SPH Simulation of a Twin-Fluid Atomizer Operating with a High Viscosity Liquid

Conference Paper · August 2015with128 Reads
DOI: 10.13140/RG.2.1.4320.7128
Conference: ICLASS 2015, the 13th Triennial International Conference on Liquid Atomization and Spray Systems, At Tainan, Taiwan
Abstract
A Smooth Particles Hydrodynamics (SPH) 2D simulation of a twin-fluid atomizer is presented and compared with experiments in the context of bio-fuel production. The configuration consists in an axial high viscosity liquid jet (µ l ≈ 0.5 Pa.s) atomized by a coflowing high-speed air stream (u g ≈ 100 m/s) at atmospheric conditions, and the experiment shows two types of jet instability (flapping or pulsating) depending on operating conditions and the nozzle geometry. In order to capture the 3D effects of the axial geometry with a 2D simulation, the surface tension force and the viscosity operator are modified. The mean and RMS velocity profiles of the single phase simulations show a good agreement with the experiment. For multiphase simulations, despite a qualitative good agreement, the type of instabilities as well as its frequency are rarely well captured, highlighting the limitation of 2D geometry in the prediction of 3D configurations.
1 Figures
ICLASS 2015, 13th Triennial International Conference on Liquid Atomization and Spray Systems, Tainan, Taiwan, August 23–27, 2015
SPH Simulation of a Twin-Fluid Atomizer Operating with a High Viscosity Liquid
G. Chaussonnet*,1, S. Braun1, L. Wieth1, R. Koch1, H.-J. Bauer1
A. Sänger2,3, T. Jakobs2, N. Djordjevic2, T. Kolb2,3
Karlsruher Institut für Technologie (KIT), Karlsruhe, Germany
1Institute of Thermal Turbomachines, KIT Campus South
2Institute of Technical Chemistry, KIT Campus North
3Engler-Bunte-Institute, KIT Campus South
*geoffroy.chaussonnet@kit.edu
Abstract
A Smooth Particles Hydrodynamics (SPH) 2D simulation of a twin-fluid atomizer is presented and compared with
experiments in the context of bio-fuel production. The configuration consists in an axial high viscosity liquid jet
l0.5 Pa.s) atomized by a coflowing high-speed air stream (ug100 m/s) at atmospheric conditions, and the
experiment shows two types of jet instability (flapping or pulsating) depending on operating conditions and the
nozzle geometry. In order to capture the 3D effects of the axial geometry with a 2D simulation, the surface tension
force and the viscosity operator are modified. The mean and RMS velocity profiles of the single phase simulations
show a good agreement with the experiment. For multiphase simulations, despite a qualitative good agreement, the
type of instabilities as well as its frequency are rarely well captured, highlighting the limitation of 2D geometry in
the prediction of 3D configurations.
Keywords: Numerical simulation, atomization, viscous fluids, air-assisted atomizer, SPH
Introduction
Recent predictions estimate the depletion of coal, oil and gas to year 2040, 2112 and 2042, respectively [1],
which leaves approximately thirty years to find alternative and sustainable energy sources. The Bioliq®process
(Fig. 1) proposes a solution based on the refinement of agricultural residuals, decoupled in two steps: (i) a de-
centralized stage where the biomass (mainly straw) is refined via fast pyrolysis in a compound of higher energy
density called bioSyncrude®, and (ii) a centralized stage that converts bioSyncrude®into synthetic gas (Syngas) at
high temperature (TG1500C) and pressure (PG= 80 bars). Syngas is finally transformed to methanol, motor
fuel [2] or even gas [3].
Biomass bioSyncrude®Syngas Synfuel
EFG
Gas
Gasoline
Diesel
Decentralized process Centralized process
Raw gas
Figure 1 The Bioliq®process
At the first stage of the centralized process, bioSyncrude®is turned into a spray in a so-called Entrained Flow
Gasifier [4] (EFG, depicted in Fig. 1) operating at PG, through an air-assisted atomizer: the axial liquid jet of
bioSyncrude®is sheared by a coaxial gas stream flowing at high velocity. Due to chemical equilibrium require-
ments, the Gas-to-Liquid Ratio (GLR), expressed as ˙mg/˙ml, should be in the range 0.5 to 0.8 for a typical biomass
based fuel, which limits the amount of atomizing material. In addition, the bioSyncrude®has a very large viscosity
(10 Pa.s at low temperature in the low shear range) and a non-Newtonian behaviour. These constraints have a
strong influence on the atomizing process, and the nozzle must be carefully designed in order to optimize the spray
generation.
