AIAA-2010-215

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American Institute of Aeronautics and Astronautics1

On the Modeling of a Spray Impinging on a Surface

A. R. R. Silva1 and J. M. M. Barata2

Universidade da Beira Interior, Covilhã, 6200-001,Portugal

The present paper reports a numerical study of a spray impinging on a surface through a

crossflow and is aimed at studying the fundamental aspects of the spray impingement

phenomena in a three-dimensional configuration, which is relevant to practical engines.

Different impinging models were used and the results are compared with measurements and

predictions of other authors. The results show a general good agreement with the

experiments, and reveal that the splash droplets are very important for the spray

development. The performance of droplet impinging models depends strongly on the

conditions of pre-impingement.

Nomenclature

c f = friction coefficient

d = generic diameter of a droplet

d 32 = Sauter Mean Diameter (SMD)

d V = volumetric mean diameter E K = droplet kinetic energy

E σ = droplet surface energy

E D = dissipation energy H = height of wind tunnel

h f = height of film disc

K = splashing/deposition dimensionless parameter

k = turbulent kinetic energy La = Laplace number

m = mass

N S = total number of secondary droplets

ni = number of droplets each parcel

Oh = Ohnesorge number p = number of secondary parcels

Re = Droplet Reynolds number

r = droplet radius

r m = mass ratio

t e = lifetime of an incident dropletV = velocity

W = horizontal velocity component

We = Weber number

ε = turbulent kinetic energy dissipation rate

δ = non-dimensional wall film thickness;

ρ = density

∀ f = volume of the fluid when the droplet is flattened out in the shape of a discσ = surface tension

µ = kinematic viscosity

φ = azimuthal angle

θ S = ejection angle of secondary droplets

1 Assistent Professor, Aerospace Sciences Department, Rua Marques Avila e Bolama, Member of AIAA.2 Full Professor, Aerospace Sciences Department, Rua Marques Avila e Bolama, Associate Fellow of AIAA.

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition4 - 7 January 2010, Orlando, Florida

AIAA 2010-215

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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Subscripts

a = after impactb = before impact

c = critical valuewf wall film I incoming droplet or incident droplets

in injection point

N normal componentsS splash or secondary droplets; refer to surface conditions

T tangential components

I. Introduction

HE present work is devoted to the turbulent dispersion and spray impinging on a solid surface, which have

major importance in systems optimization and performance. Sprays studies have had in the last decades high

interests due to its applications in industry, agricultural, science and medical purposes. In the past scientists have

been studying intensively spray properties trying always to achieve the best model, even for comparison, for thecorrect application.

The spray combustion application has been a concern due to pollutants particles limitations which affect our

society nowadays. Therefore, efforts are being made to improve direct injection gasoline engine performance

lowering nitrogen oxide emissions ( NOx) and other pollutants from aircraft gas turbine engines1. Other pollutants

are carbon oxide, carbon monoxide, soot and unburned hydrocarbons2. Spray optimum conditions for better

combustor performance are not yet completely clear so it’s perfectly understandable that it affects combustionstability, efficiency and pollutant formation. Aerodynamic efficiency of redistribution and fuel and air mixing in

combustion chamber, the desired temperature level and proper temperature profile are important factors for

combustion quality and generated emissions levels. Due to the uncertainty of the most favorable spray conditions tooptimize the combustor performance all empirical findings have been difficult to generalize or extrapolate.

Therefore, prediction methods based on theoretical basis are needed and expected hoping to achieve reliable

methods for computer aided design of engines, fuel burners, etc.

Spray-wall interaction is considered important phenomena in internal combustion engines (IC). In an attempt to

achieve desirable air-fuel mixing and combustion, the fuels are sprayed in either the carburetor, port, pre-chamber,or directly in cylinder. In all these designs, the fuel spray may impinge on engine surfaces before vaporization and

mixing are complete. Spray impingement has been shown to influence engine performance and emissions in both

compression ignited (CI) and spark ignited engines (SI).A better understanding of these interactions between the liquid and induction surfaces will help in designing

injection systems and control strategies to engine performance and to control emissions.

