Modelling of Gasoline Spray Impingement
C. X. Bai, H. Rusche and A. D. Gosman
Department of Mechanical Engineering
Imperial College of Science, Technology and Medicine
Abstract
This paper is concerned with aspects of gasoline spray droplet impingement simulation,
for which an improved model has been developed for predicting the outcomes of spray droplets
impacting on a wall. The model is assessed by simulating experiments on oblique spray
impingement in a wind tunnel. This is done with the aid of a specially-devised procedure
for deducing the specification of initial droplet sizes and velocities at the gasoline injector
from downstream measurements. The calculated wall spray characteristics show favourable
agreement with the measurements.
INTRODUCTION
Spray impingement on walls occurs in a wide range of situations. These include various types
of reciprocating engines, gas turbines, spray cooling systems, ink-jet printing and many other
applications in agriculture and medicine. In small high speed direct-injection Diesel engines,
the fuel is directly injected into the compact chamber at a high speed and strikes the walls due
to short free spray path. In direct injection spark ignition engines, the fuel droplets may also
impact onto the combustion chamber walls for similar reasons. In port fuel injection gasoline
engines, it is often the case that a large portion of the spray impinges on the walls of the port
or the intake valve(s).
In the aforementioned applications the hydrodynamic, and in some cases thermal, characteristics of the post-impingement droplets are important issues in injection system design. Of
particular interest in the engine context are : (i) the total fuel mass, momentum and energy
deposited as and to wall films which, if not evaporated completely during combustion, are responsible for contributing to enhanced levels of unburnt hydrocarbon emissions [1, 2]; and (ii)
the fuel vapour distribution in the near-wall region. The latter is closely related to the flame
quenching phenomenon [3] which occurs when the flame closely approaches the cool walls of the
chamber. The unburnt fuel may also contribute to emissions.
A basic physical picture of the impingement process can be constructed by considering a
single impinging droplet (see Figure 1) which, following its impact on a solid surface, first undergoes deformation and spreads out at a certain velocity under the impingement-induced pressure
gradients. This spreading flow either remains stable or becomes unstable, leading to different
impingement regimes (eg. stick, spread, rebound, and splash) as observed experimentally [4–
7]. The outcome is, as described in detail by Bai [8], determined by a number of parameters
characterising the impingement conditions. These include droplet diameter dI , temperature Td ,
velocity VI , incidence angle θI wall temperature Tw as well as fluid properties such as viscosity
µ, density ρ and surface tension σ. Also important are the surface roughness rs and, if present,
pre-existing wall film thickness δ0 and gas boundary layer characteristics in the near-wall region.
These quantities may be combined to yield a number of dimensionless parameters [8]. The most
2 d /σ, (where V
important are: (i) droplet Weber number We = ρVIN
I
IN is droplet incident normal
impact velocity); and (ii) droplet Laplace number La = ρσdI /µ2 .
1
Two basic issues need to be addressed in the modelling of spray impingement processes. The
first is to establish regime transition criteria for predicting which regime occurs under given
conditions. The second is to quantitatively estimate post-impingement characteristics, notably
the rebound velocity magnitude and its direction for the rebound regime, the fraction of the
mass deposited on the wall and the size and velocity distributions of the secondary droplets for
the splash/breakup regime.
Numerous models have emerged for the simulation of both Diesel [9–18] and gasoline impinging sprays [19, 20]. These have all been formulated in the statistical Lagrangian framework,
in which the liquid phase is represented by discrete ‘droplet parcels’, each representing a group
of ‘real’ droplets possessing the same physical properties (eg. size, velocity, and temperature).
In the early model of Naber and Reitz [9], an impinging droplet is assumed either to stick to the
wall as a spherical droplet, or bounce back elastically (without energy loss), or move tangentially
with the same velocity magnitude (thus also same kinetic energy) as before impact. Droplet
secondary breakup is, however, not allowed irrespective of the impact energy.
All the models subsequently developed account in some way for secondary breakup occurring
at high impact energy and involve the use of transition criteria to distinguish between two or
more impingement regimes. One group of the models [17, 18, 20] considers the spread and
splash regimes, which occur on a ‘cold’ dry wall with Tw < TB where TB is the fuel boiling
temperature. The transition Weber number can then be expressed as : We = αLa−β where α
and β are positive constants. A second group of the models [10–12, 19] account for two other
regimes - rebound and breakup - which may occur for impingement on a hot dry wall whose
temperature is above the Leidenfrost temperature Tleid . In this case the transition condition is
set as Rebound → breakup : Wec ≈ 80.
As for the treatment of post-impingement characteristics for the breakup or splash regime,
some modellers [10, 11] have made assumptions about the sizes and velocities of secondary
droplets. For instance, Watkins and Wang [11] assume that they move tangentially to the wall
at a velocity equal to that of the incident droplet tangential velocity, and that the size of each
ejected droplet is one-quarter of its parent droplet. Other researchers [17, 18] employ empirical
correlations which were derived using limited experimental data.
The model of Bai and Gosman [15], which is the basis for the improved version proposed in
this paper, was formulated using a combination of simple theoretical analysis and experimental
data from a wide variety of sources. It considers both dry and wetted wall conditions, allows for
mass deposition and quantifies the regime transition conditions and post-impingement characteristics of several impingement regimes. Validation of the original model was performed using
experimental data for a number of published experimental studies of Diesel spray impingement,
for which good agreement was obtained. A similar approach was subsequently proposed by [16]
who utilise some different correlations for evaluating the post-impingement characteristics.
The present paper focuses on gasoline spray impingement and the refinement of the BaiGosman model for this application. The need for the refinement arises mainly from the recognition of: Firstly, recent experience with this model has revealed that it under-estimates the
dissipation of energy by splashing a droplet when its impact energy is above a certain level.
Secondly, the impinging droplets are larger in port injection (PI) gasoline engines than those in
high speed direct-injection engines for two reasons : (i) The fuel injection pressures in PI gasoline
engines are substantially lower, typically around 2.5 to 3 bar, and this yields an atomised spray
with a typical Sauter mean diameter (SMD) of around 100 µm which is much larger than the
SMD (about 20 µm) in high speed direct-injection Diesel engines; and (ii) droplet aerodynamic
breakup and droplet evaporation (especially during cold start) are much weaker in the intake
manifolds of PI engines due to the lower injection pressures and gas temperature. By way of
illustration, in the present study the simulations revealed that impinging droplet Weber numbers
are mainly in the range from 800 to 9000 in PI gasoline engines, whereas they range from 100
2
to 600 in a typical high speed direct-injection Diesel engines. This clearly indicates that the
typical droplet impact energy is substantially higher in the former circumstances, thus casting
doubts about the applicability of the Bai-Gosman model to gasoline sprays. Accordingly, in the
modified model to be described in the next section, efforts are made to improve the treatment
of post-splashing characteristics so that it is applicable for a much wider range of impingement
conditions.
