Research Article Numerical Investigation on Primary ...downloads.hindawi.com/journals/ijrm/2016/1201497.pdf · Research Article Numerical Investigation on Primary Atomization Mechanism

Research ArticleNumerical Investigation on Primary Atomization Mechanism ofHollow Cone Swirling Sprays

Jia-Wei Ding Guo-Xiu Li Yu-Song Yu and Hong-Meng Li

School of Mechanical Electronic and Control Engineering Beijing Jiaotong University Beijing 100044 China

Correspondence should be addressed to Guo-Xiu Li li guoxiuyahoocom

Received 23 December 2015 Revised 27 March 2016 Accepted 10 April 2016

Academic Editor Sourabh V Apte

Copyright copy 2016 Jia-Wei Ding et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The atomization process of swirling sprays in gas turbine engines has been investigated using a LES-VOF model With fine gridresolution the ligament and droplet formation processes are captured in detail The spray structure of fully developed sprays andthe flow field are observed firstly A central recirculation zone is generated inside the hollow cone section due to the entrainmentof air by the liquid sheet and strong turbulent structures promote the breakup of ligaments At the exit of injector nozzle surfaceinstability occurs due to disturbance factors Axial and transverse mode instabilities produce a net-like structure ligament zoneFinally the generation mechanism of the droplet is analyzed It is found that the breakup mechanism of ligaments is located at theRaleigh capillary region Axial symmetry oscillation occurs due to the surface tension force and the capillary waves pinch off fromthe neck of the ligaments Secondary breakup and coalescence occur at the ldquodroplet zonerdquo resulting in a wider distribution curveat the downstream area

1 Introduction

Liquid atomization is an important process in internal com-bustion engines The quality of spray atomization directlyaffects fuel combustion which consequently determinesengine performance In gas turbine engines pressure swirlinjectors are widely used because of their good atomizationcapability and geometrical simplicity [1] In a pressure swirlinjector liquid is injected through twisty slots thus tan-gential velocity is endued to the fluid in orifice and spraycone emerges due to the centrifugal force The liquid sheetbecomes unstable and breaks up into ligaments and thenligaments break up into droplets and secondary breakupoccurs downstream of the spray The atomization of swirlingjet is a complex process that is affected bymany factors and itsmechanism needs to be understood properly [2]

Over the past several decades a series of theoreticaland experimental investigations have been performed inboth industry and academia for a better understanding ofthe atomization process of swirling jet [3ndash5] Ponstein [6]investigated the growth of disturbance of an annular swirlingliquid sheet based on instability analysis In his research the

viscosity of both phases has been neglected Liao et al [7]developed a theoretical model to predict the performance ofsimplex atomizer based on the study of an inviscid swirlingannular liquid sheet Ibrahim and Jog [8] studied the nonlin-ear instability and breakup of an annular liquid sheet usinga perturbation expansion method the effect of liquid Webernumber initial disturbance and gas swirl strength on thebreakup characteristics is investigated So far the literature ontheoretical investigation was based on many simple assump-tions and it is difficult to predict the sheet breakup accuratelywithout taking into account the complex interaction betweenliquid and gas

Experimentally studies are carried out to predict theatomization characteristics (spray angle liquid film breakuplength and drop size distribution) of swirling spray [9ndash13]Although there have been many investigations on the spraycharacteristics of swirling jet most of them focus on themacroscopic properties of atomization and investigations onliquid film instability and ligament breakup process are stilllacking Also to observe the small and dense region whereligaments and droplets occur high spatiotemporal resolutionof visualization technology is needed So far the entire

Hindawi Publishing CorporationInternational Journal of Rotating MachineryVolume 2016 Article ID 1201497 11 pageshttpdxdoiorg10115520161201497

2 International Journal of Rotating Machinery

breakup mechanism of swirling jet has not been revealed yetby experiment and further investigations are demanded

In recent years with the development of interface captur-ing methods numerical simulations have been carried out topredict the breakup process of liquid jet Menard et al [15]used coupled level setVOFghost methods to investigate theatomization of a liquid jet injected into still gas Desjardinset al [16] applied combined level setVOF method to theprimary breakup of a straight liquid jet De Villiers et al [17]used LES-VOF method to investigate the atomization of around jet influenced by nozzle flow Herrmann et al [18ndash20]discussed the influence of gasliquid density ratio on liquidjet penetration and the primary breakup characteristics usinglevel set method and fine grid Shinjo and Umemura [21 22]performed a detailed numerical simulation of straight liquidjets of diesel fuel As a result they were able to characterizeligament generation and surface instability development onthe liquid jet core influenced by aerodynamics Siamas et al[23] investigated the surface instability and flow field of aswirling annular jet using VOF method but the simulationonly focuses on the region close to the nozzle exit Usinghigh performance computer system and with fine grid res-olution the ligament and droplet formation process can becaptured correctlywhich is hard to be observed in experimentinvestigation allowing a detailed study of liquid atomizationmechanism

In the present study a volume of fluid (VOF) interfacetracking method and a large eddy simulation (LES) modelwere used for computing the atomization process of swirlingsprays The present research mainly focuses on the breakupprocess of liquid film and the droplet formation process Theligament structure and droplet formation mechanism will beidentifiedThe remainder of this paper is organized as followsSection 2 presents the numerical methodology and thesimulation setup procedures Section 3 presents the numer-ical results and discussion Finally Section 4 presents theconcluding remarks

2 Numerical Method

21 Governing Equations In large eddy simulation the sub-grid structures are modelled while the large eddy turbulentstructures are resolved on a computational grid

In the present model the simultaneous flow is treatedas immiscible incompressible continuum fluids with aneffective viscosity and surface tension The continuity andmomentum equations are as follows

120597119906119894

120597119909= 0

120597120588119906119894

120597119905+120597120588 (119906119894119906119895)

120597119909119894

= minus120597119901

120597119909119894

+120597

120597119909119894

(120583120597119906119894

120597119909119895

) minus120597120591119894119895

120597119909119895

+ 119865119904

+ 119866

(1)

where 119906119894and 119906

119895are velocities and the subscript 119894 119895 indicated

the coordinate (119909 119910) indices 120588 is density 119901 is pressure 120583 is

kinetic viscosity 120591119894119895is subgrid scale (SGS) stress 119865

119904is surface

tension and 119866 is the force of gravityThe surface tension force119865

119904is represented as a continuous

surface force model [24]

119865 = int119904(119905)

1205901198961015840997888119899120575 (

997888119909 minus

9978881199091015840

) 119889119878 asymp 120590119896120575119904

997888119899 (2)

where the interface unit normal vector 997888119899 and the curvatureof the interface 120581 are given by

120581 = nabla sdot (

99788811989910038161003816100381610038161003816

99788811989910038161003816100381610038161003816

) (3)

SGS stress can be approximated by the SGS model In thepresent simulation the Smagorinsky model [25] is used andit can be written as

