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Turbulent Couette-Poiseuille and Couette flows inside a square duct at bulk Reynolds number 10,000 are investigated by the Large Eddy Simulations. Mean secondary flow is observed to be modified by the presence of moving wall where the symmetric vortex pattern vanishes. Secondary flow near the top corner shows a gradual change of vortex size and position as the moving wall velocity increased. It is interesting to note that a linear relation exits between the angle and the parameter r = W_ω/W_Bulk, and a change in slope occurs at r ~ 1.2. Near the moving wall due to the reduction of the streamwise velocity fluctuation at the moving wall, turbulence structure gradually moves towards a rodlike axi-symmetric turbulence as r increases. As the wall velocity increases further for r > 1.2, the rod like structure disappears, and turbulence reverts to the disk like structure.