ILASS-Americas 25th Annual Conference on Liquid Atomization and Spray Systems, Pittsburgh, PA, May 2013

Effects of Fuel Spray Modeling on the Combustion Dynamicsof Lean Direct Injection Model Combustor

Changjin Yoon, Rohan Gejji, and William E. Anderson∗

Maurice J. Zucrow LaboratoriesPurdue University

West Lafayette, IN 47907 USA

and

Venkateswaran SankaranPropulsion Directorate

Air Force Research LaboratoryEdwards AFB, CA 93524

AbstractThe current study focuses on comprehensive fuel spray modeling and its effects on combustion dynamics ofa lean direct injection mode combustor. The fuel spray was modeled using an Eulerian-Lagrangian approachdescribing the free surface atomizer flow, primary atomization, and secondary atomization. To anchor thefuel spray model, a series of experiments has been conducted on the fuel atomizer with and without co-flowingair for comparison. Spray cone angle, drop-size and velocity distributions were obtained using a high speedcamera and Phase Doppler Anemometry (PDA). The fuel spray model results show reasonable agreementwith the measured spray cone angles. The computed drop size and velocity distribution however indicatesome discrepancies compared with the experimental results suggesting model limitations in describing sec-ondary atomization. In addition, effects of fuel spray modeling on combustion dynamics were studied. Threefuel spray models—specified drop size distribution, single droplet injection and hollow-cone injection—havebeen used. Among the three models, the hollow cone injected fuel spray shows good qualitative comparisonof chamber acoustics with the experimental results. The pressure fluctuation amplitudes from the simulation,however, underestimate the measured amplitudes. Insufficient description of secondary atomization in thespray model appears to be a critical factor that leads to the discrepancies in the fuel spray and combustiondynamics simulations.

∗Corresponding Author: wanderso@purdue.edu

Introduction

Lean Direct Injection (LDI) is a promising de-sign concept for low-emission gas turbine combus-tors. In this concept, the liquid fuel is directly in-jected into the flame zone, and is quickly atomized,mixed, vaporized and reacted with the air withinthe shortest length and time-scales possible. TheLDI-fed combustor is operated under fuel-lean con-ditions to reduce the overall flame temperatures andconsequently to minimize thermal NOx formation.Also, this design inherently precludes the chance ofauto-ignition and flashback, which may appear inadvanced high pressure ratio engines.

The characteristics of the fuel spray is a key fac-tor in LDI engine performance and stability. In theabsence of pre-vaporized fuel and premixing with theincoming air, good atomization of the fuel and rapidand uniform mixing with the air are essential for lowdry NOx emissions and efficient combustion. Localhigh flame temperatures leading to undesirable NOxformation can result if the fuel spray is not uniformlydistributed. Furthermore, the heat addition into thecombustor is directly associated with the fuel spraypattern. If the unsteady heat release is in phase withthe chamber acoustics, combustion instabilities mayarise resulting in potential structural damage of thecombustor components and large amounts of NOxemissions. In fact, the LDI design can be more sus-ceptible to thermoacoustic instabilities. [1] Since theLDI engine is operated at fuel-lean conditions, thechemical kinetics and flame surface are more sen-sitive to disturbances. Consequently, the unsteadyheat release can oscillate and lean blowout can occurif there is a significant level of local equivalence ratiofluctuation due to non-uniform mixing or acousticdisturbances.

The emission and flow characteristics of the LDIcombustor has been characterized experimentally byseveral research groups. Tacina et al. (1990) [2]reported NOx emissions from LDI combustors andreported results similar to lean-premixed gas tur-bine combustors. They also characterized the fuel-air mixing in LDI combustors and compared it to rel-evant pre-atomized spray results. Fu et al. [3] char-acterized non-reacting spray behavior in LDI config-urations using PDA, LDV and 3-D PIV using multi-ple swirler configurations and fuel injector locationsat atmospheric pressure conditions. Both single-element and multiple-element LDI configurationswere tested and drop-size and velocities in the spraywere measured. A strong relationship was observedbetween the spray behavior and the swirl number,Reynolds’ number and injector location in the LDIelement. Besides the multi-phase flow characteris-

tics, several experimental studies have also consid-ered combustion instabilities in LDI-based combus-tors. Santavicca et al. [1] reported self-excited lon-gitudinal mode combustion dynamics in an opticallyaccessible LDI combustor. Half-wave and full-wavelongitudinal mode combustion instabilities were seento be excited in the combustor at pressure ampli-tudes of 5-7% of the mean chamber pressure. Mostof the heat release from the combustion was foundto be in a narrow region downstream of the fuelinjector on account of a stable and compact pre-cessing vortex core. Recent experiments conductedby the Purdue group have also reported longitudi-nal mode combustion instabilities up to 5% of themean chamber pressure using multiple combustorconfigurations and equivalence ratios [4]. These ex-periments provide the configuration studied in thepresent simulation. A brief description of the Pur-due combustor and experiments is provided in a latersection of this paper.

