kinetically simulate partially cracked JP-7 – was injected both upstream and downstream of the cavities [40].

Fig. 2. Simplified schematic of the cavity flowfield oscillation mechanism proposed by Rossiter [74]. (a) Shed vortex is advected through the shear layer downstream towards the cavity trailing edge. (b) Upstream propagating acoustic disturbances – which can be supersonic relative to the freestream – are generated by the interaction of the shed vortex with the trailing edge. (c) Interaction of the acoustic disturbances with the developing shear layer stimulates further vortex shedding. Resonance occurs when shear layer vortex shedding becomes phase-locked with the cavity’s acoustic modes resulting in constructive interference and highly dynamic motion of the shear layer.

base. The flameholding regions effectively increase the Damköhler number for a fraction of the reactant mixture. The resulting localized heat-release and transport of reactive species is then utilized to accelerate chemical reactions in the primary flow in an attempt to drive the primary flow Damköhler number sufficiently above unity. As flowpath total pressure losses strongly degrade engine performance these piloting zones must have a minimal impact on the supersonic core flow. Hence, wall-mounted cavities are an attractive means of flameholding in scramjet engines. Although their non-intrusive nature translates into reduced drag, total pressure losses, and aerodynamic heating when compared with other flameholder designs, it also leads to a limited influence of the piloting zone on the core flow and large local wall heat fluxes. Nonetheless, their effectiveness in enabling sustained combustion and improving supersonic combustor performance has been demonstrated in both ground and flight test experiments [51,61,49,28,32,40]. The Hypersonic International Flight Research Experimentation Program (HIFiRE) recently completed a supersonic combustor flight test experiment (HIFiRE 2) in which cavities were employed for flameholding. The hydrocarbon-fueled scramjet combustor payload, shown in Fig 1, was accelerated from Mach 5.5 to over Mach 8 by a three-stage sounding rocket while data was collected to examine ram-scram transition and supersonic combustion. Fig. 1 shows the primary elements of the HIFiRE 2 scramjet combustor flowpath. Note the parallel cavity configuration with the flameholders placed at the same axial location on opposite walls. Due to fuel–air mixing limitations imposed by scramjet combustor residence time constraints and the consequential non-

uniformity in chemical composition and temperature identification of the dominant flameholding mechanisms and prediction of flame stability limits – required for cavity flameholder design/ scaling – are substantially more difficult than in the case of premixed systems hence cavity-based flameholding in supersonic flows is still not well established [80]. The following is a review of research efforts focused on studying the mechanics of cavity-based flameholding in supersonic flows. Aspects of the non-reacting and reacting cavity flowfield are first discussed with particular emphasis on the impact of fuel injection location relative to the flameholder. Results obtained to date in the attempt to describe the operability of cavity flameholders in terms of experimentally determined flame stability limits are also presented.

2. Non-reacting flowfield 2.1. Cavities in external flows The first systematic studies of cavity flows were prompted by problems associated with flow-induced resonance in the external recesses of high-performance aircraft. To date, external cavity flow research efforts have been concerned primarily with the development of semi-empirical models to predict the pressure power spectrum – dominant frequencies and corresponding amplitudes – for a given cavity geometry, set of freestream conditions and an assumed oscillation mechanism. Some success has been achieved in predicting the dominant frequencies associated with the fluctuating pressure field present in resonant cavity flows, though

F.W. Barnes, C. Segal / Progress in Aerospace Sciences 76 (2015) 24–41

27

prediction of the corresponding amplitudes has proven more difficult. The use of these models for guiding the design of passive and active methods of attenuating and controlling cavity flowfield oscillations is an area of active research [9,17,76,85,99]. Although a complete fluid mechanical description of cavity flows continues to elude researchers, substantial progress has been made towards understanding their structure and behavior. 2.1.1. Cavity oscillations Oscillations in cavity flows are largely attributed to a fluid resonant interaction between the cavity-freestream shear layer and propagating acoustic disturbances within the cavity recirculation zone. Rossiter [74] developed a model for this phenomenon based on the concept of a hydrodynamic–acoustic feedback loop. The proposed mechanism is illustrated in Fig. 2. Vortices shed by the shear layer that grow into large-scale coherent structures and later impinge on the cavity rear wall are assumed to be a source of directed acoustic radiation that in turn stimulates further vortex shedding. Resonance occurs when shear layer vortex shedding becomes phase-locked with the cavity’s acoustic modes resulting in constructive interference and highly dynamic motion of the shear layer. The frequencies associated with the discrete, high-amplitude pressure spectra characteristic of resonant cavity flows are predicted quite well by Rossiter’s [74] semi-empirical formula:

St =

fm* L U∞

=

m* − α 1 K

+ M∞

,

m* = 1, 2, 3, … (1)

Heller and Bliss [35] proposed a modification to Rossiter’s formula to account for the higher speed of sound of the cavity fluid compared to that of the freestream:

St =

fm* L U∞

= 1 K

+

m* − α , ⎛ ⎞ 2 M ∞ ⎜ ⎟ ⎜ 1 + r T (γ − 1)M 2 ⎟ ∞⎠ ⎝ 2

( )

m* = 1, 2, 3, …

⎛T ⎞ 2 ⎜ cav − 1⎟ 2 T ⎝ ⎠ (γ − 1)M∞ ∞

acoustics model is given by

St =

fm* L U∞

=

a cav 2L U∞ L

1+ =

rT (γ − 1) 2 M∞ 2

2M∞

m*,

m* = 1, 2, 3, … (4)

Unalmis et al. [89] attribute this transition to a primarily acoustic phenomenon, a departure from the feedback loop proposed by Rossiter, to a disparity between the acoustic impedance of the cavity fluid and that of the freestream. This difference is a strong function of the freestream Mach number and can be expressed as

(2)

Here, a Strouhal number, St , is defined based on the cavity length where fm* is the matched frequency between shear layer vortex shedding and longitudinal acoustic wave propagation within the cavity recirculation zone, m* is the frequency mode number, α is the phase lag between the arrival of a shed vortex at the cavity rear wall and the emission of an upstream travelling acoustic disturbance, K is the fraction of the freestream speed at which the shed vortices are advected downstream and rT is the temperature recovery factor of the cavity fluid, given by

rT =

Fig. 3. Basic geometric parameters and flow features of a cavity. Cavities are commonly described in terms of their length-to-depth ratio (L/D) and rear wall ‘closeout’ angle (θ) relative to the cavity floor. A shear layer separates the subsonic cavity recirculation zone from the supersonic freestream and impinges on the rear wall creating an unsteady stagnation zone. Waves emanating from the cavity leading and trailing edges and shear layer are unsteady in nature and may alternate between shocks and expansion waves. Waves generated at the cavity trailing edge are likely to be compressive in nature owing to the impingement of the shear layer – see Heller and Delfs [36] for a more detailed description of the wave phenomena associated with the cavity flowfield. The recirculation zone contains trapped vortices driven by the shear layer whose relative size and strength are related to the cavity’s geometry.

(3)

Although the predictive capability of this model has been experimentally validated to an acceptable degree of accuracy for both low and high-speed cavity flows its success is contingent upon proper selection of the empirical parameters α and K [3,59,68]. Furthermore, it has been shown that these parameters are not constants but rather functions of freestream and initial interfacial conditions and can vary across the shear layer. Experiments performed by Unalmis et al. [89] on supersonic and hypersonic cavity flows suggest a decoupling of shear layer dynamics and cavity acoustics as compressibility effects become more pronounced. It was found that a simple closed-box acoustics model of longitudinal standing waves within the cavity provides increasingly accurate estimates of the measured resonant frequencies – asymptotically approaching those values predicted by Rossiter’s formula – as hypersonic freestream Mach numbers are approached. The Strouhal number derived from the closed-box

Z∞ (ρa)∞ T = ≅ cav Zcav (ρa)cav T∞

T∞ = Tcav

1+

rT (γ − 1) 2 M∞ 2

(5)

This effective reduction in the shear layer’s acoustic receptivity renders it less susceptible to acoustic perturbations, and is likely partially responsible for the decrease in large-scale motion – ‘flapping’ – of the shear layer observed at higher freestream Mach numbers [86–88]. For flameholding applications in internal flows fluid resonant cavity oscillations present contradicting effects. The fluctuating motion of the shear layer may be leveraged to promote intracavity and cavity-freestream transport in order to enhance flame spreading. Yet, the associated flowfield unsteadiness may lead to locally unstable flame base anchoring and/or promote the occurrence of thermoacoustic instabilities. As was shown above, the oscillatory behavior of the flowfield is intimately tied to cavity length. In the following section the magnitude of shear layer excursions above and below the cavity-freestream interfacial plane and the structure of the cavity recirculation zone will be related to both cavity length and rear wall inclination. Thus for a given range of freestream operating conditions the cavity geometry plays a major role in determining its effectiveness as a flameholder. 2.2. Effect of cavity geometry An understanding of the impact of cavity geometry on local mixing, mass exchange, thermodynamic conditions, and flow stability is paramount for flameholder design. The basic geometric parameters and flow features of a cavity are shown in Fig. 3.

