Understanding trajectories of natural and artificial helical swimmers under confinement is important in biology and for controlled swimming in potential medical applications. Swimmers follow helical or straight trajectories depending on whether the helical tail is pushing or pulling the swimmer. To investigate swimming dynamics of helical swimmers further, we present a Computational Fluid Dynamics (CFD) model for simulation of an artificial microswimmer in cylindrical channels. The microswimmer has a cylindrical head and a left-handed helical tail. The kinematic model solves for the position and rotation of the swimmer based on the linear and angular velocities of the force-free swimmer from a CFD model. Third-order Adams-Bashforth solver is used to obtain the orientation and the position of the swimmer. Viscous, gravitational, magnetic and contact forces and torques are considered in the model. The model is validated with experimental results. 3D trajectories, propulsion and tangential velocities are reported.