ABSTRACT Este documento resume el desarrollo de las herramientas computacionales inflow, basadas en el método de elementos finitos, para la solución de problemas de mecánica de fluidos bi-dimensionales bajo régimen de flujo incompresible. Se desarrollan algoritmos de solución de las ecuaciones de Navier-Stokes incompresibles, que podrán ser utilizados para fines de desarrollo o investigación. Se implementó un paquete básico de herramientas computacionales, bajo una lógica de programación modular, sobre el cual se podrán ir anexando subrutinas para solucionar otras condiciones de flujo (otros mode-los de turbulencia, el caso de flujos con rotación, estabilización para casos de rotación domi-nante, flujos debidos a gradientes térmicos, etc.). Aunque las funciones elementales que se han programado corresponden a elementos bidi-mensionales, las subrutinas de ensamble y solución se implementaron teniendo en cuenta el caso más general tridimensional, con lo que la extensión al mismo resulta directa.

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    ABSTRACT: Design tools have been developed for ultra-low Reynolds number rotors, combining enhanced actuator-ring / blade-element theory with airfoil section data based on two-dimensional Navier-Stokes calculations. This performance prediction method is coupled with an optimizer for both design and analysis applications. Performance predictions from these tools have been compared with three-dimensional Navier Stokes analyses and experimental data for a 2.5 cm diameter rotor with chord Reynolds numbers below 10,000. Comparisons among the analyses and experimental data show reasonable agreement both in the global thrust and power required, but the spanwise distributions of these quantities exhibit significant deviations. The study also reveals that three-dimensional and rotational effects significantly change local airfoil section performance. The magnitude of this issue, unique to this operating regime, may limit the applicability of blade-element type methods for detailed rotor design at ultra-low Reynolds numbers, but these methods are still useful for evaluating concept feasibility and rapidly generating initial designs for further analysis and optimization using more advanced tools.
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    ABSTRACT: The steady state incompressible Navier-Stokes equations in 2-D are solved numerically using the artificial compressibility formulation. The convective terms are upwind-differenced using a flux difference split approach that has uniformly high accuracy throughout the interior grid points. The viscous fluxes are differenced using second order accurate central differences. The numerical system of equations is solved using an implicit line relaxation scheme. Although the current study is limited to steady state problems, it is shown that this entire formulation can be used for solving unsteady problems. Characteristic boundary conditions are formulated and used in the solution procedure. The overall scheme is capable of being run at extremely large pseudotime steps, leading to fast convergence. Three test cases are presented to demonstrate the accuracy and robustness of the code. These are the flow in a square-driven cavity, flow over a backward facing step, and flow around a 2-D circular cylinder.
    AIAA Journal 01/1990; 28(2):253-262. · 1.08 Impact Factor
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    ABSTRACT: The objective of this paper is to analyze the pressure stability of fractional step finite element methods for incompressible flows that use a pressure Poisson equation. For the classical first-order projection method, it is shown that there is a pressure control which depends on the time step size, and therefore there is a lower bound for this time step for stability reasons. The situation is much worse for a second-order scheme in which part of the pressure gradient is kept in the momentum equation. The pressure stability in this case is extremely weak. To overcome these shortcomings, a stabilized fractional step finite element method is also considered, and its stability is analyzed. Some simple numerical examples are presented to support the theoretical results.
    Journal of Computational Physics 01/2001; · 2.14 Impact Factor


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