Multiscale modeling of heat exchangers for aircraft propulsion systems

Improving the efficiency of heat exchangers is one of the key technological challenges to curb aircraft greenhouse gas emissions. While recent advances in geometric optimization and additive manufacturing have led to ever more complex heat exchanger designs, they have also made it exponentially difficult to predict their performances. The goal of this thesis is to develop and assess multiscale heat exchanger models based on upscaling methods of transfers in porous media. Macroscopic models offer a good trade-off between accuracy and computational cost, providing relevant transport features are accurately treated in the upscaling procedure. This work focuses on the coupling of inertial flow and non-equilibrium heat transfer in porous media. The Volume Averaging Method (VAM) is employed to derive macroscopic transport equations and determine their effective properties. Predictions of the macroscopic models are assessed against Direct Numerical Simulations (DNS) of heat exchanger models from the engineering literature. First, the upscaling of incompressible and laminar inertial flow without heat transfer is studied. The Forchheimer equation describes macroscopic momentum transport, accounting for inertial effects at the pore-scale level through a non-linear correction tensor to permeability. The VAM involves solving a non-linear problem for the velocity field deviations, commonly tackled by decoupling the inertial convective velocity from the velocity deviations. Here, an alternative approach is proposed using regular perturbation expansion, leading to a series of linear closure problems. The Forchheimer correction tensor values from both methods are compared for various Reynolds numbers and flow orientations. The proposed linearized closure approach is shown to be self-consistent and independent of Reynolds number and flow orientations. However, it is limited to Reynolds numbers below one and requires solving higher-dimensional closure problems. Then, macroscopic simulations are performed, highlighting the importance of varying pressure gradient orientations on inertial flows and revealing the necessity to account for extra-diagonal terms in the Forchheimer tensor. Next, the coupling of inertial flow and heat transfer in isothermal porous media is considered. Macroscopic fluid inertial heat transfer models developed with the VAM are compared to the Periodically Developed Flow (PDF) model. Numerical comparisons are conducted first on a reference unit cell and then on macroscopic test cases against DNS. Results reveal discrepancies between VAM and other models at high Péclet numbers. Revisited formulations of the VAM with a different averaged temperature definition and limited length-scale assumptions are proposed to improve accuracy. Additional results show excellent agreement between the revisited VAM models, the PDF model, and DNS for high Péclet number flows. Finally, fluid/solid heat transfer in porous media where a secondary fluid phase maintains a constant temperature is considered. VAM and PDF models are revisited theoretically to account for non-equilibrium fluid/solid heat transfer. Numerical comparisons are performed on a plate-fin heat exchanger 3D unit cell. In the case of an ideally conductive solid phase, numerical results align with previous findings, even for complex geometries. For a solid phase with finite conductivity, the generalized PDF model shows excellent agreement with DNS, while VAM models accurately compute the average temperature in the solid phase. Overall, this work highlights the strengths and limitations of upscaling methods for heat transfer and inertial flow. Methodological developments to the VAM were proposed to improve its predictions for out-of-equilibrium heat transfers, demonstrating its potential as a general framework for modeling complex aircraft heat exchangers.