After a long time interaction, governed by the magnetohydrodynamic (MHD) equations, between the Parker solar wind flow and a potential magnetic field combined by a dipole and a hexapole, a special streamer background structure in the solar meridian plane is presented. With the background structure, two tube models containing spiral magnetic field lines with a small length-scale can move in the computational domain step by step, interact afterward and trigger a Coronal Mass Ejection (CME) finally. The tube model is approached by a structure made up of two-dimensional co-circular magnetic field lines, with a ratio of the plasma pressure at its center to that at its edge m=2 and with a radius a for two cases: a=0.07 Rs (Rs is the solar radius) and a=0.1 Rs respectively. Corresponding to the two cases, two typical numerical results are obtained. In the case a=0.07 Rs, the two tube models interact with each other, merge into one set of co-circular magnetic field lines in seven solar radii and propagate outward. In the other case a=0.1 Rs, the two tube models do not merge into one and keep two sets of co-circular magnetic field lines exist in the computational domain during their propagation as a whole.