Modeling Fuel Film Formation and Wall Interaction in Diesel Engines

17 Pages·0.717 MB·English

by  Stanton D., Rutland C.

960628

Modeling Fuel Film Formation and Wall
Interaction in Diesel Engines

Donald Stanton and Christopher Rutland
Engine Research Center
University of Wisconsin - Madison

ABSTRACT chamber, or directly in cylinder. In all these designs, the
fuel spray may impinge on engine surfaces before
vaporization and mixing are complete. Spray
A fuel film model has been developed and impingement has been shown to influence engine
implemented into the KIVA-II code to help account for performance and emissions in both compression ignited
fuel distribution during combustion in diesel engines. (CI) and spark ignited engines (SI).
Spray-wall interaction and spray-film interaction are also Impingement in port injected engines causes
incorporated into the model. difficulties, especially in transient control of the system.
The model simulates thin fuel film flow on solid A major factor affecting air-fuel ratio during transient
surfaces of arbitrary configuration. This is achieved by operation is the time lag resulting from a film of liquid
solving the continuity and momentum equations for the fuel deposited on the surface of the induction system*
two dimensional film that flows over a three dimensional [1,2]. This time lag is responsible for decreased engine
surface. The major physical effects considered in the response, increased fuel consumption, and increased
model include mass and momentum contributions to the emissions [3]. In port injection engines, a strategy used
film due to spray drop impingement, splashing effects, to decrease the time lag is to spray the fuel on the back
various shear forces, piston acceleration, and dynamic of the intake valve to decrease the amount of liquid fuel
pressure effects. In order to adequately represent the spread on the walls of the induction system. Yoshikawa
drop interaction process, impingement regimes and [4] performed 3-D modeling of the spray-valve
post-impingement behavior have been modeled using interaction and observed extensive drop interaction
experimental data and mass, momentum and energy between the induction port and intake valve. This
conservation constraints. The regimes modeled for interaction is an important source of liquid atomization
spray-film interaction are stick, rebound, spread, and and vaporization. A better understanding of these
splash. interactions between the liquid and induction surfaces
Numerical simulations are compared to experimental will help in designing injection systems and control
data for spray impingement normal to the wall. The film strategies to improve engine performance and to control
model compared extremely well with experimental data emissions.
for secondary droplet velocities, spray radius, spray Spray-wall interactions are also important in direct
height, film thickness estimations, and percent of fuel injection (DI) diesel engines. Several investigators have
adhering to the wall. In addition, diesel engine shown that spray impingement affects engine
simulations are also presented. The film spreading performance and exhaust emissions [5,6]. The influence
characteristics, amount of fuel deposited on the wall, of spray impingement is extremely important in small
and fuel film thickness provide insight into cold starting bore DI engines where the decreased distance between
spray-wall interactions. the injector and the piston make impingement more
Finally, recommendations are given concerning the likely. In most small bore engines at high load where the
addition of thermal and evaporative processes to the fueling is increased, the spray impingement results in a
model. liquid film formed on the piston and cylinder wall. Under
these conditions, fuel impingement is nearly unavoidable
INTRODUCTION and in some cases it is desirable. Werlberger and
Cartellieri [7]observed the impinging spray in a small
Spray-wall interaction is considered an bore (85 mm) DI diesel engine and determined that at
important phenomena in internal combustion engines high loads more than 50 percent of the fuel impinged
(IC). The majority of the fuels used in IC engines must upon the piston bowl. In computational studies,
be vaporized and mixed with the gas charge in order to Gonzales et al. [8] also found that spray impingement
combust, expand, and produce power. In an attempt to
achieve desirable air-fuel mixing and combustion, the
fuels are sprayed in either the carburetor, port, pre- * Numbers in brackets designate references
listed at the end of this paper.
was an important factor in cold start. The smoke levels film interaction model.
have been shown to increase during cold start as a In general, the impingement regimes are
result of the accumulation of fuel on the cylinder wall [9]. determined by the parameters describing the arriving
While some engine designers seek to eliminate fuel drops, the wall surface conditions and (if present) the
impingement, others invite increased spray impingement gas boundary layer characteristics in the near-wall
as a means of increasing fuel distribution and mixing region. Of particular interest in identifying impingement
[10]. In some DI engines, the fuel spray has been regimes is the wall temperature relative to the following
intentionally impinged on a surface in the engine as a temperatures
method to control combustion. One early system to use
such a technique was the M-combustion system
T <T <T <T <T
developed by MAN (Maschinefabrik Augsburg Nürnberg) B pa N pr Leid
[11]. In the conventional M-combustion system, the fuel

