Abstract

The entrainment coefficient reflects the air–fuel mixing quality, which is one of the foremost concerns for the development of cleaner and higher power-density internal combustion engines. Previous prediction models constructed by the change of axial mass flow rate have lower accuracy under high injection pressure conditions. During modeling in the work, a new construction method based on local entrainment velocity and local entrainment area is developed, and the influences of dilution effect and forces such as flow resistance, lateral pressure, etc. on the local entrainment velocity are considered. With the modified model, its prediction accuracy can be effectively extended to high injection pressure and detailed information about entrainment can be provided for analysis. It is found that, with the increase of injection pressure, the entrainment coefficient rises in the whole flow field. When increasing to high injection pressure, the entrainment coefficient constantly decreases with distance in the far-field, which is consistent with the experiments, but not a constant value predicted by previous models. Besides, the decreased rate of entrainment coefficient rises with the increase of injection pressure. Meanwhile, the increase of ambient pressure also makes the entrainment coefficient rise, but barely influences the decreased rate in the far-field. The large decrease of local entrainment velocity in the far-field caused by strong shear stress and flow resistance can explain the decrease of entrainment coefficient with distance. Overall, the modified model is able to rapidly predict the spray mixing quality over a wider range of operational conditions and provide more detailed entrainment information for analysis.

