DC4: Fast stability analysis and control of transonic/supersonic flows interacting with compliant structures

PhD Position
Fast stability analysis and control of transonic and supersonic flows interacting with compliant structures
(MSCA-DN FairCFD, DC4)

RECRUITMENT ON THIS POSITION IS CLOSED. APPLICATIONS ARE NO LONGER CONSIDERED

This is much more than just a PhD position!

Within the FairCFD Doctoral Network, you will benefit from a unique three-fold experience:

–  Contribute to technological innovation in the field of aerospace and  energy production industry by developing advanced and efficient CFD strategies.

–  Take part in a network-wide interdisciplinary effort to define and promote numerical sustainability in scientific research.

–  Join a vibrant network of 15 doctoral candidates, across 9 European countries, with access to cutting-edge network events, high-level training to technical and transverse skills, and secondments in both academic and industrial environments.

 See our website for more details on the network’s philosophy and actions, along with description of the other PhD positions (https://www.imft.fr/faircfd/project-presentation/).

Scientific background

Shock waves are an ubiquitous phenomenon when transonic and supersonic flows are concerned, as frequently encountered in typical aeronautical application, such as the transonic flow around the wing of a commercial aircraft in cruise [1]. These phenomena are also found in transonic compressors and supersonic turbines [2]. When these phenomena couple to vibration phenomena in the structural part, dangerous instabilities can arise, that can lead to structural failures or performance depletion [2,3]. The increasing flexibility of aircraft, due to weight saving, makes this kind of aeroelastic phenomena increasingly relevant, dangerous and, therefore, worth of investigation because the underlying mechanisms of instability are still not fully understood [4,5]

This kind of phenomena are usually investigated using mid-fidelity approaches by running time simulations coupled to structural models. This approach requires large computational resources. In this Individual Research Project (IRP), we propose to apply more frugal computational techniques typical of stability analysis to transonic and supersonic flows coupled with compliant structures [6, 7]. The aim is threefold: Firstly, to develop efficient tools for the stability analysis of aeroelastic systems in transonic and supersonic flow conditions; Secondly, to investigate the linear and nonlinear stability of notable systems, such as transonic buffeting, transonic aileron buzz, transonic compressor flutter, supersonic turbine flutter; Thirdly, to devise closed-loop control strategies based on available technologies to control such instabilities.

The objectives of the present IRP are:

  1. To develop efficient, time stepping-free, numerical tools for the investigation of the stability of transonic and supersonic flows with shock waves.
  2. To extend such advanced tools to deal with blade cascades in transonic compressors/supersonic turbines by exploiting Bloch’s decomposition and related approaches [8].
  3.  To extend the tools developed for purely fuild-dynamic problems to the analysis of fluid-structure interaction problems by the Arbitrary Lagrangian-Eulerian approach.
  4. To develop tools to synthetize feedback control laws for this kind of problems to alleviate instabilities by leveraging optimal-control or more advanced techniques.

Selected references:

[1] Timme S . Global instability of wing shock-buffet onset. J. Fluid Mech. 885, A37 (2020)

[2] Xia, K., Chen, H., Deng, H., Zhu, M., Qiang, X., Teng, J., Impact of non-axisymmetric tip clearance on the aerodynamic and aeroelastic stabilities of a transonic compressor, Aerospace Science and Technology, Volume 153, 109457 (2024).

[3] Kemme, R., Kahl, G., Schmitt, S. (2004). Flutter Stability of a Transonic Compressor Rotor – Application and Comparison of Different Numerical Methods. In: Breitsamter, C., Laschka, B., Heinemann, HJ., Hilbig, R. (eds) New Results in Numerical and Experimental Fluid Mechanics IV. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 87. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39604-8_56

[4] Houtman J., Timme S. Global stability analysis of elastic aircraft in edge-of-the-envelope flow. J. Fluid Mech. 967, A4 (2023)

[5] Gao, C., Zhang, W., Transonic aeroelasticity: A new perspective from the fluid mode, Progress in Aerospace Sciences, 113, 100596 (2020).

[6] Gong, Y., Nie, L., Zhang, W., Gao, C., On the mechanism of transonic buzz passive suppression with global stability analysis, Aerospace Science and Technology, 154, 109490 (2024).