Spray impaction phenomena is difficult to analyze in operating engines because of the problems of access,

although useful information can be obtained by, for example, photographic techniques in specially adapted engines3.However, the details of the data that can be obtained in this way are very limited, and it is difficult to alter the test

conditions. For these reasons, most of the recent experimental investigations of impacting sprays have been

conducted in specially constructed test rigs or bombs. To make the analysis of results as simple as possible, the

"wall" on which the spray is impacted is often a flat plate. Both normal and oblique impaction has been studied in

this way4,5

. Some experiments have also attempted to simulate the effect of swirling flows in engines by

incorporating a cross-flowing gas into the rig6. Hence, it is extremely difficult to measure droplet size and velocitydistributions in the near-wall region. Computational modeling offers a promising alternative for the purpose of

obtaining detailed information on spray impingement characteristics. The first experimental scientific investigationsinto certain aspects of drop impact were then conducted by Tomlinson7,8, Worthington9,10,11, Thompson and Newall12

in the second half of the nineteenth century. While the first droplet wall interaction model was proposed by Nabber

and Reitz13 in the end of the last century. In their model an impinging droplet is assumed to stick on the wall in a

spherical form (“Stick” model), reflect elastically (“Reflect” model) or move tangentially along the surface like a jet

(“Jet” model). One of the limitations of this model is the conditions for the occurrence of each regime which is not

specified in relation to experimental data.Recently, three models were developed for the case where the wall temperature was below the boiling

temperature of the droplet liquid: Lee and Ryou model14, Bai and Gosman model15 and the Grover and Assanis

model16. All the spray wall impingement models are based on the conservation laws and experimental data. The

T

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The impingement models presented in this study were developed for impinging droplets on a dry- and/or wetted

wall bellow the boiling temperature. The regime transition conditions for the impingement models are presented inTable 1.

The original Bai and Gosman model15 considers four impingement regimes: stick, rebound, spread and splash.

The existence of these regimes depends on the properties of the impinging droplets and the impingement surface,

including whether the latter is dry or wetted 15,21. The quantitative criterion for the regime transitions for both the

dry- and wet-wall situations was refined in Ref. 21.The Lee and Ryou model14 consists of three representative regimes such as rebound , deposition and splash. The

transition criteria between deposition and rebound is given as Weber number of 5 from the work Bai and Gosman15.

Ref. 18 have investigated multi-droplet impingement on a rough surface and found the criterion between thedeposition and splash regime. This empirical correlation based on droplet Reynolds number and Ohnesorge number

is the regime transition criterion between deposition and splash to the Lee and Ryou model14.

The Grover and Assanis model16 uses different splash criteria for dry and wet wall impacts. For dry wall droplet

collisions the splash-deposition criteria of Ref. 18 is used. In case of wet wall impact, the splash-deposition criteria

of Ref. 17 are the chosen instead.

Deposition is a combination of two physical phenomena, namely “ stick ” and “ spread ”. Where the arrivingdroplets are assumed to coalescence to form a local film. No secondary droplets are ejected. The normal component

of droplet kinetic energy prior to impingement is assumed to transform into a dynamics pressure, while the original

droplet tangential momentum acts to increase the local film tangential momentum.

Rebound applies when a droplet bounces against a wetted wall at low impact energy. The air trapped between

the bouncing droplet and the liquid film causes low energy loss. To determine the rebound velocity components, therelations for a solid particle on a wetted surface have been used 28.

Splashing occurs when a droplet with considerable high impact energy collides with a dry and wetted wall,

forms a crown from kinematic discontinuity29 and lateral cusps emerge, which become unstable and eventually breakup into smaller fragments. In each splash event may produce secondary droplets numbering in the hundreds or

thousands, so the expense of tracking all such droplets would be prohibitive. For all spray wall impingement models

it is assumed that each incident droplet parcel can produces p secondary parcels and the total number of secondary

droplets is computed by requiring mass conservation (see Table 2). Only the Grover and Assanis model16 consider a

wallfilm parcel is formed in the splashing event.There are three available methods for modeling droplet size distributions in spray: the maximum entropy

method, the discrete probability function method and empirical method. In the present study, the predictions of

secondary droplets sizes resulting from splashing follow ‘standard’ empirical distributions18,29,30,31, a Rozin-

Rammler distribution is used in the Bai and Gosman model21 while for the Grover and Assanis model16 is employed

a Nukiyama-Tanasawa distribution.

