Uncertainty Quantification of Grid Refinement applied to the Fluid Dynamics of a Hollow Fiber Membrane
Daniel S. Lira1; Severino Rodrigues de Farias Neto1; Antonio Gilson Barbosa de Lima1
1 Universidade Federal de Campina Grande
doi:10.20906/CPS/CILAMCE2017-0646
Resumo
It is not rare that uncertainties can arise in computational calculations. Grid convergence assessment is one of the major drawbacks in performing several computational calculations such as finite element analysis and computational fluid dynamics. These types of analysis use grids for the discretization of differential equations which represent physical properties and phenomena. In general, hexahedral structured grids are associated with high quality solutions, whereas unstructured tetrahedral grids may increase numerical diffusion, and therefore uncertainty of the solution. The most common method for assessing grid convergence is the systematic grid refinement. However, this method by itself is incapable of quantifying the uncertainties of a solution of a particular grid. In this context, the Grid Convergence Index (GCI) is a well-accepted method of evaluation of grid convergence. The GCI is an uncertainty estimation parameter based on the Richardson extrapolation developed with the objective to standardize and give more reliability to the results of grid convergence. In this work, the GCI was employed to evaluate the grid convergence of a systematically refined structured hexahedral grid, applied to model the laminar flow of fluid through a hollow fiber membrane using the resistance in series model in presence of concentration polarization. Three grids were produced, with respectively 1080, 10863 and 87759 elements. The model used in this study is an axisymmetric model of the flow through a membrane hollow fiber tube. For the solution of the Navier-Stokes equations, the Ansys CFX 15.0 package was used with a convergence criterion of 10-6 RMS. The variables analyzed to determine the GCI were the velocity at the position x = 100 mm and solute concentration at (x; y; z) = (100; 0.775; 0) mm. Results showed that there is monotonic convergence for the solute concentration, also, the GCI decreases as the number of elements in the grid increases for all variables, reaching values close to zero, indicating there is gre
Palavras-chave: grid; GCI; solution concentration