In this paper, the numerical simulation of a simplified nozzle supplied with a viscous Newtonian fluid is compared
to experiments [5], in terms of gas velocity profiles and liquid instabilities frequency. The employed numerical
approach is Smooth Particle Hydrodynamics (SPH), a method originally developed for astrophysics [6] and later
adapted to free surface flow [7], especially when the gas phase can be neglected. In the field of air-assisted liquid
atomization, the gas/liquid momentum transfer is the driving phenomenon so that both phases (of large density and
viscosity ratio) must be accurately resolved. This particular context constitutes an original use of the SPH method
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ICLASS 2015, 13th Triennial International Conference on Liquid Atomization and Spray Systems, Tainan, Taiwan, August 23–27, 2015
that was initiated by Höfler et al. [8, 9].
The experimental setup and its main observations are presented in the next part, followed by a description of
the SPH method and the modifications added in this particular configuration. The results of the single phase and
the multiphase 2D simulations will be presented in the fourth and fifth part, and a final conclusion will end the
paper.
Experiment
In order to have a deeper insight into the atomization process occurring in the EFG, Sänger et al. [5] studied the
fragmentation mechanism of a viscous fluid in a twin-fluid external mixing atomizer at atmospheric pressure and
temperature conditions. It consists in an axial liquid jet sheared by a co-flowing high speed gas stream discharging
into an open and quiescent atmosphere.
DlDg
Hg
es
Figure 2 Schematics of external mixing twin fluid atomizer with parallel streams (left) and angle (right) nozzle.
Geometrical parameters (middle) are detailed.
Two different nozzles were studied: (i) both gaseous and liquid streams are parallel (Fig. 2 left) and (ii) the gas
stream has an incident angle of 30(Fig. 2 right). In both configurations, the liquid diameter Dland the gas height
Hgare equal to 2 and 1.6 mm respectively. In the parallel configuration, the separator thickness esand the gas
diameter Dgare equal to 0.1 and 5.4 mm respectively and to 0.5 and 6.2 mm in the angle configuration. Although
several types of liquid were experimentally investigated, only two types of Newtonian liquid (L1 and L2) of differ-
ent viscosity are discussed here. Their physical properties, as well as the gaseous ones, are summarized in Table 1.
Fluid type Density Dyn. viscosity Surface tension Mass flow rate Bulk velocity
ρ[kg/m3]µ[Pa.s] σ[N/m] ˙m[kg/h] U [m/s]
L1 1233 0.2 0.0646 10 0.717
L2 1236 0.3 0.0643 10 0.713
Gas 1.2 1.73 10-5 - 4 - 8 54.9 - 107.8
Table 1 Physical properties of investigated fluids in atmospheric conditions.
The non-dimensional numbers that characterize this configuration are:
Re = DhU
ν,We = ρgDlU2
rel
σ,Oh = µl
Dlρlσ,GLR = ˙mg
˙mg
,M = ρgU2
g
ρlU2
l
(1)
Equation (1) shows, in order of appearance: the Reynolds number where Dhis the hydraulic diameter equal to
Dliq for the liquid and 2Hgas for the gas, the Weber number where Urel is the liquid/gas relative velocity, the
Ohnesorge number, the Gas-To-Liquid ratio, and the momentum flux ratio.
