1,720,986 research outputs found
An adjoint based pressure boundary optimal control approach for fluid-structure interaction problems
No full textIn this work we investigate a new pressure boundary optimal control approach to the fluid-structure interaction problem based on Lagrangian multipliers and adjoint variables. We consider the steady FSI problem written in variational monolithic form in order to balance automatically solid and liquid forces at the interface and propose a pressure boundary optimal control method with the purpose to control the solid deformation in a well defined region by changing the fluid pressure on domain boundaries. The optimality system is obtained by imposing the first order necessary condition to the Lagrangian functional. In order to couple also the adjoint variables we must introduce a fictitious velocity field in the solid region that balances automatically interface adjoint forces as well. The system is solved in a segregated approach with different optimization schemes, such as the steepest descent and the quasi-Newton methods. We implemented the algorithms in a finite element code with mesh-moving capabilities for the study of large solid displacements. In order to support the proposed approach we perform numerical tests in two and three-dimensional spaces
An adjoint-based temperature boundary optimal control approach for turbulent buoyancy-driven flows
No full textThis paper deals with the adjoint optimal control for turbulent buoyancy-driven flows. The aim of this optimal control problem is to obtain a desired velocity profile and enhance the turbulence intensity in a well defined region by controlling the fluid temperature on domain boundaries and consequently the buoyancy forces. The fluid is assumed to be incompressible within the Boussinesq approximation, while turbulence is considered by coupling the Wilcox k-ω model with the Reynolds Averaged energy and Navier Stokes equations. The state, adjoint and control equations are derived by employing the Lagrangian multipliers method. The optimality system is solved with a finite elements code where a steepest descent algorithm has been implemented in order to find the optimal boundary control parameter. Numerical results are reported to show the robustness of the method in solving strongly-coupled optimality systems with a large number of unknowns
VOF evaluation of the surface tension by using variational representation and Galerkin interpolation projection
No full textIn this work we propose a variational approach with cell-to-point Galerkin projections for studying two-phase interface advection problems dominated by surface tension. A Volume Of Fluid (VOF) algorithm is used for tracking and locating the evolution of the two-phase interface on a Cartesian grid and a finite element numerical scheme for solving the velocity-pressure state. The velocity field that drives the evolution of this interface is computed from the weak form of the Navier-Stokes equation where the surface tension force is represented in variational form by the continuous surface force (CSF) and continuous surface stress (CSS) methods. Standard numerical approaches solve the strong form of the Navier-Stokes equations and define the CSS term by taking the divergence of the surface tension tensor. This computation of the divergence term results in a singular force which is difficult to compute when the grid is refined since the tensor is computed in a discontinuous cell-by-cell way. In this work we use the variational formulation of the Navier-Stokes equation and avoid differentiation. The tensor, which is a function of the unit normal, is evaluated over regular Sobolev spaces by using a cell-to-point Galerkin projection. This allows a regular piece-wise continuous representation of the surface tensor and the unit normal based on the VOF reconstruction. In standard approaches the CSF surface force is computed by using the curvature, which is the divergence of the unit normal. In this paper we recover the curvature with point-wise Galerkin projection avoiding direct differentiation. Tests on convergence for two and three-dimension in the static and dynamical cases are reported to show the correct representation in the desired spaces. This method is also natural for coupling non uniform grid computation of the fluid with Cartesian grid of the VOF algorithm
On the optimal control of stationary fluid⇓structure interaction systems
Full text linkFluid–structure interaction (FSI) systems consist of a fluid which flows and deforms one or more solid surrounding structures. In this paper, we study inverse FSI problems, where the goal is to find the optimal value of some control parameters, such that the FSI solution is close to a desired one. Optimal control problems are formulated with Lagrange multipliers and adjoint variables formalism. In order to recover the symmetry of the stationary state-adjoint system an auxiliary displacement field is introduced and used to extend the velocity field from the fluid into the structure domain. As a consequence, the adjoint interface forces are balanced automatically. We present three different FSI optimal controls: inverse parameter estimation, boundary control and distributed control. The optimality system is derived from the first order necessary condition by taking the Fréchet derivatives of the augmented Lagrangian with respect to all the variables involved. The optimal solution is obtained through a gradient-based algorithm applied to the optimality system. In order to support the proposed approach and compare these three optimal control approaches numerical tests are performed
A multigrid local smoother approach for a domain decomposition solver over non-matching grids
No full textIn this paper we consider a multigrid approach for solving elliptic equations over non-matching grids with domain decomposition methods. The domain is partitioned into subdomains with different mesh levels that do not match at the interface. The proposed algorithm searches for the global solution over different levels by projecting the residuals on the overlap region. This method is used in conjunction with a domain decomposition solver which only requires, in each iteration step, the solutions of several small local subproblems over finite element blocks. This algorithm is shown to converge to the solution of the corresponding Lagrange multiplier problem for non-matching grids. The convergence properties of the algorithms are analyzed and numerical examples are presented. When the multigrid and domain decomposition approaches are combined, the method is shown to be reliable and easy to implement. Furthermore the local nature of the solver allows for a straightforward implementation on multiple parallel computers and graphics processing unit (GPU) clusters
