Modélisation par une approche milieu poreux de l'instabilité fluidélastique dans un faisceau de tubes soumis à un écoulement diphasique transverse

This work deals with the prediction the fluidelastic instability onset in a tube bundle subject to a two-phase cross-flow. The study of two-phase flows leads to numerous industrial applications, in particular in the nuclear energy field. Indeed, nuclear plants steam generators are subject to two-phase cross-flows that cause damaging vibrations. Repetitive stresses in the structure lead to mechanical fatigue that have many important consequences ranging from regular maintenance partial shutdowns of the plant to a nuclear incident. Steam generators are immense tube arrays counting up to hundreds of thousands of tubes, which makes their study a difficult task. Among the cause of these vibrations, the fluidelastic mechanism is certainly the most destructive one. Therefore, a lot of effort is being put within the research community into understanding this phenomenon and developing tools to predict its triggering. The present study aims at modeling and numerically simulating this instability in a tube bundle subject to a two-phase cross-flow. The main challenge is to develop a model able to simulate a bundle counting numerous tubes with a low computational cost, which is not possible with a direct approach (Direct Numerical Simulations, DNS). First, the averaging technique is presented and then applied to continuity and momentum conservation equations for both the flow and the structure. As the consequence, the model of the porous medium is obtained, in which the fluide-structure interactions are modeled and lumped into the equations. The modified form of the Navier--Stokes equations obtained is significantly cheaper in terms of computational cost. First, the volume averaging process filters many details of the flow such as the geometry of the tubes and small-scale vortices. The resulting macroscopic model presents smoother variations so that coarser meshes may be used. Second, the fluid mesh and the tubes are independent. Therefore, fixed meshes may be used to simulate unsteady problems. The averaged equations are solved by a finite element method and the code is verified using the method of manufactured solutions. Calibration and validation are conducted by comparing the results of simple test cases simulations to the results obtained by DNS simulations. The latter corresponds to the full-order model and results of fluid-structure simulations were presented in recent publications. Simulations were run for a tube bundle subject to a single-phase cross-flow using the porous medium model. The values of the fluidelastic onset critical velocity were compared to those obtained using DNS and to experimental data found in the literature. The predictions obtained tend to be overestimated with respect to reference data. The reason may be that the model itself fails to accurately represent the coupling of neighboring tubes. However, the porous medium approach is significantly less costly than DNS. The porous medium model is then extended to two-phase flows and more precisely to gas-liquid mixtures. The investigation is restricted to bubbly flows and low void fraction in order to stay within the physical boundaries of the model. The two-phase mixture is modeled by an Euler-Euler approach and gas-liquid interactions are modeled. The resulting code is again verified and validated and the results of the numerical simulations are compared to experimental data from the literature and local technical reports. The results obtained overestimate the values of the fluidelastic instability onset critical velocity. Nevertheless, the gap observed seems to be due to the single-phase fluid-structure coupling model. The reasons of scatter between the numerical results and experimental data are investigated and suggestions are made in order to improve the porous medium model.