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1 Copyright © 2015 by ASME

Proceedings of the ASME 2015 International Mechanical Engineering Congress & Exposition

IMECE2015

November 13-19, 2015, Houston, TX, USA

IMECE2015-53028

APPLICATION OF A HYBRID RANS-LES CFD METHODOLOGY TO PRIMARY

ATOMIZATION IN A COAXIAL INJECTOR

Wayne Strasser

Eastman Chemical Company

Kingsport, TN, USA

Francine Battaglia

Virginia Polytechnic Institute and

State University

Blacksburg, Virginia, USA

Keith Walters

Mississippi State University

Starkville, MS, USA

ABSTRACT

Non-zonal hybrid RANS-LES models, i.e. those which do

not rely on user-prescribed zones for activating RANS or LES,

have shown promise in accurately resolving the energy-

containing and highly anisotropic large-scale motions in

complex separated flows. In particular, the recently proposed

dynamic hybrid RANS-LES (DHRL) approach, a method

which relies on the continuity of turbulence production through

the RANS-to-LES transition zone, has been validated for

several different compressible and incompressible single phase

flow problems and has been found to be accurate and relatively

insensitive to mesh resolution. Time-averaged source terms are

used to augment the momentum balance. An added benefit of

the DHRL is the ability to directly couple any combination of

RANS and LES models into a hybrid model without any

change to numerical treatment of the transition region. In this

study, an attempt is made to extend the application of this

model to multiphase flows using two open literature coaxial

two-stream injectors involving non-Newtonian liquids. For the

first time, the new model has been successfully implemented in

a multiphase framework, combining the SST RANS model with

MILES LES approach. Favre averaging is used to ensure

consistency between the momentum equations and the density

fluctuations. It was found that the momentum source terms

must be density weighted in order to ensure stability of the

solution. Primary atomization findings with a stable model are

encouraging. The spray character with the new model was

somewhere between that of a RANS model and the LES result.

Droplet sizes, which are indicative of the shear layer energy, for

the RANS model were greater than the hybrid results, which

were comparable to the LES result and matched the

experimental expectation. Additionally, the new approach

showed a liquid core breakup length close to that expected from

the literature.

INTRODUCTION

Atomization

The agricultural, chemical, food, fire protection, and

energy-production industries have all advanced as a result of

the study and understanding of the breakup and atomization of

jets since Felix Savart in 1833. Controlling the droplet

characteristics and trajectories can be critical for high yields

and productivity of reactors, process equipment, gas turbines,

and reciprocating engines. A thorough introduction to injectors

and sprays is given in Lefebvre [1]. Correlations for Sauter

mean diameter (SMD) are often given in terms of Weber

number (We) and Ohnesorge (Oh) and attempt to approximate

the effects of primary and secondary atomization. These two

dimensionless parameters can be thought of as measures of the

restraining forces for atomization. Designs which reduce the

mean droplet size also tend to narrow the size distribution of

droplets, including an increase in air velocity and/or a reduction

in liquid feed rate.

A fundamental study of primary atomization was carried

out by Lienemann, Shrimpton, and Fernandes [2]. As We

increases, a Kelvin-Helmholtz (KH) instability (driven by

shear) was shown to disturb the balance between momentum

and surface forces and cause sheet flapping. Typical wave

thicknesses were above the theoretical inviscid thickness value.

Wave propagation thins the sheets further. In addition, sheet

perforations can be caused by entrained air and/or boundary

layer (vorticity) development from the orifice and bulk orifice

turbulence. These perforation events depend on the length and

time scales of the turbulence structures. They studied in-tact

sheet radius and show a LCWe-x effect, where “x” ranges from

0.33 to 0.42. A similar power law dependence on phase density

ratio, , was also displayed. Thinner sheets are obviously

advantageous to fine droplets. Close to the rim of the sheet,

waves changed from a sinusoidal shape (linear instability) to a

zigzag pattern (non-linear) as vortices were shed off wave

2 Copyright © 2015 by ASME

crests and move into wave troughs. This is the onset of break-

up. Their work outlined dominant wave frequencies and sheet

thickness dependence on feed conditions and feed stream

angles. They discussed how the local sheet We value can

produce a shift in the preferred mode of instability, with

symmetric waves (in-phase) produced below 1 and dilatational

(phase opposition) above 1. Symmetric modes grew faster.

Lastly, they addressed azimuthal sheet curvature. When the

inner sheet diameter is small compared to the outer (as in a

two-stream injector), it behaved like a full jet. For large values,

like a three-stream injector, it behaved like a thin, inviscid

sheet, favoring linear stability analysis. Above a certain liquid

viscosity, however, linear analysis could vastly over-predict

droplet size.

The effect of viscosity and surface tension for non-

Newtonian fluids on SMD has been explored by Aliseda et al.

[3]. They found that that instability wavelength was

substantially affected by higher viscosities. As expected, higher

viscosities hindered the growth of instabilities resulting in

larger droplets, but only when viscosity was well above ten

times that of water. In fact, there was an extremely pronounced

coupling effect of surface tension and viscosity. They proposed

that the lower surface tension of the non-Newtonian solutions

(about one third that of water) prevented their SMD values

from being orders of magnitude larger than that of water,

instead of just two to three times its value.

Also in 2008, Dumouchel [4] outlined theories and

findings related to cylindrical liquid jets, flat liquid sheets, air-

assisted cylindrical jets, and air-assisted flat liquid sheets. It

was hypothesized that in order for a spray to form, there has to

be initial disturbance(s) at the liquid-gas interface and a

mechanism for those disturbances to grow. The final spray

droplet sizes are individually set by a balance of local

disturbances and local liquid cohesion force. Although [5]

demonstrated the importance of feed liquid profiles for

situations without gas co-flow, [4] found the details of the

liquid flow to be of lesser importance than those of the

surrounding gas for gas-assisted flows. The important effects

include total liquid momentum, gas vorticity, gas phase

turbulence, and the recirculation zone outside of the nozzle.

Similarly, Fuster et al. [6] investigated the effect of gas

momentum ratio (M) and gas boundary layer thickness on the

dominant response frequency of wave growth from a simple

gas/liquid splitter plate arrangement. They modulated the gas

stream and found that the excited wave response dynamics

were dependent upon the thickness the gas boundary layer.

Turbulence Effects

The importance of the surrounding gas phase turbulence

field has already been shown to play a role in primary

atomization. Lasheras et al. [7] showed how breakup from

turbulent resonance with droplets can supersede shear

atomization. Chen et al. [8] discussed resonance in the

turbulence field playing a role in break-up when the small scale

turbulence frequency matches the natural mode of an entrained

droplet. It was surmised that the size of the smallest droplets is

comparable to the size of the coherent turbulent structures that

are just large enough to overcome the surface energy when We

is less than 10. They assumed turbulence isotropy and the

existence of an inertial subrange in the turbulence spectrum.