120591119894119895= 2120592119905119878119894119895minus1

3120575119894119895120591119896119896 (4)

where 120592119905

= 119862119904Δ2(2119878119894119895119878119894119895)12 is SGS viscosity 119878

119894119895=

(12)(120597119906119894120597119909119895+ 120597119906119895120597119909119894) is the constant and 119862

119904is the

Smagorinsky model coefficient of 018The liquid volume fraction 120574 represents the indicator

functionwith 120574 = 0 for gas and 120574 = 1 for liquidThe local den-sity and viscosity in a computational cell are given in terms ofthe liquid volume fraction by

120588 = 120574120588119897+ (1 minus 120574) 120588

119892

120583 = 120574120583119897+ (1 minus 120574) 120583

119892

(5)

where subscripts 119897 and 119892 represent the liquid and gas phasesrespectively

The indicator function obeys a transport equation asfollows

120597120574

120597119905+ nabla sdot (119906120574) = 0 (6)

22 VOF Scheme The interface of liquid phase and gas phasecan be computed with interface tracking or interface cap-turing methods For the interface tracking methods such asSLIC [26] PLIC [27] and their variations [28] the interfacesare reconstructed using geometric formulations While forthe interface capturing methods (CICSAM [29] and HRIC[30]) algebraic methods are employed to identify the inter-face locations InHRICmethod the compressive scheme thatis used to avoid the smearing of the interface could lead tointerface stepping problem To remedy this a switching strat-egy that switches between compressive and noncompressivescheme called CICSAMwas proposed by Ubbink [29] In thepresent paper CICSAM is used to capture the interface ofliquid phase and gas phase

CICSAM is implemented in the framework of Open-FOAM [31] as an explicit scheme which uses normalisedvariable diagram (NVD) and switches among different dif-ferencing schemes to furnish a bounded scalar field Suchapproach could create an interface which is as sharp as

International Journal of Rotating Machinery 3

that produced by geometric reconstruction schemes such aspiecewise linear interface

The finite volume discretization of the volume fractionconvection equation based on the integral form is as follows

(120574119905+120575119905

119875minus 120574119905

119875) sdot 119881119875

= minus

119899

sum

119891=1

1

2[(120574119891sdot 119876119891)119905

+ (120574119891sdot 119876119891)119905+120575119905

] 120575119905

(7)

where 119875 indicates the center of control volume 119891 is the cellface centroid and 119876

119891is the the volumetric flux through the

cell faceFor a sufficiently small time step the diversion of 119876

119891on

the cell face is negligible and (7) is reduced to

120574119905+120575119905

119875= 120574119905

119875minus120575119905

119881119875

119899

sum

119891=1

1

2120574lowast

119891sdot 119876119891 (8)

where 120574lowast119891is the new volume fraction distribution described

as

120574lowast

119891= (1 minus 120573

119891)120574119905

119863+ 120574119905+120575119905

119863

2+ 120573119891

120574119905

119860+ 120574119905+120575119905

119860

2 (9)

The weighting factor 120573119891is given by NVD and can be

expressed as

120573119891=

119891minus 119863

1 minus 119863

(10)

Using the boundedness constraint in the upwind controlcell 119880 the normalised variable

119891and 119863are given by

119891=120574119891minus 120574119880

120574119860minus 120574119880

119863=120574119863minus 120574119880

120574119860minus 120574119880

(11)

where119863 119860 and119880 are the donor acceptor and upwind cellsThe cell face values of 120574 are resolved by convection bound-

edness criteria (CBC) The HYPER-C based normalisedvariable is given by

119891CBC =

min119863

119888 1 0 le

119863le 1

119863

119863lt 0

119863gt 1

(12)

The ULTIMATE-QUICKEST-based normalised variableis given by

119891UQ

=

min8119888119863+ (1 + 119888) (6

119863+ 3)

8 119891CBC 0 le

119863le 1

119863

119863lt 0

119863gt 1

(13)

where 119888 is the local value of Courant number at the face

Ubbink [29] introduced the following weighting factor toswitch smoothly between the less compressive differencingscheme and the upper bound of CBC

119891= ]119891119891CBC + (1 minus ]

119891) 119891UQ (14)

Theweighting factor ]119891is based on the cosine of the angle

120579119891between the vector normal to the interface and the vector

119889119891 which connects the centers of the donor and acceptor

cells

119873119891= min120581

119903

cos (2120579119891) + 1

2 1

120579119891= cosminus1

10038161003816100381610038161003816100381610038161003816100381610038161003816

(nabla120574)119863sdot 119889119891

1003816100381610038161003816(nabla120574)1198631003816100381610038161003816 sdot10038161003816100381610038161003816119889119891

10038161003816100381610038161003816

10038161003816100381610038161003816100381610038161003816100381610038161003816

(15)

where 120581119903

ge 0 is a constant introduced to control thedominance of different schemes The recommended value is120581119903= 1

23 Numerical Methodology The employed transient multi-phase solver of OpenFOAM [31] utilizes a cell center-basedfinite volumemethod and provides a comprehensive range ofdiscretization schemes that can be selected for each term inthe equations being solved Crank-Nicholson method withsecond-order accuracy is used for the time discretion ofgoverning equations For general field interpolations a linearform of central differencing scheme is applied Convectivefluxes are discretized with the Gauss linear scheme Pressurevelocity coupling is addressed with the pressure implicit splitoperator (PISO) algorithm

24 Code Validation

241 A 2D Droplet Test To validate the code accuracy incapturing the liquid-gas interface a test case of a 2D drop issimulated similar to Zheng et al [14] In the test case a dropof radius 119886 = 1 is located in a square domain of 64times64 whichis sheared by a gas flow At the top and bottom of the domainthe tangential velocity is prescribed as 119880

0and minus119880

0 The right

and left sides of the domain are set as velocity inlet and outletboundary The velocity of the boundary is given by

119880 =21198800119910

119871 (16)

Figure 1 shows the shape of the droplet at 119905 = 16 andthe circular droplet becomes elliptical due to the shear flowFigure 2 contains the evolution of the half-length of the2D drop The result shows good agreement with the valuecalculated by Zheng et al [14]

242 Experiment of Swirling Spray To validate the accuracyof the LES-VOFmodel in simulating the atomization processof swirling spray a set of experiment results are carried outto compare with the simulation results As shown in Figure 3the experiment system contains a water supply system and


Figure 1 The shape of the drop at 119905 = 16

0 2 4 6 8 10 12 1410

11

12

13

14

15

16

17

Leng

tha

TimeZheng et alSimulation

Figure 2 The droplet half-length for simulation and Zheng et al[14]

Watertank

Injector

Airtank

Pressuretransducer

Solenoid

Light

CCDcamera

PC

Figure 3 Schematic of the experimental system

an optical system The water supply system is composed ofwater tank air tank pressure transducers and solenoid Theoptical system is composed of CCD camera and LED panellight The atomization process and spray angle are measuredusing instantaneous spray images taken by the CCD camera