A pressure-swirl atomizer has been used in thecurrent work. Extensive experimental and compu-tational literature exists that has characterized theinternal and external flow through various pressure-swirl atomizer configurations. Jeng et al. [5] stud-ied the liquid sheet emanating from a simplexpressure-swirl atomizer using both computationsand experiments and found good agreement betweenthem. An arbitrary Lagrangian-Eulerian numericalmethod was employed for the computations. Ex-perimental validation was performed using an opti-cally accessible injector and flow visualization wasdone using a CCD camera. Cousin et al. [6] mea-sured drop-sizes in a pressure swirl atomizer usinga Malvern particle-sizer and compared it to resultsusing a theoretical formulation based on the maxi-mization of entropy and reported good agreement.

Computational studies of LDI combustor flowshave been conducted by several groups using La-grangian fuel spray modeling injected from apressure-swirl atomizer. These studies have fo-cused primarily on the flow characteristics of spraycombustion. Patel and Menon [7] employed largeeddy simulations (LES) with an atomizing spray de-scribed by Reitz’s Kelvin-Helmholtz (KH) breakupmodel [8, 9] using single drop injection. The LESresults showed the flow characteristics for atomizingand non-atomizing fuel sprays as well as the pres-ence of precessing vortex core instabilities near theLDI element. Consequently, they concluded that theunsteady flow structures and atomization play a sig-nificant role in distributing the fuel spray uniformlyand widely. Dewanji et al. [10] used the KH breakupmodel for their multipoint LDI combustor simula-

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tions. In their work, injected drops were atomizedas soon as the drop was exposed to the swirling flowand the Sauter Mean Diameter (SMD) of the result-ing broken drops near the LDI element ranged from18 to 22 micron. El-Asrag et al. [11] analyzed com-bustor flows using a flamelet/progress variable ap-proach with Stanford CDP code and reported thatthe recirculation bubble structure in the combustorhead can be altered by the heat release. Further-more, Senoner et al. [12] compared computationalresults from the Stanford CDP and the CERFACSAVBP codes. They specified the fuel injection con-ditions from empirical relations [13] and no atom-ization process was modeled. Their results showedthat both the Eulerian-Lagrangian approach and theEulerian-Eulerian approach can provide reasonablepredictions of the measured axial velocity profiles.

The present study aims to investigate the ef-fects of fuel spray on the combustion dynamics in aLDI model combustor. First, the fuel spray is mod-eled by a comprehensive approach that accounts forthe atomizer internal flow, primary and secondaryatomization. Next, experimental measurements areconducted to characterize the fuel spray and to val-idate and guide the development of the computa-tional fuel spray model. For this purpose, a series ofnon-reacting and atomizing sprays, with and with-out co-flowing air, are studied experimentally andcomputationally. Finally, computations and exper-iments of reacting sprays are used to characterizethermoacoustic instabilities in the LDI gas turbinecombustor.

Fuel Spray Modeling

The fuel spray model in the present study aimsto describe the key physical processes during thespray breakup as shown in Fig. 1. The spray breakupprocess can be simplified into three major mecha-nisms: free surface atomizer flow, primary atom-ization and secondary atomization. In the currentstudy, the free-sureface internal flow is computed in-dependently by an Eulerian Volume-Of-Fluid (VOF)method and its results are utilized to describe theLagrangian spray drop injection. Specifically, theexit flow information from the atomizer flow anal-ysis serves as the initial condition for the spray in-jection using the hollow-cone injection model. Here,the spray drop size is determined by the liquid filmthickness at the orifice exit which is based on theassumption that the liquid film disintegrates intospherical drops. These broken drops can furtherundergo secondary atomization due to strong iner-tial and aerodynamic forces. The drop vaporizationtakes place during the entire process and atomiza-

Gas core

Liquid Free surface

Primary Atomization

Secondary Atomization

Figure 1. Lagrangian phase events during the spraybreakup process

tion can contribute to faster vaporization because ofthe increased total wetted area.

The spray computations reported here exceptfor the atomizer internal flow are carried out withour in-house research code GEMS (General Equa-tion and Mesh Solver) [14]. GEMS solves theEulerian-phase governing equations using a dual-time implicit scheme that is second-order accuratein time and space. Governing equations for theEulerian phase consist of the continuity, momen-tum, energy, turbulence and species conservationequations. Turbulence motions are described bya hybrid RANS/LES method using a length scalemodification based on Wilcox’s k − ω two-equationmodel. [15, 16, 17]. The Lagrangian phase equa-tions are coupled with the Eulerian phase througha source vector. Vaporization is described by theclassical D2-law and, for the chemistry, Westbrook’ssimplified 2-step global reaction for kerosene/air isassumed [18]. Further details are given in Ref. [4].The rest of this section describes the Lagrangianmodeling of the spray breakup process.

