processes

Article
Effects of Low Pressure Injection on Fuel Atomization and
Mixture Formation for Heavy Fuel Engines
Rui Liu 1,2 , Kaisheng Huang 1, * , Yuan Qiao 1 , Haocheng Ji 2 , Lingfeng Zhong 2 and Hao Wu 3

1 State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China
2 School of Mechanical and Power Engineering, Nanjing Tech University, Nanjing 211816, China
3 Nanjing Changkong Technology Co., Ltd., Nanjing 211106, China
* Correspondence: huangks@tsinghua.edu.cn

Abstract: The application of direct injection (DI) technology can effectively improve the atomization
effect of heavy fuel to reduce the fuel loss of heavy fuel engines (HFE). The fuel spray characteristics
directly affect the combustion performance of the engine. To investigate the atomization process and
evaporation characteristics of heavy fuel in-cylinder for an air-assisted direct injection (AADI) engine,
a simulation calculation model of AADI HFE was established with the use of a computational fluid
dynamics tool. The air-assisted injector model and the one-dimensional performance calculation
model were verified by test data. The influences of injection timing and injection pressure on the
spray characteristics and mixture formation in the engine cylinder were discussed. The results show
that the mixture concentration distribution is uniform after the injection timing is advanced, and the
mass fraction of the fuel evaporation increases. The earlier injection timing can provide the fuel with
sufficient time to evaporate, while the later injection timing will result in increasing the Sauter mean
diameter (SMD) of the fuel droplets, and the unevaporated heavy fuel in the combustion chamber
tends to become concentrated. With the increase in air injection pressure, the distribution of the mixed
gas in the cylinder becomes uniform, and the SMD of the fuel droplets in the cylinder decreases.
Citation: Liu, R.; Huang, K.; Qiao, Y.;
When the injection pressure is 0.65 MPa and 0.75 MPa, the difference between the SMD of the fuel
Ji, H.; Zhong, L.; Wu, H. Effects of
droplets in-cylinder decreases, and a favorable fuel atomization effect can be maintained.
Low Pressure Injection on Fuel
Atomization and Mixture Formation
for Heavy Fuel Engines. Processes
Keywords: HFE; two-stroke; injection control; air-assisted atomization; fuel–air mixture
2022, 10, 2276. https://doi.org/
10.3390/pr10112276

Academic Editors: Dezhi Zhou and

1. Introduction
Jing Li
Aviation piston engines have the characteristics of low manufacturing and mainte-
Received: 16 September 2022 nance costs, high power-to-weight ratio, and strong compatibility, which make them widely
Accepted: 31 October 2022 used in the field of small aviation power plants [1–3]. Typical aviation piston engines
Published: 3 November 2022 mainly use gasoline, with favorable evaporation and ignitability, as the fuel. Heavy fuel
Publisher’s Note: MDPI stays neutral (light diesel and aviation kerosene) has a high flash point, and the fuel is safer in the
with regard to jurisdictional claims in processes of storage, transportation, and usage [4,5]. Heavy fuel has high viscosity and
published maps and institutional affil- favorable stability, and its atomization effect is weaker than that of ordinary gasoline under
iations. the same conditions. When the traditional two-stroke aviation piston engine burns heavy
fuel, the injected fuel droplets will easily condense into fuel film when they meet the cold
wall, and the evaporation process of fuel film is slower than that of gasoline [6,7]. In recent
years, the DI technology of heavy fuel has attracted much attention. The application of DI
Copyright: © 2022 by the authors. technology can effectively improve the atomization effect of heavy fuel, reduce the fuel loss
Licensee MDPI, Basel, Switzerland. of the heavy fuel aviation piston engine, and improve engine performance. Direct injec-
This article is an open access article
tors are divided into different types, including high pressure swirl injectors, slit injectors,
distributed under the terms and
shaped injectors, and air-assisted injectors. Among these, as one of the types of gas-assisted
conditions of the Creative Commons
injectors, low-pressure air-assisted injectors are usually used for power systems such as
Attribution (CC BY) license (https://
small-scale fuel-powered unmanned aerial vehicles, motorcycles, and off-board machines,
creativecommons.org/licenses/by/
showing favorable atomization performance and remarkable fuel saving effects.
4.0/).

Processes 2022, 10, 2276. https://doi.org/10.3390/pr10112276 https://www.mdpi.com/journal/processes

Processes 2022, 10, 2276 2 of 15

In the application case of a two-stroke or four-stroke DI spark-ignition (SI) HFE, the

fuel spray characteristics directly affect the combustion performance of the engine [8,9].
Chen et al. [10] calibrated a simulation model using test data from a DISI engine to inves-
tigate the behavior of diesel combustion. Their research indicates that diesel combustion
is slower compared to that of gasoline, and the knock tendency is higher. For a diesel–
air mixture with equivalence ratios of 0.6 to 1.4, higher combustion pressure and faster
burning rate occur when the equivalence ratios are 1.2 and 1.0; however, the latter has
a higher knock possibility. Moreover, they also established a combustion model of the
two-stroke engine to study the heavy-fuel combustion at different ignition timings and
equivalence ratios. The results show that aviation kerosene is less prone to knock than diesel
and can achieve better combustion performance under the condition of rich mixture [11].
Zhao et al. [12] studied the air scavenging and mixture formation process of a two-stroke
DISI engine fueled with kerosene. Postponing fuel injection reduces the short-circuit time
of fuel and avoids the free exhaust phase with large exhaust mass flow, which can improve
the fuel capture rate. Late injection will result in incomplete evaporation and the uneven
mixture of fuel and air. In addition, the formation process of the mixture in-cylinder of
a two-stroke ignition HFE was simulated by Huang [13]. The ideal mixing distribution
can be formed in the whole working condition range through the mutual organization
and coordination of fuel injection control and in-cylinder air flow. Wang et al. [14,15]
calculated the gas-phase flow field and spray field as kerosene and gasoline fuel were
injected into the constant-volume chamber at different inlet pressures under the condition
that the needle valve was fully open. The simulation results indicate the influence of the
change in the gas-phase pressure ratio of the Laval nozzle on the penetration distance,
SMD, and particle size distribution of air-assisted atomization. Ji et al. [16] numerically
analyze the process of air-assisted atomization for diesel spray. Their calculation model
considering the diesel injection process in the fuel–air premixing chamber was established
without changing the injector structure. The air-assisted injection process of diesel–air
two-phase flow was investigated in a constant volume chamber. The effects of air injection
pressure, ambient back pressure, and fuel temperature on diesel spray characteristics were
investigated, revealing great theoretical reference significance. In summary, the traditional
SI HFEs produce a homogeneous fuel mixture by means of port injection such that the
fuel control strategy is simplified. With the application of air-assisted atomization in the
DISI HFEs, the whole spray size of the fuel droplets is greatly reduced, which is of great
significance in promoting stable fuel–air mixing and combustion.
In this paper, an improved three-dimensional calculation model will be established
based on low pressure air-assisted atomization injection. For this model, the needle valve
lift will be given according to the experimental measured data. The dynamic mesh method
will be used to simulate the transient spray field of the direct injector in the engine cylinder
when the needle valve moves. The influence of the control parameters, including the
injection pressure and the injection timing, on the spray characteristics of the air-assisted
injector will be evaluated, and the SMD at different crankshaft positions after injection will
be statistically analyzed. The droplet size of the fuel spray in the engine cylinder and the
distribution characteristics of the fuel–air mixture will be investigated.

