Flow of a third grade fluid due to an accelerated disk

The magnetohydrodynamic (MHD) flow induced by non‐coaxial rotation of porous disk and a third grade fluid at infinity is investigated. The disk is moving with uniform acceleration and rotating with a uniform angular velocity. Numerical solution of the governing nonlinear initial and boundary value problem is obtained. The effects of physical parameters on the velocity profiles are examined in detail. The present study shows that the constant acceleration part has a greater influence than the time part of the assumed variable velocity of the disk. Copyright © 2009 John Wiley & Sons, Ltd.     

Flow of a Casson fluid on a rotating disk

The flow of a thin layer of a Casson fluid on a fast rotating disk is considered. The film thickness distribution at various times for various initial thickness distribution is calculated. The stability of the flow is examined.     

MHD UNSTEADY FLOWS DUE TO NON—COAXIAL ROTATIONS OF A DISK AND A FLUID AT INFINITY

Exact analytical solution for flows of an electrically conducting fluid over an infinite oscillatory disk in the presence of a uniform transverse magnetic field is constructed. Both the disk and the fluid are in a state of non-coaxial rotation. Such a flow model has a great significance not only due to its own theoretical interest, but also due to applications to geophysics and engineering. The resulting initial value problem has been solved analytically by applying the Laplace transform technique and the explicit expressions for the velocity for steady and unsteady cases have been established. The analysis of the obtained results shows that the flow field is appreciably influenced by the applied magnetic field, the frequency and rotation parameters.     

Combined effects of rotation and translation on a MHD flow due to compressible viscous fluid

Summary The modification of an axi-symmetric viscous flow due to a relative rotation of a disk or fluid by a translation of the boundary are studied. The fluid is taken to be compressible and electrically conducting. The equations governing the motion are solved iteratively through a central-difference scheme. The effect of an axial magnetic field and disk temperature on the flow and heat transfer are included in the present analysis. The translation of the disk or fluid generates a velocity field at each plane parallel to the disk (secondary flow). The cartesian components of the velocity due to the secondary flow are oscillatory in nature when a rigid body rotation of the free stream along with a translation of the disk is considered. The magnetic field damps out the velocity field, and reduces the thickness of the boundary layer. The cross component of wall shear due to secondary flow acts in a direction opposite to the rotation of the disk or fluid for all cases of the motion. The rise in disk temperature produces an increment in the magnitude of the wall shear associated with the secondary flow.     

Unsteady compressible flow due to relative rotation and translation of a viscous fluid on a disk

Summary The modification of the axisymmetric viscous flow due to relative rotation of the disk or fluid by a translation of the boundary is studied. The fluid is taken to be compressible, and the relative rotation and translation velocity of the disk or fluid are time-dependent. The nonlinear partial differential equations governing the motion are solved numerically using an implicit finite difference scheme and Newton's linearisation technique. Numerical solutions are obtained at various non-dimensional times and disk temperatures. The non-symmetric part of the flow (secondary flow) describing the translation effect generates a velocity field at each plane parallel to the disk. The cartesian components of velocity due to secondary flow exhibit oscillations when the motion is due to rotation of the fluid on a translating disk. Increase in translation velocity produces an increment in the radial skin friction but reduces the tangential skin friction.     

Flows around rotating disks with and without rim-shroud gap

Experimental and numerical approaches have been used to study the effect of the radial rim-shroud gap on the flow structures found around a rotating disk in a finite cylindrical casing. When the radius of the disk and the inner radius of the casing are comparable and there is no radial gap, instabilities bring spiral rolls with a positive front angle in the Bödewadt layer on the end wall of the stationary casing. When the disk radius is smaller than the inner radius of the casing, vortex flows appear within the radial gap between the disk rim and the side wall of the casing. If the disk is thin, but not too thin, disturbances generated by these vortex flows proceed inward and the spiral rolls with a negative front angle appear in the Bödewadt layer. In the case of a thick disk, wavy Taylor vortex-like flow appears in the radial gap. The disturbances formed by the vortex flow do not well propagate into the inner region, and a flow pattern of bead-like vortices or a chain of vortices consisting of a series of small vortices are found around the disk in the visualized figure parallel to the disk.     

Simultaneous measurements of disk vibration and pressure fluctuation in turbulent flow developing in a model hard disk drive

The complex flow features inside hard disk drive models are investigated in an axisymmetric and a semi-open shroud configurations. For the axisymmetric case, we have employed both experimental and computational approaches. The experiment focuses on both flow dynamics and the disk vibration, where measurements of the fluctuating pressure and velocity are undertaken at some representative points. The correlation between the disk vibration and the fluctuating pressure in the turbulent flow between disks is evident from the spectral analysis. The experimentally observed fluctuating pressure and velocity are partly due to the disk vibration and its contribution could be estimated by comparing the experiment with the results of a large eddy simulation. For the semi-open shroud case, although the characteristic peaks attributable to the large-scale vortical structure are still observed in the power spectra, the pressure fluctuation and the disk vibration are suppressed when the arm is inserted.     