Their primary atomization models took the common form in

which the SMD is proportional to LCWe-x with modifications

for a “real” radial turbulence kinetic energy (k) distribution, as

opposed to a uniform value. They show SMD related to k-x,

which indicates that droplet size increases as k decreases. The

implication is that, ideally, primary atomization would occur in

a region of high turbulence energy for a lower equilibrium

droplet size.

Maniero et al. [9] discussed treating a droplet (in a liquid-

liquid co-flowing system) as a harmonic oscillator to predict its

secondary breakup. Here, the proposal is that the droplet does

not respond instantly to its surrounding turbulent field, and

some past examples include an eigenfrequency of 43 Hz for a

low-viscosity fluid droplet. The authors conclude that the

droplets in their study had length scales in the inertial subrange

of the continuous phase turbulence, but the Reynolds number of

the study was so low that clear distinctions of turbulent length

scales could not be determined with confidence. The oscillator

forcing function is equal to a constant times the turbulent

Weber number, for which the typical velocity scale is replaced

by a structure function; an Eulerian calculation is employed to

estimate the velocity differences at scales on the order of the

expected droplet size. Only the maximum over the considered

space dimensions is taken as the structure function. Instead of

breakup occurring at a critical Weber number, it occurs at a

critical deformation of approximately unity, making the

constant equal to ~ 0.06. In addition, sub-grid scale (SGS)

VOF modeling has been addressed by Krause et al. [10] for

cases in which droplet coalescence immediately upon droplet

contact is not a true representation of reality. For completeness,

it should be mentioned that the bi-directional coupling of the

turbulence field with entrained materials, i.e. continuous phase

turbulence attenuation/enhancement by droplets or particles has

been addressed by many (Strasser [11] and Ling et al.[12] to

name two); however, that will not be quantified here.

Hybrid Turbulence Modeling

It is well-known that the RANS approach to computation-

ally quantifying the effects of turbulence leaves much to be

desired, even in many single phase flow scenarios and

especially with those involving separation. Adding a second

phase only complicates the situation. Co-axial injectors have

separated shear layers proceeding from the feed nozzle, as well

as separation and boundary layer development around

individual ligament/droplets. Moreover, large density gradients

are present. In RANS modeling, all of the key length scales of

turbulence are lumped into a single model, often employing

gradient diffusion, and the effects of the fluctuations are

superimposed onto the mean. A substantial improvement

would be to invoke the use of LES, in which only the largest

turbulent motions are resolved and characterized; these contain

most of the energy and anisotropy. As a result, treating the

3 Copyright © 2015 by ASME

smaller, more uniform scales in a sub-grid scale (SGS)

statistical model poses less of a risk. There is an obvious

expense associated with LES, as a much higher grid resolution

(and the commensurate smaller time step) is required to

evaluate those larger scale motions. Steep velocity gradients,

such as those near walls, dramatically increase the expense. In

atomization, however, walls are not the only items that are

much slower than the gas; accelerating droplets and ligaments

could be included in this category as well. The term "slip

velocity" is applied to the difference between the two phases. It

would be expected to be the same, or very close to, the value of

the gas velocity near the feed injector.

A hybrid approach is often sought to mitigate the expense

of LES. Using this method, LES is employed primarily for

unsteady separated flow regions, while RANS is employed in

near-wall regions or regions with insufficient mesh resolution

to resolve fine-grained turbulence structures. In general, there

are two categories of hybrid modeling. "Zonal" relies on a

priori knowledge and/or decision-making regarding the

placement of LES and RANS regions. The grid is demarcated

accordingly at the outset. An obvious disadvantage of this,

especially in regards to atomization, is that the LES region

changes in time. A "non-zonal" approach implies that the

location of the RANS and LES regions are allowed to

dynamically adjust to the flowfield of interest, with no need for

explicit demarcation a priori. The acute challenge with non-

zonal models is the handling of the communication of resolved

fluctuating quantities from the LES section(s) of the domain to

the completely modeled quantities in the RANS section(s).

Another critical aspect of the non-zonal is the switching

criteria, i.e. how to determine when to transition from one

model type to the other. Depending on where the dominant

supply of turbulence production occurs, the outcome could vary

greatly.

A few of these switching mechanisms and criteria are

explored in Breuer et al. [13]. The most common approach is

to use grid resolution metrics, such that the LES model is

invoked in refined mesh zones via suppression of the turbulent

viscosity, either directly or through an increase in modeled

turbulent dissipation rate. The latter, for example, is the method

adopted in the well-known Detached Eddy Simulation (DES)

model. An alternative to this was proposed and discussed by

Bhushan et al. [14] and Walters et al. [15]. The transition

between the two modes is determined by the continuity of total

turbulence production. The advantages include 1) the ability to

couple any RANS model with any LES model, 2) freedom from

explicit grid dependence, and 3) the return to the baseline

RANS model in steady-state flow. This method will be tested

in this work, and more details are provided below.

Multiphase Complications

In gas-liquid multiphase studies, the two immiscible

phases, liquid and gas, often exist in the same computational

cell. Given the large difference in viscosity and density

between liquid and gas, there are substantial jump conditions at

the phase interface. This interface exists at the subgrid (SGS)

level; its reconstruction is often sought through the particular

multiphase algorithm in ways somewhat analogous to how

shocks are captured in high Mach number flows. Aside from

discretization and flux computational challenges outlined in

Rider and Kothe [16], Gueyffier et al. [17], and Davidson [18]

(in regards to the importance of instantaneous pressure-velocity

coupling in LES structure resolution), turbulence production

and transport at the SGS may be compromised by assuming a

homogenous approach. Tavangar et al. [19] studied non-

Newtonian slurry atomization using a homogenous LES and

found strong agreement with experimental results; however,

formal mathematical consideration of the governing equations

shows that filtering operations produce new SGS terms and

their associated instabilities. Liovic and Lakehal [20], [21, 22],

Vallee et al. [23], and Navarro-Martinez [24] highlight various

approaches taking into account these effects as sources of

turbulence in LES and RANS approaches. The authors of [24]

described how SGS surface tension, for example, is important

in cases of high surface tension, unresolved interface curvature,

and flow relaminarization. Obviously, unresolved curvature is

a risk for all CFD modeling. Navarro-Martinez [24] discovered

the fact that SGS effects are not important until after

approximately 20 jet diameters. At the same time, however,

velocity gradients at the interface can induce modeled

turbulence that is actually not present in the real flow and

requires a modeled damping function (Hansch et al. [25]).