The remainder of this paper is organised as follows. Firstly, we describe the main features of
the refined impingement model. We then outline a specially-derived computational procedure
for determining the initial droplet conditions for a gasoline injector used in the experiments on
gasoline spray impingement, which are chosen for our model validation. Subsequently, we assess
the impingement model against experimental data and discuss the results in detail. Finally, we
present our conclusions and provide suggestions for future work.
DROPLET IMPINGEMENT MODEL
In what follows, the basic elements of the impingement model of Bai and Gosman [15] and the
modifications made in this paper are described.
Regime Transition Criteria
The original Bai-Gosman model considers four impingement regimes: stick, rebound, spread and
splash, shown schematically in Figure 2. The existence of these regimes depend on properties
of the impinging droplets and the impingement surface, including whether the latter is dry
or wetted, as discussed by Bai and Gosman [15]. In the case of a dry wall at sub-boiling
temperatures rebound has not been observed experimentally. This is probably due to the fact
that there is insufficient air/vapour trapped between the drop and the wall, thus causing higher
energy consumption in the course of adhesion energy formation.
Quantitative criteria for the regime transitions for both the dry- and wet-wall situations at
sub-boiling temperatures derived from the earlier study Bai and Gosman [15] and refined in
the present work are presented in Table 1 below. The nature of the refinement will now be
explained.
Table 1: Regime transition conditions
Wall status
Dry
Wetted
Regime transition state
Adhesion(Stick/Spread) → Splash
Stick → Rebound
Rebound → Spread
Spread → Splash
Critical Weber number
Wec ≈ 2630La−0.183
Wec ≈ 2
Wec ≈ 20
Wec ≈ 1320La−0.183
The transition criteria used in Bai and Gosman [15] were derived from experimental data
on single water droplets impacting on a dry or wetted wall and it was recognised then that
they might not properly account for interference effects of neighbouring previously-impacting
droplets. Subsequent examination of the literature has revealed evidence that the reboundspread transition is indeed affected in this way. For instance, in their experiments involving
sprays impinging in an annular duct, Lee and Hanratty [21] observed that droplet bounce occurs
even at Weber numbers which are apparently higher than the critical value above which a single
droplet would otherwise spread on the surface. They further noticed that, under the conditions
of their investigation, the likelihood of droplet coalescence with the film is increased by a fourfold compared to the case of single droplet impingement. Ching et al. [22] also found evidence
3
that droplet bouncing is promoted by the presence of neighbouring droplets. This phenomenon
may be explained by the fact that those droplets which strike the surface may encounter a
pre-existing crater and thus must perform less work in the process of crater formation. In view
of these observations, the critical Weber number for the transition from rebound to spread has
been increased in this study to 20, as opposed to the value of 5 previously used.
Post-impingement Characteristics
The other aspect of the model requires modification of the treatment of post-impingement
characteristics for each regime. For the stick/spread and rebound regimes, the approach adopted
in [15] is carried over unchanged. However, for the splash regime modifications are made. Firstly,
the sizes of the secondary droplets are evaluated from a probability density function (PDF) fit
to existing experimental data, instead of the uniform probability previously assumed. Second,
a more realistic energy budget for splashing droplets is made, in order to enable more accurate
evaluation of the secondary droplet velocity magnitudes. Details are given below.
Estimation of secondary sizes - Each splash event may produce secondary droplets numbering
in the hundreds or thousands, so the expense of tracking all such droplets would be prohibitive.
A similar problem applies to the spray itself, which is circumvented in the stochastic Lagrangian
spray modelling framework used in this and many other studies by calculating a statistical sample
of the full population, each computational droplet thus representing a parcel of real droplets.
It is therefore logical and consistent to use the same practice for the secondary droplets. Thus,
in the Bai-Gosman model it is assumed that each incident droplet parcel produces p secondary
parcels where p ≥ 1. Each of these parcels contains an equal proportion of mass, ms /p. Here
ms is the total mass of secondary droplets, and p can be varied depending on the considerations
of both accuracy and computational cost. In the previous study p was fixed as 2 in [15]. Value
up to 6 were investigated in the present study, with the conclusion that the original practice is
a reasonable compromise between accuracy and cost.
In the original model the sizes of secondary droplets are assigned number-mean values randomly selected within the appropriate range. In reality the secondary sizes follow characteristic
distributions, as demonstrated by the experimental data of [4, 23],as well as some recent measurements of [24, 25]. In the present work we have determined that these data can be fitted by
a Chi-squared distribution function (a special case of the more general Rozin-Rammler distribution) given by :
d
1
f (d) = ¯ exp −
d
d̄
(1)
where d¯ denotes the number mean diameter which is related to the volumetric mean diameter
dV by :
dV
1
d¯ = 1/3
= 1/3
6
6
rm
NS
1/3
dI
(2)
Here dI is the incident droplet diameter and rm = ms /mI is the total splashing to incident
droplet mass ratio. The latter ratio is believed to be affected by several parameters such as
the droplet Weber and Laplace numbers, wall roughness, and pre-existing wall film thickness.
Unfortunately, it is extremely difficult to establish a general correlation for rm in terms of
these parameters and neither a experimental correlation nor a theoretical equation of has been
established. Nevertheless, the most-likely range of variation for rm has been identified by [15]
from the existing experimental data. Thus, following [15], rm is taken to have a random value
evenly distributed in the experimentally-observed range [0.2; 0.8] for a dry wall [4, 23, 26] and
[0.2; 1.1] for a wetted wall [27, 28]. Note that in the latter case, the ratio can take values larger
4
than 1, since splashing droplets may entrain liquid from the wall film. The quantity NS is the
total number of secondary droplets per splash, obtained in [15] as :
NS = a0
We
−1
Wec
(3)
where a0 = 5 and Wec is the critical Weber number for splashing.
The probability density function (1) can now be integrated to obtain a cumulative probability
function, which is then used to determine the sizes of p secondary droplets, di (i = 1...p) by
taking p random samples, each with a probability γi (0 < γi < 1).
