Large low speed hydrogenerators - UMP and additional damper losses in eccentricity conditions

The present thesis is an advanced contribution to the design process of large synchronous generators with high number of poles. It proposes two original contributions, the first one allowing a very precise prediction of the no-load voltage and of the no-load losses in the damper winding, the second one allowing a rigorous calculation of the unbalanced magnetic pulls and of the associated losses in the damper winding in the case of a machine in eccentricity conditions or with any kind of rotor and stator deformation. Both contributions are based on the same strategy, apart from the fact that it has to be taken into account that the geometry is not the same in both cases, it is supposed perfect in the first case and damaged in the second. The magnetostatic 2D finite element method (FEM) is used to determine the magnetic coupling of the machine conductors as a function of the rotor position. These values of magnetic coupling are then used in the voltage equations of the machine which are solved using a numerical method. A particularity is the calculation of the magnetic flux coupled with a conductor in two situations, once with only the field winding currents, fixing the levels of saturation, and once with field winding currents and a current in one damper bar. This strategy leads to the concept of differential inductances. The two contributions are different because for the first one the geometric, cyclic periodicity of the machine is of one stator slot pitch and for the damaged machine no short cyclic periodicity can be found. In the first case the values of flux linkage and the inductances necessary for the voltage prediction are therefore calculated only for some rotor positions within one stator slot pitch. These values are then reused for all other rotor positions. This method allows to predict the currents and the losses in the damper winding, as well as the no-load voltage waveform with the same precision as a transient magnetic FEM simulation but reducing the simulation time by a factor of about 20. Comparisons with measurements and with transient magnetic FEM simulations on several operating units prove the precision of this approach. As in the case of the calculation of the unbalanced magnetic pulls and of the associated losses in the damper winding for a machine with damaged geometry one can not take advantage of a short geometric periodicity, the procedure has to be different. Again the magnetic coupling of the different circuits is calculated in advance using the magnetostatic FEM, but in this case without rotation of the rotor. The stator slotting can be neglected because it does not influence the aimed results. Any kind of geometric deformation is represented by contiguous segments, placed on the interior stator surface, which can be displaced radially in both directions. A correct adjustment in time of the air gap value of each segment allows to represent any combination of static and dynamic deformation of the air gap for any position of the rotor. The use of a linear superposition of the linearized influences of all segments on the values of magnetic coupling and on the inductances allows to reduce the number of preliminary magnetostatic FEM calculations to the minimum. It has to be specified that the preliminary magnetostatic 2D FEM calculations are carried out only once for a given machine. They can then be used for different deformations of the geometry. If one wants to use the transient magnetic 2D FEM the whole approach has to be repeated for every geometric deformation to be analyzed. The results obtained haven been systematically compared to results obtained through transient magnetic FEM calculations. The agreement is excellent and the reduction of calculation time is enormous. Both contributions were implemented in highly automatized tools; they are therefore well adapted to an industrial application.

Adaptive analysis-aware defeaturing

Ondine Gabrielle Chanon

Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, depending on the partial differential equation that one wants to solve in the geometrical model of interest, removing some important geometrical features may greatly impact the solution accuracy. For instance, in solid mechanics simulations, such features can be holes or fillets near stress concentration regions. Unfortunately, the effect of geometrical simplification on the accuracy of the problem solution is often neglected, because its analysis is a time-consuming task that is often performed manually, based on the expertise of engineers. It is therefore important to have a better understanding of the effect of geometrical model simplification, also called defeaturing, to improve our control on the simulation accuracy along the design and analysis phase.In this thesis, we formalize the process of defeaturing, and we analyze its impact on the accuracy of solutions of some partial differential problems. To achieve this goal, we first precisely define the error between the problem solution defined in the exact geometry, and the one defined in the simplified geometry. Then, we introduce an a posteriori estimator of the energy norm of this error. This allows us to reliably and efficiently control the error coming from the addition or the removal of geometrical features. We subsequently consider a finite element approximation of the defeatured problem, and the induced numerical error is integrated to the proposed defeaturing error estimator. In particular, we address the special case of isogeometric analysis based on (truncated) hierarchical B-splines, in possibly trimmed and multipatch geometries. In this framework, we derive a reliable a posteriori estimator of the overall error, i.e., of the error between the exact solution defined in the exact geometry, and the numerical solution defined in the defeatured geometry.We then propose a two-fold adaptive strategy for analysis-aware defeaturing, which starts by considering a coarse mesh on a fully-defeatured computational domain. On the one hand, the algorithm performs classical finite element mesh refinements in a (partially) defeatured geometry. On the other hand, the strategy also allows for geometrical refinement. That is, at each iteration, the algorithm is able to choose which missing geometrical features should be added to the simplified geometrical model, in order to obtain a more accurate solution.Throughout the thesis, we validate the presented theory, the properties of the aforementioned estimators and the proposed adaptive strategies, thanks to an extensive set of numerical experiments.