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F.W. Barnes, C. Segal / Progress in Aerospace Sciences 76 (2015) 24–41

The growth rate of a compressible free shear layer can be approximated by [16]

δ (r , s; Mc1) x

⎧ 1 ⎪ ⎪ (1 − r ) 1 + s 2 ⎨ ≈ Cδ 1 ⎪ 2 1 + s 2r ⎪ ⎩

(

(

(0.8e

−3Mc21

)

+ 0.2

)

)

1 ⎧ ⎫⎫ 1 − s2 ⎪ ⎪⎪ 1 ⎪ ⎪⎪ 1 + s2 ⎨1 − ⎬⎬ 1 + 2.9(1 + r )(1 − r ) ⎪⎪ ⎪ ⎪ ⎪⎪ ⎩ ⎭⎭

(6)

Here, the parameter r = U∞/Ucav is the velocity ratio between the bounding streams; s = ρ∞ /ρcav is the density ratio; Cδ is a constant found to be in the range of 0.25 ≤ Cδ ≤ 0.45; and Mc1 is the convective Mach number [7,67] of the large-scale shear layer structures defined with respect to the high-speed stream: Fig. 4. Experimental results obtained for compressible free shear layer growth rate as a function of convective Mach number. The growth rate is normalized by the value corresponding to an incompressible shear layer (Mc1 → 0) with the same velocity and density ratio. Increases in subsonic convective Mach numbers are accompanied a strong decrease in shear layer growth rate and fluid entrainment. In the supersonic convective Mach number range this trend is less severe [11,15,29,33,53,75,78,80,96].

Cavities are commonly described in terms of their length-to-depth ratio (L/D) and rear wall ‘closeout’ angle (θ) relative to the cavity floor. A shear layer separates the subsonic cavity recirculation zone from the supersonic freestream and impinges on the rear wall creating an unsteady stagnation zone. Waves emanating from the cavity leading and trailing edges and shear layer are unsteady in nature and may alternate between shocks and expansion waves, although waves generated at the cavity trailing edge are likely to be compressive in nature owing to the impingement of the shear layer – see Heller and Delfs [36] for a more detailed description of the wave phenomena associated with the cavity flowfield. The recirculation zone contains trapped vortices driven by the shear layer whose relative size and strength are related to the cavity’s geometry. Ultimately, tradeoffs between flameholder performance – flame spreading, flame stability, etc. – and drag limit the number of geometries suitable for cavity-based flameholding in supersonic combustors. 2.2.1. Effect of cavity geometry on the shear layer Cavity geometry has a strong influence on the development and behavior of the shear layer. The boundary condition imposed by the cavity length effectively constrains shear layer development and fluid entrainment. Additionally, reasonable cavity length-todepth ratios, i.e., L/Do7–10, resulting in a shear layer that spans the cavity – ‘open’ cavities – prevent the possible transition to large-scale shear layer instabilities that could lead to enhanced bulk mixing but at the expense of increased drag [24,25]. However, even for longer cavities such a transition is less likely due to the increased hydrodynamic stability of the shear layer at the high freestream Reynolds and Mach numbers to be encountered in supersonic combustors [76].

Mc1 =

U∞ − Uc = (1 − K )M∞ a∞

(7)

The expression in brackets describes the growth rate of an incompressible free shear layer as a function of the velocity ratio and density ratio, while the additional term accounts for the effect of compressibility. Furthermore, the rate at which fluid becomes mixed at molecular level and the rate of chemical product formation within a reacting free shear layer can be expressed as [16]

δm ⎛ δm ⎞⎛ δ ⎞ = ⎜ ⎟⎜ ⎟ ⎝ δ ⎠⎝ x ⎠ x δp

x

(8)

⎛ δp ⎞⎛ δ ⎞⎛ δ ⎞ = ⎜ ⎟⎜ m ⎟⎜ ⎟ ⎝ δm ⎠⎝ δ ⎠⎝ x ⎠

(9)

where the extent of molecularly mixed fluid within the shear layer is represented by δm/δ , and the extent of chemical product formation within the molecularly mixed layer is δp/δm . In addition to the constraint imposed by cavity length flow compressibility serves to further suppress shear layer development and fluid entrainment (δ /x ), ultimately limiting the rate of local mixing (δm/x )

( )

and combustion δp/x . The experimental shear layer growth rate data plotted along with Eq. (6) and shown in Fig. 4 demonstrates this trend. Hydroxyl-tagging-velocimetry (HTV) measurements performed by Lahr et al. [43] suggest that even the presence of an adverse pressure gradient strong enough to force separation of the shear layer from the cavity – a condition likely to exist in dualmode scramjet combustors – has a negligible impact on shear layer growth rate and is thus ineffective in counteracting the effect of compressibility. The cavity closeout angle (θ ), in turn, influences the shear layer attachment process. For cavities with a closeout angle of 90°, the canonical configuration, the attachment process is highly unsteady and is accompanied by a mass exchange cycle. Freestream fluid is forced into the cavity when the shear is periodically deflected below the trailing edge. Ingestion and subsequent advection of this high-momentum fluid stimulates mixing along the periphery

Fig. 5. Streamlines obtained from a Reynolds–Averaged Navier–Stokes (RANS) computation, where the effects of cavity length and closeout angle on the mean recirculation zone flowfield were examined. Flow is from left to right. The streamline patterns show an expansion of the primary vortex relative to the secondary vortex over the (a) baseline case, (b) as either the closeout angle is decreased below 90° or (c) the cavity length-to-depth ratio is increased [30].

F.W. Barnes, C. Segal / Progress in Aerospace Sciences 76 (2015) 24–41

29

Fig. 6. Surface oil flow visualization showing the streakline patterns along the walls for two different cavity geometries (a) L/D ¼ 3, and (b) L/D ¼ 4 in a Mach 5 airflow. The locations and orientations of the primary and secondary vortices are visible. A small corner vortex at the rear wall is also apparent in both cases. The shape of the ‘separation line’ between the vortices changes between the two cases as a result of changing the cavity length. Note the lateral symmetry and presence of spanwise vortex cells [17].

of the cavity. Once the cavity pressure builds sufficiently some recirculation zone fluid is expelled in concert with an upward deflection of the shear layer. As the closeout angle is reduced below 90° the angle of incidence between the shear layer’s stagnation streamline and cavity rear wall is altered in such a way that the attachment process occurs with increased stability [68,97,6]. The resulting stabilizing effect as evidenced by a more limited range of shear layer motion is also attributed to a simultaneous redirection of acoustic radiation away from the cavity leading edge, such that incipient instability waves are amplified to a lesser extent. Significant reduction of the closeout angle below 90°, the limiting case being a rearward-facing step, leads to the formation of a leading edge Prandtl–Meyer expansion with the effect of reduced cavity pressure and increased base drag. This reduction in local pressure can adversely impact chemical kinetics in the reacting case. Combined with the resulting increase in rear wall wetted surface area where the flow is recompressed, reduction of the closeout angle can cause an overall increase in pressure drag over the baseline case of a vertical rear wall [79,97,30]. 2.2.2. Effect of cavity geometry on the recirculation zone flowfield Within the recirculation zone trapped vortices dictate fluid mixing and advection. A streamwise-oriented vortex with its core situated near the aft portion of the cavity is driven via shear layer momentum transfer. This ‘primary’ vortex in turn drives a smaller and weaker counter-rotating ‘secondary’ vortex located adjacent to the cavity front wall. The relative size of these trapped vortices is determined by the cavity geometry. For moderately deep cavities increasing the length-to-depth ratio and/or reducing the closeout angle below 90° leads to an expansion of the primary vortex. This is shown in Fig. 5 via the computational results obtained by Gruber et al. [30]. Beyond a certain length vortex breakdown occurs and multiple trapped vortices are likely to be present within the recirculation zone [4]. Length-to-depth ratio has also been shown to affect the mode – transverse or longitudinal – in which the vortices oscillate about their mean positions, which can affect the extent of mass exchange between them [98]. The presence of corners and sidewalls further complicates the structure of the recirculation zone. These boundaries engender spanwise variations in the flowfield, one of the more striking consequences being the formation of multiple vortex cells across the cavity span [50,98,95]. Secondary flows due to wall effects assist in compartmentalizing the cavity flowfield into regions of enhanced and diminished mixing. Issues related to local mixing will be discussed below. The complexity of the recirculation zone flowfield is illustrated in Fig. 6a and b, which show the streakline patterns along the walls of two different cavity geometries (L/D = 3 & 4) in a Mach 5 airflow obtained via surface oil flow visualization [17]. For both geometries the streakline patterns indicate the locations and orientations of the primary and secondary

vortices, as well as the existence of a small corner vortex at the rear wall. The shape of the ‘separation line’ between the primary and secondary vortices, which is made visible through this technique, is altered as a result of changing the cavity length; this is evidence of a change in the mean recirculation zone flow pattern – in both the spanwise and streamwise directions – corresponding to a new hydrodynamic equilibrium. Additionally, the presence of spanwise vortex cells and the lateral symmetry of the flowfield are discernible. 2.2.3. Effect of cavity geometry on residence time The mean residence time is defined as the time scale associated with the rate of decay of cavity fluid due to mass exchange with the freestream [4], and is governed by the coupled behavior of the shear layer and recirculation zone flowfield. Results from experiments performed by Winterfeld [93] on turbulent transport in the wakes of bluff body flameholders in subsonic flows, suggest that the following relationship between exchange rate and mean residence time can be applied to subsonic cavity recirculation zones embedded in supersonic flows:

ṁ exchange = −

ρ WL2 ⎛ L ⎞−1 dmcav m ⎜ ⎟ = cav = cav τr τr ⎝ D ⎠ dt

mcav (t ) ~ exp(−t /τr )

(10)

(11)

where ṁ exchange is the rate at which fluid originating in the cavity is transported into the freestream – assumed to be equivalent to the rate at which freestream fluid enters the cavity, mcav (t ) is the

Fig. 7. Top: Snapshots of the time evolution of cavity (L/D¼ 7.76) fluid mass decay from the LES study performed by Baurle et al. [4]. Lighter regions correspond to mixtures with a higher fraction of fluid originating in the cavity. Note the largescale shear layer instability and the existence multiple trapped vortices in this relatively long cavity. The flow (M ¼ 2) is from left to right. Bottom: Cavity (L/D ¼3) fluid mass distribution 3 ms after initiation of the RANS computation performed by Gruber et al. [30]. Darker regions correspond to mixtures with a higher fraction of fluid originating in the cavity. The flow (M ¼3) is from left to right. The larger exchange rate between the primary vortex/aft cavity region and the freestream is apparent in both images.