Numerical simulation of a turbulent Lead Bismuth Eutectic flow inside a 19 pin nuclear reactor bundle with a four logarithmic parameter turbulence model
No full textComputational Fluid Dynamic allows scientists and engineers to investigate fluid flow in complex geometries and evaluate heat transfer between a solid body and a fluid. In the present paper we study the heat transfer of a Lead Bismuth Eutectic (LBE) turbulent flow in a bare 19 pin nuclear reactor bundle. When dealing with low Prandtl number fluids, like LBE for which Pr = 0.025, proper turbulence models are needed to improve the prediction of heat transfer. We use here a four logarithmic parameter turbulence model in order to calculate Reynolds stresses and turbulent heat flux. In particular, an equation for temperature fluctuations and one for their dissipation are solved. These variables are used to model thermal characteristic time scales. The results are reported for different values of the Peclet number and a fixed value of the pitch to diameter ratio. The obtained values of the Nusselt number are compared with experimental correlations, that can be found in literature, and with the ones obtained using a Simple Eddy Diffusivity model, where the eddy thermal diffusivity is calculated as proportional to eddy viscosity through a modeled turbulent Prandtl number
A new surface tension VOF evaluation by using variational representation and Galerkin interpolation projection
No full textIn this work we propose a new algorithm for studying two-phase interface advection problems dominated by surface tension. We use a Volume Of Fluid (VOF) algorithm for studying the evolution of the two-phase interface on a Cartesian grid and a finite element numerical scheme for the velocity-pressure state. The velocity field that drives the evolution of this interface is obtained by solving the weak form of the Navier-Stokes equation where the surface tension force is not defined in a singular way. With standard numerical approaches that solve the strong form of the Navier-Stokes equations the surface force is determined by taking the divergence of the surface tension tensor. The computation of the divergence term results in a force which is non-convergent when the grid is refined since the tensor is computed in a discontinuous cell-by-cell way. In the past this approach was proposed with artificial different smoothing schemes in order to compute such a singular force. In this work we use the variational formulation of the Navier-Stokes equation and avoid differentiation. The tensor which is a function of the unit normal is evaluated by a Galerkin projection over regular Sobolev spaces. This allows the piece-wise continuous representation of the surface tensor and the unit normal based on the VOF reconstruction. Tests on convergence for two and three-dimension in the static and dynamical cases are reported to show the correct representation in the desired spaces. This method is also natural for coupling non uniform grid computation of the fluid with Cartesian grid of the VOF algorithm
A multiscale fluid structure interaction model derived from Koiter shell equations
No full textIn this work we propose the numerical simulation of fluid structure interaction (FSI) problem by using a membrane model, derived from the Koiter shell equations. With this approach the thickness of the solid wall can be neglected, with a meaningful reduction of the computational cost of the numerical problem. The fluid structure problem is then reduced to the fluid equations on a moving mesh together with a particular Robin boundary condition imposed on the surface corresponding to the solid moving wall. Furthermore an artificial absorbing outflow boundary condition has been implemented in order to reduce the damping and reflections of the pressure waves at the domain's outlet. This model is implemented and solved with an in-house finite elements code, and tested through axisymmetric cases that show the robustness of the developed algorithm. Finally, we report a comparison of the implemented model with results of a FSI monolithic model, based on non-linear incompressible structure
Numerical simulation of a liquid sodium turbulent flow over a backward facing step with a four parameter logarithmic turbulence model
No full textIn recent years a great interest has grown around liquid metals. These fluids are characterized by much higher thermal conductivity, if compared with standard fluids like air and water and can be used in applications where large heat fluxes are present while being subjected to small temperature gradients. In the present paper we simulate a turbulent flow of liquid sodium, with a Prandtl number equal to 0.0088, over a vertical backward-facing step. A uniform heat flux is applied on the vertical wall next to the change of cross section. Reynolds stresses and turbulent heat flux are modeled with a four logarithmic parameter turbulence model. We investigate the cases of purely forced convection, where the temperature field is just a passive scalar, and of mixed convection, where temperature has an impact on the fluid behavior through a buoyancy term that is introduced in the momentum equation with the Boussinesq approximation. The results are reported for various values of the Richardson number, i.e. Ri=0 for the purely forced convection and Ri>0 for the mixed convection case, and compared with data coming from Direct Numerical Simulations that are available in literature
Optimal pressure boundary control of steady multiscale fluid-structure interaction shell model derived from koiter equations
Full text linkFluid-structure interaction (FSI) problems are of great interest, due to their applicability in science and engineering. However, the coupling between large fluid domains and small moving solid walls presents numerous numerical difficulties and, in some configurations, where the thickness of the solid wall can be neglected, one can consider membrane models, which are derived from the Koiter shell equations with a reduction of the computational cost of the algorithm. With this assumption, the FSI simulation is reduced to the fluid equations on a moving mesh together with a Robin boundary condition that is imposed on the moving solid surface. In this manuscript, we are interested in the study of inverse FSI problems that aim to achieve an objective by changing some design parameters, such as forces, boundary conditions, or geometrical domain shapes. We study the inverse FSI membrane model by using an optimal control approach that is based on Lagrange multipliers and adjoint variables. In particular, we propose a pressure boundary optimal control with the purpose to control the solid deformation by changing the pressure on a fluid boundary. We report the results of some numerical tests for two-dimensional domains to demonstrate the feasibility and robustness of our method
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