eﬀect of swirl on combustion dynamics in a lean … institute...eﬀect of swirl on combustion...

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Proceedings of the Combustion Institute 30 (2005) 1775–1782

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CombustionInstitute

Effect of swirl on combustion dynamicsin a lean-premixed swirl-stabilized combustor

Ying Huang*, Vigor Yang

The Pennsylvania State University, University Park, PA 16802, USA

Abstract

The effect of inlet swirl on the flow development and combustion dynamics in a lean-premixed swirl-sta-bilized combustor has been numerically investigated using a large-eddy-simulation (LES) technique alongwith a level-set flamelet library approach. Results indicate that when the inlet swirl number exceeds a crit-ical value, a vortex-breakdown-induced central toroidal recirculation zone is established in the downstreamregion. As the swirl number increases further, the recirculation zone moves upstream and merges with thewake recirculation zone behind the centerbody. Excessive swirl may cause the central recirculating flow topenetrate into the inlet annulus and lead to the occurrence of flame flashback. A higher swirl number tendsto increase the turbulence intensity, and consequently the flame speed. As a result, the flame surface area isreduced. The net heat release, however, remains almost unchanged because of the enhanced flame speed.Transverse acoustic oscillations often prevail under the effects of strong swirling flows, whereas longitudi-nal modes dominate the wave motions in cases with weak swirl. The ensuing effect on the flow/flame inter-actions in the chamber is substantial.� 2004 Published by Elsevier Inc. on behalf of The Combustion Institute.

Keywords: Combustion instabilities; Premixed; Swirl; Large-eddy simulation; Level-set

1. Introduction

Combustion instabilities are commonly en-countered in the development of lean-premixed(LPM) gas-turbine engines [1–4]. The spontane-ous generation of unsteady flow oscillations inthe combustion chamber may cause structuralvibration and excessive heat transfer to the cham-ber, and consequently lead to failure of the sys-tem. Most LPM gas-turbine engines utilizeswirling flows to stabilize the flame for efficientand clean combustion. One of the most impor-tant flow features produced by a swirl injector

1540-7489/$ - see front matter � 2004 Published by Elsevier Idoi:10.1016/j.proci.2004.08.237

* Corresponding author. Fax: +1 814 865 3389.E-mail address: [email protected] (Y. Huang).

is a central toroidal recirculation zone (CTRZ),which serves as a flame stabilization mechanism.Flows in this region are, in general, associatedwith high shear rates and strong turbulence inten-sities resulting from vortex breakdown. Althoughthis type of flows has been extensively studied,there remain many unresolved issues, such asswirl generation, vortex breakdown, axisymmetrybreaking, and azimuthal instability [5–7]. In par-ticular, the effect of flow swirl on combustiondynamics has not been well studied, at least ina quantitative sense. Swirling flows may affectflame dynamics in two aspects. First, large-scale unsteady motions arising from shear-layerinstability and vortex breakdown, as well as pre-cession of vortex core (PVC), may couple reso-nantly with acoustic waves in the combustor,

nc. on behalf of The Combustion Institute.

1776 Y. Huang, V. Yang / Proceedings of the Combustion Institute 30 (2005) 1775–1782

and subsequently cause combustion instabilities.Second, flow swirl may alter the flame structureand combustion intensity, and as a consequenceinfluence the heat-release behavior in a combus-tion chamber. The ensuing effects on the stabilitycharacteristics could be substantial.

Several attempts have been conducted to inves-tigate the effect of swirl on the flow and flamedynamics in combustion systems. Tangirala et al.[8] studied the influence of swirl and heat releaseon the flow structures and flame properties in anon-premixed swirl burner. Their results showedthat mixing and flame stability can be improvedby increasing the swirl number up to approxi-mately unity, beyond which further increase inswirl actually reduced the turbulence level andflame stability. Broda et al. [9] and Seo [10] per-formed an experimental study of combustiondynamics in a lean-premixed swirl-stabilized com-bustor. The dominant acoustic motion corre-sponds to the first longitudinal mode of thechamber. An increase in swirl number tends to de-crease the instability amplitude. Numerical simu-lations based on large-eddy-simulation (LES)techniques have also been performed. Stone andMenon [11,12] investigated a swirl-stabilized com-bustor flow. The impact of varying swirl andequivalence ratio on flame dynamics was studied.Grinstein et al. [13] simulated the flow dynamicsin a swirl combustor with either a single swirleror triple swirlers. Emphasis was placed on the ef-fect of inlet conditions (including swirl number,inlet length, and characteristic velocity) on the un-steady flow dynamics in the combustors. Wanget al. [14] recently examined the vortical flowdynamics in a swirl injector with radial entry.Various flow instability mechanisms, such as theKelvin–Helmholtz, helical, and centrifugal insta-bilities, as well as their mutual interactions, wereinvestigated in detail.

