Note on porous rotating disk flow

We revisit the classical Karman rotating disk problem. A series analysis is used to derive estimates of boundary conditions at the surface. Using these estimates, computed thermal and flow fields for large mass transfer through the disk are readily obtained using a shooting method. The relevance of the problem to practical flows is discussed briefly.

Nonlinear effects on rotating disk flow in a cylindrical casing

The flow due to a finite disk rotating in an incompressible viscous fluid has been studied. A modified Newton-gradient finite difference scheme is used to obtain the solution of full Navier-Stokes equations numerically for different disk and cylinder sizes for a wide range of Reynolds numbers. The introduction of the aspect ratio and the disk-shroud gap, significantly alters the flow characteristics in the region under consideration, The frictional torque calculated from the flow data reveals that the contribution due to nonlinear terms is not negligible even at a low Reynolds number. For large Reynolds numbers, the flow structure reveals a strong boundary layer character.

On the laminar-turbulent transition of the rotating-disk flow: The role of absolute instability

© 2014 Cambridge University Press. This paper describes a detailed experimental study using hot-wire anemometry of the laminar-turbulent transition region of a rotating-disk boundary-layer flow without any imposed excitation of the boundary layer. The measured data are separated into stationary and unsteady disturbance fields in order to elaborate on the roles that the stationary and the travelling modes have in the transition process. We show the onset of nonlinearity consistently at Reynolds numbers, R, of ∼ 510, i.e. at the onset of Lingwood's (J. Fluid Mech., vol. 299, 1995, pp. 17-33) local absolute instability, and the growth of stationary vortices saturates at a Reynolds number of ∼ 550. The nonlinear saturation and subsequent turbulent breakdown of individual stationary vortices independently of their amplitudes, which vary azimuthally, seem to be determined by well-defined Reynolds numbers. We identify unstable travelling disturbances in our power spectra, which continue to grow, saturating at around R=585, whereupon turbulent breakdown of the boundary layer ensues. The nonlinear saturation amplitude of the total disturbance field is approximately constant for all considered cases, i.e. different rotation rates and edge Reynolds numbers. We also identify a travelling secondary instability. Our results suggest that it is the travelling disturbances that are fundamentally important to the transition to turbulence for a clean disk, rather than the stationary vortices. Here, the results appear to show a primary nonlinear steep-fronted (travelling) global mode at the boundary between the local convectively and absolutely unstable regions, which develops nonlinearly interacting with the stationary vortices and which saturates and is unstable to a secondary instability. This leads to a rapid transition to turbulence outward of the primary front from approximately R=565 to 590 and to a fully turbulent boundary layer above 650.

The turbulent rotating-disk boundary layer

© 2014 Elsevier Masson SAS. All rights reserved. The turbulent boundary layer on a rotating disk is studied with the aim of giving a statistical description of the azimuthal velocity field and to compare it with the streamwise velocity of a turbulent two-dimensional flat-plate boundary layer. Determining the friction velocity accurately is particularly challenging and here this is done through direct measurement of the velocity distribution close to the rotating disk in the very thin viscous sublayer using hot-wire anemometry. Compared with other flow cases, the rotating-disk flow has the advantage that the highest relative velocity with respect to a stationary hot wire is at the wall itself, thereby limiting the effect of heat conduction to the wall from the hot-wire probe. Experimental results of mean, rms, skewness and flatness as well as spectral information are provided. Comparison with the two-dimensional boundary layer shows that turbulence statistics are similar in the inner region, although the rms-level is lower and the maximum spectral content is found at smaller wavelengths for the rotating case. These features both indicate that the outer flow structures are less influential in the inner region for the rotating case.

Unsteady mhd flow and heat transfer on a rotating disk in an ambient fluid

An unsteady flow and heat transfer of a viscous incompressible electrically conducting fluid over a rotating infinite disk in an otherwise ambient fluid are studied. The unsteadiness in the flow field is caused by the angular velocity of the disk which varies with time. The magnetic field is applied normal to the disk surface. The new self-similar solution of the Navier-Stokes and energy equations is obtained numerically. The solution obtained here is not only the solution of the Navier-Stokes equations, but also of the boundary layer equations. Also, for a simple scaling factor, it represents the solution of the flow and heat transfer in the forward stagnation-point region of a rotating sphere or over a rotating cone. The asymptotic behaviour of the solution for a large magnetic field or for a large independent variable is also examined. The surface shear stresses in the radial and tangential directions and the surface heat transfer increase as the acceleration parameter increases. Also the surface shear stress in the radial direction and the surface heat transfer decrease with increasing magnetic field, but the surface shear stress in the tangential direction increases. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

Nonaxisymmetric unsteady motion over a rotating disk in the presence of free convection and magnetic field

The nonaxisymmetric unsteady motion produced by a buoyancy-induced cross-flow of an electrically conducting fluid over an infinite rotating disk in a vertical plane and in the presence of an applied magnetic field normal to the disk has been studied. Both constant wall and constant heat flux conditions have been considered. It has been found that if the angular velocity of the disk and the applied magnetic field squared vary inversely as a linear function of time (i.e. as (1??t*)?1, the governing Navier-Stokes equation and the energy equation admit a locally self-similar solution. The resulting set of ordinary differential equations has been solved using a shooting method with a generalized Newton's correction procedure for guessed boundary conditions. It is observed that in a certain region near the disk the buoyancy induced cross-flow dominates the primary von Karman flow. The shear stresses induced by the cross-flow are found to be more than these of the primary flow and they increase with magnetic parameter or the parameter ? characterizing the unsteadiness. The velocity profiles in the x- and y-directions for the primary flow at any two values of the unsteady parameter ? cross each other towards the edge of the boundary layer. The heat transfer increases with the Prandtl number but reduces with the magnetic parameter.

Cavitation erosion characteristics of poly(methyl methacrylate) in a rotating disk device

Experimental results pertaining to the initiation, dynamics and mechanism of cavitation erosion on poly(methyl methacrylate) specimens tested in a rotating disk device are described in detail. Erosion normally starts at the location nearest to the center of rotation (CR). As the exposure time to cavitation increases, additional erosion areas or sites appear away from the CR and secondary erosion (induced by eroded pits) spreads upstream and merges with the main pit. The microcracks increase in density towards the end of the incubation period and transform into macrocracks in most cases. A study of light optical photographs and scanning electron micrographs of the eroded area shows that material particles are removed from the network of cracks because of crack joining and pits indicate particle debris. Optical degradation (loss of transmittance) is observed to be greater on the back of the specimen than on the front.