Application of the grid convergence index to a laminar axisymmetric sudden expansion flow
Abstract
RESUMEN
El uso de modelos numéricos para la representación de procesos naturales es cada vez más común, gracias al desarrollo de herramientas avanzadas problemas cada vez más complejos pueden ser abordados. Sin embargo, mientras sistemas avanzados pueden ser solventados, la incertidumbre de la precisión de la solución obtenida se mantiene. La comparación entre los valores experimentales y los obtenidos mediante las simulaciones no es evidencia suficiente de la calidad de los resultados. El método del índice de convergencia de la grilla (GCI) se propone como una alternativa para calcular y reportar la estimación del error de discretización en la aplicación de mecánica de fluidos computacional (CFD) para las simulaciones, este método permite la estimación del error de discretización mediante la aplicación de la teoría de Extrapolación de Richardson, este procedimiento es aplicado a un caso de flujo laminar en una tubería que experimenta una expansión repentina. Los resultados de un estudio experimental se utilizan para verificar tanto la simulación numérica como los resultados de GCI. Como resultado de la aplicación de este método el orden de precisión del esquema numérico utilizado fue verificado. Comparando los resultados numéricos con los valores experimentales se obtuvo un máximo error de 6%. Finalmente, considerando las dos grillas más finas se puede concluir que el rango asintótico se ha alcanzado y que una grilla más fina no mejorara considerablemente la precisión de la solución como lo hará el costo del procedimiento.
Palabras clave: Análisis de incertidumbre, dinámica de fluidos computacional, extrapolación de Richardson, error de discretización.
ABSTRACT
The use of numerical models to represent natural processes is increasingly common. The development of advanced numerical tools allows a more physically-based representation of complex flow phenomena. While more advanced systems can be solved, the uncertainty of the accuracy of the solutions obtained remains. The mere comparison between experiments and simulations is not enough proof of strength of the results. The Grid Convergence Index (GCI) methodology has been proposed with the aim to provide a mechanism to calculate and report discretization errors estimates in computational fluid dynamics (CFD) simulations. It permits the quantification of the uncertainty present in grid convergence. This method uses a grid convergence error estimator that is obtained by applying the generalized Richardson Extrapolation theory. The process is applied to an axisymmetric sudden expansion laminar flow case. Experimental results are used to verify the numerical simulation and GCI outcome. As a result of the application of this method the order of accuracy of the numerical scheme was verified. Additionally, comparing the numerical results with the experimental values, a maximum error of 6% was obtained. Finally, considering the two finest meshes, it can be concluded that the asymptotic range has been reached and that a finer Mesh won’t improve the accuracy of the solution when considering the increased numerical cost.
Keywords: Uncertainty analysis, computational fluid dynamics, Richardson extrapolation, discretization error.
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