Modelling and simulation of the construction of a ceramic coating produced by plasma suspension spraying

Modelling and simulation of the construction of a ceramic coating produced by plasma suspension spraying.

12-month post-doctorate
Funding: University of Bordeaux/SAFRAN
Location: I2M (Talence), Start date: November 2024

Introduction

Suspension plasma spraying (SPS) is an emerging industrial process, particularly for the creation of ceramic coatings capable of withstanding the very high temperatures and mechanical stresses inside an aircraft engine for a long time (thermal barrier). For the aeronautics industry, it is classified as a special process whose output elements can only be verified by monitoring or post-measurement, and whose deficiencies therefore only become apparent once the product is in use. The SPS process creates thermal barriers by injecting and melting ceramic powder into a plasma. The plasma flow accelerates the particles, and the molten droplets are then crushed onto a substrate. They spread out and solidify rapidly successively to form the coating. The study carried out at I2M, in collaboration with the IRCER laboratory of the University of Limoges and SAFRAN, concerns the last stage of the process at the droplet scale, with the aim of contributing to the understanding of the phenomena (dynamic and thermal) and analyzing the influence of physical impact conditions on the final shape of the deposit.
Our study differs from existing studies in that it uses submicrometric particle sizes. In addition, the limitations of the incompressible models used by many authors led us to study a compressible two-phase model, taking into account the phase change. The massively parallel Notus CFD code (https://notus-cfd.org), developed at I2M, is used to solve the Navier-Stokes equations, to track the free surfaces involving the action of interfacial tension and to take account of heat transfer and solidification through the energy equation. Numerical experiments with up to a hundred drops are carried out on regional supercomputers. The results of these initial simulations show both the current ability of the models and methods employed to reproduce physical phenomena, and the need for more computing capacities to characterize a coating formed by the impact of hundreds to thousands of particles, in order to interpret the relationships between impact conditions and post-impact drop morphology.

Objective

The aim of this post-doctoral project is to continue the work undertaken, using GENCI's national HPC resources. By increasing the number of processors from a few hundred to several thousand, we will be able to study numerically, for the first time in the literature, the birth of a finely structured coating with a large number of particles. The post-doctorate will be divided into several stages:

• determination of the simulation parameters needed to match actual operating conditions as closely as possible: spatio-temporal distribution of particles, particle velocity and size, etc.
• implementation of a numerical procedure for droplet generation in the upper part of the domain, taking into account successive passes of the torch over the impact surface;
• preliminary simulations at the MCIA mesocomputing center on a few hundred processors to check the entire calculation chain, from the initial condition to the solidification of two droplet trains on a reduced impact surface;
• simulations on a GENCI supercomputer (around ten thousand processors will be used).
• analysis and interpretation of results

Methods

The Navier-Stokes equations governing fluid flow and the energy conservation equation are solved in compressible form using a newly proposed pressure correction method [1]. Consideration of the liquid-solid change of state is approximated by an adaptation of the enthalpy linearization method to two-phase compressible flows [2]. The liquid/gas interface is tracked using the VOF-PLIC method of linear interface reconstruction [3]. The WENO scheme is used for the advection terms of the Navier-Stokes and energy equations. A centered implicit scheme of order 2 is chosen for the stress/diffusion terms. The Brinkman term is used to penalize the velocity of the solidified part of the phase-change material. Surface tension is treated using the CSF (Continuous Surface Force) method. Diffusion terms are discretized using the finite volume method. Linear systems are solved using the massively parallel Hypre library.

Skills

Computational fluid mechanics, heat transfer. Experience of development on a large research code (in Fortran 2008) and massively parallel simulations will be particularly appreciated.

Contact

Cédric Le Bot : cedric.lebot@bordeaux-inp.fr, Stéphane Glockner : glockner@bordeaux-inp.fr

References

[1] J. Jansen, S. Glockner, D. Sharma, A. Erriguible, Incremental pressure correction method for subsonic compressible flows, submitted to Journal of Computational Physics, 2024.

[2] B.J. Kaaks, J.W.A. Reus, M. Rohde, J L Kloosterman et D Lathouwers. « Numerical Study of Phase-Change Phenomena: A Conservative Linearized Enthalpy Approach ». 2022.

[3] G.D. Weymouth et D.K. Yue. « Conservative Volume-of-Fluid method for free-surface simulations on Cartesian-grids ». Journal of Computational Physics, 229(8):2853–2865, avril 2010