Although much useful information has beenobtained from the preceding studies, the effectsof flow swirl on turbulent flame dynamics andthe way it modifies the flow/flame interactions re-quire further investigation. The purpose of thepresent work was to explore the influence of swirlon the combustion dynamics in a lean-premixedswirl-stabilized combustor using an LES tech-nique, simulating the experimental conditions re-ported in [9,10]. In our previous work [1,2], wehave investigated stable flame evolution, theflame bifurcation phenomenon, and unstableflame dynamics for a fixed inlet swirl numberbut with different inlet flow conditions. In thispaper, the flow and flame dynamics under vari-ous swirl intensities will be addressed. The spe-cific objectives were to: (1) study the effect ofswirl on flow development, acoustic properties,and flame evolution; and (2) investigate the inter-actions between turbulent flame dynamics andflow oscillations.

2. Theoretical formulation and numerical method

The basis of the analysis is the LES techniquepreviously developed for investigating LPM com-bustion instabilities in swirl-stabilized combustors[1,2]. The formulation employs the Favre-filteredconservation equations of mass, momentum, andenergy in three dimensions. The subgrid-scale(SGS) terms are modeled using a compressible-flow version of the Smagorinsky model suggestedby Erlebacher et al. [15]. The damping function ofVan-Driest is used to account for the flow inho-mogeneities near the walls. A level-set flamelet li-brary approach, which has been successfullyapplied to simulate premixed turbulent combus-tion [1,2,16], is used here. In this approach, the fil-tered flame surface evolution is modeled using alevel-set G-equation, where G is defined as adistance function outside the flame front. Ther-mophysical properties are obtained using a pre-sumed probability density function (PDF) alongwith a laminar flamelet library. The model, as cur-rently implemented, does not explicitly considerthe flame stretch effect, which may alter the localflame structure and cause flame extinction. Theseeffects need to be eventually included and will beexplored in subsequent work.

Boundary conditions must be specified to com-plete the formulation. At the inlet boundary, themass flow rate and temperature are specified.The pressure is obtained from a one-dimensionalapproximation to the axial momentum equation,i.e., op/ox = �qou/ot � quou/ox. The mean axi-al-velocity distribution follows the one-seventhpower law by assuming a fully developed turbu-lent pipe flow. The radial and azimuthal velocitiesare determined from the swirler vane angle. Tur-bulence properties at the inlet are specified bysuperimposing broad-band disturbances with anintensity of 15% of the mean quantity onto themean velocity profiles. In addition, the acousticresponse to disturbances arising downstream ismodeled by means of an impedance function[1,16]. At the outlet boundary, the characteristicconditions proposed by Poinsot and Lele [17]are applied, and a time-invariant back pressureis specified as obtained from a simplified one-di-mensional momentum equation op=or ¼ qU 2

h=rin the radial direction, where Uh is the mean azi-muthal velocity. The pressure at r = 0 is fixed asa pre-specified value. Finally, the no-slip adiabaticconditions are enforced along all the solid walls.

The resultant governing equations and bound-ary conditions are numerically solved by means ofa density-based, finite-volume methodology. Thespatial discretization employs a second-order, cen-tral-differencing method in generalized coordi-nates. Fourth-order matrix dissipation alongwith a total-variation-diminishing switch devel-oped by Swanson and Turkel [18], and testedby Oefelein and Yang [19] is included to ensure

Y. Huang, V. Yang / Proceedings of the Combustion Institute 30 (2005) 1775–1782 1777

computational stability and to prevent numericaloscillations in regions with steep gradients. Tem-poral discretization is obtained using a four-stepRunge–Kutta integration scheme. A multi-blockdomain decomposition technique along with staticload balance is used to facilitate the implementa-tion of parallel computation, with a message-pass-ing interface at the domain boundaries. Thetheoretical and numerical framework describedabove has been validated by Huang et al. [1,16],and Apte and Yang [20] against a wide varietyof flow problems to establish its credibility andaccuracy.

