ILASS-Americas 30th Annual Conference on Liquid Atomization and Spray Systems, Tempe, AZ, May 2019

Numerical investigation of air bubbles formation and internal flows inflow-blurring atomizers and its impact on liquid breakup

Delin Jiang1, Lulin Jiang2 and Yue Ling1∗1Department of Mechanical Engineering, Baylor University, Waco, Tx 76706 USA

2Department of Mechanical Engineering, University of Louisiana, Lafayette, LA 70504 USA

AbstractFlow-blurring atomization is a novel fuel injection technique and has been shown to generate finer spraysthan conventional airblast atomizers with the same air-to-liquid mass flux ratio. In flow-blurring atomizers,high speed air impinge on the liquid stream through an orifice gap. Under certain geometric and flowconditions, the air stream cuts through the bulk liquid and portion of the air stream penetrate back intothe liquid stream, forming a back-flow region inside the nozzle. Air bubbles formed in the back-flow regionhas been shown to significantly enhance the breakup of bulk liquids downstream of the nozzle exit. Theunderlying mechanisms are not fully understood, since the internal flow inside the nozzle is difficult tomeasure in experiments. In this paper, we aim to use direct numerical simulation to investigate the internalflow structure inside the FB atomizer and to explore its effect on the liquid breakup. We simulate half of theFB nozzle in a 2D domain, assuming symmetric boundary condition. The volume-of-fluid method is used toresolve the gas-liquid interface, and the multiphase flow solver, Basilisk, is used for simulation.

∗Corresponding Author: Stanley Ling@baylor.edu

Introduciton

Atomization is a process to break bulk liquidsinto small droplets. Atomization is critical to fuelinjection in automotive and aerospace engines andagricultural sprays. A desired atomization processshould produce fine sprays with minimum possibleenergy input. A fine spray exhibit a high surface-area-to-volume ratio, which is essential to achievinghigh fuel efficiency and low emission pollution in en-gines.

Ariblast atomizers are widely used in aerospaceengines for fuel injection [1]. In airblast atomiza-tion process, a high speed co-flowing gas flow is em-ployed to assist the breakup of the low speed liq-uid. The shear instability at the gas-liquid interfaceplays the dominant role in destabilizing the liquidand breaks the bulk liquid into sprays [2]. Airblastatomizers perform well for low viscosity fuels. How-ever, when the liquid viscosity increases, experimen-tal works have shown that airblast atomizers pro-duce poor atomized spray [3].

Recently, Ganan-Calvo introduced a novel air-assisted atomization approach which was referred toas flow-blurring (FB) atomization. Flow-blurringatomizers have been shown to be more efficient ingenerating fine sprays than conventional airblast at-omizers [4]. The fundamental difference between theflow-blurring and airblast atomization processes lieat the air flow direction. For airblast, the gas streamis generally parallel to the liquid stream. In contrast,the gas stream is perpendicular to the liquid stream.Further than that in flow-blurring atomization, theair penetrates into the liquid, forming a back flowregion. Air bubbles are formed in the region andthe bursts of these bubbles form small droplets.

It should be reminded that, changing the air flowdirection does not guarantee the formation of backflow region as in typical flow-blurring atomizationprocess. Under different geometric and flow condi-tions, the resulting internal flow structure can beflow-focusing (similar to those used in microfluidics)and flow-blurring. The transition between the twoare still not fully understood. For a cylindrical noz-zle, when the ratio between the gas inlet gap (H)and the liquid inlet diameter (D) is fixed at 0.25,then the formation of the back flow region mainlydepends on the air-to-liquid mass flux ratio (ALR).When ALR is low, liquid flow is stable and no backflow occurs [5]. As ALR is increased, the gas was ob-served to cut through the liquid stream and portionof the gas penetrates back into the liquid channel[4, 5]. The entrained gas form bubbles near the liq-uid inlet, which enhances the two-phase mixing andsubsequently generate fine sprays outside the noz-

zle. Furthermore, as ALR increases, the penetrationdepth of the entrained gas [5] increases as well.

Though flow-blurring atomization seem to be avery promising approach to generate fine sprays [6],the underlying mechanisms are still not fully under-stood. Two important questions we aim to addressin the present study,

• how does ALR influence the gas-liquid interfa-cial instability inside the nozzle?

