Based on the vector diffraction theory, this paper investigated the energy flow evolution of focusing an azimuthally polarized Lorentz-Gaussian beam modulated by concentric vortex phase mask. Three concentric zones make up the concentric vortex phase mask: the center zone, middle circular zone, and outer circular zone. Each zone has an adjusted phase. The findings demonstrate that flexible transverse energy flow rings can be obtained in the focal plane and that transverse energy flows with various polygonal forms can be produced by varying the middle circular radius or phase distribution. By adjusting the phase of the center zone and outer circular zone, the normalized transverse energy flow distribution can be rotated or changed. Findings demonstrate that this technique offers a potent means of controlling the distribution and orientation of Poynting vectors and electromagnetic fields. Moreover, a series of energy flow rings are generated to facilitate the transportation of absorptive particles to predetermined positions. These phenomena may provide a new approach for particle capture and optical particle manipulation.