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In the present study two-phase flow within the effervescent atomizer has been simulated by the volume of fluid interface tracing model using 0.08%, 0.32%, 1.24%, and 4.9% gas-to-liquid mass ratios and 0.38 L/min liquid flow rate. The purpose of this simulation is to study two-phase flow regimes within the effervescent atomizer and their effect on the atomization quality. This study also considers the gas-liquid interface instabilities in different two-phase flow regimes inside the atomizer. The compressibility of gas phase which is rear in literature survey included in gas-to-liquid mass ratios of 1.24% and 4.9%, due to the high gas phase velocity in constant liquid flow rate and high gas-to-liquid mass ratios. The effect of gravitational force is considered in all simulations. The results of the simulation indicate that by increasing the gas-to-liquid mass ratio, the two-phase flow regime inside the discharge passage transfers from bubbly flow regime with long bubbles to annular flow regime. In addition to decreasing the liquid film thickness coming out from discharge orifice (during transform of the flow regime from bubbly flow to annular flow), the liquid interface instabilities increase in the annular flow regime and besides, where segregated ligaments from the liquid interface become shorter, thinner and more unstable. This type of regime is the most efficient flow behavior for the effervescent atomizer.

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The Griffith crack, a central crack in an infinite plane under uniform loading, is converted to a subsurface one by moving close to a loaded edge of the plane. Subsurface cracks initiate under rolling contact fatigue conditions. In this paper, first, finite element model of the Griffith crack has been developed and validated by calculating stress intensity factors (SIFs) under uniform tension and shear loadings. Then, by moving the crack close to a parallel edge of the plane, mixed mode SIFs of the subsurface crack have been determined for a wide range of the cracks depths. Non-symmetrical geometry with respect to the crack edge causes coupling between fracture modes and so, considerable shear and tension fracture modes under tension and shear loadings, respectively. The ratio of SIF for the coupling mode to the direct mode is creased up to 69% for the length to depth ratio of 20. Also, by fitting third-degree polynomials to the mixed mode SIFs, four geometry correction factors have been obtained for SIFs of subsurface cracks under uniform loadings. These approximate equations can be used easily and efficiently by engineers. Also, the relations can be utilized as a primary estimation for non-uniform loadings, especially when the crack length as well as the load variation along it is small.