Model for transient n -heptane droplet ignition at elevated pressure
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Model for transient n‑heptane droplet ignition at elevated pressure Neel Kanth Grover1 Received: 25 October 2019 / Accepted: 13 July 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
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 bar and at constant ambient temperature of 1000 K . The range of diameter was varied from 0.5 to 2.0 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. Keywords Combustion · Ignition · Droplet · n-Heptane · Microgravity List of symbols c Constant pressure specific heat of gas Di Diffusion coefficient of species, i d Diameter do Initial diameter of droplet di Instantaneous droplet diameter E Activation energy f Fugacity hof Standard heat of formation of species i k Coefficient of thermal conductivity kij Coefficient of binary interaction L Latent heat of vaporization of mixture m Mass ṁ Mass flow rate ṁ ′′ Mass per unit area or heat flux P Pressure Pr Reduced pressure, PP c
r Radial distance Ru Universal gas constant Ro Initial droplet radius R(t) Instantaneous droplet radius t Time * Neel Kanth Grover [email protected] 1
Department of Mechanical Engineering, IKGPTU, Kapurthala, India
T Temperature in gas phase Tad Adiabatic flame temperature Tb Boiling temperature of liquid fuel Tr Reduced temperature, TT c
Subscripts c At critical conditions s At drop surface ∞ At infinity F Flame f Fuel g Gaseous phase i, j Species in Initial l Liq. phase O Oxidizer o At standard ambient conditions v Fuel vapor Superscripts + A non-dimensional quantity m A parameter in finite reaction equation with fuel n A parameter in finite reaction equation with oxidizer o At atmospheric pressure Greek symbols Δ𝜂 Non-dimensional grid size in gas phase 𝜙 Fugacity coefficient 𝜂 Transformed coordinate in gas phase
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𝜅 Frequency factor 𝜈1i Stoichiometric coefficients of reactants 𝜈2i Stoichiometric coefficients of products 𝜃 Temperature in liquid phase 𝜌 Density 𝛩 A non-dimensional number in reaction term 𝜔̇ Reaction rate 𝜔 Acentric factor 𝜔m Acentric factor of mixture
Introduction Vaporization and ignition of fuel droplet at high pressure are of great importance in the development of high pres
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