In the following paragraphs the present model is described in detail with special attention to the differences to

the Grover and Assanis model16 which has revealed to be inapplicable to the present situation.Information on the velocities of secondary droplets resulting from impingement is very scarce, especially for

oblique impingement angles. The secondary droplet velocities resulting from oblique impingement can be analyzed

as a superposition of those arising from normal impingement and wall-tangential component. The splash velocity

vector,→

S V , of a secondary droplet is calculated from→→→

+= SN ST S V V V , where,→

ST V and→

SN V are due to the tangential

Table 1. Regime transition conditions for the impingement modelsModel Wall status Regime transition state Critical Weber number

Dry Deposition (stick/ spread)→ splash Wec ≈ 2630 La-0.183

Stick→ rebound Wec ≈ 2

Rebound→ spread Wec ≈ 20Bai et al.

Wetted

Spread→ splash Wec ≈ 1320 La-0.183

Rebound→ spread Wec ≈ 5Lee andRyou

WettedDeposition→ splash K = Oh Re1.25 = 57.7

Dry Deposition→ splash K = Oh Re1.25 = 57.7Groverand

AssanisWetted Deposition→ splash K = Oh-0.4 We = 2100+5880δ1.44

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and normal components of the incident velocity, respectively. (Note that V SN is not in general normal to the surface.)

The component V ST is assumed to be related to the incident tangent velocity V IT by IT f ST V cV = , where the friction

coefficient c f is estimated to be in the range of [0.6 ; 0.8] for a water drop splashing on soil surface32. This approach

results from the point of view that the impact energy imparted to the disintegration process of a splashing event isdue mainly to normal incident velocity, V IN , while the effect of incident tangential velocity, V IT , is simply to transfera portion of its tangential momentum (with friction loss included) to each secondary droplet. As a consequence,

evolution of V SN can be obtained by considering a nominal impingement case with incident velocity V IN .

The velocity magnitude V SN, i of a droplet i is estimated by considering the energy conservation law as follow:

σ σ S D KS I KI E E E E E ++=+ (1)

where E KI is the incident kinetic energy based on the incident velocity, E I σ is the incident droplet surface energy, E S σ

is the total surface energy of splashing droplets, and E D is the dissipative energy loss, which is a parcel that assumesa special formulation for each particular model (Table 3).

Table 3. Splash regime – secondary droplets velocity

Model Kinetic energy Dissipation energy Velocity

Baiet al. ( )INKIKI VEE = ⎟⎟ ⎠

⎞⎜⎜⎝

⎛ = 2

1280 I

cKID d

We,E.maxE πσ

→→→

+= SNSTS VVV ;

⎟⎟ ⎠

⎞⎜⎜⎝

⎛

⎟⎟ ⎠ ⎞⎜⎜

⎝ ⎛

≈⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

I

i

I

i,SN

,SN

d

dln

ddln

V

V

1

1 ; ITf ST VcV = ;

Lee andRyou

( )IKIKI VEE =

∫ ∫∀ ∀=e

f

t

f D dtdE0

Φ

4

2

0

2

ef sp

t

f

INdf

thd

h

Vdtd

e

f

π µ Φ ∫ ∫ ⎟⎟ ⎠

⎞⎜⎜⎝

⎛ ≈∀

∀

12124

−⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −−=

m

w

INm

maxINwV

m

TIwT

Sr

C

Rer

WeCK

r

WeCWe

γ ;

Ψ

ININf ST

VRec.V

⋅⋅=

814520; φ cosVVV STx,ITx,ST += ;

Presentwork

(variant ofthe Grover

and Assanismodel)

( )IKIKI VEE =

( )[ ]diswf IKID EE,EE.minE ++= σ 80

2

330

8302

20 ⎟⎟ ⎠

⎞

⎜⎜⎝

⎛

= I

max

.

.