In the experiment water is used as the stimulant ofliquid fuel and injection pressures are set as 04MPa and08MPa Figure 4 compares the snapshots of experimentsand simulations for the spray Similar spray patterns areobserved for direct image comparison In particular generalcharacteristics of liquid jet such as the spray angle andbreakup length show up good agreement between simulationand experiment

3 Results and Discussion

31 Simulation Setup In the present investigation the inter-nal flow of the injector and the atomization process weresimulated entiretyThe geometry of the pressure swirl hollowcone injector is shown in Figure 1 The injector has twotwisty slots and during the injection process liquid fuel flowsthrough the twisty slot thus tangential velocity is enduedto the fluid in orifice and spray cone emerges due to thecentrifugal force

For the objective stated in the present paper the coldflow conditions are set similar to aviation kerosene injectionThree cases are calculated the injection pressures (Δ119875) are04MPa 06MPa and 08MPa respectively and the ambientpressures are 09MPa The detailed flow conditions are listedin Table 1

Figure 5 also shows the three-dimensional calculationdomain and boundary condition of the present simulationAs shown in Figure 1 the axial extent of external domainis 12mm and the divergence angle of the conical frustumis 70∘ large enough to contain the whole cone spray Theresolution of the finest mesh is 75 120583m small enough tocapture small droplets of 10sim20120583m For the computationalgrid the total number of cells is 15 million and the boundaryconditions include a nonreflective outlet uniform pressureon the cylindrical boundary and no-slip walls For eachcase the computational time is approximately 360 h on a 72-processor computer cluster

32 Spray Structure and Flow Field For a pressure swirlinjector as the liquid injection pressure increases fromzero the spray structure passes through five stages such asldquodribblerdquo ldquodistorted pencilrdquo ldquoonionrdquo and ldquotuliprdquo stages andfully developed spray [1] As shown in Figure 6 the spraysare fully developed at the working injection pressure of 04sim08MPa

For a fully developed swirling spray the pressure differ-ential and the swirl inside the orifice created a liquid filmat the exit of the injector The disturbance at the nozzleand the relative velocity between the liquid and the ambientgas induce K-H instability to the liquid film The surfacewave grows as the liquid film moves away from the injectornozzle and eventually breaks up into several ligamentsTheseligaments are deformed due to the aerodynamic and surfacetension generating droplets Downstream of the spray sec-ondary breakup and coalescence occur and daughter dropletsare generated

As shown schematically in Figure 7 a hollow coneswirling spray can be divided into three zones Zone A is the


Table 1 Flow conditions

Injection pressure119901 (MPa)

Ambient pressure119901 (MPa)

Gas density120588119892(kgm3)

Liquid density120588119897(kgm3)

Liquid viscosity120583119897(Pa s)

Gas viscosity120583119892(Pa s)

Surface tension coefficient120590 (Nm)

04 06 08 09 129 780 08119890 minus 3 179119890 minus 5 0026

56∘ 54∘

(a) Δ119875 = 04MPa

60∘ 59∘

(b) Δ119875 = 08MPa

Figure 4 Comparison of experimental and simulation photography of the spray at 04MPa and 08MPa injection pressure (Δ119875) 01MPaambient pressure and 119905 = 3ms

Inlet

Atmosphere

Figure 5 Geometry of the injector calculation domain and boundary condition

ΔP = 04MPa

(a)

ΔP = 06MPa

(b)

ΔP = 08MPa

(c)

Figure 6 Spray structures of fully developed spray at different injection pressures


Zone A

Zone B

Zone C

Liquid film

Ligament

Droplet(breakup and coalescence)

(a) (b)

Figure 7 Spray profile of a hollow cone swirling spray (a) Simulation (b) experiment

(a) (b)

(c) (d)

Figure 8 Velocity field of a central plane (Δ119875 = 06MPa (a) 119905 = 10ms (b) 119905 = 15ms (c) 119905 = 20ms and (d) 119905 = 30ms)

ldquoliquid film zonerdquowhere surface instability occurs and growsZone B is the ldquoligament zonerdquo where liquid film breaks upand ligaments are generated Zone C is the ldquodroplet zonerdquowhere ligaments break up into droplets Droplet deformationsecondary breakup and coalescence occur in this region

Figure 8 shows the velocity vector field of a central planefor the spray Due to the complex droplet motion and inter-action between gas and liquid strong vortices are generatednear the gas-liquid interface Inside the hollow cone sectiona vortical flow field is generated at downstream locations andthe recirculation zone is generated due to the entrainment ofair by the liquid sheet Strong turbulent structure is created

inside the recirculation zone thus promoting the breakup ofligaments and droplets secondary atomization

Figure 9 shows the axial velocity profile of different timesat center line for the spray at Δ119875 = 06MPa which indicatesthe characteristics of the recirculation zone As shown inFigure 10 two recirculation zones exist in the hollow conespray they are called the geometric recirculation zone and thecentral recirculation zone The geometric recirculation zoneexists near the exit of the injector nozzle which is emergeddue to the bluff body effect of cylindrical liquid sheet For thiscase the length of the geometric recirculation zone is about2D Downstream of the spray cone the central recirculation


minus2 0 2 4 6 8 10 12 14

minus20

minus15

minus10

minus5

0

xD

t = 10mst = 15ms

t = 20mst = 30ms

Ux

(ms

)

Figure 9 Axial velocity profile at center line (Δ119875 = 06MPa)

U

1523

12

8

4

0

Figure 10 Ligament formation from liquid sheet (Δ119875 = 06MPa119905 = 3ms)

zone is generated near the location of 119909119863 = 4 located atthe ldquoligament zonerdquo As time passes the central recirculationzone grows larger and moves downstream The length of thecentral recirculation zone is about 6D which is larger thanthe length of the geometric recirculation zone

33 Ligament Formation The breakup process of swirlingliquid sheet could be described as follows at the exit ofinjector nozzle initial perturbation is generated due to dis-turbance factors such as inner-nozzle turbulence boundarylayer effect and aerodynamic force As shown in Figure 10surface waves can be observed in the axial direction and thetransverse direction as pointed out by dashed lines and solidlines respectively As the wave grows ligaments are createdTwo types of ligaments exist in the spray One is the strip-type ligament created by the transverse instabilityThis type ofligaments spread along the axial direction and capillary wavesare created on the ligament due to surface tension Anothertype is the ring-like ligament created by the axial instabilityThese two types of ligament interweave and net-like structureof ligament zone can be observed

The features of surface waves directly affect the primarybreakup of liquid film and the droplets distribution statusFigure 11 shows the spray structure observed from the front

U

1523

12

8

4

0

Figure 11 The front elevation of spray structure (Δ119875 = 06MPa119905 = 3ms)

elevation from which the droplets distribution status can beobserved Due to the net-like structure of ligament dropletsare dispersed around the circumferential direction

