Iwao Harada

A Numerical Study of Source-Sink Flows in a Rotating Cylinder

Numerical investigations are made on the source-sink flows in a rotating cylinder. A finite difference method is used to solve the time-dependent full Navier-Stokes equations to an incompressible, viscous and axisymmetric flow. Computations are carried out for three cases with different Ekman numbers and a fixed aspect ratio. Transient aspects of flows are discussed focusing on the developments of the Ekman layers on both disks, and the E 1/4 layers vertically formed at the radii of a source and sink located on the upper and lower disk, respectively. Numerical results based on a similarity analysis of the nonlinear E 1/4 layer agree well with the experimental ones.

On the Mechanically Induced Unsteady Compressible Ekman Layer

The compressibility effect on a mechanically induced unsteady Ekman layer has been investigated by using the boundary layer theory. The analytic solution is obtained for the case in which the Prandtl number is equal to unity. It is found that the period of the inertial oscillations expressed by the Fresnel integral S (2 σ 2 τ) becomes short as the compressibility is increased, and the unsteady Ekman layer of a compressible fluid (σ>1) reaches the steady state faster than that of an incompressible fluid (σ=1). Here σ is the compressibility parameter and time τ is nondimensionalized by an inverse of the angular velocity \(\varOmega ^{-1}\).

Measurements of velocity profiles of gas in a rapidly rotating cylinder

The azimuthal and axial velocity of the source‐sink flow in a rapidly rotating cylinder were measured by using the back scattered mode of the laser‐Doppler velocimeter. A rotating optical system was devised for measuring the gas flow with a high angular velocity of 5.2×102 rad/s. The incident laser beams were introduced into the cylinder through the rotating optical system which synchronously, but independently, rotating with the cylinder. The Doppler‐shifted signal was observed from the light back‐scattered by small paraffin mist particles of about 1 μm in diameter. The accuracies of the measurements were within ±5% for the azimuthal flow‐velocity component and ±8% for the axial one. The E1/4 layers formed on the sidewall and the feed radius were clearly observed due to the small Ekman number E=2.2×10−5. The theoretical results (boundary layer theory and numerical calculation) agree quantitatively with the experimental ones, except in the case of the feed radius.

On Three Kinds of Solutions of a Flow between Two Rotating Disks

Numerical investigations are made on the flow between two rotating disks using von Karmans similarity hypothesis. Solutions strongly depend on the initial angular velocity and three kinds of solutions are obtained for the same boundary condition, even for two disks in the rigid body rotation. Three kinds of solution exist in the range of β=1.0∼-0.3698970 (where β is a ratio of angular velocities of the two disks), while one of them changes into the other kind of solution when β<-0.3698970.

On the Split of the Compressible Stewartson Layer due to a Surface-Mounted Obstacle

The obstacle effects are clarified on the thermally driven compressible flow in a rapidly rotating annulus by using our finite difference method based on the DuFort-Frankel/upwind schemes. It is found that the circulation within the Stewartson layer separates partially or completely into two circulations whether the obstacle (mounted on the outer sidewall) height is smaller than the upstream width or not.