Numerical simulation of aeroacoustics using the variational multiscale method : application to the problem of human phonation

The solution of the human phonation problem applying computational mechanics is covered by several research branches, such as Computational Fluid Dynamics (CFD), biomechanics or acoustics, among others. In the present thesis, the problem is approached from the Computational Aeroacoustics (CAA) point of view and the first main objective consists in developing numerical methods of general application that can take part in the solution of any scenario related to human phonation with a reasonable cost. In this sense, only the compressible Navier-Stokes equations can describe all flow and acoustic scales without any modeling, which is known as Direct Numerical Simulation (DNS), but its computational cost is usually unaffordable. Even in the case of a Large Eddy Simulation (LES), where the small scales are modeled, the cost can still be a handicap due to the complexity of the problem. This drawback gets worse in the low Mach regime due to the large disparity between flow velocity and sound speed, which leads to an ill-conditioning of the system of equations, specially for conservative schemes. At this point, it makes sense to move towards the incompressible flow approximation, bearing in mind the low velocities expected in human phonation problems. Incompressible flows do not yield any acoustics, for which a second problem containing the propagation of the sound sources needs to be modeled and solved. These are the so called hybrid methods, which allow a better conditioning of the problem by segregating flow and acoustic scales. Lighthill's analogy has been taken as starting point for the present work, but its restriction to free-field scenarios has motivated the extension of the method to arbitrary geometries and non-uniform flows. The first development in this direction consists in a splitting of Lighthill's analogy into a quadrupolar and dipolar component, which does not change the original problem but allows assessing the contribution of solid boundaries to the generation of sound. The second step consists in the development of a stabilized Finite Element (FEM) formulation for the Acoustic Perturbation Equations (APE) which account for non-uniform flows and perform a complete filtering of the acoustic scales. The final step assumes the compressible approach but omitting the energy equation and thus considering both flow and acoustic propagation as isentropic. In this case the solver is unified and hence a method for applying compatible boundary conditions for flow and acoustics has been developed. Moreover, the whole numerical framework has been extended to dynamic phonation cases, which require using an Arbitrary Lagrangian Eulerian (ALE) reference. Also, a novel remeshing strategy with conservative interpolation between meshes is presented. In the last chapter a challenging case in human phonation has been chosen for testing the developed computational framework: the fricative phoneme /s/. Unlike vowels, which are voiced sounds defined by a few characteristic frequencies, fricatives cannot be simulated as the propagation of a known analytic solution (glottal pulse) because the sound sources correspond to a wide range of turbulent scales. Therefore, a CFD calculation is mandatory in order to capture all relevant eddies behind the generation of sound. This problem is solved with an LES together with the Variational Multiscale (VMS) stabilization method as turbulence model, which is supplemented with several acoustic formulations when using incompressible flow. The analysis of the results focuses on the numerical representation of turbulence and the acoustic signal at the far-field, which has been compared to experimental recordings. Finally, the role of the upper incisors in the generation of the fricative sound has been evaluated. All simulations have been run with the parallel multiphysics FEM code FEMUSS, based on FORTRAN