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instantaneous mass of fluid originating in the cavity and that remains in the cavity after a time t has elapsed, τr is the mean residence time, ρ is the mean fluid density in the recirculation zone and L , D , and W are the cavity length, depth, and width respectively. Davis [14] developed an analytical expression to estimate the mean residence time in cavity flows by evaluating the mass flow rate of freestream fluid into the cavity at the rear wall. The cavity velocity was assumed to be negligible and the shear layer velocity profile was approximated by

⎛ σy ⎞⎞ u(x, y)SL 1⎛ = ⎜1 + erf⎜ ⎟⎟ ⎝ x ⎠⎠ U∞ 2⎝

(12)

where the origin is located at the cavity leading edge, and 13 ≤ σ ≤ 30 depending on the convective Mach number Mc1. Along with the assumption of constant fluid density within the cavity, the mass flow rate into the cavity and mean residence time were approximated by

ṁ exchange = (ρU )∞W

τr =

mcav ṁ exchange

=

⎛

0

ρcav WLD

(

⎛

⎞⎞

∫−∞ 21 ⎜⎝1 + erf⎝ σLy ⎠⎟⎠dy =

(ρU )∞WL 2σ π

)

⎜

⎟

(ρU )∞WL 2σ π

⎛ ⎞ 2σ π ⎟ D =⎜ r 1 γ − ⎜ 1 + T ( ) M 2 ⎟ U∞ ⎝ ∞⎠ 2

(13)

(14)

Davis’ [14] expressions show that the exchange rate scales with the freestream mass flux and the mean cavity residence time scales with the cavity depth and inversely with the freestream velocity. Baurle et al. [4,5] studied local mixing, cavity-freestream mass exchange and the effect of cavity geometry on these processes in the absence of fuel injection through the use of ‘numerical fluid tagging’ in both 2-D RANS computations and 2-D/3-D large-eddy simulations (LES). Numerical markers were used to distinguish between fluid originating in the cavity and that originating in the freestream prior to simulating the flowfield. Upon initiation of the numerical analyses the decay of cavity fluid was tracked. An example of the time evolution of intra-cavity mixing and cavity-freestream mass exchange captured in one of the LES cases is shown on the top in Fig. 7. Note the large-scale shear layer instability and the existence of multiple trapped vortices – breakdown of the stable vortex system – present in this case for a relatively long cavity (L/D = 7.76). For each cavity configuration studied the largest degree of mixing was found to occur in the shear layer and substantial mixing around the periphery of the trapped vortices was also observed; consequently fluid near the center of the recirculation zone and/or within the secondary vortex(es) was the last to ‘mix out.’ The time history of numerically tagged cavity fluid within the cavity was used to

Fig. 8. Commonly employed injection configurations for fueling cavity flameholders. Upstream injection: fuel is injected into the flow upstream of the cavity and is entrained into the recirculation zone by the shear layer; floor injection: fuel is injected directly into the shear layer; rear wall injection: fuel is injected directly into the cavity recirculation zone.

estimate the mean residence time for an array of cavity geometries. Results from the RANS computations indicated that the mean residence time scales primarily with cavity depth, a validation of Davis’ [14] analytical expression. The residence time was also found to scale inversely with the size of the primary vortex relative to the secondary one, i.e. shorter residence times correspond to shallower closeout angles where the primary vortex increases in size. This is attributable to the strong circulation of the primary vortex. On the contrary, the LES study, which was able to capture the intrinsic unsteadiness of the flowfield, revealed that shear layer oscillations are the primary driver for cavity-freestream transport. Cavities with geometric features that enhanced shear layer development, fluid entrainment, and oscillations – i.e. larger lengths, steeper closeout angles – were found to have the lowest mean residence times and highest exchange rates. Gruber et al. [30] also performed a 2-D RANS computation using numerical fluid tagging to examine the effect of cavity geometry on residence time in non-reacting cavity flows. A snapshot of the fluid mass distribution in a cavity (L/D = 3) 3 ms after initiation of one of the numerical analyses is shown on the bottom in Fig. 7. The trends obtained matched those of the RANS computations performed by Baurle et al. [4].

3. Fuel injection and mixing The manner in which fuel is introduced to the cavity is critical to its performance as a flameholder. Fig. 8 shows three of the most often employed injection configurations for fueling cavity flameholders in supersonic flows. A strong coupling between the fuel injection process and the local flowfield exists both for the case of ‘passive’ injection, where the fuel injectors are located external to the cavity, and for ‘direct’ injection, where the injectors are embedded within one or more of the cavity walls. Hence, changes in the baseline cavity flowfield in response to fueling result in a mixing process that is more complicated than indicated by the mass exchange computations by Baurle et al. [4,5] and Gruber et al. [30] – see Fig. 7. A select of number of studies in which aspects of the fuel–air mixing process within a supersonic cavity flameholder were examined are presented in Table 1. 3.1. Upstream Injection Fuel injection from the wall upstream of the cavity leading edge is an attractive option as it can provide fuel to both the engine core and flameholder. With this scheme a portion of the injected fuel is entrained by the cavity shear layer and subsequently delivered to the recirculation zone. In general, reliance on upstream injection results in a flameholder recirculation zone fuel distribution that is largely dependent on the extent of fuel jet penetration, lateral spreading, and interaction with the shear layer. For example, Ortwerth et al. [62] found that the operational conditions of a rearward-facing step flameholder were quite sensitive to fueling rate – hence fuel jet penetration – for the case of upstream ‘preinjection’ from the isolator walls. Ultimately the local stoichiometry is dictated by fuel injector geometry, e.g. size, shape, inclination, lateral spacing, distance from cavity leading edge, freestream conditions, e.g. Mach number, upstream boundary layer momentum thickness, level of back pressure, fuel type, e.g. molecular weight, mass diffusivity and fueling parameters, e.g. fuel temperature, flow rate, jet-to-freestream dynamic pressure ratio. Upstream injection can also promote the onset of upstream interaction, resulting in movement of the isolator shock train and alteration of the local mixing processes [12]. Gruber et al. [31] used nitric oxide planar laser-induced fluorescence, NO-PLIF, to examine fuel–air mixing in an ethylene-fueled cavity in a Mach 2 airflow with both transverse and angled

F.W. Barnes, C. Segal / Progress in Aerospace Sciences 76 (2015) 24–41

31

Table 1 Fuel–air mixing studies. Reference

Technique

Combustor inlet conditions (M , T0)

Injection type (Fuel, Location)

Cavity geometry (L/D, θ )

Cavity modification

Baurle et al. [4] Gruber et al. [30] Baurle et al. [5] Gruber et al. [31] Kim et al. [42] Rasmussen et al. [70] Liu et al. [48] Lin et al. [45] Lin et al. [46] Milligan [56] Yang et al. [94] Ebrahimi et al. [21] Yeom et al. [95] Li et al. [44] Barnes et al. [2]

RANS/LES RANS LES PLIF RANS PLIF RANS RANS RANS RANS RANS RANS RANS RANS PLIF

2.0; 300 3.0; 300 2.0; 300 2.0; 300 2.5; 2250 2.0, 3.0; 300 2; 590 1.8, 2.2; o 1100 1.8, 2.2; o 1100 1.8; 600, 670, 690 2.2; 1100 2.0; 1730 3.5; 2810 2.2; 1100 2.2; 300

Numerical Fluid Tagging Numerical Fluid Tagging Numerical Fluid Tagging NO; UP/FL/RW H2; UP NO; FL/RW C2H4; RW C2H4; UP/RW C2H4; UP/RW C2H4, CH4 þ C2H4; UP C2H4; UP C2H4; UP/FW/FL/RW H2; UP C2H4; UP C3H6Oþ N2; FL/FW

3.88, 7.76; 22.5°, 56.25°, 90° 3, 5; 16°, 30°, 90° 7.76; 90° 4; 22.5° 3; 30° 4; 22.5°, 90° 4; 22.5° 4; 22.5° 4, 5, 6; 22.5° 3.88; 22.5° 4; 22.5° 4; 22.5° 3; 90° 4; 22.5° 4; 45°

– – – – – – – – – Tandem Cavities – – – – –

Fig. 9. Equivalence ratio distribution for angled injection of ethylene upstream of a cavity in a Mach 2 airflow. Note the lack of substantial lateral spreading, minimal fuel jet–shear layer interaction, and distinct fuel jets that persist in the far-field. Only a small fraction of injected fuel reaches the cavity recirculation zone as evidenced by its lean mixture [21].

upstream injection configurations. Minimal jet–cavity interaction was observed and distinct fuel jets were still visible in the plane containing the cavity trailing edge. Lateral spreading of the fuel jets and mixing were noticeably improved when backpressure was applied to simulate dual-mode conditions. Yet, the resulting deflection of the shear layer into the core flow and enhanced jet penetration were accompanied by a dilution of the recirculation zone fuel–air mixture. In a recent RANS computation, Li et al. [44] similarly observed minimal fuel entrainment into a cavity employing angled upstream injection of ethylene in a Mach 2.2 crossflow. The use of a downstream air throttle to simulate combustor backpressure resulted in significantly improved local mixing and entrainment into the cavity. Ebrahimi et al. [21] performed a 3-D RANS computation of a cavity exposed to a Mach 2 freestream and examined a variety of fuel injection configurations. For the case of angled upstream injection, only a small fraction of fuel was entrained into the cavity and distinct fuel jets were still visible in the far field. The equivalence ratio distribution for this injection configuration is shown in Fig. 9. Kim et al. [42] performed a 2-D RANS computation of a cavity in a Mach 2.5 freestream fueled by transverse upstream injection of hydrogen. Fuel entrained by the shear layer remained largely within the primary vortex, and the upstream cavity volume was comparatively leaner. Merging of the separated region downstream of the fuel jet with the cavity recirculation zone was observed, enabling a flammable mixture to be transported upstream of the cavity leading edge. Results of a computation by Lin et al. [45] highlighted the dependence of the cavity recirculation zone fuel distribution on upstream injector placement. Fueling the cavity from a set of

