Liquid breakup in fuel spray and atomization significantly affects the consequent mixture formation, combustion behavior, and emission formation processes in a direct injection diesel engine. In this paper, different models for liquid breakup processes in high-pressure dense diesel sprays and its impact on multi-dimensional diesel engine simulation have been evaluated against experimental observations, along with the influence of the liquid breakup models and the sensitivity of model parameters on diesel sprays and diesel engine simulations. It is found that the modified Kelvin-Helmholtz (KH)–Rayleigh-Taylor (RT) breakup model gives the most reasonable predicted results in both engine simulation and high-pressure diesel spray simulation. For the standard KH-RT model, the model constant Cbl for the breakup length has a significant effect on the predictability of the model, and a fixed value of the constant Cbl cannot provide a satisfactory result for different operation conditions. The Taylor-analogy-breakup (TAB) based models and the RT model do not provide reasonable predictions for the characteristics of high-pressure sprays and simulated engine performance and emissions.
Caterpillar 3401E single cylinder oil test engine (SCOTE)
Bore×stroke/mm
137.2 ×165.1
Compression ratio
16.1:1
Displacement/L
2.44
Connecting rod length/mm
261.6
Squish height/mm
1.57
Intake valve closing/(°) ATDC
–143
Exhaust valve opening/(°) ATDC
130
Tab.1
Injector type
Electronic unit injector (EUI)
Maximum injection pressure/MPa
190
Number of nozzle holes
6
Nozzle hole diameter/mm
0.214
Included spray angle
130˚
Injection rate shape
Rising
Tab.2
Fig.1
Physical process
Model
Drop collision
NTC model [11]
Drop turbulent dispersion
O’Rourke turbulent dispersion model
Drop vaporization
Amsden-Chiang model [23]
Ignition and combustion (Only used in the engine simulation)
Shell+characteristic time combustion (CTC) model [24]
Pollutant formation (Only used in the engine simulation)
Extended Zel’dovich model &Hiroyasu-NS coxidation soot model [25,26]
Tab.3
Fig.2
Injection pressure/MPa
Injection duration/ms
Ambient temperature/K
Ambient density/(kg·m–3)
Injector diameter Dn/mm
180
1.0
950
60
0.1
Tab.4
Case
Breakup Model
1
KH-RT modified model
2
KH-RT model with the breakup length constant Cbl=10 in Eq. (20)
3
KH-RT model with Cbl=20 in Eq. (20)
4
KH-RT model with Cbl=40 in Eq. (20)
5
TAB model (without the drop size distribution)
6
TAB-CHI model (with the chi-squared drop size distribution)
7
TAB-RR model (with the Rosin-Rammler drop size distribution)
Tab.5
Fig.3
Fig.4
Fig.5
Fig.6
Fig.7
Engine speed
Start of injection/(˚) ATDC
Injection duration
EGR/%
Intake pressure/kPa
Intake temperature/K
821
–9
5.5˚
48.34
103
393
Tab.6
Fig.8
Fig.9
Fig.10
1
Badami M, Nuccio P, Trucco G. Influence of injection pressure on the performance of a diesel engine with a common rail fuel injection system. SAE Paper, 1999, Paper No.1999-01-0193
2
Baumgarten C. Mixture Formation in Internal Combustion Engines. Berlin: Springer, 2006
3
Felice E C, Bianca M V, Giuseppe E C. Potential of multiple injection strategy for low emission diesel engines. SAE Paper, 2002, Paper No. 2002-01-1150
4
Reitz R D. Modeling atomization processes in high-pressure vaporizing sprays. Atomization and Spray Technology, 1987, 3(4): 309–337
5
Reitz R D, Bracco F V. Mechanism of Breakup of Round Liquid Jets, Cheremisnoff N ed. The Encyclopedia of Fluid mechanics. Houston: Gulf Publishing, 1986, 233–249
6
Taylor G I. The Instability of liquid surfaces when accelerated in a direction perpendicular to their planes. Proceedings of the Royal Sociaty A, 1950, 201(1065): 532–536
