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Modeling of Cavitation in Fuel Injectors with Single- and Two-Fluid Approaches

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Two-Phase Flow for Automotive and Power Generation Sectors

Part of the book series: Energy, Environment, and Sustainability ((ENENSU))

Abstract

In high-pressure fuel injection systems, cavitation is known to affect spray atomization processes. Modeling the cavitation phenomenon has become a necessity to ensure predictive quality and higher fidelity of the fuel spray simulations. Inside the fuel injectors, local pressures drop below the saturation pressure of fuels in regions of flow separations, such as inlet of holes and periphery of needles at low-lift conditions. Several cavitation models and multiphase modeling approaches have been employed in the literature to predict the extent of cavitation in the fuel injection systems. A review of these modeling approaches will be presented. Amongst the cavitation models, bubble-based and semi-empirical timescale-based ones are widely used. Mixture/single-fluid and Eulerian–Eulerian/two-fluid approaches have been adopted for fuel injection cavitation modeling. Two-fluid approach captures the interaction between the two phases, which is usually ignored in single-fluid approach. Comparative studies in the literature will be reviewed here to provide a comprehensive idea of the cavitation modeling approaches to the readers. The advantages and disadvantages of these models will be discussed in depth. Keeping in mind the conflicting requirements of accuracy and constraints of computational cost, recommendations will be provided for suitable cavitation modeling approaches.

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Abbreviations

CFL:

Courant Friedrichs Lewy number

D :

Mass diffusivity (m\(^2\)/s)

\(f_v,~f_l,~f_g\) :

Mass fraction of vapour, liquid and gas, respectively

k :

Turbulent kinetic energy (m\(^2\)/s\(^2\))

\(m_\mathrm{vap}, m_\mathrm{liq}\) :

Mass of vapour and liquid phases in a cell (kg)

\(N^{\prime \prime \prime }\) :

Bubble number density (1/m\(^3\))

p :

Local pressure (Pa)

\(p_\mathrm{crit}\) :

Critical pressure (Pa)

\(P_\mathrm{inj}\) :

Injection pressure (MPa)

\(P_\mathrm{sat}, p_\mathrm{sat}\) :

Saturation pressure (Pa)

\(\varDelta P\) :

Pressure differential, MPa

R :

Bubble radius, m

\(R_P\) :

Source term for cavitation modeling, kg/(m\(^3\) s)

\(S_{11}\) :

Strain rate (1/s)

t :

Time (s)

\(T_\mathrm{fuel}\) :

Fuel temperature (K)

\(T_\mathrm{sat}\) :

Saturation temperature (K)

u :

Local cell velocity (m/s)

\(u_i\) :

Advected mean velocity (m/s)

\(u_j\) :

Advecting mean velocity (m/s)

V :

Volume of a cell (m\(^3\))

x :

Local cell vapour quality

\(\bar{x}\) :

Local cell equilibrium quality

\(Y_m\) :

Mass fraction of mth species

\(\alpha \) :

Void fraction (vapour + non-condensable gases)

\(\alpha _q\) :

Volume fraction of the qth phase

\(\epsilon \) :

Turbulence dissipation rate (m\(^2\)/s\(^3\))

\(\theta \),\(\theta _0\):

Equilibrium timescale and empirical time constant(s)

\(\mu \),\(\mu _t\):

Dynamic and turbulent viscosity coefficient (kg/m s)

\(\rho , \rho _v, \rho _l, \rho _g\) :

Density of mixture, vapour, liquid and gas (kg/m\(^3\))

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Acknowledgements

UChicago Argonne, LLC, Operator of Argonne National Laboratory (Argonne), a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357. The US Government retains for itself, and others acting on its behalf, a paid-up nonexclusive, irrevocable worldwide licence in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government. This research was partially funded by the U.S. Department of Energy (DOE) Office of Vehicle Technologies, Office of Energy Efficiency and Renewable Energy under Contract No. DE-AC02-06CH11357. The authors wish to thank Gurpreet Singh and Leo Breton at DOE, for their support. The authors are grateful to ASME Publishing section for granting the permission for using published materials in this chapter.

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Authors and Affiliations

  1. Centre for Energy Studies, IIT Delhi, New Delhi, India

    Kaushik Saha

  2. Mechanical Engineering, University of Perugia, Perugia, Italy

    Michele Battistoni

  3. Energy Systems Division, Argonne National Laboratory, Lemont, IL, USA

    Sibendu Som

  4. Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, Canada

    Xianguo Li

Authors
  1. Kaushik Saha
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  2. Michele Battistoni
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  3. Sibendu Som
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  4. Xianguo Li
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Corresponding author

Correspondence to Kaushik Saha .

Editor information

Editors and Affiliations

  1. Centre for Energy Studies, Indian Institute of Technology Delhi, New Delhi, India

    Kaushik Saha

  2. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Avinash Kumar Agarwal

  3. Department of Mechanical Engineering, Jadavpur University, Kolkata, India

    Koushik Ghosh

  4. Argonne National Laboratory, Lemont, IL, USA

    Sibendu Som

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Saha, K., Battistoni, M., Som, S., Li, X. (2019). Modeling of Cavitation in Fuel Injectors with Single- and Two-Fluid Approaches. In: Saha, K., Kumar Agarwal, A., Ghosh, K., Som, S. (eds) Two-Phase Flow for Automotive and Power Generation Sectors. Energy, Environment, and Sustainability. Springer, Singapore. https://doi.org/10.1007/978-981-13-3256-2_7

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  • DOI: https://doi.org/10.1007/978-981-13-3256-2_7

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