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

A Computational Study of Nozzle Internal Flow and its Effect on SprayAtomization

A. Agarwal and M. F. Trujillo∗

Department of Mechanical EngineeringUniversity of Wisconsin–Madison

Madison, WI 53706 USA

AbstractIn the present computational work, the effect of nozzle surface features on the atomization behavior of aliquid jet is analyzed through a comparison of internal and external flow from three representative injectorconfigurations. The first two nozzle geometries consist of surface data generated by X-ray tomographyscans of the ECN Spray A nozzle. The first geometry is based on a single such scan and the secondgeometry is a spline reconstruction of surface data generated by multiple scans. Both of these geometriesare obtained from the ECN database. Boundary fitted grids are employed to capture the surface featuresaccurately. The third geometry is a canonical one based on purely external flow from a circular orifice,i.e., no internal flow resolution. For the simulations, the two-phase flow is solved based on algebraic VoFmethodology utilizing the OpenFoam solver, interFoam. The solver has recently been validated againstX-Ray projected-mass-density data for Spray A at engine-like conditions. Across these three configurations,we find that the breakup length of the topologically connected liquid varies appreciably, with the firstgeometry yielding the shortest breakup length. While the liquid turbulent kinetic energy plays an importantrole in the accelerated breakup of the first configuration, it is by far not the only contributing factor. Ananalysis of the temporally-averaged velocity near the orifice openings reveals that the flow field orthogonalto the streamwise direction contains key features that have a significant effect on the breakup. The meanradial velocity near the injector walls directly affects the morphology of the emanating liquid jet. It notonly leads to a quick growth of surface disturbances but is also responsible for producing secondary featureson the liquid surface. The third configuration is characterized by milder surface disturbances in the nearfield and consequently longer breakup lengths.

Keywords: ECN Spray A; Injector Nozzle; Surface Roughness; Spray Atomization; Primary Breakup; HighFidelity Simulation.

∗Corresponding Author: mtrujillo@wisc.edu

Introduction

Flow characteristics inside the injector nozzleare crucial to the spray atomization process [1, 2].However, the internal flow and its effect on the atom-izing jet are not well understood due to complexitiesarising from nozzle geometry, needle motion, turbu-lence, and flow cavitation. Therefore, the study ofnozzle effects on spray formation remains an activearea of research [3, 4, 5, 6].

Capturing all the details of in-nozzle turbulenceis computationally challenging. Therefore, whilemuch of previous work has been done on tuning andevaluating the different turbulence models [7, 8, 9],fewer studies focus on characterizing or analyzingthe turbulent scales. Among some recent studies,Jiao et al. [10] attempt to characterize and studythe effect of nozzle turbulence by obtaining turbu-lence data from DNS simulations of fully developedpipe flow, and use the time-varying velocity data asinput for their atomization simulations. They high-light three different mechanisms leading to dropletformation in their work. Moon et al. [11] show the ef-fect of the orifice inlet geometry on the velocity gra-dients and the turbulence intensity inside the nozzle.They also establish connections between the velocitygradients and the turbulence intensity. Salvador etal. [12] provide hydraulic characterization with re-spect to different levels of needle lift. They show thedependence of the turbulence development, intensityand concentration on needle lift. Chouak et al. [13]have performed a transient analysis with respect tocontinuous needle lift. They provide an explanationfor hysteresis with respect to needle motion and findthat needle motion is one of the most important fac-tors that affects in-nozzle turbulence.

The scope of the present work is to study theeffect of internal nozzle asymmetries and imper-fections on primary atomization during the quasi-steady period of injection, i.e., beyond the initialtransient. We provide detailed, quantitative charac-terization of the nozzle geometry surface along withthe internal nozzle flow and external flow. We at-tempt to establish the sensitivity of the bulk atom-ization behavior to small differences in the nozzlesurface features. The present work also examinesthe underlying mechanism that is responsible for thissensitivity.