7
Senecal P K, Richard K J, Pomraning E. A new parallel cut-cell cartesian CFD code for rapid grid generation applied to in-cylinder diesel engine simulations. SAE Paper, 2007, Paper No. 2007-01-0159
8
Senecal P K. Development of a methodology for internal combustion engine design using multi-dimensional modeling with validation through experiments. Dissertation for the Doctoral Degree. University of Wisconsin-Madison, 2000
9
O’Rourke P J, Amsden A A. The TAB method for numerical calculation of spray droplet breakup. SAE Paper, 1987, Paper No. 872089
10
O’Rourke P J, Amsden A A. A spray/wall interaction submodel for the KIVA-3 wall film model. SAE Paper, 2000, Paper No. 2000-01-0271
11
Schmidt D P, Rutland C J. A new droplet collision algorithm. Journal of Computational Physics, 2000, 164(1): 62–80
https://doi.org/10.1006/jcph.2000.6568
12
Sone K, Menon S. Effect of subgrid modeling on the in-cylinder unsteady mixing process in a direct injection engine. Journal of Engineering for Gas Turbines and Power, 2003, 125(2): 435–443
https://doi.org/10.1115/1.1501918
13
Hori T, Senda J, Kuge T, Fujimoto H. Large eddy simulation of non-evaporative and evaporative diesel spray in constant volume vessel by use of KIVALES. SAE Paper, 2006, Paper No. 2006-01-3334
14
Larmi M, Tiainen J. Diesel spray simulation and KH-RT wave model. SAE Paper, 2003, Paper No. 2003-01-3231
15
Fujimoto H, Hori T, Senda J. Effect of breakup model on diesel spray structure simulated by large eddy simulation. SAE Paper, 2009, Paper No. 2009-24-0024
16
Su W, Sun T, Guo H. Quantitative study of concentration and temperature of a diesel spray by using planar laser induced exciplex fluorescence technique. SAE Paper, 2010, Paper No. 2010-01-0878
17
Klingbeil A E, Juneja H, Ra Y, Reitz R. Premixed diesel combustion analysis in a heavy-duty diesel engine. SAE Paper, 2003, Paper No. 2003-01-0341
18
Wilcox D C. Turbulence Modeling for CFD. California: DCW Industries, 1994
19
Han Z, Reitz R D. Turbulence modeling of internal combustion engines using RNG κ-εmodels. Combustion Science and Technology, 1995, 106(4-6): 267–295
https://doi.org/10.1080/00102209508907782
20
Launder B E, Spalding D B. Lectures in Mathematical Models of Turbulence. Academic Press, 1972
21
Yakhot V, Smith L M. The renormalization group, the E-expansion and derivation of turbulence models. Journal of Scientific Computing, 1992, 7(1): 35–61
https://doi.org/10.1007/BF01060210
22
Ren Y, Li X G. Numerical study on combustion and emissions characteristics of a direct injection (DI) diesel engine. In: Proceedings of the Combustion Institute–Canadian Section. Montreal, Canada, 2009, 18–23
23
Chiang C H, Raju M S, Sirignano W A. Numerical analysis of a convecting, vaporizing fuel droplet with variable properties. International Journal of Heat and Mass Transfer, 1992, 35(5): 1307–1324
https://doi.org/10.1016/0017-9310(92)90186-V
24
Xin J, Montgomery D, Han Z, Reitz R D. Multidimensional modeling of combustion for a six-mode emissions test cycle on a DI diesel engine. Journal of Engineering for Gas Turbines and Power, 1997, 119: 683–691
https://doi.org/10.1115/1.2817041
25
Hiroyasu H, Kadota T. Models for combustion and formation of nitric oxide and soot in direct injection diesel engines. SAE Paper, 1976, Paper No.760129
26
Nagle J, Strickland-Constable R F. Oxidation of carbon between 1000–2000°C. In: Proceedings of the 5th Carbon Conference. Elsevier Inc., 1962, 154–164
27
Abani N, Munnannur A, Reitz R D. Reduction of numerical parameter dependencies in diesel spray models. Journal of Engineering for Gas Turbines and Power, 2002, 130: 032809-1–9