The test rig was instrumented with Laser Doppler Anemometry (LDA) for gaseous velocity measurement on ver-
tical line at x= 1.6 and 1.4 mm for the parallel and angle nozzle respectively, and the liquid instabilities were
recorded with a high-speed camera at a sampling frequency of 1200 Hz and with a pixel size of 143 µm. The time
series were then post-processed by Proper Orthogonal Decomposition (POD) in order to extract the frequency and
the wavelength of the instabilities. It was also observed that the jet undergoes different types of instability depend-
ing on the liquid viscosity and the GLR as illustrated in Fig. 3, leading to two different spray characteristics [5]. A
pulsating mode is observed and consists in a longitudinal and axisymetric mode triggered by a Kelvin-Helmholtz
instability. Approximately five diameters downstream, the jet disrupts into a non-axisymetric structure composed
of bags and ligaments (Fig. 3a). A flapping mode is characterized by an deflection in the radial direction, in the
early stage of the jet at approximately two diameters after the nozzle exit (Fig. 3b). The objective of the numerical
simulation is to predict the onset of these modes at the right operating conditions.
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ICLASS 2015, 13th Triennial International Conference on Liquid Atomization and Spray Systems, Tainan, Taiwan, August 23–27, 2015
Figure 3 Side and oblique view of primary instabilities of a liquid jet with different dynamic viscosities at
GLR = 0.4. (a) pulsating mode at µl= 200 mPa.s and (b) flapping mode at µl= 300 mPa.s, from [5]
Numerical Model
SPH Formalism
The SPH method is a mesh-free method that relies on a Lagrangian description of the fluid through particles
moving at the fluid velocity and carrying physical properties such as mass, volume, momentum and energy.
The starting point of the SPH discretization is the convolution of a field f(r)by a Dirac function δ(r):
f(r) = Zf(r)δ(rr) dr(2)
In order to apply Eq. (2) to discrete particles, the Dirac function is replaced by a smooth interpolation function
W(rr,h)called the kernel and depicted in Fig. 4 (top). This function is defined on a compact support, the
so-called sphere of influence that depends on the smoothing length h, and must fulfill mathematical properties such
as the unity integral (RW(rr,h)dr= 1) and the convergence to δwhen h0. The kernel is chosen here
as a quintic spline and h= 3∆xwhere xis the mean particle spacing. The function fis thus expressed at the
particle location raby:
f(ra) = X
b
Vbf(rb)W(rbra, h)(3)
where Vbis the volume of particle b. The index brefers to neighbour particles located in , the sphere of influence
of the particle a, as illustrated in Fig. 4 (bottom). For the sake of clarity, in the following, f(ra),f(rb)and
W(rbra, h)are shortened to fa,fband Wab, respectively.
Figure 4 Bottom part: particle distribution superimposed with the kernel value and illustration of the sphere of
influence. Top part: surface of a 2D kernel
The differential operators needed to evaluate the contact forces such as pressure, viscosity and surface tension
are computed with the gradient of the kernel. The gradient [10] faand the Laplacian [11] faare expressed as:
fa=X
b
Vb(fb+fa)Wab and ∆fa= 2 X
b
Vb(fbfa)∂Wab
∂r (4)
Governing Equations
The Navier-Stokes equations are turned to a SPH form. The flow is considered isothermal so that the energy
equation can be neglected. The continuity equation is solved algebrically by computing the particle volume and
density:
Va= 1/X
b
Wab and ρa=ma/Va(5)
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ICLASS 2015, 13th Triennial International Conference on Liquid Atomization and Spray Systems, Tainan, Taiwan, August 23–27, 2015
where mais the constant mass of particle a. Equations (5) exactly conserve mass and as it relies only on the
particle volume, the density expression avoids numerical diffusion of density near the liquid/gas interface. The
momentum equation is given by:
ρa
du
dt
a
=fa,p +fa,v +fa,st (6)
where uis the particle velocity and the terms fp,a,fv,a and fst,a are the forces due to pressure, viscosity and
surface tension, respectively. They write:
fa,p =X
b
Vb(pb+pa)Wab ,fa,v =KX
b
Vbµuab ·rab
r2
ab +η2Wab and fa,st =σaκ(·n)n(7)
The expression of the pressure term conserves the linear momentum locally by ensuring Fab =Fba where
Fab =VaVb(pb+pa)Wab is the elementary force that particle bexerts on particle a. Although the accuracy
of this expression is significantly reduced by particle disorder [12], it artificially creates a term proportional to the
background pressure that avoid "holes" of particle during the simulation.