[7] He W., Timme S. Triglobal infinite-wing shock-buffet study. J. Fluid Mech. 925, A27 (2021)

[8] Schmid, P.J., Fosas de Pando, M., Peake, N., Stability analysis for n-periodic arrays of fluid systems.  Phys. Rev. Fluids, 2, 113902 (2017)

[9] Felics Project: https://www.tu.berlin/en/flow/research/projects/felics-projekt (accessed on October 4th 2024)

Your research program

The direct application of the Newton-Raphson iteration to compressible flows with shock waves leads to severely ill-conditioned linear systems. This difficulty prevented the use of such kind of methods to compute the steady state base flow. In the present project two different approaches will be studied and compared: a pseudo-time stepping scheme based on a fully implicit discretization of the compressible Navier-Stokes equations and a time-stepping free approach leveraging Krylov-subspace linear solvers that have the nice property to preserve the initial component of the solution in the kernel of the operator. A classical Arbitrary Lagrangian-Eulerian approach will be employed to couple the flow to the structure, and model reduction techniques will be employed to minimise the computational cost of the coupled problem. Finally, projection on a suitably selected subspace will be exploited to formulated the flow control problem avoiding computationally intractable Riccati equations and keeping the workload to a minimum, while insuring the effectiveness and practical applicability of the designed control laws. The programs will be implemented leveraging the Open-Source Finite Element library Fenics, contributing to the development of the Felics project [9], that will be partially released as Open-Source in the near future.

The time schedule of the IRP is as follows:

Year 1: Development of numerical tools for linear stability analysis of compressible flows with shock waves

  • Formulation, implementation and validation of a steady-state solver suitable for compressible flows with shock waves by implementing an effective stabilisation strategy and an efficient solution algorithm (secondment to UNISA).
  • Formulation, implementation and validation of the linear stability eigenvalue solver, with particular attention to the role of artificial diffusion (secondment to TU Berlin).
  • Perform global stability analyses of test configurations (transonic buffeting, stability of flow in De Laval nozzles).

Year 2: Coupling the flow solver with the structural solver

  • The flow solver developed in the first year will be coupled to a structural model to obtain a fluid-structure solver for both the base flow and the linear stability analysis by an Arbitrary Lagrangian-Eulerian approach.
  • The coupled solver will be validated and applied to different configurations.
  • Development of the flow control tools, test and validation.

Year 3: Extension to blade cascades in compressors and turbines

  • The linear stability solver will be extended to deal with periodic cascades of airfoils in compressors and turbines by Floquet-Bloch approach (secondment to ONERA).
  • The solver will be validated and applied to relevant cases, such as transonic flutter in a compressor.
  • Paper and thesis finalisation.
  • Final uploading of the developed software on the project platform.

Where you will work

For the main part of your work, you will be hosted in Milano, at Politecnico di Milano, the most prestigious technical university in Italy, and one of the best in Europe.

Integration within the FairCFD Network

Within the FairCFD network, you will contribute mainly to WP1: Efficient physics-based numerical methods. You will regularly exchange with other DCs of the network applying similar approaches to other problems, and/or applying different numerical methods to similar problems.
Three secondments (short research stays in other partners of the network) are planned during the PhD: with 1/ TUB (3 months): training on the development of stability software using Fenics/Felics; 2/ UNISA (3 months): development of the steady-state solver for transonic/supersonic flows with shocks; 3/ ONERA (7 months) training on Floquet-Bloch theory, extension of the tools for stability of the transonic/supersonic flow past blade cascades in compressors/turbines.

Interdisciplinary task: co-designing numerical frugality

Beyond your individual research program described above, you will contribute along with all other FairCFD doctoral candidates to a network-wide multidisciplinary effort (WP5) addressing the environmental and societal dimensions of numerical simulation.
Each DC will participate in the definition of practical metrics for numerical frugality (computational cost, energy use, resource impact) and contribute data from their simulations to a collective meta-analysis. This initiative will be supported by interdisciplinary experts and accompanied by a dedicated DC in social sciences, who will lead a qualitative study on evolving practices in simulation across the network. Together, we aim to build concrete, informed recommendations for sustainable scientific computing.

Network Training Program — More Than Just a PhD

As a Doctoral Network funded by Marie Sklodowska-Curie Actions (MSCA-DN), FairCFD will offer to you a rich and engaging training experience, including

–       Four one-week training events; (i) an induction week devoted to team-building, open-science practices and sustainability issues, (ii) an Essential Skills Accelerator event combining aiming to to equip DCs with essential technical and transferable skills, (iii) a Hackathon event where DCs will collaborate in teams to solve complex physics problem and compare various simulation strategies in terms of precision and sobriety, and (iv) a Career and Leadership Development Forum Aiming to equip DCs with transferable skills essential for their future careers.

–       Five On-line courses combining technical training to state-of-the art simulation methods ranging from physics-based approaches to data-driven ones, exposition to industrial applications, along with Social, ethical and environmental aspects of decision-making in modelling practices.

–       Involvement in the organisation of scientific events, including a mini-symposium as part of a large-audience scientific conference, a scientific symposium allowing to share the output in terms of new methods, innovation, and applications to industrial processes, and a Societal colloquium to deliver the outputs of the multidisciplinary tasks of the network.

This programme is designed to support your growth as a researcher, innovator, and engaged citizen, fully equipped to lead the next generation of responsible simulation science. See our website for more details (https://www.imft.fr/faircfd/project-presentation/)