Experiments on the flow of a thin liquid film over a horizontal stationary and rotating disk surface

Experiments on characterization of thin liquid films flowing over stationary and rotating disk surfaces are described. The thin liquid film was created by introducing deionized water from a flow collar at the center of an aluminum disk with a known initial film thickness and uniform radial velocity. Radial film thickness distribution was measured using a non-intrusive laser light interface reflection technique that enabled the measurement of the instantaneous film thickness over a finite segment of the disk. Experiments were performed for a range of flow rates between 3.0 lpm and 15.0 lpm, corresponding to Reynolds numbers based on the liquid inlet gap height and velocity between 238 and 1,188. The angular speed of the disk was varied from 0 rpm to 300 rpm. When the disk was stationary, a circular hydraulic jump was present in the liquid film. The liquid-film thickness in the subcritical region (downstream of the hydraulic jump) was an order of magnitude greater than that in the supercritical region (upstream of the hydraulic jump) which was of the order of 0.3 mm. As the Reynolds number increased, the hydraulic jump migrated toward the edge of the disk. In the case of rotation, the liquid-film thickness exhibited a maximum on the disk surface. The liquid-film inertia and friction influenced the inner region where the film thickness progressively increased. The outer region where the film thickness decreased was primarily affected by the centrifugal forces. A flow visualization study of the thin film was also performed to determine the characteristics of the waves on the free surface. At high rotational speeds, spiral waves were observed on the liquid film. It was also determined that the angle of the waves which form on the liquid surface was a function of the ratio of local radial to tangential velocity.     

Some features of the flow around rapidly rotating bodies made of cellular-porous materials

Two types of gas flows arising near a rapidly rotating cellular-porous disk are studied numerically and experimentally. Steady-state limits for the flow around a disk rotating in free space and the type and scenario of the loss of stability are determined. Transitional flows are characterized by formation of a vortex sheet at the boundary of the exhausting jet. Numerical simulations of the flow around a cellular-porous disk rotating near a flat screen show that it is possible to form a closed swirl flow responsible for redistribution of swirl in the gap between the disk and the flat screen. The computed results offer an explanation for the experimentally observed excess of tangential velocity of the flow in the gap over the velocity of disk rotation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 86–96, January–February, 2007.     

高速转动圆盘流动数值模拟研究

重点研究高速离心压气机叶轮与机匣间的间隙流动及其温度分布。研究将离心压气机简化为高速转动圆盘,搭建了相关实验平台,并开展了相应的数值模拟研究。通过改变转动圆盘的转速和轴向进入的冷却流的流量,研究了转速和流量对于间隙内温度和速度分布的影响。结果显示,转速是影响温度变化的最主要因素,转速越大,温度越高;同等幅度的流量变化对温度的影响则较小。研究发现,在实验和模拟对应的大雷诺数条件下,无量纲的速度分布基本不受到圆盘转速、冷却流量和温度场的影响。     

Casson流体在旋转圆盘上的流动

本文研究Casson流体在旋转圆盘上的涂层流动特性,得到基本流动的速度分布,并且用Runge-Kutta法进行数值计算,得到薄膜厚度随时间和流态参数的变化规律,还用能量法检验了流动稳定性。     

Oscillatory flow due to eccentrically rotating porous disk and a fluid at infinity

An analytical solution of the unsteady Navier–Stokes equations is obtained for the flow due to non-coaxial rotations of an oscillating porous disk and a fluid at infinity, rotating about an axis parallel to the axes of rotation of the disk through a fixed point. The velocity distributions and the shear stresses at the disk are obtained for three different cases when the frequency parameter is greater than, equal to or less than the rotation parameter. The flow has a boundary layer structure even in the case of blowing at the disk.     

Dynamical responses of non-isothermal flow between two independently rotating disks with time-dependent wall conditions

The present work develops a theoretical model of rotational convection and uses it to investigate the dynamical responses of the flow and heat transfer between two disks rotating at different rates under the influences of time-dependent disturbances. The unsteady non-isothermal flow model is formulated by extending a recently developed steady-state similarity model of axi-symmetric rotational convection. In the new model all the rotation-induced buoyancy forces are considered. Using one disk as reference, effects of the time-dependent changes in wall temperature or rotating rate of the other disk on the flow and heat transfer are explored. Various rotational modes with asymptotic or fluctuating change in boundary condition of temperature or disk rotation are studied. The present time-dependent model for this non-isothermal rotating flow is numerically solved by a finite-difference method. By using the present results, the complicated flow and heat transfer mechanisms with thermal-flow coupling in the class of time-dependent rotational convection are manifested.     

