Abstract
Numerical simulation of biodiesels is conducted under ultra-high injection pressure by applying a new breakup model. A combined modified breakup model that considers transient phenomenon of high-pressure spray is incorporated into OpenFOAM Computational Fluid Dynamics code. Effects of injection pressure and fuel properties on spray parameters such as spray penetration, spray angle, and spray volume are studied. To accomplish this task, an Eulerian–Lagrangian multiphase formulation is used in the OpenFOAM software to model in-cylinder flow by RANS method and to track the fuel droplet by lagrangian scheme. Simulation results are validated by the existing experimental data for biodiesels at various conditions. Numerical results indicate good agreement with experimental data, especially at ultra-high pressure. At these pressures, biodiesel fuel sprays geometrical properties are similar to those of diesel fuel sprays. Results of the current study show that biodiesels have longer penetration at lower injection pressure, as reported by published experimental data. Overall, it is concluded that the newly added breakup model to OpenFOAM software provides accurate results for biodiesels under ultra-high pressures.
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Abbreviations
- \( B_{0} \) :
-
Breakup constant [–]
- \( B_{1} \) :
-
Breakup constant [–]
- \( C_{\text{D}} \) :
-
Drag constant [–]
- h :
-
Enthalpy
- \( L_{\text{b}} \) :
-
Breakup length [m]
- \( L_{\text{S}} ,\,L_{\text{bu}} ,\,L \) :
-
Penetration length [m]
- \( {\text{Oh}} \) :
-
Ohnesorge number [–]
- \( P \) :
-
Pressure [Pa]
- \( \Pr \) :
-
Prandtl number [–]
- \( r_{0} \) :
-
Droplet radius before breakup [m]
- \( r_{\text{c}} \) :
-
Radius of child droplets [m]
- \( Re_{\text{p}} \) :
-
Particle Reynolds number [–]
- \( \dot{S} \) :
-
Source term
- \( {\text{Ta}} \) :
-
Taylor number [–]
- \( u \) :
-
Velocity vector [m s−1]
- \( u_{\text{p}} \) :
-
Particle velocity [m s−1]
- \( u_{\text{g}} \) :
-
Gas velocity [m s−1]
- \( U_{\text{m}} \) :
-
Jet velocity [m s−1]
- \( {\text{We}}_{\text{g}} \) :
-
Gas Weber number [–]
- \( {\text{We}}_{\text{l}} \) :
-
Liquid Weber number [–]
- \( \Lambda_{\text{KH}} \) :
-
Kelvin–Helmholtz wavelength [m]
- \( \Omega_{\text{KH}} \) :
-
Kelvin–Helmholtz growth rate [s−1]
- \( \Lambda_{\text{RT}} \) :
-
Rayleigh–Taylor wavelength [m]
- \( \Omega_{\text{RT}} \) :
-
Rayleigh–Taylor growth rate [s−1]
- \( \mu \) :
-
Dynamic viscosity [N s m−2]
- \( \mu_{\text{k}} \) :
-
Turbulent viscosity [kg m−1 s−1]
- \( \rho \) :
-
Density [kg m−3]
- \( \rho_{\text{p}} \) :
-
Particle density [kg m−3]
- \( \tau_{ij} \) :
-
Resolved stress tensor [kg m−1 s−2]
- \( \tau_{\text{KH}} \) :
-
Kelvin–Helmholtz breakup time [s]
References
Baumgarten C (2006) Mixture formation in internal combustion engines. Springer, New York
Bellman R, Pennington R (1954) Effects of surface tension and viscosity on Taylor instability. Q Appl Math 12:151–162
Delacourt E, Desmet B, Besson B (2005) Characterization of very high pressure diesel sprays using digital imaging techniques. Fuel 84:859–867
Demoulin FX, Borghi R (2002) Modeling of turbulent spray combustion with application to diesel like experiment. Combust Flame 129(3):281–293
Ferziger JH, Peric M (2002) Computational methods for fluid dynamics. Springer, New York
Ghurri A, Kim J, Kim HG et al (2012) The effect of injection pressure and fuel viscosity on the spray characteristics of biodiesel blends injected into an atmospheric chamber. J Mech Sci Technol 26(9):2941–2947
Gjesing R, Hattel J, Fritsching U (2009) Coupled atomization and spray modelling in the spray forming process using OpenFOAM. Eng Appl Comput Fluid Mech 3(4):471–486