34 Droplet Formation from Ligament In Section 33 wehave indicated that for a swirling jet liquid sheet breaks upinto several ligaments firstly and then droplets pinch off fromligaments The ligaments generated from the liquid sheet aresimilar as several liquid jets with no ldquoinjection nozzlerdquo andthe breakup mechanism of ligaments is approximate to thebreakup of a liquid jet As the velocity of liquid jet increasesfour regimes of breakup mechanism can be distinguished ona plot of Re versus Oh They are Rayleigh capillary regionfirst wind-induced region second wind-induced region andatomization region [32] The local Reynoldrsquos number andlocal Ohnesorge number are defined by

Oh =120583119897

(120588119897119886120590)12

Re =120588119897119886119906

120583119897

(17)

The plot of ligament local Re and Oh for the cases of thepresent study is shown in Figure 12 In the present study theRenumber of ligaments is scattered in a range of 600sim800 andthe Oh number of ligaments is scattered in a range of 001sim002 As shown in Figure 13 the four regions are separatedby lines The points in the present study are located at theRayleigh capillary region

Strutt and Rayleigh [33] introduced the mechanism ofbreakup of a low speed cylindrical liquid jet (ligament)For unstable cylindrical ligaments axisymmetric oscillationoccurs and grows due to the surface tension force and liga-ments break up into dispersed droplets eventually According


620 640 660 680 700 720 740 760 780

0012

0013

0014

0015

0016

0017

0018

Oh

Re

ΔP = 04MPaΔP = 06MPaΔP = 08MPa

Figure 12 Ligament local Re and Oh for cases in the present study

1 10 100 1000 10000 100000

001

01

1

10

Rayleigh mechanism

Atomization

Oh

Re

Second wind induced

First wind induced

1E minus 3

Figure 13 Four regimes of breakup mechanism in dependence on local Re number and Oh number

to the Rayleigh theory the ideal diameter of resultant dropletis estimated as

119863 = 189119889 (18)

Figure 14(a) shows the ideal model of Rayleigh breakupthe ligament is expected to break up into droplets of samediameter with even space Figure 14(b) shows the ligamentbreakup example of numerical simulation The wavelengthof capillary wave is about 40sim43 times the diameter of theligament The capillary waves pinch off from the neck of theligament and spherical droplets are formed due to the surfacetension force The diameter of droplet is about 17sim20 timesthe ligament diameter which shows a similar tendency to theideal model But the actual flow field is complex the dropletgeneration process is more random and the droplet diameterdistribution range is wider than the ideal model

Figure 15 shows the temporal droplet formation process(Δ119875 = 06MPa) The breakup of ligament is much more

complex than the ideal model of Rayleigh theory At theprimary breakup zone ligaments break up into numerousirregularly shaped droplets After the primary breakup sec-ondary breakup and coalescence occur downstream of thespray As pointed out by the blue arrow in Figure 15 smalldroplets generated by primary breakup collide due to theirvelocity difference Larger droplet is formed after the collisionand its shape becomes spheroid under the effects of surfacetension Another important behavior of primary breakupdroplets is secondary breakup As shown in Figure 15 pointedout by the red arrow the large ligament generated by primarybreakup becomes deformeddue to the aerodynamic force theneck becomes thinner and is pinched off by surface tensionand smaller droplets are generated

The secondary breakup and coalescence directly affectthe distribution characteristic of droplets Figure 16 showsthe droplet size distribution at different axial location (Δ119875 =06MPa) At the primary breakup zone (Figure 16(a)) most


d

189d

(a)

d

120582

(b)

Figure 14 Rayleigh mode of ligament breakup (a) ideal model (b) ligament breakup example of numerical simulation

(a) 119905 = 210ms (b) 119905 = 211ms (c) 119905 = 212ms

(d) 119905 = 213ms (e) 119905 = 214ms (f) 119905 = 215ms

Figure 15 The temporal droplet formation process (Δ119875 = 06MPa)

of the droplets are generated by the Rayleigh breakup ofligaments and the size of droplets is about 100sim175 120583mand the size distribution of droplets is intensive at thisregion At the downstream location secondary breakup andcoalescence create larger and smaller droplets resulting in awider distribution curve as the axial direction increase

4 Conclusions

In the present study a LES-VOFmodel is used for computingthe atomization process of swirling sprays in gas turbine

engines With fine grid resolution the ligament and dropletformation processes are captured in detail The mechanismsof ligament and droplet formation are investigated by analyz-ing the simulation results at various injection pressures Thefindings are summarized as follows

The hollow cone swirling spray can be divided into threezones They are the ldquoliquid film zonerdquo the ldquoligament zonerdquoand the ldquodroplet zonerdquo Inside the hollow cone section ofthe ldquoligament zonerdquo a central recirculation zone is generateddue to the entrainment of air by the liquid sheet and strongturbulent structures promote the breakup of ligaments


0 50 100 150 200 250 3000

5

10

15

20

25

30

35

Cou

nt

D (120583m)

(a)

0 50 100 150 200 250 3000

5

10

15

20

25

Cou

nt

D (120583m)

(b)

0 50 100 150 200 250 3000

5

10

15

20

Cou

nt

D (120583m)

(c)

Figure 16 Droplet size distribution at different axial location (Δ119875 = 06MPa) (a) 7mm axial location (b) 9mm axial location and (c) 11mmaxial location

At the exit of injector nozzle surface instability occursdue to disturbance factors such as inner-nozzle turbulenceboundary layer effect and aerodynamic force The featuresof surface waves directly affect the primary breakup of liquidfilm Axial and transverse mode instabilities produce a net-like structure ligament zone

According to the local Re and Oh of ligaments in thepresent study the breakupmechanism of ligaments is locatedat the Raleigh capillary region Axisymmetric oscillationoccurs due to the surface tension force and the capillarywaves pinch off from the neck of the ligamentThe diametersof droplets formed by the primary breakup are about 17sim20 times the ligament diameter Secondary breakup andcoalescence occur at the ldquodroplet zonerdquo resulting in a widerdistribution curve as the axial direction increase

The results presented here can contribute towards a fullunderstanding of the breakup of swirling jet and can behelpful in the design of injector system in gas turbine engines

Competing Interests

The authors declare that they have no competing interests

References

[1] A LefebvreAtomization and Sprays CRC Press New York NYUSA 1988

[2] K Ramamurthi and T J Tharakan ldquoFlow transition in swirledliquid sheetsrdquo AIAA Journal vol 36 no 3 pp 420ndash427 1998

[3] M Sommerfeld and H-H Qiu ldquoDetailed measurements in aswirling particulate two-phase flow by a phase-Doppler anemo-meterrdquo International Journal of Heat and Fluid Flow vol 12 no1 pp 20ndash28 1991