Idis d

d

Re

We

d.E σ π ;

2

2

1wf wf wf vmE = ;

( ) 02 321212122 12221 =−+−+ CCmVCCmVCmm ,ST,ST

( ) 041322 333 =−+++ KKVKVamK ,ST,ST β β β ;

1212 ,ST,ST VCCV −= ; Si,STi,SN tanVV θ = ;

Table 2. Splash regime – secondary droplets diameter

Model Parcels Distribution function Number of droplets in parcel i Total number of droplets

Bai et al. 1≤ p≤ 6 ( ) dd

e.d

df −

=1

p

dr dn Imii

33 = ⎟

⎟ ⎠

⎞⎜⎜⎝

⎛ −= 10

c

SWe

WeaN

Lee andRyou

p = 1 IwdCd =1 SNn =1 4541870 .We.NS −=

p = 3 ( )

23

3

2

2

3 ⎟⎟ ⎠

⎞⎜⎜⎝

⎛ −

= md

d

m

e.d

ddf

( )( ) 11

ndf

df n ii =

Groverand

Assanis

pwf = 13

1

6

2

1⎟⎟ ⎠

⎞⎜⎜⎝

⎛ =

wf

wf wf

n

mr

ρπ Iwf nn =

wf iS nnN +=∑

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r

injecto

80 mm

plane of measurements

10º20º

Figure 3. Diagram showing plane for

measurements for a free spray experiment.

Table 4. Thermo-physical properties for 2,2,4-

trimethypentane and air at 298 K.

Property Air 2,2,4-trimethylpentane

ρ [kg/m

3

]1.205 692

µ [Pa.s.10-6] 18.1 469.9

σ [N/m] - 0.01832

As in other models, with the Grover and Assanis model16 the secondary velocity component of splashed droplet

is determined from the mechanical energy conservation equation links the total energy of impinging parcel before

the impact to the splashing parcel.

This model distinguishes between the energy loss due toviscous dissipation and wall film formation. According to Ref.19, viscous effects can dissipate approximately 80 % of the

energy available for the secondary droplets or wall film.

Grover and Assanis16 show that as Weber number decreased,viscous effects become less important as more energy is used

to form the wall film. In this study the Weber number is much

smaller than in the case of Grover and Assanis22, and their

model leads to viscous dissipation term in Eq. 1 which is larger

than the total available. So, in the present work a modifiedversion of the Gover and Assanis model16 was developed, that

considers that the sum of the viscous dissipation and wall film

formation is equal to 80% the total energy available (described

in detail by Ref. 22).

III. Results and Discussion

The numerical predictions presented in this section are

compared with measurements20 and calculations21. The main

objective is to incorporate the additional effect of impact and to

evaluate the performance of the droplet impinging models ofBai and Gosman15, Lee and Ryou14, and the present model

which is a variant Grover and Assanis model22. These models

which were developed for impinging droplets on a dry- and/orwetted wall bellow the boiling temperature are incorporated in

the present three-dimensional computational method based on

the solution of the Reynolds-averaged Navier-Stokes equation

for the gas phase, and a SSF (stochastic separated flow) model

based on eddy lifetime for the particle phase.Figure 2 presents a dimensionless vertical profile of the

horizontal velocity, normalized by the maximum velocity and

height of wind tunnel, in the plane of the injector, and showsthat the numerical results are in agreement with the Laser

Doppler measurements of air flow in the absence of the fuel

droplets. The boundary layer has 5 mm of thickness and the

remainder of the velocity profile across the channel is

uniform20.To assess the performance of the impingement models it is

necessary to ensure the appropriate specification of the initial

conditions of the spray at the injector exit. In this study the

method used by Ref. 21 to obtain the initial conditions from theexperiments were also used. The initial values are estimated

using data from free spray measurements that were measured

by Ref. 33 and described in Refs. 20 and 21. In the free spray

experiments, which are portrayed in Figure 3, a hollow cone

spray is produced by a single-hole Bosch 0280 150 701 injector with a 30 mm3 of 2,2,4-trimethylpentane injected per 7 ms pulse. The injection frequency is 10 Hz , yielding a pulse spacing of 100 ms. The injection pressure was 3

bar, and the spray produced had an external half-cone angle of 20 degrees and an internal half-cone of 10 degrees.

Table 4 shows the thermo-physical properties of 2,2,4-trimethylpentane and air at 298 K .

