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Polydisperse Spray Modeling Using Eulerian Method

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Sustainable Development for Energy, Power, and Propulsion

Part of the book series: Green Energy and Technology ((GREEN))

Abstract

Sprays play a significant role in many engineering applications such as liquid fuel injectors, industrial spray coaters, water sprinklers and agricultural sprayers. In most of the numerical study, Eulerian and Lagrangian formulations have been used for the gas and liquid phases, respectively. However, modeling of droplets using Lagrangian approach is computationally expensive for complex configuration. An Eulerian–Eulerian approach, also referred to as multi-fluid method in the literature, is developed in recent time to reduce the computation cost. This chapter presents a brief review of the recent studies on spray modeling using Eulerian multi-fluid method. Initially, one-dimensional transport of polydisperse evaporating water spray in a spatially varying velocity and temperature field is reported. A comprehensive analysis on droplet clustering pattern in an oscillating flow field is presented. Then, transport of polydisperse evaporating liquid spray in crossflow configuration using multi-fluid method is reported.

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Abbreviations

\(B_{M}\) :

Splading mass transfer number

\(C_{D}\) :

Coefficient of drag

\(c_{pg}\) :

Specific heat of gas

D :

Diameter of droplet

\(D_{i,m}\) :

Mass diffusivity of the ith species in gas phase

\(D_{P}\) :

Diameter of the pth size class

\(h_{d}^{p}\) :

Enthalpy of the pth size class

K :

Wave number

\(K_{e}\) :

Evaporation constant

\(k_{g}\) :

Thermal conductivity of gas phase

L :

Axial length of channel

\(L_{v}\) :

Latent heat of vaporization

\(m^{(p)}\) :

Concentration of the pth size class

\(\left[ {\dot{m}_{p} } \right]\) :

Mass transfer rate of a droplet

n :

Number density of droplets

\(S^{m}\) :

Mass source to continuous phase

\(S^{\text{mom}}\) :

Momentum source to continuous phase

\(S^{\text{enth}}\) :

Enthalpy source to continuous phase

\({\text{Sc}}\) :

Schmidt number

\({\text{Sh}}_{C}\) :

Corrected Sherwood number

\(T_{g}\) :

Gas temperature

\(T_{l}\) :

Liquid phase temperature

t :

Time

\(u_{d}^{p}\) :

Velocity of the pth size class

\(u_{g}\) :

Gas phase velocity

x :

Axial distance along channel

\(Y_{i}\) :

Mass fraction of the ith species

\(\rho_{l}\) :

Density of liquid phase

\(\rho_{g}\) :

Density of gas phase

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Authors and Affiliations

  1. Department of Mechanical Engineering, Jadavpur University, Kolkata, 700032, India

    Sourav Sarkar, Achintya Mukhopadhyay & Swarnendu Sen

  2. Department of Mechanical Engineering and Mechanics, Lehigh University, 19 Memorial Drive, West Bethlehem, USA

    Joydeep Munshi

Authors
  1. Sourav Sarkar
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  2. Joydeep Munshi
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  3. Achintya Mukhopadhyay
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  4. Swarnendu Sen
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Corresponding author

Correspondence to Swarnendu Sen .

Editor information

Editors and Affiliations

  1. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Ashoke De

  2. Department of Mechanical Engineering, University of Maryland, College Park, MD, USA

    Ashwani K. Gupta

  3. Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL, USA

    Suresh K. Aggarwal

  4. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Abhijit Kushari

  5. Analytic and Computational Research Inc. (ACRi), Los Angeles, CA, USA

    Akshai K. Runchal

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Sarkar, S., Munshi, J., Mukhopadhyay, A., Sen, S. (2021). Polydisperse Spray Modeling Using Eulerian Method. In: De, A., Gupta, A., Aggarwal, S., Kushari, A., Runchal, A. (eds) Sustainable Development for Energy, Power, and Propulsion. Green Energy and Technology. Springer, Singapore. https://doi.org/10.1007/978-981-15-5667-8_19

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  • DOI: https://doi.org/10.1007/978-981-15-5667-8_19

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