2. Modeling and Settings

2.1. Meshing of the Three-Dimensional Calculation Model
With the help of the ICEM tool, the three-dimensional calculation meshing model
for the DI HFE is given. The size of the air-assisted direct injector, the scavenging port,
the combustion chamber, and the exhaust port are defined, respectively. The meshing
model file required for the three-dimensional numerical simulation calculation is generated
after completing each division and process for these ports. The meshing model is then
imported into the workbench of FLUENT to perform the calculation routine. Figure 1
shows the three-dimensional structural model of the engine and its meshing model for
Processes 2022, 10, x FOR PEER REVIEW 3 of 15
Processes 2022, 10, x FOR PEER REVIEW 3 of 15

file required for the three-dimensional numerical simulation calculation is generated after
file required for the three-dimensional numerical simulation calculation is generated after
Processes 2022, 10, 2276 completing each division and process for these ports. The meshing model is then imported 3 of 15
completing each division and process for these ports. The meshing model is then imported
into the workbench of FLUENT to perform the calculation routine. Figure 1 shows the
into the workbench of FLUENT to perform the calculation routine. Figure 1 shows the
three-dimensional structural model of the engine and its meshing model for all computa-
three-dimensional structural model of the engine and its meshing model for all computa-
tional
alldomains. It is worth noting It
computational that the meshes at the junctions of the air-assisted injec-
tional domains. It isdomains.
worth notingisthat
worth noting
the meshes that
at thethe meshes
junctions ofatthe
theair-assisted
junctions of the
injec-
tor, air-assisted
outlets of the scavenging
injector, port,
outlets of and
the inlet of
scavenging the exhaust
port, and port
inlet are
of refined.
the exhaust port are refined.
tor, outlets of the scavenging port, and inlet of the exhaust port are refined.

Figure 1. Three-dimensional engine model and meshing model of computational domains.

Three-dimensionalengine
Figure1.1.Three-dimensional
Figure enginemodel
modeland
andmeshing
meshingmodel
modelof ofcomputational
computationaldomains.
domains.

2.2. Dynamic MeshMesh

2.2. Dynamic
2.2. Dynamic Mesh
In order to truly
In order simulate
to truly the operational
simulate statestate
the operational of theof engine, it is it
the engine, necessary
is necessaryto set
tothe
set the
In order to truly simulate the operational state of the engine, it is necessary to set the
dynamic
dynamicmesh reflecting
mesh the piston
reflecting operation
the piston and and
operation the opening and and
the opening closing process
closing of the
process of the
dynamic mesh reflecting the piston operation and the opening and closing process of the
needle valve in the calculation model. For the whole simulation process
needle valve in the calculation model. For the whole simulation process for fuel spray for fuel spray in
needle valve in the calculation model. For the whole simulation process for fuel spray in
the engine cylinder
in the engine and combustion
cylinder chamber,
and combustion the piston
chamber, themotion
pistonmust
motion covermusta single
covercom-a single
the engine cylinder and combustion chamber, the piston motion must cover a single com-
pletecomplete
workingworking
cycle; that is, the
cycle; crankshaft
that rotation period
is, the crankshaft rotation must be at
period leastbe360
must at °CA 360 ◦ CA
least (°CA
plete working cycle; that is, the crankshaft rotation period must be at least 360 °CA (°CA
(◦ CA
refers to crankshaft angle). Figure
refers to crankshaft 2 shows
angle). the2dynamic
Figure shows the meshes of the
dynamic pistonof
meshes andthecylinder
piston and
refers to crankshaft angle). Figure 2 shows the dynamic meshes of the piston and cylinder
wallcylinder
in the engine
wall in fluid
thedomains underdomains
engine fluid three crankshaft
under three positions (TDCpositions
crankshaft refers to top(TDCdead refers
wall in dead
the engine fluid domains under three crankshaft positions (TDC refers to top dead
center, BTDC
to top refers
center,to before TDC, and
BTDC refers ATDC
to before refers
TDC, and toATDC
after TDC).
refers Figure
to after3TDC).
showsFigure
the 3
center,
shows BTDC refers
thedynamic
needle to before TDC,
valve andofATDC refers to after TDC). Figure 3 shows the
needle valve meshdynamic mesh
of the air-assistedthe air-assisted
direct injector.direct injector.
needle valve dynamic mesh of the air-assisted direct injector.

(a) 180 °CA ATDC (b) 270 °CA ATDC (c) TDC
(a) 180 °CA ATDC (b) 270 °CA ATDC (c) TDC
Figure 2. Dynamic
Figure meshes
2. Dynamic of the
meshes ofpiston and and
the piston cylinder wallwall
cylinder in the
inengine fluidfluid
the engine domains.
domains.
Figure 2. Dynamic meshes of the piston and cylinder wall in the engine fluid domains.
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(a) Full closing (b) Partial opening (c) Full opening

Figure 3. 3.
Figure Dynamic mesh
Dynamic of of
mesh thethe
needle valve
needle forfor
valve thethe
air-assisted injector.
air-assisted injector.

2.3.
2.3. Injector
Injector Model
Model
The
The premixed
premixed process
process forfor fuel
fuel andand compressed
compressed airair realized
realized byby anan air-assisted
air-assisted direct
direct
injector is a typical two-phase flow problem. The fluid phase is treated
injector is a typical two-phase flow problem. The fluid phase is treated as a continuous as a continuous
phase
phase bybythethe Lagrange
Lagrange method,
method, and
and thethe fuel
fuel droplets
droplets are
are treated
treated asas discrete
discrete phases
phases and
and
distributed in the continuous phase. The realizable k-ε
are distributed in the continuous phase. The realizable k-ε turbulence model, which is is
are turbulence model, which
improved
improved onon the
the basis
basis ofof the
the standard
standard k-εk-εmodel,
model,was
wasselected
selectedfor forthe
thespray
spraycalculation
calculation
model [17]. This model adds a constraint formula for turbulent viscosity
model [17]. This model adds a constraint formula for turbulent viscosity and a transmis- and a transmission
equation
sion equationfor for
the the
dissipation rate,rate,
dissipation which can better
which realize
can better rotaryrotary
realize flow, flow
flow,separation,
flow separa- and
complex secondary flow. Turbulent kinetic energy k and turbulent
tion, and complex secondary flow. Turbulent kinetic energy 𝑘 and turbulent dissipationdissipation rate ε in the
model transport equation are as follows:
rate 𝜀 in the model transport equation are as follows:
  
∂ (𝜌𝑘) +∂ (𝜌𝑘𝑢 ) =∂
(ρk) + (ρkui ) = µ𝜇 +
+ µt ∂k + 𝐺 + G+k 𝐺+ G −b𝜌𝜀
− ρε− 𝑌− Y+M𝑆+ Sk (1)(1)
∂t ∂xi ∂xi σk ∂xi

(𝜌𝜀) + ∂ (𝜌𝜀𝑢 ) =∂ 𝜇+ ∂ + 𝜌𝐶 µ𝑆t −∂𝜌𝐶 + 𝐶 𝐶 𝐺 ε+ 2

𝑆
  
ε ε (2)
(ρε) + (ρεui ) = µ+ + √ρC1 Sε − ρC2 √ + C1ε C3ε Gb + Sε (2)
∂t ∂xi ∂xi σε ∂xi k + νε k
In Equation (1), 𝜎 equals 1.0; 𝜇 is the turbulent viscosity; 𝜌 is the gas density ; 𝐺
In Equation (1), σ equals 1.0; µ is the turbulent viscosity; ρ is the gas density; G
represents the turbulentk kinetic energyt due to the average velocity gradient ; 𝐺 is the k
represents the turbulent kinetic energy due to the average velocity gradient; Gb is the
turbulent kinetic energy due to buoyancy ; 𝑌 represents the contribution of fluctuation
turbulent kinetic energy due to buoyancy; YM represents the contribution of fluctuation
expansion in compressible turbulence to the total dissipation rate; 𝑆 is a custom source
expansion in compressible turbulence to the total dissipation rate; Sk is a custom source
item. In Equation (2), 𝜎 equals 1.2; 𝐶 equals 1.9; 𝐶 equals 1.44; other relevant param-
item. In Equation (2), σε equals 1.2; C equals 1.9; C ε equals 1.44; other relevant parameters
eters can be calculated by referring to 2the references1[17].
can be calculated by referring to the references [17].
The TAB (Taylor analogy breakup) model is selected as the droplet breakup model.
The TAB (Taylor analogy breakup) model is selected as the droplet breakup model.
Based on the theory of elastic mechanics, the breakup process of oscillating droplets is
Based on the theory of elastic mechanics, the breakup process of oscillating droplets is
compared with the vibration of the spring damping system. The mass block is subjected
compared with the vibration of the spring damping system. The mass block is subjected to
toexternal
externalforce
forcesimilar
similartotothethe droplet
droplet andand is also
is also subjected
subjected to aerodynamic
to aerodynamic force.force. The
The spring
spring
elastic force is similar to the surface tension of the droplet, and the damping is similaristo
elastic force is similar to the surface tension of the droplet, and the damping
similar to the viscosity
the viscosity of the
of the liquid liquid
[18]. The[18]. The calculation
calculation formula formula is as follows:
is as follows:

