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Experiments in Fluids

, 56:1871 | Cite as

Experimental analysis and semicontinuous simulation of low-temperature droplet evaporation of multicomponent fuels

  • S. LehmannEmail author
  • S. Lorenz
  • E. Rivard
  • D. Brüggemann
Research Article

Abstract

Low-pollutant and efficient combustion not only in internal combustion engines requires a balanced gaseous mixture of fuel and oxidizer. As fuels may contain several hundred different chemical species with different physicochemical properties as well as defined amounts of biogenic additives, e.g., ethanol, a thorough understanding of liquid fuel droplet evaporation processes is necessary to allow further engine optimization. We have studied the evaporation of fuel droplets at low ambient temperature. A non-uniform temperature distribution inside the droplet was already considered by including a finite thermal conductivity in a one-dimensional radial evaporation model (Rivard and Brüggemann in Chem Eng Sci 65(18):5137–5145, 2010). For a detailed analysis of droplet evaporation, two non-laser-based experimental setups have been developed. They allow a fast and relatively simple but yet precise measurement of diameter decrease and composition change. The first method is based on collecting droplets in a diameter range from 70 to 150 µm by a high-precision scale. A simultaneous evaluation of mass increase is employed for an accurate average diameter value determination. Subsequently, a gas chromatographic analysis of the collected droplets was conducted. In the second experiment, evaporation of even smaller droplets was optically analyzed by a high-speed shadowgraphy/schlieren microscope setup. A detailed analysis of evaporating E85 (ethanol/gasoline in a mass ratio of 85 %/15 %) and surrogate fuel droplets over a wide range of initial droplet diameters and ambient temperatures was conducted. The comparison of experimental and numerical results shows the applicability of the developed model over a large range of diameters and temperatures.

Keywords

Droplet Diameter Droplet Generator Droplet Velocity Droplet Evaporation Initial Droplet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

A

Orthographic projection of the droplet on a plane perpendicular to the direction of motion (m2)

Bn

Spalding molar transfer number (−)

Bh

Spalding heat transfer number (−)

cd

Drag coefficient (−)

\(\overline{c}_{g}\)

Average molar density of gas phase (mol m−3)

cl

Molar density of the liquid phase (mol m−3)

Cp,l

Molar-specific heat capacity of the liquid phase (J mol−1 K−1)

\(\overline{C}_{p,g,s}\)

Average molar-specific heat capacity of gas phase at surface (J mol−1 K−1)

\(\overline{C}_{p,v}\)

Average molar-specific heat capacity of the vapor phase (J mol−1 K−1)

d0

Initial droplet diameter (m)

Dl,I,m

Diffusivity of a species (m2 s−1)

\(\overline{D}_{v,g}\)

Average vapor diffusivity in the surrounding gas phase (m2 s−1)

f

Distribution function (−)

F(d)

(Drag) force (N)

ΔHv,l,s

Enthalpy of vaporization of the liquid phase at droplet surface (J mol−1)

I

Molar mass of a species (kg mol−1)

kl

Liquid thermal conductivity (W m−1 K−1)

md

Droplet mass (kg)

nd

Fraction of substance in the droplet (mol)

\(\dot{n}\)

Molar flow rate (mol s−1)

Nu

Nusselt number (−)

\(\dot{Q},\dot{Q}_{i} , \dot{Q}_{o}\)

Heat flow, heat flow from the inside/outside of the droplet (J s−1)

rs

Droplet radius (m)

Sh(*)

(Modified) Sherwood number (−)

t

Time (s)

\(T_{a}, T_{l} , T_{s} , T_{\infty }\)

Ambient temperature, liquid temperature, droplet surface temperature, gas-phase temperature in infinite distance (K)

vrel

Relative velocity of the droplet (m s−1)

x(l,)i

(Liquid) molar fraction of species i (−)

\(x_{g,v,s},\,x_{g,v,\infty }\)

Molar fraction of vapor in gas phase at the droplet surface and in infinite distance (−)

κ

Correlation factor (−)

ρf

Mass density of the flow (kg m−3)

χ

Internal recirculation factor (−)

DL

Diffusion-limited model

HY

Hybrid model

WM

Well-mixed model

Notes

Acknowledgments

The authors are grateful for the financial support of the German Research Foundation (DFG) under Grant No. BR 1713/10 and the reviewers’ supportive remarks.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • S. Lehmann
    • 1
    Email author
  • S. Lorenz
    • 1
  • E. Rivard
    • 1
  • D. Brüggemann
    • 1
  1. 1.Chair of Engineering Thermodynamics and Transport Processes (LTTT), Bayreuth Engine Research Center (BERC)University of BayreuthBayreuthGermany

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