EPFL2022

Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization

Elena Faggiano, Andrea Manzoni, Alfio Quarteroni, Gianluigi Rozza

In this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD-Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to carry out sensitivity analysis studies, so far out of reach. In particular, a reduced-order simulation takes only a few minutes to run, resulting in computational savings of 99% of CPU time with respect to the full-order discretization. Moreover, the error between full-order and reduced-order solutions is also studied, and it is numerically found to be less than 1% for reduced-order solutions obtained with just O(100) online degrees of freedom. (C) 2016 Elsevier Inc. All rights reserved.

Elsevier2016

Stabilized isogeometric discretizations on trimmed and union geometries, and weak imposition of the boundary conditions for the Darcy flow

Riccardo Puppi

Modern manufacturing engineering is based on a

design-through-analysis'' workflow. According to this paradigm, a prototype is first designed with Computer-aided-design (CAD) software and then finalized by simulating its physical behavior, which usually involves the simulation of Partial Differential Equations (PDEs) on the designed product. The simulation of PDEs is often performed via finite element discretization techniques.A severe bottleneck in the entire process is undoubtedly the interaction between the design and analysis phases. The prototyped geometries must undergo the time-consuming and human-involved meshing and feature removal processes to become

analysis-suitable''. This dissertation aims to develop and study numerical solvers for PDEs to improve the integration between numerical simulation and geometric modeling. The thesis is made of two parts. In the first one, we focus our attention on the analysis of isogeometric methods which are robust in geometries constructed using Boolean operations. We consider geometries obtained via trimming (or set difference) and union of multiple overlapping spline patches. As differential model problems, we consider both elliptic (the Poisson problem, in particular) and saddle point problems (the Stokes problem, in particular). As it is standard, the Nitsche method is used for the weak imposition of the essential boundary conditions and to weakly enforce the transmission conditions at the interfaces between the patches. After proving through well-constructed examples that the Nitsche method is not uniformly stable, we design a minimal stabilization technique based on a stabilized computation of normal fluxes (and on a simple modification of the pressure space in the case of the Stokes problem). The main core of this thesis is devoted to the derivation and rigorous mathematical analysis of a stabilization procedure to recover the well-posedness of the discretized problems independently of the geometric configuration in which the domain has been constructed. In the second part of the thesis, we consider a different approach. Instead of considering the underlying spline parameterization of the geometrical object, we immerse it in a much simpler and readily meshed domain. From the mathematical point of view, this approach is closely related to the isogeometric discretizations in trimmed domains treated in the first part. In this case, we consider the Raviart-Thomas finite element discretization of the Darcy flow. First, we analyze a Nitsche and a penalty method for the weak imposition of the essential boundary conditions on a boundary fitted mesh, a problem that was not studied before, not needed for our final goal, but still interesting by itself. Then, we consider the case of a general domain immersed in an underlying mesh unfitted with the boundary. We focus on the Nitsche method presented for the boundary fitted case and study its extension to the unfitted setting. We show that the so-called ghost penalty stabilization provides an effective solution to recover the well-posedness of the formulation and the well-conditioning of the resulting linear system.

EPFL2022

Stabilized isogeometric discretizations on trimmed and union geometries, and weak imposition of the boundary conditions for the Darcy flow

Riccardo Puppi

Modern manufacturing engineering is based on a

design-through-analysis'' workflow. According to this paradigm, a prototype is first designed with Computer-aided-design (CAD) software and then finalized by simulating its physical behavior, which usually involves the simulation of Partial Differential Equations (PDEs) on the designed product. The simulation of PDEs is often performed via finite element discretization techniques.A severe bottleneck in the entire process is undoubtedly the interaction between the design and analysis phases. The prototyped geometries must undergo the time-consuming and human-involved meshing and feature removal processes to become

EPFL2022

Adaptive analysis-aware defeaturing

Ondine Gabrielle Chanon

EPFL2022