16 research outputs found

    The Feasibility of Multidimensional CFD Applied to Calandria System in the Moderator of CANDU-6 PHWR Using Commercial and Open-Source Codes

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    The moderator system of CANDU, a prototype of PHWR (pressurized heavy-water reactor), has been modeled in multidimension for the computation based on CFD (computational fluid dynamics) technique. Three CFD codes are tested in modeled hydrothermal systems of heavy-water reactors. Commercial codes, COMSOL Multiphysics and ANSYS-CFX with OpenFOAM, an open-source code, are introduced for the various simplified and practical problems. All the implemented computational codes are tested for a benchmark problem of STERN laboratory experiment with a precise modeling of tubes, compared with each other as well as the measured data and a porous model based on the experimental correlation of pressure drop. Also the effect of turbulence model is discussed for these low Reynolds number flows. As a result, they are shown to be successful for the analysis of three-dimensional numerical models related to the calandria system of CANDU reactors

    A POD-Galerkin reduced order model for a LES filtering approach

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    We propose a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for a Leray model. For the implementation of the model, we combine a two-step algorithm called Evolve-Filter (EF) with a computationally efficient finite volume method. The main novelty of the proposed approach relies in applying spatial filtering both for the collection of the snapshots and in the reduced order model, as well as in considering the pressure field at reduced level. In both steps of the EF algorithm, velocity and pressure fields are approximated by using different POD basis and coefficients. For the reconstruction of the pressures fields, we use a pressure Poisson equation approach. We test our ROM on two benchmark problems: 2D and 3D unsteady flow past a cylinder at Reynolds number 0 <= Re <= 100. The accuracy of the reduced order model is assessed against results obtained with the full order model. For the 2D case, a parametric study with respect to the filtering radius is also presented.Comment: 29 pages, 16 figures, 9 table

    Numerical Simulation of Selected Two-Dimensional and Three-Dimensional Fluid-Structure Interaction Problems Using OpenFOAM Technology

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    Fluid-structure interaction (FSI) problems are increasing in various engineering fields. In this thesis, different cases of FSI in two- and three-dimensions (2D and 3D) are simulated using OpenFOAM and foam-extend. These packages have been used to create a coupling between fluid and solid. The vortex-induced vibration (VIV) phenomenon of flow past a circular cylinder is studied using PIMPLE algorithm for pressure-velocity coupling. This VIV study is restricted to incompressible flow simulation at a Reynolds number (Re) of 100. The changes of drag and lift coefficient values depend on the study case and the spring-mass-damper system for the flow past a free oscillatory cylinder. The free vibrating cylinder examined in one-degree-of-freedom (1DOF) and two-degrees-of-freedom (2DOF) systems with linear damping and spring properties. Both will affect the behaviour of the cylinder within the flow with some noticeable differences. The response time of the cylinder and the drag coefficient are the most affected by the spring and damper. Besides the vortex-induced vibration test cases, the two-dimensional and three-dimensional fluid-structure interaction benchmarking is also studied. A partitioned solution method for strongly coupled solver with independent fluid and solid meshes for transient simulation has been applied. The fluid domain dynamics is governed by the incompressible Navier-Stokes equations; however, the structural field is described by the nonlinear elastodynamic equations. Fluid and solid domains are discretised by finite volume method (FVM) in space and time. A strong coupling scheme for partitioned analysis of the thin-walled shell structure exposed to wind-induced vibration (WIV) is presented. The achievement of the 3D membrane roof coupling scheme is studied by applying the 2D model. Additionally, numerical models for the slender shell structures coupling and the 3D flows indicate possible applications of the presented work. The computational fluid dynamics (CFD) simulation results revealed that even the flow is considered as a laminar, turbulence modelling or more refined meshes should be used to capture the generation and release of vortices. A partitioned solution procedure for FSI problems in the building aeroelasticity area is also studied. An illustrative real-world model on the coupled behaviour of membrane structure under wind flow influence is given. A four-point tent subjected to wind motion is a typical application of this work applying with various physical factors that are a necessity for the thin membrane structure. The fluid domain is described by the incompressible Navier-Stokes equations at a Reynolds number of Re = 3,750. However, the motion of the solid field is modeled by total Lagrangian strategy for nonlinear elastic deformation. The FSI simulation, particularly 3D problems require in very long calculation time. Some limitations of the FSI solver in foam-extend package called fsiFoam is discussed. All solvers that used in this thesis are considered to be applied to a wide use of the implementation of FSI models, despite some problems in parallelisation, particularly in the latest FSI solver version. The analysis results are presented to demonstrate accuracy, convergence, and stability