..
𝑦 =C ρ g u2 − C σ𝑦 − C µ𝑦 . (3)
y= F − k
y − d 1
y (3)
In Equation (3), 𝑦 is the dimensionless Cb ρl r2 deformation
ρ1 r 3 r2 droplet maximum diameter;
ρ1of
𝜌 is the gas density;
In Equation (3), 𝜌y isisthe
thedimensionless 𝑢 is the relative
liquid density;deformation velocity
of droplet of the gas
maximum and theρ
diameter; g
droplet; 𝑟 isdensity;
is the gas the droplet
ρl is radius;
the liquid 𝐶 , 𝐶 ,uand
𝐶 ,density; 𝐶 relative
is the are thevelocity
dimensionless
of the gasconstants
and the deter-
droplet;
mined bydroplet
r is the mathematical
radius;analysis
CF , Ck , Cand the experiments.
d , and Cb are the dimensionless constants determined by
mathematical analysis and the experiments. in the spray process. If the deformation is
The initial droplet will oscillate normally
affected by initial
The aerodynamic
droplet force and exceeds
will oscillate a certain
normally in thevalue;
spraythat is, 𝑦 > 1,Ifthe
process. theinitial droplet is
deformation
will break up and produce smaller secondary droplets. The normal velocity
affected by aerodynamic force and exceeds a certain value; that is, y > 1, the initial droplet of the second-
ary droplet
will break is
upequal to the normal
and produce smalleroscillation
secondaryvelocity
droplets. of The
the initial
normaldroplet
velocitywhen
of thethe drop-
secondary
let breaks, so the cone angle of the spray can be calculated automatically by the model.
Processes 2022, 10, 2276 5 of 15

droplet is equal to the normal oscillation velocity of the initial droplet when the droplet
breaks, so the cone angle of the spray can be calculated automatically by the model. The
SMD (r32 ) of sub-droplets can be calculated by the following energy conservation equation:

8·K ρ r3 . 2 6 · K − 5
 
r
= 1+ + 1 y (4)
r32 20 σ 120

K is used to adjust the size ratio of the initial droplet to the secondary droplet. The
larger the value, the smaller the size of the broken droplet.
In addition, after droplet evaporation, the flow field medium contains multiple com-
ponents, and the following component transport equation needs to be solved:

∂
(ρYi ) + ∇ · (ρvYi ) = −∇ J i + Ri + Si (5)
∂t

where Yi represents the mass fraction of each component, Si is the original, J i is the
diffusion flux caused by the concentration gradient, and Ri is the net production rate of the
chemical reaction [19].
The R–R (Rosin–Rammler) model is selected for droplet size distribution.

R( D ) = 100 exp −( D/De )n (%)

 
(6)

where R( D ) represents the cumulative mass percentage of sieve corresponding to droplet

size D; when D = De , the cumulative mass percentage of sieve R( De ) = 100 / e % = 0.368,
and the corresponding droplet size is the characteristic particle size De of the particle group,
which can roughly reflect the thickness of the fuel droplet. n is the uniformity coefficient,
which is used to characterize the range of droplet distribution [20].
The definition of SMD is as follows:

∑ Ni d3i
SMD = (7)
∑ Ni d2i

where N represents the number of droplets, d represents the diameter of the droplets, and
the physical meaning of SMD is the corresponding diameter after converting the cube into
an equal volume sphere.
The direct injector assembly includes three parts: fuel injector, premixing chamber,
and air-assisted injector. The gaseous medium is air. To simulate the entire process that
conforms with the actual scenario, fuel is first ejected through the outlet of fuel injector
to the premixing chamber and then delivered by air-assisted injector into the constant
volume chamber or engine cylinder. In order to verify the simulation model for AADI, the
calculation results are analyzed according to the injection process of the air-assisted injector.
The fuel spray characteristics obtained by a high-speed photography experimental system
and the simulation calculation are compared. Table 1 shows the high-speed spray images
and the spray simulation images at different times during the opening process of the needle
valve under the conditions of 6.5 bar air injection pressure and 0 bar ambient pressure
(gauge pressure). The fuel used is light diesel, and the fuel properties can be obtained in the
reference [21]. Figure 4 shows the comparison results of the spray characteristic parameters
between the experimental measurement and the simulation calculation. It can be seen
from the figure that the penetration distance measured by the experiment is slightly larger
than that of the simulation calculation value. This is mainly due to the fact that the fuel
injection rate used in the simulation is the average rate, which has a certain influence on the
spray change. Overall, the ratio of fuel SMD to penetration distance is basically consistent,
and the calculation results from the simulation model are close to those of the actual
situation. Therefore, the results can lay the foundation for the calculation and analysis of
the fuel spray characteristics and mixture formation process in the engine cylinder under
 Processes 2022, 10, 2276 6 of 15

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the
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Table
Table
Table
Table
Table 1.Comparison
Comparison
1.1.Comparison
1.1.Comparison
Comparison offuel
ofofof
fuelfuel
offuel spray
spray
spray
spray
fuel tests
tests
tests
spray tests
and and
and
and
tests calculation
calculation
andcalculation
calculation results.
results.
results.
calculation results.
results.
Table
Table
Table
Table 1.1. Comparison
1.1.Comparison
Table Comparison of
ofofof
1.Comparison
Comparison fuel
of fuel
fuelfuel
fuel spray
sprayspray
spray
spray tests
tests and
tests
tests
testsandand
and
and calculation
calculation
calculation
calculation
calculation results.
results.
results.
results.
results.
Injection
Injection
Injection
Injection
Injection Time
Time
Time
Time
Time 11ms
11ms ms
1ms
ms 22ms
22ms ms
2ms
ms 33ms
33ms ms
3ms
ms 44ms
44ms ms
4ms
ms
Injection
Injection Time
Injection
Injection
Injection Time
Time
Time
Time 11ms
1ms 1ms
1ms ms 222ms 2ms
2ms
ms ms 333ms3ms
3ms
msms 44ms 4ms
44msms
ms

Test
Test
Test
Test
Test
TestTest
Test
Test
Test

Calculation
Calculation
Calculation
Calculation
Calculation
Calculation
Calculation
Calculation
Calculation
Calculation