Given the fact that these effects are not always important and

are partially offsetting, they are ignored in the present work.

Aside from SGS instability sources, a first order

consideration is the fact that the gas “sees” the liquid as a wall

with a differential velocity of varying degrees, depending on

the local phase slip velocity. Near the nozzle, the gas is moving

much faster than the liquid (hence the purpose of gas-assisted

atomization). The relatively stationary liquid should enhance

turbulence production in the gas phase while decelerating the

gas. At some distance from the nozzle, where the liquid has

been disintegrated, and the droplets are moving nearly the

speed as the decelerated gas, the slip velocity is much lower.

Here, there is very little production between the two phases.

Lastly, in the far-field, the higher density liquid droplets retain

their momentum. The gas, now slower than the liquid, is

dragged along by the liquid, once again enhancing turbulence.

A large body of literature is available to address this for

Lagrangian methods (see Crowe [26] and Strasser [11] for

example). However, for SGS drag, these effects are often

ignored. Liovic and Lakehal [20] described an alternative to the

homogenous approach such that these effects can be included.

They discussed the need to construct phase-dependent velocity

gradient scaling and the associated “wall distance” (actually,

distance from the gas-liquid interface) to feed a Van Driest-

style damping algorithm. Implementing a phase-dependent

turbulence transport methodology will be foregone herein as a

first step towards progress in hybrid modeling. At the macro

scale, these discussed gas-liquid velocity gradients are going to

support turbulence generation, and this will be explored.

4 Copyright © 2015 by ASME

NOMENCLATURE

a Speed of sound

D Liquid orifice diameter

F Surface tension body force

i Summation index

k Turbulence kinetic energy

La Laplace num. = Re2/We = Suratman num.

LC Some characteristic length scale

M Gas/liquid momentum ratio = (U2)G/(U2)L

Oh Ohnesorge number = /Re = 1/

p Pressure

Re Reynolds number = UD/

SMD Sauter mean diameter (“D32”)

u Velocity component

U Velocity magnitude

y+ uty/

We Weber number = GUG2D/

Greek

Stress DHRL coefficient, 1 = fully LES

Complimentary DHRL stress coefficient

Turbulence dissipation rate

Surface tension

Density

Specific dissipation rate

Stress tensor

Phase volume fraction

γ Outer gas/liquid annular approach angle

μ Molecular viscosity

Subscripts and Superscripts

L Liquid

G Gas

t Turbulent

OBJECTIVE AND SCOPE

It is hoped that the broader three-stream coaxial injector

focus of Strasser [27] and the associated works will be unified

and extended in this document as methods enhancements are

sought. Although the overall project is concentrated on a three-

stream self-sustaining pulsatile injector involving compressible

flow and breakup of a non-Newtonian slurry, the new dynamic

hybrid RANS-LES (DHRL) method will be explored and

validated using the studies of incompressible, non-pulsatile

two-stream coaxial primary atomization of non-Newtonian

liquids by Mansour and Chigier [28] and Zhao et al. [29].

Additionally, Strasser and Battaglia [30] showed that the ratio

of integral length scale to mesh element length scale of the two-

stream injectors, relative to the pulsatile injector, were more

conducive to hybrid modeling. It should be noted that all

coaxial atomization may fundamentally be considered

“pulsatile” to some extent in that, from a fixed reference frame

watching the passing spray, there are temporal oscillations in

liquid volume fraction and spray droplet number density. (Plus,

two fluids merging at different velocities will encourage

fluctuations at some scale.) However, the three-stream injector

in the cited works is tuned such that there is substantial mass

flow variability in the bulk feed boundary conditions.

Table 1 (SI units) shows the important parameters in the

first study. Note that the Weber number is the average, but the

instantaneous values of the Weber number can be very different

from the average and can cause the liquid to span multiple

breakup regimes ([31]) caused by polydisperse gas fluid

structures. Of the available liquids from their study, the 0.3%

(by mass) Xanthan gum solution is the closest to the non-

Newtonian liquid of the pulsating injector. Figure 1 offers a

schematic of the computational representation of their nozzle.

The liquid is fed in a central jet of about 3.72 m/s, while gas is

fed in an annular region at 93.4 m/s. The feed liquid Reynolds

number is about 4000 when defined using the high-shear

viscosity, making it transitional. Consequently, in CFD, a flat

profile was used. Although the Xanthan gum solution has a

strong viscosity dependence on shear, they echoed the

commonly known view that only the highest shear viscosity is

the droplet size controlling factor ([3], [32]). Using an optical

method called phase Doppler particle analyzer (PDPA), they

assessed the local droplet SMD at 0.254 meters (10") from the

liquid outlet. As described in Dumouchel [33], the

disadvantages to the method are 1) only spherical droplets can

be measured, 2) only one droplet in an optical volume can be

measured at a time, and 3) a validation study of the ratio of

correctly measured events to the total events was not given. In

effect, if large ligaments (non-spherical) are present at the

measurement location, the reported SMD will be

underestimated. [31] communicated that most objects are non-

spherical at initial breakup. If the view of smaller droplets is

blocked by larger ones, the reported SMD will be

overestimated. Regardless, [28] showed 134 m at the

measurement location for the conditions in Table 1.

Table 1: Important quantities and boundary conditions for

study # 1 (Mansour and Chigier [28]); All are in SI units.

Liquid density

1000

Liquid viscosity at highest shear

0.00282

Liquid surface tension

0.0735

Liquid orifice inner diameter

0.00305

Liquid orifice outer diameter

0.00385

Liquid mass flow

0.0272

Liquid velocity

3.72

Gas density

1.20

Gas viscosity

1.86×10-05

Gas orifice inner diameter

0.0127

Gas mass flow

0.0129

Gas velocity

93.4

Gas to liquid mass ratio

0.474

Weber number

434

Ohnesorge number

0.00595

5 Copyright © 2015 by ASME

Based on the work of Farago and Chigier [34], liquid feed

Reynolds number, and Weber number, this disintegration

processed would be termed “Fiber” type and would be

characterized by fibers peeling off the main liquid core and then

subsequent fiber breakup by non-axisymmetric Rayleigh

breakup. It is “pulsating” in the sense that pockets/bursts of

varying liquid density fields are passing through the domain;

however, it does not contain the bulk axial mass flow rate

fluctuations of a three-stream injector.