3. Physical model and grid resolution

The physical model considered here consists ofa single swirler injector, an axi-symmetric cham-ber, and a chocked nozzle, simulating the experi-mental setup described in [9,10]. Natural gas isinjected radially from the center body throughten holes immediately downstream of the swirlervanes. The fuel/air mixture is assumed to be per-fectly premixed before entering the combustor.The chamber measures 45 mm in diameter and235 mm in length. The baseline condition includesan equivalence ratio of 0.573 and a chamber pres-sure of 0.463 MPa. The mass flow rates of thenatural gas and air are 1.71 and 50.70 g/s, respec-tively. The inlet flow velocity of 86.6 m/s givesrise to a Reynolds number of 35,000 based onthe height of the inlet annulus. The inlet tempera-ture of 660 K corresponds to the case of unstablecombustion reported in [9,10]. Two different swirlangles of 30� and 55� are investigated in the cur-rent study. The corresponding swirl numbers, de-fined as the ratio of the axial flux of the tangentialmomentum to the product of the axial momentumflux and a characteristic radius, are 0.44 and 1.10,respectively.

According to the experimental observations,the dominant acoustic motion in the axial direc-tion corresponds to the first longitudinal mode.Since there exists an acoustic pressure node atthe middle of the chamber, the computational do-main includes both a portion of the inlet annulusdownstream of the swirler vane and the upstreamhalf of the chamber with a time-invariant backpressure specified at the exit plane. To avoid thenumerical singularity along the combustor center-line, a central-square grid system (which consistsof a square grid near the centerline and a cylindri-cal grid in the outer region) is adopted. The entiregrid system has 3.44 million points, which areclustered in the shear layers downstream of thedump plane and near the solid walls to resolvethe steep flow gradients in these regions. The larg-est grid size (around 0.7 mm) falls in the inertialsub-range of the turbulent kinetic energy spec-trum based on the inlet Reynolds number. The

computational domain is divided into 72 blocks.All the calculations are conducted on a distribut-ed-memory parallel computer with each block cal-culated on a single processor.

4. Results and discussion

4.1. Flow evolution

For each swirl number, calculations were per-formed for about four flow-through times (around12 ms) after the flowfield had reached its station-ary state to obtain statistically meaningful datafor analyzing the flow dynamics. Figure 1 showsthe streamline patterns and mean temperaturefields on the x–r plane. Three distinct recirculationzones are observed in the low-swirl number casewith S = 0.44, including a separation wake recir-culation zone (WRZ) behind the centerbody, acorner recirculation zone (CRZ) due to the sud-den enlargement of the combustor configuration,and a central toroidal recirculation zone (CTRZ)resulting from vortex breakdown. The wake recir-culation zone, however, disappears at the highswirl number of S = 1.10. The overall flow devel-opment with respect to the inlet swirl number canbe described as follows. If there is no swirl, onlythe wake and corner reciruclation zones exist. Asthe swirl number increases and exceeds a criticalvalue, vortex breakdown takes place and leadsto the formation of a central recirculation zone.As the swirl number increases further, the centralrecirculation zone moves upstream and mergeswith the wake recirculation zone. Consequently,the corner reciruclation zone becomes diminished.Similar results were reported by Chao [21] in hisexperimental study of the recirculation structurein a co-annular swirl combustor. The mean tem-perature fields clearly exhibit enveloped flames an-chored at the rim of the centerbody and the cornerof the backward-facing step. The flame is muchmore compact for the high swirl number case withS = 1.10, which is due to the enhanced flamespeed resulting from the increased turbulenceintensity, as we will show later.