Figure
Figure
Figure
Figure
Figure
Figure 4.
4. Comparisons
4.Comparisons
Comparisons
4.4.Comparisons
4. Comparisonsofofof
Comparisons ofof spray
ofspray
spray
spray
spray characteristics
characteristics
characteristics
characteristics
spraycharacteristics between
between
between
between
characteristicsbetweenthethe
the
between thethe
test
test
thetesttest
test
and
and
and
test and
and simulation.
simulation.
simulation.
simulation.
and simulation.
simulation.
Figure
Figure 4.4.Comparisons
Figure
Figure 4.Comparisons ofofof
4.Comparisons
Comparisons spray
of
spray characteristics
spray
spraycharacteristicsbetween
characteristics
characteristicsbetween
betweenthe
between
the test
the
the test and
test
testand simulation.
and
and simulation.
simulation.
simulation.
2.4. Initial Conditions and Boundary Conditions
2.4.
2.4.
2.4.
2.4.
2.4. Initial
Initial
Initial
Initial
Initial Conditions
Conditions
Conditions
Conditions
Conditions and and
and
and Boundary
Boundary
andBoundary
Boundary
Boundary Conditions
Conditions
Conditions
Conditions
Conditions
2.4.
2.4.
2.4.Initial
2.4. Initial
The Conditions
Initial
Initial Conditions
Conditions
Conditions
specific and
and
andBoundary
and
technical Boundary
Boundary
Boundary
parameters Conditions
Conditions
Conditions
Conditions of the AADI SI HFE are listed in the reference [22].
The
TheThe
TheThe specific
specific
specific
specific
specific technical
technical
technical
technical
technical parameters
parameters
parameters
parameters
parameters of
ofofof
the
of the
the
theAADI
the AADI
AADI
AADI
AADI SISI
SISISI
HFE
HFEHFE
HFEHFEare
areare
are listed
listed
listed
are listed
listed inininin
the
the
in the
the reference
reference
reference
the reference
reference [22].[22].
[22].
[22].
[22].
According
The
TheThespecific
The to the
specific
specific
specific structure
technical
technical
technical
technical of the test
parameters
parameters
parameters
parameters ofofofengine,
the
of
thetheAADI
theAADI
AADIone-dimensional
AADI SISISI
HFE
SI
HFE HFE
HFE areare listed
are
are modeling
listed
listed
listed inininthe
in
the the
the can
reference be divided
reference
reference
reference [22].
[22].[22].
[22].
According
According
According
According
According tototo
to
the
the
to the
the
the structure
structure
structure
structure
structure ofofof
of
the
of the
the
thetest
the testtest
test engine,
engine,
engine,
test engine,
engine, one-dimensional
one-dimensional
one-dimensional
one-dimensional
one-dimensional modeling
modeling
modeling
modeling
modeling can can
can
can be
can be be
be divided
divided
divided
be divided
divided
into
According
According
According
According intake
tototoand
the
to
thethe exhaust
structure
the structure
structure
structure systems,
ofofof
the
of
thethe test
the fuel
test test
test injection
engine,engine,
engine,
engine, systems,
one-dimensional
one-dimensional
one-dimensional
one-dimensional cylinders,modeling and crank
modeling
modeling
modeling can
can be
can
can linkages
bebedivided
be divided
divided
divided [23].
into
into
into
into intake
intake
intake
intake and and
and
and exhaust
exhaust
exhaust
exhaust systems,
systems,
systems,
systems, fuel
fuelfuel
fuel injection
injection
injection
injection systems, cylinders, and crank linkages [23].
into
into
intoA
into
into
intake
one-dimensional
intake and
intake
intake
intake
and
and and
and
exhaust
exhaustexhaust
exhaust
exhaust
systems,
simulation
systems,
systems,
systems,
systems, model
fuelfuel
fuel
fuel injection
fuel thesystems,
injection
ofinjection
injection
injection
systems,
systems,
systems,
engine,
systems,
systems,
systems,
systems,
cylinders,
cylinders,
cylinders,
cylinders,
established
cylinders,
cylinders,
cylinders,
cylinders,
and
byand
and
and
and
crank
and
and
crank
crank
selecting
crank
and
crank
crank
linkages
crank
crank
linkages
linkages
thelinkages
linkages
linkages
linkages
linkages
[23].
[23].
[23].
correspond-
[23].
[23].
[23].[23].
[23].
AAAA A one-dimensional
one-dimensional
one-dimensional
one-dimensional
ing one-dimensional
module in GT-Power, simulation
simulation
simulation
simulation
simulation ismodel model
model
model
shown model ofof of
of
the
the
of the
thethe engine,
engine,
engine,
engine,
engine, established
established
established
established
established by bybyby selecting
selecting
byselecting
selecting
selecting thethethe
the corre-
corre-
thecorre-
corre-
corre-
AAA one-dimensional
A one-dimensional
one-dimensional
one-dimensional simulation
simulation
simulation
simulation model
model model
model ofin
ofof Figure
the
of
thethe engine,
the 5. In
engine,
engine,
engine, order
established to ensure
established
established
established byby byby the
selecting accuracy
selecting
selecting
selecting thethe corre-
the
the of the
corre-
corre-
corre-
sponding
sponding
sponding
sponding
sponding
one-dimensional module
module
module
module
module inin in
in in GT-Power,
GT-Power,
GT-Power,
GT-Power,
GT-Power,
performance isis is
is
shown
is shown
shown
shown
shown
calculation in in in
in
Figure
in Figure
Figure
Figure
Figure
simulation5.5. 5.
5.
InIn
5. In
In
orderorder
order
In order
order
model, toto to
toensure
it ensure
ensure
tois ensure
ensure the
necessary thethe
the accuracy
accuracy
accuracy
the accuracy
accuracy
to check of
ofofof of
the
sponding
sponding
sponding
sponding module
module
module
module inininGT-Power,
in GT-Power,
GT-Power,
GT-Power, isisis shown
is shown
shown
shown inininFigure
in Figure
Figure
Figure 5.5.5.
In5. order
InInIn order
order
order tototoensure
to
ensureensure
ensure the
the accuracy
the
the accuracy
accuracy
accuracy ofof ofof
thethe
the
the
the one-dimensional
one-dimensional
one-dimensional
one-dimensional
one-dimensional
simulation performance
resultsperformance
performance
performance
of performance
the established calculation
calculation
calculation
calculation
calculation
model simulation
simulation
simulation
simulationthe model,
simulation
with model,
model,
model,
bench model, ititis
ititis
test isnecessary
itis necessary
necessary
isnecessary
necessary to
tototo
checkcheck
check
to check
check
the
the
theone-dimensional
the one-dimensional
one-dimensional
one-dimensional performance
performance
performance
performance calculation
calculation
calculation
calculation simulation
simulation
simulation
simulation model,model,
model,
model, ititisitdata.
is necessary
itis is In this
necessary
necessary
necessary study,
toto check
toto
checkcheck
check the
thethe
the
the
the simulation
simulation
simulation
simulation
engine simulation
power results
results
results
results
results
for of
theofof
of
thethe
of the
the
the established
established
established
established
established model model
model
model
model with with
with
with the
withthethe
thebenchbench
bench
the bench
bench test test
test
testdata.
test data.
data.
data.
data.In In In
In
this this
this
Inthisstudy,
this study,
study,
study,
study,the the
the
thethe
the
the
thesimulation
the simulation
simulation
simulation resultsresults
results
results ofofone-dimensional
the
ofof
the established
the
the established
established
established model
model
modelmodel
model is
with calibrated.
with
with the
with the
thebench
thebench
bench The
bench test
testthrottle
testdata.
test data.data.
data. opening,
InIn this
InIn
this study,
this
this rotational
study,
study,
study, the
the the
the
engine
engine
engine
engine
engine
speed, powerpower
power
power
powerfor
excess forfor
for
the
for
airthe
the
the
the one-dimensional
one-dimensional
one-dimensional
one-dimensional
one-dimensional
coefficient, and ignition modelmodel
model
model
model iscalibrated.
calibrated.
isistiming
calibrated.
isiscalibrated.
calibrated.
angle The
TheThe
The throttle
throttle
The
used throttle
throttle
throttle
in the opening,
opening,
opening,
opening,
opening,
bench rotational
rotational
rotational
testrotational
rotational
are input
engine
engine
engine
engine powerpower
power
power forfor the
for
for the one-dimensional
the
the one-dimensional
one-dimensional
one-dimensional model
modelmodel
model isiscalibrated.
iscalibrated.
calibrated.
iscalibrated. TheThe
The throttle
The throttle
throttle
throttle opening,opening,
opening,
opening, rotational
rotational
rotational
rotational
speed,
speed,
speed,
speed,
speed, excess
excess
excess
excess air
excess airair
airair coefficient,
coefficient,
coefficient,
coefficient,
coefficient, and
andand
andand ignition
ignition
ignition
ignition
ignition timingtiming
timing
timing
timing angleangle
angle
angle used
angle used
used
used inin
ininin
used the
thethe
thebenchbench
bench
the bench
bench test
testtest
testare
are
test are
are
input
are input
input
input
inputinto into
into
into
into
speed,
speed,
speed,
speed, excess
excess
excess air
excess air coefficient,
airair coefficient,
coefficient,
coefficient, and
and
and ignition
and ignition
ignition
ignition timing timing
timing
timing angle
angle
angle used
angle usedused
used ininin
the
in
the
thebench
thebench bench
bench test
test are
test
test are input
are
are input
input
input into
into into
into
thethe
the
the
the corresponding
corresponding
corresponding
corresponding
corresponding module,
module,
module,
module,
module, and and
and
and aaset
and aaset set
asetof
set ofof
ofof combustion
combustion
combustion
combustion
combustion parameters
parameters
parameters
parameters
parameters consistent
consistent
consistent
consistent
consistent with with
with
with the
with thethe
thepower
the power
power
power
power
the
the
thecorresponding
the corresponding
corresponding
corresponding module,module,
module,
module, and
and
and aaset
and aset
aset of
set combustion
ofof of combustion
combustion
combustion parameters
parameters
parameters
parameters consistent
consistent
consistent
consistent with
with
with the
with the power
the
the power
power
power
 Processes 2022, 10, 2276 7 of 15
Processes
Processes 2022,
2022, 10,
10, xx FOR
FOR PEER
PEER REVIEW
REVIEW 77 of
of 15
15