[4] M Vanierschot and E Van den Bulck ldquoHysteresis in flowpatterns in annular swirling jetsrdquo Experimental Thermal andFluid Science vol 31 no 6 pp 513ndash524 2007

[5] E A Ibrahim and T R McKinney ldquoInjection characteristics ofnon-swirling and swirling annular liquid sheetsrdquo Proceedings


of the Institution of Mechanical Engineers Part C Journal ofMechanical Engineering Science vol 220 no 2 pp 203ndash2142006

[6] J Ponstein ldquoInstability of rotating cylindrical jetsrdquo AppliedScientific Research vol 8 no 1 pp 425ndash456 1959

[7] Y LiaoA T Sakman SM JengMA Jog andMA BenjaminldquoA comprehensive model to predict simplex atomizer perform-ancerdquo Journal of Engineering for Gas Turbines and Power vol121 no 2 pp 285ndash294 1999

[8] A A Ibrahim andM A Jog ldquoNonlinear instability of an annu-lar liquid sheet exposed to gas flowrdquo International Journal ofMultiphase Flow vol 34 no 7 pp 647ndash664 2008

[9] K-C Chang M-R Wang W-J Wu and C-H Hong ldquoExper-imental and theoretical study on hollow-cone sprayrdquo Journal ofPropulsion and Power vol 9 no 1 pp 28ndash34 1993

[10] Y Khavkin ldquoAbout swirl atomizer mean droplet sizerdquo Atomiza-tion and Sprays vol 11 no 6 pp 757ndash774 2001

[11] A Tratnig and G Brenn ldquoDrop size spectra in sprays frompressure-swirl atomizersrdquo International Journal of MultiphaseFlow vol 36 no 5 pp 349ndash363 2010

[12] L-J Yang Q-F Fu Y-Y QuW ZhangM-L Du and B-R XuldquoSpray characteristics of gelled propellants in swirl injectorsrdquoFuel vol 97 pp 253ndash261 2012

[13] J Liu XQ ZhangQ L Li andZGWang ldquoEffect of geometricparameters on the spray cone angle in the pressure swirl injec-torrdquo Proceedings of the Institution of Mechanical Engineers PartG Journal of Aerospace Engineering vol 227 no 2 pp 342ndash3532013

[14] X Zheng J Lowengrub A Anderson andV Cristini ldquoAdaptiveunstructured volume remeshingmdashII application to two- andthree-dimensional level-set simulations of multiphase flowrdquoJournal of Computational Physics vol 208 no 2 pp 626ndash6502005

[15] T Menard S Tanguy and A Berlemont ldquoCoupling level setVOFghost fluidmethods validation and application to 3D sim-ulation of the primary break-up of a liquid jetrdquo InternationalJournal of Multiphase Flow vol 33 no 5 pp 510ndash524 2007

[16] O Desjardins V Moureau and H Pitsch ldquoAn accurate con-servative level setghost fluid method for simulating turbulentatomizationrdquo Journal of Computational Physics vol 227 no 18pp 8395ndash8416 2008

[17] E De Villiers A D Gosman and H G Weller ldquoLarge eddysimulation of primary diesel spray atomizationrdquo SAE TechnicalPaper 2004-01-0100 SAE International 2004

[18] M Herrmann ldquoA balanced force refined level set grid methodfor two-phase flows on unstructured flow solver gridsrdquo Journalof Computational Physics vol 227 no 4 pp 2674ndash2706 2008

[19] M Herrmann ldquoDetailed numerical simulations of the primaryatomization of a turbulent liquid jet in crossflowrdquo Journal ofEngineering for Gas Turbines and Power vol 132 no 6 ArticleID 061506 2010

[20] M Herrmann M Arienti and M Soteriou ldquoThe impact ofdensity ratio on the primary atomization of a turbulent liquidjet in crossflowrdquo in Proceedings of the ASME Turbo Expo 2010Power for Land Sea and Air pp 823ndash832 American Society ofMechanical Engineers October 2010

[21] J Shinjo and A Umemura ldquoSimulation of liquid jet primarybreakup dynamics of ligament and droplet formationrdquo Inter-national Journal of Multiphase Flow vol 36 no 7 pp 513ndash5322010

[22] J Shinjo and A Umemura ldquoSurface instability and primaryatomization characteristics of straight liquid jet spraysrdquo Interna-tional Journal of Multiphase Flow vol 37 no 10 pp 1294ndash13042011

[23] G A Siamas X Jiang and L C Wrobel ldquoNumerical investi-gation of a perturbed swirling annular two-phase jetrdquo Interna-tional Journal of Heat and Fluid Flow vol 30 no 3 pp 481ndash4932009

[24] J U Brackbill D B Kothe and C Zemach ldquoA continuummethod formodeling surface tensionrdquo Journal of ComputationalPhysics vol 100 no 2 pp 335ndash354 1992

[25] J C Harris and S T Grilli ldquoA perturbation approach to largeeddy simulation ofwave-induced bottomboundary layer flowsrdquoInternational Journal for Numerical Methods in Fluids vol 68no 12 pp 1574ndash1604 2012

[26] W F Noh and P Woodward ldquoSLIC (Simple Line Interface Cal-culation)rdquo in Proceedings of the Fifth International Conferenceon Numerical Methods in Fluid Dynamics June 28ndashJuly 2 1976Twente University Enschede vol 59 of Lecture Notes in Physicspp 330ndash340 Springer Berlin Germany 1976

[27] D L Youngs ldquoAn interface tracking method for a 3D Eulerianhydrodynamics coderdquo Tech Rep AWRE449235 AtomicWeapons Research Establishment 1987

[28] Y Renardy and M Renardy ldquoPROST a parabolic reconstruc-tion of surface tension for the volume-of-fluid methodrdquo Journalof Computational Physics vol 183 no 2 pp 400ndash421 2002

[29] O Ubbink Numerical Prediction of Two Fluid Systems withSharp Interfaces University of London 1997

[30] S Muzaferija and M Peric ldquoComputation of free-surface flowsusing interface-tracking and interface-capturing methodsrdquo inNonlinear Water Wave Interaction O Mahrenholtz and MMarkiewicz Eds pp 59ndash100 Computational Mechanics Pub-lications Southampton UK 1998

[31] OpenCFD Ltd OpenFoam-16 Documentation The OpenSource CFD Toolbox OpenCFD Ltd 2009

[32] WA Sirignano andCMehring ldquoReviewof theory of distortionand disintegration of liquid streamsrdquo Progress in Energy andCombustion Science vol 26 no 4 pp 609ndash655 2000

[33] J W Strutt and L Rayleigh ldquoOn the instability of jetsrdquo Pro-ceedings London Mathematical Society vol 10 no 1 pp 4ndash131878

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



breakup mechanism of swirling jet has not been revealed yetby experiment and further investigations are demanded

