The monotone streamline upwind finite element method, which was proposed to treat convection-dominated flows, is applied to the linear triangular element which is thought to be adequate for solving flows with complex boundaries. The upwind method is implicitly formulated in a segregated finite element scheme which is designed to solve the incompressible Navier-Stokes equations on moving grids. Two modifications are proposed in order to remove the numerical diffusion of the upwind method. An alignment technique of unstructured grids with given velocity fields is used to prevent the interpolation error produced in evaluating the convection term. A blending technique of the convection term is proposed in an unstructured manner using an upwind parameter similar as in the SU/PG method.
Two pure advection problems and laminar jet impingement flows are considered to demonstrate the efficiency of the present approach for solving the convection-dominated flow on the unstructured grid. The present upwind method can reasonably treat the convection-dominated flows with the linear triangular element and solutions obtained with aligned grids are much closer to the exact solutions or experimental results than those with initial regular grids. The blending technique improves the solution accuracy of the region in which the diffusion term becomes dominant.
The application problem of the present study is the convection heat transfer from a transversely oscillated cylinder for various dimensionless oscillation frequencies($S_c$), dimensionless oscillation amplitudes(A/D) and Reynolds numbers(Re). The ranges of these parameters considered in this study are 0≤$S_c$ ≤0.35, 0≤A/D≤0.7 and 0≤Re≤1000. It is found that present laminar calculations predict the increase of heat transfer at high amplitude and frequency which has been thought as 0a resultant of the turbulent effect. The approximate method introducing a vibrational velocity concept into the heat transfer verifies that the mechanism of the increase of heat transfer at that range is the increase of the oscillating velocity of the cylinder relative to the flow.
비정렬 삼각형 격자를 이용한 비압축성 유동장의 해석이 가능하도록 단조유선 상류차분법을 유한요소법에 맞게 제안하였다. 제안된 상류차분법의 정확도를 높히기 위하여 격자선의 정렬과 대류항의 혼합방법을 제시하고 검증하였다. 제안된 상류차분법은 정상, 비정상 문제를 통하여 타당한 해를 줌을 검증하였고 격자선 정렬과 대류항의 혼합방법은 본 상류차분법의 정확도를 높이는 데에 기여함이 증명되었다. 본 연구의 알고리즘으로 수직으로 진동하는 실린더에서의 강제 열전달을 해석하였는데 그 동안 난류효과로 알려졌던 고진폭, 고주기에서의 열전달증가가 본 층류해석에서도 나타나는 것으로 보아 난류의 영향이 아닌 것으로 판단되었다. 이 조건에 대하여 근사방법을 이용하여 해석해 본 결과 고진폭, 고주기에서의 열전달 증가는 실린더의 상대속도 증가에 의한 것임이 밝혀졌다.