Finally, the number of droplets ni in each secondary parcel i is determined by requiring mass
conservation :
rm d3I
(4)
ni d3i =
p
Evaluation of secondary velocities - Information on the velocities of secondary droplets resulting from impingement is very limited, especially for oblique impingement angles. Given this
and the need for a practical model, a number of simplifying assumptions, mainly without justification, have been made in this and the previous study. A basic premise is that the secondary
droplet velocity fields resulting from oblique impingement can be analysed as a superposition
of those arising from normal impingement and a wall-tangential component. To this end, the
splash velocity vector VS , of a secondary droplet is calculated from :
VS = VST + VSN
(5)
where as shown in Figure 1 VST and VSN are due to the tangential and normal components of
the incident velocity, VST and VST respectively. In other words, VST is assumed to dependent
solely on VIT whilst VSN solely on VIN . Note that VSN is not in general normal to the surface.
The componentVST is assumed to be related to the incident tangential velocity VIT by:
VST = Cf VIT
(6)
where the friction coefficient Cf is taken somewhere in the experimentally-observed range
[0.6; 0.8] [28].
The above approach comes from the view that the impact energy imparted to the disintegration process of an splashing event is mainly due to normal incident velocity, VIN ,whilst the
effect of incident tangential velocity,VIT , is simply to transfer a portion of its tangential momentum (with friction losses included) to each secondary droplet. Thus, evaluation of VSN can
be performed by considering a nominal impingement case with incident velocity VIN , without
involvement of VIT and VST , as is now described.
The problem of determining the velocity vector VSN,i of droplet i due to normal impingement is equivalent to finding its three defining quantities: (i) the azimuthal angle φS,i in the
circumferential direction within the plane tangential to the wall; (ii) the ejection angle θS,i ; and
(iii) the velocity magnitude VIN,i . The first quantity φS,i is randomly sampled in the range [0; 2π]
with an equal probability. This does not conserve tangential momentum in detail, but ensures
overall conservation in a statistical manner.
To determine the remaining two quantities, we first note that all VSN ’s must be symmetrically
distributed about VIN as illustrated in Figure 3. We then rely on findings for splashing droplets
resulting from droplet normal impingement to complete the model, as follows.
According to experimental observations [28, 29], the ejection of secondary droplets in the
whole splashing process lasts for a finite duration and the secondary droplet properties are
strongly dependent on the ejection time. An experimentally established fact is that the earlier
an droplet is ejected the larger its ejection velocity and angle. The ejection angle θS increases
5
monotonically with time from a bounding angle θb at the start of ejection to a value of around
90◦ at the end of ejection. The bounding angle θb depends on the surface roughness and the
pre-existing liquid layer thickness.
However, it should be noted that θS is usually not distributed uniformly in the whole range
and that sub-ranges with higher probabilities exist. The bounds of such a sub-range depend
on the surface roughness and liquid layer thickness. For instance, Gahdiri [29] found that, θS
varies in the range of [20◦ ; 60◦ ] in situations where droplets splash on a rough soil surface; whilst
Allen [30] noted that for droplets splashing on a deep water layer, θS is more likely to fall within
[30◦ ; 70◦ ]. Mutchler [28] examined the case of smooth hard walls with a roughness of 0.83µm
and found that the high probable sub-range for θS was [5◦ ; 50◦ ].
In view of the above, in the present study we randomly sample θS,i within Mutchler’s result
(i.e. [5◦ ; 50◦ ]) and ignore the range [50◦ ; 90◦ ] on the basis that the probability of finding droplets
in this range is low. It should also be noted that trial spray impingement simulations using the
full range resulted in substantial overprediction of wall spray height.
The remaining step is to estimate the velocity magnitude VSN,i . This is done by considering
energy conservation which yields the following equation :
i
1 ms h
(VSN,1 )2 + ... + (VSN,p )2 = EKS
2 p
(7)
where EKS is the splash kinetic energy due to VIN only, given as :
EKS = EKI + EIσ − ED − ESσ
(8)
2 is the incident kinetic energy based on the normal incident velocity; E
in which EKI = 12 mI VIN
Iσ
is the incident droplet surface energy, ESσ is the total surface energy of splashing droplets, and
ED is the dissipative energy loss, which was previously evaluated in [15] as the critical kinetic
energy below which no splashing occurs, given by :
ED =
Wec
πσd2I
12
(9)
where Wec is the critical Weber number for splashing. This equation for ED appears to under−ED
estimate the energy dissipation when EKIEKI
> 20%, for a phenomenological analysis [31] shows
that the viscous dissipation due to deformation accounts for around 80% − 90% of EKI . As
mentioned earlier, in Diesel engines the sizes and velocities of the impacting droplets are normally
−ED
< 20% and the use of Eq. (9) is justified. However, in port-injection
small, so that EKIEKI
gasoline engines, the sizes and velocities of impinging droplets are normally high and ED is
therefore bound by a postulated value of 0.8EKI :
Wec
ED = max 0.8EKI ,
πσd2I
12
(10)
Eqs. (7), (8) and (10) are adequate to enable determination of VSN,i if only one secondary
parcel is introduced, i.e. , p = 1. Otherwise, when p > 1, a size-velocity correlation derived by
[15] from the experimental data is used as a supplemental equation :
VSN,1
VSN,i
!
d1
≈ ln
dI
di
/ln
dI
(i = 2...p)
(11)
which, upon substitution into Eq. (7), yields VSN,1 . The latter velocity is then substituted into
(11) to obtain VSN,i (i = 2...p).
6
ATOMISATION CONDITIONS FOR A PORT INJECTOR
A key issue in assessing properly the performance of the impingement model in spray calculations is to ensure that pre-impingement conditions of each incoming droplet are estimated
with reasonable accuracy. It is thus necessary to determine the appropriate initial conditions
in the near-nozzle region of the spray. Due to the limitations of current understanding of the
mechanisms involved in the thin liquid sheet breakup mechanism of port injectors, no reliable
atomisation model is yet available for them and it is outside the scope of this study to attempt
development of such a model. We have therefore devised an empirical procedure for estimating
these effective initial conditions for a typical single-hole port injector (in the present case Bosch
0280 150 701), from downstream measurements, based on an early approach of Grunditz [32]
which was subsequently refined by Rusche [33]. It relies on experimental inputs on droplet sizes
and velocities at a downstream plane normal to spray injection direction. These inputs include:
(i) Probability Density Function (PDF) for droplet sizes; (ii) droplet velocity-size correlation;
and (iii) average droplet mass flux as a function of radius.
