scholarly journals A note on the boundary layer equations with linear slip boundary condition

2008 ◽  
Vol 21 (8) ◽  
pp. 810-813 ◽  
Author(s):  
Miccal T. Matthews ◽  
James M. Hill
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Slip Boundary Condition ◽  
Boundary Layer Equations ◽  
Slip Boundary

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 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.

scholarly journals The appearance of boundary layers and drift flows due to high-frequency surface waves

2012 ◽  
Vol 707 ◽  
pp. 482-495 ◽  
Author(s):  
Ofer Manor ◽  
Leslie Y. Yeo ◽  
James R. Friend
Keyword(s):  
Boundary Layer ◽  
Surface Waves ◽  
High Frequency ◽  
Slip Boundary Condition ◽  
Inertial Effects ◽  
Velocity Amplitude ◽  
Slip Boundary ◽  
Long Period ◽  
Bulk Waves ◽  
Schlichting Streaming

AbstractThe classical Schlichting boundary layer theory is extended to account for the excitation of generalized surface waves in the frequency and velocity amplitude range commonly used in microfluidic applications, including Rayleigh and Sezawa surface waves and Lamb, flexural and surface-skimming bulk waves. These waves possess longitudinal and transverse displacements of similar magnitude along the boundary, often spatiotemporally out of phase, giving rise to a periodic flow shown to consist of a superposition of classical Schlichting streaming and uniaxial flow that have no net influence on the flow over a long period of time. Correcting the velocity field for weak but significant inertial effects results in a non-vanishing steady component, a drift flow, itself sensitive to both the amplitude and phase (prograde or retrograde) of the surface acoustic wave propagating along the boundary. We validate the proposed theory with experimental observations of colloidal pattern assembly in microchannels filled with dilute particle suspensions to show the complexity of the boundary layer, and suggest an asymptotic slip boundary condition for bulk flow in microfluidic applications that are actuated by surface waves.

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