Boundary Layers on a Rotating Disk

Cebeci, Tuncer; Abbott, D. E.

doi:10.2514/3.60447

Cited by 26 publications

(13 citation statements)

References 14 publications

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“…This problem has been the subject of a wide variety of previous investigations including experimental studies (Erian &Tong 1971 andLittell &Eaton 1994) and numerical solutions involving the use of an eddy viscosity model (Cooper 1971 andCebeci &Abbott 1975), an energy-dissipation model (Launder & Sharma 1974) and largeeddy simulation (Wu & Squires 2000). The present investigation will adopt a similar starting point to that of Cooper in that we also use the RANS equations simplified by the boundary layer approximation and the Cebeci-Smith eddy viscosity model; however our approach will differ from that of Cooper as we seek a more analytical solution and unlike Cooper we will ignore intermittency.…”

Section: Rotating Diskmentioning

confidence: 99%

“…Instability and transition from the laminar state are addressed by Gregory, Stuart & Walker (1955) and more recently Lingwood (1995Lingwood ( , 1996, Davies & Carpenter (2003) and Davies, Thomas & Carpenter (2007) from various different and interesting perspectives. The fully turbulent state which is our central concern has been the subject of a significant range and variety of investigations, including Cooper (1971), Erian & Tong (1971), Launder & Sharma (1974), Cebeci & Abbott (1975), Littell & Eaton (1994) and Wu & Squires (2000). Further background references of note here include Prandtl (1952), Clauser (1956), and Schlichting (1960).…”

Section: Introductionmentioning

confidence: 99%

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Turbulent flow on a planar moving belt and a rotating disk: modelling and comparisons

McDARBY

Smith

2007

J. Fluid Mech.

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Modelling of the fully turbulent flow produced on a moving belt and of that induced on a rotating disk is described, for each of which a more analytical approach is adopted than previously seen. The analysis for the two-dimensional moving belt indicates novel structures and these are found to carry over directly to the rotating disk flow which, ignoring the transitional regime, is three-componential but twodimensional due to axisymmetry. This is based on addressing the Reynolds-averaged Navier-Stokes equations together with an eddy viscosity model, with the flow structure being analysed for high Reynolds numbers. A classical (von Kármán) constant within the model plays an important and surprising role, indicating that each of the belt and the disk flows has quite a massive thickness. Comparisons made with previous work show varying degrees of agreement. The approach, including the new prediction of massive thicknesses independent of the Reynolds number, is expected to extend to flows induced by rotary blades, by related rotary devices and by other configurations of industrial interest.

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Section: Rotating Diskmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Turbulent flow on a planar moving belt and a rotating disk: modelling and comparisons

McDARBY

Smith

2007

J. Fluid Mech.

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“…The fully turbulent state which is our central concern has been the subject of a significant range and variety of investigations, including [6][7][8][9][10][11]. Further background references of note here include [12][13][14].…”

Section: On a Moving Belt Or A Rotating Diskmentioning

confidence: 99%

On turbulent separation

2010

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The present theoretical article, dedicated to the memory of James Lighthill and his research contributions, is directed towards the central features of turbulent separation. The focus is on the time-mean equations, where the ensemble-averaged motion for an incompressible fluid is modelled as planar and steady. Specific major recent developments are discussed which are closely concerned in one way or another with turbulent separation at increased Reynolds numbers. These developments include in particular the behaviour of relatively thick boundary layers, on the one hand, and the intricate behaviour of breakaway separation on the other. The article brings the two behaviours together in a discussion of large-scale separation structure and accompanying interactions. The work presented here applies to quite general turbulence models and for specific cases enables direct comparisons to be made with experiments. The work also leads to new suggestions involving a combination of low-and high-intensity turbulence for the fluid motion around a bluff body and in its wake.

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“…The fluid motion induced is usually turbulent in practice. For example, one motivation for the current theoretical work is from industry, where the possible application to rotor-blade flows represents a potentially significant area of research not least because of its use in the study of helicopter dynamics and the desire within industry to develop a theoretical understanding of such flows in the hope that this may lead to improvements in design [1][2][3][4][5][6][7][8][9][10]. The detailed link with the present work may be quite indirect throughout as our emphasis is on fundamental properties and asymptotic description; indeed, the apparent breaks of both symmetry and periodicity associated with forward movement (rather than hovering) of a helicopter and the resulting complex vortex streets are not addressed.…”

Section: Introductionmentioning

confidence: 99%

“…The present study considers a rotating blade system in otherwise still fluid, corresponding to a simple hovering motion [1][2][3][4][5][6][7][8]. The fluid motion induced is usually turbulent in practice.…”

Section: Introductionmentioning

confidence: 99%

Turbulent interactions for rotating blades and wakes

McDARBY

Smith

2010

J Eng Math

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Modelling and asymptotic analysis of the fully turbulent flow produced on a rotating blade system or cut-disk are described, the cut-disk being a thin disk with a significant amount of solidity removed. This is based on addressing the Reynolds-averaged Navier-Stokes equations in three-dimensional boundary-layer form together with an eddy-viscosity model, with the flow structure being analyzed for high Reynolds numbers. Interaction between blades and wakes plays a substantial part. The relationship between the present three-dimensional flow and the two-dimensional or axisymmetric flow over an isolated blade and a rotating disk is considered and leads to the finding that for the most part the flow on a cut-disk is, to leading order, the same as that on a rotating disk. A physical parameter, the disk solidity, plays an important role linking these two flows. The limiting case of low disk solidity yields the flow past an isolated blade locally, with global wake effects acting to provide the necessary azimuthal periodicity. This low-solidity limit also permits more analytical solutions which show agreement with numerical findings.

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Boundary Layers on a Rotating Disk

Cited by 26 publications

References 14 publications

Turbulent flow on a planar moving belt and a rotating disk: modelling and comparisons

Turbulent flow on a planar moving belt and a rotating disk: modelling and comparisons

On turbulent separation

Turbulent interactions for rotating blades and wakes

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