Lagrangian description of energy conversion in the Taconis oscillations

Abstract

Energy conversion in the Taconis oscillations is studied from the Lagrangian point of view. Numerical simulations are performed for the spontaneous thermoacoustic oscillations of helium gas which are observed in a tube with a strong temperature gradient along the tube axis. Flow fields in a closed straight cylindrical tube are obtained by solving the axisymmetric compressible Navier-Stokes equations. The amount of net work done by each fluid particle during one period is estimated for the fundamental mode as well as the second mode. In the second mode, moving fluid particles in the region of finite temperature gradient perform work, and those near the tube end walls absorb work. Almost no net work is done by fluid particles in the region of the tube center. Displacement of fluid particles is large in the fundamental mode, while fluid particles move in the vicinity of their starting points in the second mode. In the fundamental mode, pressure amplitudes are larger than other cases and the oscillation of the temperature in the tube is large. Both in the region of finite temperature gradient and in the region of the tube center, fluid particles are concerned with energy conversion in the fundamental mode oscillation.