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Numerical errors at walls: on the sensitivity of RANS models to near-wall cell size

Lloyd, C. J.; Peakall, J.; Burns, A. D.; Keevil, G. M.; Dorrell, R. M.

Authors

J. Peakall

A. D. Burns

G. M. Keevil



Abstract

The sensitivity of a large range of turbulence closures to the near-wall grid resolution is assessed through analytical and numerical techniques. We determine model boundedness, limiting behaviour, and solution dependence of channel flow simulations to the near-wall cell size y+1. The sensitivity of present simulations to y+1 is strongly dependent on the choice of scale determining variable; ε and ω based models can lead to friction velocity errors of 1.5% and 4.74% at y+1 ≈ 1, the latter due to the singular behaviour of ω close to the wall. Here this is mitigated by adopting mathematically equivalent k − ω', k − g or k − τ models, which reduce errors by an order of magnitude to < 0.1% at y+1≈0.3. The k−τ model is insensitive to y+1 motivating a new closure with updated coefficients and a cross diffusion term, with the aim to ensure its applicability to a wider range of flows.

Citation

Lloyd, C. J., Peakall, J., Burns, A. D., Keevil, G. M., & Dorrell, R. M. (in press). Numerical errors at walls: on the sensitivity of RANS models to near-wall cell size. International Journal of Computational Fluid Dynamics, 34(3), 204-225. https://doi.org/10.1080/10618562.2020.1732941

Journal Article Type Article
Acceptance Date Jan 29, 2020
Online Publication Date Mar 3, 2020
Deposit Date Jun 25, 2020
Journal International Journal of Computational Fluid Dynamics
Print ISSN 1061-8562
Publisher Taylor & Francis
Peer Reviewed Peer Reviewed
Volume 34
Issue 3
Pages 204-225
DOI https://doi.org/10.1080/10618562.2020.1732941
Keywords RANS; Numerical error; Boundary layer; Near-wall grid resolution; k−ω alternatives
Public URL https://hull-repository.worktribe.com/output/3516079
Publisher URL https://www.tandfonline.com/doi/abs/10.1080/10618562.2020.1732941?journalCode=gcfd20