Analysis of the Instability of the Boundary Layer over a Rotating Disk

2019 ◽

Vol XVI (2) ◽

pp. 13-22

Author(s):

Muhammad Ehtisham Siddiqui

Keyword(s):

Boundary Layer ◽

Boundary Layer Flow ◽

Three Dimensional ◽

Rotating Disk ◽

Careful Analysis ◽

Laboratory Frame ◽

Transition To Turbulence ◽

Turbulent Regime ◽

Mean Velocity ◽

Layer Flow

Three-dimensional boundary-layer flow is well known for its abrupt and sharp transition from laminar to turbulent regime. The presented study is a first attempt to achieve the target of delaying the natural transition to turbulence. The behaviour of two different shaped and sized stationary disturbances (in the laboratory frame) on the rotating-disk boundary layer flow is investigated. These disturbances are placed at dimensionless radial location (Rf = 340) which lies within the convectively unstable zone over a rotating-disk. Mean velocity profiles were measured using constant-temperature hot-wire anemometry. By careful analysis of experimental data, the instability of these disturbance wakes and its estimated orientation within the boundary-layer were investigated.

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Discontinuous solutions of the unsteady boundary-layer equations for a rotating disk of finite radius

Journal of Fluid Mechanics ◽

10.1017/jfm.2021.88 ◽

2021 ◽

Vol 915 ◽

Author(s):

A. Djehizian ◽

A.I. Ruban

Keyword(s):

Boundary Layer ◽

Rotating Disk ◽

Unsteady Boundary Layer ◽

Finite Radius ◽

Discontinuous Solutions ◽

Boundary Layer Equations

Abstract

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Numerical Integration of the Navier-Stokes Equations for a Disk Rotating in a Housing

Zeitschrift für Naturforschung A ◽

10.1515/zna-1985-0802 ◽

1985 ◽

Vol 40 (8) ◽

pp. 789-799 ◽

Cited By ~ 1

Author(s):

A. F. Borghesani

Keyword(s):

Boundary Layer ◽

Cylindrical Cavity ◽

Boundary Layer Thickness ◽

Stokes Equations ◽

Fluid Motion ◽

Rotating Disk ◽

Infinite Medium ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Viscous Torque

The Navier-Stokes equations for the fluid motion induced by a disk rotating inside a cylindrical cavity have been integrated for several values of the boundary layer thickness d. The equivalence of such a device to a rotating disk immersed in an infinite medium has been shown in the limit as d → 0. From that solution and taking into account edge effect corrections an equation for the viscous torque acting on the disk has been derived, which depends only on d. Moreover, these results justify the use of a rotating disk to perform accurate viscosity measurements.

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Boundary Layers on a Rotating Rough Disk

ASME 1994 International Computers in Engineering Conference and Exhibition ◽

10.1115/cie1994-0470 ◽

1994 ◽

Author(s):

Ali Heydari ◽

Ramin Miryan ◽

Saeid Sharifi

Keyword(s):

Boundary Layer ◽

Surface Roughness ◽

Parabolic Equations ◽

Roughness Parameter ◽

Rotating Disk ◽

Turbulent Fluid Flow ◽

Uniform Wall Temperature ◽

Curve Fit ◽

Uniform Wall ◽

Finite Difference Solution

Abstract In this paper the turbulent fluid flow over a rotating disk with roughness is considered. The disk is assumed to be at uniform wall temperature. The surface roughness is assumed to influence the turbulent boundary layer by adding a roughness parameter height k. Boundary-layer approximation reduces the elliptic Navier-Stockes equations to parabolic equations, where the Keller-Cebeci method of finite-difference solution is used to solve the resulting system of partial-differential equations. The resulting curve-fit equations to the numerically calculated results for three regions of laminar, transition and turbulent flow is shown to be consistent to those obtained for flow over a flat plate or inside a circular cylinder. Calculations for various surface roughness parameters are made and results are presented.

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Experimental Investigation of the Three-Dimensional Boundary Layer on a Rotating Disk

Turbulent Shear Flows 8 ◽

10.1007/978-3-642-77674-8_27 ◽

1993 ◽

pp. 403-414

Author(s):

Howard S. Littell ◽

John K. Eaton

Keyword(s):

Boundary Layer ◽

Experimental Investigation ◽

Three Dimensional ◽

Rotating Disk ◽

Dimensional Boundary

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Absolute Instability of the Rotating-Disk Boundary Layer

Laminar-Turbulent Transition ◽

10.1007/978-3-642-79765-1_46 ◽

1995 ◽

pp. 389-396 ◽

Cited By ~ 2

Author(s):

R. J. Lingwood

Keyword(s):

Boundary Layer ◽

Rotating Disk ◽

Absolute Instability

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Turbulent boundary layer on a rotating disk calculated with an effective viscosity

AIAA Journal ◽

10.2514/3.6160 ◽

1971 ◽

Vol 9 (2) ◽

pp. 255-261 ◽

Cited By ~ 16

Author(s):

PAUL COOPER

Keyword(s):

Boundary Layer ◽

Turbulent Boundary Layer ◽

Effective Viscosity ◽

Rotating Disk

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Instabilities of the von Kármán Boundary Layer

Applied Mechanics Reviews ◽

10.1115/1.4029605 ◽

2015 ◽

Vol 67 (3) ◽

Cited By ~ 19

Author(s):

R. J. Lingwood ◽

P. Henrik Alfredsson

Keyword(s):

Boundary Layer ◽

Three Dimensional ◽

Rotating Disk ◽

Direct Numerical Simulations ◽

Layer Model ◽

Complex Flow ◽

Von Karman ◽

Dimensional Boundary ◽

Flow Configurations ◽

Von Kármán

Research on the von Kármán boundary layer extends back almost 100 years but remains a topic of active study, which continues to reveal new results; it is only now that fully nonlinear direct numerical simulations (DNS) have been conducted of the flow to compare with theoretical and experimental results. The von Kármán boundary layer, or rotating-disk boundary layer, provides, in some senses, a simple three-dimensional boundary-layer model with which to compare other more complex flow configurations but we will show that in fact the rotating-disk boundary layer itself exhibits a wealth of complex instability behaviors that are not yet fully understood.

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