FairCFD

Expected profile and skills

This PhD position is part of the FairCFD Doctoral Network, funded by the European “Marie Skłodowska-Curie Actions” (MSCA) programme. The network aims to define and promote numerical sustainability in the field of Computational Fluid Dynamics (CFD). The successful candidate will join a cohort of 15 doctoral researchers distributed across 9 European countries, benefiting from access to cutting-edge training events, advanced scientific and technical courses, and secondments in both academic and industrial environments. The doctoral researcher will be primarily hosted at the Department of Aerodynamics, Aeroelasticity and Acoustics of ONERA – The French Aerospace Lab, located in Meudon, France. The position offers an attractive salary in accordance with MSCA regulations for Doctoral Researchers, including a living allowance, a mobility allowance, and, where applicable, a family allowance. The PhD funding is guaranteed for 36 months. In line with the international mobility rule of the MSCA-DN programme, applicants must not have resided or carried out their main activity in France for more than 12 months within the 36 months preceding the start of the PhD.
Apart from this eligibility criterion, applications are welcome from outstanding research Master’s students worldwide.

Overview of the doctoral project: background and objectives

A shell-and-tube heat exchanger is one of the most widely used and versatile types of heat exchangers in industry. It consists of a bundle of tubes enclosed within a cylindrical shell, as illustrated in the figure (left). Its purpose is to transfer heat between two fluids—one flowing inside the tubes and the other flowing outside the tubes but within the shell—without allowing the fluids to mix. In specialized heat exchangers developed for air-breathing rocket engines (Varvill, 2010), the strong reduction in tube diameter may lead to excessive tube failures caused by flow-induced vibrations (Pettigrew & Taylor, 2003). While flow-induced vibrations of single cylinders have been extensively studied, fewer investigations have addressed the case of multiple interacting cylinders (Tang et al., 2020; Zhao et al., 2024). Using direct numerical simulations of the interaction between turbulent flow and moving cylinders, Zhao et al. (2024) identified three distinct interaction regimes as the flow velocity increases: turbulence-induced vibration, vortex-induced resonance, and fluid–elastic instability, with vibration amplitudes progressively increasing from one regime to the next.

The objective of this PhD thesis is to investigate the mechanisms underlying these regimes using linear stability and bifurcation analyses. The small-amplitude motion of the cylinders, coupled to perturbations developing around a time-independent mean flow, can be studied by determining the eigenvalues of an operator describing the coupled dynamics between fluid and structural perturbations. Such analyses have been successfully applied to the flow-induced vibrations of a single rigid cylinder (Mittal 2016) and of an elastic splitter plate (Pfister et al. 2020). Applying the same framework to the present configuration would, however, require tremendous computational resources, as it would involve the coupled dynamics of all cylinders in the array.

On the other hand, the tubes are usually arranged in a periodic lattice, a property that can be exploited to reduce the modal analysis to a single unit cell, i.e. the elementary pattern forming the lattice. Bloch theory provides a classical framework for investigating wave propagation in spatially periodic, non-dissipative media, such as electromagnetic, elastic, or acoustic waves in metamaterials. This decomposition can also be applied to analyse the growth or decay of flow perturbations in dispersive, spatially periodic mean flows. In this approach, the perturbation wavenumber becomes a free parameter that can be varied to investigate disturbances of arbitrary wavelength, while the eigenvalue problem is discretized over a single unit cell only. As an illustration, the steady flow in an infinite array of cylinders is shown in the figure (right, top). This spatially periodic flow becomes unstable to flow waves (figure, right, bottom) that clearly break the spatial periodicity. Although the results are displayed over a computational domain containing six unit cells, both the steady base flow and the unsteady perturbations were computed on the single unit cell highlighted in blue, by imposing generalized periodic boundary conditions on its left and right boundaries.

Recently, this formalism was extended to study the interaction between flow waves and the motion of cylinders mounted vertically on springs, that are introduced to model the flexibility of the tubes in heat exchangers. After getting familiar with the existing mathematical formalism and numerical tools, you will develop new algorithms to efficiently track the eigenvalues of interest, thereby further reducing the computational cost of the method. During the first year, you will focus on the flow transition around rigid and spring-mounted cylinders at low Reynolds numbers, considering various configurations (e.g. cylinder size, flow orientation, array geometry, natural vibration frequency of springs). In the second year, you will extend the analysis to turbulent mean flows described by the Reynolds-Averaged Navier–Stokes (RANS) equations, in order to obtain a more realistic description of the flow conditions encountered in industrial heat exchangers. Finally, a mathematical framework will be developed to analyse the nonlinear saturation of the unstable modes and their collective interactions over a range of wavenumbers.

Beyond your individual research program described above, you will contribute along with all other FairCFD doctoral candidates to a network-wide multidisciplinary effort addressing the environmental and societal dimensions of numerical simulation.

References :

Varvill, R. (2010). Heat exchanger development at Reaction Engines Ltd. Acta Astronautica, 66(9-10), 1468-1474.

Pettigrew, M. J., & Taylor, C. E. (2003). Vibration analysis of shell-and-tube heat exchangers: an overview—Part 1: flow, damping, fluidelastic instability. Journal of fluids and structures, 18(5), 469-483.

Tang, D., Liu, D., Ding, Z., Zhu, H., & Yuan, W. (2020). Numerical investigation on the interactions of flow induced vibrations among neighboring cylinders in a cylinder bundle. Annals of Nuclear Energy, 140, 107156.

Zhao, H., Gao, P., Li, X., Tian, R., Wei, H., & Tan, S. (2024). The interaction between cross-flow induced vibration and convection heat transfer in tube bundle at subcritical Reynolds number. Applied Thermal Engineering, 236, 121920.

Mittal, S. (2016). Lock-in in vortex-induced vibration. Journal of Fluid Mechanics, 794, 565-594.

Pfister, J. L., & Marquet, O. (2020). Fluid–structure stability analyses and nonlinear dynamics of flexible splitter plates interacting with a circular cylinder flow. Journal of Fluid Mechanics, 896, A24.

Expected collaborations 

At least two secondments, i.e. research visits of a minimum duration of two months, will be planned in partner universities of the project (IMFT, University of Salerno, University of Cambridge, TU Berlin).

Laboratoire d’accueil à l’ONERA

Département : Aérodynamique, Aéroélasticité, Acoustique

Lieu (centre ONERA) : Meudon

Contact : Olivier Marquet, Vincent Mons

 Email : vincent.mons@onera.fr

Directeur de thèse

Nom : Olivier Marquet

Laboratoire : DAAA

Tél. :  0146235197

Email : olivier.marquet@onera.fr