The expression of the viscous term is a SPH form of the velocity Laplacian (µ∂u/∂x)/∂x. It exhibits the
prefactor Kequal to 8 in 2D [13], the inter-particle viscosity µderiving from a density-based average µ=
(ρaµb+ρbµa)/(ρa+ρb). It also invloves the scalar product of velocity difference uab =uaubby the
inter-particle distance vector rab =rarb. The term η= 0.1havoids the singularity when r2
ab = 0.
In the surface tension force, σais the surface tension at particle aand κis the interface curvature. The terms nand
(·n)are the interface normal and its divergence, respectively, computed with the method proposed by Adami
et al. [14].
To close the system, the pressure is expressed through a Tait state equation that depends on the particle density
only:
pa=ρ0c2
γρa
ρ0γ
1+pback (8)
where ρ0is the nominal particle density and γis the polytropic ratio that controls the stiffness of the pressure: due
to the term (ρa0)γ, the pressure varies more intensively with regards to density variations when γis larger. Note
that γintervenes directly in the compressibility βof the fluid, defined by β= (∂ρ/∂p)at constant entropy:
inverting Eq. (8) leads to β= [γ(ppback) + ρ0c2]1so the larger γthe lower the compressibility.
The term cin Eq. (8) is the fictive speed of sound and must be chosen to verify c>10 umax in order to fulfill the
weakly compressible condition by ensuring that density variation is lower than 1% [15], the final purpose being to
increase the time step through the CFL condition. In the present configuration, the liquid and gaseous real Mach
numbers are of different orders of magnitude, inducing different type of flow. With a velocity of the order of
magnitude of 1 m/s, the liquid Mach number is 10-3 so that setting the fictive liquid speed of sound clto 50 m/s
is appropriate. As a lower speed of sound increases the compressibility, it is necessary to increase γfor the liquid,
so γlis set to 7. On the contrary, in the gas phase, the Mach number is 0.3 and the flow is compressible. The
gaseous sound speed is therefore set to its real value (340 m/s in the experiment conditions) and γgis set to 1, so
that Eq. (8) yields pa,g =c2
g(ρaρ0) + pback.
Finally the background pressure pback is added in Eq. (8) to ensure that pressure is always positive. Additionally,
pback controls the stiffness of the pressure gradient: rewriting Eq. (8) as p=δp +pback and injecting it in Eq. (7)
leads to:
fa,p =X
b
Vb(δpb+δpa)Wab 2pback X
b
VbWab (9)
where the second term of the RHS, proportional to pback, is the artificial part of the pressure gradient that avoids
holes formation in the lattice.
Three Dimensional Terms
As the simulations conducted in this paper are 2D, two modifications are added to the numerical method to
represent the 3D effects of the experiment. First, in order to take into account the curvature of the round jet
interface, an artificial surface tension force fa,curv is added to the momentum equation:
fa,curv =ǫxǫy
σa
|y|(·n)nwith ǫy= 1 exp y2
h2and ǫx=1x
Lc0.2
(10)
where yis the radial coordinate and ǫya damping function to avoid the singularity at y= 0. The function ǫx
ensures that far from the nozzle, when the jet is fragmented in small droplets, the artificial surface tension force is
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ICLASS 2015, 13th Triennial International Conference on Liquid Atomization and Spray Systems, Tainan, Taiwan, August 23–27, 2015
zero. It is defined between 0 and Lc= 4 Dl, and is equal to zero otherwise.
The second modification is to adapt the particularities of vectorial operators expressed in a cylindrical system to
their Cartesian expressions, in order to take into account the divergence of the fields with y(rin the cylindrical
system). The comparison between Cartesian (x,y)and cylindrical (r,z)coordinates show no difference for the
gradient operator whereas the Laplacian differences yield, for the velocity:
CYL(Ur) = ∆CART (Uy) + 1
y
∂Uy
∂y Uy
y2(11)
CYL(Uz) = ∆CART (Ux) + 1
y
∂Ux
∂y (12)
The Laplacian operator, used for viscosity, is thus modified according to Eqs (11) and (12), the additional terms
being also multiplied by ǫy(Eq. 10) to avoid the singularity at y= 0. Physically, these modifications render the
difference of the shearing surface between the inner and the outer radius of an infinitesimal element. This differ-
ence is particularly significant at small radius (terms in "1/y").
