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.

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