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Analysis of polydisperse fuel spray flame

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Abstract

In this paper we analyzed the model of polydisperse fuel spray flame by using the sectional approach to describe the droplet-droplet interaction within the spray. The radii of the droplets are described by a probability density function. Our numerical simulations include a comparative analysis between three empirical droplet size distributions: the Rosin–Rammler distribution, the log-normal distribution and the Nakiyama–Tanasawa distribution. The log-normal distribution was found to produce a reasonable approximation to both the number and volume size distribution function. In addition our comparative analysis includes the application of the homotopy analysis method which yields convergent solutions for all values of the relevant parameters. We compared the above results to experimental fuel spray data such as \({\textit{Tetralin}}\), \(n-{\textit{Decane}}\), and \(n-{\textit{Heptane}}\).

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Abbreviations

A :

Pre-exponential rate factor

B :

Universal gas constant

C :

Vaporization coefficient

E :

Activation energy

\(c_{p}\) :

Specific heat of capacity

D :

Diffusion

L :

Liquid evaporation energy (i.e., latent heat of evaporation, enthalpy of evaporation)

Le :

Lewis number

m :

Mass

N :

Number of collisions

P :

Probability

p :

Pressure

Q :

Heat of reaction

\(Q_{i}\) :

\(i=0, 1, 2, 3\) the distribution function of the ith moment

R :

Radius of droplet

T :

Temperature

u :

Velocity

V :

Volume

v :

Average relative velocity

\(^{*}\) :

Denotes the non dimensional parameter

\(\rho\) :

Density

\(\eta\) :

Dimensionless parameter defined in Eq. (2.11)

\(\mu\) :

Dimensionless parameter defined in Eq. (2.11)

\(\alpha\) :

Dimensionless parameter defined in Eq. (2.11) and refer to volumetric droplet content

\(\lambda\) :

Thermal conductivity

coll :

Collision

cell :

Cell of parcel

F :

Fuel

f :

Flame

rel :

Relative

0:

Refers to condition at \(x=0\)

O :

Oxygen

g :

Gas

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Authors and Affiliations

  1. Department of Mathematics, Ben-Gurion University of the Negev (BGU), Beersheba, Israel

    Ophir Nave & Vladimir Gol’dshtein

  2. Jerusalem College of Technology (JCT), Jerusalem, Israel

    Ophir Nave

  3. Department of Physics, The David Yellin Academic College, Jerusalem, Israel

    Yaron Lehavi

  4. Department of Mathematics, Faculty of Science, O.A.U, Ife, Nigeria

    Suraju Ajadi

Authors
  1. Ophir Nave
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  2. Yaron Lehavi
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  3. Suraju Ajadi
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  4. Vladimir Gol’dshtein
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Correspondence to Ophir Nave.

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Nave, O., Lehavi, Y., Ajadi, S. et al. Analysis of polydisperse fuel spray flame. Heat Mass Transfer 53, 649–660 (2017). https://doi.org/10.1007/s00231-016-1844-z

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  • DOI: https://doi.org/10.1007/s00231-016-1844-z

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