Note that the modifications do not aim to model an axisymmetric domain but only the center slice of an axial
configuration, so that it is not necessary to modify the computation of density.
Geometry and Boundary Conditions
The numerical domain depicted in Fig. 5 is composed of the inlet ducts and the cavity (length of 40 mm)
where atomization takes place. The length of inlet ducts are seven diameters for the gas and three diameters for
the liquid and the inlet velocity profiles are turbulent and laminar, respectively. A no-slip boundary condition is
imposed at the walls of the inlets duct and the nozzle. In order to reproduce the entrainment rate ˙
Qeinduced by
the gaseous jets, the cavity is fed with a coaxial gas stream with a bulk velocity ueover a slit of height He= 6.67
mm. This ensures a proper entrained volume flow rate up to x= 10 mm such as (ueHe) = ˙
Qe(x=10 mm), and
lead to ue0.15 U. The restriction of the distance to 10 mm is to avoid a too large uethat could perturb the
atomizing gas streams. On the sides of the cavity, the velocity is mainly axial due the entrainment flow, and the use
of an outflow boundary condition would generate a strong numerical noise. Therefore, the cavity sides are set to
slipping walls and they slightly open (semi-angle of 10) to mimic the free jet opening after the nozzle. The outlet
is set to a constant pressure equal to pback.
Gas inlet
Liquid inlet
Entrainment inlet
Slip wall
No-slip wall
Outlet
Probes location Velocity profile location Probes location
Velocity profile location
Figure 5 Sketch of the numerical domains and zoom on the nozzle exit. Left: parallel nozzle. Right: angle nozzle
Test Cases
Single-phase simulations assess for the accuracy of the SPH method when modeling low viscosity fluids such
as air. Two different mass flows are tested on both nozzles. With the parallel nozzle, multiphase simulations are
conducted to verify that 2D SPH can capture the pulsating mode at two different mass flows, and with the angle
nozzle, the transition pulsating/flapping is studied by varying the gaseous mass flow and the liquid viscosity. All
test cases are summarized in Table 2 where bold letters indicate how the case names are constructed.
Results and Discussion of Single-Phase Simulations
Figure 6 shows a velocity profile comparison, for the angle and parallel nozzle at two gaseous mass flow rates.
The mean and RMS values are displayed for the axial (u) and radial (v) component. Note that as the radial compo-
nent is Cartesian, it can have negative values. The simulations are averaged over 1000 snapshots regularly sampled
over 18 convective times based on the cavity length.
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ICLASS 2015, 13th Triennial International Conference on Liquid Atomization and Spray Systems, Tainan, Taiwan, August 23–27, 2015
Name [-] PG6 PG8 PL4 PL6 PL8 AG4 AG6 AL1M4 AL1M5 AL1M6 AL2M4 AL2M5 AL2M6
Nozzle [-] PAR PAR PAR PAR PAR ANG ANG ANG ANG ANG ANG ANG ANG
Liq. type [-] Gas Gas L1L1L1Gas Gas L1 L1 L1 L2 L2 L2
˙mg[kg/h] 6 8 4 6 8 4 6 4 5 6 4 5 6
Ug[m/s] 81.9 107.8 54.9 81.9 107.8 54.9 81.9 54.9 68.5 81.9 54.9 68.5 81.9
GLR [-] - - 0.4 0.6 0.8 - - 0.4 0.5 0.6 0.4 0.5 0.6
Reg[×1000] 18.3 24.1 12.3 18.3 24.1 12.3 18.3 12.3 15.3 18.3 12.3 15.3 18.3
We [-] - - 175 393 684 - - 175 274 393 176 274 395
M[-] - - 5.72 12.7 22.1 - - 5.72 8.91 12.74 5.76 8.96 12.81
Table 2 Test-case matrix
For the angle nozzle, the mean values are in good agreement with the experiment for the two mass flows but
(i) ushows a too smooth profile, possibly due to the lack of turbulence model, and (ii) the extrema of vare slightly
over-predicted, resulting in too opened jet. The predicted uRMS show peaks at the right yposition but they are
smoother than experimental results, highlighting more widespread fluctuations. The model cannot capture the cen-
tral peak, probably due to the too large jet opening. The radial RMS velocity is slightly unsymmetrical and predicts
a too large peak in the center for AG6. The same comments are valid for the parallel nozzle with the difference
that (i) uextrema are slightly over-predicted, (ii) the jet is even more opened and (iii) uRMS is predicted with the
right intensity, except for the central peak.
