The efficiency of water purification system is largely affected by the concentration polarization. This can be reduced by increasing the mixing, mass transfer above the membrane and shear rate over the membrane surface. It is easy to increase shear rate and mixing in a roto-dynamic system than spiral wound system. A closed roto-dynamic filtration system without retentate outlet can be used when the supply of feed water is limited and reuse of water should be maximized. In a closed system, concentration inside the rotor cavity increases with time. We simulated unsteady flow and transport processes along with reverse osmosis through the membrane using ANSYS-Fluent for different values of rotor speed, feed pressure and aspect ratio. We compared the effects of these parameters on concentration polarization and permeate flux reduction. We also estimated the energy input for rotating the rotor and pressure driven flow. The specific energy consumptions for all cases were compared. The permeate flux increases with rotor speed but specific energy consumption also increases rapidly with rotor speed. So high rotor speed may not be always very effective. The present study and computational framework would be useful for optimum design of roto-dynamics cross-flow RO system. © 2016 Elsevier B.V.