• how does the interfacial instability in turn influ-ence droplet and bubble formation in the backflow region?

In the present study, 2D direct numerical simula-tions are performed. A single geometry conditionis considered, namely H

D = 0.25, and a parametricstudy is performed by varying the inlet gas velocity.

Simulation Methods

Governing equations

One-fluid approach is employed to resolve themulti-phase flow problem, and the two phases cor-responding to air and water are treated as onefluid with material property change abruptly acrossthe interface. The incompressible, variable-density,Navier-Stokes equations with surface tension areshown below, along with continuity equation.

ρ(∂tu + u · ∇u) = −∇p +∇ · (2µD) + σκδsn ,(1)

∇ · u = 0 ,(2)

where ρ, µ, u and p represent density, dynamic vis-cosity, velocity vector and pressure, respectively. Dis the deformational tensor Dij = (∇iuj +∇jui)/2.The last term in Equation 1 represents the surfacetension force at the interface. σ is the surface tensioncoefficient, δs is the Dirac distribution function. κand n are curvature and unit normal of the interface,respectively.

To identify different phases in the simulation,volume fraction variable C is introduced. The com-putational cell is filled completely with liquid in thecomputational cell when C = 1, and completely airwhen C = 0. Furthermore, its time evolution satis-fies the advection equation

∂tC + u · ∇C = 0 (3)

The density and viscosity are determined by

2

ρ = Cρl + (1− C)ρg (4)

µ = Cµl + (1− C)µg (5)

where subscripts g and l stand for gas and liquid,respectively.

Numerical methods

Equations 1 and 2 are solved by the open-source solver, Basilisk 1, which utilizes a finitevolume approach based on the projection method.A staggered-in-time discretization of the volume-fraction or density and pressure gives a second-orderaccurate time discretization. Volume of fluid (VOF)method [7] is implemented to resolve the interface.A quadtree grid is used for spatial discretization,which allows a dynamic mesh refinement in user-defined regions. Finally, the height function methodis used to calculate the local interface curvature, anda balanced-force method is used for surface tensioncalculation [8]. The minimum cell size used in sim-ulations is denoted by ∆min and ∆min = R/128.

Boundary conditions

The simulation domain is shown in Figure 1.The height of the liquid channel is R and the widthof the gas inlet is H = 0.5R. No-slip velocityboundary condition is applied the channel walls.Dirichlet velocity boundary conditions are appliedto the gas and liquid inlets, namely u = ul andv = −ug, respectively. The bottom of the domainis treated as a symmetric boundary. An outflowboundary condition is used at the outlet of the chan-nel (p = 0, ∂u/∂n = 0). At t = 0, the liquid isfilled up to the edge of the gas inlet. Then the liq-uid and gas are injected into the domain from thecorresponding inlets.

Key parameters

The liquid and gas phases here are water andair, respectively. The material properties, injectionvelocities, and geometric parameters are provided inTable 1. To investigate the effect of gas velocity oninterfacial instability, droplet and bubble formation,four different values of gas velocity are selected from25 to 200 m/s. Based on dimensional analysis, thereexist six dimensionless parameters for the presentproblem, which are summarized in Table 2. Bothof the gas-to-liquid density and viscosity ratios arequite small for the present cases. The Ohnesorgenumber is about 5.35 × 10−4, which is quite small,so the effect of liquid viscosity is small compared tothat of surface tension. The Weber number varies

1http://basilisk.fr/

from about 2.7 to 171. Airblast atomization for thisrange of We will be mild. Yet it will be shown laterin the results section that when flow-blurring occursat We = 171, the liquid actually breaks up quiteviolently. The gas-to-liquid dynamic pressure ratiosare all very large here. In former studies of airblastatomization, M is important in characterizing theinterfacial instability and the most-unstable mode.Finally, the gas-to-liquid mass flux ratio is from 0.3to 2.4, which are similar to the experiments [5].

Gas inlet

Liquid inlet

Wall

Outlet

Symmetric

Liquid nozzle

Liquid GasR

ug

ul

H

Figure 1. Simulation setup.