COMPUTATIONAL METHOD

Mesh and Boundary Conditions

The 360° azimuthal mesh contained 8.3 million

hexahederal cells, and an interior slice is shown in Fig. 1. As

mentioned in the figure, the mesh length scale was around 80

m near the center line in all three dimensions. Each run

required approximately a month on 32 Intel Xeon E5-2643 3.3

GHz cores. Due to industrial sponsor funding limitations, an

axial span of only 0.0635 m was modeled. For validation

purposes, the resulting time-averaged droplet size from this

work will be compared to those of Mansour and Chigier [28]

from much farther away from the nozzle. An estimate will,

therefore, be sought for the droplet size change from a distance

of 0.0635 m (computational measurement location) from the

liquid nozzle outlet to a distance of 0.254 m (experimental

measurement location) from the outlet. Dumouchel [33],

utilizing the work of Shraiber, Podvysotsky, and Dubrovsky

[35], provided an estimate for the critical droplet size of 90 m

above which secondary atomization is likely. A dimensionless

period of oscillation is estimated to be ~0.029 and a

deformation time scale of about 84 s. That gives plenty of

time for more breakup and a final diameter ratio of about 3.3:1.

In other words, a coarse estimate of the droplet size at the

computational measurement location is ~440 m. As a first

approximation, all of this ignores the fact that the presence of

solid particles will make breakup easier for a given viscosity as

described in Zhao et al. [29]

Fig.1: Computational Mesh of the Co-axial Injector

Governing Equations

A subset of the Eulerian-Eulerian methodology is the VOF.

The method is described in detail in the authors' prior works,

but an overview will be given here. The continuity equation

governing the mass balance of each phase is:

0

u

t

(1)

The phase-averaged Reynolds-averaged linear momentum

balance is:

Fguuu

reft p

t

ττ

(2)

It can be seen that the gas and liquid share a common

momentum field, and properties are mass-averaged among the

phase volume fractions present in a cell. With this method, film

formation, ligament production, and droplet onset, as well as

turbulence, are explicitly accounted for. The air density is

assumed constant. Liquid droplet evaporation due to gas

humidity effects has been ignored. Surface energy effects are

treated via the continuum surface force method of Brackbill et

al. [36].

Two groups of turbulence models are compared here. The

first is the shear stress transport (SST) two-equation linear eddy

viscosity model of Menter [37] and is used for computing the

turbulent contributions to momentum such that gradient

diffusion hypothesis has been used to separate the molecular

and turbulent effects in Eq. 2. A homogenous approach is

considered in that only one turbulence field is computed for

both phases. In the SST model, additional consideration is

given to the transport of the principal turbulent shear stress via

1) an eddy viscosity limiting function and 2) a cross diffusion

term in the transport equation for ω. Also, there is a turbulence

production limiter, as discussed in ANSYS [38], preventing the

artificial build-up of fluctuating velocity in regions of

irrotational strain. "Scalable" wall functions, discussed in

ANSYS [38], are an alternative to standard wall functions.

They have the advantage of being less sensitive to variation in

near-wall grid resolution throughout the domain. The distance

of a given computational cell center from the wall is computed

via a Poisson equation with a uniform source value of -1.

The second model compared here is the DHRL approach,

which was introduced earlier and has been documented

thoroughly in the associated references. Additionally, a brief

outline is provided. First, an incompressible version of

equation 2 without body forces is filtered (additional needs

associated with the multiple phases highlighted later) as

(3)

with the turbulent stress (last term, any residual stress) given

below.

(4)

Liquid Inlet Gas Inlet

Cell length scale is

~ 80 m in all

three dimensions.

6 Copyright © 2015 by ASME

Now, a decision has to be made on how the ensemble-averaged

velocity field (Reynolds stress) is bridged with the spatially-

filtered velocity field (subgrid stress). To that aim, the

instantaneous velocity () is decomposed as follows.

(5)

where is the velocity extracted from the simulation in each

cell, is the mean (RANS) velocity, is the resolved

fluctuating velocity, and is the unresolved fluctuating

velocity. Only requires modeling through the stress term.

After substitution, assuming there is no correlation between the

resolved and unresolved velocity fluctuations, and applying

scale similarity, the subfilter stress term becomes that below.

(6)

Taking the coefficients and to be complimentary, the result

is a residual stress that is an -weighted function of the SGS

component and the RANS component. Each individual term on

the RHS of equation 6 is normally a linear function of the SGS

and RANS inputs. A secondary filter operation is applied to

dynamically compute equal to:

(7)

In other words, ranges from 0 in pure RANS regions (no

resolved fluctuations) to 1 in pure LES regions. Again, there is

no explicit grid dependence. It should be noted that the RANS

inputs are computed based a running time-averaged flow field,

and this is appropriate for statistically stationary flows. In

effect, what is occurring is that a time-averaged RANS source

term is being added back into the momentum equation for the

non-LES regions. This is quite different from a typical

URANS model which adds in an ever-adjusting source term

responding to a local stress/strain balance.

In the present work, the DHRL is comprised of SST for the

RANS inputs and MILES for the LES input. The premise of

the MILES (implicit filtering) approach is that dissipative

discretization techniques, such as those available in commercial

codes, filter the flowfield a sufficient amount to represent SGS

turbulent diffusion. Any additional SGS model removes too

much of the higher wave number structures. This concept is

described in Pope [39] and is utilized by Semlitsch [40]. The

risks associated with implicit filtering were discussed by Batten

et al. [41] and Lesieur and Metais [42]. The former group

studied acoustic resonance in a cavity with various LES

approaches. They illustrated that the dissipation in an SGS

model is different from the dissipation introduced purely

through upwinding. Properly formulated upwind introduces

zero shear-stress when the shear is perfectly aligned with the

cell interfaces. They showed that effective viscosity can

suppress pressure oscillations, especially when the separation

characteristics are not defined by the geometry. However, the

use of bounded central differencing (BCD) along with MILES

produces a balanced level of dissipation superior to even the

typical dynamic Smagorinsky approach of Germano [43] as

was shown in Adetokunbo et al. [44]. Additionally, the use of a

hybrid approach, where RANS is used to make up for

unresolved LES turbulence, should help mitigate the

uncertainty associated with implicit filtering.

Since the original, single phase formulation of the DHRL

model assumed incompressible fluids, the model has been

extended to take into account strong density gradients. The

source of these density gradients could be high Mach number

flows of a gas, multiphase flows like those shown here, or

compressible multiphase flows like those in related to the cited

three-stream pulsatile injector work. Initially, the removal of

the aforementioned cross-diffusion term in the SST model was

required. This term is the dot product of dk/dxi and d/dxi. In

shear layers, the alignment of these can provide constructive

feedback and unboundedness in the turbulence model. By

removing this term, the standard k- model is approached. The

RANS portion is invoked mainly in boundary layers, where the

SST switching function would transition to the equation for

the length scale. However, the computational issues which

necessitated this were later resolved.