Goldsworthy L (2006) Computational fluid dynamics modeling of residual fuel oil combustion in the context of marine diesel engines. Int J Engine Res 7:181–199
Hosseinpour S, Binesh AR (2009) Investigation of fuel spray atomization in a DI heavy-duty diesel engine and comparison of various spray breakup model. Fuel 88:799–805
Jones WP, Launder BE (1972) The prediction of laminarization with a two-equation model of turbulence. Int J Heat Mass Transf 15:301–314
Kassem HI, Saqr KM, Aly HS et al (2011) Implementation of the eddy dissipation model of turbulent non-premixed combustion in OpenFOAM. Int Commun Heat Mass Transfer 38:363–367
Kyriakides N, Chryssakis C and Kaiktsis L (2009) Influence of heavy fuel properties on spray atomization for marine diesel engine applications. SAE 2009-01-1858
Moreira A, Moita A, Panao M (2010) Advances and challenges explaining fuel spray impingement: how much of single droplet impact research is useful? Prog Energy Combust Sci 36:554–580
Nordin N (2001) Complex chemistry modeling of diesel spray combustion. PhD Thesis, Chalmers University of Technology
Payri R, Salvador FJ, Gimeno J et al (2008) A new methodology for correcting the signal cumulative phenomenon on injection rate measurements experimental techniques. Exp Tech 32(1):46–49
Pogorevc P, Kegl B, Skerget L (2008) Diesel and biodiesel fuel spray simulations. Energy Fuels 22:1266–1274
Reitz RD, Diwakar R (1987) Structure of high-pressure fuel sprays. SAE Technical Paper 870598
Roisman IV, Araneo L, Tropea C (2007) Effect of ambient pressure on penetration of a diesel spray. Int J Multiph Flow 33:904–920
Sazhin SS, Martynov SB, Kristyadi T et al (2008) Diesel fuel spray penetration, heating, evaporation and ignition: modeling versus experimentation. Int J Eng Syst Model 1(1):1–19
Som S, Aggarwal SK, El-Hannouny EM, Longman DE (2010) Investigation of nozzle flow and cavitation characteristics in a diesel injector. J Eng Gas Turbine Power 132(042802):1–12
Shervani-Tabar MT, Sheykhvazayefi M, Ghorbani M (2013) Numerical study on the effect of the injection pressure on spray penetration length. Appl Math Model Appl Math Model 37(14–15):7778–7788
Som S, Aggarwal SK (2010) Effects of primary breakup modeling on spray and combustion characteristics of compression ignition engines. Combust Flame 157:1179–1193
Stiesch G (2003) Modeling engine spray and combustion processes. Springer, New York
Tanner FX (1997) Liquid jet atomization and droplet breakup modeling of non-evaporating diesel fuel sprays. SAE paper 970050
Turner MR, Sazhin SS, Healey JJ et al (2012) A breakup model for transient diesel fuel sprays. Fuel 97:288–305
Vuorinen V, Duwig C, Fuchs L, et al. (2011) Large-eddy simulation of a compressible spray using Eulerian–Eulerian approach. In: Proceeding of the 24th European conference on liquid atomization and spray systems 5–7 September 2011, Estoril, Portugal
Wang X, Huang Z, Kuti OA et al (2010) Experimental and analytical study on biodiesel and diesel spray characteristics under ultra-high injection pressure. Int J Heat Fluid Flow 31:659–666
Zhang J, Fang T (2011) Spray combustion of biodiesel and diesel in a constant volume combustion chamber. SAE paper 2011-01-1380
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Technical Editor: Luis Fernando Figueira da Silva.
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Yousefifard, M., Ghadimi, P. & Mirsalim, M. Numerical simulation of biodiesel spray under ultra-high injection pressure using OpenFOAM. J Braz. Soc. Mech. Sci. Eng. 37, 737–746 (2015). https://doi.org/10.1007/s40430-014-0199-y
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DOI: https://doi.org/10.1007/s40430-014-0199-y