Effect of the dynamic slip boundary condition on the near-wall turbulent boundary layer

2020 ◽  
Vol 901 ◽  
Author(s):  
Cong Wang ◽  
Morteza Gharib
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Turbulent Boundary Layer ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
Image Position ◽  
Dynamic Slip ◽  
Near Wall

Abstract

Accurate PIV Measurement on Slip Boundary using Single-Pixel Algorithm

2021 ◽  
Author(s):  
Hongyuan Li ◽  
Yufan Cao ◽  
Xiangyu Wang ◽  
Xia Wan ◽  
Yaolei Xiang ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Slip Boundary Condition ◽  
Complex Flow ◽  
Wall Velocity ◽  
Slip Boundary ◽  
Micro Piv ◽  
Piv Measurement ◽  
Wall Flow ◽  
Single Pixel ◽  
Near Wall

Abstract To accurately measure the near-wall flow by particle image velocimetry (PIV) is a big challenge, especially for the slip boundary condition. Apart from high-precision measurements, an appropriate PIV algorithm is important to resolve the near-wall velocity profile. In our study, single-pixel algorithm is employed to calculate the near-wall flow, which is demonstrated to be capable of accurately resolving the flow velocity near the slip boundary condition. Based on the synthetic particle images, the advantages of the single-pixel algorithm are manifested in comparison with the conventional window correlation algorithm. Specially, the single-pixel algorithm has higher spatial resolution and accuracy, and lower systematic error and random error for the case of slip boundary condition. Furthermore, for experimental verification, micro-PIV measurements are conducted over a liquid-gas interface and the single-pixel algorithm is successfully applied to the calculation of near-wall velocity under the slip boundary condition, especially the negative slip velocity. The current work demonstrates the advantage of the single-pixel algorithm in analyzing the complex flow under the slip boundary condition, such as drag reduction, wall skin friction evaluation and near-wall vortex structure measurement.

On coupling between the Poincaré equation and the heat equation: non-slip boundary condition

1995 ◽  
Vol 284 ◽  
pp. 239-256 ◽  
Author(s):  
K. Zhang
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Free Boundary ◽  
Explicit Solution ◽  
Numerical Solutions ◽  
Slip Boundary Condition ◽  
Onset Of Convection ◽  
Slip Boundary ◽  
Ekman Boundary Layer ◽  
Stress Free Boundary

In contrast to the well-known columnar convection mode in rapidly rotating spherical fluid systems, the viscous dissipation of the preferred convection mode at sufficiently small Prandtl numberPrtakes place only in the Ekman boundary layer. It follows that different types of velocity boundary condition lead to totally different forms of the asymptotic relationship between the Rayleigh numberRand the Ekman numberEfor the onset of convection. We extend both perturbation and numerical analyses with the stress-free boundary condition (Zhang 1994) in rapidly rotating spherical systems to those with the non-slip boundary condition. Complete analytical solutions – the critical parameters for the onset of convection and the corresponding flow and temperature structure – are obtained and a new asymptotic relation betweenRandEis derived. While an explicit solution of the Ekman boundary-layer problem can be avoided by constructing a proper surface integral in the case of the stress-free boundary problem, an explicit solution of the spherical Ekman boundary layer is required and then obtained to derive the solvability condition for the present problem. In the corresponding numerical analysis, velocity and temperature are expanded in terms of spherical harmonics and Chebychev functions. Accurate numerical solutions are obtained in the asymptotic regime of smallEandPr, and comparison between the analytical and numerical solutions is then made to demonstrate that a satisfactory quantitative agreement between the analytical and numerical analyses is reached.

scholarly journals Dynamic slip wall model for large-eddy simulation

2018 ◽  
Vol 859 ◽  
pp. 400-432 ◽  
Author(s):  
Hyunji Jane Bae ◽  
Adrián Lozano-Durán ◽  
Sanjeeb T. Bose ◽  
Parviz Moin
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Channel Flow ◽  
A Priori ◽  
Wall Stress ◽  
Turbulent Channel Flow ◽  
Slip Boundary Condition ◽  
Wall Model ◽  
Slip Boundary ◽  
Eddy Simulation