Figure 2 shows the radial distributions of themean velocity components and turbulent kineticenergy at various axial locations, where r = 0 cor-responds to the centerline of the chamber. Thenegative axial velocities in the central and cornerregions indicate the existence of recirculationzones. The incoming flows from the inlet annulusspread outward from the chamber centerline un-der the effect of the centrifugal force, producingpositive radial velocities in the main flow passage.The stronger the swirl strength is, the faster themain flow moves toward the wall. As a result,the size of the corner recirculation zone is consid-erably reduced at the high swirl number ofS = 1.10. The mean azimuthal velocity fields sug-

Fig. 2. Radial distributions of mean velocity compo-nents and turbulent kinetic energy at various axiallocations for two different swirl numbers.

Fig. 1. Mean temperature fields and streamline patternsfor two different swirl numbers.

Fig. 3. Snapshots of vorticity magnitude field on an x–rplane for two different swirl numbers.


gest that the flow motion in the central regionbears a close resemblance to solid-body rotation.The distributions of the turbulent kinetic energy

indicate that a high turbulence-intensity regiondevelops downstream of the centerbody and thebackward-facing step, where large velocity fluctu-ations are produced because of the strong turbu-lent mixing in the shear layers between theincoming flow and the recirculation flows. Theevolution of turbulent kinetic energy is governedby the following equation:

Dðu2i =2Þ=Dt ¼ oð�ujp=q0 � u2i uj=2þ 2vuieijÞ=oxj� uiujoUi=oxj � 2veijeij;

where eij = (oui/oxj + ouj/oxi)/2. The existence ofthe steep velocity gradient oUi/oxj due to thestrong swirling and reverse flow at the high swirlnumber case facilitates the high production of tur-bulent kinetic energy, �uiujoUi=oxj. Conse-quently, a much stronger turbulent kineticenergy is observed for the high swirl number casewith S = 1.10.

Figure 3 shows snapshots of the vorticity mag-nitude field on an x–r plane. For the low swirlnumber case with S = 0.44, large vortical struc-tures, arising from the shear layers downstreamof the dump plane and centerbody, are convecteddownstream, and then dissipated into small-scaleeddies. The same phenomenon is also observedfor the high swirl number case, in which well-organized vortices are shed from the edge of thebackward-facing step. The vortex motions down-stream of the centerbody, however, become quite

Fig. 4. Snapshots of iso-vorticity surface at x =75,000 s�1 (r > 0.02 m is blanked) for two different swirlnumbers.

Fig. 5. Power spectral densities of pressure fluctuationsimmediately downstream of the dump plane for twodifferent swirl numbers.


disordered due to the presence of the strong cen-tral recirculating flow. In both cases, the vortexshedding frequencies are close to that of the firsttangential mode of acoustic wave in the chamber.

Figure 4 shows snapshots of the iso-vorticitysurface at x = 75,000 s�1. The flowfield in the re-gion r > 2 cm is blanked to provide a clear pictureof the vortex structures. For the low swirl numbercase with S = 0.44, a vortex spiral evolves fromthe shear layer originating at the backward-facingstep due to the Kelvin–Helmholtz instabilities inboth the axial and azimuthal directions. This vor-tical structure gyrates around the centerline andpersists for about several turns before breakingup into small fragments. For the high swirl-num-ber case with S = 1.10, a spiral vortex structurecan also be observed. The structure, however, ismuch more complex, due to the high centrifugalforce. It spreads outward rapidly and soon breaksup into small-scale structures.

4.2. Combustion dynamics

The oscillatory flowfield was carefully surveyedto provide direct insight into the driving mecha-nism for acoustic oscillations. A vast number ofprobes were employed to register the flow motionsin various parts of the chamber. Figure 5 shows

the frequency contents of the pressure fluctuationsimmediately downstream of dump plane. ForS = 0.44, the dominant frequencies of 1761,10,367, and 17,618 Hz correspond to first longitu-dinal (1L), first tangential (1T), and second tan-gential (2T) modes of acoustic motions in thechamber, respectively. For S = 1.10, the longitu-dinal wave disappears, and the frequencies ofthe 1T and 2T modes shift slightly to 10,795 and18,133 Hz due to the change in the temperaturefield. The inlet swirl number exerts little influenceon the acoustic frequencies but plays a significantrole in determining the wave amplitudes. The sup-pression of low-frequency oscillations for the highswirl number case may be attributed to the en-hanced flame stiffness, which reduces flame sensi-tivity to imposed disturbances.