into the corresponding module, and a set of combustion parameters consistent with the
under the test conditions are obtained by repeatedly calculating and adjusting the com-
power under the test conditions are obtained by repeatedly calculating and adjusting the
bustion parameters for the in-cylinder module [24]. Figure 6a shows the power compari-
combustion parameters for the in-cylinder module [24]. Figure 6a shows the power com-
son results of the calculated values from this model and the test values at conditions of an
parison results of the calculated values from this model and the test values at conditions of
engine speed of 4000 r/min and different throttle opening positions. At the same time,
an engine speed of 4000 r/min and different throttle opening positions. At the same time,
taking
takingthe
thefull
fullload
loadoperation
operationpoint
pointas
asan
anexample,
example,Figure
Figure6b 6bshows
showsthe
thecylinder
cylinderpressure
pressure
verification results of the test and simulation under full load. The resulting errors between
verification results of the test and simulation under full load. The resulting errors between
the
thesimulation
simulation and
and the test are
the test are within
within5%,
5%,which
whichverifies
verifiesthe
the accuracy
accuracy and
and rationality
rationality of
of the
the one-dimensional calculation
one-dimensional calculation model. model.

Figure
Figure5.
Figure 5.5.One-dimensional
One-dimensionalperformance
One-dimensional performancecalculation
performance calculationmodel
calculation modelfor
model forthe
for thetest
the testengine.
test engine.
engine.

Figure 6. Cont.
Processes 2022, 10, x FOR PEER REVIEW 8 of 15
Processes 2022, 10, x FOR PEER REVIEW 8 of 15
Processes 2022, 10, 2276 8 of 15

Figure 6. Validation of the calculation model with the test data: (a) engine output; (b) combustion
Validationof
Figure6.6.Validation
Figure ofthe
thecalculation
calculationmodel
modelwith
withthe
thetest
testdata:
data:(a)
(a)engine
engineoutput;
output;(b)
(b)combustion
combustion
pressure.
pressure.
pressure.
InInthe
thethree-dimensional
three-dimensionalnumerical
numericalsimulation,
simulation,thetheinitial
initialconditions
conditionsare arebased
basedon onthe
the
benchIntest
the three-dimensional numerical simulation, the initial conditions are based on the
bench test data, while the boundary conditions must be set in the calculation case for thisthis
data, while the boundary conditions must be set in the calculation case for cal-
bench test data,
calculation while
model. the boundary conditionspressure
must be parameters
set in the calculation case for this
culation model. AllAll
thethe required
required boundary
boundary pressure parameters for three-dimensional
for the the three-dimen-
calculation
sional model.
numerical All the required
simulation boundary pressuretoparameters for one-dimensional
the three-dimen-
numerical simulation can becan be obtained
obtained according
according the calibrated
to the calibrated one-dimensional perfor-
sional numerical
performance simulation
simulation can
model, be obtained
as described according to the calibrated one-dimensional
mance simulation model, as described in theinreference
the reference [25]; Figure
[25]; Figures 5 and 5 and Figurethe
6 provide 6
performance
provide the simulation
basis for model,pressure
boundary as described in the reference
calculation. As shown [25];
in Figure7,5the
Figure andcrankcase
Figure 6
basis for boundary pressure calculation. As shown in Figure 7, the crankcase pressure
provide the
pressure andbasis for boundary
exhaust pressure pressure
are calculation.
calculated through As
theshown in Figure
calibrated 7, the crankcase
one-dimensional sim-
and exhaust pressure are calculated through the calibrated one-dimensional simulation
pressuremodel
ulation and exhaust
under pressure
the are calculated
condition of an through
engine speedtheofcalibrated
4000 one-dimensional
r/min and a partial sim-
load.
model under the condition of an engine speed of 4000 r/min and a partial load. Therefore,
ulation
Therefore,model under the condition of an engine speed of 4000 r/min and a partial load.
accordingaccording
to this group to this group
of data, ofcrankcase
the data, the crankcase
pressure can pressure canthe
be set as beinlet
set as the inletof
pressure
Therefore,
pressure of according
the scavenging to this group ofthree-dimensional
data, the crankcasemodel,pressureandcan
the be set as the inlet
the scavenging port in theport in the
three-dimensional model, and the transient transient
exhaust exhaust
pressure
pressure can
pressure of thebescavenging
set as the port in
outlet the three-dimensional model, and the transient exhaust
pressure.
can be set as the outlet pressure.
pressure can be set as the outlet pressure.

Figure 7. Cont.
esses 2022, Processes
10, x FOR2022,
PEER 10,REVIEW
2276 9 of 15 9 of 15