is injected on the surface of the piston bowl forming a
where TB is the liquid boiling temperature, Tpa is the
liquid film. The advantage of the fuel impingement is
pure adhesion temperature below which drop adhesion
that vaporization of this liquid film controls the rate of
combustion which allowed the use of low cetane fuels occurs at low impact energy, TN is the Nakayama
such as gasoline (cetane number = 20) in the engine. temperature at which a drop reaches its maximum
Since various researcher's conclusions about the evaporation rate, Tpr is the pure rebound temperature
effects of spray impingement in DI engines are above which bounce occurs at low impact energy, and
inconsistent, it becomes more apparent how TLeid is the Leidenfrost temperature [10]. The collision
complicated the processes of injection, impingement, of a drop with a liquid surface, where the wall
mixing, and combustion are in the engine. To better temperature (Tw) is less than the liquid boiling
understand how the variables in these individual temperature (TB), may result in sticking, bouncing,
processes influence the overall engine performance and spreading, or splashing (Kolpakov et al., 1985). These
emissions, it is often necessary to concentrate on a
impingement regimes are shown in Fig. 1.
single process occurring in the engine to better

understand how it may influence overall engine

performance. The objective of this research is to
investigate spray-film impingement, liquid film formation,
and post-impingement processes as related to DI diesel
engines. More specifically, this research will examine in
detail what happens to drops that impinge on solid
surfaces that eventually form a liquid fuel film. Also,
keeping an account of the fuel film distribution during the
mixing and combustion processes is a goal of this
Stick Rebound
research. Consequently, drop impingement on a wetted
surface is examined along with post-impingement
processes including splashing phenomena. By
examining the effects of spray impingement and fuel film
formation, this work can be incorporated with wall heat
transfer effects in order to complete the formulation and
validation of a wall-spray interaction model to be
employed in the KIVA-II code [12].
Spread Splash

Figure1: The various impingement regimes identified in

the spray- film interaction model.
MODEL FORMULATION

SPRAY-FILM INTERACTION MODEL - Many different
The stick regime occurs when an impinging drop
scenarios of drop impact can be distinguished according
adheres to the film surface in nearly a spherical form.
to the circumstances under which the impact happens.
This often happens when the impact energy is extremely
The outcome of a collision depends on the properties of
low, and the wall temperature is below the pure
the drop, of the impact surface, and of the fluid which the
adhesion temperature, Tpa. The transition criteria for
drop traverses before impact. The surface impacted can
the stick regime is We < 5, where the Weber number is
be either solid or liquid. In this case, the solid surface is
calculated using the normal velocity of the incident drop.
covered by a thin, liquid film. In diesel engine spray

impingement, a collection of drops impinge onto the
ρd V 2
wetted surface simultaneously or successively with the We= d nd
likelihood that each impinging drop will feel the effects of σ
its neighboring drops. Information on multi-drop