A phase-Doppler anemometer (PDA) was utilized by Ref. 33 to measure the ensemble-averaged droplet size and

velocity characteristics at a horizontal cross section 80 mm downstream of the injector (Fig. 6). The measurement plane is a circular region with a radius of 32 mm, and data were obtained at a number of positions in this plane.

W/Wmax

Y / H

0 0.25 0.5 0.75 10

0.1

0.2

0.3

0.4

0.5

Arco uman is et al. (1 997)

Present work (WC

= 5 m/s)

Figure 2. Dimensionless vertical profile of the

horizontal velocity component, W, at the

centreline of tunnel, X/H = 0.005 and

upstream of the injector, Z/H = 1.3.

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Figure 4 shows the pulse averaged diameter probability density functions ( pdf ) measured, where the cross-

section of the spray is divided into four regions 0 mm < r < 5 mm, 5 mm < r < 10 mm, 10 mm < r < 15 mm and 15

mm < r < 22.5 mm. And, in Fig. 5 is presented the correlation between droplet diameter and the pulse averaged axial

velocity, velocity-diameter function. From the measurements at 80 mm downstream of the nozzle, presented in thelast two figures, Ref. 21 devised an empirical procedure for estimating the initial conditions for a single-hole portinjector. The estimation of initial droplets sizes is determined from the measured pdf , the measured ensemble-

average mass flux and takes into consideration the maximum and minimum droplet sizes. The initial droplets

velocities were determined with the help of an iterative trial-and-error procedure21. The calculations presented inFigs. 4 and 5 indicate that the empirical procedure proposed by Ref. 21 to estimate the initial droplet sizes and

velocities can reproduce fairly well the measured mean droplet size and velocity at the measurement plane 80 mm

downstream.

It should be pointed out that the empirical procedure proposed by Ref. 21 does not necessarily guarantee that

similar agreement will apply near the nozzle, or in any other particular plane. Nevertheless, due to the limitedexperimental data available and the lack of information in the initial conditions obtained by Ref. 21 an additional

approach for the estimation of the initial conditions at the injector plane was developed. For initial droplets sizes, the

measured pdf is reproduced at the exit injector, and it is assumed that the droplets are spherical, the spray is

dispersed, so that the droplet collision/coalescence can be neglected, and the droplet aerodynamic breakup andevaporation are ignored (the measurements were performed at ambient pressure and temperature). This means that

the droplet size range observed at the measured plane corresponds to the size range encountered in the near nozzle

region. Finally, the measured correlation droplet velocity-size is used at exit nozzle.Figure 6 shows the four different measurements locations, where the present results will be compared with the

experimental data of Ref. 20 and the predictions of Ref. 21 for the cases of crossflow velocities of 5 and 15 m/s. Thefour different positions a, b, c and d , are located in the centre of the wind tunnel and lie respectively 12, 15, 20 and

25 mm downstream of the injector and within a horizontal plane 5 mm above the impingement wall.

Droplet diameter [µm]

N o r m a l i s e d P

D F

0 100 200 300 4000

0.004

0.008

0.012

5 mm < r < 10 mm


N o r m a l i s e

d P D F

0 100 200 300 4000

0.004

0.008

0.012

10 mm < r < 15 mm


N o r m a l i s e

d P D F

0 100 200 300 4000

0.004

0.008

0.012

15 mm < r < 225 mm


N o r m a l i s e d P

D F

0 100 200 300 4000

0.004

0.008

0.012

0 mm < r < 5 mm

Figure 4. Diameter probability density functions for four radial regions of the spray. Predictions:

Bai et al. 21

. Measurements: Arcoumanis et al. 20

.

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Figures 7 and 9 show the droplet size distribution at the locations a, b, c and d , while the dimensionless droplets

mean size and velocity correlation are displayed in Figs. 8 and 10. In order to reduce the influence of initialconditions of the spray at the injector exit, the droplet mean size and velocity are normalized by its mean diameter

and corresponding velocity. In Figs. 7 to 10 the dashed line with closed symbols correspond to the measurements of

Ref. 20 and the solid line with open symbols to predictions: the triangles are predictions reported by Ref. 21; the

open diamond, square and right triangle symbols are associated with the present predictions that used the wall

impingement models of Bai and Gosman21; Lee and Ryou14; and modified Grover and Assanis22, respectively.