Fig. 10. Processed ensemble average images of injectant (acetone-seeded nitrogen) streamwise mole fraction distribution X N2 for three cavity floor injection tests obtained using acetone–PLIF. Injection location and orientation are indicated with an arrow. Injection pressure and corresponding global equivalence ratios are included to the left of the figure. The freestream flow (M¼ 2.2) is from left to right. The outer line represents the lower flammability limit contour, X N = 0.027, cor2 responding to an ethylene–air mixture; the inner line represents the upper flammability limit contour, X N = 0.34 . The mixture bounded by the upper 2 flammability limit contour is too rich for combustion. Whereas the region between the two flammability limit contours, including the shear layer and upstream cavity volume, is indicative of where combustion is likely to occur [2].

injectors further upstream than the baseline injection case resulted in earlier merging of the fuel jets causing an effective aerodynamic blockage and subsequent reduction in air entrainment into the recirculation zone. Milligan [56] examined the effect of upstream fueling rate on the recirculation zone fuel distribution. The results indicated that higher fueling rates lead to increased jet penetration and a leaner cavity mixture. The use of a tandem ‘feed injector’ operating at a lower fueling rate – and hence lower penetration – enabled more effective control over the cavity fuel distribution. Yeom et al. [95] simulated angled injection of hydrogen upstream of a cavity in a Mach 3 crossflow. The recirculation zone fuel mass fraction was found to be spatially nonuniform with spanwise variations reflective of the injector spacing. Fuel rich regions were confined primarily to the center of a single trapped vortex. The periphery of the recirculation zone was found to be considerably leaner. 3.2. Floor injection Transverse injection from the cavity floor has also been investigated as a candidate solution. In this case, the shear layer is directly fueled and as with upstream injection shear layer dynamics dictate the amount of fuel transported into the recirculation zone. Hence, the local stoichiometry resulting from this

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Fig. 12. Direct image of flame luminosity in a cavity fueled by transverse floor injection of ethylene. The flame is clearly visible in the shear layer and is anchored near the cavity leading edge. The flame bounds a less luminous zone where recirculating hot products, reactive intermediate species, and unburned fuel assist in flame stabilization. Flow is from left to right [70].

Fig. 11. Processed ensemble average images of injectant (acetone-seeded nitrogen) streamwise mole fraction X N distribution for three cavity front wall injection tests 2 obtained using acetone–PLIF. Injection location and orientation are indicated with an arrow. Injection pressure and corresponding global equivalence ratios are included to the left of the figure. The freestream flow (M ¼2.2) is from left to right. The outer line represents the lower flammability limit contour, X N2 = 0.027, corresponding to an ethylene-air mixture; the inner line represents the upper flammability limit contour, X N2 = 0.34 . The mixture bounded by the upper flammability limit contour is too rich for combustion. Whereas the region between the two flammability limit contours, within the shear layer and near the fuel injectors, is indicative of where combustion is likely to occur [2].

configuration is equally susceptible to shear layer fluctuations via freestream transients. Gruber et al. [31] observed that shear layer oscillations were stimulated by the action of the impinging fuel jets, providing a plausible explanation for improved near-field mixing and recirculation zone entrainment over the case of upstream injection. Yet, images obtained via NO-PLIF revealed localized fuel pockets in the shear layer, likely reflective of the injector spacing. Using NO-PLIF, Rasmussen et al. [70] also observed significant spanwise non-uniformity in the recirculation zone fuel distribution when employing transverse injection from the floor of a cavity in Mach 2 and Mach 3 airflows. Mohamed Ali and Kurian [58] studied the effect of transverse floor injection and its location relative to the cavity front wall in a Mach 1.8 freestream. Cavity wall pressure measurements indicated that floor injection can either suppress or intensify flowfield oscillations depending on the injection location along the floor. Pressure measurements also indicated enhanced entrainment of freestream fluid into the cavity over the baseline no injection case regardless of floor injection location. A 2-D RANS computation by Mishra and Sridhar [57] showed significant entrainment of fuel into the primary vortex and a leaner upstream cavity volume for several angled floor injection configurations at a location 0.3 L from the front wall. Barnes et al. [2] utilized acetone–PLIF to study fuel–air mixing in a directly-fueled cavity exposed to a Mach 2.2 airflow. Acetoneseeded nitrogen was injected as a surrogate for ethylene. Trapping of fuel within the primary vortex and minimal transport of fuel towards the upstream cavity volume were reported when employing downstream angled injection from the cavity floor at a location 3D from the front wall. The injectant mole fraction distribution corresponding to this injection configuration is shown in Fig. 10. 3.3. Parallel Injection Parallel fueling from either the front or rear cavity wall has been shown to provide the largest degree of recirculation zone mixture homogeneity and offers a greater level of control of the local stoichiometry than either upstream or floor injection. Yet as was reported by Barnes et al. [2] in the study mentioned above, recirculation zone equivalence ratios may be up to an order of

magnitude higher than indicated by global values. In this study [2] acetone–PLIF images for the case of parallel injection from the front cavity wall, as shown in Fig. 11, revealed that even for very small global equivalence ratios the majority of the cavity recirculation zone may be too rich for flameholding. This is in line with the earlier observations by Thakur and Segal [83] for the case direct injection into the recirculation zone created by a rearwardfacing step. NO–PLIF images obtained by Gruber et al. [31] and Rasmussen et al. [70] for the case of parallel rear wall fueling indicate a marked improvement in spanwise and transverse recirculation zone mixture homogeneity when compared with upstream and floor injection configurations. Most notably, Gruber et al. [31] found that when fueled from the rear wall, imposed combustor backpressure primarily results in a diluted recirculation zone mixture while the spatial distribution of fuel is affected minimally. Liu et al. [48] performed a RANS computation to examine the effect of fueling rate on the fuel distribution in a cavity with rear wall fueling and exposed to a Mach 2 airflow. Increased fueling progressively flooded the cavity volume and pushed the stoichiometric mixture fraction contour into the shear layer, similar to the experimental observations of Barnes et al. [2] for the case of front wall fueling. When chemical reactions are present the effects of heat release further modify the flowfield structure, therefore the mixing process. A strong coupling ensues between local mixing, heat release, and transport across the shear layer.

4. Reacting flowfield In general, the fluid dynamic features of non-reacting cavity flows are retained in the reacting case. The shear layer and trapped vortices continue to drive intra-cavity and cavity-freestream transport, influencing the location and extent of chemical reactions. These flow features are discernible in PLIF and flame luminosity images of the reacting cavity flowfield, as shown in the example in Fig. 12. by Rasmussen et al. [70]. In this direct image of flame luminosity in a cavity fueled by transverse floor injection of ethylene, the flame is clearly visible in the shear layer and is anchored near the cavity leading edge. The flame bounds the less luminous recirculation zone where recirculating hot products, intermediate species, and unburned fuel assist in flame stabilization. Though these flow features are still present heat release and changes in the local composition alter thermodynamic and transport properties resulting in a modification of the baseline non-reacting flowfield. Experimental [37,38] and numerical [52,69]) studies of reacting, turbulent, compressible shear layers have shown that shear layer growth rate and entrainment are attenuated as a consequence of heat release. This result is attributed to a reduction in turbulent shear stresses and the generation of an outward velocity component, both accompanying a local decrease in density. Redistribution of vorticity within the shear layer due to baroclinic

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33

Table 2 Reaction zone imaging studies. Reference

Technique

Combustor inlet conditions (M , T0) Injection type (Fuel, Location)

Cavity geometry (L/D, θ ) Cavity modification

Donbar et al. [18] Mathur et al. [49] Gruber et al. [31] Allen [1] Rasmussen et al. [70] Rasmussen et al. [71] Lin et al. [45] Jeong et al. [41] Micka and Driscoll [54] Micka and Driscoll [54] Ryan et al. [77] Hsu et al. [39] Retaureau [72] Pan et al. [65] Pan et al. [66] Fotia and Driscoll [23] Wang et al. [91] Wang et al. [91] Hammack et al. [34] Donohue [19]

PLIF DI PLIF PLIF DI PLIF DI, PLIF DI, PLIF PLIF DI (4 kHz) PLIF DI, PLIF DI DI, SCH DI, SCH SI (1 kHz) DI, SCH, PLIF DI, SCH, PLIF PLIF (10 kHz) DI

1.8; 780–1220 1.8, 2.2; 945–1220 2.0; 590 2.0; 580 2.0, 3.0; 590, 640 2.4; 430 1.8, 2.2; o1100 3.7–4.0; 3090–4420 2.2; 1270, 1470 2.2; 1040–1490 2.8; 1388 2; 590 2.5; 300–750 2.6; 1300 2.6; 1480 2.2; 1400 2.5; 1490 2.5; 1490 2; 610 2.2, 3.3; o 1200

4.8; 22° 4.8; 22° 4; 22.5° 4; 22.5° 4; 22.5°, 90° 4; 90° 4; 22.5° 4.8; 22.5° 4; 90° 4; 90° 3.2; 22.5° 4; 22.5° 2.84, 3.84; 90° 5, 7; 45° 5, 7; 45° 4; 30° 7; 45° 4, 7; 22.5°, 45°, 90° 4; 22.5° 4; 22.5°

