# Ramjet Nozzle Analysis for Transport Aircraft Configuration for Sustained Hypersonic Flight
## 1 Introduction
### Hypersonic Propulsion  
Hypersonic air-breathing vehicles utilise the air they operate in to propel the vehicle to speeds ranges beyond the Mach 5 (5 times the local speed of sound) envelope. Historically, rocket-based propulsive systems have been utilised for the purpose of propelling aircrafts and spacecrafts to hypersonic flight speeds. However, air-breathing modes of propulsion tend to be preferable for sustained atmospheric flights due to their virtue of operation without the necessity of carrying oxidisers, resulting in significant weight and space savings and thus allowing for a proportionately much larger payload to be carried.  
Air-breathing engines for hypersonic vehicles require a scramjet system to operate and are often proposed in combined cycle form in that they also contain a conventional gas turbine and ramjet in the same package. The reason for this is that each engine can operate within a different flight speed regime and all three are required for successful operation at hypersonic speeds.  
The present paper focusses on the intermediate component: the ramjet. Engines that take advantage of ram air compression are classified as ramjet engines, which eliminate the need to rely on axial compression. The compression is achieved in the aerodynamic diffusing (ram) process created by the inlet and diffuser. The engine utilises the aircraft's forward momentum for the compression of air, requiring the ramjet engine to operate supersonically. This renders the engine practically inoperable at lower Mach numbers.  
Figure 1 depicts the schematic of an ideal ramjet. The engine consists of a diffuser, a combustion chamber, and an exhaust nozzle. A typical ramjet includes an air inlet followed by a diffuser, allowing the air to be supersonically decelerated to subsonic conditions and compressed utilising a train of shocks, accompanying a rise in temperature that provides ample conditions for the air being fed into the combustion chamber [4].  
The compressed air is mixed with fuel and combusted and fed straight into the exhaust system for expansion, contrary to gas-turbine engines, where high temperature gas is passed through the turbines utilised to drive the compressors. The nozzle, of convergent-divergent geometry, accelerates the high temperature gas from subsonic at the nozzle inlet to supersonic speeds, creating a high velocity exit jet producing the required positive momentum for thrust generation from the overall engine. Ramjets are typically utilised primarily for military applications for the propulsion of missiles. Nevertherless, aircrafts have also utilised ramjets for propulsion. Examples include the SR-71 Blackbird, which featured a turboramjet propulsion system capable of Mach 3.5 speeds.  
In the present paper, a concept aircraft was powered by a combined cycle hypersonic propulsion system which features a gas turbine, ramjet, and scramjet layout, and was first presented in Reference [5]. The focus was on maximising the thrust component from the ramjet as an important criterion and pre-cursor to allowing the aircraft to achieve hypersonic speeds.  
To achieve the above goal, three different nozzle types were investigated. Namely, conical, bell, and dual bell nozzles were tested to comprehensively investigate the possibilities available to the propulsion system designer with respect to nozzle type choices and their specific features. This paper focussed on axisymmetric nozzle configurations without consideration for planar or other three-dimensional nozzle configurations. For this reason, wide-ranging computational fluid dynamics (CFD) was undertaken to highlight the most promising design through a parametric analysis. A full description of the CFD setup and validation is provided in later sections, covering thrust and altitude suitability, while the fundamentals are covered in the sections immediately following.