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Model for transient n-heptane droplet ignition at elevated pressure

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Abstract

The present work deals with transient droplet evaporation and ignition process of an isolated n-heptane droplet at high pressure. The vapor–liquid equilibrium has been described by Peng–Robinson equation of state. In present numerical model, the effects due to elevated pressure, inert species mixing in the liquid phase and thermo-physical properties are considered as variable. The evaporation model has been comprehensively validated with experimental results available in the literature. For the present investigation, the ambient pressure has been varied from \(5\) to \(80\;{\text{bar}}\) and at constant ambient temperature of \(1000\;{\text{K}}\). The range of diameter was varied from \(0.5\) to \(2.0\;{\text{mm}}\). The ignition delay was found to be strong functions of temperature, pressure and diameter. There is monotonic decrease in the ignition time due to increasing ambient temperature and pressure. At each pressure, there existed a minimum diameter below which ignition does not takes place and this minimum diameter decreases with increase in pressure.

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Abbreviations

\(c\) :

Constant pressure specific heat of gas

\(D_{\text{i}}\) :

Diffusion coefficient of species, \(i\)

\(d\) :

Diameter

\(d_{\text{o}}\) :

Initial diameter of droplet

\(d_{\text{i}}\) :

Instantaneous droplet diameter

\(E\) :

Activation energy

\(f\) :

Fugacity

\(h_{\text{f}}^{\text{o}}\) :

Standard heat of formation of species \(i\)

\(k\) :

Coefficient of thermal conductivity

\(k_{\text{ij}}\) :

Coefficient of binary interaction

\(L\) :

Latent heat of vaporization of mixture

\(m\) :

Mass

\(\dot{m}\) :

Mass flow rate

\(\dot{m}^{\prime\prime}\) :

Mass per unit area or heat flux

\(P\) :

Pressure

\(P_{\text{r}}\) :

Reduced pressure, \(\frac{P}{{P_{\text{c}} }}\)

\(r\) :

Radial distance

\(R_{\text{u}}\) :

Universal gas constant

\(R_{\text{o}}\) :

Initial droplet radius

\(R(t)\) :

Instantaneous droplet radius

\(t\) :

Time

\(T\) :

Temperature in gas phase

\(T_{\text{ad}}\) :

Adiabatic flame temperature

\(T_{\text{b}}\) :

Boiling temperature of liquid fuel

\(T_{\text{r}}\) :

Reduced temperature, \(\frac{T}{{T_{\text{c}} }}\)

\({\text{c}}\) :

At critical conditions

\({\text{s}}\) :

At drop surface

\(\infty\) :

At infinity

\({\text{F}}\) :

Flame

\({\text{f}}\) :

Fuel

\({\text{g}}\) :

Gaseous phase

\(i, j\) :

Species

\({\text{in}}\) :

Initial

\({\text{l}}\) :

Liq. phase

\({\text{O}}\) :

Oxidizer

\({\text{o}}\) :

At standard ambient conditions

\({\text{v}}\) :

Fuel vapor

\(+\) :

A non-dimensional quantity

\({\text{m}}\) :

A parameter in finite reaction equation with fuel

\({\text{n}}\) :

A parameter in finite reaction equation with oxidizer

\({\text{o}}\) :

At atmospheric pressure

\(\Delta \eta\) :

Non-dimensional grid size in gas phase

\(\phi\) :

Fugacity coefficient

\(\eta\) :

Transformed coordinate in gas phase

\(\kappa\) :

Frequency factor

\(\nu_{1}^{i}\) :

Stoichiometric coefficients of reactants

\(\nu_{2}^{i}\) :

Stoichiometric coefficients of products

\(\theta\) :

Temperature in liquid phase

\(\rho\) :

Density

\(\varTheta\) :

A non-dimensional number in reaction term

\(\dot{\omega }\) :

Reaction rate

\(\omega\) :

Acentric factor

\(\omega_{\text{m}}\) :

Acentric factor of mixture

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  1. Department of Mechanical Engineering, IKGPTU, Kapurthala, India

    Neel Kanth Grover

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Grover, N.K. Model for transient n-heptane droplet ignition at elevated pressure. J Therm Anal Calorim 141, 2453–2461 (2020). https://doi.org/10.1007/s10973-020-10067-5

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