The second modification was much more entailed and

involved Favre averaging all of the velocity and stress

components so that density changes are correlated with phase

velocity changes. Additionally, the momentum source terms

are time-averaged density weighted. The risks associated with

this can be described as follows. The turbulence is being

generated primarily in the gas phase, but the averaged velocity

field is dominated by the liquid phase since it is a density-

weighted average. There is some evidence from industrial

sponsor testing that this leads to falsely smoothing oscillatory

behavior. Early work before employment of density-weighted

sources with a simple multiphase splitter plate showed no

smoothing, while it will be shown here (and in other

unpublished work) that smoothing may be occurring.

The third change involved how RANS and LES

components are assembled in the individual terms of Eq. 6.

Instead of a linear combination, a harmonic averaging is used,

which favors the lower turbulent viscosity values. The guiding

principle is that the boundary layers are typically going to be

present in the gas (lower viscosity) phase. In other words, what

is important to capture is the momentum diffusivity. If air is on

one side of a face and water on the other, the computed

turbulent (dynamic) viscosity will be much closer to the air.

Lastly, there is some discussion necessary around whether

the multiplier on μt gets applied to cell values or face fluxes

in the momentum source terms. Large cell density gradients

can strongly influence the source terms; if gets applied at

faces, there can be a substantial difference in μt at the different

cell faces, resulting in a very high source term applied even if

the mean velocity gradient is smooth. However, to retain the

conservative nature of the flux balances, face assignment was

pursued.

7 Copyright © 2015 by ASME

Numerics

Equations 1-7 were solved in ANSYS Fluent’s segregated

single precision commercial cell-centered solver version 14.5.7.

The explicit “geometric reconstruction scheme” [45] is used as

the time-marching scheme to solve equation 1 for cell face

fluxes and for interface assembly; a piecewise-linear function

(“PLIC”) is assumed for the shape of the interface across each

cell. This method was rigorously defined and tested in the

authors' prior works. See Strasser [27], Strasser and Battaglia

[46-48], for details on the PLIC and the droplet size analysis

method. A very small time step size of 4.5×10-7 seconds was

required, along with 10 sub-loops, in order to keep the VOF

reconstruction scheme well-posed and the Courant number

below unity. In fact, there are various bases for quantifying CN

according to Menter [49], most of which are less conservative

for this gas-liquid interface-driven system. Pressure-velocity

coupling is coordinated via the Pressure Implicit with the

Splitting of Operators (PISO) scheme with skewness and

neighbor corrections. A Green-Gauss node-based gradient

method is used for discretizing derivatives and is more rigorous

than a simple arithmetical grid cell center average. The pressure

field is treated with the PRESTO! (PREssure STaggering

Option) scheme. PRESTO! uses mass balances to obtain face

pressures, instead of a traditional second order upwinding

scheme, which uses geometric interpolation to obtain face

pressures from cell-centered pressures. This could be beneficial

in areas of high pressure of volume fraction gradient. The

QUICK scheme, which is formally higher than second order

accuracy on structured meshes, was used on the advection

terms for the SST approach, while BCD was used for the

DHRL turbulence model evaluation. First order upwinding was

used for SST turbulence quantities, which were dominated by

source terms. A total variation diminishing (TVD) slope limiter

(not to be confused with flux limiters) termed

“multidimensional” of Kim et al. [50] is considered for the

second order advection schemes. More details, and the

associated references, can be found in ANSYS [38]. Due to the

additional computational load of the DHRL subroutine, the

time-step solution time increases approximately 20%.

RESULTS

Three models will be discussed. The first is based on the

SST model, while the second is a MILES (no SGS model)

solution, and the third is the DHRL (MILES + SST). The

MILES solution is from 26 convective times (CT) worth of

time-averaging, while the DHRL (referred to as “13E”) is from

20 CT. Unless otherwise noted, all contours are taken from the

same center cut mesh plane shown in Fig. 1.

First, typical instantaneous density (directly related to

liquid volume fraction) distributions are highlighted in Fig 2 at

random sampling times among the three models. Here, red

designates liquid, while blue designates gas. There is a much

less restrained momentum field in the DHRL and MILES

models away from the liquid entry point, allowing more energy

for droplet breakup; however, the opposite is true up near the

liquid entry point. The onset of a response to the shear field is

delayed. This makes sense given that the gradient diffusion

hypothesis of SST is not upheld in DHRL or MILES. In terms

of atomization, the effect is a much larger breakup length,

which is the distance that the liquid core is intact. Menard,

Tanguy, and Berlemont [51] studied the primary atomization of

a liquid jet using DNS and found the extent of the liquid core

was shown to be about 7 jet diameters. Others will be

discussed later. Below this liquid core, the droplets get smaller,

and the spray distribution widens. All three models exhibited

this behavior, but they were different. The SST model broke up

into larger scales but very early on. The MILES approach

produced smaller droplets and also very early. This approach

showed a substantial amount of lateral movement relative to the

others, and this will be revisited later. The DHRL approach, on

the other hand, allowed much longer of a time before breakup

and then a mix of droplet length scales. Similarly, the time-

averaged density field is shown in Fig. 3. It can be see that, on

average, the liquid core length increases from left to right.

More about liquid phase ligament/droplet length scale

quantification will be discussed later.

Fig. 2: Instantaneous density contours; red designates

liquid.

Fig. 3: Time averaged density contours; red designates

liquid.

8 Copyright © 2015 by ASME

The relative comparison of instantaneous liquid length

scales is depicted again in in Figs. 4 and 5. Fig. 4 is a front

view of a typical liquid surface outline, similar to Fig. 2 but at

different time stamps. As before, a longer liquid core and

smaller primary liquid fragmentation by the MILES and DHRL

approaches is seen. Fig. 5 illustrates the same time stamp’s

liquid surfaces, except that the view is from the model outlet,

looking back up into the flow. The DHRL appeared to have the

narrowed spray distribution although that is not quantified here.

Fig. 4: Instantaneous liquid surfaces

Fig. 5: Instantaneous liquid surfaces, bottom view of those

in Fig. 4

Figs. 6 and 7 show instantaneous and time-averaged,

respectively, velocity magnitude contours. In both cases, the

contours scale linearly between the colors of blue = 0 m/s and

red = 93 m/s, which is the feed velocity. As expected, the

MILES and DHRL results exhibited a much more spatially

diverse flowfield. Eddy viscosity models are known to diffuse

velocity gradients, and the results corroborate that here. A

much larger range of scales of motion in the MILES, more

similar to those of DNS and LES jet studies, is evident.

