The Effect of the DNS Data Averaging Time on the Accuracy of RANS-DNS Simulations

Abstract

Statistical data obtained from direct numerical simulations (DNS) are often used as reference data for validating turbulence models. Thus, accuracy of the DNS data itself is of particular importance for understanding the potential error in Reynolds-averaged Navier- Stokes (RANS) simulations. Recent studies demonstrate that when the DNS data is used to represent budget terms in the RANS equations, simulations of wall-bounded turbulent flows conducted with such equations (herein referred to as RANS-DNS simulations) produce unphysical results. The current paper analyzes the contribution that convergence of DNS statistics makes to this discrepancy. The Reynolds stresses and budget terms in the RANSequations are collected in a fully developed channel flow ( = ) at increasing sample sizes and analyzed using the RANS-DNS simulation. The results demonstrate that statistical convergence is not the only contributing factor to the spurious RANS-DNS results, and further study is required. Nomenclature U = mean flow velocity in the streamwise direction U ∞ = free stream velocity + = / U u τ P = mean flow pressure u, v, w = turbulent velocity fluctuations in streamwise, normal-to-wall, and spanwise directions u i = turbulent velocity fluctuation in the i-direction u τ = friction velocity h = half-channel width t = time t n = averaging time of DNS data δ = boundary layer thickness = boundary layer momentum thickness ν = kinematic viscosity 1 Assistant Professor, Mechanical Engineering, MSC01 1104, 1 UNM Albuquerque, NM, 87131-00011, AIAA Associate Fellow. 2 AIAA Member.

Analysis of high-order velocity moments in a strained channel flow

“…Higher-order statistics were not collected in [21], but as has already been mentioned above, their statistical convergence was found acceptable in [14] using standard approaches to the statistical error estimation. As for the systematic error discovered in [21] in the second-order statistics, it is unlikely to expect higher-order statistics to be free from this error. Moreover, one would expect such error to be larger in odd moments as they are sensitive to the direction of velocity fluctuations in contrast to even moments.…”

“…However, convergence of statistics including highorder moments was tested, discussed at length and found adequate in [14]. In addition, the same DNS in the unstrained channel were run about ten times longer in our separate study [21]. In [21],…”

“…In addition, the same DNS in the unstrained channel were run about ten times longer in our separate study [21]. In [21],…”

“…9a shows the non-dimensional balance errors xx Err in the < 𝑢𝑢 2 >-budget obtained at the end of simulations at 𝑡𝑡 = 1.22 • 10 5 (compare with the simulation time of 𝑡𝑡 = 5.06 • 10 4 in [14]). The simulation times in [21] and [14] correspond to 1000 and 159 instantaneous flow field realizations, respectively. In this and following figures, the balance errors and other budget terms in the Reynolds-stress transport equations are normalized by 𝑢𝑢 𝜏𝜏0 4 /ν [19].…”

Analysis of uncertainty sources in DNS of a turbulent mixing layer using Nek5000

“…When RANS-DNS simulations were conducted in planar wall-bounded turbulent flows such as a channel flow and a zero-pressure gradient boundary layer over a flat plate using DNS data from [9][10][11], it was found that errors in such data were significant for their use in such simulations. The following work [12] demonstrated that statistical errors are unlikely to be the leading source of uncertainties in DNS data. That is, uncertainties in numerical procedures used in DNS have to be explored further, with the grid resolution near a wall raising questions in particular.…”