The jet propulsion exhaust nozzle system is an integral part of an airbreathing gas turbine engine and critical to its overall performance. Challenges associated with the design and manufacturing of an exhaust nozzle increases with the cruise speed of the aircraft. The exhaust nozzle system for a supersonic cruise aircraft mandates additional features such as variable throat and exit area, jet noise suppression, and reverse thrust. In the past, in order to address this challenge, an ejector nozzle with clamshells was designed and fabricated. The experimental investigation and computation of the nozzle at low subsonic conditions showed the presence of a recirculation zone at the inner surface of the clamshells. The present work summarizes the computational simulation of the ejector nozzle with clamshells at flight conditions. Similar recirculation zones were predicted at the inner surface of the clamshells. Initiatives were taken to improve the ejector performance by the elimination of the recirculation zone. The current nozzle design was modified by the application of chevrons on the nozzle throat. A preliminary design and computational analysis of the ejector nozzle with clamshells and chevrons was carried out. Two design cases with different number of chevrons were implemented and their computational analysis was successfully carried out. It was observed that the nozzle flow features were improved because of enhanced mixing and the recirculation zone was decreased in its extent.