The geometric effects of Coanda trailing edges on the aerodynamic performance of an airfoil are numerically evaluated for a range of different freestream Mach numbers and momentum coefficients. A Circulation control (CC) airfoil with a circular trailing edge (ACTE) proves to have better control effectiveness at low subsonic freestream speeds (Mach = 0.1). A CC airfoil having an elliptic trailing edge (AETE) outperforms the ACTE at high subsonic flow conditions. The occurrence of C μ-stall for the AETE is greatly postponed, and meanwhile the maximum net lift coefficient increment achieved for the AETE (Δ C L = 0.51) is slightly higher than that of the ACTE (Δ C L = 0.50) at Mach 0.6. Compared to the ACTE, the AETE is found to have better control consistency at different operating velocities and better control stability when the Coanda jet is supersonic. Through careful consideration of the aerodynamic performance and the control effects, the most appropriate axial ratio for an AETE ellipse is within the interval from 1.5 to 2. Finally, the flow field instability phenomenon and the jet detachment induced by the supersonic Coanda jet are investigated. A self-sustained shock-wave instability phenomenon without jet detachment is first observed in this paper.