Boundary Element and Finite Element Coupling for Aeroacoustics Simulations

We consider the scattering of acoustic perturbations in a presence of a flow. We suppose that the space can be split into a zone where the flow is uniform and a zone where the flow is potential. In the first zone, we apply a Prandtl-Glauert transformation to recover the Helmholtz equation. The well-known setting of boundary element method for the Helmholtz equation is available. In the second zone, the flow quantities are space dependent, we have to consider a local resolution, namely the finite element method. Herein, we carry out the coupling of these two methods and present various applications and validation test cases. The source term is given through the decomposition of an incident acoustic field on a section of the computational domain's boundary.Comment: 25 page

Etude mathématique et numérique de la propagation acoustique d'un turboréacteur

This thesis deals with the industrial problem of modelisation andnumerical simulation of the acoustic radiation from fan duct air entry. The physicalhypothesis subsequent to the industrial framework give way to a simplifiedmodel of linear acoustic propagation upon a non linear potential flow. Enginemodal noise source modelisation requires acoustic boundary conditions througha Dirichlet-Neumann operator. Existence and uniqueness of the global mathematicalproblem (a convected Sommerfeld condition is added) of the potentialand local perturbation from a uniform flow are prooved. A discrete couplingbetween the volumic acoustic potential (finite volumic elements) and its ellipticnormal derivate (boundary finite element) through an integral equation isexhibed. Computing code is validated analytically and comparatively. Originalresults are described and prove the necessity to consider the nonlinearity of theflow by differences greater than 5 dBs in the far field acoustic diagrams. Optimalpositionning of the radiating surface and the plugability of the fast multipolemethod make this coupling unmissable. Simplified potential-linear model, evenif its range of validity is restricted to the fan duct air entry, gets his whole interestas a brick in a global domain decomposition code. By the way, let's mentionthe achievement of a natural axisymetric finite element and an alternative methodto the calculus of the non linear flow by a fixed point method.Cette thèse traite du problème industriel de la modélisation et dela simulation numérique du rayonnement acoustique à l'entrée d'air des nacellesd'Airbus. Les hypothèses physiques subséquentes au contexte industrielprécis conduisent à un modèle simplifié de propagation acoustique linéaire surun écoulement porteur potentiel et non-linéaire. La modélisation de la sourcemodale de bruit du moteur se traduit par une condition de bord exprimée parun opérateur Dirichlet-Neumann. L'existence et l'unicité du problème mathématiquegénéral (auquel on a rajouté une condition de Sommerfeld convectée)de la perturbation potentielle et locale autour d'un écoulement uniforme sontdémontrées. Un couplage discret alliant le potentiel acoustique (éléments finisde volume) et sa dérivée conormale de bord (éléments finis de frontière) par uneéquation intégrale est proposé. Le code informatique est validé analytiquementet comparativement. Les résultats originaux prouvent la nécessité de la prise encompte des non-linéarités de l'écoulement par des différences de plus de 5 décibelsen champ lointain. Le positionnement optimal de la surface rayonnante etla possibilité d'adaptation de la méthode multipôle rapide rendent ce couplageincontournable. Le modèle simplifié potentiel-linéaire, même si il n'est a prioriapte qu'à traiter l'entrée d'air, trouve toute sa justification en tant que briqued'un code global basé sur la décomposition de domaine. Finalement, soulignonsl'avènement d'un élément fini axisymétrique naturel et d'une alternative originalede calcul de l'écoulement non-linéaire par une méthode de point fixe

Etude mathématique et numérique du rayonnement acoustique d'un turboréacteur

Cette thèse traite du problème industriel de la modélisation et de la simulation numérique du rayonnement acoustique à l entrée d air des nacelles d Airbus. Les hypothèses physiques subséquentes au contexte industriel précis conduisent à un modèle simplifié de propagation acoustique linéaire sur un écoulement porteur potentiel et non-linéaire. La modélisation de la source modale de bruit du moteur se traduit par une condition de bord exprimée par un opérateur Dirichlet-Neumann. L existence et l unicité du problème mathématique général (auquel on a rajouté une condition de Sommerfeld convectée) de la perturbation potentielle et locale autour d un écoulement uniforme sont démontrées. Un couplage discret alliant le potentiel acoustique (éléments finis de volume) et sa dérivée conormale de bord (éléments finis de frontière) par une équation intégrale est proposé. Le code informatique est validé analytiquement et comparativement. Les résultats originaux prouvent la n ecessit e de la prise en compte des non-linéarités de l écoulement par des différences de plus de 5 décibels en champ lointain. Le positionnement optimal de la surface rayonnante et la possibilité d adaptation de la méthode multiple rapide rendent ce couplage incontournable. Le modèle simplifié potentiel-linéaire, même si il n est a priori apte qu a traiter l entrée d air, trouve toute sa justification en tant que brique d un code global basé sur la décomposition de domaine. Finalement, soulignons l avènement d un élément fini axisymétrique naturel et dune alternative originale de calcul de l écoulement non-linéaire par une méthode de point fixe.This thesis deals with the industrial problem of modelisation and numerical simulation of the acoustic radiation from fan duct air entry. The physical hypothesis subsequent to the industrial framework give way to a simplified model of linear acoustic propagation upon a non linear potential flow. Engine modal noise source modelisation requires acoustic boundary conditions through a Dirichlet-Neumann operator. Existence and uniqueness of the global mathematical problem (a convected Sommerfeld condition is added) of the potential and local perturbation from a uniform flow are prooved. A discrete coupling between the volumic acoustic potential (finite volumic elements) and its elliptic normal derivate (boundary finite element) through an integral equation is exhibed. Computing code is validated analytically and comparatively. Original results are described and prove the necessity to consider the nonlinearity of the flow by differences greater than 5 dBs in the far field acoustic diagrams. Optimal positionning of the radiating surface and the plugability of the fast multipole method make this coupling unmissable. Simplified potential-linear model, even if its range of validity is restricted to the fan duct air entry, gets his whole interest as a brick in a global domain decomposition code. By the way, lets mention the achievement of a natural axisymetric finite element and an alternative method to the calculus of the non linear flow by a fixed point method.NANCY1-SCD Sciences & Techniques (545782101) / SudocSudocFranceF