In recent years with the development of interface captur-ing methods numerical simulations have been carried out topredict the breakup process of liquid jet Menard et al [15]used coupled level setVOFghost methods to investigate theatomization of a liquid jet injected into still gas Desjardinset al [16] applied combined level setVOF method to theprimary breakup of a straight liquid jet De Villiers et al [17]used LES-VOF method to investigate the atomization of around jet influenced by nozzle flow Herrmann et al [18ndash20]discussed the influence of gasliquid density ratio on liquidjet penetration and the primary breakup characteristics usinglevel set method and fine grid Shinjo and Umemura [21 22]performed a detailed numerical simulation of straight liquidjets of diesel fuel As a result they were able to characterizeligament generation and surface instability development onthe liquid jet core influenced by aerodynamics Siamas et al[23] investigated the surface instability and flow field of aswirling annular jet using VOF method but the simulationonly focuses on the region close to the nozzle exit Usinghigh performance computer system and with fine grid res-olution the ligament and droplet formation process can becaptured correctlywhich is hard to be observed in experimentinvestigation allowing a detailed study of liquid atomizationmechanism

In the present study a volume of fluid (VOF) interfacetracking method and a large eddy simulation (LES) modelwere used for computing the atomization process of swirlingsprays The present research mainly focuses on the breakupprocess of liquid film and the droplet formation process Theligament structure and droplet formation mechanism will beidentifiedThe remainder of this paper is organized as followsSection 2 presents the numerical methodology and thesimulation setup procedures Section 3 presents the numer-ical results and discussion Finally Section 4 presents theconcluding remarks

2 Numerical Method

21 Governing Equations In large eddy simulation the sub-grid structures are modelled while the large eddy turbulentstructures are resolved on a computational grid

In the present model the simultaneous flow is treatedas immiscible incompressible continuum fluids with aneffective viscosity and surface tension The continuity andmomentum equations are as follows

120597119906119894

120597119909= 0

120597120588119906119894

120597119905+120597120588 (119906119894119906119895)

120597119909119894

= minus120597119901

120597119909119894

+120597

120597119909119894

(120583120597119906119894

120597119909119895

) minus120597120591119894119895

120597119909119895

+ 119865119904

+ 119866

(1)

where 119906119894and 119906

119895are velocities and the subscript 119894 119895 indicated

the coordinate (119909 119910) indices 120588 is density 119901 is pressure 120583 is

kinetic viscosity 120591119894119895is subgrid scale (SGS) stress 119865

119904is surface

tension and 119866 is the force of gravityThe surface tension force119865

119904is represented as a continuous

surface force model [24]

119865 = int119904(119905)

1205901198961015840997888119899120575 (

997888119909 minus

9978881199091015840

) 119889119878 asymp 120590119896120575119904

997888119899 (2)

where the interface unit normal vector 997888119899 and the curvatureof the interface 120581 are given by

120581 = nabla sdot (

99788811989910038161003816100381610038161003816

99788811989910038161003816100381610038161003816

) (3)

SGS stress can be approximated by the SGS model In thepresent simulation the Smagorinsky model [25] is used andit can be written as

120591119894119895= 2120592119905119878119894119895minus1

3120575119894119895120591119896119896 (4)

where 120592119905

= 119862119904Δ2(2119878119894119895119878119894119895)12 is SGS viscosity 119878

119894119895=

(12)(120597119906119894120597119909119895+ 120597119906119895120597119909119894) is the constant and 119862

119904is the

Smagorinsky model coefficient of 018The liquid volume fraction 120574 represents the indicator

functionwith 120574 = 0 for gas and 120574 = 1 for liquidThe local den-sity and viscosity in a computational cell are given in terms ofthe liquid volume fraction by

120588 = 120574120588119897+ (1 minus 120574) 120588

119892

120583 = 120574120583119897+ (1 minus 120574) 120583

119892

(5)

where subscripts 119897 and 119892 represent the liquid and gas phasesrespectively

The indicator function obeys a transport equation asfollows

120597120574

120597119905+ nabla sdot (119906120574) = 0 (6)

22 VOF Scheme The interface of liquid phase and gas phasecan be computed with interface tracking or interface cap-turing methods For the interface tracking methods such asSLIC [26] PLIC [27] and their variations [28] the interfacesare reconstructed using geometric formulations While forthe interface capturing methods (CICSAM [29] and HRIC[30]) algebraic methods are employed to identify the inter-face locations InHRICmethod the compressive scheme thatis used to avoid the smearing of the interface could lead tointerface stepping problem To remedy this a switching strat-egy that switches between compressive and noncompressivescheme called CICSAMwas proposed by Ubbink [29] In thepresent paper CICSAM is used to capture the interface ofliquid phase and gas phase

CICSAM is implemented in the framework of Open-FOAM [31] as an explicit scheme which uses normalisedvariable diagram (NVD) and switches among different dif-ferencing schemes to furnish a bounded scalar field Suchapproach could create an interface which is as sharp as




(120574119905+120575119905

119875minus 120574119905

119875) sdot 119881119875

= minus

119899

sum

119891=1

1

2[(120574119891sdot 119876119891)119905

+ (120574119891sdot 119876119891)119905+120575119905

] 120575119905

(7)




119891on


120574119905+120575119905

119875= 120574119905

119875minus120575119905

119881119875

119899

sum

119891=1

1

2120574lowast

119891sdot 119876119891 (8)


as

120574lowast

119891= (1 minus 120573

119891)120574119905

119863+ 120574119905+120575119905

119863

2+ 120573119891

120574119905

119860+ 120574119905+120575119905

119860

2 (9)


expressed as

120573119891=

119891minus 119863

1 minus 119863

(10)



119891=120574119891minus 120574119880

120574119860minus 120574119880

119863=120574119863minus 120574119880

120574119860minus 120574119880

(11)



119891CBC =

min119863

119888 1 0 le

119863le 1

119863

119863lt 0

119863gt 1

(12)


119891UQ

=

min8119888119863+ (1 + 119888) (6

119863+ 3)

8 119891CBC 0 le

119863le 1

119863

119863lt 0

119863gt 1

(13)



119891= ]119891119891CBC + (1 minus ]

119891) 119891UQ (14)




cells

119873119891= min120581

119903

cos (2120579119891) + 1

2 1

120579119891= cosminus1

10038161003816100381610038161003816100381610038161003816100381610038161003816

(nabla120574)119863sdot 119889119891

1003816100381610038161003816(nabla120574)1198631003816100381610038161003816 sdot10038161003816100381610038161003816119889119891

10038161003816100381610038161003816

10038161003816100381610038161003816100381610038161003816100381610038161003816

(15)

where 120581119903



24 Code Validation


0and minus119880

0 The right


119880 =21198800119910

119871 (16)





0 2 4 6 8 10 12 1410

11

12

13

14

15

16

17

Leng

tha



Watertank

Injector

Airtank

Pressuretransducer

Solenoid

Light

CCDcamera

PC




















04 06 08 09 129 780 08119890 minus 3 179119890 minus 5 0026

56∘ 54∘

(a) Δ119875 = 04MPa

60∘ 59∘

(b) Δ119875 = 08MPa


Inlet

Atmosphere


ΔP = 04MPa

(a)

