Previous velocity and scalar measurements in both single-phase jets and two-phase diesel fuel sprays indicate that after the flow at the nozzle decelerates, ambient-gas entrainment increases compared to a steady jet. Previous studies using simplified analytical models and computational fluid dynamics (CFD) simulations using a one-dimensional (1D) inviscid, incompressible momentum equation have predicted that an “entrainment wave” propagates downstream along the jet axis during and after the deceleration, increasing entrainment by up to a factor of 3. In this study, entrainment is analyzed using the full compressible, unsteady Navier–Stokes momentum equations in axisymmetric two-dimensional (2D) CFD simulations of single-pulsed transient round gas jets. The 2D simulations confirm the existence of the entrainment wave, although the region of increased entrainment is distributed over a wider axial region of the jet than predicted by the simplified 1D model, so that the peak entrainment rate increases by only 50% rather than by a factor of 3. In the long time limit, both models show that the rate of mixing relative to the local injected fluid concentration increases significantly, approaching a factor of 3 or more increase in the wake of the entrainment wave (relative to a steady jet). Analysis of the terms in the momentum equation shows that the entrainment wave in the full 2D CFD predictions occurs in two phases. The entrainment first increases slightly due to a radial pressure gradient induced by a relatively fast acoustic wave, which the simple 1D model does not account for. The acoustic wave is followed by a slower momentum wave of decreased axial velocity initiated at the nozzle, which is convected downstream at the local flow velocities. The largest increase in entrainment accompanies the momentum wave, which is captured by the 1D momentum-equation model.

1.
Hardy
,
W. L.
, and
Reitz
,
R. D.
, 2006, “
An Experimental Investigation of Partially Premixed Combustion Strategies Using Multiple Injections in a Heavy-Duty Diesel Engine
,” SAE Paper No. 2006-01-0917.
2.
Yun
,
H.
,
Wermuth
,
N.
, and
Najt
,
P. M.
, 2009, “
Development of Robust Gasoline HCCI Idle Operation Using Multiple Injection and Multiple Ignition (MIMI) Strategy
,” SAE Paper No. 2009-01-0499.
3.
Kook
,
S.
,
Bae
,
C.
,
Miles
,
P. C.
,
Choi
,
D.
, and
Pickett
,
L. M.
, 2005, “
The Influence of Charge Dilution and Injection Timing on Low-Temperature Diesel Combustion and Emissions
,”
SAE Trans.
0096-736X,
114
(
4
), pp.
1575
1595
.
4.
Takeda
,
Y.
,
Keiichi
,
N.
, and
Keiichi
,
N.
, 1996, “
Emission Characteristics of Premixed Lean Diesel Combustion With Extremely Early Staged Fuel Injection
,”
SAE Trans.
0096-736X,
105
(
4
), pp.
938
947
.
5.
Abraham
,
J.
, 1996, “
Entrainment Characteristics of Transient Gas Jets
,”
Numer. Heat Transfer, Part A
1040-7782,
30
, pp.
347
364
.
6.
Ricou
,
F. P.
, and
Spalding
,
D. B.
, 1961, “
Measurements of Entrainment by Axisymmetrical Turbulent Jets
,”
J. Fluid Mech.
0022-1120,
11
, pp.
21
32
.
7.
Bremhorst
,
K.
, and
Hollis
,
P. G.
, 1979,
Unsteady Turbulent Sonic Jets, Recent Development in Theoretical and Experimental Fluid Mechanics: Compressible and Incompressible Flows
,
Springer-Verlag
,
Berlin
.
8.
Witze
,
P. O.
, 1983, “
Hot-Film Anemometer Measurements in a Starting Turbulent Jet
,”
AIAA J.
0001-1452,
21
(
2
), pp.
308
309
.
9.
Andriani
,
R.
,
Coghe
,
A.
, and
Cossali
,
G. E.
, 1996, “
Near Field Entrainment in Unsteady Gas Jets and Diesel Sprays: A Comparative Study
,”
Proc. Combust. Inst.
1540-7489,
26
, pp.
2549
2556
.
10.
Zhang
,
Q.
, and
Johari
,
H.
, 1996, “
Effects of Acceleration on Turbulent Jets
,”
Phys. Fluids
0031-9171,
8
, pp.
2185
2195
.
11.
Turner
,
J. S.
, 1962, “
The Starting Plume in Neutral Surroundings
,”
J. Fluid Mech.
0022-1120,
13
, pp.
356
368
.
12.
Atassi
,
N.
,
Boree
,
J.
, and
Charnay
,
G.
, 1993, “
Transient Behavior of an Axisymmetric Turbulent Jet
,”
Appl. Sci. Res.
0003-6994,
51
, pp.
137
142
.
13.
Joshi
,
A.
, and
Schreiber
,
W.
, 2006, “
An Experimental Examination of an Impulsively Started Incompressible Turbulent Jet
,”
Exp. Fluids
0723-4864,
40
, pp.
156
160
.
14.
Cossali
,
G. E.
,
Brunello
,
G.
, and
Coghe
,
A.
, 1991, “
LDV Characterization of Air Entrainement in Transient Diesel Sprays
,” SAE Paper No. 910178.
15.
Hiroyasu
,
H.
, and
Arai
,
M.
