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Singularly Perturbed Vector Field Method (SPVF) Applied to Combustion of Monodisperse Fuel Spray

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Abstract

In this paper we present the concept of singularly perturbed vector field (SPVF) method, and its application to thermal explosion of diesel spray combustion. Given a system of governing equations, which consist of hidden Multi-scale variables, the SPVF method transfer and decompose such system to fast and slow singularly perturbed subsystems. The resulting subsystem enables us to understand better the complex system, and to simplify the calculations. Later powerful analytical, numerical and asymptotic methods [e.g method of integral (invariant) manifold, the homotopy analysis method etc.] can be applied to each subsystem. In this paper, we compare the results obtained by the methods of integral invariant manifold and SPVF as applied to the spray droplets combustion model.

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Abbreviations

A :

Pre-exponential factor (1 / s)

B :

Universal gas constant (\(J k mol^{-1} K^{-1}\))

C :

Molar concentration (\(k mol m^{-3}\))

c :

Specific heat capacity (\(Jkg^{-1}K^{-1}\))

E :

Activation energy (\(J k mol^{-1}\))

L :

Liquid evaporation energy (i.e., latent heat of evaporation, Enthalpy of evaporation) (\(Jkg^{-1}\))

m :

Different size of droplets’ radii

n :

Number of droplets per unit volume (\(m^{-3}\))

Q :

Combustion energy (\(J kg^{-1}\))

R :

Radius of droplet (m)

T :

Temperature (K)

t :

Time (s)

d :

Liquid fuel droplets

f :

Combustible gas component of the mixture

g :

Gas mixture

p :

Under constant pressure

0:

Initial state

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  1. Department of Mathematics, Jerusalem College of Technology, Jerusalem, Israel

    OPhir Nave

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Nave, O. Singularly Perturbed Vector Field Method (SPVF) Applied to Combustion of Monodisperse Fuel Spray. Differ Equ Dyn Syst 27, 57–74 (2019). https://doi.org/10.1007/s12591-017-0373-7

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