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.

Skin friction and surface temperature of an insulated flat plate fixed in a fluctuating stream

1971 ◽  
Vol 46 (1) ◽  
pp. 165-175 ◽  
Author(s):  
Hiroshi Ishigaki
Keyword(s):  
Boundary Layer ◽  
Surface Temperature ◽  
Flat Plate ◽  
Skin Friction ◽  
High Frequency ◽  
Energy Equation ◽  
Oscillation Amplitude ◽  
Flow Oscillation ◽  
Velocity Amplitude ◽  
The Mean

The time-mean skin friction of the laminar boundary layer on a flat plate which is fixed at zero incidence in a fluctuating stream is investigated analytically. Flow oscillation amplitude outside the boundary layer is assumed constant along the surface. First, the small velocity-amplitude case is treated, and approximate formulae are obtained in the extreme cases when the frequency is low and high. Next, the finite velocity-amplitude case is treated under the condition of high frequency, and it is found that the formula obtained for the small-amplitude and high-frequency case is also valid. These results show that the increase of the mean skin friction reduces with frequency and is ultimately inversely proportional to the square of frequency.The corresponding energy equation is also studied simultaneously under the condition of zero heat transfer between the fluid and the surface. It is confirmed that the time-mean surface temperature increases with frequency and tends to be proportional to the square root of frequency. Moreover, it is shown that the timemean recovery factor can be several times as large as that without flow oscillation.

scholarly journals The mechanics of the Tollmien-Schlichting wave

1996 ◽  
Vol 312 ◽  
pp. 107-124 ◽  
Author(s):  
Peter G. Baines ◽  
Sharan J. Majumdar ◽  
Humio Mitsudera
Keyword(s):  
Boundary Layer ◽  
Outer Part ◽  
Slip Boundary Condition ◽  
Slip Condition ◽  
Linear Solution ◽  
Slip Boundary ◽  
Uniform Shear ◽  
Blasius Boundary Layer ◽  
Partial Mode ◽  
Tollmien Schlichting

We describe a mechanistic picture of the essential dynamical processes in the growing Tollmien-Schlichting wave in a Blasius boundary layer and similar flows. This picture depends on the interaction between two component parts of a disturbance (denoted ‘partial modes’), each of which is a complete linear solution in some idealization of the system. The first component is an inviscid mode propagating on the vorticity gradient of the velocity profile with the free-slip boundary condition, and the second, damped free viscous modes in infinite uniform shear with the no-slip condition. There are two families of these viscous modes, delineated by whether the phase lines of the vorticity at the wall are oriented with or against the shear, and they are manifested as resonances in a forced system. The interaction occurs because an initial ‘inviscid’ disturbance forces a viscous response via the no-slip condition at the wall. This viscous response is large near the resonance associated with the most weakly damped viscous mode, and in the unstable parameter range it has suitable phase at the outer part of the boundary layer to increase the amplitude of the inviscid partial mode by advection.

scholarly journals Fluid dynamics of the slip boundary condition for isothermal rimming flow with moderate inertial effects

2019 ◽  
Vol 31 (3) ◽  
pp. 033602 ◽  
Author(s):  
J. M. P. Nicholson ◽  
H. Power ◽  
O. Tammisola ◽  
S. Hibberd ◽  
E. D. Kay
Keyword(s):  
Fluid Dynamics ◽  
Boundary Condition ◽  
Slip Boundary Condition ◽  
Inertial Effects ◽  
Slip Boundary ◽  
Rimming Flow

scholarly journals Asymptotic theory of resonant flow in a spheroidal cavity driven by latitudinal libration

2012 ◽  
Vol 692 ◽  
pp. 420-445 ◽  
Author(s):  
Keke Zhang ◽  
Kit H. Chan ◽  
Xinhao Liao
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Asymptotic Solution ◽  
Slip Boundary Condition ◽  
Viscous Boundary Layer ◽  
Slip Boundary ◽  
Oblate Spheroidal ◽  
Spheroidal Cavity ◽  
Viscous Boundary