C2H4, JP-7; UP C2H4; UP C2H4; UP/FL/RW C2H4 þAir; RW CH4, C2H4; FL/RW C2H4; FL/RW C2H4; UP/RW H2; UP C2H4 þH2; UP/RW(p) H2, C2H4 þ H2; UP/FL(p)/RW(p) CH4, C2H4; UP/DN C2H4 þAir; UP/RW H2 þ CH4 þ C2H4; FL Kerosene, H2(p); UP/UP(p) Kerosene, H2(p); UP/UP(p) H2; UP/RW(p) H2; UP/RW H2; UP/RW C2H4; RW C2H4; UP/RW

effects and increased kinematic viscosity also play a role in the observed reduction in shear layer growth rate and entrainment [16]. In the same experimental study mentioned previously, Winterfeld [93] observed an increase in the measured flameholder recirculation zone mean residence time in the reacting flow case. This was attributed to a reduction in shear layer velocity gradients, hence turbulent stresses, resulting in attenuated shear layer entrainment and a diminished exchange rate between the recirculation zone and freestream. Tuttle et al. [84] studied changes in the kinematic properties of a supersonic cavity flow due to combustion heat release. Velocity and vorticity distributions obtained via titanium dioxide particle image velocimetry TiO2–PIV revealed shear layer thickening and a corresponding decrease in shear layer velocity gradients with cavity combustion, a validation of Winterfeld’s explanation for the increase in mean recirculation zone residence time in the reacting case. The location and magnitude of these kinematic changes were found to be a strong function of fueling rate, combustion intensity, and flame location. Much of the current insight regarding the structure and behavior of reacting cavities in supersonic flows has come from PLIF investigations examining the spatial distribution of select combustion intermediates for given freestream and fueling conditions. A select number of studies in which the cavity reaction zone was examined using PLIF and/or an additional imaging technique – direct imaging of flame luminosity (DI), Schlieren (SCH), shearing interferometry (SI) – are listed in Table 2. 4.1. Upstream injection In the last two decades a number of experimental studies at the Air Force Research Laboratory (AFRL) have focused on the problem of combustion of hydrocarbon fuels injected upstream of a cavity flameholder in a supersonic crossflow [18,49,31,45,46,77,39]. Freestream conditions in these studies were representative of flight Mach numbers between 4 and 6, the regime corresponding to dual-mode ramjet operation. In most cases a proclivity for sidewall/corner burning as well as combustion in the cavity shear layer and the boundary layer upstream of the flameholder were noted. Hydroxyl radical OH–PLIF images in several cases confirmed that intense flame spreading from the cavity was confined to the combustor sidewalls. This behavior was attributed to the lowspeed, kinetically favorable conditions that exist within thick

– – – Direct Air Injection – – – – – – Downstream Steps LE Pylon, Direct Air Injection – Parallel, Tandem Cavities Tandem Cavities – – – – –

boundary layers and peripheral separated flow regions. Images obtained in a study performed more recently by Donohue [19] where flame emissions were collected through a window in the ‘cowl’ wall directly opposing the cavity flameholder, provided additional evidence that flame spreading as seen in integrated side view images occurs primarily through the sidewall boundary layers. Spanwise OH–PLIF images obtained by Donbar et al. [18] indicated some degree of premixing in the near-field above the cavity for both ethylene and JP-7 upstream injection. A broadening of the spatial extent of the reaction zones in the vicinity of the cavity with increases in air stagnation temperature, was also observed while increasing the freestream dynamic pressure counteracted this effect pushing flames closer to the combustor sidewalls. Micka and Driscoll [54] used methylidyne radical CH–PLIF to study the combustion process in a thermally choked dual-mode combustor with freestream conditions representative of flight Mach numbers between 5 and 6. A 50/50 blend of hydrogen and ethylene was injected upstream of a cavity flameholder. Direct fueling from the cavity rear wall was employed simultaneously. At higher air stagnation temperatures combustion was initiated upstream of the cavity leading edge in the fuel–jet wake – see Fig. 13a for an example of a cavity-assisted jet wake-stabilized flame. With lower temperatures and/or removal of the thermal throat, i.e. via lowering the equivalence ratio, combustion was forced to stabilize within the cavity shear layer – see Fig. 13b for an example of a cavity shear layer stabilized flame. For an intermediate range of temperatures the reaction base oscillated between the fuel jet-wake and the cavity shear layer. In experiments where the upstream fuel injector was moved closer to the cavity leading edge, the shear layer flame base was pushed further downstream – see Fig. 13c for an example of a combined shear layer, jet wake-stabilized flame. This was attributed to a reduction in the time available for premixing. Fotia and Driscoll [23] observed similar flame stabilization behavior while studying the dynamics of ram-scram transition in a scaled supersonic combustor employing a cavity flameholder and upstream injection of hydrogen. Wang et al. [91] emphasized the role of jet-to-freestream dynamic pressure ratio in explaining the same observed changes in flame stabilization mode for a cavity with upstream injection of hydrogen. The cavity was exposed to a freestream corresponding to Mach 5 flight. It was highlighted that increases in jet-to-freestream dynamic pressure ratio result in

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Fig. 14. Instantaneous formaldehyde CH2O–PLIF images of a cavity exposed to a Mach 2.4 freestream with floor injection of ethylene. (a) Corresponds to conditions near lean blowout, (b) represents a moderate fueling condition, and (c) corresponds to conditions near rich blowout. As the fueling rate is increased from the baseline case (a) where the flame is apparently anchored near the cavity leading edge, the formaldehyde signal shifts downstream indicative of an analogous movement of the flame base. Additionally, the amount of formaldehyde present in the upstream portion of the cavity volume diminishes with increased fueling rate, which is attributable to the presence of larger quantities of unburned fuel [71].

Fig. 13. Common flame stabilization modes corresponding to upstream fuel injection. (a) Cavity-Assisted Jet Wake-Stabilized Flame: this flame stabilization mode is found to occur at higher values of combustor backpressure – dual-mode operation –, air stagnation temperature, and fuel injection pressure (b) Cavity Shear Layer-Stabilized Flame: this flame stabilization mode is found to occur at lower values of combustor backpressure – scram-mode operation –, air stagnation temperature, and fuel injection pressure and (c) Combined Shear Layer, Jet Wake-Stabilized Flame: this flame stabilization mode is found when the injector is moved closer to leading edge, and/or for moderate values of combustor backpressure, air stagnation temperature, and fuel injection pressure.

increased aerodynamic blockage, leading to a stronger upstream bow shock, larger separated flow regions upstream/downstream of the fuel injector, and stronger vortex interactions within – counter-rotating vortex pair – and around the periphery – horseshoe, jet-shear layer, wake vortices – of the fuel jet; all consequences acting in favor of enhanced near-field mixing, reaction kinetics, flame stabilization and flame spreading. Furthermore, if the additional quantity of injected fuel resulting from an increase in jet-to-freestream dynamic pressure ratio releases enough heat to thermally choke the combustor, flameholding is improved due to the corresponding compression and deceleration of the adjacent flow. Wang et al. [91] examined the spatial extent of flame spreading through spanwise OH–PLIF. Flame spreading from the cavity shear

layer was clearly confined to the wake of the upstream fuel jet. In an additional study, Wang et al. [91] varied cavity length-to-depth ratio, closeout angle, and the distance from the upstream fuel injector to the cavity leading edge to examine their impact on flame stabilization. It was found that longer cavities with steep aft wall angles and with a closely placed upstream injector demonstrate the most robust flameholding. This behavior was attributed to the following: the increased capacity for shear layer growth and entrainment allowed by a longer cavity, the amplification of shear layer oscillations via directed acoustic radiation from a steeper aft wall resulting in increased fuel jet-shear layer exchange and the effective enlargement of the recirculation region due to a merger with the downstream fuel jet separation region. Similar to the observations by Micka and Driscoll [54] and Fotia and Driscoll [23], Wang et al. [91] observed intermittent oscillations between cavity-assisted jet wake-stabilized flames and cavity shear layer-stabilized flames. It was noted that cavity shear layer-stabilized flames were less sensitive to perturbations and hence provided more stable flameholding. In an additional study employing the same injection/flameholding configuration mentioned previously, Micka and Driscoll [54] examined the effect of fuel type on flame stabilization mode. The use of hydrogen instead of a 50/50 hydrogen–ethylene blend resulted in a further upstream located flame base and a tendency to transition from a cavity shear layer-stabilized flame to a jet wake-stabilized flame at lower air stagnation temperatures. The faster kinetics and consequently larger flame speed of hydrogen was deemed responsible for both observed effects. Owing to the same chemical kinetic explanation, Donbar et al. [18] reported reduced flame spreading for JP-7 combustion over that of ethylene, and Ryan et al. [77] observed weaker and more intermittent OHPLIF signals for methane combustion over that of ethylene.

F.W. Barnes, C. Segal / Progress in Aerospace Sciences 76 (2015) 24–41

35

located near the front wall. Formaldehyde was used a marker for partially-oxidized fuel and the occurrence fuel breakdown in lower temperature reaction zone regions. It was found that shear layer-stabilized combustion was sustained via hot products within the primary vortex. Heat release from reactions occurring within a fuel jet-driven recirculation near the front wall was believed to enable mixture preheating prior to entering the flame front at the cavity leading edge. At lower fueling rates the fuel jet-driven recirculation was not observed. Increased fueling towards rich blowout corresponded to a downstream shift of the formaldehyde signal indicating an analogous shift of the reaction base. This trend is shown in Fig. 14. Retaureau [72] employed a similar configuration using ethylene-methane and hydrogen–methane fuel blends. At lower fueling rates, reactions were not observed to extend upwards into the shear layer. Rather, combustion was confined to the upstream cavity volume near the fuel injectors. Increased fueling pushed combustion into the shear layer where the reaction base stabilized near the cavity leading edge. With larger quantities of injected fuel the reaction based was pushed further downstream similar to that observed by Rasmussen et al. [71].

Low Fueling Rates

4.3. Parallel Injection Moderate Fueling Rates

High Fueling Rates

Fig. 15. Schematic illustrating changes in flame location and distribution in a cavity with parallel rear wall fueling as the fuel flow rate is increased. Flow is from left to right.

