This document presents a study that predicts the thermodynamic properties of rapeseed methyl ester (RME) for droplet evaporation modeling. It outlines methods for predicting RME vapor pressure using the Antoine and Ceriani equations given its variable fatty acid composition. A single droplet evaporation model is implemented in KIVA-3V and validated against other models and experiments. Results show the temporal evolution of normalized RME droplet diameter at different ambient temperatures, demonstrating the effect of vapor pressure uncertainties on evaporation.

1. Predicting the Thermodynamic Properties of
RME for Droplet Evaporation
Guo Li, Cai Shen, and
Chia-fon F. Lee
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2. OUTLINE
 Introduction
 RME Vapor Pressure Prediction and Droplet
Evaporation Model
 Results and Discussions
 Conclusion
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3. Biodiesel and FAMEs
Introduction
- Weight percent of fatty acids in various fat and oils feedstock
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4. FAMEs Compositions
- Typical FAMEs Structure:
 Saturated acid: methyl palmitate, C17:0
 Unsaturated acid: methyl oleate, C19:1
- FAMEs category by Carbon numbers:
 C8:0~C24:0
 C18:1, C18:2, C18:3
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5. Vapor Pressure
- Vapor Pressure
 Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium
with its condensed phases (solid or liquid) at a given temperature. It is an indication
of a liquid's evaporation rate.
- Normal Boiling Point
 The normal boiling point is the temperature at which the vapor pressure equals
the ambient atmospheric pressure.
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6. Motivation
- Vapor pressure and boiling point are basis for the prediction of the critical
properties, and temperature-dependent properties such as density, latent heat
of vaporization and surface tension of biodiesel. These properties are required
for biodiesel evaporation and combustion modeling.
- Since the vapor pressure and normal boiling points of real-world RME is not a
certain value but an expected range due to variance of the fatty acid
composition. Effects of variable vapor pressure on RME droplet vaporization
are investigated in this research.
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7. Research on FAMEs Property
- Experimental Measurements of fatty acid methyl esters (FAMEs)
 Scott
 Rose and Supina
 Goodrum – TGA Method
1952
1961
2009
- Predicting Methods
 Clapeyron equation
 Wagner equation
 Antoine equation
 Ceriani and Meirelles method
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8. Droplet Evaporation Model Overview
- Development of 0-D models
 Infinite diffusion limiting
 Green function expansion
 Fourier’s number concept
 Phenomenological model
(Law, 1976)
(Tong & Sirignano, 1986)
(Renksizbulut, et al., 1992)
(Abraham & Magi, 1998)
- Development of 1-D models
 Diffusion limiting
 Similarity Transformation
 Effective diffusivity concept
(Law, 1978)
(Tong & Sirignano, 1986)
(Jin & Borman, 1985)
(Abramzon & Sirignano, 1989)
(Ayoub & Reitz, 1995)
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9. Antoine equation
-
A simple method for estimating the vapor pressure of methyl esters of fatty
acids is to use the empirical relation developed by Antoine.
𝐵
𝑇+ 𝐶
 Where T (K) is the temperature, Pv (bar) is the vapor pressure and the component
dependent empirical constants A, B and C are reported in Table 1.
log 𝑃𝑣 = 𝐴 −
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10. Ceriani and Meirelles method
-
Ceriani and Meirelles recommended a group contribution method to
predict the vapor pressure of these methyl esters.
ln𝑃𝑖,𝑣𝑝 =
𝑘
𝑁𝑘
𝐴1𝑘 +
𝐵1𝑘
𝑇 1.5
− 𝐶1𝑘 𝑙𝑛𝑇 − 𝐷1𝑘 𝑇
+ 𝑀𝑖
𝑘
𝑁𝑘
𝐴2𝑘 +
𝐵2𝑘
𝑇 1.5
− 𝐶2𝑘 𝑙𝑛𝑇 −
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11. Single Droplet Evaporation Model
- KIVA-3V is a fully three-dimensional fluid dynamics model for chemically
reacting flows .
 We integrate the RME properties to the fuel library.
- Single Droplet Evaporation Model _ Zeng and Lee (2001)
 Governing Equations
𝜕Φ
1 𝜕
= 2
𝜕𝑡
𝑟 𝜕𝑟
𝑒
𝑟 2 𝐷Φ
𝜕Φ
𝜕𝑟
𝜕Φ
𝜕Φ
| = 0,
|
= 𝛽Φ
𝜕𝑟 𝑟=0
𝜕𝑟 𝑟=𝑅
Φ = T or 𝑌𝑖
Φ 𝑑 = Φ𝑠 −Φ
𝑚
𝑒
= 𝑓 Φ 𝑑 , 𝛽Φ , 𝐷Φ , 𝑅
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12. Results and Discussions
- RME Vapor Pressure Prediction:
 Real world RME Compositions
 FAMEs Vapor Pressure Predictions
- RME Droplet Evaporation Simulation & Analysis:
 Model validation
 RME droplet evaporation in different ambient temperatures
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13. RME Compositions
- RME Vapor Pressure Prediction:
 Real world RME Composition
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14. FAMEs Vapor Pressure Predictions
Figure 1. Calculated and measured boiling points of selected FAMEs at various pressures.
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15. Model validation
- Comparison with other models and Experiments:
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16. RME droplet evaporation in different ambient temperatures
Figure 1. Temporal evolution of normalized droplet squared diameter at ambient
temperatures 590 K.
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17. RME droplet evaporation in different ambient temperatures
Figure 1. Temporal evolution of normalized droplet squared diameter at ambient
temperatures 748 & 803 K.
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18. Summary
- The vapor pressure of a rapeseed oil based methyl ester biodiesel was
estimated by two widely used methods.
- A single droplet evaporation model was implemented into KIVA 3V2 to
consider the effect of the vapor pressure uncertainties to droplet evaporation.
- Although this study focuses on rapeseed oil methyl ester biodiesel, it can be
applied to other biofuel with the same methodology.
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19. THANK YOU
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