Figure 7 shows the measured and the predicted droplet size distributions for a crossflow velocity of 5 m/s that are

in good agreement. The results present values that correspond to droplets with a downward moving velocity, but the

peak values at some locations are overpredicted and show a slight rightward shift in the predictions. The

measurements and calculations published in Ref. 21 used a size class of approximate 25 µ m and 60 µ m, respectively,

while in the present study is used a more precise size class of 15 µ m was used, and it can be associated with some ofdiscrepancies. At the location d , the measurements show that more droplets with larger sizes are measured than

predicted. The Grover and Assanis modified model22 allowed a considerable number of droplets with sizes less than

20º

WC

a b c d 5 mm

25 mm

20 mm

15

mm

12

mm

Figure 6. Illustration of the measurements.


A v r g . a x i a l v e l o c i t y v a

[ m

/ s ]

0 100 200 300 4000

10

20

30 5 mm < r < 10 mm


A v r g . a x i a l v e l o c i t y

v a

[ m / s ]

0 100 200 300 4000

10

20

30 10 mm < r < 15 mm


A v r g . a x i a l v e l o c i t y

v a

[ m / s ]

0 100 200 300 4000

10

20

30 10 mm < r < 15 mm


A v r g . a x i a l v e l o c i t y v a

[ m

/ s ]

0 100 200 300 4000

10

20

30 0 mm < r < 5 mm

Figure 5. Pulse averaged axial velocity for four radial regions of the spray. Predictions: Bai et al. 21

.

Measurements: Arcoumanis et al. 20

.

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15 µ m at the location d , which are probably splash droplets. The discrepancies between calculations of Ref. 21 andthe measurements of Ref. 20, and with our predictions for the same Bai and Gosman model, may be related to the

uncertainties in the estimated initial conditions of the spray (and in case of our predictions with the different

procedures used to estimate the initial conditions). These are more obvious in Fig. 9, where the our predictions andcalculations of Ref. 21 size distribution for the upward-moving droplets present distinct behavior compared with

experimental data. The peak values at all locations are over-predicted so much for the predictions as for thecalculation, however, the predictions show a slight leftward shift unlike to the calculations that show a small

rightward shift.

Figures 8 and 10 show dimensionless velocity-size correlation of downward and upward-moving droplets,

respectively. For droplets with descending moving velocities, Fig. 8, the agreement between the predictions and the

experimental data is better near the injection plane. From Fig. 7 and for the present predictions and those of Ref. 21

it is clear that droplet mean size is larger than measurements at the location a and b. At location d , the present

predictions with the Grover and Assanis modified model22, the droplets with a diameter less than 15 µ m present asmall vertical velocity. These secondary droplets are due to droplet to wall collision that can induce high droplet

rotations. The rotation of the droplets results in deformation of the flow field around the particle, associated with ashift of the stagnation points and a transverse lift force34. This lift force is acting towards the direction of wall and in

the case of droplets with a small Reynolds numbers this slip-rotation lift force have more influence than slip-shear

lift force. The slip-shear lift force is due to the non-uniform relative velocity over a droplet and resulting non-uniform pressure distribution by droplets moving in a shear layer 26,34. This lift force is acting towards the direction

of higher slip velocity (oppose direction slip-rotation lift force in this case).

In the case of droplets with ascending movement (Fig. 10) the predictions have reasonable concordance with

measurements for droplets sizes close to droplet mean diameter. However, Fig. 10 shows considerable differences

between predictions and calculations of Ref. 21, reinforcing the influence of the initial conditions. The sizes and


N o r m a l i s e d P D F

0 100 200 3000

0.01

0.02

0.03

0.04 Location b



0 100 200 3000

0.01

0.02

0.03

0.04 Location c



0 100 200 3000

0.01

0.02

0.03

0.04 Location d



0 100 200 3000

0.01

0.02

0.03

0.04 Location a

Figure 7. Size distributions of downward-moving droplets at four locations for a crossflow velocity of 5

m/s. Predictions: Bai et al. 21

; present work with Bai and Gosman model , with Lee and Ryou

model , and with Grover and Assanis modified model . Measurements: Arcoumanis et al. 20

.

