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# Approximate Analysis of Thermal Radiation Absorption in Fuel Droplets

[+] Author and Article Information
S. S. Sazhin1

School of Engineering, University of Brighton, Cockcroft Building, Brighton BN2 4GJ, U.K.

School of Engineering, University of Brighton, Cockcroft Building, Brighton BN2 4GJ, U.K.

W. A. Abdelghaffar

Mechanical Engineering Department, Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt

S. Begg, M. R. Heikal

School of Engineering, University of Brighton, Cockroft Building, Brighton, BN2 4GJ, U.K.

S. V. Mikhalovsky, S. T. Meikle

School of Pharmacy and Biomolecular Sciences, University of Brighton, Cockcroft Building, Brighton BN2 4GJ, U.K.

O. Al-Hanbali2

School of Pharmacy and Biomolecular Sciences, University of Brighton, Cockcroft Building, Brighton BN2 4GJ, U.K.

1

Corresponding author. e-mail: S.Sazhin@brighton.ac.uk

2

Presently at: Faculty of Pharmacy, An-Najah National University, P. O. Box-7, Jordan, e-mail: othman4791@hotmail.com

J. Heat Transfer 129(9), 1246-1255 (Jan 18, 2007) (10 pages) doi:10.1115/1.2740304 History: Received June 23, 2006; Revised January 18, 2007

## Abstract

The values of absorption coefficients of gasoline fuel (BP Pump Grade 95 RON ULG (research octane number unleaded gasoline)), 2,2,4-trimethylpentane $(CH3)2CHCH2C(CH3)3$ (iso-octane) and 3-pentanone $CH3CH2COCH2CH3$ have been measured experimentally in the range of wavelengths between $0.2μm$ and $4μm$. The values of the indices of absorption, calculated based on these coefficients, have been compared with those previously obtained for low sulphur ESSO AF1313 diesel fuel. These values are generally lower for pure substances (e.g., iso-octane and 3-pentanone) than for diesel and gasoline fuels. The values of the average absorption efficiency factor for all fuels are approximated by a power function $aRdb$, where $Rd$ is the droplet radius. $a$ and $b$ in turn are approximated by piecewise quadratic functions of the radiation temperature, with the coefficients calculated separately in the ranges of droplet radii $2–5μm$, $5–50μm$, $50–100μm$, and $100–200μm$ for all fuels. This new approximation is shown to be more accurate compared with the case when $a$ and $b$ are approximated by quadratic functions or fourth power polynomials of the radiation temperature, with the coefficients calculated in the whole range $2–200μm$. This difference in the approximations of $a$ and $b$, however, is shown to have little effect on modeling of fuel droplet heating and evaporation in conditions typical for internal combustion engines, especially in the case of diesel fuel and 3-pentanone.

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## Figures

Figure 1

Indices of absorption of four types of fuel (low sulphur ESSO AF1313 diesel fuel, gasoline fuel (BP Pump Grade 95 RON ULG), 2,2,4-trimethylpentane (iso-octane), and 3-pentanone) versus wavelength λ. The results for diesel fuel are reproduced from Ref. 10.

Figure 2

Plots Q¯a versus droplet radius for diesel fuel and three radiation temperatures: 1000K, 2000K, and 3000K (indicated near the curves), as calculated from Eq. 2. Thick solid curves are based on the values of κ in the range 0.2–6μm, as reported in Ref. 10. Thin solid curves are based on the values of κ in the range 0.2–4μm, as shown in Fig. 1.

Figure 3

Plots Q¯a and its three approximations Λ versus droplet radius for diesel fuel. Three radiation temperatures: 1000K, 2000K, and 3000K (indicated near the curves) were considered. Thick solid curves refer to the values of Q¯a as calculated from Eq. 2. Thick dots refer to piecewise approximation for Λ, as calculated from Eq. 3. Thin solid curves refer to a single quadratic approximation for Λ. Dashed–dotted curves refer to a singe fourth power approximation for Λ.

Figure 4

The same as Fig. 3 but for gasoline fuel

Figure 5

The same as Figs.  34 but for iso-octane

Figure 6

The same as Figs.  345 but for 3-pentanone.

Figure 7

Plots of Ts and Rd for a diesel fuel droplet versus time for an initial air temperature Tg0=600K, air pressure pg0=3MPa, droplet temperature Td0=300K, radius Rd0=10μm, and velocity vd0=1m∕s. The overall volume of injected liquid fuel was taken equal to 1mm3, and the volume of air was equal to 639mm3. The results were obtained based on the effective thermal conductivity (ETC) model and the analytical solution of the heat conduction equation inside the droplet (22). Dashed curves refer to the case when the effects of thermal radiation are ignored. Thick, intermediate, and thin solid curves refer to the case when the thermal radiation is generated by a source with external temperatures 1000K, 2000K, and 3000K, respectively, and calculated using the model based upon a piecewise approximation of the coefficients a and b in Eq. 3. Dashed-dotted curves refer to the case when the thermal radiation is generated by a source with external temperatures of 3000K and the model based on single quadratic approximations of these coefficients.

Figure 8

The same as Fig. 7 but for gasoline fuel, injected into a gas volume equal to 620mm3

Figure 10

The same as Figs.  789 but for 3-pentanone, injected into a gas volume equal to 712mm3

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