4.2. Floor injection Rasmussen et al. [71] utilized OH and formaldehyde CH2O–PLIF to study ethylene combustion in a cavity with floor injectors

Lin et al. [45] used direct imaging of flame luminosity to observe changes in cavity flame shape and spatial distribution when fueled from the rear wall. At low fueling rates reactions occurred near the cavity floor and extended upstream following the recirculating flow pattern towards the front wall. Increased fueling quenched reactions in the upstream cavity volume and pushed combustion into the shear layer, anchored at the cavity leading edge. This was attributed to fuel pooling within the recirculation zone. Additional fuel injection forced the flame base to shift further downstream. Near rich blowout, flames were attached to the fuel injectors and combustion was confined to the rear wall and downstream boundary layer. Fig. 15 illustrates these changes in flame location and distribution as rear wall fueling rates are increased. The RANS computation performed by Liu et al. [48] exhibited a similar movement of the reaction zone from ignition to rich blowout. In the same study mentioned above, Rasmussen et al. [71] also studied rear wall injection. At low fuel flow rates it was inferred that the flame was anchored in the shear layer near the cavity leading edge and piloted by recirculating hot products in both trapped vortices. With increased fueling, OH and CH2O signals were no longer found in the upstream portion of the cavity, indicating the presence of unburned fuel. Reactions were

Table 3 Temperature, species, and reaction kinetics studies. Reference

Davis [14] Owens et al. [63]

Technique

PSR, RANS IFP IFP Kim et al. [42] RANS Choi et al. [10] RANS Liu et al. [48] RANS Gokulakrishnan et al. [27] RANS/LES Edens et al. [22] IFP, MS Lin et al. [45] Gas Analyzer Milligan [56] RANS Yang et al. [94] RANS Hsu et al. [39] IFP, MS Ghodke et al. [26] LES Mishra and Sridhar [57] RANS Wang et al. [91] RANS/LES Yeom et al. [95] RANS Bermejo-Moreno et al. [8] LES

Injection type (Fuel, Location) Cavity geometry (L / D , θ )

Cavity modification

(M, T0) 1.9; 830 1.8; 300, 1000 2.0; 300 2.5; 2250 3.0; 1680 2; 590 2.0; 590 2; 580 1.8, 2.2; o 1100 1.8; 600, 670, 690 2.2; 1100 2; 590 2; 600 2; 600 2.5; 1490 3.5; 2810 2.5, 3.5; 2040, 2980

H2, C3H8; – Kerosene, H2(p); UP/FW(p) C2H4 þ CO2 þH2O; UP H2; UP H2; UP C2H4; RW C2H4; FL/RW C2H4 þ Air; RW C2H4; UP/RW C2H4, CH4 þC2H4; UP C2H4; UP C2H4 þ Air; UP/RW H2 þCH4; UP/RW H2; FL H2; UP/RW H2; UP C2H4 þ CH4; UP/DN

Beveled Front/Rear Wall Beveled Front Wall Tandem Cavities – – – – Direct Air Injection – Tandem Cavities – LE Pylon, Direct Air Injection LE Pylon – – – –

Combustor inlet conditions

4; 30° 3.65, 3.75; 15°, 30° 0.5, 1, 2, 3, 5; 26.6°, 90° 3; 30° 4; 90° 4; 22.5° 4; 90° 4; 22.5° 4; 22.5° 3.88; 22.5° 4; 22.5° 4; 22.5° 2.79; 22.5° 6.67; 90° 7; 45° 3; 90° 4; 22.5°

36

F.W. Barnes, C. Segal / Progress in Aerospace Sciences 76 (2015) 24–41

increasingly confined to the aft portion of the shear layer and cavity volume. It was believed that the flameholding mechanism provided by the hot recirculating combustion products was diminished as they mixed with relatively colder fuel. Gruber et al. [31] used spanwise OH–PLIF to study the effect of combustor backpressure on combustion in a cavity with rear wall fueling. For the low backpressure case (i.e. shock train positioned downstream of cavity) an increase in spanwise non-uniformity was observed as the fuel flow rate was increased. The bulk of the OH signal was confined to the shear layer near the cavity side walls. A region of diminished signal and less vigorous reactions in the center of the recirculation zone was attributed to fuel pooling. With an increase in backpressure placing the shock train above the flameholder, the OH signal was found to be more uniformly distributed and reactions appeared to be occurring in a larger portion of the cavity volume. Allen [1] used OH–PLIF to study the effect of direct air injection from the rear wall on a cavity employing parallel rear wall fueling. For a given fueling rate, increasing the air injection flow rate resulted in increased OH signal intensity throughout the entire cavity but especially in the upstream cavity volume. This was attributed to a dilution of the fuel rich secondary vortex and subsequent improvement in combustion intensity. Beyond a certain optimum air injection flow rate a decrease in combustion intensity was observed. Hsu et al. [39] reported similar findings when examining the effect of direct air injection on rear wallfueled cavity combustion. Additionally, at high fueling rates, spanwise images obtained from OH–PLIF indicated a slightly broader shear layer reaction zone when the rear wall fuel injectors were located closer to the cavity floor than the air injectors. Both numerical simulations (RANS/LES) employing reduced kinetic mechanisms [10,14,26,27,42,48,56,57,8,92,94,95] and experimental studies [63,22,45,39] where in-flow probing (IFP), mass spectrometry (MS), and/or specialized spectroscopic techniques were utilized to obtain information regarding the local distribution of temperature and species, have provided further and in some cases more detailed insight into the structure and dynamics of the reacting cavity flowfield. The general consensus from these studies is that the local flowfield is characterized by a large degree of non-uniformity in both temperature and species concentration, and the distribution of these quantities is highly sensitive to

injector placement as well as changes in fueling rate. Details of these studies are listed in Table 3.

5. Flame stability Flameholding devices in premixed systems are scaled by nondimensional parameters that map the locus of conditions for which flame blowout occurs [64]. The scaling/stability parameters (SP), typically representative of a globally-defined Damköhler number, are formulated based on assumptions regarding the dominant flameholding mechanism. For example, perfectly stirred reactor (PSR) models assume that the flameholder recirculation zone is homogeneous in composition and blowout occurs when the reaction time exceeds the recirculation zone residence time. A common stability parameter used in PSR models is given by [14]

SP =

(15)

where the assumption of ideal gas behavior has been employed, and it is assumed that the chemical time scales as

τc ~

ρ 1 ~ P n ρn − 1(RT )n

(16)

V is the recirculation zone (reactor) volume, ṁ is the net flow rate of reactants, τr is the mean residence time, ρ and T are the mean fluid density and static temperature in the recirculation zone respectively, P is the static pressure; R is the specific gas constant and n is an empirically determined constant. Zukoski and Marble [100] proposed a model where blowout occurs when the contact time between premixed freestream reactants and hot products in the recirculation zone becomes less than the mixture ignition delay time. Citing a large database of previous studies of flameholding in premixed subsonic flows, Ozawa [64] formulated a scaling/stability parameter given by

SP =

1.5 U∞ 1 atm ⎛ 1000 K ⎞ fD ⎜ ⎟ ~ Da−1 D P∞ ⎝ T0∞ ⎠

(17)

where fD is an empirically determined flameholder shape factor and P∞ and T0∞ are the static pressure and stagnation temperature in the freestream, respectively. Moreover, scaling parameters of the general form:

SP ~

Fig. 16. Illustration of a contraction of the stability loop – region of stable flameholding – which may be caused by reduced combustor inlet temperature and pressure, reduced combustor backpressure, and/or with the use of un-heated, liquid, and/or less reactive fuels. Changes in fueling and/or combustor operating conditions that result in the occurrence of one or more of the aforementioned trends will lead to reduced flameholder operability – actualized in terms of reduced lean/rich fueling limits. The minimum combustor inlet temperature is the temperature at which the time scale associated with local reaction kinetics sufficiently exceeds the flameholder residence time forcing the local Damköhler number below unity. Dissociation effects limit the maximum combustor inlet temperature.

ṁ 1 = = Da−1 Vpn τrρn − 1(RT )n

ε U∞ ~ η κ λ L P∞T0∞

Da−1

(18)

where ε, η, κ , and λ are empirical constants, have been successfully used to correlate flame stability limits in gas–turbine dump combustors and afterburners [82,13,14]). On a plot of equivalence ratio, ϕ , versus the scaling/stability parameter, a curve called the ‘stability loop’ separates the region of stable flames from the region in which blowout occurs. Curves of this type have a maximum at stoichiometric conditions – see Fig. 16. For premixed systems, complete or a large degree of reactant homogeneity allows the local stoichiometry to be defined. Hence, quantities such as equivalence ratio, reaction rate, and ignition delay time have some global significance. Yet in the case of systems like supersonic combustors, which face a largely non-premixed combustion environment, significant variations in the stoichiometry can exist and identification of the dominant flameholding mechanism is not straightforward. Globally defined parameters, which mask the effect of local non-uniformities, have been applied to correlate blowout limits in non-premixed systems but with limited success. Strokin and Grachov [81] suggested a scaling parameter for hydrogen combustion in scramjet flows based on an exponential

F.W. Barnes, C. Segal / Progress in Aerospace Sciences 76 (2015) 24–41

temperature dependence:

( )

dF U∞ dx

SP =

(

1000

P∞exp − 1.12T where

dF dx

0∞

)

~ Da−1 (19)

is the local combustion chamber cross-sectional area

change. Orodnikov et al. [60] formulated a scaling parameter for flameholding in a dual-mode ramjet environment that directly describes a local Damköhler number:

U∞

SP =

(

1000

Pinjexp − T

local

)

