The flow hydrodynamic effects and film cooling effectiveness placing two small coolant ports just upstream the main jet (combined triple jets) were numerically investigated. Cross sections of all jets are rectangular and they are inclined normally into the hot cross-flow. The finite volume method and the SIMPLE algorithm on a multiblock nonuniform staggered grid were applied. The large-eddy simulation approach with three different subgrid scale models was used. The obtained results showed that this flow configuration reduces the mixing between the freestream and the coolant jets and hence provides considerable improvements in film cooling effectiveness (both centerline and spanwise averaged effectiveness). Moreover, the effects of density and velocity differences between the jets and cross-flow and between each of the jets were investigated. The related results showed that any increase in density ratio will increase the penetration of the jet into the cross-flow, but increasing the density ratio also increases the centerline and spanwise average film cooling effectiveness. Increasing the smaller jet velocity ratios, compared with the main jet, significantly improve the cooling effectiveness and uniform coolant distribution over the surface by keeping the main jet coolant fluid very close to the wall.
Nonlinear phenomena widely occur in practical engineering applications. A typical example in aerospace structures is the creation of a breathing crack that opens and closes under cyclic loads, which causes bilinear behavior in the structural response. Late detection of such cracks can lead to a catastrophic failure that results in extensive structural damage. Therefore, analyzing the behavior of the structure because of the presence of a breathing crack is very important and needs to be investigated in detail. In this article, the nonlinear response of a single-degree-of-freedom nonlinear cantilever beam with a transverse breathing crack and bilinear behavior was studied. To investigate the nonlinear behavior, bilinear functions of the beam stiffness and nonlinear geometric stiffness were converted to polynomial functions. The proposed model is validated by comparing the time history responses of the approximated polynomials with the bilinear model of the cracked beam. Moreover, by considering damping changes because of the presence of the breathing crack, the nonlinear behavior was investigated. The results indicated that the proposed method is sensitive to the presence of a breathing crack. Also, the nonlinearity increases with an increase in the crack depth and location ratios associated with the jump phenomenon in the vibration response of the cracked beam.
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