impingement (i.e., a train of drops with a known
This criteria is based on the experimental results of
frequency) exists that is useful in formulating the spray-
various investigations [14, 15, 16]. In this spray-film
model, a drop that is in this regime is assumed to of the liquid film as described in the next section.
coalesce completely with the liquid film. The spreading regime is similar to the sticking
Next, the rebound regime occurs when the regime but occurs at higher We. In this regime, the drop
impinging drop bounces off the film when the impact merges with the liquid film upon impact. The transition
energy is low. The air layer trapped between the drop criteria for spreading is:
and the liquid film causes low energy loss resulting in
1
bouncing. The transition criteria for the rebounding ρ2 1 3
regime is 5 < We < 10. This criteria is based on the 10 < We <18.02dd σ ν4 f 4 (4)
experimental work of [14] and [17]. In this regime, the
rebound drop velocity magnitude and direction need to

be determined. The velocity of the rebounding drop is
where ρ , σ, ν, and f are the drop density, surface
determined using Eqs. (1) and (2) which were developed
tension, kinematic viscosity, and frequency. The last
by [18] for small particles bouncing on a wetted surface:
term, containing f, in Eq. (4) is known as the splashing

threshold for the multi-drop impact with a thin liquid film
5 as reported by [22].
V′ = V
τd 7 τd (1) The final regime is splashing and occurs at high
impact energy. Upon impact, a crater is formed with a
crown at the periphery where liquid jets become
V′ = −eV
nd nd (2) unstable and break up into many secondary droplets
(see Fig. 3).

where V is the incident drop tangential velocity, V is
τ n
the incidednt drop normal velocity, V′ is the reboundding
τ
drop tangential velocity, V′ is thed rebounding drop
n
d
normal velocity, and e is the coefficient of restitution.
The coefficient of restitution is obtained using Eq. (3) as
reported by [19]:

e = 0.993 - 1.76Θ + 1.56Θ2 − 0.490Θ3 (3)
I I I

where Θ is the incident angle of impingement as
I
measure from the wall surface (see Fig. 2). The in-plane
angle, Ψ, is randomly chosen to vary between 90° and
270° as measure from the x' axis as shown in Fig. 2.

Impinging Dr
Figure 3: The development of a crater and secondary
Rebounding Drop droplets created during the splashing of a drop witj thin
film.
Vn
d
In this regime, many quantities need to be calculated in
'
Vnd ' ΘΙ order to describe the process. These quantities include
Vτ x' the proportion of incident drop mass deposited as part of
d
Vτd the liquid film and the sizes, velocities, and ejection
angles of secondary droplets. The formulation of these
x' Ψ splashing quantities is based on the experimental work
of [22] and [23]. Mundo et al. [23] investigated multi-
drop impingement on rough surfaces, while [22]
Figure 2: Velocity components of a rebounding drop investigated multi-drop impingement on thin liquid films.
from a thin liquid film.
The transition criteria for the splashing regime is

given by the following expression developed by [22]:
The variation in Ψ is consistent with experimental
1
observations of [20] and [21] for drop impingement on ρ2 1 3
rdoifufegrhe nscuer bfaectewse.e n dTrhoeps iem piancvte wstiitgha ato trhsi n rleiqpuoidrt efidlm laitntlde 18.02dd σ ν4 f 4 < We (5)
that of a rough surface. The lost momentum of the
In order to calculate the splashing threshold, the drop
rebounding drop contributes to the momentum balance
frequency, f, needs to be determined. This is
accomplished by calculating f for each impinging drop, process is the total ejected mass. Figure 4 shows the
irregardless of its associated impingement regime. By experimental results of [22] for the mass fraction of
calculating the frequency and using expression (5), each secondary droplets. According to [22], the splashing
impinging drop can be tested for the onset of splashing. threshold occurs at a non-dimensional impact velocity, u,
The frequency is calculated as the inverse of the time of 18. The non-dimensional impact velocity is defined
between drop impacts. The frequency for the first drop as:
to impact the film is ambiguous so it is calculated by:
1
ρ4 − 1 − 3
u =V   ν 8 f 8 (9)
V nd σ
f = nd (6)