Atomizer Internal Flow Model

Separate computations of the free surface inter-nal flow are used to provide the spray injection con-ditions for the fuel spray. The atomizer geometryused in the present study is shown in Fig. 2. Evi-dently, it is too complicated to describe with an an-alytical model. For this reason, Ibrahim and Jog’snumerical model [19] is employed here. This modelis based on a 2D axisymmetric approximation of thegeometry, for which the liquid film thickness, sprayangle and discharge coefficient have been reportedto be within 3 % error compared with experimen-tal measurements. The two-phase flow in the at-

3

text

φ 0.012

100°

Fuel

Swirl Chamber

Swirling Slots

Swirling Slots

0.007"

0.007"

Injector Schematic

Figure 2. Design of the atomizater

Figure 3. Computational grid and boundary con-ditions for atomizer internal flow analysis

omizer is described by the Eulerian VOF methodusing FLUENT. The Reynolds Stress Model (RSM)is used for turbulence closure of the strongly swirlingflow in the atomizer. Boundary conditions are indi-cated along with the computational grid in Fig. 3.

The swirling slots in the atomizer are locatednear a downstream location in the vortex cham-ber just before the converging section, unlike in aconventional simplex atomizer in which the swirlingports are located at the vortex chamber head. Dueto the axisymmetric approximation, the incomingradial and swirl velocity components are written as:

Vr =m

2πDcLs(1)

Injection Plane Origin

Figure 4. Schematic of hollow cone injection model

Vθ =

√(m

ρNAs

)2

− Vr2 (2)

where As and N are the slot area and the numberof slots respectively. In the LDI experiments, theequivalence ratio is controlled by varying the fuelmass flow rate and fixing the air flow rate. For thisreason, the radial and swirl components of velocitiesused for the model inputs can be expressed in termof the equivalence ratio.

Hollow Cone Injection Method

Major parameters taken from the atomizer anal-ysis are the liquid film thickness, velocity vector andspray angle at the atomizer exit plane. Spray dropsize at the injection location is approximated by theliquid film thickness and the spray drop is injectedusing the given velocity components.

The spray produced by pressure swirl atomizeris assumed to be a hollow cone as shown in Fig. 4.The spray cone is defined by the ray origin and an-nular injection plane. The annulus here is defined bythe center of the plane, and inner and outer radius.The spray drops are randomly generated within thegiven injection plane and their velocity vector is de-termined by the orientation angle from the originand angular velocity component. The location wherethe liquid film is disintegrated (see Fig. 4) is em-ployed for the injection plane.

Secondary Atomization Model

Secondary atomization is modeled by Reitz’sbreakup model. [8, 9] According to Patel andMenon’s study, this model exhibits better accuracythan other models in LDI combustor environments.The atomization process in Reitz’s model is based onKelvin-Helmholtz instability and results of the lin-ear stability analysis are directly used for determin-ing the important atomization parameters. For eas-ier use of the linear stability results, the maximum

4

growth rate, Ω, and corresponding wavelength, λ, ofthe Kelvin-Helmholtz instability mode are expressedby curve-fits in terms of nondimensional numbers asfollows:

Ω

[ρla

3

σ

]0.5=

(0.34 + 0.38Weg

2)

(1 + Oh) (1 + 1.4Ta0.6)(3)

Λ

a= 9.02

(1 + 0.45Oh0.5

) (1 + 0.4Ta0.7

)(1 + 0.87Weg1.67)

0.6 (4)

where Weg is the Weber number for the gas phase,

Weg = ρ|U−V|2dσ , Oh is the Ohnesorge number,

Oh = ν1√

ρlσa and Ta is the Taylor parameter,

Ta = Oh√

Weg. The liquid breakup is modeled byadding new child parcels with their size determinedby

r =

B0Λ (B0Λ ≤ a)

min

[ (3πa2 |U−V| /2Ω

)0.33(3a2Λ/4

)0.33 (B0Λ > a)

(5)where B0 is a model constant and set equal to 0.61by Reitz [8]. Simultaneously, the parent drop size isreduced by

da

dt= − (a− r)

τ(6)

where τ is a time constant and determined from

τ = 3.726B1a/ΛΩ (7)

where the model coefficient, B1 is recommended tobe 10 by Reitz [8] and 2 by Patel and Menon. [7]Child parcels are released when the stripped mass re-moved from the parent parcel exceeds a few percentof the average injected parcel mass. Newly formedparcels have a random velocity direction within aconfined cone angle defined by

tan (θ/2) = A1ΛΩ/U (8)

where A1 = 0.188. In addition, while the parentparcel reduces, its mass is preserved by controllingthe drop numbers contained within a parcel, i.e.,Na3 = N0a

30.

Experimental Setup for Spray Characteriza-tion

The pressure swirl atomizer (FN = 1.32) ob-tained from Woodward (Fig. 2) has been used forthe spray characterization tests. Phase DopplerAnemometry (PDA) and high speed videos are usedto characterize drop sizes, velocities, and spray coneangle. For the spray, the fuel flow rate is maintainedat the same values as the spray combustion exper-iments for equivalence ratios of 0.4, 0.5, and 0.6.

