Towards a New Turbulence Model Based on Lagrangian Flows, Reduced Order Models, and Global-Local Approximations

Although the Navier-Stokes equations represent correctly both, laminar fluid flows as well as turbulent ones, the current power of the computers does not allow solving the latter without making empirical approximations that make the results are only predictable within the same margins from which the empirical approximation was realized. Taking into account that the vast majority of fluid flows that must be simulated by the industries are indeed of a turbulent nature, this makes it worthwhile to continue improving the models so that they fit more and more with the physicsmathematic equations. The current project in which we are working is in that sense. Based on previous work, we are proposing a new turbulence model that fits more with the physic and can be solved in one of the current computer. Always within the multi-scale models, in which all the turbulence model are based, the new idea consists in: a) treating the macro-scale with lagrangian particles, which convect and diffuse the turbulence; b) solving the micro-scale as a problem of unstable laminar fluid flow subjected to velocity gradients; c) applying a Reduction Order Model (ROM) to the micro-scale; d) going from the microscale to the macro-scale as in a Global-Local Model with a ROM.Publicado en: Mecánica Computacional, vol. XXXV, no 1.Facultad de Ingenierí

Towards a New Turbulence Model Based on Lagrangian Flows, Reduced Order Models, and Global-Local Approximations

Although the Navier-Stokes equations represent correctly both, laminar fluid flows as well as turbulent ones, the current power of the computers does not allow solving the latter without making empirical approximations that make the results are only predictable within the same margins from which the empirical approximation was realized. Taking into account that the vast majority of fluid flows that must be simulated by the industries are indeed of a turbulent nature, this makes it worthwhile to continue improving the models so that they fit more and more with the physicsmathematic equations. The current project in which we are working is in that sense. Based on previous work, we are proposing a new turbulence model that fits more with the physic and can be solved in one of the current computer. Always within the multi-scale models, in which all the turbulence model are based, the new idea consists in: a) treating the macro-scale with lagrangian particles, which convect and diffuse the turbulence; b) solving the micro-scale as a problem of unstable laminar fluid flow subjected to velocity gradients; c) applying a Reduction Order Model (ROM) to the micro-scale; d) going from the microscale to the macro-scale as in a Global-Local Model with a ROM.Publicado en: Mecánica Computacional, vol. XXXV, no 1.Facultad de Ingenierí

Incompressible lagrangian fluid flow with thermal coupling

A method is presented for the solution of an incompressible viscous fluid flow with heat transfer and solidification using a fully Lagrangian description of the motion. The originality of this method consists in assembling various concepts and techniques which appear naturally due to the Lagrangian formulation. First of all, the Navier-Stokes equations of motion coupled with the Boussinesq approximation must be reformulated in the Lagrangian framework, whereas they have been mostly derived in an Eulerian context. Secondly, the Lagrangian formulation implies to follow the material particles during their motion, which means to convect the mesh in the case of the Finite Element Method (FEM), the spatial discretisation method chosen in this work. This provokes various difficulties for the mesh generation, mainly in three dimensions, whereas it eliminates the classical numerical difficulty to deal with the convective term, as much in the Navier-Stokes equations as in the energy equation. Even without the discretization of the convective term, an efficient iterative solver, which constitutes the only viable alternative for three dimensional problems, must be designed for the class of Generalized Stokes Problems (GSP), which could be able to behave well independently of the mesh Reynolds number, as it can vary greatly for coupled fluid-thermal analysis. Moreover, it offers a natural framework to treat free-surface problems like wave breaking and rough fluid-structure contact. On one hand, the convection of the mesh during one time step after the resolution of the non-linear system provides explicitly the locus of the domain to be considered. On the other hand, fluid-to-fluid and fluid-to-wall contact, as well as the update of the domain due to the remeshing, must be accurately and efficiently performed. Finally, the solidification of the fluid coupled with its motion through a variable viscosity is considered An efficient overall algorithm must be designed to bring the method effective, particularly in a three dimensional context, which is the ambition of this monograph. Various numerical examples are included to validate and highlight the potential of the method

Particle finite element method in fluid-mechanics including thermal convection-diffusion

A method is presented for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of the motion. Due to the severe element distortion, a frequent remeshing is performed in an efficient manner. An implicit time integration through a classical fractional step is presented. The non-linearities of the formulation are taken into account and solved with the fixed-point iteration method. The displacement and temperature solutions are coupled through the Boussinesq approximation. The Lagrangian formulation provides an elegant way of solving free-surface problems with thermal convection as the particles are followed during their motion. To illustrate the method, the Rayleigh–Bénard instability with and without free surface in two dimensions has been computed

Fractional step like schemes for free surface problems with thermal coupling using the Lagrangian PFEM

