A "poor man's" approach for high-resolution three-dimensional topology optimization of natural convection problems

This paper treats topology optimization of natural convection problems. A simplified model is suggested to describe the flow of an incompressible fluid in steady state conditions, similar to Darcy's law for fluid flow in porous media. The equations for the fluid flow are coupled to the thermal convection-diffusion equation through the Boussinesq approximation. The coupled non-linear system of equations is discretized with stabilized finite elements and solved in a parallel framework that allows for the optimization of high resolution three-dimensional problems. A density-based topology optimization approach is used, where a two-material interpolation scheme is applied to both the permeability and conductivity of the distributed material. Due to the simplified model, the proposed methodology allows for a significant reduction of the computational effort required in the optimization. At the same time, it is significantly more accurate than even simpler models that rely on convection boundary conditions based on Newton's law of cooling. The methodology discussed herein is applied to the optimization-based design of three-dimensional heat sinks. The final designs are formally compared with results of previous work obtained from solving the full set of Navier-Stokes equations. The results are compared in terms of performance of the optimized designs and computational cost. The computational time is shown to be decreased to around 5-20% in terms of core-hours, allowing for the possibility of generating an optimized design during the workday on a small computational cluster and overnight on a high-end desktop

A level-set model for thermocapillary motion of deformable fluid particles

A new level-set model is proposed for simulating immiscible thermocapillary flows with variable fluid-property ratios at dynamically deformable interfaces. The Navier–Stokes equations coupled with the energy conservation equation are solved by means of a finite-volume/level-set approach, adapted to a multiple marker methodology in order to avoid the numerical coalescence of the fluid particles. The temperature field is coupled to the surface tension through an equation of state. Some numerical examples including thermocapillary driven convection in two superimposed fluid layers, and thermocapillary motion of single and multiple fluid particles are computed using the present method. These results are compared against analytical solutions and numerical results from the literature as validations of the proposed model.Peer ReviewedPostprint (author's final draft

Coupling different discretizations for fluid structure interaction in a monolithic approach

In this thesis we present a monolithic coupling approach for the simulation of phenomena involving interacting fluid and structure using different discretizations for the subproblems. For many applications in fluid dynamics, the Finite Volume method is the first choice in simulation science. Likewise, for the simulation of structural mechanics the Finite Element method is one of the most, if not the most, popular discretization method. However, despite the advantages of these discretizations in their respective application domains, monolithic coupling schemes have so far been restricted to a single discretization for both subproblems. We present a fluid structure coupling scheme based on a mixed Finite Volume/Finite Element method that combines the benefits of these discretizations. An important challenge in coupling fluid and structure is the transfer of forces and velocities at the fluidstructure interface in a stable and efficient way. In our approach this is achieved by means of a fully implicit formulation, i.e., the transfer of forces and displacements is carried out in a common set of equations for fluid and structure. We assemble the two different discretizations for the fluid and structure subproblems as well as the coupling conditions for forces and displacements into a single large algebraic system. Since we simulate real world problems, as a consequence of the complexity of the considered geometries, we end up with algebraic systems with a large number of degrees of freedom. This necessitates the use of parallel solution techniques. Our work covers the design and implementation of the proposed heterogeneous monolithic coupling approach as well as the efficient solution of the arising large nonlinear systems on distributed memory supercomputers. We apply Newton’s method to linearize the fully implicit coupled nonlinear fluid structure interaction problem. The resulting linear system is solved with a Krylov subspace correction method. For the preconditioning of the iterative solver we propose the use of multilevel methods. Specifically, we study a multigrid as well as a two-level restricted additive Schwarz method. We illustrate the performance of our method on a benchmark example and compare the afore mentioned different preconditioning strategies for the parallel solution of the monolithic coupled system

A semi-implicit hybrid finite volume / finite element scheme for all Mach number flows on staggered unstructured meshes

In this paper a new hybrid semi-implicit finite volume / finite element (FV/FE) scheme is presented for the numerical solution of the compressible Euler and Navier-Stokes equations at all Mach numbers on unstructured staggered meshes in two and three space dimensions. The chosen grid arrangement consists of a primal simplex mesh composed of triangles or tetrahedra, and an edge-based / face-based staggered dual mesh. The governing equations are discretized in conservation form. The nonlinear convective terms of the equations, as well as the viscous stress tensor and the heat flux, are discretized on the dual mesh at the aid of an explicit local ADER finite volume scheme, while the implicit pressure terms are discretized at the aid of a continuous $\mathbb{P}^{1}$ finite element method on the nodes of the primal mesh. In the zero Mach number limit, the new scheme automatically reduces to the hybrid FV/FE approach forwarded in \cite{BFTVC17} for the incompressible Navier-Stokes equations. As such, the method is asymptotically consistent with the incompressible limit of the governing equations and can therefore be applied to flows at all Mach numbers. Due to the chosen semi-implicit discretization, the CFL restriction on the time step is only based on the magnitude of the flow velocity and not on the sound speed, hence the method is computationally efficient at low Mach numbers. In the chosen discretization, the only unknown is the scalar pressure field at the new time step. Furthermore, the resulting pressure system is symmetric and positive definite and can therefore be very efficiently solved with a matrix-free conjugate gradient method. In order to assess the capabilities of the new scheme, we show computational results for a large set of benchmark problems that range from the quasi incompressible low Mach number regime to compressible flows with shock waves