Much of the explanation for the slurry breakup behavior

lies in the understanding Fig. 6. As most evident in the MILES

contour set, this two-stream atomization system involves a

wake flow where the liquid core meets the inner gas layer and a

jet flow where the outer gas layer meets the mostly quiescent

outer field. Turbulence of different character is produced in

each of these regions. In the wake, many small scale structures

are produced, while in the jet, larger bulk nearly sinusoidal

shaped waves are produced. The interaction of the two, and

especially the larger scale jet motion, is responsible for the

lateral motion previously discussed. As shown in Fig. 4, the

lateral motion of the MILES case actually creates an area of

liquid discontinuity very early in the breakup process. As will

be shown in upcoming figures of kinetic energy and breakup

length, this lateral motion is too strong. The very thin laminar

layers of velocity gradient (vorticity concentration) produces

too much turbulence and too early. The SST result, on the other

hand, also shows more lateral motion than the DHRL result but

for different reasons. The RANS approach, by design,

computes larger length scales throughout the domain; the lateral

jet energy comes from the wake as much as the jet flow.

Fig. 6: Instantaneous velocity magnitude

(red = feed velocity)

Fig. 7: Time averaged velocity magnitude (red = feed

velocity)

9 Copyright © 2015 by ASME

Fig. 8: Time-averaged turbulent kinetic energy

(red 500 m2/s2)

Fig. 9: Time-averaged turbulent specific dissipation rate

contours (red 1×105 s-1)

In considering DHRL, the jet flow is shown to be much

diffused. There are nearly no structures seen in the outer gas

periphery. This is one reason for the longer liquid core and

brings into question the source of the jet smoothing. Certainly

the incorporation of a hybrid approach is partially responsible.

However, the breakup length is too much retarded. Smoothing

results from either density weighting or from the first order

transient stencil. Based on unpublished work from the authors,

it is much more likely that the transient stencil is responsible

for the jet smoothing. The mandate for using first order in time

is set by an ANSYS solver limitation. More work would be

required to develop and implement a custom higher order

transient scheme.

The time-averaged SST velocity does not look very

different from the instantaneous liquid velocity, implying that

the MILES and DHRL motion scales vary not only more in

space but also in time. This makes sense given that the RANS

approach is already time-averaging, to a large extent, the

various scales of motion. The MILES field is widened after the

initial breakup of the liquid central core, which is consistent

with the increased MILES radial spreading of the spray shown

in Fig. 2. The DHRL solution showed results somewhere in

between the two extremes with a much higher axial penetration

of the mean velocity. An interesting feature of the MILES

result, however, is unexpected striations (axial gradients) in the

time-averaged velocity field of Fig. 7. These striations result

from Favre averaging the velocity field and the “scarring”

caused by passing droplets. The droplets raise the local density,

and many CT are required to wash these gradients out. The

more energetic and dispersed (sparsely passing a single point)

the droplets, the more CT is required for a smooth field. Notice

how 13E has a smooth field after 20CT due to the less energetic

spray.

There is dramatically larger time-averaged turbulent

kinetic energy in Fig. 8 for the MILES approach. Here, blue =

0, while red 500 m2/s2 resulting from too steep of a velocity

gradient without the stabilizing effect of turbulent viscosity.

Fig. 9 illustrates time-averaged contours of specific dissipation

rate over the range blue = 0 to red 1x105 s-1. From this figure,

the main distinguishing feature is the widening of the flowfield

at the end of the MILES liquid core as has been already

discussed.

Further elucidation of the relative comparison between the

two results will be provided in axial plots Figs. 10-15. Each of

these reflects time-averaged and mass flow-weighted area-

averages of a given quantity on 10 evenly spaced planar cross-

cuts. All x-axes are distances normalized by liquid orifice ID.

“13E” utilizes second order upwinding momentum

discretization, while “13D” employs bounded central

differencing. Both incorporate 20 CT of time-averaging. The

lack of differentiation between these two cases illustrates that

the space stencil is not a limiting issue.

The first plot, Fig. 10, quantifies k. As with the contour

plots, a strikingly different k field is present in the MILES

model, so much so that the MILES results are plotted on the

secondary (right) axis. The units are the same. All models

show a generally increasing trend as the shear layers take

energy from the mean flow and add it to the fluctuations. The

DHRL results are like one another, similar to SST, but increase

approximately linearly. Higher turbulence intensities indicate a

wider range of turbulent gas phase length scales and, through

fluctuating Rayleigh-Taylor instabilities, can produce a wider

range of droplet sizes [31].

Axial omega plots are shown in Fig. 11. All models

produce similar trends. Omega peaks at 4 liquid orifice

diameters from the orifice and then generally decreases for SST

and MILES models, but they were fairly smooth for the two

DHRL versions. An estimate for the integral time scale (ITS)

of motion is offered by Fig. 12 with results nearly overlapping

between the SST and MILES models; however, the two DHRL

models produce ITS values about double that of the former.

Liquid breakup occurs on timescales the local ITS, because it

takes time for the instabilities to be communicated throughout

the liquid surface [31]; at higher turbulence intensities

(fluctuating We), ITS is the controlling factor.

10 Copyright © 2015 by ASME

The next two plots are concentrated on the various length

scales present. Fig. 13 shows the estimate for the raw integral

length scale (ILS), while Fig. 14 compares these values to other

scales. Any reference to the ILS implies a local computation of

0.5k1.5/. This is a RANS-based estimate of the a length scale

such that a range of 1/6 ILS to 6 ILS contains 80% of the

energy of motion for an ideal spectrum (Pope [39]). Its

invocation herein is only meant to imply an order of magnitude

estimate for the largest scales of energy (and isotropy)-

containing motion. It is apparent from Fig. 13 that the MILES

solution exhibited much larger length scales. Both the SST and

MILES showed similar increasing trends, while the two DHRL

results are consistently lower. The ratio of this scale to the

mesh length scale is shown in Fig. 14. Davidson [18] discussed

measures “adequate” LES resolution (and making SGS length

scale be a function of magnitude of the resolved strain) says

this ratio should be 10. The MILES solution is in that range

for some of the domain, while the DHRL models showed

values around unity. This implies that, from a laterally

averaged standpoint, mesh resolution may not be ideal;

however, the consistency between the results of 13D and 13E

reminds that the spatial stencil is not a limiting issue.

Additionally, the data down the centerline of the model (not

shown) shows higher ratios for the DHRL models. Moreover,

the ILS is only an order-of-magnitude estimate.

Fig. 10: Time-averaged mass flow-weighted area-averaged

turbulent kinetic energy on 10 evenly spaced cross-cuts.

Fig. 11: Time-averaged mass flow-weighted area-averaged

specific turbulent dissipation rate on 10 evenly spaced

cross-cuts.