AbstractWe consider a homogeneous fluid of viscosity $\nu $ confined within an oblate spheroidal cavity, ${x}^{2} / {a}^{2} + {y}^{2} / {a}^{2} + {z}^{2} / ({a}^{2} (1\ensuremath{-} {\mathscr{E}}^{2} ))= 1$, with eccentricity $0\lt \mathscr{E}\lt 1$. The spheroidal container rotates rapidly with an angular velocity ${\mbit{\Omega} }_{0} $, which is fixed in an inertial frame and defines a small Ekman number $E= \nu / ({a}^{2} \vert {\mbit{\Omega} }_{0} \vert )$, and undergoes weak latitudinal libration with frequency $\hat {\omega } \vert {\mbit{\Omega} }_{0} \vert $ and amplitude $\mathit{Po}\vert {\mbit{\Omega} }_{0} \vert $, where $\mathit{Po}$ is the Poincaré number quantifying the strength of Poincaré force resulting from latitudinal libration. We investigate, via both asymptotic and numerical analysis, fluid motion in the spheroidal cavity driven by latitudinal libration. When $\vert \hat {\omega } \ensuremath{-} 2/ (2\ensuremath{-} {\mathscr{E}}^{2} )\vert \gg O({E}^{1/ 2} )$, an asymptotic solution for $E\ll 1$ and $\mathit{Po}\ll 1$ in oblate spheroidal coordinates satisfying the no-slip boundary condition is derived for a spheroidal cavity of arbitrary eccentricity without making any prior assumptions about the spatial–temporal structure of the librating flow. In this case, the librationally driven flow is non-axisymmetric with amplitude $O(\mathit{Po})$, and the role of the viscous boundary layer is primarily passive such that the flow satisfies the no-slip boundary condition. When $\vert \hat {\omega } \ensuremath{-} 2/ (2\ensuremath{-} {\mathscr{E}}^{2} )\vert \ll O({E}^{1/ 2} )$, the librationally driven flow is also non-axisymmetric but latitudinal libration resonates with a spheroidal inertial mode that is in the form of an azimuthally travelling wave in the retrograde direction. The amplitude of the flow becomes $O(\mathit{Po}/ {E}^{1/ 2} )$ at $E\ll 1$ and the role of the viscous boundary layer becomes active in determining the key property of the flow. An asymptotic solution for $E\ll 1$ describing the librationally resonant flow is also derived for an oblate spheroidal cavity of arbitrary eccentricity. Three-dimensional direct numerical simulation in an oblate spheroidal cavity is performed to demonstrate that, in both the non-resonant and resonant cases, a satisfactory agreement is achieved between the asymptotic solution and numerical simulation at $E\ll 1$.

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.

The effect of oscillation on flat plate heat transfer

1971 ◽  
Vol 47 (3) ◽  
pp. 537-546 ◽  
Author(s):  
Hiroshi Ishigaki
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Flat Plate ◽  
Viscous Dissipation ◽  
High Frequency ◽  
Small Amplitude ◽  
Oscillation Amplitude ◽  
Flow Oscillation ◽  
Velocity Amplitude ◽  
Dissipation Effect

The time-mean heat transfer of the incompressible laminar boundary layer on a flat plate under the influence of oscillation is studied analytically. Flow oscillation amplitude outside the boundary layer is assumed constant along the surface and the viscous dissipation effect is considered. First, the small velocity–amplitude case is treated and the approximate formulae are obtained in the extreme cases when the frequency is low and high. Next, the finite velocity–amplitude case is treated under the condition of high frequency and it is found that the formulae obtained for the small amplitude and high frequency case are also valid. These results show that, when the oscillation is of high frequency, the time-mean heat flux to the wall can be several times as large as that without oscillation. This is due wholly to the viscous dissipation effect combined with oscillation.

Nonlinear interaction of electrostatic surface waves in a semi-infinite plasma. Part 1. Derivation of the coupled mode equations

1981 ◽  
Vol 26 (2) ◽  
pp. 217-230 ◽  
Author(s):  
V. Atanassov ◽  
R. Mateev ◽  
I. Zhelyazkov
Keyword(s):  
Surface Waves ◽  
Nonlinear Interaction ◽  
High Frequency ◽  
Low Frequency ◽  
Density Perturbation ◽  
Coupled Mode ◽  
Hybrid Nature ◽  
Bulk Waves ◽  
Amplitude Attenuation

We have derived a set of coupled mode equations which govern the nonlinear interaction of three high-frequency electrostatic surface waves through a low-frequency density perturbation produced by them. The set is compared with that obtained when a similar problem is solved for bulk waves in an infinite plasma. Some differences are shown to exist caused by the specific features of surface waves such as the amplitude attenuation normal to the interface and their hybrid nature.

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