The methodology invokes two major simplifications. Firstly, a set of spherical droplets are
used to represent the continuous liquid sheet emerging from the injector which travels a certain
distance (called the breakup length) before it starts to disintegrate.
Secondly, droplet aerodynamic breakup, collision/coalescence and evaporation are all ignored
in the process of inferring the initial conditions from the measurements, which were performed
at normal ambient pressure and temperature. This implies that each injected droplet parcel
keeps the same size as assigned at the injector throughout the pulse duration, and the whole
size range observed at the measured plane therefore corresponds to that encountered in the nearnozzle region. Thus, we can ascribe droplet initial sizes in the experimentally-observed range.
Neglect of collision/coalescence is justified by the fact that hollow cone sprays are normally welldispersed, so the probability of collision is small. Disregard of aerodynamic breakup is justified
since for the experimental conditions, the droplet Weber number Weg = ρg Vrel d/σ (where Vrel is
the relative velocity between the droplet and gas) never exceeds 8 which is well below the critical
value for breakup, eg. 12. As for evaporation, order of magnitude estimates and full simulations
of the spray with this effect included show that it has negligible effect on the droplet sizes over
the distance considered.
The procedure estimating the initial droplet conditions consists of two steps, as detailed
below.
Estimation of Initial Droplet Sizes
N parcels are introduced from the nozzle at each computational step, where N is chosen to
be large enough that the whole spray can be properly represented statistically. Moreover, we
require that the computational parcels be ‘evenly’ distributed over the spray cross-section in the
sense that the number of parcels per unit area (parcel flux) is constant. To achieve this, the
spray circular cross-section at the measurement plane is divided into K (which is divisible to N )
annular regions of equal area, as illustrated in Figure 4. The i-th region is of thickness ri − ri−1 .
The N parcels are divided into K groups, one for each section, each of which contains
M = N/K parcels. Each of the parcels in group i is ‘captured’ at a particular instant in region
i (i=1...N) of the measurement plane. Consider parcel k (k=1...M) of group i to be introduced
from the injector. Its size, dk , and the radial position in the measurement plane, rk , are evaluated
as:
dk = dmin + γ1 (dmax − dmin ); rk = ri−1 + γ2 (ri − ri−1 )
(12)
where γ1 and γ2 are uniformly distributed random numbers in the range [0; 1]; and dmin and
7
dmax are experimentally-identified minimum and maximum sizes, respectively, in the annular
region i : ri−1 ≤ r ≤ ri .
The number of droplets in parcel k is calculated as :
nk = ck · fk
(13)
where ck is determined from mass conservation and the measured ensemble-average mass flux;
and fk is the measured PDF value associated with dk .
Determination of Initial Droplet Velocities
The initial velocity vector components of parcel k are specified by : (i) the velocity magnitude
Vk ; (ii) the injection angle φk measured circumferentially; and (iii) the angle θk between the
injection direction and the spray axis. The angle φk is taken to have a random value in the
range [0; 2π], and Vk and θk are evaluated using an iterative trial-and-error procedure, aimed at
reproducing as best as possible the measured size distributions and mean droplet size-velocity
correlations at the downstream measurement plane.
In the iterative procedure, θk is determined by requiring that parcel k has a radial position
rk in the measurement plane. As illustrated in Figure 5, the droplet trajectory is usually curved
and depends on the droplet size and the induced gas velocity, hence there is a difference in the
measurement plane between the actual intersection radius rk and the nominal radius rn obtained
by assuming a straight trajectory at angle θk . This gap is called the radial shift rsh :
rsh = rk − rn
(14)
Clearly, the shift is a function of droplet size and gas flow field and hence is not known a priori.
To determine it, we start with a guessed value, and make corrections in the course of iteration
by reference to the experimental data.
The angle θk is then evaluated from :
rn
θk = arctan
L
(15)
where L is the axial distance from the nozzle to the measurement plane.
To evaluate the velocity magnitude Vk , we decompose it into two parts :
Vk = V̄inj + vk
(16)
in which V̄inj is the mean injection velocity which is estimated from the measurement, and
vk is the deviation velocity which depends on the droplet size dk . Estimation of vk follows
a similar iterative procedure to that of rsh : one commences with a guessed value and makes
repeated corrections until close agreement is obtained with the measured downstream droplet
size-velocity correlations.
EXPERIMENTAL VALIDATION
Two sources of experimental data are employed to assess the spray initialisation procedure and
the modified impingement model. They are described below.
8
Experiments of Posylkin [34]
These were made to investigate free spray characteristics. A single-hole Bosch 0280 150 701
injector was used to inject Trimethylpentane fuel in a pulsed manner into the test chamber
containing initially quiescent atmospheric air at 25◦ C. One pulse lasts for a period of 7 ms,
introducing a total volume of 30mm3 Trimethylpentane per pulse. The injection frequency
is 10 Hz, yielding a pulse spacing of 100 ms. The injection pressure is 3 bar, which gives a
typical injection velocity of around 20 m/s. A phase-Doppler anemometer (PDA) was utilised
to measure ensemble-averaged droplet size and velocity characteristics at a horizontal crosssection 80 mm downstream of the injector (see Figure 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.
Experiments of Arcoumanis et al. [35]
Using the same injector and injection conditions as just described in the above experiments,
Arcoumanis et al. [35] performed experiments on oblique gasoline spray impingement inside a
wind tunnel which had a rectangular cross-section of 32 × 172 mm. The geometry is illustrated
in Figure 7. The injector was positioned at the top along the centre line of the tunnel, and
the injection direction is 20◦ inclined to the vertical, in the downstream sense. The air is at
atmospheric pressure and room temperature.
Two cases were investigated in the experiments, involving mean cross flow air velocities of
5 m/s (Case A) and 15 m/s (Case B) respectively. Measurements were made using the PDA
technique of ensemble-averaged droplet sizes and velocities at four different positions a, b, c, d,
which, as illustrated in Figure 8, 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 5mm above the
impingement wall.
In addition, a high speed cine camera was used to take photographs of the injected spray at
regular time intervals for both cases. No quantitative data were deduced from these photographs.
RESULTS AND DISCUSSION
Both the impingement model and the spray initialisation procedure are implemented into the
STAR-CD code, which uses a finite-volume methodology and the k − ε−model for the gas phase
and a stochastic Lagrangian method for the spray. The results of the comparisons between the
prediction and measurements are presented and discussed below.
