<p>Acoustic topologies have received attention mainly due to their extreme acoustic transport capabilities. However, previous acoustic topologies were derived from arrays of scatterers. The pseudo-spin positions of phononic crystals tend to exist only at the K or Г points in the Brillouin zone. This paper proposes a periodic sandwich acoustic topology without scatterers. By gouging out the periodic cylindrical structure in the bottom plate, the air sandwich in the center is made to have acoustic topological properties. This sandwich structure allows for a pseudo-spin acoustic flow at both the K and Г points in the Brillouin zone, thus enabling a stronger acoustic transmission. The absence of scatterers means that applications will be possible in more fields. Meanwhile, this research proposes a method to control the intensity of acoustic flow based on this structure. By introducing a specially designed acoustic flow switch, arbitrary control of the acoustic flow intensity on the edge-state path can be realized. The proposed method will help to cope with scenarios where different acoustic flow intensities need to be output. This has a high potential for applications such as separating particles with different masses in microfluidics.</p>