François Guibault

Assessment Study of K-ɛ Turbulence Models and Near-Wall Modeling for Steady State Swirling Flow Analysis in Draft Tube Using Fluent

Abstract The accuracy of k-ε turbulence models for the swirling flow in the Turbine 99 draft tube is the subject of this work. The relation of the first-order upwind, second-order upwind, third-order upwind (QUICK) and Power Law schemes used with these models has been studied. As the turbulent flows are significantly affected by the presence of walls, the wall function and the near-wall models were tested for modeling the near-wall region. Two different grid concentrations near the wall y+1 and y+50 were used to study the flow behavior for case 1 of Turbine 99 Workshop III. Discussion is based on graphical results and by comparing numerical simulations and experiments in operational mode T (close to best efficiency). The results of this study indicate a very good representation of the flow at different cross sections by the RNG turbulence model but a poor level of convergence.

Three-dimensional anisotropic geometric metrics based on local domain curvature and thickness

Abstract A three-dimensional anisotropic Riemannian metric is constructed from a triangulated CAD model to control its spatial discretization for numerical analysis. In addition to the usual curvature criterion, the present geometric metric is also based on the local thickness of the modeled domain. This local thickness is extracted from the domain skeleton while local curvature is deduced from the model triangulated boundaries. A Cartesian background octree is used as the support medium for this metric and skeletonization takes advantage of this structure through an octree extension of a digital medial axis transform. For this purpose, the octree has to be refined according to not only boundary curvature but also a local separation criterion from digital topology theory. The resulting metric can be used to geometrically adapt any mesh type as long as metric-based adaptation tools are available. To illustrate such an application, geometric adaptation of overlay meshes used in grid-based methods for unstructured hexahedral mesh generation is presented. However, beyond mesh generation, the present metric may also be useful as a shape analysis tool and such a possibility could be explored in future developments.

Steady and unsteady flow computation in an elbow dr aft tube with experimental validation

Steady state computations are routinely used by design engineers to evaluate and compare losses in hydraulic components. In the case of the draft tube diffuser, however, experiments have shown that while a significant number of operating conditions can adequately be evaluated using steady state computations, a few operating conditions require unsteady simulations to accurately evaluate losses. This paper presents a study that assesses the predictive capacity of a combination of steady and unsteady RANS numerical computations to predict draft tube losses over the complete range of operation of a Francis turbine. For the prediction of the draft tube performance using k-epsilon turbulence model, a methodology has been proposed to average global performance indicators of steady flow computation such as the pressure recovery factor over an adequate number of periods to obtain correct results. The methodology will be validated using two distinct flow solvers, CFX and OpenFOAM, and through a systematic comparison with experimental results obtained on the FLINDT model draft tube.

Analysis and visualization tools in CFD, part I: a configurable data extraction environment

Abstract The objective is to present new ideas for the implementation of visualization and analysis environments. This is carried out with a software interface allowing the design and configuration of project-specific environments built around a core library that performs all the data extraction and manipulation. This includes processing of solutions for rendering as well as for extraction of flow features for active control on the solution procedure. While the first function is highly interactive, the second is usually a batch oriented process coupled to the numerical algorithm. To achieve this goal, it is necessary to interpret solution data in a generic sense. The grid, the primary variables of the problem, and the derived variables are all considered as a number of simple scalar (discrete) fields defined on the domain. Basic entities in the library then provide building blocks to create images for rendering purposes or new fields as required in the grid adaption control loop. A data analysis language has been created. Its entities and grammar are oriented towards the description of both the rendering and the analysis processes. This customized environment is saved in an user configuration file, with an easily understandable syntax, which is loaded at execution time, hence providing the proper configuration for each application.

