Lagrangian analysis of energy conversion in the taconis oscillations

Abstract eng:
Energy conversion in the Taconis oscillations is numerically studied from the Lagrangian point of view. By solving the axisymmetric compressible Navier-Stokes equations, spontaneous thermoacoustic oscillations in a closed cylindrical tube are observed when a strong temperature gradient is imposed along the tube axis. The ratio of the high wall temperature near both ends of the tube to the low wall temperature of the central part is fixed at 15. Temporal evolution of dynamical and thermodynamical properties of fluid particles in the fundamental mode oscillation of a standing wave and the second mode oscillation is obtained from the field data. The state of the fluid particle is represented on a pressure-volume diagram. Fluid particles moving near the tube end perform a nearly cyclic transformation in both modes. When displacement of fluid particles is large, a regular pattern is not found on a pressure-volume diagram.

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