Free Spray Simulation
The purpose here is to assess the procedure for determining the initial conditions for the Bosch
0280 150 701 injector from the downstream data. In the calculations, the injector is located at
one face of a cubic computation domain with a side length of 80 mm. The computational time
step is 0.1 ms, and droplet introduction rate is 1000parcels/ms. The initial droplet sizes and
velocities at the nozzle location are estimated by the procedure described earlier
Figure 9 shows the predicted spray patterns at four times after start of injection. It can be
seen that as time goes on, the spray moves downward along its axis and expands radially, causing
a continuous increase of spray volume. This behaviour corresponds qualitatively to photographs
of the spray development which are not reproduced here.
The calculated and measured time-average droplet size distributions for a pulse are compared
in Figure 10 at the 80 mm downstream plane for four different annular regions. Here the
measured PDF was obtained as follows. First, for a particular cycle, the maximum and minimum
droplet sizes, dmax , dmin , were recorded, along with the total number, N of the droplets collected
in each annular region during the whole cycle. Then, the size range [dmin ; dmax ] is divided into
9
a number of bins. By counting the number of droplets collected in each bin and dividing it by
N , one obtains the normalised PDF value for this bin. The final PDF data are obtained by
ensemble-averaging to the PDF values obtained in each bin and each cycle of the measurements.
In the calculations, the PDF is obtained by time-averaging the data for any spray pulse.
Inspection of each plot in Figure 10 reveals that the calculated PDF captures fairly well
the general trend of the measured PDF in nearly all regions. Appreciable discrepancies are
noticeable in the central circular region (0 < r < 5 mm) where the occurrence probability of
droplets with sizes in the range 50 − 100 µm is substantially underestimated in the calculations.
However, the calculated correlation between droplet size and velocity agrees quite closely with
the measured one, as evidenced in Figure 11. Note that in this figure, each plot shows a dip at
a mean size of around 300 µm. This appears difficult to understand, for one would normally
expect that larger droplets experience less air drag and therefore travel faster. This abnormal
behaviour may be due to insufficient droplet samples with size around 300 µm being collected
at the measurement locations for statistical accuracy. Nevertheless, we have made the efforts
here to reproduce well the measured trend.
The above results indicate that the proposed estimation procedure for initial droplet sizes
and velocities can reproduce fairly well the measured mean droplet size and velocity behaviour
at the measurement plane 80 mm downstream. However, it should be noted that this does not
necessarily guarantee that similar agreement will apply near the nozzle, in particular at the
closer plane 32 mm downstream, which is the distance between the nozzle and the impingement
wall.
Simulation of Wind-tunnel Gasoline Spray Impingement
Presented and discussed next are the calculated results for the wind tunnel experiments, using
the above initial conditions. The results are obtained using the new modified model unless
stated otherwise. Droplet aerodynamic breakup and collision/coalescence are allowed for in
these calculations.
Figures 12 and 13 compare the predicted and measured spray patterns at three times after
start of injection for cases A and B, respectively. It can be seen that the computed spray
corresponds well with the experimental pictures. The wall spray formed by impingement consists
mostly of smaller droplets produced by splashing, and moves mainly along the wall in the
downstream direction, although a few droplets are seen to move upstream. It can be further
observed that the calculated wall spray dimensions appear to be larger than the measured one,
although the discrepancy is acceptable, since that the real droplets are less visible. It is also
noticeable that the very small droplets are carried away by the cross flow before they reach the
wall.
The calculated and measured droplet size distributions at locations a, b, c, and d (see Figure
8) are presented in Figures 14, 16, 18 and 20 for both cases, whilst the results for droplet
mean size and velocity correlations are displayed in Figures 15, 17, 19 and 21. Here the curves
with solid and open triangular symbols stand for the measurements and calculations respectively;
and the open square symbols in Figures 14 and 15 represent the corresponding calculated results
using the original model of Bai and Gosman [15]. Also, two different populations of droplets
are distinguished: one set, represented by downward-facing triangular symbols, consists of the
droplets which are moving towards the wall; and the other, displayed by upward-facing symbols,
comprises the droplets moving away from the wall.
Both the measured and calculated data on droplet sizes and velocities were obtained by taking
into account all the droplets passing through the PDA measurement volume (in the experiment)
or the computed volume of 10×2× 4 mm (in the calculations) containing the location P , over
a time window of 100 ms which is the pulse time.
10
Let us consider first the results for Case A involving an air flow rate of 5 m/s. The improved
performance of the modified impingement model is evidenced in Figures 14 and 15 which shows
that the measured data on droplet size distributions and size-velocity correlations at four locations are in better agreement with the calculations obtained with the modified impingement
model than with the old model. In particular, the outgoing droplet velocities in the near-wall
region are substantially over-predicted by the old model, due to its under-estimation of the
energy dissipation of splashing droplets when the impact energy is above a certain level.
The calculated size distributions for the upward-moving droplets with the modified model
show reasonable agreement with the measurements, as evidenced in Figure 14. However, the
peak values at all locations are overpredicted and show a slight rightward shift in the calculations.
This implies that the calculations exhibit a higher occurrence probability of large droplets within
the wall spray. Also noticeable in Figure 14 is that droplets with sizes less than 50 µm were
not predicted at locations a, b, and c, whilst they were detected in the measurements. These
differences may be linked to the behaviour of those droplets coming directly from the nozzle,
as illustrated in Figure 16 which shows further noteworthy features. Firstly, there is reasonable
agreement between the measured and calculated size distributions for those droplets coming
directly from the nozzle. Secondly, the calculations show that more droplets with larger sizes
are predicted than measured. In particular, no droplets with sizes less than 60 µm make their
appearance in the calculations. This may explain why the same problem appears in Figure 14,
as explained earlier. The discrepancies exhibited in Figure 16 may be linked to the uncertainties
in the estimated initial conditions for the spray.
Figures 15 and 17 depict the droplet mean velocities in the direction normal to the wall
for upward and downward moving droplets, respectively. It is evident in Figure 15 that the
calculated correlation between mean droplet sizes and upward velocities shows close agreement
with the measurements at all locations for droplet sizes ranging from around 40 − 220 µm. We
also note that the calculations predict no droplets with sizes larger than about 220 µm, whilst
the measured droplet sizes cover a range from 20 to 380 µm. Also, except at location c, the
largest droplet (with d ≈ 380 µm) has a peak velocity magnitude of around 2 m/s. This latter
behaviour appears to be quite peculiar and may be due to experimental error, for analysis shows
it violates the energy conservation.