Fig. 12: Time-averaged mass flow-weighted area-averaged

integral time scale on 10 evenly spaced cross-cuts

Fig. 13: Time-averaged mass flow-weighted area-averaged

integral length scale on 10 evenly spaced cross-cuts

11 Copyright © 2015 by ASME

Fig. 14: Time-averaged mass flow-weighted area-averaged

ratio of integral length scale to the average mesh length

scale on 10 evenly spaced cross-cuts

Fig. 15: Time-averaged mass flow-weighted area-averaged

ratio of droplet length scale to mesh length scale

Fig. 16: Time-averaged mass flow-weighted area-averaged

ratio of integral length scale to average droplet length scale

Now, attention will be shifted to quantifying the scales of

liquid fragments and droplets, and the results are embodied in

Fig. 15. Instead of the raw data, however, the ratio of droplet

length scale to mesh length scale is given. It is important to

always test and make sure that there are enough cells present to

reconstruct the interface of a droplet or liquid contiguous body.

It has been shown by Herrmann [52] that values ranging from

at least 2 to 6 are sufficient, so both models pass. This depends

on the droplet shapes/curvature as discussed in Strasser and

Battaglia [30]. The raw values at the end of the modeled

domain are given on the plot. Note specifically that the MILES

value of 450 m is close to the adjusted experimental coarse

estimate of 440 m, while the SST value is more than double

that. The use of a differential Reynolds stress turbulence (linear

pressure strain) model resulted in an ending droplet size (not

shown) of around 2/3 of the SST value. It is clear that DHRL

ended up at nearly the same slurry length scale, and the scale

diffusivity (rate of decline, [53]) was much greater after a

longer liquid core delay. Though the ending value was higher

than target, the decay rate implies that the slurry lengths scale

would hit the target only slightly beyond the modeled domain.

In Fig. 16 the ratio of the integral scale of turbulence is

compared to the droplet length scale. For the SST and DHRL

outcomes, the droplet scale was about ten times the integral

scale, but for the MILES result, the two scales are about the

same order. This implies that the droplets would efficiently

directly interact with the turbulent structures for only the

MILES approach.

Early figures displayed the time-averaged volume fraction

contours, giving indication of a continuous liquid core length.

Table 2 shows the expected breakup length values (normalized

by the liquid orifice diameter) from various authors when their

correlations are framed for this geometry and flow conditions.

Lasheras et al. [7] explained that the liquid core length

definition could vary among authors and could be at volume

fraction equal to 0.5. Additionally, it is not clear if authors of

the experimental studies, using frame-by-frame video analysis,

considered liquid cores as being continuous when the liquid jet

was laterally oscillatory and off-centerline. Another issue that

is not discussed in these sources is the fact that the turbulence

intensity (through We fluctuations) can have a strong effect on

breakup length; higher gas intensity values reduce the length

[31]. Even though the primary instability wavelength dictates

ligament sizes, the gas phase turbulence can determine the

ligament forming distance. As a result, there is some

uncertainty in how to directly compare CFD with the

experimental counterpart. Core length will be reported at two

liquid volume fractions, 99.5% and 50%, respectively:

2.70/4.16 (SST), 3.88/5.44 (MILES), and 6.93/14.4 (DHRL). It

is evident that only the DHRL solution comes close to the

expected values. A laminar liquid jet relies on the gas phase

structures and gas boundary layer thickness to deform the liquid

interface [54]. That buffeting then competes with surface

tension for the primary instability mechanism. The liquid feed

Reynolds number is about 4000 (based on the high-shear

12 Copyright © 2015 by ASME

viscosity), making it transitional and the condition of the

boundary layer uncertain. The SST model assumes boundary

layers are everywhere turbulent. Since that is not the case in

the liquid feed, the use of SST likely causes breakup too early.

The DHRL and MILES models produced a more realistic liquid

feed, but the MILES approach had too much kinetic energy.

Only the DHRL model addresses both of these issues, although,

as previously discussed, the lateral motion of the DHRL result

is artificially smoothed.

Table 2: Normalized breakup length estimates from other

correlations

Zhao et al. [29]

7.22

Eroglu et al. [55]

8.74

Engelbert et al. [56]

10.4

Lasheras et al. [7]

6.90

Porcheron et al. [57]

6.67

Leroux et al. [58]

10.9

Matlab routines were written to quantify velocity spectra

using the “Multi-taper method”. A time-bandwidth product of

4, FFT length of the nearest 2n data set size, and Thomson’s

adaptive nonlinear combination were utilized. Experimentation

showed these settings to be the most resolute. Fig. 17 shows

energy spectra from a point 12.5 orifice diameters downstream

of the liquid outlet and about 1.74 orifice diameters off the

centerline for all models (except MILES, which is not

available) at a sampling frequency of 1 million Hz and 214 data

points. The point was placed in the shear zone towards the

outer liquid layer. For reference, the grid wavenumber (/grid

length scale since two cells per period are needed to satisfy the

Nyquist criterion) was on the order of 4×104. The results imply

that not much changes at this particular point with changes in

turbulence model.

Fig. 17: Energy spectra

The time-averaged fraction resolved by LES is depicted in

Fig. 18 for the DHRL model. The blue regions represent areas

using RANS only, while the red regions represent areas using

LES only. Values in between indicate that the solution uses a

blending between RANS and LES. There is a fair amount of

RANS support needed in the interfacial shear layers, indicating

diffusivity there. This diffusivity can be related to the temporal

stencil, time step size, spatial stencil, grid size, and/or or SGS

model (zero in this case). From a cross-sectionally averaging

standpoint, the mesh resolution was likely sufficient. However,

locally, there are areas of sufficient and insufficient resolution.

Additionally, the temporal stencil is based on first-order

upwinding, and that is a current limitation with Fluent. It is

apparent, based on the droplet size analysis that the DHRL

RANS compensation balances these issues.

Fig. 18: Time-averaged (fraction resolved by LES)

contours from DHRL model

Second Case Study

In a similar way as the work of Mansour and Chigier was

mimicked in CFD, the coaxial system of Zhao et al. [29] was

investigated computationally using a similar transient PLIC

method and 360° mesh layout. The mesh element length scale

for the latter work was closer to 120 microns down the

centerline. Two models will be discussed, an SST result and a

MILES result; time did not permit running this with a DHRL

model. Comparisons of mesh, slurry, and integral length scales

13 Copyright © 2015 by ASME

for the SST result can be found in Strasser and Battaglia [30].

Table 3 (SI units) shows important setup information for their

experimental case designated “A1”. The liquid feed to the gas

was laminar-parabolic in the experiment and in CFD. Based on

the work of Farago and Chigier [34], the liquid Reynolds

number (~1, not shown) and Weber number, this disintegration

processed would be termed “Superpulsating” type and would

be characterized to be similar to “Fiber” type, except with

larger waves between major bursts of droplets. If the liquid

flow were larger, it would be more like the Fiber type.

