Wave breaking and shock waves for a periodic shallow water equation

This paper is devoted to the study of a recently derived periodic shallow water equation. We discuss in detail the blow-up scenario of strong solutions and present several conditions on the initial profile, which ensure the occurrence of wave breaking. We also present a family of global weak solutions, which may be viewed as global periodic shock waves to the equation under discussion.

Computation of Unsteady Flowfield and Blade Response Due to Impeller-Diffuser Interaction

Numerical analysis of a modern centrifugal compressor is carried out to calculate the high strains observed during testing at overspeed condition. Three-dimensional, viscous, time accurate, CFD analysis of the centrifugal compressor stage is carried out to obtain the unsteady forces on the impeller blades due to impeller-diffuser interaction. Analysis showed a strong interaction between the impeller and the diffuser with periodic shock impingement on the impeller pressure surface. The unsteady forces were found to be largely limited to last 20 percent of the impeller meridional chord. Strain calculations were carried out by applying the 1st harmonic of the diffuser blade count of the unsteady pressures and using ANSYS to perform a sweep through the frequencies of interest. It was found that the impeller mode shape contained a 25 nodal diameter vibration mode in the frequency of interest which was excited by the pressure waves from the 25 count diffuser resulting in high resonant stresses. Analysis also showed a strong interaction between various system modes. The response was found to be very sensitive to this interaction. Utilizing this interaction, an analytical redesign of the impeller predicted significantly reduced blade response.