15 Mars 2022
- Influence of Radiative Effects on Buoyancy-induced Flows in High-pressure Compressor Inter-disk Cavities / PhD defense Ahmed HODAIB
Doctorant : Ahmed HODAIB
Date de soutenance : le 15 mars 2022 à 15h00 ; Amphi 3 Centrale Marseille
Abstract : In aircraft engines, a secondary air flow is obtained from an intermediate compressor stage, to be used to cool the turbine disks. This flow passes through the high-pressure compressor inter-disk cavities (Farthing et al., ASME J. Turbomach., 1992). A better understanding of this complex buoyancy-induced flow is essential to determine the thermal stresses, the radial growth of the blades, due to thermal expansion, and the temperature rise of the air used for cooling. Besides, to be able to determine the optimum clearance between the rotating blades and the surrounding casing, in order to improve the engine performance. This convective flow is not only unsteady and three-dimensional, it is unstable. Due to high temperature differences, the flow and heat transfer give rise to a strongly conjugate problem: the flow is affected by the temperature of the disks, and vice versa (Owen & Long, ASME J. Turbomach., 2015). The compressible Navier-Stokes equations, coupled with the energy equation and perfect gas law, are solved in the framework of the Low Mach Number (LMN) approximation, allowing a reduction of computational costs by filtering the high-speed waves while keeping a good accuracy by considering the compressibility effects (Motheau & Abraham, J. Comput. Phys., 2016). A fourth-order compact spatial discretisation scheme combined with parallelised Fourier method is implemented on a staggered grid. A second-order semi-implicit scheme is introduced for time integration. A two-step algorithm is developed for the solution of the LMN equations. In a first step, the thermodynamic variables are calculated through an iterative process, and used to compute the velocity divergence. In a second step, the variable density continuity and momentum equations are solved using a projection-type method. A parallelized iterative domain decomposition technique is implemented for the simulation of the three-dimensional flow and heat transfer in a T-shape model cavity. The parallelisation of the resulting computational code is performed through a hybrid MPI/OpenMP approach. Spatial and temporal accuracies of the proposed algorithm are checked on a manufactured solution in a simplified configuration. Then, the algorithm is applied to study the flow and heat transfer in an idealised compressor inter-disk cavity, while considering conduction inside the walls, to allow for a more accurate thermal balance. The results are compared with data available in the literature based on local Nusselt numbers. A parametric study is done for a range of the two main parameters governing the flow, according to Farthing et al. (ASME J. Turbomach., vol. 114, pp. 229-236 and pp. 237-246, 1992): the temperature difference and the Rossby number. To include surface radiation exchanges, the discrete radiative heat transfer equation is solved based on the zonal method. The adequacy of the proposed Low Mach number approach is shown, compared to Boussinesq approximation. Moreover, the validity of neglecting the gravitational acceleration with respect to the centrifugal acceleration in the equations is discussed. Then, the definition of an effective Rayleigh number is established, where both centrifugal and gravitational accelerations are taken into account in the buoyancy terms. The results reveal that the flow exhibits a Poiseuille-Rayleigh-Bénard-like instability, and that this effective Rayleigh number governs the flow structure and the heat transfer in the whole cavity, and hence the stability of the flow. In the end, it is shown that radiative exchanges become more significant the more we get closer to the inner radius of the cavity, in agreement with the results reported by Tang & Owen (ASME J. Turbomach., 2021). It is observed that the temperature profiles at the upstream and downstream disks approach each other, when radiation is considered, where the upstream disk temperatures increase.
Jury
Directeur de these M. Anthony RANDRIAMAMPIANINA Aix Marseille Université
Rapporteur M. Gary D. LOCK University of Bath, UK
Rapporteur M. Artur TYLISZCZAK Czestochowa University of Technology, Poland
Président M. Pierre SAGAUT Aix-Marseille Université
Examinateur M. Innocent MUTABAZI Normandie Université
Examinateur M. Stéphane ABIDE Université de Perpignan Via Domitia
CoDirecteur de these Mme Isabelle RASPO Aix-Marseille Université
CoDirecteur de these M. Stéphane VIAZZO Aix-Marseille-Université
