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Research Papers: Internal Combustion Engines

# Modified Single-Fluid Cavitation Model for Pure Diesel and Biodiesel Fuels in Direct Injection Fuel Injectors

[+] Author and Article Information
Kaushik Saha

e-mail: kaushik.sahaju@gmail.com

e-mail: ehabar@gmail.com

Xianguo Li

e-mail: xianguo.li@uwaterloo.ca
Department of Mechanical and Mechatronics Engineering,
University of Waterloo,
Waterloo, ON, N2L 3G1, Canada

1Corresponding author.

Contributed by the IC Engine Division of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received November 27, 2012; final manuscript received January 15, 2013; published online May 22, 2013. Editor: David Wisler.

J. Eng. Gas Turbines Power 135(6), 062801 (May 22, 2013) (8 pages) Paper No: GTP-12-1455; doi: 10.1115/1.4023464 History: Received November 27, 2012; Revised January 15, 2013

## Abstract

A cavitation model has been developed for the internal two-phase flow of diesel and biodiesel fuels in fuel injectors under high injection pressure conditions. The model is based on the single-fluid mixture approach with newly derived expressions for the phase change rate and local mean effective pressure—the two key components of the model. The effects of the turbulence, compressibility, and wall roughness are accounted for in the present model and model validation is carried out by comparing the model predictions of probable cavitation regions, velocity distribution, and fuel mass flow rate with the experimental measurement available in literature. It is found that cavitation inception for biodiesel occurs at a higher injection pressure, compared to diesel, due to its higher viscosity. However, supercavitation occurs for both diesel and biodiesel at high injection pressures. The renormalization group (RNG) $k-ɛ$ model for turbulence modeling is reasonable by comparing its performance with the realizable $k-ɛ$ and the shear stress transport (SST) $k-ω$ models. The effect of liquid phase compressibility becomes considerable for high injection pressures. Wall roughness is not an important factor for cavitation in fuel injectors.

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## Figures

Fig. 1

Computational domain consisting of a section before the nozzle, the nozzle itself, and a section after the nozzle. For the rectangular cross section, d is the width of the nozzle and for the circular cross section d is the diameter of the nozzle.

Fig. 2

Qualitative comparison of the present model predictions with the experimental images from the work of Winklhofer et al. [9]

Fig. 3

Comparison of the mass flow rate predictions from the present study and Som et al. [15] with the experimental data [9] as a function of the injection pressure differential (Δp)

Fig. 4

Comparison of the velocity profiles between the present model prediction and the experimental results by Winklhofer et al. [9] at a location 53 μm from the nozzle inlet

Fig. 6

Comparison of the discharge coefficient (CD) and Reynolds number (Re) for diesel and biodiesel for different cavitating conditions at different injection pressure differentials (between the inlet and outlet, Δp) with the outlet pressure being 5 MPa

Fig. 7

Comparison of the vapor volume fraction contours for diesel obtained from different turbulence models: (a) RNG k-ɛ, (b) realizable k-ɛ, and (c) SST k-ω model, with the inlet pressure of 50 MPa and outlet pressure of 5 MPa

Fig. 8

Comparison of the velocity and liquid volume fraction profiles at the exit of the nozzle section for the inlet pressure of 150 MPa and outlet pressure of 5 MPa

Fig. 9

Vapor volume fraction contours for (a) a smooth wall, and (b) a wall roughness height of 5 μm for diesel at the inlet pressure of 15 MPa and outlet pressure of 5 MPa

Fig. 5

Comparison of vapor contours of diesel and biodiesel for the inlet pressure of 25 MPa and outlet pressure of 5 MPa: (a) diesel, (b) diesel with biodiesel saturation pressure, (c) diesel with biodiesel viscosity, and (d) biodiesel

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