An open-source 2D Reynolds-averaged Navier–Stokes (RANS) simulation model was presented and applied for a laboratory-scaled cross-flow hydrokinetic turbine and a twin turbine system in counter-rotating configurations. The computational fluid dynamics (CFD) model was compared with previously published experimental results and then used to study the turbine power output and relevant flow fields at four blockage ratios. The dynamic stall effect and related leading edge vortex (LEV) structures were observed, discussed, and correlated with the power output. The results provided insights into the blockage effect from a different perspective: The physics behind the production and maintenance of lift on the turbine blade at different blockage ratios. The model was then applied to counter-rotating configurations of the turbines and similar analyses of the torque production and maintenance were conducted. Depending on the direction of movement of the other turbine, the blade of interest could either produce higher torque or create more energy loss. For both of the scenarios where a blade interacted with the channel wall or another blade, the key behind torque enhancement was forcing the flow through its suction side and manipulating the LEV.