d
d
where V and d are the drop normal component of
n d
d
velocity and drop diameter, respectively. 1
The formulation of the splashing events begins
by determining the number of parcels, Nparcel, to be 0.8
used. Each parcel contains a calculated number of n
o
droplets, Ni, with the same kinematic and ti 0.6
c
thermodynamic properties. The choice of the number of a
r
parcels used in the model is influenced by the F
s 0.4
computational effort and memory requirements of the s
a
KIVA-II code. The number of parcels chosen is equal to M
the number of sampling points along the secondary 0.2
droplet distribution curves. The droplet distribution
curves were obtained from the experimental work of [23] 0
for multi-drop impingement on rough surfaces. The 18 20 22 24 26 28 30 32 34
number of sampling points, or parcels, used in this study Non-Dimensional Velocity (u)
is three which provides a minimal, but adequate Figure 4: Total mass of secondary droplets in units
sampling of the curves. of drop volume.
The sampling process begins by determining an
expression for the cumulative probability function (CPF)
for the droplet size distributions given by [23]. The data The mass fraction grows monotonically from zero at the
are fitted to a Weibull distribution equation of the form splashing threshold, apparently tending to a limiting
value which is less than 1 for larger values of u. Also
shown in Fig. 4 is a curve-fit to the data which is given
 b d d b−1  d /d b by the following equation:
pdf(di /dd) = Θ  Θi d  exp− iΘ d   (7)
 w w   w  m
s = −27.2 + 3.15u − 0.116u2 + 1.40×10−3u3 (10)
where m
b = 2.71−9.25×10−4We and d
Θ = 0.210−7.69×10−5We.
w

Once the droplet diameters and mass fraction are
Once the CPF equation for the droplet size distribution is
known, the total number of droplets, Ntot, can be
determined by integrating Eq. (7), three random
determined using mass conservation as expressed in
samples, RNi, can be taken to determine the size of the
Eq. (11):
droplets, di, with i = 1,2,3. Next, the number of particles
with size di can be expressed in terms of the total πN N∑parcel(pdf d3) = ms m (11)
number of secondary droplets, Ntot , using Eq. (7) for 6 tot i i m dd
the pdfi i=1 d
where Nparcel is the number of parcels and m is the
d
d
N = N pdf (8) mass of the incident drop. After Ntot has been
i tot i
calculated, the number of particles, Ni, in each parcel
can be determined using Eq. (8).
with i = 1,2,3 . Equation (8) contains two unknown Finally, the last quantity to be calculated is the
droplet velocity. This involves calculating the normal
quantities, the total number of droplets and the number
component of velocity of the i-th droplet by the empirical
of particles of size di . Both quantities can be calculated
formula:
by an expression for mass conservation once the total
ejected mass, ms/md, is determined.
Thus, another important issue in the splashing
 b V V bv−1  V V bv
pdfi(Vni /Vnd) = Θvv  niΘvnd  exp− niΘvnd   Es = 12mdVs2 (16)
(12)

where
using the velocity at the splashing threshold, Vs, given
 2.1 Θ ≤50(cid:68) by:
b =  I
v 1.10+0.020ΘI ΘI >50(cid:68) σ14 1 3
and Vs = 18ρ ν8 f 8 (17)
Θ = 0.158e0.017ΘI
v
All quantities in Eq. (15) are known; therefore, Eq. (15) is
used to provide a conservation of energy constraint on
This formula was developed using the data from the
the splashing process in the form of a correction factor
experimental work of [23]. These results show that the

influence of the fluid properties on the velocity is rather
small, thus the dominate factor becomes the 1
m V2 + πσN d2 − E
impingement angle, ΘI. Equation (12) is a Weibull 2 d d d d s
ddiissttrriibbuuttiioonn . s imInil ara tsoi mEilaqr. p(7ro) cefodru reth, e thdreroep lerat ndsoizme K = 1 N∑parcel(mV2) + πσN∑parcel(N d2) (18)
samples are used to determine the normal velocity 2 i i i i
i=1 i=1
components using Eq. (12).
The tangential component of velocity of the i-th
droplet is calculated by first determining the reflection
The correction factor is used to compensate for the
angle, Θs, from the linear data fit of the experimental small number of sampling points used to determine the
data given by [23].
normal velocity of the secondary droplets. The

correction factor is applied to the normal and tangential
Θ = 65.4+0.266Θ (13) components of velocity:
s I
V′ = K V (19)
nj nj
Once the normal component of velocity and the and
reflection angle are known, the tangential component of
V′ = K V (20)
velocity can be calculated by: τ τ
j j