Figure 5. Schematic diagram of PDA test arrange-ment

The spray tests are performed at atmospheric pres-sure with and without a co-flow of air around the fuelinjector. The fuel flow rate is measured across a cav-itating venturi (0.025” throat diameter) and verifiedbased on the pressure differential across the injector.For experiments with co-flow of air, the air flow rateis regulated to maintain a ∆P/P of 4% across the in-jector which is similar to the values measured in thespray combustion experiments. The co-flowing airpasses through a swirler and subsonic venturi. Theswirler has six helical axial vanes with a lead angle of60 yielding a swirl number of approximately 0.8. Aschematic diagram of the test arrangement is shownin Fig. 5.

Drop sizes and velocities are recorded with aPDA. The PDA determines the velocity of individ-ual particles based on the frequency shift of lightwhich is reflected or refracted by a moving particle.Drop size is estimated by comparing the phase shiftbetween two detectors at known locations. For theresults reported here, a Dantec Dynamics Dual-PDAsystem was utilized. This system uses an argon-ion laser, beam splitter (514.5 and 488.0 nm wave-lengths), and transmitter (400 mm focal length) tocreate orthogonal measurement volumes for simul-taneous recording of two velocity components. Thereceiver (310 mm focal length) was placed at a scat-tering angle of 45 degrees, resulting in a theoreti-cal maximum detectable drop diameter of 126 µm,as reported by the PDA software (BSA Flow Soft-ware version 4.00.00.42). To capture the local statis-tics, 20,000 individual drops were recorded at eachmeasurement location. Data rates (20-4300 Hz) andspherical validation values (90 - 100 %) varied de-

5

pending upon the operating conditions and measure-ment locations.

High speed visible imaging is used to visual-ize the spray. A high-speed visible camera (VisionResearch Phantom v7) with a 105 mm lens wasmounted perpendicular to the spray axis, and a 150W light source and diffuser plate were positioned be-hind the spray to provide backlighting. The spatialresolution of the visible intensity measurements was167 µm for each pixel at the center of the spray. Thevisible camera integration time (20 µs) and aperturesize (f/22) were selected to optimize the camera sen-sitivity.

For the spray measurements, the uncertaintyin measurement location in the spray was approx-imately ± 1 mm for both axial and radial traverses.The fuel flow rate was measured across a choked ven-turi with a known discharge coefficient. The uncer-tainty in measurement in the flow rate of fuel was atmost 3%. The flow rate of air was set based on pres-sure drop across the pressure swirl atomizer. Thismeasurement was made using a differential pressuregauge with an uncertainty of 0.12 psid (= 827 Pa).

Model Combustor and Experimental Setup

A single element Lean Direct Injection (LDI)combustor developed to characterize combustion dy-namics in a multiphase combustion environment athigh pressure (∼1 MPa) was used in this study.The combustor operates with Jet-A as the fuel andheated air (up to 800 K) air as the oxidizer. Thecombustor is designed in a modular configuration sothat various lengths of the air plenum section andcombustion chamber section can be utilized to tunethe combustor dynamics to different pressure fluctu-ation amplitudes and frequencies. Figure 6 shows aschematic diagram of the combustor.

In the combustor, heated air passes through ahelical vane swirler (60 vane angle) before beingaccelerated into the combustion chamber via a sub-sonic converging diverging venturi. The swirler hassix helical vanes and is fixed to the fuel injector asshown in Fig. 7. The inlet section of the combustionchamber has a thermal barrier coating applied to itto avoid heat loss through the walls and provide anear adiabatic boundary condition. This allows forbetter comparison with computational results wherean adiabatic wall boundary condition is employed.The combustion chamber has a choked exit orificethat sets the chamber pressure in the combustor.Choked inlet and exit orifices on the combustor helpset a closed acoustic boundary condition. Major op-eration and design parameters are summarized inTable 1.

Comprehensive fuel spray modeling and mea-surements

The fuel spray model begins with the atomizerinternal flow analysis as indicated in Fig. 8. Thisanalysis is based on an Eulerian VOF method andis conducted independent of the Lagrangian spraysimulations. The liquid fuel is supplied into the at-omizer through two inlet ports located in the down-stream section of the vortex chamber. A gas core isobserved to exist in the center of the chamber dueto the centrifugal force of the liquid fuel. About onediameter away from the orifice exit, the liquid sheetsdynamically disintegrates into droplets.

Liquid sheet data at the orifice exit plane is in-vestigated to define the spray injection in the La-grangian simulation. The sheet thickness, spray an-gle and velocity are used to describe the initial dropsize, drop injection angle and speed respectively.These variables are investigated in terms of fuel massflow rates within the operating range (Φ = 0.4, 0.5and 0.6). Results are summarized in Table 2.

