# Navier-Stokes-ω model with slip and friction boundary conditions at high Reynolds numbers

## DOI:

https://doi.org/10.15282/jmes.18.2.2024.7.0794## Keywords:

Slip With Friction Boundary Conditions, Reattachment Point, Friction Coefficient, Turbulence, Navier-Stokes-ω Model (NS-ω)## Abstract

The no-slip boundary condition is indeed a fundamental concept in fluid dynamics, especially for flows at lower Reynolds numbers where viscous effects dominate. However, inertial effects become more significant at higher Reynolds numbers, and the no-slip condition might not accurately represent the behavior of the fluid near the boundary. In such cases, partial slip or slip boundary conditions become more relevant as they take into account the slip between the fluid and the boundary. This study offers the presentation of numerical experiments for a 2-dimensional channel flow, through a step Navier-Stokes-ω model at high Reynolds numbers. The slip boundary conditions with friction is used in these numerical tests, namely along the step and on the lower and upper walls. The impact of the friction coefficient on the flow characteristics is illustrated. Especially for large Reynolds numbers, the effect of the friction coefficient on the flow region is examined. In the numerical tests, the Crank-Nicolson method is used for time discretization, while the Galerkin finite element method is applied for space discretization. It can be observed that as the coefficient of friction decreased, the eddies are further away from the step and moved towards the outer flow. In addition, the size of the eddies are larger for small coefficients of friction. For

Re = 5000, the reattachment length calculated on a fine mesh at time *T* = 50 is close to the step. For Re = 10000, the reattachment lengths determined for different friction coefficients on both meshes are very similar, with eddies forming just behind the step. Similarly, for Re = 15000 and *β* = 0.0001, the reattachment lengths calculated on the fine mesh are farther from the step. Conversely, for other values of* β*, the reattachment lengths are close to the step. The results are explained according to flow physics.

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*J. Mech. Eng. Sci.*, vol. 18, no. 2, pp. 10058–10068, Jun. 2024.

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