This concludes the development of the various
V spray-film impingement regimes, the transition criteria,
Vτi = tan(nΘi ) (14) and post-impingement behavior.
s

LIQUID FILM MODEL - According to [24], spray
Next, an energy balance is performed on the splashing impingement models should include the possibility of the
process: formation of a liquid film on the combustion chamber
surfaces to accurately model spray-wall phenomena.
1Nparcel Nparcel Thus, there exists the need to formulate and validate a
∑ (mV2) + πσ∑ (N d2) = fuel film model to be implemented into the KIVA-II code
2 i i i i to help account for the fuel distribution during
i=1 i=1
combustion in DI diesel engines. The liquid film model is
1 based on the physics involved with fuel film flow over
m V2 + πσN d2 − E (15)
2 d d d d s three dimensional surfaces (see Fig. 5). The fuel film
model simulates thin fuel film flow on solid surfaces of
arbitrary configuration.

where mi is the mass of the i-th parcel ejected, Ni is the

number of particles in the i-th parcel ejected, dd is the

incident drop diameter, Nd is the number of particles in
the incident parcel, and Es is the energy below which no
splashing occurs. Es is estimated using Eq. (16):
Impinging Splashing
fuel drop
Droplets
Film thickness
(exaggerated)
bowl
Shear
force
z
y Liquid film
piston
x
Gravity Driven Flow
Liquid Fuel
Figure 5: Schematic of the liquid film flowing over the
Film
piston bowl.
Wall
The continuity and momentum equations are applied
to each wall film cell as shown in Fig. 6. By integrating Figure 7: The major physical phenomena governing
across the film thickness, X3, and using 'thin film' film flow.
assumptions, the equations are reduced to a two-
dimensional film flowing across a three-dimensional Note that thermal and evaporative processes are not
surface. A typical wall film cell, shown in Fig. 6, has a included as part of this first phase of the model
local coordinate system defined by X1 and X2. By using implementation.
a local coordinate system, the model can be The assumptions used in the formulation of the film
implemented into a computational fluid dynamics code model are the mass flux due to incident drops that
which contains block structure or unstructured grids. impinge is averaged over the wall cell area, lost
tangential momentum of impinging drops is added to the
film tangential momentum, and the velocity profile in the
cross-film direction is prescribed to be either laminar or
nˆ turbulent.
3 After integrating in the cross-film direction, the
X
2 4 continuity equation is transformed into the following form
Flux
14
∂δ 1 Nside →  S
3 δ V nˆ ∂t + A ∑Vfilm⋅nˆδili = ρAd (21)
film 4 wall i=1 i l wall
nˆ

2 X
3
X →
1 1 where Awall is the wall cell area, V is the film
film
nˆ velocity, (cid:65)i is the length of side i, ρl is the film density, δi
2 1 Flux is the film thickness at side i, and Sd is a source term.
21 The film velocity now has two components located at the
liquid-gas interface . The source term, Sd, is the mass
Figure 6: A typical wall film cell used in the formulation
flux of drops that impinge upon the film or secondary
of the film model.
droplets that leave the film which result from splashing.

The continuity equation for the film thickness resembles
The major mechanical physical processes affecting the
the compressible form, because in the two-dimensional
liquid film are shown in Fig. 7. The physical processes formulation the variation of the film thickness is
considered include: mathematically analogous to a virtual compressibility.

