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Numerical simulation of biodiesel spray under ultra-high injection pressure using OpenFOAM

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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]

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Authors and Affiliations

  1. Department of Marine Technology, Amirkabir University of Technology, Hafez Ave., No 424, P.O. Box 15875-4413, Tehran, Iran

    Mahdi Yousefifard & Parviz Ghadimi

  2. Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran

    Mostafa Mirsalim

Authors
  1. Mahdi Yousefifard
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  2. Parviz Ghadimi
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  3. Mostafa Mirsalim
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Correspondence to Parviz Ghadimi.

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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

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