Wall modelling in large-eddy simulation (LES) is necessary to overcome the prohibitive near-wall resolution requirements in high-Reynolds-number turbulent flows. Most existing wall models rely on assumptions about the state of the boundary layer and require a priori prescription of tunable coefficients. They also impose the predicted wall stress by replacing the no-slip boundary condition at the wall with a Neumann boundary condition in the wall-parallel directions while maintaining the no-transpiration condition in the wall-normal direction. In the present study, we first motivate and analyse the Robin (slip) boundary condition with transpiration (non-zero wall-normal velocity) in the context of wall-modelled LES. The effect of the slip boundary condition on the one-point statistics of the flow is investigated in LES of turbulent channel flow and a flat-plate turbulent boundary layer. It is shown that the slip condition provides a framework to compensate for the deficit or excess of mean momentum at the wall. Moreover, the resulting non-zero stress at the wall alleviates the well-known problem of the wall-stress under-estimation by current subgrid-scale (SGS) models (Jiménez & Moser, AIAA J., vol. 38 (4), 2000, pp. 605–612). Second, we discuss the requirements for the slip condition to be used in conjunction with wall models and derive the equation that connects the slip boundary condition with the stress at the wall. Finally, a dynamic procedure for the slip coefficients is formulated, providing a dynamic slip wall model free of a priori specified coefficients. The performance of the proposed dynamic wall model is tested in a series of LES of turbulent channel flow at varying Reynolds numbers, non-equilibrium three-dimensional transient channel flow and a zero-pressure-gradient flat-plate turbulent boundary layer. The results show that the dynamic wall model is able to accurately predict one-point turbulence statistics for various flow configurations, Reynolds numbers and grid resolutions.

scholarly journals On the dynamic slip boundary condition for Navier–Stokes-like problems

2021 ◽  
pp. 1-48
Author(s):  
Anna Abbatiello ◽  
Miroslav Bulíček ◽  
Erika Maringová
Keyword(s):  
Boundary Condition ◽  
Shear Stress ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Slip Boundary ◽  
Boundary Terms ◽  
The Moment ◽  
Dynamic Slip ◽  
Proper Generalization ◽  
Slip Phenomenon

The choice of the boundary conditions in mechanical problems has to reflect the interaction of the considered material with the surface. Still the assumption of the no-slip condition is preferred in order to avoid boundary terms in the analysis and slipping effects are usually overlooked. Besides the “static slip models”, there are phenomena that are not accurately described by them, e.g. at the moment when the slip changes rapidly, the wall shear stress and the slip can exhibit a sudden overshoot and subsequent relaxation. When these effects become significant, the so-called dynamic slip phenomenon occurs. We develop a mathematical analysis of Navier–Stokes-like problems with a dynamic slip boundary condition, which requires a proper generalization of the Gelfand triplet and the corresponding function space setting.

scholarly journals Predictor homotopy analysis method (PHAM) for nano boundary layer flows with nonlinear Navier boundary condition: Existence of four solutions

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1687-1697 ◽  
Author(s):  
Elyas Shivanian ◽  
Hamed Alsulami ◽  
Mohammed Alhuthali ◽  
Saeid Abbasbandy
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Homotopy Analysis Method ◽  
Boundary Layer Equation ◽  
Slip Boundary Condition ◽  
Analysis Method ◽  
Slip Boundary ◽  
Navier Boundary Condition ◽  
Homotopy Analysis ◽  
Analytical Series

In the present work, the classical laminar boundary layer equation of the flow away from the origin past a wedge with the no-slip boundary condition replaced by a nonlinear Navier boundary condition is considered. This boundary condition contains an arbitrary index parameter, denoted by n > 0, which appears in the differential equation to be solved. Predictor homotopy analysis method (PHAM) is applied to this problem and more, it is proved corresponding to the value n = 1/3, there exist four solutions. Furthermore, these solutions are approximated by analytical series solution using PHAM for further physical interpretations.

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