• Mass and momentum contributions to the
film due to spray impingement.
• Splashing effects.
• Shear forces on the film.
• Piston acceleration.
• Dynamic pressure effects.
• Gravity driven flow.
pressure term, pd, which results from incident drop
impingement and splashing effects.
τ

liq/gas P = P + p (24)
cell d
with
nˆ Ndrop A Nsplash A
δ wall p = ρ∑V2 dk + ρ ∑ V2 j (25)
d l nd A l nj A
k=1 k wall j=1 wall
V
τwall film
τ
edgei Pcell is the free-stream pressure (i.e., gas pressure).
τedge i Tthhee ivnecliodceintyt , dVrondp, aisn tdh eV no rmis atlh ceo mnopromnaeln ct oomf vpeolnoecintyt ooff
nj
velocity of the i-th secondary droplet resulting from
Figure 8: A typical momentum cell for the liquid film
model. splashing. Ndrop and Nsplash are the total number of
incident drops and the total number of splashed

droplets, respectively. The term, Adk, is the area of the
Figure 8 shows a typical control volume used to k-th incident drop while the Aj is the area of the j-th
formulate the momentum equation for the liquid film. secondary drop. The pressure was assumed not to vary
The momentum equation is transformed into the in the cross-film direction due to the 'thin film'
following form: assumption. The dynamic pressure term (Eq. 25) is
assumed constant normal to the wall.
(cid:71)
( ) The fourth term in Eq. (22) captures the gravity
∂δ⋅V film + 1 Ns∑ideV(cid:71) (V(cid:71) ⋅nˆ )δ(cid:65)φ = effect of the liquid film flow. This effect is important in
∂t Awall i=1 film film i i i film flow along the cylinder wall of the combustion
chamber. The fifth term in Eq. (22) is the
1 2 tangential momentum contribution to the film as a result
of spray impingement and splashing of secondary
droplets. This term is calculated using Eq. (26).
Nside (cid:7) Nedge (cid:71)
∑ (P n )δ(cid:65) ∑ (τ A)
− i=1 i i + g(cid:71)δ + Mtang + i=1 i + a(cid:71)δ (22)
ρA ρA ρA Ndrop →  Nsplash → 
l wall l wall l wall MTang = ∑miVτdi  - ∑ mjVτj  (26)
3 4 5 6 7 i=1 j=1

The first term on the right side of Eq. (26) is the
momentum contribution of the incident drops, while the

second term on the right side is the momentum
The first term is the time derivative of the product of the contribution due to the secondary droplets.
film thickness and film velocity. The second term in Eq. The sixth term in Eq. (22) is the viscous film term
(22) is the convective momentum term and is and is calculated using Eqs. (27):
approximated using Eqs. (23) :

1 Θ 1 Nedge (cid:71) Nside((cid:71) ) (cid:71) (cid:71)
φ = − t (23) ∑(τA) = ∑ τ δ(cid:65) + τ A + τ A
1−δt δ 1−δt 2 i=1 i i j=1 edgei j j wall wall liq/air wall
δ   (27)
 δ
(cid:71)
where τ is the viscous shear along the edges of the
edgei
(cid:71) (cid:71)
Equation (23) results from the approximation of the film cell, τwall is the wall shear, and τliq/air is the shear
integration of the non-linear convective term in the at the liquid-gas interface (see Fig. 8). The wall shear is
cross-film direction. The displacement thickness, δt, calculated once the velocity profile in the cross-film
and the momentum thickness, Θt, in Eq. (23) can be direction is chosen.
calculated once the velocity profile in the cross-film The liquid film equations (21) and (22) are
numerically solved using a predictor-corrector scheme.
direction has been chosen.
The predictor-corrector scheme consists of using the
The third term in Eq. (22) is the pressure term and is
Euler method as a predictor followed by the trapezoid
described by Eq. (24) which includes the dynamic
rule as a corrector. At the edges of the film, an
upwinding scheme is used instead of the central
differencing previously stated.

