Numerical errors at walls: on the sensitivity of RANS models to near-wall cell size. Issue 3 (15th March 2020)

• Record Type: Journal Article
• Authors: Lloyd, C. J.; Peakall, J.; Burns, A. D.; Keevil, G. M.; Dorrell, R. M.
• Is Part Of: International journal of computational fluid dynamics. Volume 34:Issue 3(2020)
• Page Start: 204
• Page End: 225
• Publication Date: 2020-03-15
• Subjects: RANS -- numerical error -- boundary layer -- near-wall grid resolution -- k−ω alternatives; Fluid dynamics -- Data processing -- Periodicals; 532.05
• DOI: 10.1080/10618562.2020.1732941
• Languages: English
• ISSNs: 1061-8562

Abstract

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.