Modelling of heating and evaporation of kerosene droplets · composition and approximation of the...
Transcript of Modelling of heating and evaporation of kerosene droplets · composition and approximation of the...
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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
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Plan
Background
Kerosene droplets
Surrogate droplets
Final thoughts
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Background
Current mathematical models of sprays use spherical approximation for droplets.
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Dimensionless numbers
Current mathematical models of sprays use spherical approximation for droplets.
Bi= 2 ℎ𝑅𝑅𝑑𝑑2
𝑘𝑘𝑙𝑙
Biot number
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Dimensionless numbers
Current mathematical models of sprays use spherical approximation for droplets.
Bi= 2 ℎ𝑅𝑅𝑑𝑑2
𝑘𝑘𝑙𝑙
Biot number Fourier number
Fo =𝑘𝑘𝑙𝑙 𝑡𝑡
𝑐𝑐𝑙𝑙𝜌𝜌𝑙𝑙𝑅𝑅𝑑𝑑2
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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
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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
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Realistic Diesel fuel
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Multi-dimensional quasi-discrete model
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Kerosene droplets
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Kerosene composition
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Kerosene composition (revised)
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Kerosene droplets
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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
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Surrogate droplets
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Surrogate droplets
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Surrogate droplets
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Surrogate (n-decane dominated)
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Surrogate (n-dodecane dominated)
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Surrogate (n-decane dominated)
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Surrogate (n-dodecane dominated)
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Papers23
Under review in International J Thermal Science
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Papers24
In preparation
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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
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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.
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Thank you for your attention 27
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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