RESULTS AND DISCUSSION

In an attempt to validate the spray-film interaction
model and the liquid film model, KIVA-II is used to
simulate various experiments involving diesel fuel
injectors. The aim is to focus on the transient behavior
of the two-phase wall-jet resulting from spray
impingement on a wall with the eventual formation of a Figure 9: Grid geometry used for normal impingement
thin liquid film. The numerical results are compared to simulation.
experimental data for spray radius, spray height, liquid
film thickness estimations, secondary droplet velocities,
and secondary droplet size. In addition, diesel engine Figure 10 shows the spray images for C1 at three
simulations are presented in an attempt to demonstrate different times after the start of injection. A wall spray
the capabilities of the liquid film model to follow film structure can be identified comprising of a dense region
flowing over a three-dimensional surface. near the wall spray tip with small secondary droplets
produced by splashing which penetrate out and up away
CNPM EXPERIMENTS - Normal spray impingement from the impingement point. Also shown in the spray
experiments in test bombs under atmospheric conditions images are larger drops that have developed in the later
were performed by Coghe and associates with results stages of the spray impingement which can be attributed
reported by [19]. Phase Doppler anemometry (PDA) to the leading wall vortex. Figure 11 shows the gas
was employed to measure droplet velocities in the near-
velocity profiles which reveal a wall-jet emanating
wall region at particular locations. Table 1 contains a
radially outward from the spray impingement region,
summary of the experimental conditions for the normal
near the tip of which there is a vortex. This vortex is
impingement experiment C1.
progressively radially stretched at later times. It is this

vortex structure which influences the movement of

drops, especially the smaller secondary droplets that
Table1: Specification for normal impingement test
result from splashing. Consequently, drops have the
case.
opportunity to coalesce and form larger drops.

The film thickness profiles are shown in Fig. 12 for
Case No. C1
various times after the start of injection. The area
Wall Distance (mm) 25
around the stagnation point of the spray is immediately
Gas Pressure (bar) 1 flooded. This occurs within a 2 mm radial distance.
Gas Temperature (K) 293 Beyond this distance, the film thickness increases from
Nozzle Diameter (mm) 0.25 approximately
Injection Duration (ms) 3.4
Injection Angle (°) 90
Fuel Injected (mm3/pulse) 36
Fuel Diesel
Injection Schedule Mass flow rate profile

The calculations for C1 were performed using a three- (a) (b)
dimensional sector with physical dimensions shown in
Fig. 9.

(c)
Figure 10: Spray images for C1 at (a) t = 2.4 ms,
(b) t = 3.6 ms, and (c) t = 4.0 ms.
30
25
20 t = 0.5 ms
t = 2.0 ms
(a) t = 2.5 ms
15
s
s
e
10n
m ck
Fil 5Thi (µm)
0
0 5 10 15 20 25 30 35
Radial Distance (mm)
Figure 12: Liquid Film thickness profiles at various times
for case C1.
(b)