ΔP = 06MPa

(b)

ΔP = 08MPa

(c)



Zone A

Zone B

Zone C

Liquid film

Ligament


(a) (b)


(a) (b)

(c) (d)







minus2 0 2 4 6 8 10 12 14

minus20

minus15

minus10

minus5

0

xD

t = 10mst = 15ms

t = 20mst = 30ms

Ux

(ms

)


U

1523

12

8

4

0





U

1523

12

8

4

0




Oh =120583119897

(120588119897119886120590)12

Re =120588119897119886119906

120583119897

(17)




620 640 660 680 700 720 740 760 780

0012

0013

0014

0015

0016

0017

0018

Oh

Re



1 10 100 1000 10000 100000

001

01

1

10

Rayleigh mechanism

Atomization

Oh

Re

Second wind induced

First wind induced

1E minus 3



119863 = 189119889 (18)






d

189d

(a)

d

120582

(b)


(a) 119905 = 210ms (b) 119905 = 211ms (c) 119905 = 212ms

(d) 119905 = 213ms (e) 119905 = 214ms (f) 119905 = 215ms



4 Conclusions





0 50 100 150 200 250 3000

5

10

15

20

25

30

35

Cou

nt

D (120583m)

(a)

0 50 100 150 200 250 3000

5

10

15

20

25

Cou

nt

D (120583m)

(b)

0 50 100 150 200 250 3000

5

10

15

20

Cou

nt

D (120583m)

(c)





Competing Interests


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












(120574119905+120575119905

119875minus 120574119905

119875) sdot 119881119875

= minus

119899

sum

119891=1

1

2[(120574119891sdot 119876119891)119905

+ (120574119891sdot 119876119891)119905+120575119905

] 120575119905

(7)




119891on


120574119905+120575119905

119875= 120574119905

119875minus120575119905

119881119875

119899

sum

119891=1

1

2120574lowast

119891sdot 119876119891 (8)


as

120574lowast

119891= (1 minus 120573

119891)120574119905

119863+ 120574119905+120575119905

119863

2+ 120573119891

120574119905

119860+ 120574119905+120575119905

119860

2 (9)


expressed as

120573119891=

119891minus 119863

1 minus 119863

(10)



119891=120574119891minus 120574119880

120574119860minus 120574119880

119863=120574119863minus 120574119880

120574119860minus 120574119880

(11)



119891CBC =

min119863

119888 1 0 le

119863le 1

119863

119863lt 0

119863gt 1

(12)


119891UQ

=

min8119888119863+ (1 + 119888) (6

119863+ 3)

8 119891CBC 0 le

119863le 1

119863

119863lt 0

119863gt 1

(13)



119891= ]119891119891CBC + (1 minus ]

119891) 119891UQ (14)




cells

119873119891= min120581

119903

cos (2120579119891) + 1

2 1

120579119891= cosminus1

10038161003816100381610038161003816100381610038161003816100381610038161003816

(nabla120574)119863sdot 119889119891

1003816100381610038161003816(nabla120574)1198631003816100381610038161003816 sdot10038161003816100381610038161003816119889119891

10038161003816100381610038161003816

10038161003816100381610038161003816100381610038161003816100381610038161003816

(15)

where 120581119903



24 Code Validation


0and minus119880

0 The right


119880 =21198800119910

119871 (16)





0 2 4 6 8 10 12 1410

11

12

13

14

15

16

17

Leng

tha



Watertank

Injector

Airtank

Pressuretransducer

Solenoid

Light

CCDcamera

PC




















04 06 08 09 129 780 08119890 minus 3 179119890 minus 5 0026

56∘ 54∘

(a) Δ119875 = 04MPa

60∘ 59∘

(b) Δ119875 = 08MPa


Inlet

Atmosphere


ΔP = 04MPa

(a)

ΔP = 06MPa

(b)

ΔP = 08MPa

(c)



Zone A

Zone B

Zone C

Liquid film

Ligament


(a) (b)


(a) (b)

(c) (d)







minus2 0 2 4 6 8 10 12 14

minus20

minus15

minus10

minus5

0

xD

t = 10mst = 15ms

t = 20mst = 30ms

Ux

(ms

)


U

1523

12

8

4

0





U

1523

12

8

4

0




Oh =120583119897

(120588119897119886120590)12

Re =120588119897119886119906

120583119897

(17)




620 640 660 680 700 720 740 760 780

0012

0013

0014

0015

0016

0017

0018

Oh

Re



1 10 100 1000 10000 100000

001

01

1

10

Rayleigh mechanism

Atomization

Oh

Re

Second wind induced

First wind induced

1E minus 3



119863 = 189119889 (18)






d

189d

(a)

d

120582

(b)


(a) 119905 = 210ms (b) 119905 = 211ms (c) 119905 = 212ms

(d) 119905 = 213ms (e) 119905 = 214ms (f) 119905 = 215ms



4 Conclusions





0 50 100 150 200 250 3000

5

10

15

20

25

30

35

Cou

nt

D (120583m)

(a)

0 50 100 150 200 250 3000

5

10

15

20

25

Cou

nt

D (120583m)

(b)

0 50 100 150 200 250 3000

5

10

15

20

Cou

nt

D (120583m)

(c)





Competing Interests


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0 2 4 6 8 10 12 1410

11

12

13

14

15

16

17

Leng

tha



Watertank

Injector

Airtank

Pressuretransducer

Solenoid

Light

CCDcamera

PC




















04 06 08 09 129 780 08119890 minus 3 179119890 minus 5 0026

56∘ 54∘

(a) Δ119875 = 04MPa

60∘ 59∘

(b) Δ119875 = 08MPa


Inlet

Atmosphere


ΔP = 04MPa

(a)

ΔP = 06MPa

(b)

ΔP = 08MPa

(c)



Zone A

Zone B

Zone C

Liquid film

Ligament


(a) (b)


(a) (b)

(c) (d)







minus2 0 2 4 6 8 10 12 14

minus20

minus15

minus10

minus5

0

xD

t = 10mst = 15ms

t = 20mst = 30ms

Ux

(ms

)


U

1523

12

8

4

0





U

1523

12

8

4

0




Oh =120583119897

(120588119897119886120590)12

Re =120588119897119886119906

120583119897

(17)




620 640 660 680 700 720 740 760 780

0012

0013

0014

0015

0016

0017

0018

Oh

Re



1 10 100 1000 10000 100000

001

01

1

10

Rayleigh mechanism

Atomization

Oh

Re

Second wind induced

First wind induced

1E minus 3



119863 = 189119889 (18)






d

189d

(a)

d

120582

(b)