Object-Oriented-Programming land the OpenMPI parallel library.La solució del problema de la veu humana des de la mecànica computacional és objecte d'estudi per part de diverses disciplines, com per exemple la Dinàmica de Fluids Computacional (CFD), la biomecànica o l'acústica. En la present tesi s'encara el problema des de l'Aeroacústica Computacional (CAA) i el primer objectiu consisteix en desenvolupar mètodes numèrics d'aplicació general que puguin ser part de la solució, amb un cost computacional raonable, de qualsevol escenari relacionat amb la fonació humana. En aquest sentit, només les equacions de flux compressible de Navier-Stokes aconsegueixen descriure totes les escales alhora, tant les dinàmiques com les acústiques, sense recórrer a cap modelització, conegut com a Simulació Numèrica Directa (DNS), però el seu cost computacional és normalment inassumible. Fins i tot en el cas d'una Large Eddy Simulation (LES), on les escales petites són modelades, el cost pot resultar excessiu a causa de la complexitat del problema. Aquest fet encara és més accentuat en el règim de baix nombre de Mach donada la gran disparitat entre la velocitat del fluid i la del so i el conseqüent mal condicionament del sistema d'equacions, sobretot en esquemes conservatius. Per tant, tenint en compte les baixes velocitats de l'aire al tracte vocal, té sentit recórrer a l'aproximació de flux incompressible. Els fluids incompressibles no inclouen la part acústica, de manera que cal calcular un segon problema que descrigui la propagació de les fonts de so. Aquests són els anomenats mètodes híbrids, que permeten un millor condicionament del problema gràcies a la segregació de les escales acústiques de les dinàmiques. S'ha pres l'analogia de Lighthill com a punt de partida, però la seva restricció a casos en camp obert ha motivat l'extensió del mètode cap a geometries arbitràries i fluxos no uniformes. El primer desenvolupament en aquesta direcció consisteix en la divisió de l'analogia de Lighthill en una component quadrupolar i una altra de dipolar, fet que no altera el problema original però que permet analitzar la contribució de cossos sòlids en la generació de so. El segon pas consisteix en el desenvolupament d'una formulació estabilitzada en elements finits (FEM) de les Acoustic Perturbation Equations (APE), que incorporen la propagació en fluxos no uniformes i que realitzen un filtrat complet de les escales acústiques. El pas final assumeix la compressibilitat del fluid però omet l'equació d'energia, i per tant considera la dinàmica i l'acústica fenòmens isentròpics. En aquest cas el solver és unificat i per tant s'ha desenvolupat un mètode per imposar condicions de contorn compatibles entre ambdues escales del fluid. Finalment, les formulacions numèriques han estat adaptades a casos de fonació dinàmica mitjançant una referència Arbitrària Lagrangiana Euleriana (ALE). A més, es presenta una estratègia de remallat amb interpolació conservativa entre malles. En l'últim capítol es presenta un cas de fonació humana que suposa un repte per la seva complexitat i que ha servit per validar les formulacions numèriques presentades: la fricativa sorda /s/. A diferència de les vocals, que són sons sonors definits per unes poques freqüències característiques, les fricatives no poden ser simulades com la propagació d'una funció analítica coneguda (pols glotal) perquè les fonts de so corresponen a un rang ampli d'escales turbulents. Per tant és necessària una simulació CFD per tal de capturar-les. El problema se soluciona amb un model de turbulència LES amb el mètode d'estabilització Variational Multiscale. L'anàlisi se centra en la representació numèrica de la turbulència i en el senyal acústic al camp llunyà, tot comparant-lo amb dades experimentals. Finalment, s'avalua la contribució dels incisius superiors en la generació del so fricatiu sord /s/. Totes les simulacions han estat realitzades amb el codi FEM multi-físic en paral·lel FEMUSS, basat en programació orientada a objectes en FORTRAN i en OpenMPI