The predicted and measured transient behavior of
the droplet peak normal velocities at two specific points
in the spray are shown in Fig. 13. Both points are
located at a height of 2 mm from the wall, with one
located 5 mm away from the spray axis and the other at
a radial distance of 6 mm. Both points of interest are
located where the majority of the spray-film interaction
occurs. Note that the positive velocities are directed
towards the wall while the negative velocities are away
(c) from the wall. For both locations, the predicted
Figure 11: Gas velocity profiles at (a) t = 2.4 ms, velocities show similar trends when compared to the
(b) t =3.6 ms, and (c) t = 4.0 ms showing the movement experimental data with the only exception being the
of the wall vortex. normal velocities of the drops at the early stages of
injection. This discrepancy could be attributed to the
modeling of the break-up of the spray upon impact with
the wall. The incident drops undergo less energetic
2 µm to a maximum of approximately 8 µm eventually impacts with the film resulting in secondary droplets with
reaching zero at the leading edge. The concaved film normal velocity less than the experimental data.
profile extending from the stagnation region at a radial Next, a comparison of the droplet velocity variation
distance of 2 mm to a transient peak value is present in above the wall surface is conducted at a radial distance
all curves. This is the result of two primary phenomena.
of 14 mm from the spray axis. Figure 14 and Fig. 15
First, a liquid wall-jet is formed at the onset of
show the predicted and measured mean normal and
impingement in this region which widens in the radial
tangential velocity components, respectively. The local
direction causing the liquid wall-jet to decelerate.
mean value is experimentally determined as the local
Second, the film experiences the majority of the spray-
ensemble-average over a 1 ms period from 1.5 ms to
film interaction in this region which results in splashing of
2.5 ms after the start of injection [19]. Also, the local
secondary droplets, thus reducing the amount of mass in
the film. Consequently, it is instructive to investigate mean is computationally defined as the arithmetic mean
droplet velocities in this region, in order to assess the for all droplets identified in the mesh cells normal to the
ability of the spray-film model to predict the splashing surface at a 14 mm distance from the spray axis. The
events. calculations are conducted for the same 1 ms time
period.
3
30 s)
Experiment m/ 2
(
KIVA y 1
y (m/s) 20 Velocit -10 Toward the wall
elocit 10 Toward the wall mal -2 KIVA
V Experiment
Droplet Normal -100 Droplet Nor ---543 1 2 3 A4way fr5om the6 wall7 8
Away from the wall Distance from wall surface (mm)
-20 Figure 14: Comparison of the droplet mean normal
0.4 0.5 0.6 0.7 0.8 0.9 1 velocity variation with height above the wall surface at a
14 mm radius from the spray axis.
Time since start of injection (ms)

(a)

In contrast, the predicted results show a maximum
30 velocity of approximately 54 m/s at a location of 1.7 mm
Experimental from the wall surface. Both curves indicate that droplets
s) KIVA near the wall exhibit large tangential velocities directed
m/ 20 away from the stagnation point. The direction changes
y ( at locations greater than 4 mm normal to the surface.
cit 10 This is also evidence of the influence that the wall vortex
o
Vel Toward the wall has on the direction of the droplets farther away from the
al 0 wall.
m
r
o
N
plet -10 Away from the wall s) 60
o m/
r Experiment
D -20 ( 50
y KIVA
0.4 0.5 0.6 0.7 0.8 0.9 1 t
ci 40
Time since the start of injection (ms) o
el
V 30
al
(b) ti 20
n
Figure13: Comparison of droplet peak normal velocities e
g 10
for case C1 (a) at a point 2 mm from the wall surface n
a
and 5 mm from the spray axis and (b) at a point 2 mm t T 0
from the wall surface and 6 mm from the spray axis. e
pl
o -10
Dr 0 1 2 3 4 5 6 7
Both the predicted and measured droplet mean Distance from the wall surface (mm)
Figure 15: Comparison of the droplet mean tangential
normal velocities show the same variation with distance
velocity variation with height above the wall
from the wall (see Fig. 14). The droplets near the wall
surface at a 14 mm radius from the spray axis.
have the tendency to move away from the surface.

However, beyond 3 mm from the surface, the droplets

move toward the wall. These observations can be

attributed to the wall vortex redirecting the droplets.
KATSURA EXPERIMENTS - Katsura et al. [25]
Figure 15 shows the variation of the droplet mean
conducted experiments in which a single spray was
tangential velocity normal to the wall surface. There
impinged on a flat plat at an angle of 90° at elevated
exists good agreement with only some small
pressure and room temperature. The investigators
discrepancy at the maximum tangential velocity value
applied the laser light extinction method to obtain
and its location. The experimental data reach a
photographs of the temporal behavior of the spray
maximum value of approximately 58 m/s at 1 mm from
patterns. From this information, they deduced the wall
the wall surface and then monotonically decrease.
spray radius, Rw, and the wall spray height, hw. Table
2 contains a summary of the test conditions for case C2