For this study we use the well characterized noz-zle geometry named ‘Spray A’ by the Engine Com-bustion Network (ECN). A significant amount of ex-perimental and computational data, especially in thenear field, is available for this non-cavitating noz-zle [8, 6, 14, 15, 16]. To accurately capture the ef-fects of nozzle imperfections and surface roughness,

the nozzle is employed with a fine, boundary-fittedgrid. In this comparative study, along with the twovariations of the ECN Spray A geometry, a canon-ical flow configuration, with only external flow, isalso considered.

To study the effect of nozzle flow on the spray at-omization we employ high fidelity, Volume-of-Fluid(VoF) simulations to track the liquid-gas interface,along with realistic nozzle geometries and engine-likeoperating conditions. Fully coupled internal nozzleflow and external flow simulations are performed toaccurately capture the interaction between the inter-nal and the external flow. This is in contrast to thedecoupled simulations where internal nozzle flow iscomputed and provided as an inflow boundary con-dition to the spray simulation [10].

An important discovery from the present workis regarding the significant role the steady (non-fluctuating) flow, specifically the steady non-axialflow, inside the nozzle plays in the atomization char-acteristics. While some studies have tried to char-acterize the axial flow profiles [8, 3, 13], no studiesto the author’s knowledge investigate the non-axialvelocity components. We find that the steady non-axial velocity components are small in magnitudebut have a significant impact on atomization.

Simulation Setup

In this comparative study, flow among three dif-ferent spray configurations is being analyzed. Thefirst two configurations employ two variations of theECN Spray A (serial# 210675) nozzle. It is a single-hole, 90µm diameter (D0) injector nozzle and hasbeen characterized extensively, particularly in thenear field [14, 15, 16]. The two variations of the noz-zle are called ‘Unprocessed Spray A’ and ‘EducatedSpray A’ through this study. The difference betweenthe two nozzle variations is small and hence not vis-ible at the scale of Figure 1; the differences are dis-cussed in detail in the next section. The third config-uration is a canonical setup where only external flowfrom a circular orifice is simulated. This external-only flow configuration is frequently used in funda-mental studies of spray atomization [17, 18, 19, 20].

A similar computational domain is used for allcases presented in this paper. Details of the com-putational domain are shown in Figure 1. For theinternal flow region, a hexahedral, boundary-fittedgrid is employed. The external flow region is dividedinto two parts, near the spray axis (highlighted withblue box in Figure 1) and away from the spray axis.All computational cells within this region are hexa-hedral as this provides much better numerical per-formance than tetrahedral cells for the algebraic VoF

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scheme used here [21]. Away from the spray axis un-structured tetrahedral cells are used that grow largerin size as we move further away from the spray axisto reduce computational cost.

Figure 1: A typical domain and grid used in thepresent study.

For this study, all simulations have been per-formed at experimental conditions reported by Kas-tengren et al. [15], which adhere to the ECN speci-fications. The ambient gas is N2 at 343 K, and thefuel is n-dodecane at 303 K. In the present simula-tions the inlet flow velocity (at the blue inlet facesin Figure 1) is specified such that the jet velocity atthe orifice opening matches the experimentally esti-mated value of 412 m/s [15].

To get an insight into the level of variation withrespect to varying numerical resolution, for all ofthe metrics being reported here, results from threedifferent levels of grid resolution are considered foreach of the three configurations. Since the grids usedhere are not uniform, there is a small level of spatialvariation in the cell sizes for each of the simulations.As a representative number for each of the cases wereport the average cell size in the near-spray region.The case matrix presented in Table 1 shows this av-erage ∆x value in the near field region for each ofthe cases.

Geometry Coarse Medium FineEducated 5.9µm 3.9µm 2.8µmUnprocessed 5.8µm 4.5µm 2.9µmOnly External 5.4µm 4.4µm 3.1µm

Table 1: Average cell size values for the differentspray configurations and grid resolution levels.

Nozzle Geometries

Kastengren et al. [16] point out that due to themanufacturing challenges associated with the smalldimensions of the nozzles the actual nozzle pro-

files deviate from the nominal specifications. In thepresent study we attempt to incorporate the asym-metries and imperfections in the nozzle geometriesand study their effects. Therefore, surface stere-olithography (STL) files based on scans of a realnozzle are used here to generate the computationaldomains.