Computing the aeroelastic disk vibrations in a hard disk drive

The turbulent flow of air caused by the spinning of a single disk inside a typical hard disk drive casing is calculated using large eddy simulation (LES). The pressure acting on the disk is recorded as a function of time and is used to compute the vibrations of the spinning disk using a self-developed hybrid-spectral finite-difference code. This unidirectional fluid–structure interaction problem is computed for two commonly occurring cases: a disk actuated on one side only (Case 1) and a disk actuated on both sides (Case 2). The pressure loading on the disk is characterized in terms of its mean, root-mean-square (r.m.s.) and its spectral content. The mean pressure acting on the disk is asymmetrical in the case where the disk is actuated on one side only, leading to a mean deformation of the disk to one side. The r.m.s. vibrations of Case 2 are higher than those for Case 1 and their spectral distributions are almost identical. Large pressure fluctuations of the flow are found in the wake of the actuator arm and near the region where the shroud expands to accomodate the actuator. The spectral content of the excitation force due to the pressure is mainly in the low kHz frequency range, while higher frequencies are seen at the disk edge. This typically results in the excitation of the first 3–4 modes of the disk; however, (asymmetric) Case 1 displays the excitation of higher modes compared with (symmetric) Case 2.     

LES Study of Flow Between Shrouded Co-rotating Disks

Large eddy simulations of turbulent flow between shrouded co-rotating disks, representing a simplified model of a hard disk drive, are performed. The computation domain surrounds a complete disk and is bounded at top and bottom by half a disk. Therefore, it is possible to compute the fluctuating pressure field surrounding the middle disk. Also, the influence of the shroud geometry is taken into account by comparing a flat shroud wall and a wall with rib chambers. In the flat shroud case, the fluctuating pressure on the upper- and lower-surface of a disk indicates a strong correlation with fluid motion travelling across the disk-tip clearance region. However, in the ribbed shroud case the organized flow structure that is observed in the flat shroud case disappears and the fluctuating pressure acting on the surface of the disk is remarkably diminished.     

Effects of air-flow and evaporation on the development of thin liquid film over a rotating annular disk

Axisymmetric flow of thin pure liquid film on a spinning horizontal annular disk is studied under the action of air shear at the liquid–air interface and evaporation. The non-linear evolution equation that is obtained by singular perturbation method is solved analytically, for small Reynolds number, by using the method of characteristic and numerically by the use of Newton–Kantorovich method for any Reynolds number. Font breakdown time and its location from the center of the disk is predicted both by analytically and numerically. The result shows that the thinning of the initial film increases as air stress increase, same result is also escalated in presence of evaporation.     

Effects of 3-D channel blockage and turbulent wake mixing on the limit of power extraction by tidal turbines

Three-dimensional incompressible Reynolds-averaged Navier–Stokes (RANS) computations are performed for water flow past an actuator disk model (representing a tidal turbine) placed in a rectangular channel of various blockages and aspect ratios. The study focuses on the effects of turbulent mixing behind the disk, as well as on the effects of channel blockage and aspect ratio on the prediction of the hydrodynamic limit of power extraction. To qualitatively account for the effect of turbulence generated by the turbine (rather than by the shear flow behind the turbine), we propose a new approach, called a blade-induced turbulence model, which does not use any additional model coefficients other than those used in the original RANS turbulence model. Results demonstrate that the power removed from the mean flow by the disk increases as the strength of turbulent mixing behind the disk increases, being consistent with the turbulent shear stress on the interface between the bypass and core flow passages acting in such a way as to decelerate the bypass flow and accelerate the core flow. The channel aspect ratio also affects the flow downstream of the disk but has less influence upstream of the disk; hence its effect on the limit of power extraction is relatively minor compared to that of the channel blockage, which is shown to be significant but satisfactorily estimated using one-dimensional inviscid theory previously reported in the literature.     

Rotationally symmetric flow over a rotating disk

The rotationally symmetric flow over a rotating disk in an incompressible viscous fluid is analyzed by a new method when the fluid at infinity is in a state of rigid rotation (in the same or in the opposite sense) about the same axis as that of the disk. Asymptotic expansions for the velocity field over the entire flow field are obtained for the general class of one-parameter rotationally symmetric flows. This method is further extended to the case when a uniform suction or injection is assumed at the rotating disk. Fluid motion induced by oscillatory suction of small amplitude at the rotating disk is also discussed.An initial-value analysis reveals that resonance is possible only when the angular velocity of the rotating fluid is greater than that of the rotating disk.