Implementation and Validation of an Algebraic Wall Model for LES in Nek5000

Abstract

Turbulent flows are most often wall-bounded, rendering the treatment of the wall essential. In this work, the near-wall layer is modelled in large eddy simulations which enables simulating high Reynolds number flows. An algebraic wall model has been implemented in the spectral element code Nek5000. It consists of an approximate boundary condition that relates the wall shear stress to the velocity measured close to the wall, on the upper edge of the first spectral element. The wall shear stress model approximates the law of the wall for hydraulically smooth cases. The model is applied to channel flow cases at $$Re_{\tau }=1000$$ R e τ = 1000 and at $$Re_{\tau }=5200$$ R e τ = 5200 . The wmLES results obtained with the present implementation are seen to compare very well with those of reference direct numerical simulations in the resolved region. They also remain remarkably close to the reference results for a large part of the under-resolved region; which is not necessarily the case when using low order implementations and even other types of high order discretizations, as found in the literature. Various parameters are studied such as the time averaging, the height of the near wall under-resolved element, and the mesh requirements. The obtained results indicate that accurate results can be obtained with Nek5000 at a reduced cost thanks to this newly implemented wmLES model. This work provides the necessary guidelines for simple flows, and it will serve as a first basis for simulating more complex flows at high Reynolds numbers.

Wind tunnel inflow data assimilation in an LES digital twin for improving validation against an experimental wind turbine wake

“…The power coefficient has more uncertainties, because of losses that were not accurately measured. More details about the design of the wind turbine can be found in [5].…”

A wall model for large-eddy simulation of highly compressible flows based on a new scaling of the law of the wall

“…Only the component of velocity tangent to the wall is used to compute the wall shear stress. Several authors (Schumann 1975;Piomelli & Balaras 2002;Gillyns, Buckingham & Winckelmans 2022) choose to average the velocity in time and/or space. However, as investigated by Lee, Cho & Choi (2013) and Frère et al (2017), imposing the value of the wall shear stress instantaneously and locally is sufficient to predict the mean velocity profile.…”

Wind turbine wake: bridging the gap between large eddy simulations and wind tunnel experiments

“…The mesh is constructed using a uniform distribution streamwise and spanwise, and is refined near the walls. Based on our previous work [5], we use the newly validated wall-modeled LES (wmLES) within a spectral element method for the wall boundary conditions. The so-called recycling plane is taken at x = 4.5 m, far enough from the outlet such that its effect is negligible.…”

“…The so-called recycling plane is taken at x = 4.5 m, far enough from the outlet such that its effect is negligible. Due to the nature of the spectral element method, Gibbs phenomena are appearing at the element boundaries when performing LES, especially for the resolved turbulent fluctuations, see [5]. The R2M is often used to scale the boundary layer height in a developing flow, by applying the scaling on the position of each point.…”