Figure 7. Boundary conditions for pressure inlet and outlet: (a) crankcase pressure; (b) exhaust pressure.
Figure 7. Boundary conditions for pressure inlet and outlet: (a) crankcase pressure; (b) exhaust pressure.
3. Heavy Fuel Atomization and Mixture Formation Analysis
3. Heavy Fuel Atomization and Mixture
Under the condition Formation
of partial loads, Analysis
the throttle opening is limited, and the air intake
Under the condition
locates at a low oflevel.
partial loads,
The the throttleengine
corresponding opening is limited,
heat and the operation
load during air intake is relatively
locates at a small.
low level.
The The corresponding
evaporation engine of
characteristics heat loadfuel
heavy during the operation
in-cylinder is rela-
are sensitive to the control
tively small.ofThe evaporation
injection characteristics
parameters, of heavy fuel
and the distribution of ain-cylinder
combustible aremixture
sensitive to also
will the be affected
control of injection parameters,
accordingly. and the the
In this section, distribution
simulation of calculation
a combustible for mixture will also
the formation be spray and
of fuel
affected accordingly.
the mixture Inin-cylinder
this section,is the simulation
carried calculation
out for the condition forofthe formation
a partial load atof an
fuel
engine speed
spray and the mixture
of 4000 r/min.in-cylinder
The fuel is carriedisout
material lightfordiesel.
the condition
Adjustingofthe a partial load
injection at anand injection
timing
engine speed of 4000 to
pressure r/min. Thethe
obtain fuel material
fuel–air is lightconcentration
mixture diesel. Adjusting the injection
in-cylinder timing crankshaft
at different
and injectionpositions,
pressurethe distribution
to obtain law ofmixture
the fuel–air a fuel–air mixture is analyzed.
concentration in-cylinder at different
crankshaft positions, the distribution law of a fuel–air mixture is analyzed.
3.1. Effects of Injection Timing on Fuel Atomization and Mixture Formation
3.1. Effects of Injection Timingthe
To analyze on Fuel Atomization
influence and Mixture
of injection timingFormation
on the fuel atomization characteristics
and mixture distribution characteristics in the engine
To analyze the influence of injection timing on the fuel atomization cylinder, Figure 8 shows the fuel–air
characteristics
◦
and mixture distribution characteristics in the engine cylinder, Figure 8 shows theCA
mixture concentration distribution at the crankshaft positions from 330 ATDC to TDC
fuel–
◦
air mixture with the engine
concentration speed of 4000
distribution r/min.
at the The injection
crankshaft timings
positions from (start
330 °CA of injection)
ATDC toare 126 CA
BTDC, 176 ◦ CA of
BTDC ◦
TDC with the engine speed 4000 and
r/min.226TheCA BTDC,timings
injection respectively. Forinjection)
(start of these calculation
are 126 cases, the
°CA BTDC, 176◦°CA BTDC and 226 °CA BTDC, respectively. For these calculation cases, timing of
injection pressure is 6.5 bar and the fuel temperature is 293 K. The injection
the injection126 CA BTDC
pressure is 6.5 presents
bar and thethe fuel
late fuel injectionisstrategy.
temperature 293 K. TheIt can be observed
injection timingfrom
of the figure
◦ CA ATDC, the air–fuel ratios around the spark
that as the engine crankshaft position is 340
126 °CA BTDC presents the late fuel injection strategy. It can be observed from the figure
plugs installed at the intake side and exhaust side are about 23.7. Therefore, the fuel–air
that as the engine crankshaft position is 340 °CA ATDC, the air–fuel ratios around the
mixture concentration is relatively thin, which indicates the injection timing is too late. The
spark plugs installed at the intake side and exhaust side are about 23.7. Therefore, the
comprehensible reason is that as the fuel spray is injected with late timing, the ambient
fuel–air mixture concentration is relatively thin, which indicates the injection timing is too
pressure in the engine combustion chamber is relatively high, and most of the fuel droplets
late. The comprehensible reason is that as the fuel spray is injected with late timing, the
gather at the top of the combustion chamber. In addition, the insufficient evaporation
ambient pressure in the engine combustion chamber is relatively high, and most of the
time for the fuel droplets makes the formation of the fuel-air mixture inhomogeneous in
fuel droplets gather at the top of the combustion chamber. In addition, the insufficient
the combustion chamber, and the distribution area is small. As the injection timings are
evaporation time for the fuel droplets makes the formation of the fuel-air mixture inho-
advanced from 176 ◦ CA BTDC to 226 ◦ CA BTDC, the mass fraction of evaporated fuel in
mogeneous in the combustion chamber, and the distribution area is small. As the injection
the engine cylinder increases gradually. Meanwhile, the distribution area of the fuel–air
timings are advanced from 176 °CA BTDC to 226 °CA BTDC, the mass fraction of evapo-
mixture diffuses spatially, and the total amount of combustible mixture increases. The
rated fuel in the engine cylinder increases gradually. Meanwhile, the distribution area of
air–fuel ratios around the spark plugs near the intake side and exhaust side gradually
the fuel–air become
mixturethicker.
diffusesHowever,
spatially,with
andthetheadvance
total amount
of the of combustible
injection timings, mixture
a smallin-portion of the
creases. Thefuel–air
air–fuelmixture
ratios around the spark plugs near the intake
will inevitably be swept into the exhaust port. side and exhaust side
gradually become thicker. However, with the advance of the injection timings, a small
portion of the fuel–air mixture will inevitably be swept into the exhaust port.
Processes 2022, 10, x FOR PEER REVIEW 10 of 15
Processes 2022, 10, 2276 10 of 15

226 °CA BTDC 176 °CA BTDC 126 °CA BTDC

Crankshaft position: 320 °CA ATDC

Crankshaft position: 330 °CA ATDC

Crankshaft position: 340 °CA ATDC

Crankshaft position: 350 °CA ATDC

Crankshaft position: TDC

FigureFigure
8. Distribution of mixture
8. Distribution concentration
of mixture in-cylinder
concentration at different
in-cylinder injection
at different timings.
injection timings.

FigureFigure
9 shows the relationship
9 shows between
the relationship the overall
between SMD SMD
the overall of theoffuel
theatomization
fuel atomization
droplets and the
droplets injection
and timing timing
the injection at different crankshaft
at different positions.
crankshaft From theFrom
positions. figure,the It can
figure, It
be observed that, with the crankshaft position near the TDC, the overall SMD
can be observed that, with the crankshaft position near the TDC, the overall SMD of of the fuel
atomization
the fueldroplets gradually
atomization decreases.
droplets Thedecreases.
gradually main reason Theis main
that the air inisthe
reason thatcombus-
the air in the
tion chamber
combustionand chamber
the engine andcylinder above
the engine the piston
cylinder aboveisthecompressed gradually, gradually,
piston is compressed and the and
temperature in the cylinder
the temperature increases.
in the cylinder The scavenging
increases. airflow airflow
The scavenging in the in engine cylinder
the engine cylinder
drivesdrives thedroplets
the fuel fuel droplets into continuous
into continuous motion,motion, which
which is helpful
is helpful for for
thethe evaporation
evaporation of of the
fuel
the fuel droplets,making
droplets, makingthe theoverall
overallSMD
SMDsmaller.
smaller. As
As the injection timing
timing is 226◦ °CA
is 226 CA BTDC
◦ CA ATDC, the overall SMD of the fuel droplets
BTDCandandthe
thecrankshaft
crankshaftposition
positionlocates
locatesatat340
340 °CA ATDC, the overall SMD of the fuel
Processes
Processes2022,
2022,10,
10,x2276
FOR PEER REVIEW 1111ofof15
15

droplets in-cylinder
in-cylinder is 11.69
is 11.69 µm. This μm. This that
indicates indicates that the
the AADI can AADI
maintaincana maintain
favorable aatomization
favorable
atomization effect on the fuel spray. With the delaying of the injection timing,
effect on the fuel spray. With the delaying of the injection timing, the overall SMD the overall
of the
SMD of the fuel
fuel droplets dropletssignificantly
increases increases significantly
due to the due to the
shorter shorter evaporation
evaporation time and time and
increased
increased ambient pressure.
ambient pressure. As the timing
As the injection injection
is 126 ◦ CAisBTDC
timing 126 °CA BTDC
at the at the crankshaft
crankshaft position of
340 ◦ CAof
position 340 °CA
ATDC, ATDC, SMD
the overall the overall SMD
of the fuel of the fuel
droplets droplets
in the cylinderinisthe
47.23cylinder is 47.23a
µm, showing
μm,
less showing
combustiblea less combustible
mixture. mixture.
This is not This is
conducive to not conducive
forming to forming
a favorable ignitiona conditions
favorable
ignition conditions
in the engine in the engine
combustion combustion chamber.
chamber.

Atomizationsize
Figure9.9.Atomization
Figure sizeof
offuel
fueldroplets
dropletsin-cylinder
in-cylinderat
atdifferent
differentinjection
injectiontimings.
timings.