A New Formulation of the Set Covering Problem for Metaheuristic Approaches

Two difficulties arise when solving the set covering problem (SCP) with metaheuristic approaches: solution infeasibility and set redundancy. In this paper, we first present a review and analysis of the heuristic approaches that have been used in the literature to address these difficulties. We then present a new formulation that can be used to solve the SCP as an unconstrained optimization problem and that eliminates the need to address the infeasibility and set redundancy issues. We show that all local optimums with respect to the new formulation and a 1-flip neighbourhood structure are feasible and free of redundant sets. In addition, we adapt an existing greedy heuristic for the SCP to the new formulation and compare the adapted heuristic to the original heuristic using 88 known test problems for the SCP. Computational results show that the adapted heuristic finds better results than the original heuristic on most of the test problems in shorter computation times.

Cross-sectional design with curvature constraints

A practical example of B-spline curve control points manipulation for the geometric construction of a free form shape is presented. Elements of a cross-sectional design methodology are used in conjunction with a skinning type operator for the definition of a B-spline surface. Skinning process is well established in the CAD community, but further difficulties arise in producing smooth surfaces under constraints. This paper attempts to overcome the fairness problem by choosing an appropriate solution where the execution time has to be reasonably short. Main results include an industrial application in a preliminary aerodynamic design cycle where manufacturing tolerances defined by smoothness criteria are maintained.

Steady and unsteady flow computation in an elbow draft tube with experimental validation

Steady state computations are routinely used by design engineers to evaluate and compare losses in hydraulic components. In the case of the draft tube diffuser, however, experiments have shown that while a significant number of operating conditions can adequately be evaluated using steady state computations, a few operating conditions require unsteady simulations to accurately evaluate losses. This paper presents a study that assesses the predictive capacity of a combination of steady and unsteady RANS numerical computations to predict draft tube losses over the complete range of operation of a Francis turbine. For the prediction of the draft tube performance using k- turbulence model, a methodology has been proposed to average global performance indicators of steady flow computations such as the pressure recovery factor over an adequate number of periods to obtain correct results. The methodology will be validated using two distinct flow solvers, CFX and OpenFOAM, and through a systematic comparison with experimental results obtained on the FLINDT model draft tube.

Two-dimensional metric tensor visualization using pseudo-meshes

Riemannian metric tensors are used to control the adaptation of meshes for finite element and finite volume computations. To study the numerous metric construction and manipulation techniques, a new method has been developed to visualize two-dimensional metrics without interference from an adaptation algorithm. This method traces a network of orthogonal tensor lines, tangent to the eigenvectors of the metric field, to form a pseudo-mesh visually close to a perfectly adapted mesh but without many of its constraints. Anisotropic metrics can be visualized directly using such pseudo-meshes but, for isotropic metrics, the eigensystem is degenerate and an anisotropic perturbation has to be used. This perturbation merely preserves directional information usually present during metric construction and is small enough, about 1% of the prescribed target element size, to be visually imperceptible. Both analytical and solution-based examples show the effectiveness and usefulness of the present method. As an example, pseudo-meshes are used to visualize the effect on metrics of Laplacian-like smoothing and gradation control techniques. Application to adaptive quadrilateral mesh generation is also discussed.

Collision detection algorithm for NURBS surfaces in interactive applications

Video games have reached a new level of realism. Programmable shading, 3D physics simulation and curved surfaces will soon become standard features. Real time collision detection, needed for this kind of application, is a difficult problem with no known optimal solution. We present a new algorithm for interactive collision detection between dynamic NURBS surfaces. It is intended to be used in real time applications, particularly in 3D video games embedded in an environment governed by simulated physical laws. This algorithm creates oriented bounding boxes (or OBB) on the fly with the surface control points and tests them for overlapping. If this test fails, the surfaces are subdivided into smaller NURBS surfaces and the algorithm is called recursively on these new surfaces. It stops when a certain precision level is reached, that is user definable as a function of the application. The results are the world space coordinates of the contact point, and the (u, v) parametric coordinates on both surfaces. The use of OBB allows for fast and memory efficient collision tests. The construction of an OBB with the surfaces control points is simple and leads to a tight fitting bounding volume, which is the key of this fast collision detection algorithm.

An iterated-tabu-search heuristic for a variant of the partial set covering problem

In this paper, we propose a heuristic algorithm to solve a new variant of the partial set covering problem. In this variant, each element