Supersonic Inlet Design Using Method of Characteristics and Computational Fluid Dynamics

In recent years, airbreathing supersonic vehicles have garnered significant interest. A key component of these vehicles is the inlet, which captures air effectively to ensure thermodynamic and propulsion efficiencies without disrupting the aerodynamic performance or structural loading. The inlet must slow down and compress the incoming air to low-speed, high-pressure conditions suitable for the combustion chamber. Traditional supersonic inlets achieve this deceleration by directing airflow across one or more shockwaves. In contrast, streamline-traced inlets (STIs) with contoured surfaces, which are formed by integrating streamlines through flowfields, accomplish most of the flow compression isentropically. Given that STIs offer improved integration with the airframe, this study investigates the design of STIs using the method of characteristics (MOC) and evaluates their performance through computation fluid dynamics (CFD). The Busemann flowfield was selected as the parent flowfield for streamline tracing. Within this flowfield, the leading shockwave impinges on the cowl tip and reflects toward the body-side wall of the inlet. The domain of the inlet flowfield is enclosed by the leading shock, the reflected shock, and the body-side wall. A specific region on the wall gradually turns to compress the flow; the turn angle is designed such that the resultant (compressive) Mach waves also impinge on the cowl tip. Beyond this region, the wall slope remains constant up to the entrance of the internal compression or combustion system. By implementing these procedures into a MOC program, an inlet geometry for a specified freestream Mach number is generated. An in-house developed MOC program, written in MATLAB, starts with inputs including the incoming flow Mach number, inlet height, initial wall angle, and the location of the initial MOC data line. The program initiates the computational process by employing oblique shock relations to calculate the flow properties along the initial data line, which is oriented perpendicular to the wall and terminates at the shock and the wall. The local flow angle and Mach number along the initial line facilitate the generation of characteristic lines, leading to the determination of MOC nodes in three distinct manners: 1) at the intersections of characteristic lines, where interior points within the flowfield are established; 2) at characteristics incident to the shock, where the shock point is iteratively finalized using shock relations; and 3) at characteristics incident to the wall, where the wall point is mapped out using the slip-wall condition. This process continues until the reflected shockwave is reached. The output of the program is an optimized inlet geometry for the specified initial conditions (inputs). To quantify the inlet performance, two parameters are considered: pressure recovery and volumetric efficiency. Pressure recovery is the ratio of the total pressure after the inlet to the freestream total pressure. Volumetric efficiency is the ratio of the inlet volume, raised to the 2/3 power, to the wetted area. The objective is to maximize both metrics. It is observed that as the initial ramp angle increases, the pressure recovery decreases, and the volumetric efficiency increases. The second part of the study is to examine the detailed flowfield using the CFD solver in ANSYS Fluent. The inlet geometries produced by the MOC program are employed to conduct two sets of simulations: a planar two-dimensional flow and an axisymmetric flow. Preliminary results suggest that the on-design Mach number should be lower for the axisymmetric configuration to align with the given geometry. Conversely, the planar configuration indicates that a higher on-design Mach number, while showing closer alignment with the MOC results than the axisymmetric results. These discrepancies likely stem from the assumption of straight shockwaves in the MOC program and the specific numerical details involved. Current efforts include incorporating a curved shock and transitioning from a planar to an axisymmetric configuration in the MOC program, thereby enhancing its accuracy and facilitating more reliable inlet design.