Figure 17 reveals that the calculated droplets (encompassing a wide range of sizes) coming
from the nozzle possess appreciably larger velocities than the measured ones at locations a and b,
whereas the reverse trend is observed at locations c and d which are outside of the impingement
zone. The large discrepancies at location d suggest that the derived droplet initial conditions at
the nozzle from free spray measurement produce erroneous incoming droplet predictions.
Attention is now directed to the results of Case B, for the higher cross flow rate at 15 m/s.
The calculated and measured droplet size distributions are compared in Figure 18 and 20,
again for the two groups of droplets moving upward and downward respectively. Once more,
good agreement is observed for upward-moving droplets in Figure 18 where the measured and
calculated sizes fall nearly within the same range, although the model estimates more larger
droplets. Moderate agreement exists for downward-moving droplets, as depicted in Figure 20,
which shows a similar trend to that in Figure 16 for Case A.
It is of interest to compare Figures 20 and 16. We see that, as indicated by the PDF values,
in Case B fewer smaller droplets with sizes less than 50 µm appear at the locations a and b
within the impingement zone than in Case A, since in the former case the higher cross flow rate
directly carries away more smaller droplets before they reach the near-wall region. This feature
is more evident in the measured data than in the calculations.
Figure 19 shows fairly good agreement between the calculated and measured size-velocity
correlations for the droplets moving away from the wall, although the calculations consistently
underestimate the velocity magnitudes. However in Figure 21 we again see larger deviations
11
for the incoming droplet normal velocities at locations outside of the impingement zone, for the
reasons discussed earlier.
CONCLUSIONS
A modified spray impingement model has been developed for the simulation of gasoline spray
wall impact. It has been assessed against oblique gasoline spray impingement experiments in a
wind tunnel involving different cross flow rates, for which the effective spray initial conditions
have been approximated by a specially-derived empirical procedure using the measured droplet
size and velocity characteristics in a free spray case. The calculated results show in general
reasonable agreement with the measurement data. However, there is a clear need to further
validate the model against the experimental data on local quantities including mean droplet
sizes and velocities as a function of time at different locations in the near-wall region. The need
also exists to refine the model further in the aspects of regime transition correlations and the
treatment of post-impingement characteristics by including the effects of (i) neighbouring and
earlier-arrived droplets; (ii) the near-wall gas boundary layers; and (iii) elevated gas temperature
and pressure in which case the droplet is usually surrounded by a vapour layer due to the strong
evaporation which may well modify the impingement outcome. These matters are discussed
further in the next section.
FUTURE WORK
The main challenge here lies in achieving a much deeper understanding of the fundamental
mechanisms involved in the spray impingement processes, through both theoretical analysis and
experimental investigation. Recently, experimental and theoretical work by some researchers
(eg. Yarin and Weiss [24, 36], Mundo et al. [25] and Kim et al. [37] among others) has produced
additional information. For instance, Yarin and Weiss [24] have recently provided some interesting results on droplet splashing. Specifically, by allowing a mono-disperse train of droplets to
impact onto a solid surface, they have established a correlation describing the transition from
spread to splash which takes into account of the droplet impingement frequency f - a parameter characterising a group of impinging droplets. The correlation states that splash occurs if a
dimensionless impact velocity u exceeds 17 :
VIN
≥ 17
u = 1/4 1/8
µ
σ
3/8
f
ρ
ρ
(17)
Although Equation (17) is derived for specific experimental conditions and suffers from a shortage that it does not contain incident droplet diameter dI , it may well serve as a good starting
point to establish a more general transition criterion from spread to splash so that it is applicable
to practical spray impingement situations with allowance for the effects of neighbouring droplets.
Yarin and Weiss also provided measurements for the mass ratio, rm = ms /mI , which increases
monotonically with u from about 0.2 to around 0.85. (Note that these lower and upper bound
values are close to what we used for the dry wall, which are 0.2 and 0.8). This may help us to
establish a better correlation for mr . As for secondary droplet velocity distributions, Mundo
et al. [25] have provided experimental data which might be useful in the development of new
equations for the estimation of these.
12
ACKNOWLEDGEMENT
Financial support for this work was provided in part by the Commission of the European Communities in the framework of Non Nuclear Energy Programme (JOULE III). The authors wish
to express their gratitude to Professor J. H. Whitelaw and colleagues for their assistance in
providing the experimental data presented in this paper.
REFERENCES
References
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13
15. C. X. Bai and A. D. Gosman, Development of a Methodology for Spray Impingement
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17. A. Thedorakakos M. Gavaises and G. Bergeles, Modelling Wall Impaction of Diesel Sprays,
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18. C. Mundo, M. Sommerfeld, and C. Tropea, Spray Wall Impingement Phenomena: Experimental Investigations and Numerical Predictions, In 12th Annual Conference of ICLASSEurope, Lund, Sweden, pp. 19–21, Jun 1996.
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Wall for Gasoline Engines, SAE paper 940525, 1994.
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Atomisation Behaviour in SI Engine Based on the Oval-parabola Trajectories (OPT) Model,
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a Liquid Film, Int. J. Multiphase Flow, vol.14 pp. 129–140, 1988.
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Waves and Splashing as a New type of Kinematic Discontinuity, J. Fluid Mech.,vol. 283,
pp. 141–173, 1996.
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of the Deformation and Breakup Process, Int. J. Multiphase Flow, vol. 21, pp. 151–173,
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Resources Res., vol. 7, pp. 195–200, 1971.
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on Thin Water Layers, PhD thesis, University of Minnesota, 1970.
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Reading, 1978.
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31. C. X. Bai and A. D. Gosman, A Theoretical Analysis of Single Droplet Impingement Process,
In preparation.
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1996.
14
33. H. Rusche, CFD Simulation of Spray Impingement Processes, Diploma Thesis, University
of Hannover, 1997.
34. M. Posylkin. private communication, 1997.
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and Films, Atomization and Sprays, vol. 7, pp. 437–456, 1997.
36. D. A. Weiss and A. L. Yarin, Single Drop Impact onto Liquid Films: Neck Distortion,
Jetting, Tiny Bubbles Entrainment, and Crown Formation, J. Fluid Mech., vol. 385, pp.
229–254, 1999.
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upon Collision with a Solid Surface, Phys. Fluids, vol. 12, pp. 531–541, 2000.
