Cilia are hairy structures whose length is the order of millimeters and found in animals which utilize cilia for their essential lives. Although cilia are mostly found in the low-Reynolds-number regime, there exists in the high-Reynolds-number regime: comb-jelly. Considering the simple symmetric motion of a ciliary structure, the flow characteristics such as the fluid transport and mixing are numerically investigated using a two-dimensional plate model for a wide range of Reynolds numbers. The region of active transport is expanded farther from the ciliary structures with increasing the Reynolds number. Using a model where symmetric ciliary structures on each wall are in a confined channel, symmetry breaking is observed and the flow structure becomes chaotic. Symmetry breaking is classified into two regimes. Strong breaking is observed in relatively wide gap and weak breaking in narrower gap. For the mixing performance, symmetry breaking can enhance the mixing performance. However, the mixing performance cannot be improved without asymmetry of the flow structure. The breaking time of the vorticity field is also compared. As the Reynolds number increases, the breaking time becomes shorter due to an inertial effect and, as the gap width decrease, the breaking time becomes also shorter due to strong vortex-vortex interaction. When the number of ciliary structures increases, the flow field does not experience symmetry breaking even at high Reynolds number, which implies that the mixing performance cannot be improved with synchronization motion of ciliary structures.