Results

General behavior

Temporal evolution of the liquid volume fractionand vorticity for all four cases are shown in Figs.2 and 3, respectively. Different columns representdifferent cases with different gas velocity. Thoughthe times for different cases are different, the timeincrement between two rows are the same. For case1, the gas velocity is low and the liquid is observed tobe pulled and stretched by the gas stream. A longliquid sheet is formed. The breakup of the liquidis purely capillary: a big drop is formed eventuallydue to the pinching of the neck, which is a typicalflow-focusing configuration in [4]. As shown in thefirst column of Fig. 3, the gas-liquid interaction isweak as the two vorticity layers at the boundariesof the gas stream are very stable. The contact lineis pinned at the location where the liquid and gasmeets (the top-left corner of the channel wall) andthe contact line does not move throughout the timesimulated.

As gas velocity increases for case 2, the Webernumber also increases. The dynamic pressure of thegas flow starts to overcome the surface tension andthe interface becomes unstable. Interfacial waves areobserved near the gas channel, which are triggeredby the shear between the gas and liquid at the in-terface, which can be better seen in Fig. 3. Theinterfacial waves grow and later form liquid sheetswhich flap and fragment into small droplets. Thebreakup process for case 2 is actually quite simi-lar to typical airblast atomization, which are mainly

3

t*=0.5

t*=0.45

t*=0.56

t*=0.37

0.55

0.48

0.58

0.38

0.6

0.51

0.6

0.39

0.65

0.54

0.62

0.4

0.7

0.57

0.64

0.41

0.75

0.6

0.66

0.42

0.8

0.63

0.68

0.43

Cas

e 1

Cas

e 2

Cas

e 3

Cas

e 4

Figure

2.

Tem

por

alev

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ofli

qu

idvo

lum

efr

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ion

for

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tca

ses.

Red

an

db

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ate

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idan

dgas

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ase

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Th

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tim

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ast∗

=tu

l

R.

4

ρl(kgm3 ) ρg(

kgm3 ) µl(Pa · s) µg(Pa · s) ul(

ms ) ug(

ms ) σ(Nm ) R(m)

1000 1.2 10−3 1.8× 10−5 0.05

2550100200

0.07 5× 10−4

Table 1. Physical parameters.

r =ρgρl

m =µg

µlOh = µl√

ρlσRM =

ρgu2g

ρlu2l

We =ρgu

2gH

σ ALR =ρgugHρlulR

Case 1Case 2Case 3Case 4

0.0012 0.018 5.35× 10−4

3001200480019200

2.710.742.9171.4

0.30.61.22.4

Table 2. Important dimensionless numbers

shear-instability driven. The liquid is clearly pushedupstream, forming a small gas back flow region isformed. A clockwise rotating vortex is formed inthe back flow region, which is driven the injected gasstream. The Reynolds number for the cavity flow isalso large, so the vortex breaks into small ones anddissipated. The contact line is no longer pinned andcan move back and forward over time. Though aback-flow region is formed, the penetration lengthof the gas is quite small, about 0.25 to 0.4R. It isalso observed that the gas back flow is only observedat the top wall of the channel. The gas flow nevercuts through the liquid stream.

For case 3, a very different flow configuration isobserved. First, the gas flow now can cut throughthe liquid stream. Second, different from case 2, thegas bubble is formed at the bottom wall. The liq-uid layer trapping the bubble breaks later time andform small droplets. Third, no long sheets are ob-served near the bottom wall. The gas back-flow re-gion is pretty homogeneous along the vertical direc-tion. The interface becomes very unstable and theinterfacial waves trap bubbles of different size (diam-eter ranging from about 0.2 to 0.5R). The breakupof these bubbles form multiple small back-flow re-gions. Compared to case 2, actually less dropletsare formed. Due to the effect of visualization, tinydrops smaller than two cells are not shown here.Theflow configuration is clear on the transition towardthe flow-blurring regime but not there yet. The pen-etration length of the gas is similar to case 2.

Finally, for case 4, the interface becomes veryunstable. The wave length is much smaller thancases 2 and 3 and small bubbles are trap and thenlater broken. Multiple sheets and ligaments are

formed. The liquid ligaments continue to inter-act with the gas stream and break into very smalldroplets, which are barely visible. The gas can pen-etrate back deep into the liquid nozzle. From thevorticity results it can be seen that the gas flow inthe back-flow region is highly turbulent which alsocontribute to the violent breakup of liquids withinthe nozzle. The flow configuration for case 4 can beconsidered as in the flow-blurring regime.