An adaptive fixed-mesh ALE method for free surface flows

In this work we present a Fixed-Mesh ALE method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background domain. This mesh is successively refined and unrefined at each time step in order to focus the computational effort on the spatial regions where it is required. Some of the main ingredients of the formulation are the use of an Arbitrary-Lagrangian–Eulerian formulation for computing temporal derivatives, the use of stabilization terms for stabilizing convection, stabilizing the lack of compatibility between velocity and pressure interpolation spaces, and stabilizing the ill-conditioning introduced by the cuts on the background finite element mesh, and the coupling of the algorithm with an adaptive mesh refinement procedure suitable for running on distributed memory environments. Algorithmic steps for the projection between meshes are presented together with the algebraic fractional step approach used for improving the condition number of the linear systems to be solved. The method is tested in several numerical examples. The expected convergence rates both in space and time are observed. Smooth solution fields for both velocity and pressure are obtained (as a result of the contribution of the stabilization terms). Finally, a good agreement between the numerical results and the reference experimental data is obtained.Postprint (published version

Interpolation with restrictions between finite element meshes for flow problems in an ALE setting

This is the peer reviewed version of the following article: [Pont, A., Codina, R., and Baiges, J. (2017) Interpolation with restrictions between finite element meshes for flow problems in an ALE setting. Int. J. Numer. Meth. Engng, 110: 1203–1226. doi: 10.1002/nme.5444.], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5444/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The need for remeshing when computing flow problems in domains suffering large deformations has motivated the implementation of a tool that allows the proper transmission of information between finite element meshes. Because the Lagrangian projection of results from one mesh to another is a dissipative method, a new conservative interpolation method has been developed. A series of constraints, such as the conservation of mass or energy, are applied to the interpolated arrays through Lagrange multipliers in an error minimization problem, so that the resulting array satisfies these physical properties while staying as close as possible to the original interpolated values in the L2 norm. Unlike other conservative interpolation methods that require a considerable effort in mesh generation and modification, the proposed formulation is mesh independent and is only based on the physical properties of the field being interpolated. Moreover, the performed corrections are neither coupled with the main calculation nor with the interpolation itself, for which reason the computational cost is very low.Peer ReviewedPostprint (author's final draft

Residual-based stabilization of the finite element approximation to the acoustic perturbation equations for low Mach number aeroacoustics

This is the peer reviewed version of the following article: [Guasch, O., Sánchez-Martín, P., Pont, A., Baiges, J., and Codina, R. (2016) Residual-based stabilization of the finite element approximation to the acoustic perturbation equations for low Mach number aeroacoustics. Int. J. Numer. Meth. Fluids, 82: 839–857. doi: 10.1002/fld.4243], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/fld.4243/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The acoustic perturbation equations (APE) are suitable to predict aerodynamic noise in the presence of a non-uniform mean flow. As for any hybrid computational aeroacoustics approach, a first computational fluid dynamics simulation is carried out from which the mean flow characteristics and acoustic sources are obtained. In a second step, the APE are solved to get the acoustic pressure and particle velocity fields. However, resorting to the finite element method (FEM) for that purpose is not straightforward. Whereas mixed finite elements satisfying an appropriate inf–sup compatibility condition can be built in the case of no mean flow, that is, for the standard wave equation in mixed form, these are difficult to implement and their good performance is yet to be checked for more complex wave operators. As a consequence, strong simplifying assumptions are usually considered when solving the APE with FEM. It is possible to avoid them by resorting to stabilized formulations. In this work, a residual-based stabilized FEM is presented for the APE at low Mach numbers, which allows one to deal with the APE convective and reaction terms in its full extent. The key of the approach resides in the design of the matrix of stabilization parameters. The performance of the formulation and the contributions of the different terms in the equations are tested for an acoustic pulse propagating in sheared-solenoidal mean flow, and for the aeolian tone generated by flow past a two-dimensional cylinder.Peer ReviewedPostprint (author's final draft

Unified solver for fluid dynamics and aeroacoustics in isentropic gas flows

The high computational cost of solving numerically the fully compressible Navier–Stokes equations, together with the poor performance of most numerical formulations for compressible flow in the low Mach number regime, has led to the necessity for more affordable numerical models for Computational Aeroacoustics. For low Mach number subsonic flows with neither shocks nor thermal coupling, both flow dynamics and wave propagation can be considered isentropic. Therefore, a joint isentropic formulation for flow and aeroacoustics can be devised which avoids the need for segregating flow and acoustic scales. Under these assumptions density and pressure fluctuations are directly proportional, and a two field velocity-pressure compressible formulation can be derived as an extension of an incompressible solver. Moreover, the linear system of equations which arises from the proposed isentropic formulation is better conditioned than the homologous incompressible one due to the presence of a pressure time derivative. Similarly to other compressible formulations the prescription of boundary conditions will have to deal with the backscattering of acoustic waves. In this sense, a separated imposition of boundary conditions for flow and acoustic scales which allows the evacuation of waves through Dirichlet boundaries without using any tailored damping model will be presented.Peer ReviewedPostprint (author's final draft