References

1.
Morton
,
B. R.
,
Taylor
,
G. I.
, and
Turner
,
J. S.
,
1956
, “
Turbulent Gravitational Convection From Maintained and Instantaneous Sources
,”
Proc. R. Soc. London
,
234
(
1196
), pp.
1
23
.10.1098/rspa.1956.0011
2.
Turner
,
J. S.
,
1986
, “
Turbulent Entrainment: The Development of the Entrainment Assumption and Its Application to Geophysical Flows
,”
J. Fluid Mech.
,
373
, pp.
431
471
.10.1017/S0022112086001222
3.
Ricou
,
F. P.
, and
Spalding
,
D. B.
,
1961
, “
Measurement of Entrainment by Axisymmetric Turbulent Jets
,”
J. Fluid Mech.
,
11
(
1
), pp.
21
32
.10.1017/S0022112061000834
4.
Hill
,
B. J.
,
1972
, “
Measurement of Local Entrainment Rate in the Initial Region of Axisymmetric Turbulent Air Jets
,”
J. Fluid Mech.
,
51
(
4
), pp.
773
779
.10.1017/S0022112072001351
5.
Crow
,
S. C.
, and
Champagne
,
F. H.
,
1971
, “
Orderly Structure in Jet Turbulence
,”
J. Fluid Mech.
,
48
(
3
), pp.
547
591
.10.1017/S0022112071001745
6.
Falcone
,
A. M.
, and
Cataldo
,
J. C.
,
2003
, “
Entrainment Velocity in an Axisymmetric Turbulent Jet
,”
ASME J. Fluids Eng.
,
125
(
4
), pp.
620
627
.10.1115/1.1595674
7.
Han
,
D.
, and
Mungal
,
M. G.
,
2001
, “
Direct Measurement of Entrainment in Reacting/Nonreacting Turbulent Jets
,”
Combust. Flame
,
124
(
3
), pp.
370
386
.10.1016/S0010-2180(00)00211-X
8.
Liepmann
,
D.
, and
Gharib
,
M.
,
1992
, “
The Role of Streamwise Vorticity in the Near-Field Entrainment of Round Jets
,”
J. Fluid Mech.
,
245
, pp.
643
668
.10.1017/S0022112092000612
9.
Cossali
,
G.
,
Gerla
,
A.
,
Coghe
,
A.,
and Brunello, G.,
1996
, “
Effect of Gas Density and Temperature on Air Entrainment in a Transient Diesel Spray
,”
SAE Paper No. 960862
.
10.
Andriani
,
R.
,
Coghe
,
A.
, and
Cossali
,
G. E.
,
1996
, “
Near-Field Entrainment in Unsteady Gas Jets and Diesel Sprays: A Comparative Study
,”
Twenty-Sixth Symposium (International) on Combustion
, The Combustion Institute, Pittsburgh, PA, pp.
2549
2556
.
11.
Nishida
,
K.
,
Zhu
,
J.
,
Leng
,
X.
, and
He
,
Z.
,
2017
, “
Effects of Micro-Hole Nozzle and Ultra-High Injection Pressure on Air Entrainment, Liquid Penetration, Flame Lift-Off and Soot Formation of Diesel Spray Flame
,”
Int. J. Engine Res.
,
18
(
1–2
), pp.
51
65
.10.1177/1468087416688805
12.
Riess
,
S.
,
Weiss
,
L.
,
Peter
,
A.
,
Rezaei
,
J.
, and
Wensing
,
M.
,
2018
, “
Air Entrainment and Mixture Distribution in Diesel Sprays Investigated by Optical Measurement Techniques
,”
Int. J. Engine Res.
,
19
(
1
), pp.
120
133
.10.1177/1468087417742527
13.
Wei
,
Y.
,
Li
,
T.
,
Zhou
,
X.
, and
Zhang
,
Z.
,
2020
, “
Time-Resolved Measurement of the Near-Nozzle Air Entrainment of High Pressure Diesel Spray by High-Speed Micro-PTV Technique
,”
Fuel
,
268
, p.
117343
.10.1016/j.fuel.2020.117343
14.
Wei
,
Y.
,
Li
,
T.
,
Chen
,
R.
,
Zhou
,
X.
,
Zhang
,
Z.
, and
Wang
,
X.
,
2022
, “
Measurement and Modeling of the Near-Nozzle Ambient Gas Entrainment of High-Pressure Diesel Sprays
,”
Fuel
,
310
, p.
122373
.10.1016/j.fuel.2021.122373
15.
Xia
,
J.
, and
Luo
,
K. H.
,
2009
, “
Direct Numerical Simulation of Diluted Combustion by Evaporating Droplets
,”
Proc. Combust. Inst.
,
32
(
2
), pp.
2267
2274
.10.1016/j.proci.2008.05.047
16.
Shinjo
,
J.
,
Xia
,
J.
, and
Umemura
,
A.
,
2015
, “
Droplet/Ligament Modulation of Local Small-Scale Turbulence and Scalar Mixing in a Dense Fuel Spray
,”
Proc. Combust. Inst.
,
35
(
2
), pp.
1595
1602
.10.1016/j.proci.2014.06.088
17.
Shinjo
,
J.
, and
Umemura
,
A.
,
2019
, “
Fluid Dynamic and Autoignition Characteristics of Early Fuel Sprays Using Hybrid Atomization LES
,”
Combust. Flame
,
203
, pp.
313
333
.10.1016/j.combustflame.2019.02.009
18.
Umemura
,
A.
, and
Shinjo
,
J.
,
2021
, “
A New LES Approach to Trans-Critical Mixing and Combustion Processes in High-Pressure Liquid-Injectant Engines
,”
Proc. Combust. Inst.
,
38
(
2
), pp.
3107
3129
.10.1016/j.proci.2020.07.031
19.
Liu
,
P. Q.
,
2008
,
Free Turbulent Jet Theory
, 1st ed.,
Beihang University Press
,
Beijing
, China, p.
102
.
20.
Franco Medrano
,
F.
,
Fukumoto
,
Y.
,
Velte
,
C. M.
, and
Hodžić
,
A.
,
2017
, “
Mass Entrainment Rate of an Ideal Momentum Turbulent Round Jet
,”
J. Phys. Soc. Jpn.
,
86
(
3
), p.
034401
.10.7566/JPSJ.86.034401
21.
Strasser
,
W.
, and
Battaglia
,
F.
,
2018
, “
Pulsating Slurry Atomization, Film Thickness, and Azimuthal Instabilities
,”
Atomization Sprays
,
28
(
7
), pp.
643
672
.10.1615/AtomizSpr.2018026380
22.
Kuti
,
O. A.
,
Nishida
,
K.
, and
Zhu
,
J. Y.
,
2013
, “
Experimental Studies on Spray and Gas Entrainment Characteristics of Biodiesel Fuel: Implications of Gas Entrained and Fuel Oxygen Content on Soot Formation
,”
Energy
,
57
, pp.
434
442
.10.1016/j.energy.2013.05.006
23.
Lee
,
J.
,
Lu
,
T.
,
Sun
,
H.
, and
Miao
,
G.
,
2011
, “
A Novel Formula to Describe the Velocity Profile of Free Jet Flow
,”
Arch. Appl. Mech.
,
81
(
3
), pp.
397
402
.10.1007/s00419-010-0418-7
24.
Cheng
,
P.
,
Li
,
Q.
,
Xu
,
S.
, and
Kang
,
Z.
,
2017
, “
On the Prediction of Spray Angle of Liquid-Liquid Pintle Injectors
,”
Acta Astronaut.
,
138
, pp.
145
151
.10.1016/j.actaastro.2017.05.037
25.
Grabe
,
J. V.
,
2013
, “
Flow Resistance for Different Types of Windows in the Case of Buoyancy Ventilation
,”
Energy Build.
,
65
, pp.
516
522
.10.1016/j.enbuild.2013.06.035
26.
Safiullah
,
Nishida
,
K.
, and
Ogata
,
Y.
,
2021
, “
Evaporation and Mixture Formation Characteristics of Diesel Spray Under Various Nozzle Hole Size and Injection Pressure Condition Employing Similar Injection Rate Profile
,”
Int. Commun. Heat Mass Transfer
,
123
, p.
105184
.10.1016/j.icheatmasstransfer.2021.105184
27.
Arai
,
M.
,
Tabata
,
M.
, and
Hiroyasu
,
H.
,
1984
, “
Disintegrating Process and Spray Characterization of Fuel Jet Injected by a Diesel Nozzle
,”
SAE
Paper No. 840275.10.4271/840275
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