3.2. Effects of Injection Pressure on Fuel Atomization and Mixture Formation

3.2. Effects of Injection Pressure on Fuel Atomization and Mixture Formation
To investigate the effects of injection pressure on the fuel atomization characteristics
To investigate the effects of injection pressure on the fuel atomization characteristics
and mixture concentration distribution in-cylinder, the simulation results with different
and mixture concentration distribution in-cylinder, the simulation results with different
injection pressures are calculated and analyzed under the conditions that the injection
injection pressures are calculated and analyzed under the conditions that the injection
timing is 226 ◦ CA BTDC, and the fuel temperature is 293 K. Figure 10 shows the fuel–air
timing is 226 °CA BTDC, and the fuel temperature is 293 K. Figure 10 shows the fuel–air
mixture concentration distribution at the injection pressures of 5.5 bar, 6.5 bar, and 7.5 bar at
mixture concentration distribution at the injection pressures of 5.5 bar, 6.5 bar, and 7.5 bar
the engine speed of 4000 r/min. With the increase in injection pressure, the fuel–air mixture
at
isthe
moreengine
uniform.speed As of 4000 r/min. With
the injection the increase
pressure in injection
is 5.5 bar, pressure,pressure
the differential the fuel–air mix-
between
ture is more uniform. As the injection pressure is 5.5 bar, the differential
the outlet of the direct injector and the engine cylinder is small. This is not conducive to pressure between
the
theoutlet of theofdirect
expansion injector
the spray. and the engine
Therefore, most fuelcylinder is small.
droplets This is not
are gathered conducive
at the top of the to
the expansion of the spray. Therefore, most fuel droplets are gathered
combustion chamber, and the distribution area of fuel–air mixture is also quite limited. As at the top of the
combustion
the crankshaft chamber,
position and the ◦distribution
is 340 CA ATDC, the areaoverall
of fuel–air
amount mixture
of fuelis evaporated
also quite limited.
around
As the crankshaft position is 340 °CA ATDC, the overall
spark plug near the exhaust side is less, and the air–fuel ratio is about 19.8. amount of fuelTheevaporated
ignitable
around
conditionsparkfor plug near the
the fuel-air exhaust
mixture is side
poor.is Meanwhile,
less, and thewith air–fuel ratio is about
the increase in the19.8. The
injection
ignitable
pressure,condition
the distributionfor thearea
fuel-air mixture
of the fuel–airis mixture
poor. Meanwhile,
in-cylinderwith the increase
gradually in the
increases. As
injection pressure, the distribution area of the fuel–air mixture in-cylinder
the injection pressure is 6.5 bar and the crankshaft position locates at 340 CA ATDC, the ◦ gradually in-
creases.
air–fuelAs the around
ratios injectionthepressure is 6.5near
spark plugs bar and the crankshaft
the intake side andposition
exhaust locates
side areatabout
340 °CA13.2,
ATDC, the air–fuel ratios around the spark plugs near the intake side
making the fuel–air mixture more easily ignited. In addition, for different engine crankshaft and exhaust side
are about 13.2,
positions, making theof
the distribution fuel–air mixture
the fuel–air moreformed
mixture easily ignited. In addition,
at the injection for different
pressure of 7.5 bar
engine
is morecrankshaft
uniform than positions, the distribution
that formed of the fuel–air
at the injection pressure mixture
of 6.5 formed
bar. Asat thecrankshaft
the injection
pressure
positionsof are 7.5330
bar◦ CA
is more
ATDC, 340 ◦ CA
uniform than that and
ATDC, 350 ◦atCA
formed theATDC,
injection pressure the
respectively, of 6.5 bar.
air–fuel
As thearound
ratio crankshaft positions
the spark plugsare 330the
near °CA ATDC,
intake side340
and°CA ATDC, and
the exhaust side350 °CA ATDC,
is about 10.3, which re-
spectively, the air–fuel ratio around the spark plugs near the intake
is quite helpful to flame propagation and the expansion of the combustion area in the side and the exhaust
side is about
engine 10.3, which
combustion is quite helpful to flame propagation and the expansion of the
chamber.
combustion area in the engine combustion chamber.
Processes 2022, 10, x FOR PEER REVIEW 12 of 15
Processes 2022, 10, 2276 12 of 15

5.5 bar 6.5 bar 7.5 bar

Crankshaft position: 320 °CA ATDC

Crankshaft position: 330 °CA ATDC

Crankshaft position: 340 °CA ATDC

Crankshaft position: 350 °CA ATDC

Crankshaft position: TDC

FigureFigure
10. Distribution of mixture
10. Distribution concentration
of mixture in-cylinder
concentration at different
in-cylinder injection
at different pressures.
injection pressures.

FigureFigure 11 shows
11 shows the relationship
the relationship betweenbetween the overall
the overall SMD of SMD theof thespray
fuel fuel spray droplets
droplets
and theand the injection
injection pressure
pressure at different
at different crankshaft
crankshaft positions.
positions. It can Itbecan
seenbefrom
seen this
fromfigure
this figure
thatthe
that with with the increase
increase in injection
in injection pressure,pressure, the overall
the overall SMD of SMDthe of
fuelthe fuel droplets
droplets decreases.
decreases.
◦ CA ATDC, the overall SMD of the fuel droplets in the
At theAt the crankshaft
crankshaft position
position of 340of°CA340ATDC, the overall SMD of the fuel droplets in the
engineengine
cylindercylinder is 14.26
is 14.26 μm asµm theasinjection
the injection pressure
pressure is 5.5 isbar.
5.5Increasing
bar. Increasing the injection
the injection
pressures will easily reduce the overall SMD of the fuel droplets, which indicates the uni- the
pressures will easily reduce the overall SMD of the fuel droplets, which indicates
universality
versality of the air-assisted
of the air-assisted injector forinjector
fuel. Atforthefuel. At theposition
crankshaft crankshaft position
of 340 of 340 ◦ CA
°CA ATDC,
as theATDC,
injection as pressure
the injection
is 6.5pressure
bar, theisoverall
6.5 bar,SMD
the overall SMD
of the fuel of the fuel
droplets droplets
is 11.69 is 11.69 µm,
μm, which
which
is 18.1% loweris than
18.1% lower
that at 5.5than
bar.that at 5.5 bar.
Moreover, whenMoreover,
the injectionwhen the injection
pressures are 6.5 pressures
bar and are
6.5 bar and 7.5 bar, respectively, the difference of the overall SMD is gradually reduced
Processes 2022, 10, x FOR PEER REVIEW 13 of 15
Processes 2022, 10, 2276 13 of 15

7.5 bar, respectively, the difference of the overall SMD is gradually reduced as the crank-
shaft
as theposition approaches
crankshaft position TDC. However,
approaches TDC.excessive
However, injection
excessive pressure means
injection that means
pressure more
compressed air is consumed, and the power-to-mass ratio of the engine
that more compressed air is consumed, and the power-to-mass ratio of the engine will bewill be reduced.
Therefore, under the under
reduced. Therefore, conditions of reasonable
the conditions fuel–air mixture
of reasonable fuel–airformation and the accepta-
mixture formation and the
ble SMD of SMD
acceptable fuel droplets, the injection
of fuel droplets, pressure
the injection wouldwould
pressure be as appropriate as possible.
be as appropriate As
as possible.
the
As injection pressure
the injection is kept
pressure at aatlevel
is kept higher
a level than
higher 6.56.5
than bar, the
bar, thefavorable
favorablefuel
fuelatomization
atomization
effect
effectin
inthe
thecylinder
cylindercancanbebeguaranteed,
guaranteed,and andthe
theconsumption
consumptionof ofcompressed
compressedair airin
inaasingle
single
cycle can be reduced.
cycle can be reduced.

Figure11.
Figure Atomizationsize
11.Atomization sizeofoffuel
fueldroplets
dropletsin-cylinder
in-cylinderatatdifferent
differentinjection
injectionpressures.
pressures.

4. Conclusions
4. Conclusions
In this study, the numerical simulation method is used to investigate the fuel spray
In this study, the numerical simulation method is used to investigate the fuel spray
atomization and the in-cylinder fuel–air mixture formation of a two-stroke AADI HFE
atomization and the in-cylinder fuel–air mixture formation of a two-stroke AADI HFE
under partial load conditions at an engine speed of 4000 r/min. The effects of injection
under partial load conditions at an engine speed of 4000 r/min. The effects of injection
timing and injection pressure on the atomization of heavy fuel and the concentration
timing and injection pressure on the atomization of heavy fuel and the concentration dis-
distribution of the fuel–air mixture are analyzed. The main conclusions are as follows:
tribution of the fuel–air mixture are analyzed. The main conclusions are as follows:
1. The concentration distribution of a combustible mixture in-cylinder is more uniform
1. The concentration distribution of a combustible mixture in-cylinder is more uniform
and the fuel evaporation mass fraction increases after the injection timing is advanced;
and the fuel evaporation mass fraction increases after the injection timing is ad-
early injection timings can make the heavy fuel evaporate with sufficient time; the
vanced; early injection timings can make the heavy fuel evaporate with sufficient
later the injection timing, the larger the overall SMD of the fuel droplets; in addition,
time; the later the injection timing, the larger the overall SMD of the fuel droplets; in
premature injection timings will exacerbate the fuel losses.
addition, premature injection timings will exacerbate the fuel losses.
2. With the increase in injection pressure, the concentration distribution of the com-
2. With the increase in injection pressure, the concentration distribution of the combus-
bustible mixture in-cylinder is more uniform, which is conducive to the decrease in
tible mixture in-cylinder is more uniform, which is conducive to the decrease in the
the overall SMD of the fuel droplets and the propagation of the flame in the cylinder;
overall SMD of the fuel droplets and the propagation of the flame in the cylinder; as
as the air injection pressures change from 6.5 bar to 7.5 bar, the variations in fuel
the air injection pressures change from 6.5 bar to 7.5 bar, the variations in fuel particle
particle size are small, and the fuel atomization effect remains at a favorable level.
3. size
Thisareresearch
small, and the fuel
provides anatomization effect remains
improved simulation at afor
model favorable level.spray atom-
heavy fuel
3. Thisization and mixture formation. The results can provide theoretical spray
research provides an improved simulation model for heavy fuel support atomiza-
for the
tion and mixture formation. The results can provide theoretical support
optimization of the fuel injection parameters of two-stroke DISI HFEs. Due for the to
opti-
the
mization of the fuel injection parameters of two-stroke DISI HFEs. Due to the
limitation of time and conditions, this research did carried out detailed bench test limita-
tion of time
research and conditions,
under this research
different injection did carried
pressures out detailed
and injection bench
timings, testshould
which researchbe
under different injection pressures and injection timings, which should be
tested and verified in subsequent research work. This study hopes to contribute to tested and
the development of fuel injection control technology for small unmanned vehicles,
drones, and all-terrain vehicles.
Processes 2022, 10, 2276 14 of 15