Two variations of the Spray A nozzle are usedin this study, as mentioned in the previous section.The STL files corresponding to these geometries areboth based on reconstructions of raw X-ray tomog-raphy measurements that have been processed andconverted into usable STL files. The STL files usedin this study come from two different sources anddiffer in the way the raw data has been processed.These differences between the two geometries areshown in Figure 2 and described below:

1. ‘Educated Spray A’: This has been provided byGeorgia Institute of Technology. This file isa spline-reconstructed representation of a col-lection of multiple X-ray tomography measure-ments. While this processing is aimed at re-moving artificial experimental artifacts, it alsomakes the surface finish smoother.

2. ‘Unprocessed Spray A’: This file has been pro-vided by CNRS France. It is based on high-resolution X-ray tomography data that wassmoothed to create the STL file. This geom-etry is relatively unprocessed.

Figure 2: Details of the near-exit portion of the twoSpray A nozzles are presented here. A comparisonbetween the STL data (red) and the VoF grid (blue)employed for the study is shown.

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For these nozzles we report two metrics, the firstis the level of departure from a perfectly cylindri-cal geometry and the second is the level of surfaceroughness measured along the axial direction. Thesevalues are reported in Table 2.

Geometry Departure from x-Roughnesscylindrical

Educated 1.35µm 61.1 nmUnprocessed 1.21µm 393.3 nm

Table 2: Values for departure from a cylindricalshape, and roughness measured in the axial directionfor the two Spray A geometries used in the study.

Results

Deshpande et al. [21] have presented a thoroughevaluation of interFoam performance with respectto kinematics of advection, dynamics in inertia dom-inated regime, and dynamics in the surface tensiondominated regime. Validation tests have also beenpreviously presented for two-phase mixing layers andco-flow atomization [22]. Agarwal and Trujillo [14]present validation tests for the solver with the Edu-cated Spray A configuration.

Here we present results in three parts, the first isthe nozzle internal flow, the second is the liquid sur-face displacement from a base shape, and the thirdis the length of the topologically connected liquidcolumn.

Nozzle Internal Flow

Under the standard Reynolds decomposition ofthe velocity field the instantaneous velocity can bedecomposed into a mean velocity and a perturbationvelocity as,

u = 〈u〉+ u′. (1)

Considering the components separately helps differ-entiate between the effect of the underlying meanvelocity and that of the turbulent fluctuations. Inthis section we focus on the characteristics of themean velocity field.

While the flow is predominantly along the noz-zle axis, in this analysis we find that the atomizationbehavior is sensitive to the non-axial (or transverse)component of the velocity field. The non-axial com-ponent of the velocity field is represented as u⊥ andthe axial component is represented as u‖. They aredefined as,

u‖ = (u · ex)ex, (2)

u⊥ = u · (I− exex), (3)

where ex is a unit vector along the axial direction.The non-axial component of the mean velocity field,〈u⊥〉, for the Spray A nozzles is presented in Fig-ure 3 at the orifice opening for the two Spray A noz-zles. There is a stark difference between the flow inthe Educated and the Unprocessed Spray A; highermagnitudes of 〈u⊥〉 are observed in the UnprocessedSpray A. The higher magnitudes in the UnprocessedSpray A nozzle are concentrated near the nozzlewalls mainly because the flow near the wall is sus-ceptible to small but abrupt changes in direction.The velocities are high in the axial direction, and asmall change in the velocity direction due to nozzlesurface features leads to relatively high non-axial ve-locity magnitudes. Furthermore, it is observed thatthere are clear structures visible in this time aver-aged velocity field. This means that regardless ofthe turbulent fluctuations, the underlying velocityfield itself departs significantly from the canonicalsymmetric profile in purely cylindrical geometries.This is an effect of both the level of roughness in thestreamwise direction for the Unprocessed geometry,but also the level of asymmetry, i.e., no perfectly cir-cular, in both geometries. It should be emphasizedthat these profiles represent converged temporal av-erages. These are not instantaneous structures.