NOMENCLATURE
Latin Symbols
Symbol
a0
Cf
d
dv
ED
EK
Eσ
f
K
L
m
ms
M
N
NS
p
rm
rs
rsh
T
V
V̄inj
Description
Model constant
Friction coefficient
Droplet diameter
Volumetric mean droplet diameter
Dissipative energy loss
Kinetic energy
Droplet surface energy
Size distribution; Droplet impingement frequency
number of cross-sections
Axial distance from the nozzle
Droplet mass
Total mass of splashing droplets
number of parcels per cross-section
number of injected parcels
Number of secondary droplets due to splashing
Number of droplet parcels
Ratio of total mass of splashing droplets to incident droplet mass
Surface roughness
radial shift
Temperature
Velocity
Mean spray injection velocity
Greek Symbols
α
β
δ0
γ
µ
φ
ρ
σ
θ
Model constant
Model constant
Initial film thickness
Random number
Dynamic viscosity
Angle
Density
Surface tension
Angle
15
Dimensionless numbers
La
u
We
Droplet Laplace number
Dimensionless impact velocity
Droplet Weber number
Subscripts
b
B
c
d
g
i
I
k
S
min
max
N
rel
T
w
bounding
Boiling
critical
Droplet
gas
ith parcel (i=2...p); ith region (i=1...N)
Incident droplet
kth droplet parcel (k=1...M)
Splashing droplet
minimum
maximum
Normal component; due to the normal component of incident velocity
relative
Tangential component; due to the tangental component of incident velocity
Wall
List of Figures
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Diagram illustrating droplet impingement onto a wall . . . . . . . . . . . . . . .
Schematic of different impact regimes . . . . . . . . . . . . . . . . . . . . . . . .
Two dimensional representation of ejection velocity vectors, VSN ’s, all of which
form a symmetric crown. Note that VSN ’s are caused solely by normal incident
velocity VIN and the ejection angle θS actually varies from a small bounding
angle θb to around 90◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Division of measurement circular region with radius, rmax into a number of annular regions with an equal area . . . . . . . . . . . . . . . . . . . . . . . . . . .
Illustration of radial shift definition . . . . . . . . . . . . . . . . . . . . . . . . . .
Diagram showing plane of measurement for free spray experiment . . . . . . . .
Sketch of wind tunnel geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Illustration of measurement locations for wind tunnel experiments . . . . . . . .
Predicted spray development for free spray case . . . . . . . . . . . . . . . . . . .
Predicted and measured droplet size distributions for free spray case . . . . . . .
Predicted and measured droplet axial velocities within the measured plane for
free spray case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Predicted and measured spray patterns at three times for wind tunnel case A
(cross flow rate: w = 5 m/s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Predicted and measured spray patterns at three times for wind tunnel case B
(cross flow rate: w = 15 m/s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Predicted and measured size distributions of upward-moving droplets at four locations for wind tunnel case A (cross flow rate: w = 5 m/s) . . . . . . . . . . . .
Predicted and measured correlations between normal velocities and sizes for upwardmoving droplets at four locations for wind tunnel case A (cross flow rate: w = 5 m/s)
Predicted and measured size distributions of downward-moving droplets at four
locations for wind tunnel case A (cross flow rate: w = 5 m/s) . . . . . . . . . . .
16
28
29
29
30
30
31
31
32
32
33
33
34
35
36
36
37
17
18
19
20
21
Predicted and measured correlations between normal velocities and sizes for downwardmoving droplets at four locations for wind tunnel case A (cross flow rate: w = 5 m/s) 37
Predicted and measured size distributions of upward-moving droplets at four locations for wind tunnel case B (cross flow rate: w = 15 m/s) . . . . . . . . . . . 38
Predicted and measured correlations between normal velocities and sizes for upwardmoving droplets at four locations for wind tunnel case B (cross flow rate: w =
15 m/s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Predicted and measured size distributions of downward-moving droplets at four
locations for wind tunnel case B (cross flow rate: w = 15 m/s) . . . . . . . . . . 39
Predicted and measured correlations between normal velocities and sizes for downwardmoving droplets at four locations for wind tunnel case B (cross flow rate: w =
15 m/s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
VIT
dS
Tw
VST
VS
VSN
θS
VI
dI
TI
VIN
θI
Figure 1: Diagram illustrating droplet impingement onto a wall
17
θR
(b)
(a) STICK
θI
BOUNCE
(d) BOILING−INDUCED
(c) SPREAD
BREAK−UP
(e) REBOUND WITH
(f)
BREAK−UP
BREAK−UP
(g) SPLASH
Figure 2: Schematic of different impact regimes
VIN
VSN
VSN
θs
θb
Figure 3: Two dimensional representation of ejection velocity vectors, VSN ’s, all of which form
a symmetric crown. Note that VSN ’s are caused solely by normal incident velocity VIN and
the ejection angle θS actually varies from a small bounding angle θb to around 90◦
18
region i
CCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
r max
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
ri
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
AAAAAAAAA
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
AAAAAAAAA
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
AAAAAAAAA
ri−1
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
AAAAAAAAA
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
AAAAAAAAA
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
AAAAAAAAA
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
AAAAAAAAA
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
AAAAAAAAA
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
AAAAAAAAA
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
CCCCCCCCCCCCCCCCCCCCCCCCC
BBBBBBBBBBBBBBBBBBBBB
CCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCC
region 1
Figure 4: Division of measurement circular region with radius, rmax into a number of annular
regions with an equal area
θk
rk
rn
Figure 5: Illustration of radial shift definition
19
CCCCCC
CCCCCC Injector
CCCCCC
CCCCCC
CCCCCC
CCCCCC
80 mm
16 deg
r
Plane of Measurements
32 mm
172 mm
Figure 6: Diagram showing plane of measurement for free spray experiment
Air Flow
Top
Window
Injector
CCCC
CCCC Injector
CCCC
CCCC
Side
20 deg
Window CCCC
Air Flow
Figure 7: Sketch of wind tunnel geometry
20
Z= 25 mm
20 mm
15 mm
12 mm
5 mm d
c
b
a
Figure 8: Illustration of measurement locations for wind tunnel experiments
1 ms after Start of Inj.
2 ms after Start of Inj.
3 ms after Start of Inj.
4 ms after Start of Inj.