Global, regional, and national burden of diabetes from 1990 to 2021, with projections of prevalence to 2050: a systematic analysis for the Global Burden of Disease Study 2021

Background: Diabetes is one of the leading causes of death and disability worldwide, and affects people regardless of country, age group, or sex. Using the most recent evidentiary and analytical framework from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD), we produced location-specific, age-specific, and sex-specific estimates of diabetes prevalence and burden from 1990 to 2021, the proportion of type 1 and type 2 diabetes in 2021, the proportion of the type 2 diabetes burden attributable to selected risk factors, and projections of diabetes prevalence through 2050. Methods: Estimates of diabetes prevalence and burden were computed in 204 countries and territories, across 25 age groups, for males and females separately and combined; these estimates comprised lost years of healthy life, measured in disability-adjusted life-years (DALYs; defined as the sum of years of life lost [YLLs] and years lived with disability [YLDs]). We used the Cause of Death Ensemble model (CODEm) approach to estimate deaths due to diabetes, incorporating 25 666 location-years of data from vital registration and verbal autopsy reports in separate total (including both type 1 and type 2 diabetes) and type-specific models. Other forms of diabetes, including gestational and monogenic diabetes, were not explicitly modelled. Total and type 1 diabetes prevalence was estimated by use of a Bayesian meta-regression modelling tool, DisMod-MR 2.1, to analyse 1527 location-years of data from the scientific literature, survey microdata, and insurance claims; type 2 diabetes estimates were computed by subtracting type 1 diabetes from total estimates. Mortality and prevalence estimates, along with standard life expectancy and disability weights, were used to calculate YLLs, YLDs, and DALYs. When appropriate, we extrapolated estimates to a hypothetical population with a standardised age structure to allow comparison in populations with different age structures. We used the comparative risk assessment framework to estimate the risk-attributable type 2 diabetes burden for 16 risk factors falling under risk categories including environmental and occupational factors, tobacco use, high alcohol use, high body-mass index (BMI), dietary factors, and low physical activity. Using a regression framework, we forecast type 1 and type 2 diabetes prevalence through 2050 with Socio-demographic Index (SDI) and high BMI as predictors, respectively. Findings: In 2021, there were 529 million (95% uncertainty interval [UI] 500-564) people living with diabetes worldwide, and the global age-standardised total diabetes prevalence was 6·1% (5·8-6·5). At the super-region level, the highest age-standardised rates were observed in north Africa and the Middle East (9·3% [8·7-9·9]) and, at the regional level, in Oceania (12·3% [11·5-13·0]). Nationally, Qatar had the world's highest age-specific prevalence of diabetes, at 76·1% (73·1-79·5) in individuals aged 75-79 years. Total diabetes prevalence-especially among older adults-primarily reflects type 2 diabetes, which in 2021 accounted for 96·0% (95·1-96·8) of diabetes cases and 95·4% (94·9-95·9) of diabetes DALYs worldwide. In 2021, 52·2% (25·5-71·8) of global type 2 diabetes DALYs were attributable to high BMI. The contribution of high BMI to type 2 diabetes DALYs rose by 24·3% (18·5-30·4) worldwide between 1990 and 2021. By 2050, more than 1·31 billion (1·22-1·39) people are projected to have diabetes, with expected age-standardised total diabetes prevalence rates greater than 10% in two super-regions: 16·8% (16·1-17·6) in north Africa and the Middle East and 11·3% (10·8-11·9) in Latin America and Caribbean. By 2050, 89 (43·6%) of 204 countries and territories will have an age-standardised rate greater than 10%. Interpretation: Diabetes remains a substantial public health issue. Type 2 diabetes, which makes up the bulk of diabetes cases, is largely preventable and, in some cases, potentially reversible if identified and managed early in the disease course. However, all evidence indicates that diabetes prevalence is increasing worldwide, primarily due to a rise in obesity caused by multiple factors. Preventing and controlling type 2 diabetes remains an ongoing challenge. It is essential to better understand disparities in risk factor profiles and diabetes burden across populations, to inform strategies to successfully control diabetes risk factors within the context of multiple and complex drivers. Funding: Bill & Melinda Gates Foundation