Based on the nonlinear Navier-Stokes equation, the general acoustic streaming control equation was derived.The N-S equations containing the second order flow field information of a single cylindrical heat exchange tube and a double cylindrical heat exchange tube in the plane standing wave sound field were solved in whole domain by using the finite element software COMSOL.The first and second order flow field information were obtained.The effects of Reynolds number Re and Strouhal number Sr on the structure of acoustic streaming outside the heat exchange tube were studied.It is found that with the increase of Re and Sr, the vortex area in the boundary layer of the heat exchanger tube decreases until it disappears, while the vortex area outside the boundary layer increases gradually.The number of vortices outside the single heat exchanger tube is reduced from 8 to 4, and the number of vortices outside the double heat exchanger tube is reduced from 12 to 8.In addition, the vortex structures inside and outside the boundary layer are all reverse rotation.The flow field outside the boundary layer goes far away from the heat exchange tube along the direction of oscillation, and flows toward the heat exchange tube in the vertical direction.