Thermoacoustic streaming in a tube with isothermal outer surface

摘要

Thermoacoustic oscillations at a cycle-steady state in a tube with an isothermal outer wall, and with one end closed and the other end connected to a wave generator, is analyzed based on a linearized theory. From the global mass conservation, an analytical solution has been obtained for the cross-sectional and cycle averaged axial velocity. It is shown that this averaged velocity is non-vanishing due to the mass streaming effect. By analyzing the global momentum balance, it is found that the cycle-averaged pressure depends on the momentum streaming and friction force, and a conservation relationship exists between the momentum streaming and the cycle-averaged pressure for the flow oscillating at a high frequency in a wide tube. An investigation of the global energy balance leads to an expression for thermo-acoustic energy streaming. Furthermore, it is shown that the refrigeration effect is mainly caused by the non-vanishing mean velocity, and therefore the mass streaming and the energy streaming are intimately connected.