To understand the mutual coupling betweenflame dynamics and flow oscillations, the totalheat release and flame surface area were analyzedin the frequency domain. The overall heat releasein the chamber can be obtained from:

_Q ¼ quDh0f STA;

where qu is the unburned gas density, ST is thesubgrid turbulent flame speed, Dh0f is the heat ofreaction, and A is the total filtered flame surfacearea. The total filtered flame surface area can beobtained from the following integral:

A ¼Z

dð~GðxÞÞjr~GðxÞjdx;

where d is a delta function, which needs to benumerically evaluated. In the level-set flamelet li-brary approach [1,16], ~G represents a signeddistance function with jr~Gj ¼ 1, and ~G ¼ 0 corre-sponds to the filtered flame front. dð~GÞ ¼ 0 almosteverywhere except on the lower dimensional inter-face (i.e., flame surface). For the sake of simplicitywithout significant reduction in accuracy, a first-order accurate smeared out approximation ofthe delta function is usually used [22,23]:

dð~GÞ ¼ ½1þ cosðp~G=eÞ�=2e; j~Gj < e;

0; j~Gj > e;

(

Fig. 8. Time histories of pressure immediately down-stream of the dump plane (top) and flame surface-area(bottom) for S = 0.44. Thick black lines represent theextracted 1L oscillations.

Fig. 6. Power spectral densities of total flame surface-area and heat-release fluctuations for two different swirlnumbers.


where e is a tunable parameter that determines thesize of the bandwidth of numerical smearing. Atypically value is e = 1.5D, with D being the gridwidth. This method has been widely used to eval-uate the quantities defined on arbitrary interfacesin the areas of multi-phase flows, computer vision,and image processing [22,23].

Figure 6 shows the power spectral densities ofthe total filtered flame surface-area and heat-release fluctuations. At S = 0.44, there is a domi-nant mode at 1761 Hz in flame surface oscillation,which corresponds to the 1L acoustic mode of thecombustor. A higher harmonic mode is also foundat 3320 Hz, approximately twice the frequency of1L mode. Although transverse acoustic motionsincluding the 1T and 2T modes are observed,the flame surface-area oscillations do not exhibitsuch a high-frequency behavior. At S = 1.10, asmall peak (11,712 Hz) near the 1T acoustic mode

Fig. 7. Temporal evolution of temperature field on anx–r plane over one cycle of 1L mode of oscillation forS = 0.44.

is observed, but no corresponding 1L mode oscil-lation is found. The behavior of the total heat-release fluctuations in the frequency domain bearsa close resemblance to that of flame surface-areavariations, as shown in Fig. 6. However, a smallspike near the frequency of 20,532 Hz is observedfor S = 0.44, which arises from the fluctuations inthe subgrid turbulent flame speed ST [1,16]. Inlight of the above observations, one can concludethat low-frequency acoustic perturbations exert a

Fig. 9. Temporal evolution of temperature field on anx–r plane over one cycle of 1T mode of oscillation fortwo different swirl numbers.


strong influence on the fluctuations of the totalflame surface-area and heat release. In contrast,high-frequency acoustic oscillations travelthrough the flame zone without significantlyaffecting the flame surface-area and heat-releasevariations. The results agree qualitatively wellwith the predictions from a companion analyticalanalysis of flame response reported in [16]. Thecalculated mean flame surface area and the rootmean square value of fluctuation for the highswirl-number case are much smaller than thoseof the low swirl-number case. However, dueto the increased turbulence intensity and theresultant enhancement of the flame speed for thehigh swirl-number case, the mean heat-releaserate and the associated root mean square valueof the fluctuating quantity are very close in thesetwo cases.

Figure 7 presents the temporal evolution of thetemperature field in the upstream section ofthe chamber on an x–r plane over one cycle ofthe 1L mode of acoustic oscillation at S = 0.44.The phase angle h is referenced to the acousticpressure of the 1L mode at the chamber head-end. The entire process is dictated by the entrain-ment and mixing of the cold flow with hot gases inthe vortical structures in the flame zone. Flamesare contorted and convoluted by these vortexstructures, as observed in Fig. 4, thus revealingthe interactions between the local flow evolutionand flame dynamics.