~ Da

−1

(20)

where Pinj is the local injection pressure and Tlocal is the local flame temperature measured in the recirculation region. The fuel injection pressure is used in this expression to indicate the dependence of the mixing processes on the local development of fuel jet shear layers. Driscoll and Rasmussen [20] developed a semi-empirical correlation for lean and rich blowout limits of non-premixed flames stabilized by steps, cavities, and struts in high-speed airflows, which provides reasonable agreement with previous experimental data. The correlation assumes that a lifted jet flame with a premixed flame base stabilizes within the shear layer along the stoichiometric contour. Blowout occurs when the flame base is unable to find a location where the fluid velocity matches its propagation speed. This assumption leads to a definition of the local Damköhler number DaNP based on the following semi-empirical expression derived to describe a characteristic chemical timescale for a non-premixed flame τNP :

DaNP = (D/U∞)/τNP

(21)

τNP =

⎤−2⎛ p ⎞−0.6 ⎛ H ⎞ α 0 ⎡ ¯ (TAD − T0∞) fs T ⎟ ⎢A rs−1⎜ ⎟β4−1: for ϕ0 < 1 + 0∞ ⎥ ⎜ 2⎢ ⎝W ⎠ 300 K 2 300 K ⎥⎦ ⎝ 1 atm ⎠ S0 ⎣

(22)

τ NP =

⎫−2⎛ p ⎞−0.6 −1 α 0 ⎧⎡ ¯ (TAD − TF ) T (TF − T0∞) ⎤⎥ ¯ ⎟ ⎨⎢B + C + 0∞ ⎬ ⎜ D¯ : for ϕ0 > 1 300 K 300 K ⎥⎦ 300 K ⎭ ⎝ 1 atm ⎠ S 2 ⎩⎣⎢

(23)

⎪

⎪

⎪

⎪

0

−1 A¯ = ⎡⎣1 + β3(LRZ /H )rs−1ϕ0−1⎤⎦

−1 B¯ = ⎡⎣1 + β1(H /LRZ )rsϕ0⎤⎦ −1 C¯ = fs [1 − B¯ ]

(

D¯ = (LRZ /H ) 1 − C¯

−1

)

ϕ0β2

S0 is the laminar flame speed and α0 is the thermal diffusivity, both evaluated for a stoichiometric mixture at 300 K; TAD is the

37

adiabatic flame temperature; fs is the stoichiometric mixture fraction; TF is the fuel temperature; LRZ is the length of the recirculation zone, equal to L in the case of a cavity; H is the height of the flameholder, equal to D in the case of a cavity; W is the width of the flameholder; ϕ0 is the characteristic equivalence ratio defined as

(

̇

̇

)

ϕ0 = mF /mA rs−1

(24) ̇

where rs is the stoichiometric fuel–air ratio and mA is the characteristic airflow rate given by: ̇

mA = 0.01(ρU )∞HW

(25)

Note the similarity between Eq. (25) and the expression developed by Davis [14] for the cavity-freestream exchange rate, Eq. (13). The factor of 0.01 corresponds to a value of σ ≅ 30. The parameters β1, β2, β3, β4 are empirical constants that are a function of equivalence ratio and injector location. 5.1. Cavity blowout limits A number of laboratory-scale experiments have been performed in order to examine the operability of cavity flameholders in supersonic combustors. Table 4 provides a list of selected experimental studies in which cavity blowout limits were determined. Lean and rich blowout limits are typically obtained by decreasing or increasing fuel flow rates for a given freestream condition until combustion is no longer observed. Inlet air stagnation temperature ramping at fixed fueling rates has also been used to infer flame stability limits. In some cases a downstream throttle (i.e. air injection, mechanical blockage, thermal blockage) is used to hold the position of the shock train fixed, in an attempt to decouple the flameholder from the combustor flowfield for a more systematic flameholder operability investigation. Although it still remains unclear as how to best correlate blowout limits obtained from cavity flameholding experiments, trends in existing data have been identified. In several studies [31,45,46,70] where fuel ramping was employed, blowout limits were presented in terms of fueling rate versus a characteristic airflow rate. The characteristic airflow rate was assumed to scale with the product of the freestream mass flux (ρU )∞ and the cavity opening/exposed flux area (LW ), similar to the forms presented in Eq. (13) and Eq. (25). In each case, for fixed M∞ and T0 lean and rich blowout fuel flow rates increased nearly linearly with characteristic air flow rate, an indication that cavity entrainment scales with characteristic air flow rate. Changes in freestream conditions, cavity geometry, fuel injection location, and fuel type were shown to significantly affect blowout limits. Rasmussen et al. [70] observed lean and rich blowout fuel flow rates to be higher for floor injection than for rear wall fueling. This was attributed to larger quantities of unburned fuel bypassing the

Table 4 Experimental flame stability studies. Reference

Technique

Combustor inlet conditions (M , T0)

Injection type (Fuel, Location)

Cavity geometry (L/D, θ )

Cavity modification

Owens et al. [63] Gruber et al. [31] Allen [1] Rasmussen et al. [70] Lin et al. [45] Lin et al [46] Retaureau [72] Tatman et al. (2013) Vinogradov et al. [90] Donohue [19]

FR FR FR FR FR FR FR TR FR TR

1.8; 300, 1000 2.0; 590 2.0; 580 2.0, 3.0; 590, 640 1.8,2.2; o 1100 1.8, 2.2; o 1100 2.5; 300–750 2; 550–1200 3, 3.5; 2350–3250 2.2, 3.3; o 1200

Kerosene, H2(p); UP/FW(p) C2H4; UP/FL/RW C2H4 þ Air; RW CH4, C2H4; FL/RW C2H4; UP/RW C2H4; UP/RW H2 þCH4 þC2H4; FL C2H4; RW Kerosene; UP C2H4; UP/RW

3.65, 3.75; 15°, 30° 4; 22.5° 4; 22.5° 4; 22.5°, 90° 4; 22.5° 4, 5, 6; 22.5° 2.84, 3.84; 90° 5.25; 22.5° 1.76; 90° 4; 22.5°

Beveled Front Wall – Direct Air Injection – – – – – Parallel, LE Ramps –

38

F.W. Barnes, C. Segal / Progress in Aerospace Sciences 76 (2015) 24–41

recirculation zone and ultimately escaping the cavity in the case of floor injection. It was also observed that blowout limits were affected by changing the cavity closeout angle. For instance, floor injection from a rectangular cavity resulted in lower lean blowout fuel flow rates than the case of a cavity with a slanted rear wall. Changes were likely due to a modification of the shear layer and recirculation zone hence altering local mixing and entrainment. Moreover, the use of methane in place of ethylene led to reduced operability irrespective of permutations in the cavity geometry and freestream conditions. Higher lean blowout and lower rich blowout limits were attributed to methane’s lower reactivity. Retaureau and Menon [73] studied the effect of ethylene–methane and hydrogen–methane fuel blends on cavity blowout limits for the case of transverse floor injection. Cavity operability expanded with the use of more reactive fuel blends. The domain of cavity flameholding was observed to shrink with reduced air stagnation temperature and reduced cavity length. Donohue [19] reported a distinct change in the behavior of blowout limits when injection location was varied between the cavity rear wall and upstream of the cavity leading edge. Blowout limits were plotted in terms of global equivalence ratio versus inlet air stagnation temperature. Stability curves were loosely inferred from the obtained data. For both injection locations the range of stable conditions expanded with increases in combustor inlet temperature, pressure, and combustor backpressure, and/or with the use of heated, gaseous, and/or more reactive fuels, e.g., ethylene vs. JP-7. Fig. 16 illustrates the opposite effect, a contraction of the stability loop with the use of un-heated, liquid, and/or less reactive fuels, and/or with less favorable kinetic conditions in the freestream. An exception to this trend was reported by Owens et al. [63] when studying the combustion of liquid kerosene injected far upstream – in the subsonic portion of the facility nozzle – of a cavity in a Mach 1.8 airflow. It was observed that flame stability decreased with increasing air stagnation temperature. This was attributed to reduction of density in the upstream boundary layer – which was seeded with liquid kerosene – as well as in the cavity recirculation zone leading to excessively rich local mixtures. With upstream fueling Donohue [19] reported that rich blowout limits could not be obtained. Rather, increasingly higher fuel flow rates were required to sustain cavity combustion as the inlet temperature was reduced below the operational limit found for rear wall fueling. This behavior is likely due to reduced entrainment of fuel into the cavity accompanying increased core flow penetration at higher fuel flow rates. Thus in the case of upstream fueling, it is possible that the positions of the stability curve flameholding boundaries are switched, with higher global

equivalence ratios corresponding to leaner local conditions. Tatman et al. (2013) performed a study using rear wall fueling only with similar results to those reported by Donohue [19]. It was also observed that water vapor vitiation at a level of 6.7% had an undetectable impact on flame stability limits, even though the combustion-induced pressure rise was suppressed. It was suggested that the presence of additional amounts of water vapor in the recirculation zone along with that already produced from local reactions, lead to a change in the characteristic chemical time scale that was negligible compared with the mean recirculation zone fluid residence time. Lin et al. [45] examined trends in cavity blowout limits for the case of simultaneous upstream injection and rear wall fueling. Cavity fuel flow rates at rich blowout were reduced compared with the case of pure cavity fueling due to additional fuel entrainment into the recirculation zone. It was also found that cavity fueling rates at rich blowout scaled with upstream injection fueling rates, likely due to a reduction in recirculation zone fuel entrainment corresponding to a deeper penetration of the fuel jets into the core flow. Furthermore, it was reported that cavity fueling rates at rich blowout were reduced when utilizing an alternate set of injectors further upstream of the cavity leading edge. This was attributed to the effective blockage created by the merging of the fuel jets upstream of the cavity leading edge and subsequent reduction of air entrainment into the cavity recirculation zone. Lin et al. [45] also studied the effect of the presence of a shock train on cavity fueling blowout limits. Compared with the baseline case of no shock train, cavity fueling rates at blowout were increased due to additional air entrainment and an enlargement of the recirculation zone. As the shock train was strengthened and pushed further upstream into the isolator, lean blowout limits were observed to occur at progressively lower fuel flow rates. In an additional study, Lin et al. [46] examined the effect of cavity length-to-depth ratio on blowout limits. For the same characteristic airflow rate, Cavity fueling rates at lean blowout were found to increase with length-to-depth ratio, likely due to an increase in recirculation zone volume. 5.2. Unsteady Behavior Increased flame unsteadiness has been observed near lean [1,31,34,47] and rich blowout [84]. Table 5 includes a list of a select number of studies in which unsteady flame behavior was documented and/or analyzed. Gruber et al. [31] used flame emission sensors to examine the dynamic behavior of CH and OH signals for a rear wall-fueled cavity. Discrete low-frequency peaks in the emission spectra were observed at low fuel flow rates. Broadband high frequencies were found to be associated with the highest