Spray without co-flowing air

The fuel spray injected by the pressure swirlatomizer is modeled for the condition without co-flowing air at atmospheric pressure. Hollow coneinjection of the spray is assumed for the injectionconditions obtained from Table 2. For example, foran equivalence ratio of 0.6 (mf = 3.41 g/s), an initialdrop size of 78 µm is assumed and the drops are ran-domly distributed in the azimuthal direction. Theseinitial spray drops are injected from the nozzle tip at52.4 m/s with a 32 degree inclined angle measuredfrom the nozzle axis. A snapshot from the simula-tion and the high speed camera image taken fromthe experiment are shown in Fig. 9. The measuredspray cone angles are investigated with respect tothe flow conditions in Table 3. The computationalresults of the spray cone angles are within 6 % of theexperimental results based on image data.

Drop size distribution and axial velocity pro-files from PDA measurements are presented inFigs. 10(a) and 10(b) respectively. The measure-ments were conducted at multiple radial locationsin the spray at three axial planes. The z-direction inthe figures is the axial direction of the spray with theorigin being located at the exit tip of the atomizer.The drop-sizes characterized by the Sauter mean di-ameter (SMD or D32) lie between 20-50 µm. Themaximum drop size is observed in the center at themaximum axial distance, Z = 44.45 mm, and canbe attributed to droplet coalescence. We note thatthe predicted drop sizes are larger than the mea-sured drop sizes. The initial drop size estimated by

6

Heated air inlet from facility

source

Fuel inlet

Air plenumCombustion

chamber

TBC

Exit nozzle (to maintain Pc~150 psia)

Choked air inlet

Swirler- nozzle fuel injection

LCC = 1.08 mLAP = 0.56 m

DCC = 50.8 mm

DAP = 25.4 mm

Figure 6. Schematic diagram of the experimental arrangement of the LDI combustor

Figure 7. Schematic diagram of the fuel-injector-swirler-venturi configuration

Table 1. Summary of design envelope and nominal operation parametersFuel - Jet-A/JP8Oxidizer - AirInlet Air Temperature (K) 750 (nominal)Equivalence Ratio - 0.6 (nominal)Frequency (Hz) 400Inlet Boundary Condition - Constant mass inflowExit Boundary Condition - Choked nozzleDiameter of combustor (mm) 50.8Diameter of air plenum section (mm) 25.4

Table 2. Orifice exit flow conditionsmf (g/s) Φ Vr (m/s) Vθ (m/s) t (µm) θ (deg) |V| (m/s)

2.27 0.4 1.94 30.46 77 66 37.12.84 0.5 2.43 38.07 77 65 44.23.41 0.6 2.91 45.69 78 64 52.4

7

Figure 8. Instantaneous phase contour of atomizer internal flow

Figure 9. Snapshot from the fuel spray simulation (left) and high speed camera image (right) for the spraywithout co-flowing air

8

−30 −20 −10 0 10 20 300

5

10

15

20

Radial Distance (mm)

Axi

al v

eloc

ity (

m/s

)

Z = 6.35 mmZ = 31.75 mmZ = 44.45 mm

(a) SMD results

−30 −20 −10 0 10 20 300

10

20

30

40

50

Radial Distance (mm)

D32

(μm

)

Z = 6.35 mmZ = 31.75 mmZ = 44.45 mm

(b) Axial velocity profiles

Figure 10. Experimental measurements for the spray without co-flowing air

mf (g/s) Φ θ ()2.27 0.4 702.84 0.5 693.41 0.6 68

Table 3. Measured Spray Angles

Ibrahim and Jog’s model is 77 µm. It may be an-ticipated that, if this predicted size is correct, thenthe drops would need to be atomized by secondarybreakup process. However, the secondary atomiza-tion process in the present simulation does not seemto be appropriately described by the K-H instabilitymodel and no secondary atomization is predicted.As shown in Fig. 10(b), axial velocities are observedto be higher as the spray travels further downstreamimplying acceleration of the drops in the spray. Thisacceleration may be associated with a complicatedatomization process that is not predicted by the KHmodel.

Spray with co-flowing air

The fuel spray modeling and experiments arenext shown for the condition with co-flowing air.In the simulation, the spray cone is spirally dis-torted and spins along the injector axis on account ofstrong interaction with the co-flowing air as shownin Fig. 11. This dynamic motion is also observedin the experiment. The high speed camera image istaken right after the venturi end and visualizes thespinning spray cone. The fuel injector tip is locatedapproximately 15 mm upstream of the venturi exit.

