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Over the last several years, Vorticity Confinement has been shown to be a very efficient method to simulate the vortex-dominated flows over complex configurations. To calculate these flows, no high-order numerical scheme and body conforming grids are required for this method and only a fixed, uniform Cartesian grid is employed. First, an overall description of the original Vorticity Confinement method (VC1) is presented, followed by an introduction of the newly developed Vorticity Confinement method (VC2). The advantage of VC2 over VC1 is the ability to conserve the Momentum. Two different numerical schemes are shown for VC1 and VC2. The one for VC2 is much simpler than that of VC1. Results of VC1 and VC2 for convecting vortices and scalars in 1-D and 2-D will be presented. Numerical results are presented for the three dimensional flow over a surface-mounted cube. Comparisons have been made with experimental and Large Eddy Simulation (LES) data. It is observed that with a coarse uniform Cartesian grid, Vorticity Confinement is able to get results in better agreement with the experimental results than the LES simulation results on a fine grid. This method is shown to be more effective than trying to model and discretize more complex system of equations in the traditional methods, when solving complex high Reynolds number flow problems.
The objective of the present research is to investigate the recent development of the vorticity confinement method. First, a new formulation of the vorticity confinement term is studied. Advantages of the new formulation over the original one include the ability to conserve the momentum, and the ability to preserve the centroid motion of some flow properties such as the vorticity magnitude. Next, new difference schemes, which are simpler and more efficient than the old schemes, are discussed. At last, two computational models based on the vorticity confinement method are investigated. One of the models is devised to simulate inviscid flows over bodies with surfaces not aligned with the grid. The other is a surface boundary layer model, which is intended for efficiently simulating viscous flows with separations from the body surfaces. To validate the computational models, numerical simulations of three-dimensional flows over 6:1 ellipsoid at incidence are performed. Comparisons have been made with exact solutions for inviscid simulations or experimental data for viscous simulations, and data obtained with conventional CFD methods. It is observed that both the inviscid and the viscous solutions with the new models exhibit good agreement with the exact solutions or the experiment data. The new models can have much higher efficiency than conventional CFD methods, and are able to obtain solutions with comparable accuracy.
The time-accurate computational model FAST3D is used to investigate flow over a cube mounted on a flat surface. The effect of resolution, boundary conditions, and the form of the inflow velocity profile on flow evolution and passive tracer dispersion in the vicinity of the cube is considered. Computational results are compared with wind tunnel and water tank data published by a number of authors. It is found that the flow computed around a surface-mounted cube is sensitive to both the form of the upstream velocity profile as well as to conditions at the baseplate surface. Furthermore, time-dependent effects appear to be crucial to the accumulation of accurate flow field statistics and thus a correct understanding of the flow and dispersion patterns.
This text on finite element-based computational methods for solving incompressible viscous fluid flow problems shows readers how to split complicated computational fluid dynamics problems into a sequence of simpler sub-problems. A methodology for solving more advanced applications such as hemispherical cavity flow, cavity flow of an Oldroyd-B viscoelastic flow, and particle interaction in an Oldroyd-B type viscoelastic fluid is also presented.
This monograph is intended as a concise and self-contained guide to practitioners and graduate students for applying approaches in computational fluid dynamics (CFD) to real-world problems that require a quantification of viscous incompressible flows. In various projects related to NASA missions, the authors have gained CFD expertise over many years by developing and utilizing tools especially related to viscous incompressible flows. They are looking at CFD from an engineering perspective, which is especially useful when working on real-world applications. From that point of view, CFD requires two major elements, namely methods/algorithm and engineering/physical modeling. As for the methods, CFD research has been performed with great successes. In terms of modeling/simulation, mission applications require a deeper understanding of CFD and flow physics, which has only been debated in technical conferences and to a limited scope. This monograph fills the gap by offering in-depth examples for students and engineers to get useful information on CFD for their activities. The procedural details are given with respect to particular tasks from the authors’ field of research, for example simulations of liquid propellant rocket engine subsystems, turbo-pumps and the blood circulations in the human brain as well as the design of artificial heart devices. However, those examples serve as illustrations of computational and physical challenges relevant to many other fields. Unlike other books on incompressible flow simulations, no abstract mathematics are used in this book. Assuming some basic CFD knowledge, readers can easily transfer the insights gained from specific CFD applications in engineering to their area of interest.
This textbook explores both the theoretical foundation of the Finite Volume Method (FVM) and its applications in Computational Fluid Dynamics (CFD). Readers will discover a thorough explanation of the FVM numerics and algorithms used for the simulation of incompressible and compressible fluid flows, along with a detailed examination of the components needed for the development of a collocated unstructured pressure-based CFD solver. Two particular CFD codes are explored. The first is uFVM, a three-dimensional unstructured pressure-based finite volume academic CFD code, implemented within Matlab. The second is OpenFOAM®, an open source framework used in the development of a range of CFD programs for the simulation of industrial scale flow problems. With over 220 figures, numerous examples and more than one hundred exercise on FVM numerics, programming, and applications, this textbook is suitable for use in an introductory course on the FVM, in an advanced course on numerics, and as a reference for CFD programmers and researchers.
The fundamental equations for compressible flow are solved using a velocity - pressure - vorticity formulation producing a solution that satisfies continuity and vorticity definitions up to machine accuracy. Chapter 1 reviews many algorithms used to solve this problem. Unlike those methods, no pressure - velocity relation or artificial compressibility is assumed in the present formulation, so the equations for kinematics, pressure and momentum are decoupled independent building blocks in the iterative process. As a consequence, the resulting modular algorithm can be used directly for compressible or incompressible flows, contrasting with other current techniques. Moreover the present formulation also applies to two-dimensional and three-dimensional, structured and unstructured grids without any changes, even though only the two-dimensional version was implemented. In Chapter 2, the original formulation is described. A functional minimization technique is used to discretize the kinematics equations, mimicking continuous methods used in the field of functional analysis and providing a common framework to understand, model and implement the solution algorithm. Suitable preconditioning and radial interpolation techniques are employed to balance precision and computational speed. The Poisson equation for pressure is solved similarly by minimizing a suitable functional. The momentum equations are then solved using a finite volume approach adding a controlled amount of artificial viscosity according to mesh size and Reynolds number, resulting in a stable calculation. The vorticity is then obtained as the curl of the velocity. Temperature is similarly computed from the energy equation in an outer loop. Suitable adjustments to pressure and temperature enable the ideal gas equation to fit both the compressible and incompressible paradigmsSubsequent chapters deal with validation, applying the computer efficient implementation of the algorithm to a variety of well documented aerodynamic benchmark problems. Examples include compressible and incompressible flow, steady and unsteady problems and flow over cylinders and airfoils over a variety of Reynolds and subsonic Mach numbers.