Table 5 Studies in which unsteady flame behavior was documented and/or analyzed. Reference

Technique

Combustor inlet conditions (M , T0) Injection type (Fuel, Location) Cavity geometry (L/D, θ ) Cavity modification

Mathur et al. [49] Gruber et al. [31] Choi et al. [10] Allen [1] Gokulakrishnan et al. [27] Micka and Driscoll [54] Micka and Driscoll [54] Lin et al. [47] Fotia and Driscoll [23] Pan et al. [65] Wang et al. [91] Wang et al. [91] Hammack et al. [34] Donohue [19] Tuttle et al. [84]

DI DI RANS/LES PLIF RANS/LES PLIF DI (4 kHz) P.T. SI (1 kHz), P.T. DI, SCH DI, SCH (4 kHz) DI, SCH (4 kHz) PLIF (10 kHz) DI (50 kHz) PIV

1.8, 2.2; 945–1220 2.0; 590 3.0; 600 2.0; 580 2.0; 590 2.2; 1270, 1470 2.2; 1040– 1490 1.8, 2.2; 700–1100 2.2; 1400 2.6; 1300 2.5; 1490 2.5; 1490 2; 610 2.2, 3.3; o 1200 2; 590

C2H4; UP C2H4; RW H2; UP C2H4 þ Air; RW C2H4; FL/RW C2H4 þ H2; UP/RW(p) H2, C2H4 þ H2; C2H4; UP/RW(p) H2; UP/RW(p) Kerosene, H2(p); UP/UP(p) H2; UP/RW H2; UP/RW C2H4; RW C2H4; UP/RW C2H4; RW

4.8; 22° 4; 22.5° 4; 90° 4; 22.5° 4; 90° 4; 90° 4; 90° 4; 22.5° 4; 30° 5, 7; 45° 7; 45° 4, 7; 22.5° 4; 22.5° 4; 22.5° 4; 22.5°

– – – Direct Air Injection – – – – – Parallel, Tandem Cavities – – – – –

F.W. Barnes, C. Segal / Progress in Aerospace Sciences 76 (2015) 24–41

fueling conditions. OH–PLIF images obtained by Allen [1] in a cavity with rear wall fueling revealed fluctuations in the location and size of the reaction zone as fuel flow rates were reduced towards lean blowout. Several researchers [49,65,84,92,19] have reported marked unsteadiness in shear layer-stabilized flames even at conditions away from blowout for both upstream and direct fuel injection. High-speed (50 kHz) video records of flame luminosity obtained by Donohue [19] revealed random side-to-side fluctuations and propagation of the flame upstream of the cavity leading edge along the isolator floor and sidewalls at steady-state fueling conditions. He noted the possible existence of an instability associated with the coupling of these localized ignition and extinction events and shock train movement. Pan et al. [65] reported continuous movement of the combustor shock train during cavity combustion, indicating unsteady flame behavior. Tuttle et al. [84] detected intermittent streamwise oscillations of shear layer-stabilized flames through examination of the statistical variance of the shear layer vorticity distribution obtained from TiO2–PIV. The degree of unsteadiness increased as rich blowout was approached. As mentioned previously, Micka and Driscoll [54,55] observed oscillatory movement of the flame base between the wake of the upstream injected fuel jet and the cavity shear layer for an intermediate range of temperatures between those where combustion was stabilized primarily at one of these two locations. The oscillations were aperiodic and occurred in the range of 5–20 Hz with no distinct dominant frequencies. Fotia and Driscoll [23] correlated this oscillatory flame stabilization behavior with combustor shock train movement. The dominant frequency associated with movement of the reaction base was found to be  5 Hz, and 88° out of phase with respect to movement of the shock train. Using a similar upstream injection configuration, Lin et al. [47] measured combustor oscillation frequencies in the range of 100–400 Hz. The existence of three distinct feedback mechanisms to explain the range of observed frequencies were proposed: a ‘shock-flame acoustic feedback loop’ consisting of upstream propagation of acoustic disturbances from the flame zone through subsonic separated flow regions, interaction of these disturbances with the upstream shock train, and subsequent downstream propagation of acoustic disturbances from the perturbed shock train back to the flame zone; a ‘shock-flame acoustic-convective feedback loop’, similar to the aforementioned mechanism but where upstream shock train perturbations travel back downstream to the flame front at the local flow speed; and an ‘injector-flame feedback loop’ where acoustic disturbances from the flame zone propagate upstream to the fuel injector, causing a shift in the local fuel–air ratio that subsequently travels downstream at the local flow speed and perturbs the flame stoichiometry.











6. Concluding remarks A review of dedicated experimental and numerical studies concerning both the non-reacting and reacting flowfields associated with cavity flameholders embedded in supersonic flows has been presented. The following aspects and trends were highlighted:

 The mechanism of fluid resonant cavity oscillations



○ Hydrodynamic-acoustic feedback loop – shear layer vortex shedding stimulates acoustic radiation at the cavity rear wall in turn driving further vortex shedding. ○ The effect of compressibility – shear layer becomes increasingly stable at higher freestream Mach numbers. The structure and dynamics of the cavity-freestream shear layer ○ The effect of compressibility – severely reduced growth rate and entrainment at higher freestream Mach numbers.



39

○ Fluid mixing – highest degree of mixing in the cavity flowfield occurs in the shear layer. The structure and dynamics of the cavity recirculation zone ○ Primary vortex – strong circulation, responsible for majority of recirculation zone-freestream mass exchange. ○ Secondary vortex – weak circulation ‘dead zone’, is a likely region for ‘fuel pooling’. ○ Fluid mixing – good mixing around periphery of vortices, minimal mass exchange between them. The effect of cavity geometry on the local flowfield ○ Closeout angle – steeper angles enhance shear layer oscillations and cavity-freestream mass exchange. ○ Length – longer cavities allow for additional shear layer growth and entrainment. ○ Depth – deeper cavities lead to longer mean fluid residence times. ○ Length-to-depth ratio – larger values lead to larger primary vortex relative to secondary vortex, which can lead to shorter mean fluid residence times, though this may be offset by increased cavity volume. The effect of fuel injection parameters on local mixing ○ Upstream injection ■ Jet-to-freestream dynamic pressure ratio (fueling rate) – larger values lead to deeper penetration of upstream fuel jet into freestream resulting in leaner cavity recirculation zone, although early merging of fuel jets can reduce air entrainment. ■ Backpressure – shear layer separation can deprive recirculation zone of fuel. ○ Floor injection ■ Fueling rate – higher injection pressures can stimulate shear layer oscillations, growth rate and entrainment, though increasing amounts of fuel may bypass recirculation zone. ■ Backpressure – shear layer separation can deprive recirculation zone of fuel. ○ Parallel injection ■ Results in most uniform distribution of fuel within recirculation zone. ■ Fueling rate – tendency for ‘flooding’ the recirculation zone with fuel. ■ Backpressure – causes a dilution of recirculation zone mixture, although fuel distribution is unaffected. The effect of heat release on the local flowfield ○ Attenuated shear layer growth rate and entrainment, longer mean fluid residence times in cavity when compared with the non-reacting flowfield. The effect of fuel injection parameters and freestream conditions on pilot flame location and spreading ○ Shear layer-stabilized flames – common across all injection configurations, shear layer provides the most stable reaction base location. ○ Jet wake-stabilized flames – can occur in the case of upstream injection, more probable reaction base location at higher inlet air stagnation temperatures, injection pressures, high levels of combustor backpressure, and with the use of more reactive fuels. ○ Recirculation zone-stabilized flames – tend to occur at low fueling rates for floor/parallel injection. ○ Flames spread primarily from the cavity to the wakes of upstream injected fuel jets, wall boundary layers and/or separated flow regions along the periphery of the combustor. The effect of cavity geometry, fuel injection parameters, and freestream conditions on flame blowout ○ Cavity flameholder operability expands with geometric, fueling and/or operational conditions that increase the local

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F.W. Barnes, C. Segal / Progress in Aerospace Sciences 76 (2015) 24–41

Damköhler number or scale inversely with stability parameters of the following form:

⎛ U ε ⎞−1 τ Da ~ r ~ SP −1 ~ ⎜ η κ∞ λ ⎟ τc ⎝ L P∞T0∞ ⎠



○ Cavity blowout limits are sensitive to cavity geometry – primarily controls fluid residence time. ○ Cavity blowout limits are even more sensitive to fuel injection parameters. ■ Injection location, fueling rate have a strong influence on blowout limits. ■ Operability expands with the use of heated, gaseous, and/or more reactive fuels. ○ Cavity blowout limits are sensitive to freestream conditions, operability expands with: ■ Increased inlet air stagnation temperature and pressure. ■ Increased combustor backpressure – dual-mode operation. ● Creation/enlargement of low-speed, kinetically favorable (higher pressure, temperature) separated flow regions. Cavity-stabilized flame unsteadiness due to resonant oscillations and/or localized ignition/extinction events can couple with fuel injection/shock train dynamics potentially triggering combustion instability issues.

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