Gas-liquid interfacial evolution

To better illustrate the transition from flow-focusing to flow-blurring regimes and the variationof the multiphase flow characteristics along the tran-sition, the gas-liquid interfaces at different times arecollected in a single plot for each case in Fig. 4 af-ter the initial transient period. Due to the highlyflow unsteadiness for large gas inlet velocity (cases2 to 4), the limited number of The sampling rate isul∆t

∗/R = 10. The green dotted lines indicate theedge of the gas inlet, from which the gas penetrationdepth is measured, as indicated by the orange line.

For case 1 it is clearly seen that the gas inter-face is stable. The spatial variations of the inter-faces do not occur until further downstream aroundx/R = 4.5 where capillary breakup occurs. The gasflow never goes back flow for case 1 and thus thepenetration length is zero.

For case 2 the interface moves spatially in awider range than case 1. The gas is entrained intothe liquid nozzle only at the top, generating a smallpenetration depth about 0.6R. Liquid sheets areformed near the bottom of the channel. The in-terface is unstable and interfacial waves can be ob-served. The interfacial waves grow as they are ad-vected downstream and eventually break into small

5

t*=0.5

t*=0.45

t*=0.56

t*=0.37

0.55

0.48

0.58

0.38

0.6

0.51

0.6

0.39

0.65

0.54

0.62

0.4

0.7

0.57

0.64

0.41

0.75

0.6

0.66

0.42

0.8

0.63

0.68

0.43

Cas

e 1

Cas

e 2

Cas

e 3

Cas

e 4

Figure

3.

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ace

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R.

6

Figure 4. Collection of liquid-gas interfaces overtime for each cases. The dotted green line indicatesthe edge of the gas inlet and the solid orange linesat the bottom of each figure indicates the gas pene-tration depth.

droplets.Case 3 shows even more violent interface vari-

ation, at both the top and bottom of the channel.Large air bubbles are trapped at the bottom. Adeeper penetration depth is measured to be about1.2R.

For case 4, the gas can indeed penetrates all thewave back to the liquid inlet. The whole liquid noz-zle are occupied by red lines, indicating the chaoticinterface motions and dynamics within the back-flowregion.

Bubble and droplet formation

Finally, to qualitatively characterize the dropletand bubble formation, representative snapshots fromeach case are shown in Fig. 5. For case 1, there is nobubble formed. The drops are generated based oncapillary breakup. The retraction of the bridge afterbreakup is a clearly evidence that the contributionof gas flow on breakup is negligible.

Case 2 is in a transition toward flow-blurringregime, but the drops formation are driven by bothcapillary and shear instability. The majority of thedroplets are still generated at the tip of the liquidlayer and the bulk liquid break up more violently incase 2 than in case 1, generating more small droplets.Though the interface is unstable but the gas iner-

(a): Case 1

(b): Case 2

(c): Case 3

(d): Case 4

Figure 5. Droplet and bubble formation for differ-ent cases simulated.

tia is not strong enough to cut through the liquidstream. The bulk liquid is pushed upstream a littleby the gas but there is no bubble formed for thiscase.

For case 3, large bubbles are occasionallytrapped inside the bulk liquid at the bottom of theliquid channel. The breakup of the bubble becomesthe dominant mechanism to produce droplets. Sincethe liquid layers wrapping the bubbles are thick.The typical size of droplets generated is similar tothat for case 2.

When the flow configuration clearly lie at theflow-blurring regime for case 4, many small bubblesare formed in the back-flow region. The breakupsof these small bubbles produce large number ofdroplets.

Summary

In this paper, we investigated the gas-liquid in-terfacial flows in flow-blurring atomization. Partic-ular attention is paid on the multiphase flow charac-teristics, such as droplet and bubble formation, fordifferent flow regimes. Two-dimensional direct nu-merical simulations are performed and four differentgas velocities are considered. The simulation resultsclearly illustrate the transition from flow-focusing toflow-blurring regimes. At low gas velocity, the gas-liquid interface is stable and the droplets are formeddue to capillary breakup. In contrast to large gasvelocity, the gas-liquid interface becomes very un-stable and gas penetrates back to the liquid nozzle.

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Bubbles are formed in the gas back-flow region andthe bubble size decreases with increasing gas inletvelocity.

Nomenclature

H Gas channel inlet widthR Liquid channel inlet widthσ surface tension

Subscriptsg gasl liquid

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