Figure 9: Predicted spray development for free spray case
21
0mm < r < 5mm
normalized PDF
0.015
5mm < r < 10mm
Measurements
Calculations
0.010
0.005
0.000
10mm < r < 15mm
normalized PDF
0.015
15mm < r < 22.5mm
0.010
0.005
0.000
0.0
100.0
200.0
Droplet Diameter [µm]
0.0
100.0
200.0
Droplet Diameter [µm]
Droplet axial velocity [m/s]
Droplet axial velocity [m/s]
Figure 10: Predicted and measured droplet size distributions for free spray case
30.0
0mm < r < 5mm
5mm < r < 10mm
Measurements
Calculations
25.0
20.0
15.0
10.0
5.0
30.0
15mm < r < 22.5mm
10mm < r < 15mm
25.0
20.0
15.0
10.0
5.0
0.0
0.0
100.0 200.0 300.0 400.0 0.0 100.0 200.0 300.0 400.0
Droplet Diameter [µm]
Droplet Diameter [µm]
Figure 11: Predicted and measured droplet axial velocities within the measured plane for free
spray case
22
t=3 ms
32 mm
t=5 ms
t=7 ms
Figure 12: Predicted and measured spray patterns at three times for wind tunnel case A (cross
flow rate: w = 5 m/s)
23
t=3 ms
32 mm
t=5 ms
t=7 ms
Figure 13: Predicted and measured spray patterns at three times for wind tunnel case B (cross
flow rate: w = 15 m/s)
24
Measurements
Calculations with modified model
Calculations with original model
Normalised PDF
0.040
0.040
Location a
0.030
0.020
0.020
0.010
0.010
0.000
0
100
200
300
0.000
400
0.030
Normalised PDF
Location b
0.030
0
100 200 300 400
0.030
Location c
0.020
0.020
0.010
0.010
0.000
0
0.000
100 200 300 400
Droplet diameter [µm]
Location d
0
100
200
300
400
Droplet diameter [µm]
Figure 14: Predicted and measured size distributions of upward-moving droplets at four locations
for wind tunnel case A (cross flow rate: w = 5 m/s)
Droplet mean velocity [m/s]
Droplet mean velocity [m/s]
Measurements
Calculations with modified model
Calculations with original model
Location a
3.0
2.0
2.0
1.0
1.0
0.0
0
100
200
300
0.0
400
Location c
3.0
2.0
1.0
1.0
0
100
200
300
0
0.0
400
Droplet diameter [µm]
100
200
300
400
Location d
3.0
2.0
0.0
Location b
3.0
0
100
200
300
400
Droplet diameter [µm]
Figure 15: Predicted and measured correlations between normal velocities and sizes for upwardmoving droplets at four locations for wind tunnel case A (cross flow rate: w = 5 m/s)
25
Normalised PDF
0.040
0.040
Location a
0.030
0.020
0.020
0.010
0.010
0.000
0
100
200
300
Location b
0.030
0.000
400
0
100
200
300
400
Measurements
Calculations
Normalised PDF
0.040
0.040
Location c
0.030
0.020
0.020
0.010
0.010
0.000
0
100
200
300
Location d
0.030
0.000
0.0
400
Droplet diameter [µm]
100
200
300
400
Droplet diameter [µm]
Droplet mean velocity [m/s]
Droplet mean velocity [m/s]
Figure 16: Predicted and measured size distributions of downward-moving droplets at four
locations for wind tunnel case A (cross flow rate: w = 5 m/s)
25.0
25.0
Location a
Location b
20.0
20.0
15.0
15.0
10.0
10.0
5.0
0
100
200
300
5.0
400
0
100
200
300
400
300
400
Measurements
Calculations
25.0
25.0
Location c
20.0
15.0
15.0
10.0
10.0
5.0
5.0
0.0
0
100
200
Location d
20.0
300
0.0
400
Droplet diameter [µm]
0
100
200
Droplet diameter [µm]
Figure 17: Predicted and measured correlations between normal velocities and sizes for
downward-moving droplets at four locations for wind tunnel case A (cross flow rate: w = 5 m/s)
26
Normalised PDF
0.040
0.040
Location a
0.030
0.020
0.020
0.010
0.010
0.000
0.0
100.0
200.0
Location b
0.030
0.000
0.0
300.0
50.0 100.0 150.0 200.0
Measurements
Calculations
Normalised PDF
0.040
0.040
0.030
0.030
Location c
0.020
0.020
0.010
0.010
0.000
0.0
100.0
200.0
Location d
0.000
0.0
300.0
Droplet diameter [µm]
50.0 100.0 150.0 200.0
Droplet diameter [µm]
Droplet mean velocity [m/s]
Droplet mean velocity [m/s]
Figure 18: Predicted and measured size distributions of upward-moving droplets at four locations
for wind tunnel case B (cross flow rate: w = 15 m/s)
10.0
8.0
10.0
Location b
8.0
Location a
6.0
6.0
4.0
4.0
2.0
2.0
0.0
0.0 100.0 200.0 300.0 400.0
0.0
0.0 100.0 200.0 300.0 400.0
Measurements
Calculations
10.0
8.0
10.0
8.0
Location c
Location d
6.0
6.0
4.0
4.0
2.0
2.0
0.0
0.0 100.0 200.0 300.0 400.0
0.0
0.0 100.0 200.0 300.0 400.0
Droplet diameter [µm]
Droplet diameter [µm]
Figure 19: Predicted and measured correlations between normal velocities and sizes for upwardmoving droplets at four locations for wind tunnel case B (cross flow rate: w = 15 m/s)
27
Normalised PDF
0.040
0.040
Location a
0.030
Location b
0.030
0.020
0.020
0.010
0.010
0.000
0.0 100.0 200.0 300.0 400.0
0.000
0.0 100.0 200.0 300.0 400.0
Measurements
Calculations
Normalised PDF
0.040
0.040
0.030
0.030
Location c
Location d
0.020
0.020
0.010
0.010
0.000
0.0 100.0 200.0 300.0 400.0
0.000
0.0 100.0 200.0 300.0 400.0
Droplet diameter [µm]
Droplet diameter [µm]
Droplet mean velocity [m/s]
Droplet mean velocity [m/s]
Figure 20: Predicted and measured size distributions of downward-moving droplets at four
locations for wind tunnel case B (cross flow rate: w = 15 m/s)
25.0
25.0
20.0
20.0
15.0
15.0
10.0
10.0
Location a
Location b
5.0
5.0
0.0
0.0 100.0 200.0 300.0 400.0
0.0
0.0 100.0 200.0 300.0 400.0
Measurements
Calculations
25.0
20.0
25.0
20.0
Location c
Location d
15.0
15.0
10.0
10.0
5.0
5.0
0.0
0.0 100.0 200.0 300.0 400.0
0.0
0.0 100.0 200.0 300.0 400.0
Droplet diameter [µm]
Droplet diameter [µm]
Figure 21: Predicted and measured correlations between normal velocities and sizes for
downward-moving droplets at four locations for wind tunnel case B (cross flow rate: w = 15 m/s)
28