Drop size distribution and axial velocity profilesfor the spray with co-flowing air are presented inFigs. 12(a) and 12(b). It is important to note that

the axial slices at which measurements were madeare different than the case with no co-flowing air.This is on account of not being able to access theregion covered by the venturi. The overall level ofdrop size for the spray with co-flowing air is between30-50 µm. The drop-sizes for axial locations 44.75mm and 57.15 mm are quite similar. The drop-sizeimmediately downstream of the nozzle is smallest(∼20 µm). The axial velocity of the co-flowing airmay contribute to reducing the relative velocity be-tween spray drops and gas so that the larger dropsare produced particularly away from the center. Asindicated, larger axial velocities are measured at thenear-nozzle plane, Z = 31.75 mm, in Fig. 12(b). It isalso noteworthy to observe the backflow in the mid-dle at Z = 44.75 and 57.15 mm. The swirl number ofthe jet in this experimental set-up is approximately0.8. For such high swirl numbers, a central toroidalrecirculation zone (CTRZ) is commonly observed onaccount of adverse axial pressure gradients exceed-ing the inertial forces of droplets and leading to flowreversal [3]. Finally, we also note that the computedresults in Fig. 12(b) show axial velocities in the rangeof 10-30 m/s.

Effects of the fuel spray modeling on the com-bustion dynamics

Effects of fuel spray modeling on combustiondynamics are studied by comparing computed andmeasured pressure oscillations. Three distinct fuelspray modeling methods indicated in Table 4 areused. In Case 1, the spray drops are injected usinga log-normal size distribution satisfying a given fuelflow rate. No secondary atomization process is de-scribed in this case. Case 2 assumes large single dropinjection with the drop size being the same as the

9

Figure 11. Snapshot from the fuel spray simulation (left) and high speed camera image (right) for the spraywith co-flowing air

−40 −20 0 20 400

10

20

30

40

50

Radial Distance (mm)

D32

(μm

)

Z = 31.75 mmZ = 44.45 mmZ = 57.15 mm

(a) SMD results

−40 −20 0 20 40−40

−30

−20

−10

0

10

20

30

40

50

Radial Distance (mm)

Axi

al v

eloc

ity (

m/s

)

Z = 31.75 mmZ = 44.45 mmZ = 57.15 mmComputed

(b) Axial velocity profiles

Figure 12. Experimental measurements for the spray with co-flowing air

order of orifice diameter (= 300 µm). For this dropsize, secondary atomization occurs as soon as thedrop is injected into the chamber. Case 3 is the fuelspray modeling method used for the non-reactingspray simulations with and without co-flowing air.It is the most realistic spray model for the pressureswirl atomizer. This fuel spray model uses the initialdrop size and injection velocity from the EulerianVOF calculation as described earlier.

The spray formation and corresponding heat re-lease pattern are visualized in Fig. 13 for the threecases. In all cases, the fuel sprays are almost entirelyconsumed prior to the combustor head region itself.In particular, Cases 1 and 2 indicate complete fuelconsumption before drops reach the combustor head.In Case 3, the spray cone penetrates one chamberradius downstream and shows a spiral surface wavethat is driven by the swirling air. The larger momen-tum of drops in Case 3 seems to lead to the longer

spray penetration. We note that this case also cor-responds to the situation where the KH model doesnot predict secondary atomization which may fur-ther explain why the drops last longer. In additionto the spray penetration, the spray pattern can alsobe characterized distinctly for the three cases. Case1 exhibits more-or-less regularly distributed dropswithin a solid cone. The vaporization process occursover the entire spray cone including the cone axis.Case 2 shows strong secondary atomization processin the venturi diverging section. The spray cone rimis the location where the secondary atomization andthe resulting vaporization seems to occurs. In Case3, few spray drops are located along the cone axisdue to the hollow cone injection. The fuel spray isspirally supplied into the chamber and the vaporiza-tion occurs at the end of spray cone.

The heat release is distributed correspondingto the spray cone formation and drop distribution.

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Label Injection Method D (µm ) |V| (m/s) SecondaryAtomization

Case 1 Log Normal Distributed 1-100 30.0 XDrop Injection

Case 2 Single Drop Injection 200 30.0 OCase 3 Hollow Cone Injection 78 52.4 O

Table 4. Summary of fuel spray modeling in combustion dynamics simulations

(a) Case 1: Log-normal distributed drop injection

(b) Case 2: Single drop injection

(c) Case 3: Hollow cone injection

Figure 13. Instantaneous heat release contours in terms of fuel spray modeling

Strong reaction and heat release occur in the ven-turi diverging section for all cases, but the heat re-lease pattern in the combustor beyond the venturidepends upon the fuel spray model. In Case 1, thereactions take place strongly even in the central zoneof the combustor head. Case 2 shows strong heat re-lease along the spray cone rim and it continues nearthe combustor wall. Case 3 has a more stretchedflame zone than Case 2 and the strong heat releaseseems to follow the pattern of flow separation at thewalls.

Peak-to-peak pressure oscillation amplitudes ofthe combustor wall pressure are investigated for thethree simulation cases and are summarized in Ta-ble 5 along with the measured experimental result.The table also shows the dominant acoustic modein each case. The experiment indicates an ampli-tude that is 5% of the mean pressure which seems

to be within the range that other researchers havereported [1]. The computed pressure amplitudes,on the other hand, are a strong function of the fuelspray model. The log normal drop injection method(Case 1) gives the largest pressure amplitude (11%),the single drop injection method (Case 2) producesa similar level of pressure amplitude (7%) as theexperiment, and the hollow cone injection method(Case 3) indicates a much lower pressure amplitude(0.24%). It is noteworthy that Case 3 predicts thecorrect instability mode compared with the experi-ment (4L).