Figure 8 shows the time histories of pressureimmediately downstream of the dump plane(top) and the total flame surface area (bottom)for the lower swirl number case with S = 0.44.These signals involve a wide range of frequenciescorresponding to turbulent fluctuations andacoustic oscillations. The extracted 1L oscillations(denoted by the thick black lines) of the pressureand flame surface area are also plotted for clarity.The flame surface-area variation can be elucidatedby considering its interaction with the local oscil-latory flowfield. It lags behind the pressure oscilla-tion by 76�. During the period from h = �166�(t = 24.09 ms) to 14� (t = 24.38 ms), a relativelylower pressure field exists near the dump plane.This facilitates the delivery of the fresh reactantsinto the chamber. Intensive heat release then oc-curs after a short fluid mixing and chemical induc-tion time. The resultant flow expansion tends topush the flame outward and cause the flame sur-face area to increase from a trough to a crest. Un-burned mixture fragments may break up awayfrom the main stream and generate local hot spotswhen convected downstream. During the periodof h = 14� (t = 24.38 ms) to 194� (t = 24.66 ms),the relatively higher pressure field near the dumpplane prevents the fresh reactants from travelingdownstream into the chamber. The flame zone isthus reduced and becomes a little more compact.The process then repeats.

Figure 9 presents the temporal evolution ofthe temperature field in the upstream section ofthe chamber on the x–r plane over one cycleof the 1T mode of acoustic oscillation. For bothswirl numbers, new vortices are produced at theedge of the backward-facing step and bulge theflame front. They continue to distort the flameor even produce separated flame pockets whentraveling downstream, although for the highswirl number case this process is less apparentdue to the reduced flame length. This kind offlame/vortex interaction is also observed down-stream of the centerbody for the low swirl num-ber case. As the swirl number increases, the flameanchored by the center recirculating flow maypropagate upstream periodically and lead toflame flashback. Two mechanisms have beenidentified for the occurrence of flame flashback[2]. The first involves flame propagation in theboundary layer along a solid wall where the localvelocity diminishes toward the surface. The sec-ond is associated with flow reversal, which isusually caused by vortical motions or acousticoscillations. In the current case, the flashback isclosely linked to the strong reverse flow in thecenter recirculation zone. The swirl strength isso strong that sometimes it causes the centerrecirculating flow to enter into the inlet annulus.As a result, the flame attached to the centerbodytravels upstream and flashback occurs.

5. Conclusions

The effect of swirl on unsteady flame dynamicsin a lean-premixed, swirl-stabilized combustor un-der unstable operating conditions has been numer-ically investigated in depth. Turbulence closure isachieved by means of a large-eddy-simulationtechnique along with a level-set flamelet library ap-proach. The computed flow pattern and acousticproperties agree well with those experimentally ob-served, although no velocity field measurementsare available for comparison purposes. The swirlstrength has enormous effects on the flow develop-ment and flame dynamics in the combustion cham-ber. When the inlet swirl-number increases, thecentral recirculation zone due to the vortex break-down moves upstream and eventually overridesthe wake recirculation zone. A higher swirl num-ber tends to increase the turbulence intensity andthe flame speed, and consequently shorten theflame length. However, excessive swirl often causesthe central recirculating flow to enter into the inletannulus and leads to the occurrence of flame flash-back. The inlet swirl number exerts little influenceon the frequencies of the acoustic oscillations, butplays a dominant role in determining the ampli-tudes of wave motions. Another important obser-vation is that low-frequency flow oscillationssignificantly affect the global behavior of the flame,


including total surface area and heat-release rate.In contrast, high-frequency flow motions haveonly a limited effect on flame oscillation, althoughthey may impose a significant impact on the localflame properties. Results of this kind provide valu-able information about flow/flame interactions inlean-premixed combustors with swirling flows.

Acknowledgment

The research work reported in this paper wassponsored by the Air Force Office of Scientific Re-search, Grant No. F49620-99-1-0290.

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