“Superpulsating” should not be confused with the bulk

boundary mass flow variations of the three-stream injector of

the cited works.

A sample energy spectrum for the SST result at a sampling

frequency of 1 million Hz at a point located 2 orifice diameters

below the phase meeting point and half of an orifice diameter

off centerline. The MILES data are not available. For

reference, the grid wavenumber (/grid length scale since two

cells per period are needed to satisfy the Nyquist criterion) was

on the order of 3×104. There appears to be no isolated inertial

range, as most of the lower wavenumbers follow the -5/3 slope.

Table 3: Important quantities and boundary conditions for

study number 2 (Zhao et al. [29] case designated “A1”); All

are in SI units.

Liquid density

1211

Liquid viscosity at reference shear

3.047

Liquid surface tension

0.108

Liquid orifice inner diameter

0.00510

Liquid orifice outer diameter

0.00712

Liquid mass flow

0.00989

Liquid velocity

0.40

Gas density

1.20

Gas viscosity

1.86E-05

Gas orifice inner diameter

0.0149

Gas mass flow

0.0162

Gas velocity

100

Gas to liquid mass ratio

1.64

Weber number

562

Ohnesorge number

3.73

Fig. 19: Energy spectrum from SST model with -5/3 slope

Fig. 20: Instantaneous slurry spray surface

Fig. 20 illustrates instantaneous surfaces of slurry from the

SST and MILES simulations at random uncorrelated times. No

obvious differences arise given there is substantial variability in

time. It appears as though there may be slightly more lateral

motion in the spray for the MILES approach as was seen in the

prior study.

Fig. 21 illustrates instantaneous velocity contours ranged

from blue = 0.0 to red = 100 m/s (gas feed velocity). The rich,

energetic character of developing shear layers is evident. The

fraction of flow field resolved by LES is shown in Fig. 22.

Even though there is no hybrid solution being sought, this

represents a preliminary look at how much RANS support

(shades of blue and green) is necessary. It is evident that most

of the domain is treated with RANS.

14 Copyright © 2015 by ASME

Fig. 21: Instantaneous velocity contours; Red = feed

velocity

Fig. 22: Time-averaged (fraction resolved by LES)

contours from MILES model

Fig. 23: Time-averaged mass flow-weighted area-averaged

ratio of

Laterally averaged slurry length scales versus axial

distance (scaled by mesh length scale) are shown in Fig. 22.

The SST and MILES solution shows similar trends, which

corroborates the prior figure. Clearly, more fluctuating velocity

components does not imply a correct turbulence model as is

noted in Pope [39].

Investigations into the ratio of the integral length scale to

the mesh length scale revealed ratios in the range of 2 (near the

injector) to 3 (far-field), which is similar to the SST values

(prior work). Because this ratio is below 10, adequate LES

resolution is not expected.

In the original paper, the authors discussed the breakup

frequency. For the conditions of the test used herein, their

relations dictated a frequency of 105 Hz. Data were sampled at

various locations throughout the domain, and passing liquid

volume fraction was logged. It was found that the results were

extremely unpredictable, in that massive amounts of run time

would have been required to sequester enough data to make

meaningful liquid passing conclusions at any particular point.

Frequency results ranged from around 10 Hz at one point to

around 400 Hz at another. When comparing the SST

simulation data to the MILES data, there were no consistent

correlations between the two runs. More work would be

needed to asses this. However, it was found that more stable

frequency information could be extracted from droplet size

transient information in the 10 axial sampling volumes. For the

SST run, values were typically about 80 Hz and did not

strongly depend on sampling volume location. For the MILES

simulation, the results were closer to 60 Hz and also did not

strongly depend on sampling volume. This is consistent with

private communications with the authors in which it was

discussed that the frequency was not dependent upon

measurement location except very close to the nozzle. In other

words, the more energetic velocity field of the MILES run

produced less bulk cyclicality in the droplet size burst results.

The smaller length scales in the MILES approach apparently

damped the rate of droplet size temporal variability.

As with the earlier case study breakup length was

investigated. The 50% and 99.5% liquid volume fraction core

length values were 0.87/1.9 (SST) and 1.2/2.0 (MILES). The

experiment reported values of 5.7. Just like the earlier study,

the SST and MILES solutions produced far too low of a

breakup length. It is expected that, similar to above, more

accurate prediction of breakup length may be possible with a

hybrid RANS-LES approach, to be investigated in future work.

CONCLUSIONS

A computational evaluation of a dynamic hybrid RANS-

LES (DHRL) modeling approach was carried out in the context

of the turbulent atomization of a non-Newtonian fluid. Inherent

to this type of flow field are separated shear layers and strong

density gradients. The DHRL offers the advantages of 1) no

explicit mesh dependence, 2) ability to couple any RANS or

LES approach, and 3) return to the baseline RANS model for a

numerically steady simulation. The framework utilizes the

15 Copyright © 2015 by ASME

continuity of turbulence production to communicate

information between areas treated with LES and those treated

with RANS and has been validated for single phase flows in

prior works. The purpose of this work was to enhance the

model for use with multiphase flows and then compare its

performance to the well-known shear-stress transport (SST).

DHRL shows a much smaller droplet size distribution with

values in close agreement with the referenced experiment.

Additionally, the jet breakup length is closer to what is

expected from the open literature. For differing reasons, the

SST and implicit LES approaches, separately, produced too

short of a liquid core. There was some evidence that turbulence

via local instabilities was being suppressed by Favre averaging

and density-weighted sources. It is unknown, however,

whether this was a modeling flaw or diffusion due to a first

order transient stencil. To be certain of the applicability and

accuracy of the proposed modeling paradigm, more data would

have to be available for comparison. An interesting

consideration is the unknown effect that the hybrid modeling

will have on bulk pulsations of three-stream unknown, i.e. bulk

boundary feed pulses versus local instabilities.

ACKNOWLEDGMENTS

The support of a multitude of Eastman Chemical Company

personnel is greatly appreciated. Specifically, George

Chamoun and Jason Goepel deserve special recognition for

processing transient signal data sets using various methods.

Additionally, discussions with Mihai Mihaescu from Royal

Institute of Technology (KTH), Marcus Herrmann from

Arizona State University, David Schmidt from the University of

Massachusetts, Mario Trujillo from University of Wisconsin–

Madison, Daniel Fuster of Institut Jean Le Rond D'Alembert

UPMC, and Christophe Dumouchel of Université et INSA de

Rouen were extremely beneficial.

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