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velocities of secondary splash droplets depend strongly of pre-impingement conditions, which in turn depend of the

initial conditions of spray at exit injector, and may also be associated with the crossflow velocity.

Figures 11 and 14 compare, for a higher cross flow velocity of 15 m/s, the measured and the predictions size

distributions of droplets moving downward and upward, respectively. Once more, reasonable agreement is observed

for downward moving droplets. However, the predictions continue to present the peak values at all locations are

over-predicted and a slight rightward shift in the predictions. As already observed by Ref. 20, at this cross flowvelocity, the predictions and the measurements size distributions show a larger droplets at the locations a and b,

probably due to carried away the smaller droplets by the air flow. In the case of upward moving droplets, the

predictions size distributions show a good agreement with the experimental data. The present results show that theLee-Ryou model14 have difficulty to predict the size distributions of droplets with ascending movement, probably

because this model considers only one secondary parcel produced when splashing occurs, and, as demonstrated by

several authors

18,29,30,31

the secondary droplets sizes resulting from splashing follow characteristics distributions, likea Rozin-Rammler distribution in Bai-Gosman model21 or a Nukiyama-Tanasawa distribution in Grover-Assanis

model16. The distribution used in Bai-Gosman model21 to predict the secondary droplets size are at first sight more

reliable than the one proposed in the Grover-Assanis model16.Figure 12 shows good agreement between the predictions and measurements for dimensionless velocity–size

correlation for droplets with a downward-moving at location a, b and c. At a location further away from the nozzle plane considerable deviations are observed, probability due to the deflection of the spray by the cross flow it is more

pronounced for 15 m/s of cross flow velocity. The experimental results20

show that the spread of the spray tip grows

as it approaches the surface. For the small droplets from spray exit injector it is expected that the small droplets arecarried away by the crossflow before they reach the wall. The dimensionless velocity-size correlation for droplets

with upward-moving, Fig. 14, show a reasonable agreement between predictions and experimental data at location a.

At other locations, the droplet mean diameter of predictions is lower than measurements, see Fig. 13. The dropletsclass with a diameter smaller than mean droplet diameter presents a higher upward velocity.

d/dm

v / v

d m

0 1 2 3 4 5 60

1

2

3

4 Location b

d/dm

v / v

d m

0 1 2 3 4 5 60

1

2

3

4 Location c

d/dm

v / v

d m

0 1 2 3 4 5 60

1

2

3

4 Location d

d/dm

v / v

d m

0 1 2 3 4 5 60

1

2

3

4 Location a

Figure 8. Velocity-size correlation of downward-moving droplets at four locations for a crossflow velocity

of 5 m/s. Predictions: Bai et al. 21

; present work with Bai and Gosman model

, with Lee and Ryoumodel , and with Grover and Assanis modified model . Measurements: Arcoumanis et al.

20 .

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d/dm

v / v

d m

0 1 2 3 4 5 60

1

2

3 Location d

d/dm

v / v

d m

0 1 2 3 4 5 60

1

2

3 Location c

d/dm

v / v

d m

0 1 2 3 4 5 60

1

2

3

Location b

d/dm

v / v

d m

0 1 2 3 4 5 60

1

2

3

Location a

Figure 10. Velocity-size correlation of upward-moving droplets at four locations for a crossflow velocity of

5 m/s. Predictions: Bai et al. 21

; present work with Bai and Gosman model, with Lee and Ryou model

, and with Grover and Assanis modified model . Measurements: Arcoumanis et al. 20

.


N o r m a l i s e d P D

F

0 100 200 3000

0.01

0.02

0.03

0.04 Location d



F

0 100 200 3000

0.01

0.02

0.03

0.04 Location c



0 100 200 3000

0.01

0.02

0.03

0.04 Location b



0 100 200 3000

0.01

0.02

0.03

0.04 Location a

Figure 9. Size distributions of upward-moving droplets at four locations for a crossflow velocity of 5




.

