Numerical Analysis of Oscillating Square Cylinder with Corner Radius : 코너각을 가진 사각실린더의 진동 수치해석

다국어 초록 (Multilingual Abstract)

The near wake of stationary and transversely oscillating square section cylinders with different corner radii are studied by numerical method to investigate the influence of corner radius. Six models, R/D=0, 0.1, 0.2, 0.3, 0.4, 0.5 (R is the corner radius and D is the characteristic dimension of the body) at Re=500 and Re=5200 were studied. CFD software CFD-ACE was applied to simulate the flow past a cylinder with different R/D cases both at Re=500 with laminar model and Re=5200 with LES model. In stationary condition, the numerical results of St, C_(D) and C_(L) at R/D=0 and R/D=0.5 were compared with experiments to prove the feasibility and also investigate the trend of flow phenomena by the various radius corners. In oscillating condition, fe=fo (fe is exciting frequency and fo is natural vortex shedding frequency) and A_(m)/D=0.2 at Re=500 was applied and compared the phenomena of the stationary cases. The calculated results for Re=5200 with A_(m)/D=0.16 and fe=fo oscillation cases was compared with the experiment results of Strouhal number, fixed point velocity and vortex shedding phenomenon. It was found that the corner effect on square cylinder significantly influences the flow features around the cylinder both in stationary and oscillating conditions. Results indicate that, as R/D ratio is increased, the Strouhal number is increased, the minimum pressure point on the cylinder surface is moved downstream. The calculated Strouhal numbers are same for stationary and oscillation cases but the results of oscillation cases induce that the minimum pressure point moves upstream, vortex oscillation area is widen, C_(D) and C_(L) is increased than stationary cases. The calculated results of R/D=0.2 and R/D=0.3 in both stationary and oscillating condition have lower C_(D) and C_(L.) than other cases.

국문 초록 (Abstract)

고정된 그리고 가로로 진동하는 서로 다른 코너 반경의 사각 실린더에 근접한 후류의 영향을 수치해석법 의해 수행 되였다. 이 논문은 여섯 가지의 모델 R/D=0, 0.1, 0.2, 0.3, 0.4, 0.5 (R 은 코너의 반경을 의미하고 D 는 실린더의 직경을 의미한다). e=500, Re=5200 의 경우로 수행되었다.
이 논문에서 서로 다른 R/D 와 Re 의 실린더를 지나는 흐름을 실험하기 위하여 CFD-ACE 가 사용되었다. 고정된 조건에서의 R/D=0 와 R/D=0.5 St, CD, CL 에서의 결과는 수치 데이터는 다양한 반경의 코너를 실행가능성과 경향을 증명하기위하여 실험값과 비교되었다. 그리고 진동하는 조건에서 여섯 가지의 모델 fe=fo (fe 는 실존하는 진동수, fo 는 자연적으로 발산하는 와류진동이다.) 과 Re=500 에서의 Am/d=0.2 역시 고정된 그리고 진동 조건을 비교하기위해 계산되었으며 진동하는 실린더의 후류의 코너 영향을 나타내었다. 또한 Re=5200 에서 Am/d=0.16 진동하는 조건에서 fe=fo 가 실험값과 비교하기 위해서 Strouhal number 와 고정된 포인트의 속도와 와류 현상을 다시 정의 하였다. 그것은 고정된 그리고 진동 조건에서의 사각 실린더 주위의 유동 특성에서 상당한 코너에서의 영향이 발견되었다. 결과에서 R/D ratio 는 증가했고 유동흐름은 더 유니폼하게 흘렀으며 Strouhal number 는 증가한다는 것을 나타냈다.
그리고 실린더 표면에서 고정되고 진동하는 조건에서의 최소한의 압력점 은 downstream 으로 움직이고 vortex formation length 는 증가하며 고정된 조건에서 진동하는 조건으로부터의 최소한의 압력점은 upstream 로 움직인다. 교차하는 흐름 속에서 진동하는 실린더의 fe=fo, Cd 와 Cl 은 고정된 실린더 조건보다 더 높은 가치를 가진다. 진동조건 에서의 실험과 계산된 결과 R/d=0.2 그리고 R/D=0.3 에서 낮은 CD 와 CL 을 보여주었다.

목차 (Table of Contents)

• 1 Introduction = 1
• 1.1 Background = 1
• 1.2 Previous and Related Studies = 1
• 1.3 Present contributions = 3
• 2 Theoretical Background = 5
• 2.1 Square Cylinder = 5
• 2.2 Circular cylinder = 6
• 2.3 Strouhal number of flow past square cylinder and circular cylinder = 8
• 2.4 Governing equation = 10
• 2.5 Numerical model setup = 11
• 2.6 Sinusoidal cylinder oscillations = 13
• 2.7 Grid Deformation and Grid Re-meshing = 15
• 3 2-D Calculation of Stationary Condition at Re=500 = 17
• 3.1 The purpose of this calculation = 17
• 3.2 Strouhal number at Re=500 in stationary condition = 17
• 3.3 Vortex formation length at Re=500 in stationary condition = 18
• 3.4 Pressure distribution around cylinder at Re=500 in stationary condition = 20
• 3.5 Vorticity at Re=500 in stationary condition = 22
• 3.5.1 Mean vorticity distribution at Re=500 in stationary condition = 22
• 3.5.2 Separation point at Re=500 in stationary condition = 28
• 3.5.3 Instantaneous Vorticity distribution at Re=500 in stationary condition = 30
• 4 2-D Calculation for Oscillating condition at Re=500 = 37
• 4.1 Drag coefficient C_(D) and lift coefficient C_(L) at Re=500 = 37
• 4.2 Pressure distribution around cylinder at Re=500 in stationary condition = 40
• 4.3 Vorticity distribution at Re=500 in oscillating condition = 45
• 5 Corner effects of Transversely Oscillation at Re=5200 = 51
• 5.1 Introduction of experiment instrumentation. = 51
• 5.2 Check Y+ with Les model at Reynolds number=5200 = 54
• 5.3 Velocity of fixed point in 2-D calculation and experiment analysis at Re=5200 in oscillating condition = 56
• 5.4 Vortex shedding of 2-D calculation and experiment analysis at Re=5200 in oscillating condition = 66
• Conclusions = 93
• Reference = 94