The method presented in Aubry et al. (Comput Struc 83:1459–1475, 2005) for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of motion is extended to three dimensions (3D) with particular emphasis on mass conservation. A modified fractional step (FS) based on the pressure Schur complement (Turek 1999), and related to the class of algebraic splittings Quarteroni et al. (Comput Methods Appl Mech Eng 188:505–526, 2000), is used and a new advantage of the splittings of the equations compared with the classical FS is highlighted for free surface problems. The temperature is semi-coupled with the displacement, which is the main variable in a Lagrangian description. Comparisons for various mesh Reynolds numbers are performed with the classical FS, an algebraic splitting and a monolithic solution, in order to illustrate the behaviour of the Uzawa operator and the mass conservation. As the classical fractional step is equivalent to one iteration of the Uzawa algorithm performed with a standard Laplacian as a preconditioner, it will behave well only in a Reynold mesh number domain where the preconditioner is efficient. Numerical results are provided to assess the superiority of the modified algebraic splitting to the classical FS

Objectivity tests for Navier–Stokes simulations: The revealing of non-physical solutions produced by Laplace formulations

Laplace formulations are weak formulations of the Navier–Stokes equations commonly used in computational fluid dynamics. In these schemes, the viscous terms are given as a function of the Laplace diffusion operator only. Despite their popularity, recently, it has been proven that they violate a fundamental principle of continuum mechanics, the principle of objectivity. It is remarkable that such flaw has not being noticed before, neither detected in numerical experiments. In this work, a series of objectivity tests have been designed with the purpose of revealing such problem in real numerical experiments. Through the tests it is shown how, for slip boundaries or free-surfaces, Laplace formulations generate non-physical solutions which widely depart from the real fluid dynamics. These tests can be easily reproduced, not requiring complex simulation tools. Furthermore, they can be used as benchmarks to check consistency of developed or commercial software. The article is closed with a discussion of the mathematical aspects involved, including the issues of boundary conditions and objectivity

An unstructured grid-based, parallel free surface solver

An unstructured grid-based, parallel-free surface solver is presented. The overall scheme combines a finite-element, equal-order, projection-type 3-D incompressible flow solver with a finite element, 2-D advection equation solver for the free surface equation. For steady-state applications, the mesh is not moved every timestep, in order to reduce the cost of geometry recalculations and surface repositioning. A number of modifications required for efficient processing on shared-memory, cache-based parallel machines are discussed, and timings are shown that indicate scalability to a modest number of processors. The results show good quantitative comparison with experiments and the results of other techniques. The present combination of unstructured grids (enhanced geometrical flexibility) and good parallel performance (rapid turnaround) should make the present approach attractive to hydrodynamic design simulations

Buckling of circular, annular plates of non-uniform thickness

This paper deals with the solution of the title problem in the case where the outer boundary is subjected to uniform, hydrostatic pressure while the inner edge of the plate is free. It is assumed that the plate thickness varies (a) in a discontinuous fashion and (b) linearly. An approximate approach is proposed using polynomial coordinate functions which identically satisfy the boundary conditions at the outer edge, only. The eigenvalues are determined using the optimized Rayleigh-Ritz method and good engineering agreement is shown to exist with buckling parameters obtained by means of a finite element code

Implementación del flujo potencial en CALTEP

La presente Tesis de Master tiene como objetivo la modificación del programa CALTEP2000 estacionario, el cual estudia la transmisión de calor mediante el Método de Elementos Finitos (MEF). Esta modificación pretende adaptar dicho programa al estudio aerodinámico en problemas de fluidos con la aproximación de Flujo Potencial. De esta forma, la adaptación permite soslayar un problema numérico que surge, en fenómenos de flujo alrededor de objetos aerodinámicos que presentan un borde de fuga, si no se toman las precauciones adecuadas. Una vez obtenida esta adaptación, se procede a validarla con un perfil de ala sencillo y el programa educativo ED-Poiss y, posteriormente, con un cilindro circular y con perfiles NACA-63012A y NACAM-12. Debido a la complejidad de estos últimos, se utiliza para validarlos el programa comercial DesignFOIL, especializado en el estudio de perfiles de ala

Modelo de interacción viscosa-invíscida para turbinas eólicas de eje horizontal

Se desarrolla un modelo numérico de interacción viscosa-invíscida para la representación del flujo sobre la pala de una turbina eólica de eje horizontal. El modelo invíscido se basa en el método de los paneles. Las ecuaciones de Prandtl de la capa límite laminar 3D se resuelven mediante la técnica de las diferencias finitas. Se intenta así una mejor descripción del campo fluidodinámico alrededor de las palas y de las fuerzas aerodinámicas actuantes sobre la turbina eólica.A numerical model for the viscous-inviscid interaction has been developed to represent the flow around a horizontal-axis wind turbine blade. The inviscid model is based on a panel method. The Prandtl's equations for the laminar 3D boundary layer are solved by finite-difference techniques. The scope of this work is to improve the calculation of the flow-field around the blades and the aerodynamic forces acting on the wind turbine.Asociación Argentina de Energías Renovables y Medio Ambiente (ASADES