A Lagrangian relaxation towards equilibrium wall model for large eddy simulation

Fowler, Mitchell; Zaki, Tamer A.; Meneveau, Charles

doi:10.1017/jfm.2021.1156

Cited by 17 publications

(49 citation statements)

References 60 publications

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“…It is of utmost importance to reduce the time constant C t used for averaging. Previous studies such as Yang et al (2017); Fowler et al (2022) suggest that this time averaging helps significantly the computation. This present paper investigates it in the framework described in previous sections.…”

Section: Time Averaging Requirementsmentioning

confidence: 93%

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

Gillyns

Buckingham

Winckelmans

2022

Flow Turbulence Combust

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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.

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Section: Time Averaging Requirementsmentioning

confidence: 93%

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

Gillyns

Buckingham

Winckelmans

2022

Flow Turbulence Combust

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“…The most basic, yet widely used, form of WM -equilibrium wall model (EWM) [34][35][36][37][38] -is based on a simplified solution of fluid flow near the wall, in which all the non-equilibrium terms (related to e.g., pressure gradient, acceleration, and buoyancy) are neglected. While the EWM is generally effective in predicting the flow behavior, including in non-equilibrium flows 39 , its ability to accurately capture strong non-equilibrium effects in certain flow scenarios can be limited 40,41 . Recent developments in wall modeling, e.g., the integral WM 42 , the non-equilibrium WM 43 , the slip-WM 44,45 and the Lagrangian relaxation towards equilibrium WM 41 , seek improvements by incorporating a lower level of simplifications.…”

Section: Introductionmentioning

confidence: 99%

“…While the EWM is generally effective in predicting the flow behavior, including in non-equilibrium flows 39 , its ability to accurately capture strong non-equilibrium effects in certain flow scenarios can be limited 40,41 . Recent developments in wall modeling, e.g., the integral WM 42 , the non-equilibrium WM 43 , the slip-WM 44,45 and the Lagrangian relaxation towards equilibrium WM 41 , seek improvements by incorporating a lower level of simplifications. Further efforts are still needed to better predict complex flows with separation, transition, and heat transfer.…”

Section: Introductionmentioning

confidence: 99%

Log-law recovery through reinforcement-learning wall model for large-eddy simulation

Vadrot¹,

Yang²,

Bae³

et al. 2023

Preprint

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This paper focuses on the use of reinforcement learning (RL) as a machine-learning (ML) modeling tool for near-wall turbulence. RL has demonstrated its effectiveness in solving high-dimensional problems, especially in domains such as games. Despite its potential, RL is still not widely used for turbulence modeling and is primarily used for flow control and optimization purposes. A new RL wall model (WM) called VYBA23 is developed in this work, which uses agents dispersed in the flow near the wall. The model is trained on a single Reynolds number (Re τ = 10 4 ) and does not rely on high-fidelity data, as the back-propagation process is based on a reward rather than output error. The states of the RLWM, which are the representation of the environment by the agents, are normalized to remove dependence on the Reynolds number. The model is tested and compared to another RLWM (BK22) and to an equilibrium wall model, in a half-channel flow at eleven different Reynolds numbers (Re τ ∈ [180; 10 10 ]). The effects of varying agents' parameters such as actions range, time-step, and spacing are also studied. The results are promising, showing little effect on the average flow field but some effect on wall-shear stress fluctuations and velocity fluctuations. This work offers positive prospects for developing RLWMs that can recover physical laws, and for extending this type of ML models to more complex flows in the future.

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“…Yang et al (2015) introduced the integral non-equilibrium wall model based on the integrated boundary layer equations and assumed velocity profiles, which can be considered as a compromise between the aforementioned two classes of wall models. Similarly, Fowler, Zaki & Meneveau (2022) substituted the law-of-the-wall velocity profile into the wall normal integrated momentum balance and derived a Lagrangian relaxation towards an equilibrium transport equation for the friction-velocity vector. Several efforts have also been directed towards formulating wall models which are not based on RANS.…”

Section: Introductionmentioning

confidence: 99%

Wall-modelled large-eddy simulation of three-dimensional turbulent boundary layer in a bent square duct

Hayat

Park

2023

J. Fluid Mech.

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We conduct wall-modelled large-eddy simulation (WMLES) of a pressure-driven three-dimensional turbulent boundary layer developing on the floor of a bent square duct to investigate the predictive capability of three widely used wall models, namely, a simple equilibrium stress model, an integral non-equilibrium model, and a partial differential equation (PDE) non-equilibrium model. The numerical results are compared with the experiment of Schwarz & Bradshaw (J. Fluid Mech., vol. 272, 1994, pp. 183–210). While the wall-stress magnitudes predicted by the three wall models are comparable, the PDE non-equilibrium wall model produces a substantially more accurate prediction of the wall-stress direction, followed by the integral non-equilibrium wall model. The wall-stress direction from the wall models is shown to have separable contributions from the equilibrium stress part and the integrated non-equilibrium effects, where how the latter is modelled differs among the wall models. The triangular plot of the wall-model solution reveals different capabilities of the wall models in representing variation of flow direction along the wall-normal direction. In contrast, the outer LES solution is unaffected by the type of wall model used, resulting in nearly identical predictions of the mean and turbulent statistics in the outer region for all the wall models. This is explained by the vorticity dynamics and the inviscid skewing mechanism of generating the mean three-dimensionality. Finally, the LES solution in the outer layer is used to study the anisotropy of turbulence. In contrast to the canonical two-dimensional wall turbulence, the Reynolds stress anisotropy exhibits strong non-monotonic behaviour with increasing wall distance.

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A Lagrangian relaxation towards equilibrium wall model for large eddy simulation

Cited by 17 publications

References 60 publications

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

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

Log-law recovery through reinforcement-learning wall model for large-eddy simulation

Wall-modelled large-eddy simulation of three-dimensional turbulent boundary layer in a bent square duct

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