Firstly, the rayleigh problem of a gas contained in an infinitely long cylinder is considered. The time-dependent flow of the initially motionless gas driven by the rapidly rotating cylindrical sidewall is described. The flow field is determined by the two principal dynamic mechanisms: the compressible Rayleigh effect and the curvature effect. Unlike the Rayleigh problem about a flat plate, the centrifugal compression causes a small radially-outward normal velocity component in a narrow region very close to the sidewall. Also, due to the boundedness of the flow domain, the curvature effect relative to the compressible Rayleigh effect decreases as E.M decreases, where E and M denote respectively the Ekman number and the Mach number.
Secondly, a numerical study is made of the transient flow of a gas contained in an infinite circular cylinder which impulsively starts rotating about the central longitudinal axis with angular frequency $\Omega$. The descriptions are given of the flows at moderate and large times leading to the steady state. Attention is confined to the situations in which the reference system Ekam number E is small, and the compressibility effect is substantial. Two types of the sidewall thermal boundary condition are considered : an isothermal wall, and an adiabatic wall. The steady-state flow structure is attained over the diffusive time scale, $O(E^{-1}\Omega^{-1})$, which is orders-of-magnitudes greater than the Rayleigh time scale $O(\Omega^{-1})$. The evolutionary profiles of the temperature fields show profound differences between the two sidewall thermal conditions. The evolutions of the radial velocities show fluctuations due to the presence of the thermo-acoustic disturbances. The global spin-up process is more effective under the isothermal wall than under the adiabatic wall. Diagnostic analyses are undertaken to elucidate the dominant balances of the dynamic ingredients.
Thirdly, spin-up flows of a compressible gas in a finite, closed cylinder from the initial state of rest are studied. The details of the flow, temperature, and density evolutions are described. In the early phase of spin-up, due to the thermoacoustic disturbances caused by the compressible Rayleigh effect, the flows are oscillatory, and this oscillatory behavior is pronounced at higher Mach numbers. The principal dynamic role of the Ekman layer is eminent over moderate times of orders of the homogeneous spin-up time scales. Owing to the density stratification in the radial direction, the Ekman layer is thicker in the central region of the interior. The interior azimuthal flows are substantially uniform in the axial direction. As the Mach number increases, the rate of spin-up in the interior becomes slower, and the propagating shear front is more diffusive. Explicit comparisons with the results for an infinite cylinder are made to ascertain the contributions of the endwall disks. In contrast to the usual incompressible spin-up from rest, the viscous effects are relatively more important for the case of a compressible fluid. Elaborate diagnostic analyses are conducted of the extensive numerical data to demonstrate the comparative significance of each dynamic ingredient.
Fourthly, a numerical study is made of the early-stage behavior of spin-up flows of a highly compressible fluid in a rapidly-rotating cylinder. The focus is placed on describing the temporally small-scale motions within and near the Ekman layers. The numerical results are processed to render physically meaningful interpretations of the small-time behavior in and around the Ekman layer. The emergence of the corner jet is portrayed. Extensive diagnostic studies are performed to disclose the dominant dynamic effects. The time needed for the formation of the Ekman layer is seen to shorten in the nonlinear regime. The oscillatory behavior is clearly depicted, and it is demonstrated that, as the nonlinearity strengthens, the oscillatory frequency increases and more irregular oscillation patterns emerge.
고속 회전하는 원통 내의 압축성 유체의 과도 유동을 고찰 하였다. 첫번째로 무한 실린더 내의 Rayleigh문제를 고려했다. 정지된 상태로부터 갑자기 고속 회전 하는 경우, 이 유동은 두 가지의 주된 메카니즘에 의해서 지배된다. 압축성 Rayleigh효과와 curvature효과가 그 것이다. 평판과 달리 실린더에서는 원심 압축에 의해 벽 근처에서 반경 방향의 속도를 유발한다. 이 curvature효과는 EM값이 클수록 Rayleigh 효과를 압도한다. 여기서 M은 Mach수이고 E는 Ekman수이다.
두번째로, 갑자기 출발하는 무한원통 내의 유체의 과도 유동을 고찰했다. 정상상태에 도달하기 위한 특성 시간은 확산시간척도 (diffusion time scale)에 의존한다. 확산시간척도 이내의 과도 유동은 주로 확산 (diffusion)이 지배하지만 비압축성 유체와 달리 열-음향 요동(thermo-acoustic disturbance)에 의한 약한 진동을 동반한다. 또, 벽 경계조건의 영향을 고려했다.
세번째로, 유한 원통 내의 정지상태로 부터의 회전 (spin-up from rest)을 고찰했다. 이 문제는 고속 회전 유체기계의 발달과 더불어 최근 관심을 끄는 분야이다. 여기서는 잘 알려진 비압축성 문제와 비교 연구를 통하여 압축성 효과에 의한 과도유동특성을 규명하여 비압축성 경우와 달리 또 다른 하나의 시간척도 (time scale)가 존재함을 밝혔다.
마지막으로, 기존 회전상태로 부터 또 다른 회전상태로의 천이에 관한 문제를 고찰하였다. 여기서는 관성진동의 발생 메카니즘을 규명하였다. Ekman경계층 내의 힘의 상호작용에 의한 관성진동의 발생과 비선형 범위에서의 진동주기감소를 수치적으로 보였다. 압축성 유체의 특성인 요동 전파의 시간지연에 기인한 corner jet 의 발생을 밝혔다.