Concerning the axial velocity, the good predictions of its mean and the acceptable levels of its RMS in the air
20
0
20
40
60
80
100 AG6
40
20
0
20
40
0
5
10
15
20
25
30
35
40
3210 1 2 3
y [mm]
0
5
10
15
20
25
30
40
20
0
20
40
60
80
100 PG6
20
15
10
5
0
5
10
15
20
25
0
5
10
15
20
25
30
35
40
3210 1 2 3
y [mm]
6
8
10
12
14
16
18
20
22
20
10
0
10
20
30
40
50
60
70
u[m/s]
AG4
30
20
10
0
10
20
30
v[m/s]
Exp.
0
5
10
15
20
25
30
uRMS [m/s]
3210 1 2 3
y [mm]
3
4
5
6
7
8
9
10
11
vRMS [m/s]
50
0
50
100
150 PG8
40
20
0
20
40
Sim.
5
10
15
20
25
30
35
40
3210 1 2 3
y [mm]
5
10
15
20
25
Figure 6 Mean and RMS profiles of axial and radial velocity, at x= 1.6 mm and 1.4 mm for the parallel and angle
nozzle, respectively. Experiment: , simulation:
stream region ensure that the gas will shear the liquid with the right average and fluctuating intensity. As the radial
velocity is more difficult to capture, it can be expected that the dynamic pressure felt by the liquid interface (ρgv2)
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ICLASS 2015, 13th Triennial International Conference on Liquid Atomization and Spray Systems, Tainan, Taiwan, August 23–27, 2015
will slightly deviate from reality, especially in terms of fluctuations, possibly leading to an earlier destabilization
of the jet.
Results and Discussion of Multiphase Simulations
Table 3 summarizes the instability modes observed in experiment and simulation. For the parallel nozzle, the
simulation capture a transition between a sinusoidal pulsating mode (phase shift ϕ=πbetween top and bottom
probes) and a flapping mode, while experiments only show a varicose pulsating mode (ϕ= 0). Cases PL4 and
PL6 can be compared to the experiment in terms of frequency while PL8 simulation is purely flapping. With the
angle nozzle and liquid L1, experiment show a pulsating mode while simulations only predict a flapping mode,
preventing further quantitative comparisons. With the liquid L2, flapping modes in both the experiment and the
simulation are observed, but with an opposite trend with increasing gas velocity. Nevertheless, a quantitative
comparison is achieved for L2 in the following.
Case PL4 PL6 PL8 AL1M4 AL1M5 AL1M6 AL2M4 AL2M5 AL2M6
Exp. Puls. Puls. Puls. Puls. Puls. Puls. Flap. Flap. Puls./Flap.
Sim. Puls. Puls./Flap Flap. Flap. Flap. Flap. Puls./Flap. Flap. Flap.
Table 3 Observation of instability modes
Figure 7 compares experimental and simulated time series, for one case of each geometry. For PL6 (Fig. 7a-
c), similar structures are observed: a central liquid core right after injection of length 2Dlthat further disrupts
into finner ligaments. However the time series of PL6 shows a behaviour closer to flapping than pulsating, and
the second instability stage (p1) is tilted due to flapping while it remains axially oriented in the experiment. In
addition, when the liquid bubble bursts (bag breakup), the atomized droplets are ejected axially in the experiment
whereas radially in the simulation, due to the flapping motion (arrow in Fig. 7c). The AL2M5 case (Fig. 7d-f )
shows a proper flapping mode with a predicted flapping frequency qualitatively close to the experiment. In this
configuration, the second stage of the liquid core (p2and p3) is tilted in the simulation.
