科创中国

Supercavitation in the diesel nozzle increases the instability of droplets in part due to the two-phase mixture,while the effect of cavitation bubbles on the instability of drops is still unclear.In order to investigate the breakup of cavitation bubbles within the diesel droplet,a new mathematical model describing the disturbance growth rate of the diesel bubble instability is developed.The new mathematical model is applied to predict the effects of fluids viscosity on the stability of cavitation bubbles.The predicted values reveal that the comprehensive effect of fluids viscosity makes cavitation bubbles more stable.Compared with the viscosities of air and cavitation bubble,the diesel droplet's viscosity plays a dominant role on the stability of cavitation bubbles.Furthermore,based on the modified bubble breakup criterion,the effects of bubble growth speed,sound speed,droplet viscosity,droplet density,and bubble-droplet radius ratio on the breakup time and the breakup radius of cavitation bubbles are studied respectively.It is found that a bubble with large bubble-droplet radius ratio has the initial condition for breaking easily.For a given bubble-droplet radius ratio(0.2),as the bubble growth speed increases(from 2 m/s to 60 m/s),the bubble breakup time decreases(from 3.59μs to 0.17μs)rapidly.Both the greater diesel droplet viscosity and the greater diesel droplet density result in the increase of the breakup time.With increasing initial bubble-droplet radius ratio(from 0.2 to 0.8),the bubble breakup radius decreases(from 8.86μm to 6.23μm).There is a limited breakup radius for a bubble with a certain initial bubble-droplet radius ratio.The mathematical model and the modified bubble breakup criterion are helpful to improve the study on the breakup mechanism of the secondary diesel droplet under the condition of supercavitation.

Extensive studies on rotor systems with single or coupled multiple faults have been carried out. However these studies are limited to single-span rotor systems. A finite element model for a complex rotor-bearing system with coupled faults is presented. The dynamic responses of the rotor-bearing system are obtained by using the rotor dynamics theory and the modern nonlinear dynamics theory in connection with the continuation-shooting algorithm(commonly used for obtaining a periodic solution for a nonlinear system) for a range of rub-impact clearances and crack depths. The stability and Hopf instability of the periodic motion of the rotor-bearing system with coupled faults are analyzed by using the procedure described. The results indicate that the finite element method is an effective way for determining the dynamic responses of such complex rotor-bearing systems. Further for a rotor system with rub-impact and crack faults, the influences of the clearances are significantly different for different rub-impact stiffness. On the contrary, the influence of crack depths is rather small. The instability speeds of the rotor-bearing system increase due to the presence of the crack fault. The results obtained using the new finite element model, presented for computation and analysis of dynamic responses of the rotor-bearing systems with coupled faults, are in accordance with measurements in experiment. The formulations given can be used for diagnosis of faults, vibration control, and safe and stable operations of real rotor-bearing systems.