    Numerical solutions for problems with complex physics in complex geometry

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    In this dissertation, two high order accurate numerical methods, Spectral Element Method (SEM) and Discontinuous Galerkin method (DG), are discussed and investigated. The advantages of both methods and their applicable areas are studied. Particular problems in complex geometry with complex physics are investigated and their high order accurate numerical solutions obtained by using either SEM or DG are presented. Furthermore, the Smoothed Particle Hydrodynamics (SPH) (a mesh-free weighted interpolation method) is implemented on graphics processing unit (GPU). Some numerical simulations of the complex flow with a free surface are presented and discussed to show the advantages of SPH method in handling rapid domain deformation. In particular, four independent numerical examples are sequentially presented. A high-accurate SEM solution to the natural convection problem is provided. Up to the 6th order bases and the 4th order of the Runge-Kutta method are used in the simulation. Results show that our algorithm is more efficient than conventional methods, and the algorithm could obtain very detailed resolutions with moderate computional efforts (simply perform the hp-refinement). In another example, a more realistic and complete reaction model of simulating the reaction diffusion process in human neuromuscular junction (NMJ) is developed, and SEM is used to provide a high order accurate numerical solution for the model. Results have successfully predicted the distribution and amount of open receipts during a normal action potential, which helps us gain a better understanding of this process. Still, high order DG method is used intensively to study the fluid problems with moderately high Reynolds (Re) number such as: flow passing a vertical cylinder and lid-driven cavity flow in both two dimensional (2D) and three dimensional (3D). Unstructured meshes (triangular element or tetrehedron) are adopted in our DG solver, which gives a greater ability than structured meshes (quadrilateral element or hexahedron) in solving particular problems with very complex geometry. By comparing our DG results with others obtained by conventional methods (Finite Difference Method, Finite Volume Method), high accuracy similar to other numerical results are obtained; however, the total number of degree of freedom in our simulation is greaterly reduced due to the spectral accuracy of the DG method. Lastly, the SPH method is implemented on GPU to generate 2D and 3D simulations of fluid problems. The SPH solver has an advantage for solving fluid problems with complex geometries, rapid deformations and even discontinuities (wave-break) without generating computational grids. A noticeable speedup of our GPU implementation over the serial version on CPU is achieved. The solver is capable of developing further researches in real engineering problems such as: dam breaks, landslides, and near shore wave propagation and wave-structure interaction

    The EMAC scheme for Navier-Stokes simulations, and application to flow past bluff bodies

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    The Navier-Stokes equations model the evolution of water, oil, and air flow (air under 220 m.p.h.), and therefore the ability to solve them is important in a wide array of engineering design problems. However, analytic solution of these equations is generally not possible, except for a few trivial cases, and therefore numerical methods must be employed to obtain solutions. In the present dissertation we address several important issues in the area of computational fluid dynamics. The first issue is that in typical discretizations of the Navier-Stokes equations such as the mixed finite element method, the conservation of mass is enforced only weakly, and this leads to discrete solutions which may not conserve energy, momentum, angular momentum, helicity, or vorticity, even though the physics of the Navier-Stokes equations dictate that they do. It is widely believed in the computational fluid dynamics community that the more physics is built into the discretization, the more accurate and stable the discrete solutions are, especially over longer time intervals. In chapter 3 we study conservation properties of Galerkin methods for the incompressible Navier-Stokes equations, without the divergence constraint strongly enforced. We show that none of the commonly used formulations (convective, conservative, rotational, and skew-symmetric) conserve each of energy, momentum, and angular momentum (for a general finite element choice). We aim to construct discrete formulations that conserve as many physical laws as possible without utilizing a strong enforcement of the divergence constraint, and doing so leads us to a new formulation that conserves each of energy, momentum, angular momentum, enstrophy in 2D, helicity and vorticity (for reference, the usual convective formulation does not conserve most of these quantities). In chapter 3 we also perform a number of numerical experiments, which verify the theory and test the new formulation. To study the performance of our novel formulation of the Navier-Stokes equations, we need reliable reference solutions/statistics. However, there is not a significant amount of reliable reference solutions for the Navier-Stokes equations in the literature. Accurate reference solutions/statistics are difficult to obtain due to a number of reasons. First, one has to use several millions of degrees of freedom even for a two-dimensional simulation (for 3D one needs at least tens of millions of degrees of freedom). Second, it usually takes a long time before the flow becomes fully periodic and/or stationary. Third, in order to obtain reliable solutions, the time step must be very small. This results in a very large number of time steps. All of this results in weeks of computational time, even with the highly parallel code and efficient linear solvers (and in months for a single-threaded code). Finally, one has to run a simulation for multiple meshes and time steps in order to show the convergence of solutions. In the second chapter we perform a careful, very fine discretization simulations for a channel flow past a flat plate. We derive new, more precise reference values for the averaged drag coefficient, recirculation length, and the Strouhal number from the computational results. We verify these statistics by numerical computations with the three time stepping schemes (BDF2, BDF3 and Crank-Nicolson). We carry out the same numerical simulations independently using deal.II and Freefem++ software. In addition both deal.II/Q2Q1 and Freefem/P2P1 element types were used to verify the results. We also verify results by numerical simulations with multiple meshes, and different time step sizes. Finally, in chapter 4 we compute reference values for the three-dimensional channel flow past a circular cylinder obstacle, with both time-dependent inflow and with constant inflow using up to 70.5 million degrees of freedom. In contrast to the linearization approach used in chapter 2, in chapter 4 we numerically study fully nonlinear schemes, which we linearize using Newton\u27s method. In chapter 4 we also compare the performance of our novel EMAC scheme with the four most commonly used formulations of the Navier-Stokes equations (rotational, skew-symmetric, convective and conservative) for the three-dimensional channel flow past circular cylinder both with the time-dependent inflow and with constant inflow
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