Nowadays increasing energy demand and the current energy crisis in Europe highlighted the need for independent and cheap energy sources which can be produced at the place of use. A good example of this energy sources are the renewables, from which wind energy is one. Humanity is using wind energy since the beginning of the history, but electrical energy generation from the wind started at the end of the 19th Century. During the evolution of wind energy utilization, wind turbines are becoming more and more efficient. A special kind of these turbines are the non -conventional wind turbines which are aiming to be efficient in a special condition. One of these new turbine designs is the CO-DRWT (Counter -Rotating Dual Rotor Wind Turbine), where there are two rotors in one tower. During our research, we examined some layouts for a CO-DRWT. In these spatial arrangements, we were able to change the second rotor's axial and radial positions. Within two in axial and one diameter in the radial region, we were running CFD (Computational Fluid Dynamics) simulation to determine the interaction of the two turbines and for calculating the overall power coefficient (cp) for the two rotors. Meanwhile, in our analysis, we defined some spatial arrangements where the CO-DRWT's overall cp is less than the cp of a Single Rotor Wind Turbine (SRWT) from the same geometry. We also defined regions where the CO-DRWT's cp is higher than the SRWT's. With our geometry and with our simulation's boundary conditions we find the optimal place for operating a CO-DRWT is the R = 0D radial distance with A = 2.1D axial distance (where the D is the rotor's diameter) where the cp is 0.514, also the worst arrangement is the R = 0.35D with A = 1.25D where the cp = 0.354, while an SRWT's cp from the same geometry is 0.377. According to our simulations, the energy density and the power an optimized CO-DRWT are 1.363 times than an SRWT has.