(a) Unprocessed (b) Educated

Figure 3: Contours of 〈u⊥〉 are shown at differentlocations inside the nozzle orifice along with a partof the liquid jet surface.

The contours inside the nozzle at different axiallocations, along with the liquid jet emerging fromthe nozzle are presented in Figure 4. While the ve-locity field shown here is the temporal averaged, theliquid surface presented is instantaneous for ease ofinterpretation. The magnitudes of the non-axial ve-locity are higher not just at the exit plane for the Un-processed Spray A, but also further upstream. Withrespect to the gas-liquid interface, an interesting fea-ture is the presence of protrusions or striations alongthe liquid jet. Between the two geometries, a pro-duction of these striations is more pronounced in theUnprocessed geometry.

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(a) Unprocessed

(b) Educated

(c) Only external

Figure 4: Contours of 〈u⊥〉 are shown at differentlocations inside the nozzle orifice along with a partof the liquid jet surface.

Interface Displacement from Base Shape

Here we quantify an aspect of the liquid jet mor-phology, namely, the degree to which the liquid sur-face departs from the base shape. The base shape istaken to be the shape of the orifice opening at x = 0.Then the departure of the liquid jet, ξ(x, θi, tj), isgiven as,

ξ(x, θi, tj) = |R(x, θi, tj)−R(x = 0, θi, tj)|= |R(x, θi, tj)−Ro(θi)| (4)

where R(x, θ, t) represents the location of the liquidsurface as a function of space (x, θ) and time (t).R(x = 0, θi, tj) is the base shape, i.e., R as a functionof θ at x = 0, i.e., the shape of the nozzle exit.

The spatially and temporally averaged values ofξ, symbolized by

⟨ξ⟩, are presented in Figure 5. For

all the different cases, the disturbance values beginat zero near the orifice opening, and grow as we movedownstream. The values among the different gridlevels for the same nozzle configuration are groupedtogether indicating convergence of the disturbancedata with respect to grid refinement. The impor-tant observation here is that the growth rate of thesurface disturbance changes significantly for the dif-ferent injection configurations. The fastest growthis observed in the Unprocessed Spray A nozzle, fol-lowed by the smooth Spray A nozzle, and the purelyexternal flow configuration, which exhibits very slowgrowth.

Length of Topologically Connected Liquid

In this section we consider a key atomizationmetric, the length of the liquid that is topologically

Figure 5: The averaged disturbance values,⟨ξ⟩, are

shown as a function of x for the different configura-tions.

connected back to the nozzle, simply referred to asthe intact liquid core. While corrosion of the liquidjet surface commences near the orifice opening itself,the bulk of the liquid remains intact for a longer dis-tance. This liquid core breaks up downstream in theform of large oscillations. The length of the intactliquid core is shown as a function of time in Fig-ure 6. The instantaneous liquid length values arerepresented with the lighter lines in the figure. Ini-tially, from the start of injection, the length of theliquid core increases linearly for all the nozzle config-urations. At some point (between 5µs to 17µs de-pending on the nozzle configuration), the liquid coreundergoes fragmentation and its length, measuredfrom the orifice plane, exhibits chaotic fluctuationsabout a mean value. This time series is presentedonly to give a sense of the magnitudes of the fluctu-ations to the reader. Our focus is the mean value ofthe liquid lengths. Time averaged values, with theaveraging starting at t = 20µs, are presented withthe darker lines and markers. The mean length val-ues quickly converge to a constant value for each ofthe cases. These values for the different cases arerespectively reported in Table 3.

Geometry Coarse Medium Fine

Spray A (Educated) 35.7D0 37.8D0 35.7D0

Spray A (Unprocessed) 23.4D0 25.6D0 20.4D0

Only External 46.5D0 49.2D0 51.5D0

Table 3: Intact core lengths for the different sprayconfigurations and grid levels.