Simulation of CabriI Loss-Offlow Experiments With The Trace/Fred Codes

This thesis, “Simulation of CABRI loss-of-flow experiments with the TRACE/FRED codes”, is a result of cooperation with IRSN (France), who transferred to PSI the CABRI facility specification and test data. The thesis has mainly two aims: reaching a further validation of the TRACE code for two-phase sodium, currently being performed at Paul Scherrer Institut, and analyzing the fuel behaviour during the transients with the FRED code. The calculations were using coupled TRACE and FRED in frames of the FAST code system. A pure loss-of-flow transient (LOF) and two LOFs followed by transient overpower (TOP) were simulated. Several correlations for critical heat flux (CHF) and post dry-out heat transfer coefficient were implemented and tested in order to achieve a suitable initial model for these phenomena. It was the very first step towards sodium dry-out modelling in the modified version of TRACE. Both thermal-hydraulic and fuel thermal-mechanics results were compared with those provided by the CABRI Project report, and even some benchmarking against other codes was performed.Outgoin

Simulation of CabriI Loss-Offlow Experiments With The Trace/Fred Codes

This thesis, “Simulation of CABRI loss-of-flow experiments with the TRACE/FRED codes”, is a result of cooperation with IRSN (France), who transferred to PSI the CABRI facility specification and test data. The thesis has mainly two aims: reaching a further validation of the TRACE code for two-phase sodium, currently being performed at Paul Scherrer Institut, and analyzing the fuel behaviour during the transients with the FRED code. The calculations were using coupled TRACE and FRED in frames of the FAST code system. A pure loss-of-flow transient (LOF) and two LOFs followed by transient overpower (TOP) were simulated. Several correlations for critical heat flux (CHF) and post dry-out heat transfer coefficient were implemented and tested in order to achieve a suitable initial model for these phenomena. It was the very first step towards sodium dry-out modelling in the modified version of TRACE. Both thermal-hydraulic and fuel thermal-mechanics results were compared with those provided by the CABRI Project report, and even some benchmarking against other codes was performed.Outgoin

Numerical simulation of aeroacoustics using the variational multiscale method : application to the problem of human phonation