The power spectrum density (PSD) analysis ofthe wall pressure provides the dominant acousticmodes in each case as shown in Fig. 14. The PSDbased on the experimental results indicates the 4Lmode as the dominant frequency (1425 Hz). We notethat this frequency is lower than the designed 4L

11

Cases Peak-to-Peak Pressure DominantOscillation Amplitude (%) Acoustic Mode

Experiment 5 4LCase 1: Log Normal 11 1LDistributed Drop InjectionCase 2: Single Drop Injection 7 2LCase 3: Hollow cone injection 0.24 4L

Table 5. Summary of pressure oscillations in a longitudinal mode

Frequency (Hz)

PSD

(K

Pa2 /H

z)

0 1000 2000 3000 4000 500010-4

10-2

100

(a) Experiment

Frequency (Hz)

PSD

(K

Pa2 /H

z)

0 1000 2000 3000 4000 5000

10-4

10-2

100

102

(b) Case 1: Log normal distrbuted drop injection

Frequency (Hz)

PSD

(K

Pa2 /H

z)

0 1000 2000 3000 4000 5000

10-4

10-2

100

(c) Case 2: Single drop injection

Frequency (Hz)

PSD

(K

Pa2 /H

z)

0 1000 2000 3000 4000 500010-8

10-6

10-4

10-2

(d) Case 3: Hollow cone injection

Figure 14. PSD results from the experiments and simulations

frequency of 1600 Hz because the combustor dimen-sions were determined based on adiabatic and com-plete combustion. As noted earlier, the dominantacoustic modes are observed to be different for eachcase. The log normal drop injection case (Case 1)predicts a dominant 1L frequency. The single dropinjection case (Case 2) predicts a dominant 2L fre-quency. The hollow-cone case (Case 3) predicts the4L mode which is in agreement with the experimen-tal mode.

Furthermore, it is noteworthy that the broad-frequency-range PSD in Case 3 is also qualitativelysimilar to that of the experimental result as seen inFig. 15, although the peak strengths are very dif-ferent. In addition to the 4L mode at 1425 Hz, theother distinct frequencies observed are 3000, 6000and 9500 Hz. Hydrodynamic instability (or the so-called precessing vortex core instability) drives the3000 and 6000 Hz modes and the tangential acoustic

mode is observed at 9500 Hz.

Discussion

Experimental Uncertainty Factors

The spray from the pressure swirl atomizer wascharacterized using PDA and high speed videos. Allthe measurements were performed at atmosphericpressure and temperature in an unconfined flow.Measurements with an optically accessible polycar-bonate cylindrical section with dimensions similar tothe combustor were attempted. Good quality datacould not be obtained in these measurements on ac-count of fuel film formation on the surface of poly-carbonate section, even with a co-flow of air. ThePDA measurements yielded drop-sizes between 20to 50µm depending on location in the spray and fuelflow rate. The drop-sizes are also dependent on theco-flow of air around the fuel injector. The effect ofthe CTRZ is evident in the drop-sizes and the axialvelocities measured in the spray, especially beyond a

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Frequency (Hz)

PSD

(K

Pa2 /H

z)

0 2000 4000 6000 8000 10000 1200010-4

10-2

100

(a) Experiment

Frequency (Hz)

PSD

(K

Pa2 /H

z)

0 2000 4000 6000 8000 10000 1200010-8

10-6

10-4

10-2

(b) Case 3: Hollow cone injection

Figure 15. Broad range PSD results

distance of approximately 44 mm from the atomizerexit. For the case with a co-flow of air measurementswere only possible at locations 44 mm and furtherdownstream of the atomizer on account of the pres-ence of the subsonic venturi which impeded opticalaccess. The high speed videos of the spray were usedonly for the determination of the spray cone angleand for a qualitative comparison of the overall spraybehavior with computational data. Further studiesshould include optical patternation measurements tocalculate mass flux density of the spray along mul-tiple axial slices.

For the spray measurements, the uncertaintyin measurement location in the spray was approx-imately ±1 mm for both axial and radial traverses.The fuel flow rate was measured across a choked ven-turi of known co-efficient of discharge. The uncer-tainty in measurement in the flow rate of fuel was atmost 3%. The flow rate of air was set based on pres-sure drop across the pressure swirl atomizer. Thismeasurement was made using a differential pressuregauge with an uncertainty of 0.12 psid.

