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Evaluation of Near-Wall Turbulence Models for Deliberately Roughened Liquid Annular Seals

An extensive numerical evaluation of the performance of two near-wall treatments and two core-flow turbulence models has been done while simulating experimental tests of water flowing between flat plates with deliberately roughened surfaces. These flat-plate tests replicated the results of several annular seal experiments in which friction factor increased as the seal clearance increased. Annular seals are extensively used in a wide range of turbomachinery, and their design influences efficiency and rotordynamic stability. A commercial code, FLUENT, was used to solve the Reynolds-averaged Navier‐Stokes equations with the flat-plate tests as a reference. The performance of the standard wall functions, based on the law of the wall, as near-wall treatment of turbulence was evaluated and compared to the two-layer-zonal approach. Similarly, the solutions obtained with the standard and “renormalization group” method versions of the first-order closure k‐e model were contrasted to those obtained with a second-order closure, the Reynolds-stress model. Although the main features of the friction factor behavior observed in the experiments under study were reproduced with a simple two-dimensional approach, the present work concentrates on the numerical detail and lessons learned while obtaining such results. It was found that wall function solutions are extremely sensitive to the location of the first grid point near the wall, even if it is located within the overlap region. In addition, the low-Reynolds nature of the flow requires coarse meshing making any k‐e model solution grid dependent. On the other hand, the two-layer zonal model is more consistent, and it is not sensitive to the location of the first grid point near the wall, provided it is located at a y + distance no larger than 10. Solutions obtained with the latter approach and the Reynolds-stress model are found to be grid independent. In summary, a numerical solution is truly grid independent when it is consistently replicated upon variation of the discretization scheme, the pressure-to-velocity linking method, the algebraic equation solving algorithm, and the mesh size and type. In low-Reynolds-number turbulent flow, the two-layer zonal approach fulfills such statement as near-wall treatment of turbulence.