Unsteady flow phenomena within rotor–stator cavities are recognized as critical contributors to detrimental vibrations in space turbopumps. Although various palliative strategies are typically incorporated during the design phase, experimental investigations frequently reveal persistent high-amplitude flow oscillations capable of compromising the structural integrity of turbomachinery components and, in severe cases, the rocket engine as a whole. These cavity flows are characterized by rotating, three-dimensional boundary layers that are inherently unstable and prone to the development of complex flow structures, such as spiral and annular modes. Traditional computational approaches, such as Reynolds-Averaged Navier–Stokes (RANS) simulations, have demonstrated significant limitations in accurately capturing these unsteady dynamics. In contrast, Large Eddy Simulation (LES) has emerged as a more promising methodology, offering improved fidelity in predicting such flow behaviors under variable operating conditions, albeit at a substantially higher computational cost [1].

In this project, we aim to obtain RANS-based flow predictions whose fidelity is comparable to that in more expensive approaches such as LES. To this end, it is proposed to rely on the following two-step approach. In a first step, reference data, which may come from either high-fidelity simulations or experiments, are assimilated to correct the steady RANS equations and the associated mean-flow solution. In a second step, linear mean-flow analyses are performed to give access to the unsteady content of the flow. Compared to previous studies [2], one of the main challenges of the present project is to extend the above-described methodology to the prediction of complex flow dynamics as present in rotating cavity systems. To achieve this, we will in particular consider the use of non-intrusive, ensemble-based variational techniques [3], developed during a joint Ph.D. project by R. Maranelli, co-funded by CNES and ONERA, to perform the first, so-called data-assimilation step of the above methodology. A key advantage of this non-intrusive approach lies in its avoidance of direct solver differentiation, which is typically required to compute gradients in the data-assimilation procedure. Instead, gradient information is approximated through ensembles of forward RANS evaluations, making the approach both computationally efficient and compatible with legacy solvers.

After calibrating the RANS turbulence model for a reference configuration, the study will investigate machine learning techniques to generalize the model to other design conditions. Although such methods have shown promise in simpler flow configurations [4], their application to the complex, anisotropic environments of turbomachinery—such as rotor–stator cavity flows—remains largely unexplored. This work aims to extend these techniques to enable robust and transferable turbulence models across a wider range of operating regimes.

To bridge high-fidelity simulations with experimental applications, this study will explore strategies for reducing measurement requirements and optimizing sensor placement. Given the limited access to flow data in experiments, the focus will be on developing an optimal sensor placement methodology to enable reliable estimation of mean [5] and fluctuating flow quantities using the data-assimilated RANS model, potentially leveraging sparse sensing techniques [6]. This approach aims to both facilitate turbulence model development under sparse data conditions and provide a systematic framework for experimental design, thereby supporting future model validation and development efforts.

In summary, this project focuses on the rotor–stator cavity flows within space turbopumps, with the objective of developing predictive and generalizable data-driven-assisted RANS models tailored to such complex configurations. The work builds upon existing collaborations with CNES and ONERA, leveraging flexible, non-intrusive methodologies to enhance model fidelity and adaptability. By combining advanced data-driven modeling techniques with high-fidelity simulation data and experimental constraints, the proposed research aims to contribute to the design of more robust, transferable turbulence models for next-generation propulsion systems.

[1] M. Queguineur, T. Bridel-Bertomeu, L. Y. M. Gicquel, G. Staffelbach. Physics of Fluids, 2019, 31, 104109

[2] K. Sarras, C. Tayeh, V. Mons, O. Marquet. Journal of Fluid Mechanics, 2024, 1001, A41

[3] V. Mons, Y. Du, T. Zaki. Physical Review Fluids, 2021, 6 (10), pp.104607. 

[4] R. Villiers, V. Mons, D. Sipp, E. Lamballais, M. Meldi. Flow Turbulence and Combustion, 2025, pp. 1-39 

[5] V. Mons, O. Marquet. Journal of Fluid Mechanics, 2021, 923, A1

[6] K. Manohar, B. W. Brunton, J. N. Kutz, S. L. Brunton. IEEE Control Systems Maganzine, 2018, 63, pp. 63-86

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For more Information about the topics and the co-financial partner (found by the lab!); contact Directeur de thèse - taraneh.sayadi@lecnam.net

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 March 13th, 2026 Midnight Paris time!