The solution of the human phonation problem applying computational mechanics is covered by several research branches, such as Computational Fluid Dynamics (CFD), biomechanics or acoustics, among others. In the present thesis, the problem is approached from the Computational Aeroacoustics (CAA) point of view and the first main objective consists in developing numerical methods of general application that can take part in the solution of any scenario related to human phonation with a reasonable cost. In this sense, only the compressible Navier-Stokes equations can describe all flow and acoustic scales without any modeling, which is known as Direct Numerical Simulation (DNS), but its computational cost is usually unaffordable. Even in the case of a Large Eddy Simulation (LES), where the small scales are modeled, the cost can still be a handicap due to the complexity of the problem. This drawback gets worse in the low Mach regime due to the large disparity between flow velocity and sound speed, which leads to an ill-conditioning of the system of equations, specially for conservative schemes. At this point, it makes sense to move towards the incompressible flow approximation, bearing in mind the low velocities expected in human phonation problems. Incompressible flows do not yield any acoustics, for which a second problem containing the propagation of the sound sources needs to be modeled and solved. These are the so called hybrid methods, which allow a better conditioning of the problem by segregating flow and acoustic scales. Lighthill's analogy has been taken as starting point for the present work, but its restriction to free-field scenarios has motivated the extension of the method to arbitrary geometries and non-uniform flows. The first development in this direction consists in a splitting of Lighthill's analogy into a quadrupolar and dipolar component, which does not change the original problem but allows assessing the contribution of solid boundaries to the generation of sound. The second step consists in the development of a stabilized Finite Element (FEM) formulation for the Acoustic Perturbation Equations (APE) which account for non-uniform flows and perform a complete filtering of the acoustic scales. The final step assumes the compressible approach but omitting the energy equation and thus considering both flow and acoustic propagation as isentropic. In this case the solver is unified and hence a method for applying compatible boundary conditions for flow and acoustics has been developed. Moreover, the whole numerical framework has been extended to dynamic phonation cases, which require using an Arbitrary Lagrangian Eulerian (ALE) reference. Also, a novel remeshing strategy with conservative interpolation between meshes is presented. In the last chapter a challenging case in human phonation has been chosen for testing the developed computational framework: the fricative phoneme /s/. Unlike vowels, which are voiced sounds defined by a few characteristic frequencies, fricatives cannot be simulated as the propagation of a known analytic solution (glottal pulse) because the sound sources correspond to a wide range of turbulent scales. Therefore, a CFD calculation is mandatory in order to capture all relevant eddies behind the generation of sound. This problem is solved with an LES together with the Variational Multiscale (VMS) stabilization method as turbulence model, which is supplemented with several acoustic formulations when using incompressible flow. The analysis of the results focuses on the numerical representation of turbulence and the acoustic signal at the far-field, which has been compared to experimental recordings. Finally, the role of the upper incisors in the generation of the fricative sound has been evaluated. All simulations have been run with the parallel multiphysics FEM code FEMUSS, based on FORTRAN Object-Oriented-Programming land the OpenMPI parallel library.La solució del problema de la veu humana des de la mecànica computacional és objecte d'estudi per part de diverses disciplines, com per exemple la Dinàmica de Fluids Computacional (CFD), la biomecànica o l'acústica. En la present tesi s'encara el problema des de l'Aeroacústica Computacional (CAA) i el primer objectiu consisteix en desenvolupar mètodes numèrics d'aplicació general que puguin ser part de la solució, amb un cost computacional raonable, de qualsevol escenari relacionat amb la fonació humana. En aquest sentit, només les equacions de flux compressible de Navier-Stokes aconsegueixen descriure totes les escales alhora, tant les dinàmiques com les acústiques, sense recórrer a cap modelització, conegut com a Simulació Numèrica Directa (DNS), però el seu cost computacional és normalment inassumible. Fins i tot en el cas d'una Large Eddy Simulation (LES), on les escales petites són modelades, el cost pot resultar excessiu a causa de la complexitat del problema. Aquest fet encara és més accentuat en el règim de baix nombre de Mach donada la gran disparitat entre la velocitat del fluid i la del so i el conseqüent mal condicionament del sistema d'equacions, sobretot en esquemes conservatius. Per tant, tenint en compte les baixes velocitats de l'aire al tracte vocal, té sentit recórrer a l'aproximació de flux incompressible. Els fluids incompressibles no inclouen la part acústica, de manera que cal calcular un segon problema que descrigui la propagació de les fonts de so. Aquests són els anomenats mètodes híbrids, que permeten un millor condicionament del problema gràcies a la segregació de les escales acústiques de les dinàmiques. S'ha pres l'analogia de Lighthill com a punt de partida, però la seva restricció a casos en camp obert ha motivat l'extensió del mètode cap a geometries arbitràries i fluxos no uniformes. El primer desenvolupament en aquesta direcció consisteix en la divisió de l'analogia de Lighthill en una component quadrupolar i una altra de dipolar, fet que no altera el problema original però que permet analitzar la contribució de cossos sòlids en la generació de so. El segon pas consisteix en el desenvolupament d'una formulació estabilitzada en elements finits (FEM) de les Acoustic Perturbation Equations (APE), que incorporen la propagació en fluxos no uniformes i que realitzen un filtrat complet de les escales acústiques. El pas final assumeix la compressibilitat del fluid però omet l'equació d'energia, i per tant considera la dinàmica i l'acústica fenòmens isentròpics. En aquest cas el solver és unificat i per tant s'ha desenvolupat un mètode per imposar condicions de contorn compatibles entre ambdues escales del fluid. Finalment, les formulacions numèriques han estat adaptades a casos de fonació dinàmica mitjançant una referència Arbitrària Lagrangiana Euleriana (ALE). A més, es presenta una estratègia de remallat amb interpolació conservativa entre malles. En l'últim capítol es presenta un cas de fonació humana que suposa un repte per la seva complexitat i que ha servit per validar les formulacions numèriques presentades: la fricativa sorda /s/. A diferència de les vocals, que són sons sonors definits per unes poques freqüències característiques, les fricatives no poden ser simulades com la propagació d'una funció analítica coneguda (pols glotal) perquè les fonts de so corresponen a un rang ampli d'escales turbulents. Per tant és necessària una simulació CFD per tal de capturar-les. El problema se soluciona amb un model de turbulència LES amb el mètode d'estabilització Variational Multiscale. L'anàlisi se centra en la representació numèrica de la turbulència i en el senyal acústic al camp llunyà, tot comparant-lo amb dades experimentals. Finalment, s'avalua la contribució dels incisius superiors en la generació del so fricatiu sord /s/. Totes les simulacions han estat realitzades amb el codi FEM multi-físic en paral·lel FEMUSS, basat en programació orientada a objectes en FORTRAN i en OpenMPI