Limitations of KH Breakup Model

Non-reacting spray simulations with and with-out co-flowing air indicated limitations in the pre-diction of drop size distributions. This may be at-tributed to the insufficient representation of the sec-ondary atomization in the Kelvin-Helmholtz insta-bility model. This model is based on the linear sta-bility analysis subject to the velocity difference be-tween liquid and gas. In this respect, the Webernumber is a key factor for the KH breakup. Webernumbers over the spray cone were lower than thecritical Weber number (Wec = 12) for KH breakupbecause of the fine drop size resulting from the pri-mary atomization model. The small drop sizes ofabout 70 µm results in a weak aerodynamic force,which is not enough to drive KH breakup.These re-sults indicate that an alternate breakup model could

be used to describe the secondary atomization fordrop sizes less than 100 µm. The Rayleigh-Taylor(RT) breakup model which is driven by droplet ac-celeration is an ideal candidate for this, particularlygiven the low Weber numbers. Future work will con-sider augmenting the secondary atomization processwith the RT model.

Impacts of the fuel spray modeling on self-excitedcombustion instabilities

According to the results, combustion dynamicsis strongly influenced by the fuel spray modeling. Itcan be analyzed in terms of the frequency and ampli-tude characteristics. First, only the simulation us-ing the hollow cone injection indicated the 4L modedominant acoustic frequency corresponding to theexperimental result. In this case, stronger drop mo-mentum and fine drop sizes are observed, resultingfrom the atomizer internal flow analysis. Moreover,as noted earlier, the KH model does not predict sec-ondary atomization for the fine drop sizes. As a re-sult, the fuel spray cone penetrates deeply into thecombustion chamber, and the flame is distributedalong the combustor wall. Such a fuel spray and heatrelease pattern may be responsible for triggering thehigher acoustic mode since this has a pressure anti-node that is located close to the downstream heatrelease location.

The pressure amplitude from the simulation us-ing hollow cone injection is the most underestimatedresult among all cases, possible due to the insuffi-cient description of the secondary atomization pro-cess. The small acoustic perturbation seen here isdriven by the relatively weak strength of highly dis-tributed heat release pattern. We note that the sec-ondary atomization typically enhances the vaporiza-tion rate by increasing the surface area of the drops.Hence, the absence of significant secondary atomiza-tion seems to result in low vaporization rates whichin turn lead to a distributed and weak heat release

13

and, consequently, to low pressure amplitudes. Asobserved earlier, better secondary atomization mod-eling is needed to obtain more quantitatively accu-rate predictions of the pressure amplitudes.

Conclusion

This study has focused on the fuel spray model-ing and its impact on combustion dynamics. Thefuel spray model is comprehensively described bysub-models for the atomizer internal flow, hollowcone injection and secondary atomization. To vali-date the model and to guide its further development,the fuel spray modeling is exercised for non-reactingspray conditions with and without co-flowing air.Corresponding spray measurements have been per-formed using PDA and high speed image camera.

The spray angle from the simulation resultsagrees with that from the experiment to within 6%error. According to the drop size distributions mea-sured, it is found that Kelvin-Helmholtz model inthe LDI spray does not sufficiently describe the sec-ondary atomization given the fine drop sizes thatare predicted by the primary atomization process.The spray measurements with co-flowing air indicatenegative velocities in the center of chamber whichconfirms the presence of the CTRZ structure.

Three fuel spray models are compared in thecombustion dynamics simulations to investigate theeffects on thermoacoustic instabilities. The mod-els are characterized by the injection methods aslog normal distributed drop, single drop and hol-low cone injection. The fuel spray described by thehollow cone injection is most advanced and realisticchoice. Using the hollow cone injected sprays, the4L mode dominant acoustic frequency is obtainedwhich is in good agreement with the experiment. Onthe other hand, the corresponding pressure ampli-tudes are underestimated. Again, this discrepancymay be attributed to insufficient secondary atomiza-tion and the resultant low vaporization rates. Fu-ture work will concern the addition of the Rayleigh-Taylor breakup model to better describe these phe-nomena.

Acknowledgment

The authors acknowledge the support ofthe NASA Glenn Research Center under NASAResearch Announcement (NRA) grant numberNNX11AI62A, with Program Manager Kimlan Phanand Technical Monitor Kevin Breisacher. Also, wewould like to give special thanks to Drs. CharlesMerkle and Hukam Mongia who set the original di-rection of the study, Dr. Guoping Xia in the UnitedTechnology Research Center for the contribution ofthe initial computational model used in this study,

and Mr. Phil Lee of Woodward for providing the fuelnozzle used in the experiment. The help of Prof. So-jka and Varun Kulkarni with the PDA experimentand overall guidance is also greatly appreciated.

Nomenclaturea parent drop radiusd drop diameterm massr child drop radiust timem mass flow rateA AreaB KH breakup mode constantN NumberP pressureU drop speedV velocity or gas velocityFN Flow numberOh Ohnesorge numberTa Taylor numberWe Weber numberλ wave length at maximum growth rateν viscosityΩ the maximum growth rateΦ Equivalence ratioρ densityσ surface tensionθ inclined angle of drops

Subscriptsf fuelg gasl liquids slotr radialθ tangential0 previous time step

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