Transient flow near a rotating disk

Summary The solution of the time dependent flow due to the impulsive starting of a single infinite disk from rest is obtained numerically for the entire history of the transient. The primary tangential velocity exhibits a single overshoot of its steady value while the growth of the secondary flows is monotonic. The overshoot is seen to be a direct consequence of the lag in the development of the secondary flows. An analytical solution is obtained for a related linearized problem: The angular velocity of an infinite disk, initially rotating with an infinite environment, is perturbed. The oscillatory decays to the steady state, which occur in both unbounded and bounded linearized analyses, are discussed in relation to the overshoot in the impulsively started disk problem.     

Temperature distribution in a thin rotating disk

The problem of heat conduction in a thin rotating disk with heat input at a fixed point is considered. The disk is cooled by forced convection from its lateral surfaces. By defining a complex temperature, the temperature throughout the disk is presented as a series of Bessel functions of complex argument. Results are given for a range of rotational speeds.Nomenclature R radial coordinate - angular coordinate - a radius of disk - b thickness of disk - T temperature - T ambient temperature - rotational speed of disk - q heat flux into disk - k thermal conductivity of disk - density of disk - c specific heat of disk - h coefficient of convective heat transfer - r dimensionless radial coordinate, R/a - T* characteristic temperature, q ₀ a/ k - t dimensionless temperature, (T–T )/T* - C ₁, C ₂ dimensionless parameters defined in (3)     

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.     

Flow of a Viscoplastic Fluid on a Rotating Disk

ＦＬＯＷＯＦＡＶＩＳＣＯＰＬＡＳＴＩＣＦＬＵＩＤＯＮＡＲＯＴＡＴＩＮＧＤＩＳＫＦａｎＣｈｕｎ（范椿）（ＩｎｓｔｉｕｉｅｏｆＭｅｃｈａｎｉｃｓ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ）（ＲｅｃｅｉｖｅｄＮｏｖ．２０，１９９２；Ｃｏｍｍｕｎｉｃａｔ...     

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.     

Flow between a porous rotating disk and a plane

It is shown that when a viscous incompressible fluid is sucked through a stationary porous disk spontaneous rotation of the fluid sets in at a certain Reynolds number. This is consistent with the results of a specially designed experiment. Another unusual result is the existence of multicell regimes, corresponding to suction, when the force acting on the porous, rapidly rotating disk is a lift force and, moreover, anomalously large. Charts of the possible steady-state flow regimes, stable and unstable, have been constructed. In the case of fairly intense suction and rotation a stable self-oscillating regime is observed. In the limit of vanishingly small viscosity unusual boundary layer properties associated with suction are noted.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 53–65, November–December, 1989.     

On unsteady forced flow against a rotating disk

Summary The solution of unsteady forced flow against an unsteadily rotating disk is obtained when the outer flow and the angular velocity of the disk are expressed in powers series of t. The solution is established by expanding the velocity components and the pressure in powers of small time. The extension of the obtained solutions is possible by using Zeytounian's technique. Finally, an analysis is made for the problem of the time-dependent flow due to an infinite rotating disk started accelerated from rest.

---

Sommario La soluzione del flusso forzato contro un disco rotante in regime non permanente è ottenuta quando il flusso esterno e la velocità angolare del disco sono espresse in una serie di potenze t. La soluzione è formulata esponendo la componente della velocità e la pressione in potenze di tempo piccolo. L'estensione delle soluzioni ottenute è possibile usando la tecnica di Zeytounian. Infine si fa l'analisi del flusso dipendente dal tempo dovuto a un disco rotante infinito accelerato dalla quiete.

     

MHD flow of a power-law fluid over a rotating disk

Magnetohydrodynamic flow of an electrically conducting power-law fluid in the vicinity of a constantly rotating infinite disk in the presence of a uniform magnetic field is considered. The steady, laminar and axi-symmetric flow is driven solely by the rotating disk, and the incompressible fluid obeys the inelastic Ostwald de Waele power-law model. The three-dimensional boundary layer equations transform exactly into a set of ordinary differential equations in a generalized similarity variable. These ODEs are solved numerically for values of the magnetic parameter m up to 4.0. The effect of the magnetic field is to reduce, and eventually suppress, the radially directed outflow. An accompanying reduction of the axial flow towards the disk is observed, together with a thinning of the boundary layer adjacent to the disk, thereby increasing the torque required to maintain rotation of the disk at the prescribed angular velocity. The influence of the magnetic field is more pronounced for shear-thinning than for shear-thickening fluids.     

The flow of a non-Newtonian liquid near a rotating disk

Synopsis The flow of non-Newtonian liquid near a rotating disk has been discussed by using second order stress strain velocity relations of classical hydrodynamics. It is found that the effect of cross-viscosity depends on a non-dimensional number R _c. The boundary layer thickness decreases and the dimensionless moment coefficient increases with the increase of R _c.     

Development of instability in a rotating elastoplastic annular disk

The paper proposes a method, based on perfect-plasticity and perturbation theories, for instability analysis of an annular flat disk tightly set on a shaft with no interference fit. The perturbed elastoplastic state of the rotating disk is analyzed by determining the stress–strain state of a fixed elastic annular plate under in-plane loading. A characteristic equation of the first order for the critical radius of the plastic zone in the disk subject to internal pressure is derived. The critical rotation rate is calculated for different parameters of the disk     

Convective diffusion from a gas phase to a rotating disk

This paper presents a method for the analytical calculation of the flow velocity of the gas mixture and the concentration of the growth component during vapor-phase epitaxy in a reaction chamber with a rotating substrate holder disk. The concentration of the growth component is analyzed in relation to some epitaxy process parameters.     

Fluid flow in a rotating cylindrical container with a rotating disk at the fluid surface

Fluid flow in a rotating cylindrical container of radius R_w and height H with a co-axially rotating disk of radius R_d at the fluid surface is numerically investigated. The container and the disk rotate with angular velocities Ω_w and Ω_d, respectively. We solve the axisymmetric Navier-Stokes equations using a finite-volume method. The effects of the relative directions and magnitudes of the disk and container rotations are studied. The calculations are carried out with various ratios of Ω_w and Ω_d for H/R_w = 2 and R_d/R_w = 0.7. Streamlines and velocity vectors in the meridional plane and azimuthal velocities are obtained. The flow fields in the meridional plane are discussed with relation to azimuthal velocities in the interior of the container. The numerical results are also compared with experimental data.