Numerical simulation of aeroacoustics using the variational multiscale method : application to the problem of human phonation

Premi extraordinari doctorat UPC curs 2017-2018. Àmbit d’Enginyeria Civil i AmbientalThe solution of the human phonation problem applying computational mechanics is covered by several research branches, such as Computational Fluid Dynamics (CFD), biomechanics or acoustics, among others. In the present thesis, the problem is approached from the Computational Aeroacoustics (CAA) point of view and the first main objective consists in developing numerical methods of general application that can take part in the solution of any scenario related to human phonation with a reasonable cost. In this sense, only the compressible Navier-Stokes equations can describe all flow and acoustic scales without any modeling, which is known as Direct Numerical Simulation (DNS), but its computational cost is usually unaffordable. Even in the case of a Large Eddy Simulation (LES), where the small scales are modeled, the cost can still be a handicap due to the complexity of the problem. This drawback gets worse in the low Mach regime due to the large disparity between flow velocity and sound speed, which leads to an ill-conditioning of the system of equations, specially for conservative schemes. At this point, it makes sense to move towards the incompressible flow approximation, bearing in mind the low velocities expected in human phonation problems. Incompressible flows do not yield any acoustics, for which a second problem containing the propagation of the sound sources needs to be modeled and solved. These are the so called hybrid methods, which allow a better conditioning of the problem by segregating flow and acoustic scales. Lighthill's analogy has been taken as starting point for the present work, but its restriction to free-field scenarios has motivated the extension of the method to arbitrary geometries and non-uniform flows. The first development in this direction consists in a splitting of Lighthill's analogy into a quadrupolar and dipolar component, which does not change the original problem but allows assessing the contribution of solid boundaries to the generation of sound. The second step consists in the development of a stabilized Finite Element (FEM) formulation for the Acoustic Perturbation Equations (APE) which account for non-uniform flows and perform a complete filtering of the acoustic scales. The final step assumes the compressible approach but omitting the energy equation and thus considering both flow and acoustic propagation as isentropic. In this case the solver is unified and hence a method for applying compatible boundary conditions for flow and acoustics has been developed. Moreover, the whole numerical framework has been extended to dynamic phonation cases, which require using an Arbitrary Lagrangian Eulerian (ALE) reference. Also, a novel remeshing strategy with conservative interpolation between meshes is presented. In the last chapter a challenging case in human phonation has been chosen for testing the developed computational framework: the fricative phoneme /s/. Unlike vowels, which are voiced sounds defined by a few characteristic frequencies, fricatives cannot be simulated as the propagation of a known analytic solution (glottal pulse) because the sound sources correspond to a wide range of turbulent scales. Therefore, a CFD calculation is mandatory in order to capture all relevant eddies behind the generation of sound. This problem is solved with an LES together with the Variational Multiscale (VMS) stabilization method as turbulence model, which is supplemented with several acoustic formulations when using incompressible flow. The analysis of the results focuses on the numerical representation of turbulence and the acoustic signal at the far-field, which has been compared to experimental recordings. Finally, the role of the upper incisors in the generation of the fricative sound has been evaluated. All simulations have been run with the parallel multiphysics FEM code FEMUSS, based on FORTRAN Object-Oriented-Programming land the OpenMPI parallel library.La solució del problema de la veu humana des de la mecànica computacional és objecte d'estudi per part de diverses disciplines, com per exemple la Dinàmica de Fluids Computacional (CFD), la biomecànica o l'acústica. En la present tesi s'encara el problema des de l'Aeroacústica Computacional (CAA) i el primer objectiu consisteix en desenvolupar mètodes numèrics d'aplicació general que puguin ser part de la solució, amb un cost computacional raonable, de qualsevol escenari relacionat amb la fonació humana. En