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d/dm

v / v d m

0 1 2 3 4 5 60

1

2

3 Location c

d/dm

v / v d m

0 1 2 3 4 5 60

1

2

3 Location d

d/dm

v / v d m

0 1 2 3 4 5 60

1

2

3 Location b

d/dm

v / v d m

0 1 2 3 4 5 60

1

2

3 Location a

Figure 12. Velocity-size correlation of downward-moving droplets at four locations for a crossflow velocity

of 15 m/s. Predictions: Bai et al. 21



.



F

0 100 200 3000

0.01

0.02

0.03

0.04 Location d



F

0 100 200 3000

0.01

0.02

0.03

0.04 Location c



0 100 200 3000

0.01

0.02

0.03

0.04 Location b



0 100 200 3000

0.01

0.02

0.03

0.04 Location a

Figure 11. Size distributions of downward-moving droplets at four locations for a crossflow velocity of




.

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d/dm

v / v d m

0 1 2 3 4 5 60

1

2

3 Location d

d/dm

v / v d m

0 1 2 3 4 5 60

1

2

3 Location c

d/dm

v / v d m

0 1 2 3 4 5 60

1

2

3 Location b

d/dm

v / v d m

0 1 2 3 4 5 60

1

2

3 Location a

Figure 14. Velocity-size correlation of upward-moving droplets at four locations for a crossflow velocity of




.



0 100 200 3000

0.01

0.02

0.03

0.04 Location b



F

0 100 200 3000

0.01

0.02

0.03

0.04 Location c



F

0 100 200 3000

0.01

0.02

0.03

0.04 Location d



0 100 200 3000

0.01

0.02

0.03

0.04 Location a

Figure 13. Size distributions of upward-moving droplets at four locations for a crossflow velocity of 15




.

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For both crossflow velocities, all the models described before have difficulty to predict the larger droplets

observed emerging downstream region of impingement (see Figs. 9 and 11 at location c and d ) for the present

crossflow velocity, but the present model gives the better results. The experimental results of Ref. 20 and 35 shows

that the droplets diameter increased with the film thickness. The new droplets are formed close to the film as aconsequence of a combination of splash atomization and film stripping, with the latter becoming more important indownstream region as the number of droplets reaching the film from above decreased.

IV. Conclusion

A numerical study of a spray impinging on a surface through a crossflow has been performed and the predictions

were compared with measurements and calculations of other authors. Three spray impinging models, developed for

impinging droplets on a dry- and/or wetted wall bellow the boiling temperature were integrated in a three-dimensional computational method based on the solution of the Reynolds-averaged Navier-Stokes equation for the

gas phase, and a SSF model based on eddy lifetime for the particle phase.

The impinging models were tested, together with a new variant of the Grover and Assanis model 22. The

predicted results show in general reasonable agreement with the experimental data. The predictions and

experimental results revealed a concentration of smaller droplets immediately above the surface in the impingementregion. The performance of the droplet impinging models depends strongly on the conditions of pre-impingement,consequently dependent from initial conditions of the spray at the exit injector and not the air flow.

In the case of an estimated size of the secondary droplets, the impinging droplet models that follow

characteristics distribution have a more realistic performance compared with models that use other methodology. To

predict the velocity of this droplets the main difference and difficulty of the impinging spray models consist in the

calculation of dissipation energy. Some models incorporate energy dissipation terms that have not been validatedwith literature yet. Others models distinguishes between the energy loss due to viscous dissipation and wall film.

However, and according to Ref. 19, viscous effects can dissipate approximately 80% of energy available for the

secondary droplets or wallfim. As shown by Ref. 20 and Ref. 35 the film stripping becoming more important indownstream region as the number of droplets reaching the film from above decreased. From the numerical results at

the downstream region it was found that is necessary to implement the presence of the liquid film near to wall to

improve behavior of spray impinging models.

Other relevant aspect to refine the models is the treatment of post-impingement characteristics by including the

effects of collision droplets, in impact region, the near-wall gas boundary layer. In order to improve the impingingmodels more detailed measurements and calculations are required, and more work is needed to their generalization.

Acknowledgments

The present work has been performed in the scope of the activities of the AeroG – Aeronautics and

Astronautics Research Center. The financial support of the Portuguese Ministry of Science, Technology and High

Education and the Calouste Gulbenkian Foundation is gratefully acknowledged.

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