SUMMARYDerivative recovery techniques are used in a posteriori error indicators to drive mesh adaptation. Their behaviour in the core of the computational domain and on boundaries constitutes an important efficiency factor for a subsequent mesh adaptation process. A methodology to compare recovery techniques for second-order derivatives from a piecewise linear approximation is presented in this paper. A systematic approach to measuring the performance of recovery techniques using analytical functions interpolated on a series of meshes is proposed. The asymptotic behaviour of some recently published recovery techniques, as well as new ones, is numerically assessed on various type of meshes. Recommendations are done on the choice of a recovery technique.

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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.

SUMMARYIn this paper, a method is presented to measure the non-conformity of a mesh with respect to a size specification map given in the form of a Riemannian metric. The measure evaluates the difference between the metric tensor of a simplex of the mesh and the metric tensor specified on the size specification map. This measure is universal because it is a unique, dimensionless number which characterizes either a single simplex of a mesh or a whole mesh, both in size and in shape, be it isotropic or anisotropic, coarse or fine, in a small or a big domain, in two or three dimensions. This measure is important because it can compare any two meshes in order to determine unequivocally which of them is better. Analytical and numerical examples illustrate the behaviour of this measure.

This paper presents a detailed comparison of steady and unsteady turbulent flow simulation results in the U9 Kaplan turbine draft tube with experimental velocity and pressure measurements. The computational flow domain includes the guide vanes, the runner and the draft tube. A number of turbulence models were studied, including the standard k − ε, RNG k − ε, SST and SST-SAS models. Prediction of the flow behavior in the conical section of the draft tube directly below the runner cone is very sensitive to the prediction of the separation point on the runner cone. The results demonstrate a significant increase in precision of the flow modeling in the runner cone region by using unsteady flow simulations compare to stage simulation. The prediction of the flow in the runner cone region, however, remains delicate, and no turbulence model could accurately predict the complex phenomena observed experimentally.