Natural convection in a square cavity with uniformly heated and/or insulated walls using marker-and-cell method

In this study, a numerical investigation has been performed using the computational Harlow-Welch MAC (Marker and Cell) finite difference method to analyse the unsteady state two-dimensional natural convection in lid-driven square cavity with left wall maintained at constant heat flux and remaining walls kept thermally insulated. The significant parameters in the present study are Reynolds number (Re), thermal Grashof number (Gr) and Prandtl number (Pr) and Peclét number (Pe =PrRe). The structure of thermal convection patterns is analysed via streamline, vorticity, pressure and temperature contour plots. The influence of the thermophysical parameters on these distributions is described in detail. Validation of solutions with earlier studies is included. Mesh independence is also conducted. It is observed that an increase in Prandtl number intensifies the primary circulation whereas it reduces the heat transfer rate. Increasing thermal Grashof number also decreases heat transfer rates. Furthermore the isotherms are significantly compressed towards the left (constant flux) wall with a variation in Grashof number while Peclét number is fixed. The study is relevant to solar collector heat transfer simulations and also crystal growth technologies

Computational study of heat transfer in solar collectors with different radiative flux models

2D steady incompressible laminar Newtonian viscous convection-radiative heat transfer in a rectangular solar collector geometry is considered. The ANSYS FLUENT finite volume code (version 17.2) is employed to simulate the thermo-fluid characteristics. Extensive details of computational methodology are given to provide engineers with a framework for simulating radiative-convection in enclosures. Mesh-independence tests and validation are conducted. The influence of aspect ratio, Prandtl number (Pr), Rayleigh number (Ra) and radiative flux model on temperature, isotherms, velocity, pressure is evaluated and visualized in colour plots. Additionally, local convective heat flux is computed, and solutions are compared with the MAC solver for various buoyancy effects achieving excellent agreement. The P1 model is shown to better predict the actual influence of solar radiative flux on thermal fluid behaviour compared with the limited Rosseland model. With increasing Ra, the hot zone emanating from the base of the collector is found to penetrate deeper into the collector and rises symmetrically dividing into two vortex regions with very high buoyancy effect. With increasing Pr there is a progressive incursion of the hot zone at the solar collector base higher into the solar collector space and simultaneously a greater asymmetric behaviour of the dual isothermal zones

Finite amplitude electroconvection induced by strong unipolar injection between two coaxial cylinders

We perform a theoretical and numerical study of the Coulomb-driven electroconvection flow of a dielectric liquid between two coaxial cylinders. The specific case where the inner to outer diameter ratio is 0.5 is analyzed. A strong unipolar injection of ions either from the inner or outer cylinder is considered to introduce free charger carriers into the system. A finite volume method is used to solve all governing equations including Navier-Stokes equations and a simplified set of Maxwell’s equations. The flow is characterized by a subcritical bifurcation in the finite amplitude regime. A linear stability criterion and a nonlinear one that correspond to the onset and stop of the flow motion, respectively, are linked with a hysteresis loop. In addition, we also explore the behavior of the system for higher values of the stability parameter. For inner injection, we observe a transition between the patterns made of 7 and 8 pairs of cells, before an oscillatory regime is attained. Such a transition leads to a second finite amplitude stability criterion. A simple modal analysis reveals that the competition of different modes is at the origin of this behavior. The charge density as well as velocity field distributions are provided to help understanding the bifurcation behavior.Ministerio de ciencia y tecnología FIS2011-25161Junta de Andalucía P10-FQM-5735Junta de Andalucía P09-FQM-458

Parametric study of thermal-large eddy simulation (T-LES) models in turbulent anisothermal channel flow

Thermal Large eddy simulations (T-LES) are getting more and more popular becuase of the availability of computational power in the industries, thus the necessity of testing out different T-LES models are necessary. This thesis assesses two different types of thermal large eddy simulation models. This study was done for highly anisothermal flow for pressurized air as the fluid in the channel flow of a solar receiver of a tower of concentrated solar power (CSP) plant. The study was done to compare the results of the two chosen T- LES models and how they compare with the DNS data of similar settings. For this purpose, both T-LES models were simulated with similar thermal conditions, heat fluxes and mesh configurations. The mean value of the friction Reynolds number was around 800 for all simulations. In terms of solving the Navier-stokes, the equations were simplied using low- Mach number assumption. Due to the filtering operation of the LES method, two major non- linear unclosed sub-grid terms for velocity-velocity and velocity-density correlations appears that has a signficant affect on the flow characteristics, thus these terms need to be modeled. There are two types of models called functional and structural models. However, one functional and two-layererd mixed model that mixes both functional and structural models has been investigated with fourth order discretization scheme on the momentum conservation equation and 2nd order scheme on the mass conservation equation for both cases. After simulating the T-LES configurations, the errors were calculated for the mean and correlation quantites by comparing them with the DNS data to check the accuracy of each model. Also, normalized profiles were generated and assesed as a function of the distance from the wal