Atomization of fluids inside combustion chamber has been a very complex and long-lasting subject that is still researched into for maximum efficiency in mixing oxidizer and fuel. This thesis focuses on an injector called the Liquid-Liquid Swirl Coaxial Injector (LLSC) to be used in a small-scale rocket engine due to its high efficiency in spray angles and low pressure drops. Injectors are the elements that exist as a connection in between the plumbing and the combustion chamber of the rocket engine. The performance of injectors can greatly affect the stability and efficiency of the engine. Injectors proportionally help breakup the fluid into small droplets that help in the efficiency of vaporization of fluids while combusting. Helios Rocketry, Arizona State University’s student-led engineering organization, is working to design and successfully launch a small-scale bi-propellant liquid rocket engine to a 100 km (Karman Line) in space as part of the Base11 challenge. For this task a highly efficient injector element needed to be designed that can achieve high amounts of atomization with a large spray angle, to help with combustion in a relatively small sized chamber. The purpose of this thesis is to explore a specific type of injector element called a LLSC injector element. This is performed by simulating it through an LES model in computational fluid dynamics using a Voronoi based meshing scheme, by using codes from Cascade Technologies. In the end a 35-injector element design was used for an injector plate. This helped minimize the pressure drop and keep the wall stress below the safety limit.