Supersonic rocket nozzles are critical components of the propulsion systems. Optimizing the performance 
and efficiency of these engines is crucial for reducing costs and enhancing the reliability of space missions. 
One of the major challenges in supersonic nozzle design is considering the effects of hot gases and variable 
thermodynamics on propulsive jet behavior during both ignition, startup and throughout the mission. These 
factors directly influence the jet stability, the possible boundary-layer separation and its interaction with 
shock waves, mixing layes, acoustics, supersonic jets.

This study aims to model propulsive jet behavior in rocket nozzles in the presence of hot gases (combustion 
products) and the associated heat transfers. The concerns are those of the ATAC group. The objective is to 
extend the studies conducted so far on nozzle models operating with ambient air to more complex situations, 
considering the thermal reality of the engine. The interest of this study is twofold: (1) to understand the 
extent to which the knowledge gained in cold gases can be extended to hot gases, and (2) to improve the 
overall understanding of boundary-layer separation phenomena and shock formation and interaction in the 
presence of hot, multi-species, and possible reactive gases. One of the problems that still remains poorly 
understood is undoubtedly the origin of the very high thermal loads observed at the nozzle exit in the end-
effect regime. Although recompression (following the onset of separation) remains a very important factor in 
thermal heating, other elements can also come into play, such as possible post-combustion at the foot of the 
separated shock and along the supersonic mixing layer. It is, therefore, particularly important to conduct a 
reliable numerical study that can aid in the understanding of these very complex physical problems. The 
specific objectives are as follows:

• Fine characterization of the properties of combustion gases in a supersonic nozzle through modeling of the 
chemical composition of burned gases (considering a complete kinetic scheme in the case of Lox-methane 
combustion to be used as an input for the nozzle flow simulations).

• Influence of wall temperature by investigating how the wall temperature of the nozzle affects the behavior of 
the supersonic jet. This includes examining temperature gradients along the nozzle wall and their impact on 
nozzle flow stability.

• Study of the influence of hot gases on the overall flow structure, especially on the separation regime (free- 
and restricted shock separations) and associated shock train. This will help determine key parameters 
influencing these phenomena.

• Examination of critical thermodynamic conditions under which post-combustion downstream of the 
recompression wave would be possible.

• Study of the influence of variable thermodynamics fluid properties in the mixing layer originating from the 
triple point on jet separation (shock oscillations, unsteadiness of the separated region, etc.). This necessarily 
involves a detailed numerical simulation of multi-species mixing phenomena between a supersonic jet and a 
low-speed cold back flow.

• Characterization of convective heat transfer in the recirculation zone and energy exchanges between the 
reactive mixing layer and the nozzle wall.

Implications and Contributions - This thesis comprehensively analyzes the impact of hot gases and variable 
thermodynamics in supersonic rocket nozzles, specifically focusing on LOx-CH4 propulsion with realistic 
combustion chamber conditions. The research employs advanced numerical simulations, including 
aerothermodynamics models for both inert and reactive gases, computational fluid dynamics (CFD) 
techniques, and dynamic mode decomposition and data analysis. To validate the numerical methodology, it is 
advisable to conduct a comprehensive literature review to identify relevant sub-scale laboratory experiments. 
These experiments can then be utilized for validation purposes, particularly in canonical configurations that 
closely mimic operational conditions. The findings of this research may also hold significant implications for 
noise reduction within the aerospace industry. In fact, the study may involve investigating later the acoustic 
radiation from hot supersonic jets with unburst gas pockets and their influence on overall propellant jet. This 
entails assessing noise levels and exploring potential noise reduction methods. In conclusion, exploring the 
effects of hot gases, variable thermodynamics, wall temperature, and specific heat ratios in supersonic rocket 
nozzles is an important research subject especially for current and future space propulsion systems. This 
PhD proposal provides a good opportunity to make a substantial contribution to this field by offering new, in-
depth knowledge and valuable insights for improving the performance and sustainability of space propulsion 
systems.

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For more Information about the topics and the co-financial partner (found by the lab !); contact Directeur de 
thèse - abdellah.hadjadj@insa-rouen.fr

Then, prepare a resume, a recent transcript and a reference letter from your M2 supervisor/ engineering 
school director and you will be ready to apply online  before May 1st, 2024 Midnight Paris time !