Synthetic jet actuators for flow control applications have been an active topic of experimental research since the 90's. Numerical simulations have become an important complement of that experimental work, providing detailed information of the dynamics of the controlled flow. This study is part of the AVOCET (Adaptive VOrticity Control Enabled flighT) project and is intended to provide computational support for the design and evaluation of closed-loop flow control with synthetic jet actuators for small scale Unmanned Aerial Vehicles (UAVs). The main objective is to analyze active flow control of a NACA4415 airfoil with tangential synthetic jets via computational modeling. A hybrid Reynolds-Averaged Navier-Stokes/Large Eddy Simulation (RANS/LES) turbulent model (called Delayed Detached-Eddy Simulation-DDES) was implemented in CDP, a kinetic energy conserving Computational Fluid Dynamics (CFD) code. CDP is a parallel unstructured grid incompressible flow solver, developed at the Center for Integrated Turbulence Simulations (CITS) at Stanford University. Two models of synthetic jet actuators have been developed and validated. The first is a detailed model in which the flow in and out of the actuator cavity is modeled. A second less costly model (RSSJ) was also developed in which the Reynolds stress produced by the actuator is modeled, based on information from the detailed model. Several static validation test cases at different angle of attack with modified NACA 4415 and Dragon Eye airfoils were performed. Numerical results show the effects of the actuators on the vortical structure of the flow, as well as on the aerodynamic properties. The main effect of the actuation on the time averaged vorticity field is a bending of the separation shear layer from the actuator toward the airfoil surface, resulting in changes in the aerodynamic properties. Full actuation of the suction side actuator reduces the pitching moment and increases the lift force, while the pressure side actuator increases the pitching moment and reduces the lift force. These observations are in agreement with experimental results. The effectiveness of the actuator is measured by the change in the aerodynamic properties of the airfoil in particular the lift ([Delta]C[subscript t]) and moment ([Delta]C[subscript m]) coefficients. Computational results for the actuator effectiveness show very good agreement with the experimental values (over the range of -2° to 10°). While the actuation modifies the global pressure distribution, the most pronounced effects are near the trailing edge in which a spike in the pressure coefficient (C[subscript p]) is observed. The local reduction of C[subscript p], for both the suction side and pressure side actuators, at x/c = 0.96 (the position of the actuators) is about 0.9 with respect to the unactuated case. This local reduction of the pressure is associated with the trapped vorticity and flow acceleration close to the trailing edge. The RSSJ model is designed to capture the synthetic jet time averaged behavior so that the high actuation frequencies are eliminated. This allows the time step to be increased by a factor of 5. This ad hoc model is also tested in dynamic simulations, in which its capacity to capture the detail model average performance was demonstrated. Finally, the RSSJ model was extended to a different airfoil profile (Dragon Eye) with good results.