Modelling of heating and evaporation of kerosene droplets

L. Poulton, O. Rybdylova, S.S. Sazhin

Advanced Engineering Centre, School of Computing, Engineering and Mathematics, University of Brighton, Brighton, BN2 4GJ, UK

Plan

Background

Kerosene droplets

Surrogate droplets

Final thoughts

Background

Current mathematical models of sprays use spherical approximation for droplets.

Dimensionless numbers

Current mathematical models of sprays use spherical approximation for droplets.

Bi= 2 ℎ𝑅𝑅𝑑𝑑2

𝑘𝑘𝑙𝑙

Biot number

Dimensionless numbers

Current mathematical models of sprays use spherical approximation for droplets.

Bi= 2 ℎ𝑅𝑅𝑑𝑑2

𝑘𝑘𝑙𝑙

Biot number Fourier number

Fo =𝑘𝑘𝑙𝑙 𝑡𝑡

𝑐𝑐𝑙𝑙𝜌𝜌𝑙𝑙𝑅𝑅𝑑𝑑2

Effective thermal conductivity (spherical droplets)

𝑐𝑐𝑙𝑙𝜌𝜌𝑙𝑙𝜕𝜕𝑇𝑇𝜕𝜕𝑡𝑡

= 𝑘𝑘eff𝜕𝜕2𝑇𝑇𝜕𝜕𝑅𝑅2

+ 2𝑅𝑅𝜕𝜕𝑇𝑇𝜕𝜕𝑅𝑅

+ 𝑃𝑃1(R)𝑃𝑃1(R) is the power generated per unit volume inside the droplet due to thermal radiation

Boundary and initial conditions:

ℎ 𝑇𝑇𝑔𝑔∞ − 𝑇𝑇𝑠𝑠 = 𝑘𝑘eff𝜕𝜕𝑇𝑇𝜕𝜕𝑅𝑅

|𝑅𝑅=𝑅𝑅𝑅𝑅𝜕𝜕𝑇𝑇𝜕𝜕𝑅𝑅

|𝑅𝑅=0 = 0; 𝑇𝑇 𝑡𝑡 = 0 = 𝑇𝑇0(R); R ≤ 𝑅𝑅𝑑𝑑

Effective thermal conductivity 𝑘𝑘eff=χ𝑘𝑘𝑙𝑙 where χ=1.86+ 0.86 tanh [2.225 log10 Pe𝑑𝑑/30 ]

χ increases from 1 to 2.72 when Pe𝑑𝑑=Re𝑑𝑑𝑠𝑠P𝑟𝑟𝑑𝑑 increases from <10 to > 500

Discrete components model (spherical droplets)

𝜕𝜕𝑌𝑌𝑙𝑙𝑙𝑙𝜕𝜕𝑡𝑡

= 𝐷𝐷eff𝜕𝜕2𝑌𝑌𝑙𝑙𝑙𝑙𝜕𝜕𝑅𝑅2

+2𝑅𝑅𝜕𝜕𝑌𝑌𝑙𝑙𝑙𝑙𝜕𝜕𝑅𝑅

Boundary and initial conditions:

𝛼𝛼 𝜖𝜖𝑙𝑙 − 𝑌𝑌𝑙𝑙𝑙𝑙𝑠𝑠 = 𝐷𝐷eff𝜕𝜕𝑌𝑌𝑙𝑙𝑙𝑙𝜕𝜕𝑅𝑅

|𝑅𝑅=𝑅𝑅𝑅𝑅−0𝜕𝜕𝑌𝑌𝑙𝑙𝑙𝑙𝜕𝜕𝑅𝑅

|𝑅𝑅=0 = 0; 𝑌𝑌𝑙𝑙𝑙𝑙 𝑡𝑡 = 0 = 𝑌𝑌𝑙𝑙𝑙𝑙0 (R); R ≤ 𝑅𝑅𝑑𝑑Effective diffusivity 𝐷𝐷eff=χ𝑌𝑌𝐷𝐷𝑙𝑙 where χ𝑌𝑌=1.86+ 0.86 tanh [2.225 log10 Pe𝑑𝑑𝑌𝑌/30 ]

χ𝑌𝑌 increases from 1 to 2.72 when Pe𝑑𝑑𝑌𝑌=Re𝑑𝑑Sc increases from <10 to > 500

Sc=ν𝑙𝑙/𝐷𝐷𝑙𝑙 is the liquid Schmidt number; 𝜖𝜖𝑙𝑙 =𝑌𝑌𝑣𝑣𝑙𝑙𝑠𝑠∑𝑙𝑙 𝑌𝑌𝑣𝑣𝑙𝑙𝑠𝑠

𝛼𝛼 =| ̇𝑚𝑚𝑑𝑑|4𝜋𝜋𝜌𝜌𝑙𝑙𝑅𝑅𝑑𝑑2

Realistic Diesel fuel

Multi-dimensional quasi-discrete model

Kerosene droplets

Kerosene composition

Kerosene composition (revised)

Kerosene droplets

Kerosene droplets

The following models considered: Discrete Component Model (DCM) DCM as above and the contribution of supporting fibre (plots DCM1);DCM as above accounting for natural convection (plots DCM2); DCM as above accounting for natural convection and supporting fibre (plots DCM3);5 Quasi components, Multi-Dimensional Quasi-Discrete Model (5QC)

The initial average diameter of a droplet1.0 ± 0.10 mm

The ambient gas temperatureT (gas)= 500 C

Experimental data fromJaved et al (2013) Combustion and flame

Surrogate droplets

Surrogate droplets

Surrogate droplets

Surrogate (n-decane dominated)

Surrogate (n-dodecane dominated)

Surrogate (n-decane dominated)

Surrogate (n-dodecane dominated)

Papers23

Under review in International J Thermal Science

Papers24

In preparation

Final thoughts

Outstanding issues:

1. Sensitivity of the results to the choice of kerosene composition and approximation of the properties of the components.

2. Surrogates heating, evaporation and autoignition

Acknowledgements26

This work was supported by the UK Engineering and Physical Sciences ResearchCouncil [EPSRC Studentship 1792531 and grants EP/M002608/1 and EP/R012024/1].The UK Fluids network is gratefully acknowledged for its support of the SpecialInterest Group ‘Sprays in engineering applications: modelling and experimentalstudies’. This group was a platform for the exchange of ideas between researchersworking on various aspects of spray research. This presentation originated in part asa result of this exchange of ideas.

Thank you for your attention 27

Modelling of heating and evaporation of kerosene droplets

L. Poulton, O. Rybdylova, S.S. Sazhin

Advanced Engineering Centre, School of Computing, Engineering and Mathematics, University of Brighton, Brighton, BN2 4GJ, UK