Author Contributions: Conceptualization, R.L.; data curation, Y.Q., H.J., L.Z., and H.W.; formal
analysis, R.L. and H.J.; funding acquisition, R.L. and K.H.; investigation, R.L. and Y.Q.; project
administration, K.H.; resources, R.L.; software, Y.Q., L.Z., and H.W.; supervision, K.H.; writing–
original draft, R.L.; writing–review and editing, R.L. and K.H. All authors have read and agreed to
the published version of the manuscript.
Funding: This work was supported by the National Key Research and Development Program of
China (Grant No. 2018YFE0117500); the National Natural Science Foundation of China (Grant
No. 51865031); the State Key Laboratory of Engines, Tianjin University (Grant No. K2020-05);
and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant
No. 20KJB470014).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: All data used to support the findings of this study are included within
the article.
Acknowledgments: This research project was generously supported by the Jiangsu Province Key
Laboratory of Aerospace Power Systems.
Conflicts of Interest: The authors declare no conflict of interest.

References
1. Wang, C.; Lu, J.; Ren, Z.; Wan, Z.; Zhao, Z. Current development state and investigation of application for small piston aero-engine.
In Proceedings of the 9th Youth Science and Technology Forum of Chinese Aeronautical Society, Xian, China, 17 November 2020;
pp. 324–330.
2. Lu, D.; Zheng, J.; Hu, C. Study on the development status of general aviation piston engine. Intern. Combust. Engines Parts 2019,
10, 64–66.
3. Xu, J.; Nie, K.; Huang, G.; Sheng, Y. Control of torque and air-fuel ratio of compression-ignition aero piston engine. J. Aerosp.
Power 2021, 36, 1083–1093.
4. Du, C.; Tian, M.; Hu, C. Technical development analysis of two-stroke heavy fuel aero engine. Small Intern. Combust. Engine Veh.
Technol. 2020, 49, 92–96.
5. Liu, R.; Wei, M.; Yang, H. Cold start control strategy for a two-stroke spark ignition diesel-fuelled engine with air-assisted direct
injection. Appl. Therm. Eng. 2016, 108, 414–426. [CrossRef]
6. Wei, M.; Liu, R.; Yang, H.; Bei, T.; Ji, H.; Chang, C. Partial load experiments on a two-stroke spark ignition direct injection heavy
fuel engine. J. Aerosp. Power 2017, 32, 2919–2926.
7. Queiroz, C.; Tomanik, E. Gasoline Direct Injection Engines—A Bibliographical Review; SAE Technical Paper 973113; SAE International:
Warrendale, PA, USA, 1997.
8. Li, C. Study on the Mixture Formation and Combustion of Light-Weight High-Speed Heavy Oil Aeroengine. Master’s Thesis,
Beijing Jiaotong University, Beijing, China, 2014.
9. Hu, C.M.; Wang, S.D.; Bi, Y.F.; Zhong, W.J. Combustion characteristics of direct injection piston aviation kerosene engine. J. Aerosp.
Power 2017, 32, 1035–1042.
10. Chen, Z.; Qin, T.; He, T.; Zhu, L. Effect of equivalence ratio on diesel direct injection spark ignition combustion. J. Cent. South
Univ. 2020, 27, 2338–2352. [CrossRef]
11. Chen, Z.; Liao, B.; Yu, Y.; Qin, T. Effect of equivalence ratio on spark ignition combustion of an air-assisted direct injection
heavy-fuel two-stroke engine. Fuel 2022, 313, 122646. [CrossRef]
12. Zhao, Z.; Yu, C.; Dong, X.; Wang, L. Research on mixture formation of two-stroke heavy fuel direct injection engine. J. Aerosp.
Power 2021, 36, 1569–1577.
13. Huang, L. CFD Simulation Study of the Fuel-Air Mixture Formation in Cylinder of the Two-stroke Heavy Fuel Spark Ignition
Engine. Master’s Thesis, Nanjing University of Aeronautics and Astronautics, Nanjing, China, 2016.
14. Wang, S. Research on GDI Technology of Small Model Two-Stroke Kerosene Engine. Master’s Thesis, Nanjing University of
Aeronautics and Astronautics, Nanjing, China, 2017.
15. Wang, S.; Yang, H. Simulation on Atomization Mechanism of Air-Assisted Injector for Aircraft Heavy Fuel Engine. Trans. CSICE
2018, 36, 127–135.
16. Ji, H.; Wu, H.; Yang, H.; Liu, H.; Rui, L. Numerical simulation of diesel spray characteristics based on air-assisted atomization
injection. J. Aerosp. Power 2022, 37, 1284–1294.
17. Shih, T.-H.; Liou, W.; Shabbir, A.; Yang, Z.; Zhu, J. A new k- eddy viscosity model for high reynolds number turbulent flows.
Comput. Fluids 1995, 24, 227–238. [CrossRef]
18. O’Rourke, P. The TAB Method for Numerical Calculation of Spray Droplet Breakup; SAE Technical Paper 872089; SAE International:
Warrendale, PA, USA, 1987.
Processes 2022, 10, 2276 15 of 15

19. ANSYS, Inc. ANSYS Fluent Theory Guide 19.1; ANSYS, Inc.: Canonsburg, PA, USA, 2018; pp. 195–197.
20. Han, Z.; Fan, L.; Reitz, R.D. Multidimensional Modeling of Spray Atomization and Air-Fuel Mixing in a Direct-Injection Spark-Ignition
Engine; SAE Transactions: Warrendale, PA, USA, 1997; pp. 1423–1441.
21. GB 19147-2016[S/OL]; Automobile Diesel Fuels. National Technical Committee on Petroleum Products and Lubricants of
Standardization Administration of China, Standards Press of China: Beijing, China, 23 December 2016.
22. Liu, R.; Ji, H.; Wei, M. Study of low load performance on a two-stroke direct injection spark ignition aero-piston engine fuelled
with diesel. Aircr. Eng. Aerosp. Technol. 2021, 93, 473–482. [CrossRef]
23. Ma, Y.; Haiqing, Y.; Xu, G. Numerical simulation of stratified scavenging two-stroke gasoline engine. J. Aerosp. Power 2019, 34,
2001–2009.
24. Li, Z.; Hua, J.; Wei, H.; Zhang, L. Experimental and 1-D Simulation Studies of Gasoline Direct Ignition Engine. J. Combust. Sci.
Technol. 2018, 24, 238–244.
25. Bei, T.; Wei, M.; Liu, R.; Sheng, J. Effects of asynchronous ignition phase on knock combustion of two-stroke engine. J. Aerosp.
Power 2017, 32, 322–329.