, 1990, “
Structures of Fuel Sprays in Diesel Engines
,”
SAE Trans.
0096-736X,
99
, pp.
1050
1061
.
16.
Hill
,
P. G.
, and
Ouellette
,
P.
, 1999, “
Transient Turbulent Gaseous Fuel Jets for Diesel Engines
,”
ASME J. Fluids Eng.
0098-2202,
121
, pp.
93
101
.
17.
Naber
,
J. D.
, and
Siebers
,
D. L.
, 1996, “
Effects of Gas Density and Vaporization on Penetration and Dispersion of Diesel Sprays
,”
SAE Trans.
0096-736X,
105
, pp.
82
111
.
18.
Bruneaux
,
G.
, 2005, “
Mixing Process in High Pressure Diesel Jets by Normalized Laser Induced Exciplex Fluorescence Part I: Free Jet
,” SAE Paper No. 2005-01-2100.
19.
Musculus
,
M. P. B.
,
Lachaux
,
T.
,
Pickett
,
L. M.
, and
Idicheria
,
C. A.
, 2007, “
End-of-Injection Over-Mixing and Unburned Hydrocarbon Emissions in Low-Temperature-Combustion Diesel Engines
,”
SAE Trans.
0096-736X,
116
(
3
), pp.
514
541
.
20.
Cossali
,
G. E.
,
Geria
,
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.
21.
Iyer
,
V.
, and
Abraham
,
J.
, 2003, “
An Evaluation of a Two-Fluid Eulerian-Liquid Eulerian-Gas Model for Diesel Sprays
,”
ASME J. Fluids Eng.
0098-2202,
125
, pp.
660
669
.
22.
Boree
,
J.
,
Atassi
,
N.
,
Charnay
,
G.
, and
Taubert
,
L.
, 1997, “
Measurements and Image Analysis of the Turbulent Field in an Axisymmetric Jet Subjected to a Sudden Velocity Decrease
,”
Exp. Therm. Fluid Sci.
0894-1777,
14
, pp.
45
51
.
23.
Johari
,
H.
, and
Paduano
,
R.
, 1997, “
Dilution and Mixing in an Unsteady Jet
,”
Exp. Fluids
0723-4864,
23
, pp.
272
280
.
24.
Musculus
,
M. P. B.
, and
Kattke
,
K.
, 2009, “
Entrainment Waves in Diesel Jets
,” SAE Paper No. 2009-01-1355.
25.
Musculus
,
M. P. B.
, 2009, “
Entrainment Waves in Decelerating Transient Turbulent Jets
,”
J. Fluid Mech.
0022-1120,
638
, pp.
117
140
.
26.
Amsden
,
A. A.
, 1999, “
KIVA-3V: A Block-Structured KIVA Program for Engines With Vertical or Canted Valves
,” Los Alamos National Laboratory Technical Report No. LA-UR-99-915.
27.
Launder
,
B. E.
, and
Spalding
,
D. B.
, 1972,
Mathematical Models of Turbulence
,
Academic
,
New York
.
28.
Williams
,
F. A.
, 1985,
Combustion Theory
,
2nd ed.
,
Banjamin-Cummings
,
Menlo Park, CA
.
29.
Pope
,
S. B.
, 2000,
Turbulent Flows
,
Cambridge University Press
,
Cambridge
.
30.
Schefer
,
R. W.
,
Johnston
,
S. C.
,
Dibble
,
R. W.
,
Gouldin
,
F. C.
, and
Kollmann
,
W.
, 1985, “
Non-Reacting Turbulent Mixing Flows: A Literature Survey and Data Base
,” Sandia National Laboratories Technical Report No. SAND86-8217.
31.
Hinze
,
J. O.
, 1975,
Turbulence
,
2nd ed.
,
McGraw-Hill
,
New York
.
32.
Dec
,
J. E.
, 1997, “
A Conceptual Model of D.I. Diesel Combustion Based on Laser Sheet Imaging
,” SAE Paper No. 970873.
33.
Lachaux
,
T.
, and
Musculus
,
M. P. B.
, 2007, “
In-Cylinder Unburned Hydrocarbon Visualization During Low-Temperature Compression-Ignition Engine Combustion Using Formaldehyde PLIF
,”
Proc. Combust. Inst.
1540-7489,
31
, pp.
2921
2929
.
34.
Musculus
,
M. P. B.
, 2006, “
Multiple Simultaneous Optical Diagnostic Imaging of Early-Injection Low-Temperature Combustion in a Heavy-Duty Diesel Engine
,”
SAE Trans.
0096-736X,
115
(
3
), pp.
83
110
.
35.
Singh
,
S.
,
Reitz
,
R. D.
,
Musculus
,
M. P. B.
, and
Lachaux
,
T.
, 2007, “
Validation of Engine Combustion Models Against Detailed In-Cylinder Optical Diagnostics Data for a Heavy-Duty Compression-Ignition Engine
,”
Int. J. Engine Res.
1468-0874,
8
(
1
), pp.
97
126
.
36.
Akihama
,
K.
,
Takatori
,
Y.
,
Inagaki
,
K.
,
Sasaki
,
S.
, and
Dean
,
A. M.
, 2001, “
Mechanism of the Smokeless Rich Diesel Combustion by Reducing Temperature
,” SAE Technical Paper No. 2001-01-0655.
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