(a) 119905 = 210ms (b) 119905 = 211ms (c) 119905 = 212ms

(d) 119905 = 213ms (e) 119905 = 214ms (f) 119905 = 215ms



4 Conclusions





0 50 100 150 200 250 3000

5

10

15

20

25

30

35

Cou

nt

D (120583m)

(a)

0 50 100 150 200 250 3000

5

10

15

20

25

Cou

nt

D (120583m)

(b)

0 50 100 150 200 250 3000

5

10

15

20

Cou

nt

D (120583m)

(c)





Competing Interests


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















04 06 08 09 129 780 08119890 minus 3 179119890 minus 5 0026

56∘ 54∘

(a) Δ119875 = 04MPa

60∘ 59∘

(b) Δ119875 = 08MPa


Inlet

Atmosphere


ΔP = 04MPa

(a)

ΔP = 06MPa

(b)

ΔP = 08MPa

(c)



Zone A

Zone B

Zone C

Liquid film

Ligament


(a) (b)


(a) (b)

(c) (d)







minus2 0 2 4 6 8 10 12 14

minus20

minus15

minus10

minus5

0

xD

t = 10mst = 15ms

t = 20mst = 30ms

Ux

(ms

)


U

1523

12

8

4

0





U

1523

12

8

4

0




Oh =120583119897

(120588119897119886120590)12

Re =120588119897119886119906

120583119897

(17)




620 640 660 680 700 720 740 760 780

0012

0013

0014

0015

0016

0017

0018

Oh

Re



1 10 100 1000 10000 100000

001

01

1

10

Rayleigh mechanism

Atomization

Oh

Re

Second wind induced

First wind induced

1E minus 3



119863 = 189119889 (18)






d

189d

(a)

d

120582

(b)


(a) 119905 = 210ms (b) 119905 = 211ms (c) 119905 = 212ms

(d) 119905 = 213ms (e) 119905 = 214ms (f) 119905 = 215ms



4 Conclusions





0 50 100 150 200 250 3000

5

10

15

20

25

30

35

Cou

nt

D (120583m)

(a)

0 50 100 150 200 250 3000

5

10

15

20

25

Cou

nt

D (120583m)

(b)

0 50 100 150 200 250 3000

5

10

15

20

Cou

nt

D (120583m)

(c)





Competing Interests


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Zone A

Zone B

Zone C

Liquid film

Ligament


(a) (b)


(a) (b)

(c) (d)







minus2 0 2 4 6 8 10 12 14

minus20

minus15

minus10

minus5

0

xD

t = 10mst = 15ms

t = 20mst = 30ms

Ux

(ms

)


U

1523

12

8

4

0





U

1523

12

8

4

0




Oh =120583119897

(120588119897119886120590)12

Re =120588119897119886119906

120583119897

(17)




620 640 660 680 700 720 740 760 780

0012

0013

0014

0015

0016

0017

0018

Oh

Re



1 10 100 1000 10000 100000

001

01

1

10

Rayleigh mechanism

Atomization

Oh

Re

Second wind induced

First wind induced

1E minus 3



119863 = 189119889 (18)






d

189d

(a)

d

120582

(b)


(a) 119905 = 210ms (b) 119905 = 211ms (c) 119905 = 212ms

(d) 119905 = 213ms (e) 119905 = 214ms (f) 119905 = 215ms



4 Conclusions





0 50 100 150 200 250 3000

5

10

15

20

25

30

35

Cou

nt

D (120583m)

(a)

0 50 100 150 200 250 3000

5

10

15

20

25

Cou

nt

D (120583m)

(b)

0 50 100 150 200 250 3000

5

10

15

20

Cou

nt

D (120583m)

(c)





Competing Interests


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus2 0 2 4 6 8 10 12 14

minus20

minus15

minus10

minus5

0

xD

t = 10mst = 15ms

t = 20mst = 30ms

Ux

(ms

)


U

1523

12

8

4

0





U

1523

12

8

4

0




Oh =120583119897

(120588119897119886120590)12

Re =120588119897119886119906

120583119897

(17)




620 640 660 680 700 720 740 760 780

0012

0013

0014

0015

0016

0017

0018

Oh

Re



1 10 100 1000 10000 100000

001

01

1

10

Rayleigh mechanism

Atomization

Oh

Re

Second wind induced

First wind induced

1E minus 3



119863 = 189119889 (18)






d

189d

(a)

d

120582

(b)


(a) 119905 = 210ms (b) 119905 = 211ms (c) 119905 = 212ms

(d) 119905 = 213ms (e) 119905 = 214ms (f) 119905 = 215ms



4 Conclusions





0 50 100 150 200 250 3000

5

10

15

20

25

30

35

Cou

nt

D (120583m)

(a)

0 50 100 150 200 250 3000

5

10

15

20

25

Cou

nt

D (120583m)

(b)

0 50 100 150 200 250 3000

5

10

15

20

Cou

nt

D (120583m)

(c)





Competing Interests


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










620 640 660 680 700 720 740 760 780

0012

0013

0014

0015

0016

0017

0018

Oh

Re



1 10 100 1000 10000 100000

001

01

1

10

Rayleigh mechanism

Atomization

Oh

Re

Second wind induced

First wind induced

1E minus 3



119863 = 189119889 (18)






d

189d

(a)

d

120582

(b)


(a) 119905 = 210ms (b) 119905 = 211ms (c) 119905 = 212ms

(d) 119905 = 213ms (e) 119905 = 214ms (f) 119905 = 215ms



4 Conclusions





0 50 100 150 200 250 3000

5

10

15

20

25

30

35

Cou

nt

D (120583m)

(a)

0 50 100 150 200 250 3000

5

10

15

20

25

Cou

nt

D (120583m)

(b)

0 50 100 150 200 250 3000

5

10

15

20

Cou

nt

D (120583m)

(c)





Competing Interests


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










d

189d

(a)

d

120582

(b)


(a) 119905 = 210ms (b) 119905 = 211ms (c) 119905 = 212ms

(d) 119905 = 213ms (e) 119905 = 214ms (f) 119905 = 215ms



4 Conclusions





0 50 100 150 200 250 3000

5

10

15

20

25

30

35

Cou

nt

D (120583m)

(a)

0 50 100 150 200 250 3000

5

10

15

20

25

Cou

nt

D (120583m)

(b)

0 50 100 150 200 250 3000

5

10

15

20

Cou

nt

D (120583m)

(c)





Competing Interests


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 50 100 150 200 250 3000

5

10

15

20

25

30

35

Cou

nt

D (120583m)

(a)

0 50 100 150 200 250 3000

5

10

15

20

25

Cou

nt

D (120583m)

(b)

0 50 100 150 200 250 3000

5

10

15

20

Cou

nt

D (120583m)

(c)





Competing Interests


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Numerical Investigation on Primary ...downloads.hindawi.com/journals/ijrm/2016/1201497.pdf · Research Article Numerical Investigation on Primary Atomization Mechanism