aquest sentit, només les equacions de flux compressible de Navier-Stokes aconsegueixen descriure totes les escales alhora, tant les dinàmiques com les acústiques, sense recórrer a cap modelització, conegut com a Simulació Numèrica Directa (DNS), però el seu cost computacional és normalment inassumible. Fins i tot en el cas d'una Large Eddy Simulation (LES), on les escales petites són modelades, el cost pot resultar excessiu a causa de la complexitat del problema. Aquest fet encara és més accentuat en el règim de baix nombre de Mach donada la gran disparitat entre la velocitat del fluid i la del so i el conseqüent mal condicionament del sistema d'equacions, sobretot en esquemes conservatius. Per tant, tenint en compte les baixes velocitats de l'aire al tracte vocal, té sentit recórrer a l'aproximació de flux incompressible. Els fluids incompressibles no inclouen la part acústica, de manera que cal calcular un segon problema que descrigui la propagació de les fonts de so. Aquests són els anomenats mètodes híbrids, que permeten un millor condicionament del problema gràcies a la segregació de les escales acústiques de les dinàmiques. S'ha pres l'analogia de Lighthill com a punt de partida, però la seva restricció a casos en camp obert ha motivat l'extensió del mètode cap a geometries arbitràries i fluxos no uniformes. El primer desenvolupament en aquesta direcció consisteix en la divisió de l'analogia de Lighthill en una component quadrupolar i una altra de dipolar, fet que no altera el problema original però que permet analitzar la contribució de cossos sòlids en la generació de so. El segon pas consisteix en el desenvolupament d'una formulació estabilitzada en elements finits (FEM) de les Acoustic Perturbation Equations (APE), que incorporen la propagació en fluxos no uniformes i que realitzen un filtrat complet de les escales acústiques. El pas final assumeix la compressibilitat del fluid però omet l'equació d'energia, i per tant considera la dinàmica i l'acústica fenòmens isentròpics. En aquest cas el solver és unificat i per tant s'ha desenvolupat un mètode per imposar condicions de contorn compatibles entre ambdues escales del fluid. Finalment, les formulacions numèriques han estat adaptades a casos de fonació dinàmica mitjançant una referència Arbitrària Lagrangiana Euleriana (ALE). A més, es presenta una estratègia de remallat amb interpolació conservativa entre malles. En l'últim capítol es presenta un cas de fonació humana que suposa un repte per la seva complexitat i que ha servit per validar les formulacions numèriques presentades: la fricativa sorda /s/. A diferència de les vocals, que són sons sonors definits per unes poques freqüències característiques, les fricatives no poden ser simulades com la propagació d'una funció analítica coneguda (pols glotal) perquè les fonts de so corresponen a un rang ampli d'escales turbulents. Per tant és necessària una simulació CFD per tal de capturar-les. El problema se soluciona amb un model de turbulència LES amb el mètode d'estabilització Variational Multiscale. L'anàlisi se centra en la representació numèrica de la turbulència i en el senyal acústic al camp llunyà, tot comparant-lo amb dades experimentals. Finalment, s'avalua la contribució dels incisius superiors en la generació del so fricatiu sord /s/. Totes les simulacions han estat realitzades amb el codi FEM multi-físic en paral·lel FEMUSS, basat en programació orientada a objectes en FORTRAN i en OpenMPI.Award-winningPostprint (published version

Simulation of CabriI Loss-Offlow Experiments With The Trace/Fred Codes

This thesis, “Simulation of CABRI loss-of-flow experiments with the TRACE/FRED codes”, is a result of cooperation with IRSN (France), who transferred to PSI the CABRI facility specification and test data. The thesis has mainly two aims: reaching a further validation of the TRACE code for two-phase sodium, currently being performed at Paul Scherrer Institut, and analyzing the fuel behaviour during the transients with the FRED code. The calculations were using coupled TRACE and FRED in frames of the FAST code system. A pure loss-of-flow transient (LOF) and two LOFs followed by transient overpower (TOP) were simulated. Several correlations for critical heat flux (CHF) and post dry-out heat transfer coefficient were implemented and tested in order to achieve a suitable initial model for these phenomena. It was the very first step towards sodium dry-out modelling in the modified version of TRACE. Both thermal-hydraulic and fuel thermal-mechanics results were compared with those provided by the CABRI Project report, and even some benchmarking against other codes was performed.Outgoin