a) time = 0 ms b) time = 0.922 ms c) time = 1.923 ms
EXP. SIM.
d) time = 0 ms e) time = 0.587 ms f) time = 1.161 ms
p1p1
p2p2p3
p3
5 mm
Figure 7 Comparison of experiment/simulation time series for PL6 (a,b,c) and AL2M5 (d,e,f)
Figures 8aand 8bdepict the frequency fversus the gas mass flow rate, for the pulsating mode with the parallel
nozzle (a) and for the flapping mode with the angle nozzle with liquid L2 (b). Experimentally, the frequencies were
calculated by POD while in the simulation, they were computed from probes recording the liquid presence at the
location defined in Fig. 5. Several interspectra were computed via FFT and the frequency of largest intensity was
kept. The error bars in Fig. 8 correspond to the frequency resolution of the FFT. For the parallel nozzle (Fig.
8a), the frequency fpincreases with the gas mass flow rate as in experiments, but the linearity (fp˙m) is not
recovered, and two points may be not sufficient to endorse the validaty of the present linear regression. With the
angle nozzle (Fig. 8b), the trend is also recovered but the linear regression does not show a purely proportional
depency, due to a non-zero y-intercept (y=a x +bwith b6= 0). Figure 8cshows the velocity ucof the wave
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ICLASS 2015, 13th Triennial International Conference on Liquid Atomization and Spray Systems, Tainan, Taiwan, August 23–27, 2015
propagation on the interface directly downstream the injection and the associated wave length λfor PL6. The
velocity ucis computed by measuring the time difference tbetween two consecutive probes separated by x.
The velocity is then x/tand the wavelength λis equal to the ratio of the velocity by the peak frequency fp
according to λ=uc/fp. The prediction of ucshows an appropriate order of magnitude but its dependence on ˙m
is not clearly defined due to a strong uncertainty, while λis acceptably predicted with PL4 and underpredicted for
PL6.
4 5 6 7 8
˙m[kg/h]
200
300
400
500
600
700
f [Hz]
a)
Experiment
Simulation
4.0 4.5 5.0 5.5 6.0
˙m[kg/h]
200
300
400
500
600
700
800
900
f [Hz]
b)
Experiment
Simulation
45678
˙m[kg/h]
1.0
1.5
2.0
2.5
3.0
3.5
4.0
uc[m/s]
c)
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
λ[mm]
Figure 8 Comparison of experiment/simulation, a) pulsating frequency with the parallel nozzle, b) flapping fre-
quency with the angle nozzle and L2. On plot c), and represent ucfor experiment and simulation respectively,
while #and
represents λfor experiment and simulation respectively.
Conclusion
The 2D numerical simulation of a twin fluid atomizer with SPH method showed that the gaseous flow was
acceptably predicted on a two-dimensional domain, in terms of mean and RMS velocity profile. When considering
the multiphase configuration, the simplified 2D approach has shown strong limitations, despite the 3D modifi-
cations of the surface tension force and the viscosity. This emphasizes that in this particular configuration of
air-assisted atomization, the prediction of an appropriate gaseous shear stress is not sufficient to guarantee a proper
liquid behaviour. The modes of instability are not well captured and predictions even show an inverted pulsat-
ing/flapping transition with gas mass flow rate in case of angle nozzle with liquid L2. However when simulations
and experiments have the same mode, the time series show a qualitatively good agreement in terms of shape and
structure of the ligament, and the predicted frequencies have comparable values with the experiment. Finally the
wave velocities and the associated wavelengthes show the right order of magnitude but the trends are not well cap-
tured. In the optic of accurately capturing the transition of instability modes and their associated values (frequency
and wavelength) with SPH method, it is thus necessary to compute a 3D domain.
Acknowledgement
This work was performed on the computational resource ForHLR Phase I funded by the Ministry of Science,
Research and the Arts Baden-Württemberg and DFG ("Deutsche Forschungsgemeinschaft").
References
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8
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  • Progress of theoretical physics. F Maciá, M Antuono, L M González, A Colagrossi. 2011.1091-1121.
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