A clear trend across the different configura-tions emerges–the Unprocessed Spray A configura-tion shows the shortest length, followed by the Ed-ucated Spray A. Finally, the purely external flow

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0 10 20 30 40 500

10

20

30

40

50

60

Figure 6: The length of the intact liquid core is pre-sented as a function of time for the different config-urations. The instantaneous values are shown withthe lighter lines and the averaged data is shown bythe darker lines with markers.

exhibits the largest length values. Overall, for thethree configurations, the values of the mean liquidcore length show convergence with respect to gridrefinement.

Through reconstructions of ensemble averagedX-ray radiography data, Pickett et al. [23] estimatethe intact liquid core length to be approximately2.5 mm or 27.7D0. While in the present simulationsthere is a clear sensitivity of the breakup lengths tothe nozzle surface features, the experimentally esti-mated length lies in between the lengths reportedhere for the two Spray A nozzles.

Summary & Conclusions

In the present study we present high-fidelityCFD simulation and analysis of internal nozzle flowand its effect on atomization behavior. The studyuses three injection configurations: the first two cor-respond to two scans of the ECN Spray A geome-try, and the third corresponds to a canonical con-figuration where only the external flow is simulated.The algebraic volume-of-fluid method based solverinterFoam is used for the simulations. All simula-tions are performed at the ECN Spray A conditionsused by Kastengren et al. [15].

In the internal nozzle flow, we first look at timeaveraged, non-axial velocity profiles. Higher mag-nitudes of 〈u⊥〉 are observed in the rougher, Un-processed Spray A nozzle. These higher values areconcentrated near the nozzle walls. The mean ra-dial velocity is responsible for permanent striationson the liquid jet surface. The magnitude of the ra-dial velocity is directly related to the strength of thestriations.

The radial velocity component inside the nozzlelends a significant change in the shape of the emerg-ing liquid jet. We quantify the level of departure

of the liquid jet from a base shape. The liquid jetemerging from the Unprocessed Spray A nozzle de-parts the fastest from this shape, followed by thosefrom the Educated Spray A, and finally the canoni-cal spray with no-internal flow. This trend is directlyrelated to the magnitude of the non-axial velocity atthe nozzle opening and the striations of the liquid jetemerging from the nozzles.

With respect to the length of the topologicallyconnected liquid, it is found that the liquid jet fromthe Unprocessed Spray A configuration breaks upthe fastest, followed by that from the EducatedSpray A. The external-only spray breaks up the last.This trend is expected based on the trends observedearlier with respect to the departure from a baseshape. The liquid jet that shows the fastest growthof disturbances breaks up the soonest.

We establish the sensitivity of the bulk atom-ization behavior to the small nozzle surface features.Small (O(1µm)) differences in the surface roughnesslead to large (O(1000µm)) differences in the breakuplengths. We study the mechanism that leads to thissensitivity. It is found that the surface roughnessfeatures establish a small non-axial velocity compo-nent in the mean velocity field. This componentcauses the formation of striations on the liquid jetsurface, which leads to a quick departure from thebase liquid jet shape. This eventually leads to aquicker breakup of the intact liquid core.

Detailed characterization of the nozzle surfaceroughness for the two Spray A geometries has beenomitted in the current paper. The turbulent kineticenergy (TKE), which may also play a role in themechanism, has also not been discussed in this pa-per. The effect of the nozzle surface roughness onthe TKE and its effect on atomization characteris-tics will be considered in future work.

Acknowledgements

This material is based on work supported bythe Direct-Injection Engine Research Consortium(DERC) at UW–Madison. The authors would liketo thank the Engine Combustion Network (ECN)for providing injector geometry files and other re-sources. Our thanks are also due to Center forHigh Throughput Computing (CHTC) at UW–Madison for providing computing resources, alongwith Joshua Leach for administering the comput-ing resources in the group. Additionally, this workpartially used the Extreme Science and Engineer-ing Discovery Environment (XSEDE) Bridges regu-lar memory at the Pittsburgh Supercomputing Cen-ter through allocation TG-CTS180037. The authorsare grateful for the access granted to this resource.

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