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회전 원통을 통과하는 기체의 유동
Source-Sink Flows in a Rotating Cylinder
HWAHAK KONGHAK, April 1981, 19(2), 107-120(14), NONE
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Abstract
회전하는 실린더의 양끝 덮개에 원형의 slit상의 source와 sink가 있는 경우, 그 유동을 수치해석적으로 모사하였다. 반경 방향으로 밀도의 분포를 반경의 함수로 가정함으로써 기체의 압축성을 고려하였다. Stream function과 vorticity를 변수로 사용하였으며, 큰 각속도에서도 수치모사의 안정성을 유지하기 위해서 upwind difference법을 사용하였다. 유도된 차분 방정식을 푸는데는, SOR과 SIP（strongly implicit procedure）를 사용했으며, 후자가 본 system에 대해서 더욱 효율적임을 알았다. 또 SIP를 사용하는 경우 artificial viscosity에 기인하는 오차를 줄이기 위해서 Jacobs 수정법(1974)을 사용했다. 수치모사의 결과로 streamline과 축방향속도 분포, 그리고 분리된 boundary layer와 옆 벽에서의 Stewartson layer에 의한 유체의 흐름을 볼 수 있었다.
수치모사 결과를 검토하기 위해서 200∼500 rpm의 범위로 회전하는 모델실린더를 제작하였다. 실린더의 윗덮개의 중심쪽에 있는 slit를 통해 공기를 불어넣었고, 윗덮개의 바깥쪽과 아랫 덮개에 있는 slit를 통해 뽑아내었으며, 그 흐름을 관측할 수 있도록 paraffine mist를 첨가하였다. 이렇게 하여 측정한 축 방향속도를 수치모사의 결과와 비교하였다.
수치모사 결과를 검토하기 위해서 200∼500 rpm의 범위로 회전하는 모델실린더를 제작하였다. 실린더의 윗덮개의 중심쪽에 있는 slit를 통해 공기를 불어넣었고, 윗덮개의 바깥쪽과 아랫 덮개에 있는 slit를 통해 뽑아내었으며, 그 흐름을 관측할 수 있도록 paraffine mist를 첨가하였다. 이렇게 하여 측정한 축 방향속도를 수치모사의 결과와 비교하였다.
Steady axisymmetric source-sink flows of a compressible viscous fluid in a rotating cylinder is simulated numerically. The source and the sink are, respectively, the feed and the dischargo slits at the end plates of the cylinder. Compressibility of the fluid is taken into account in the form of steady-state density stratification in the radial direction formed by rigid body rotatation in the absence of the source and sink. Stream function-vorticity formulation is chosen for this study. Stability problem ocurring at high angular speed is overcome by using upwind difference scheme.
The solution techniques used for the resulting finite difference equations are SOR and SIP（Strongly Implicit Procedure）, and the latter is found to be more efficient for this set of equations. Additionally, when using SIP, we adopted the method devised by Jacobs (1974) to compensate for the error due to the artificial viscosity.
The simulation results give streamlines and axial velocity profiles for the flows through the detached shear layer and the Stewartson layer near the side wall
To check the results of numerical simulation. A model cylinder was driven at an angular velocity of 200-500r.p.m. The air containing paraffine mist as a tracers is fed into the cylinder through the inlet slit at the upper end plate and is withdrawn through the outlet slits at the upper and lower plates.
Values of axial velocity from the present numerical simulation were compared with those from experiments.
The solution techniques used for the resulting finite difference equations are SOR and SIP（Strongly Implicit Procedure）, and the latter is found to be more efficient for this set of equations. Additionally, when using SIP, we adopted the method devised by Jacobs (1974) to compensate for the error due to the artificial viscosity.
The simulation results give streamlines and axial velocity profiles for the flows through the detached shear layer and the Stewartson layer near the side wall
To check the results of numerical simulation. A model cylinder was driven at an angular velocity of 200-500r.p.m. The air containing paraffine mist as a tracers is fed into the cylinder through the inlet slit at the upper end plate and is withdrawn through the outlet slits at the upper and lower plates.
Values of axial velocity from the present numerical simulation were compared with those from experiments.
