Resolution standards for direct numerical simulation of wall turbulence in high-pressure transcritical fluids

This study investigates the resolution requirements for direct numerical simulation (DNS) of high-pressure transcritical wall-bounded turbulence, focusing on channel and square duct flow configurations subjected to cold (cw) and hot (hw) walls. The applicability of traditional DNS resolution standards to capture first- and second-order flow statistics is critically assessed, emphasizing the complex thermodynamic and hydrodynamic interactions in transcritical fluid regimes. A comprehensive analysis, incorporating spectrograms, dissipation rate distributions, and distribution of Kolmogorov (ηu), Batchelor (ηT), and density-gradient (δ∇ρ) scales has been conducted. The findings reveal that under-resolved grids significantly underestimate the intensity and proximity of the pseudo-boiling region to the hot wall, particularly in channel flows where lateral confinement is absent. In contrast, square duct flows benefit from secondary flow motions, which stabilize and stratify structures in the pseudo-boiling region. Using “traditionally standard” grid resolutions, first-order velocity and temperature statistics are captured with errors generally below 2%. However, significant discrepancies arise in the turbulent fluctuations, particularly related to energy dissipation for under-resolved cases. To address these issues, the “standard” grid resolution has been refined to better capture local property gradients, their variance, and resulting hydrodynamic and thermophysical scales. For channel flows, the proposed grid features wall-normal resolution requirements of Δyhw+<1 and Δy/ηu, Δy/ηT≲3.5, with streamwise resolutions of Δxcw+≲8, Δxhw+<10.0 and Δx/ηu, Δx/ηT≲9.0. Spanwise resolutions are limited to Δzcw+<2.5, Δzhw+<3.4 and Δz/ηu, Δz/ηu≲3.5. Slightly larger values are applicable for square duct flows. Finally, the resolution requirements obtained are applicable to a wide range of fluids, thermophysical regimes and flow geometries.