Predicting the Thermodynamic Properties of RME for Droplet Evaporation

Guo Li, Cai Shen, and

Chia-fon F. Lee

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OUTLINE

Introduction

RME Vapor Pressure Prediction and Droplet Evaporation Model

Results and Discussions

Conclusion

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Biodiesel and FAMEs

- Weight percent of fatty acids in various fat and oils feedstock

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Introduction

FAMEs Compositions

- Typical FAMEs Structure:

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- FAMEs category by Carbon numbers:

C8:0~C24:0 C18:1, C18:2, C18:3

Saturated acid: methyl palmitate, C17:0

Unsaturated acid: methyl oleate, C19:1

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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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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Research on FAMEs Property

- Experimental Measurements of fatty acid methyl esters (FAMEs)

Scott 1952 Rose and Supina 1961 Goodrum – TGA Method 2009

- Predicting Methods

Clapeyron equation Wagner equation Antoine equation Ceriani and Meirelles method

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Droplet Evaporation Model Overview

- Development of 0-D models

Infinite diffusion limiting (Law, 1976) Green function expansion (Tong & Sirignano, 1986) Fourier’s number concept (Renksizbulut, et al., 1992) Phenomenological model (Abraham & Magi, 1998)

- Development of 1-D models

Diffusion limiting (Law, 1978) Similarity Transformation (Tong & Sirignano, 1986) Effective diffusivity concept (Jin & Borman, 1985)

(Abramzon & Sirignano, 1989)(Ayoub & Reitz, 1995)

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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.

log 𝑃𝑣 = 𝐴 −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.

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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

𝑇1.5 − 𝐶1𝑘𝑙𝑛𝑇 − 𝐷1𝑘𝑇 + 𝑀𝑖 𝑘 𝑁𝑘 𝐴2𝑘 +𝐵2𝑘

𝑇1.5 − 𝐶2𝑘𝑙𝑛𝑇 −

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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

𝜕𝑡=

1

𝑟2

𝜕

𝜕𝑟𝑟2𝐷Φ

𝑒 𝜕Φ

𝜕𝑟

𝜕Φ

𝜕𝑟|𝑟=0= 0,

𝜕Φ

𝜕𝑟|𝑟=𝑅 = 𝛽Φ

Φ = T or 𝑌𝑖

Φ𝑑 = Φ𝑠 − Φ𝑚 = 𝑓 Φ𝑑, 𝛽Φ, 𝐷Φ𝑒 , 𝑅

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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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RME Compositions

- RME Vapor Pressure Prediction:

Real world RME Composition

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FAMEs Vapor Pressure Predictions

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Figure 1. Calculated and measured boiling points of selected FAMEs at various pressures.

Model validation

- Comparison with other models and Experiments:

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RME droplet evaporation in different ambient temperatures

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Figure 1. Temporal evolution of normalized droplet squared diameter at ambient temperatures 590 K.

RME droplet evaporation in different ambient temperatures

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Figure 1. Temporal evolution of normalized droplet squared diameter at ambient temperatures 748 & 803 K.

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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