This paper has developed an axisymmetric laminar and turbulent two-phase flow solver to simulate pressure-swirl atomizers. Equations include the explicit algebraic Reynolds stress model, the Reynolds-averaged Navier-Stokes, and the level set equation. Applying a high-order compact upwind finite difference scheme with the level set equation being culminated to capture the interface between air-liquid two-phase flow and decreasing the mass conservation error in the level set equation. The results show that some recirculation zones are observed close to the wall in the swirl chamber and to the axis. This model can predict converting the Rankin vortex in the swirl chamber to the forced vortex in the orifice section. The proposal model shows that some improvements are obtained compared with the previous numerical solutions, especially in the laminar flow, so that the discharge coefficient, film thickness, and spray cone angle are satisfactory with the previous experimental data.

In this paper, we model unmarried teenagers' decisions about their pregnancy outcome by considering that the teenager contrasts her expected utility (1) as a married mother, (2) as an unmarried mother, or (3) after abortion. We use cross-sectional data on 297 California teenagers aged 13-19 who were pregnant for the first time between 1972 and 1974. Both Anglo and Mexican-American girls are included. We find that pregnant girls who are eligible for or are receiving public assistance are more likely to give birth and remain unmarried. Teenagers with greater time values are more likely to choose abortion, and Mexican-American girls are more likely to carry their pregnancies to term.

The algebraic stress model developed by Launder & Ying for the secondary flow of the second kind was employed with the κ and ε model for the prediction of fully developed turbulent flows in square, rectangular and trapezoidal ducts using the numerical procedure designed for ducts of arbitrary cross-sectional shape. Results of the calculation are compared extensively with available experimental data, with strong emphasis on the local structures of turbulence to reveal full features of this particular stress model.

No abstract