F. Beux

Multi-level gradient-based methods and parametrisation in aerodynamic shape design

The present study focuses on multi-level approaches in the context of discrete gradient-based methods for aerodynamic shape design. More precisely, the minimisation is done alternatively on different control subspaces according to multigrid-like cycles, providing at each sub-level a particular gradient preconditioning. Starting from an existing multi-level gradient-based formulation associated to shape grid-points coordinates, a possible generalisation to more compact shape representations is proposed through the construction of adequate sets of embedded shape sub-parametrisations. The behaviour of the new formulation is illustrated on different 2D inverse problems for inviscid flows.

Towards the simulation of cavitating flows in inducers through a homogeneous barotropic flow model

The present paper describes the starting efforts made for constructing a numerical frame aimed at simulating propellant flows occurring in the feed turbopumps of modern liquid propellant rocket engines. A homogeneous-flow cavitation model, accounting for thermal effects and active nuclei concentration, is considered, which leads to a barotropic state law. The 3D continuity and momentum equations for compressible inviscid flows are discretized by a finite-volume approach, applicable to unstructured grids. The numerical fluxes are computed through a shock-capturing Roe-type upwind scheme, defined for barotropic flows. The accuracy of the proposed method at low Mach numbers is ensured by ad-hoc preconditioning, which only modifies the upwind part of the numerical flux; thus, the time consistency is maintained and the proposed method can also be used for unsteady problems. Time advancing is carried out by an implicit linearized scheme, in which the linearization only exploits the properties of the Roe matrix. Examples of applications are provided for flow configurations of increasing geometric complexity, viz. some 1D validation benchmarks, the flow around a hydrofoil mounted in a tunnel and the flow in a turbo-pump inducer.

Numerical Simulation of the Flow in a Turbopump Inducer in Non-Cavitating and Cavitating Conditions

A numerical methodology for the simulation of cavitating flows in real complex geometries is presented. A homogeneous-flow cavitation model, accounting for thermal effects and active nuclei concentration, which leads to a barotropic state law is adopted. The continuity and momentum equations are discretized through a mixed finite-element/finite-volume approach, applicable to unstructured grids. A robust preconditioned low-diffusive HLL scheme is used to deal with all speed barotropic flows. Second-order accuracy in space is obtained through MUSCL reconstruction. Time advancing is carried out by a second-order implicit linearized formulation together with the Defect Correction technique. The flow in a real 3D inducer for rockets turbopumps is simulated for a wide range of conditions: different flow rates and rotating speeds as well as non-cavitating and cavitating flows are considered. The results obtained with this numerical approach are compared with experimental data.

Multilevel gradient method with Bezier parametrisation for aerodynamic shape optimisation

A new multilevel strategy for gradient-based method in aerodynamic optimum shape design is nproposed. This approach acts within the development of efficient algorithms for shape optimisation nproblem, in which the governing equations resolution requires a high computational cost. nThe proposed algorithm, based on the degree elevation property of Bezier curve for the nparametrisation construction, can be interpreted in two different ways. Indeed, a descent ndirection is obtained considering as control variables shape grid-point coordinates as well nas Bezier control points. We intend to investigate the algorithm behaviour for a 2D nozzle ninverse problem and inviscid flows. n n[ DOI : 10.1685/CSC06110] About DOI

Nonlinear pressure and temperature waves propagation in fluid-saturated rocks

A numerical study for the simulation of rock deformation due to nonlinear temperature and pressure waves in fluid saturated porous rock is presented. The problem of an homogeneous, thermoelastic, and isotropic fluid-saturated matrix, lying over an aquifer in hyperthermal domain an limited by an upper free surface is considered. The equations of thermo-poro-elasticity, the energy balance and Darcy equation are employed to model the deformation induced by pressure and temperature gradients originating from the source at depth. The numerical approach adopted to solve the nonlinear problem is based on a cubic finite-element method for the spatial discretization and an implicit scheme for the temporal discretization. This work essentially provides a numerical tool for interpreting some geophysical phenomena, in particular for the study of ground uplift in volcanic areas such as Rabaul caldera, Long Valley caldera, and Campi Flegrei. Some experiments and results are presented.

Nonlinear pressure and temperature waves propagation in fluid saturated rock

In this study, we consider a non-linear one dimensional model for temperature and pressure waves in fluid saturated porous rock due to abrupt variations in depth. The geological system studied, illustrated in Fig.1, represents a horizontal medium overlying an aquifer in a hypertermal domain. The aquifer consist of a homogeneus isotropic deep horizon identified as a source of temperature or pressure change (for exemple, magma due to intrusion, friction fault phenomena, etc.). This is covered by a homogeneous isotropic upper horizon, with a lower temperature, represented by a fluid-saturated porous permeable medium.