The three-dimensional incompressible flow past a rectangular two-dimensional (2D) shallow cavity in a channel is investigated using Large Eddy Simulation (LES) and Detached Eddy Simulation (DES). The length to depth ratio of the cavity is L/D=2 and the Reynolds number defined with the cavity depth and the mean velocity in the upstream channel is 3,360. In LES, the sensitivity of the flow around the cavity to the characteristics of the upstream flow is studied by considering two extreme cases. In the first case a developing laminar boundary layer is present upstream the cavity while in the second case the upstream flow is fully turbulent. The two simulations are compared in terms of the mean statistics and temporal physics of the flow, including the dynamics of the coherent structures in the region surrounding the cavity. The structure and spectral content of the flow over the cavity are considerably affected by the characteristics of the upstream flow. For the laminar inflow case it is found that the flows becomes unstable but remains laminar as it is convected over the cavity. Due to the 3D flow instabilities and the feedback mechanism, the spanwise vortices that are shed regularly from the leading cavity edge are disturbed in the spanwise direction and, as they approach the trailing edge corner, break into an array of hairpin-like vortices that is convected downstream the cavity close to the channel bottom. In the fully turbulent inflow case the jittering of the shear layer on top of the cavity by the incoming near wall coherent structures strongly influences the formation and convection of the organized eddies inside the separated shear layer and induces a large decrease in feedback coherence. In both simulations the large scale structures in the shear layer region induce large scale pressure fluctuations at the trailing cavity edge and convection of patches of vorticity inside the cavity parallel to the trailing edge. These patches modulate the intensity of the jet like flow that develops along the trailing edge and bottom cavity walls. The mass exchange between the cavity and the main channel is investigated by considering the ejection of a passive scalar that is introduced instantaneously inside the cavity. As expected, it is found that the ejection is faster in the case in which the incoming flow is turbulent due to the interaction between the turbulent eddies convected from upstream the cavity with the separated shear layer and due to the increased diffusion induced by the broader range of scales that populate the cavity. In the turbulent case it is shown that the eddies convected from upstream the cavity can play an important role in accelerating the extraction of high concentration fluid from inside the cavity. For both laminar and turbulent inflow cases it is shown that the scalar ejection can be described using simple dead-zone theory models in which a single valued global mass exchange coefficient can be used to describe the scalar mass decay inside cavity over the whole extent of the ejection process.
In the TC simulation with a negatively buoyant contaminant, internal wave breaking is observed to occur over the initial phases of the mixing which along with turbulent mixing phenomena reduce the mean density gradient across the density interface. In the later stages, the contaminant removal and mixing process are controlled by the interaction of the trailing edge vortex with the bottom layer containing denser contaminant beneath it and upstream of it.
Finally, the capabilities of DES to predict the mean flow, velocity spectra, Reynolds stresses and the temporal decay of a passive contaminant are assessed based on comparison with results from LES and experiments. It is found that the SA-DES with turbulent fluctuations at the inlet gives the best overall predictions for the flow statistics and mass exchange coefficient. The presence of inflow fluctuations in DES is found to break the large coherence of the vortices shed in the separated shear layer present in the simulation with steady inflow and to generate a wider range of 3D eddies inside the cavity, similar to LES.
채널 내부의 사각 공동을 지나는 비압축성 3차원 유동에 대해 LES와 DES를 이용하여 수치적으로 계산하였다. 길이대 깊이비는 2이며 레이놀즈 수는 3,360이다. LES 방법에서는 두 가지 입구 유동 조건에 따른 유동의 차이를 살펴 보았는데, 하나는 섭동이 존재하지 않는 층류 유동이 흘러올 경우이며 다른 하나는 완전 난류 유동이 주어졌을 경우이다. 두 경우에 대해 평균 유동장과 응집 구조를 포함한 시간에 따른 유동 특성을 살펴보았다. 공동 위를 흐르는 유동 구조와 스펙트럴 특성은 앞에서 흘러 들어오는 유동의 특성에 큰 영향을 받았다. 층류가 흘러올 경우 전체 영역의 유동은 층류로 유지되었으며 앞전에서 횡방향 와류가 떨어져 뒷전과 부딪힌다. 이때 hairpin-like 와류가 형성되어 채널 후류로 흘러나간다. 완전 난류 유동일 경우에는 공동 앞의 벽근처 응직 구조에 큰 영향을 받아 횡방향 와류 구조는 나타나지 않았다. 스칼라 방정식을 풀어서 공동내의 물질 전달 과정에 대해 살펴보았다. 예상데로 입구 유동이 난류인 경우 난류 에디와 증가된 확산에 의해 물질 전달이 더 빨리 이루어졌으며 공동 앞전 앞에서부터 흘러오는 에디들이 높은 밀도의 물질들을 공동 밖으로 빼내는데 큰 역할을 하였다. 공동 내의 물질 양의 시간에 따른 감소는 간략화된 1 차원 모델식으로 즉 지수 함수 형태로 잘 나타남을 보였다.
음의 값의 부력을 가지는 물질이 공동 내부에 쌓였을 경우, 초기에는 뒷전 근처의 와류에 의해 밀도 구배 값이 커지면서 채널의 낮은 밀도의 물질과 혼합 현상이 발생하다가 나중에는 내부 파의 진동과 와류의 작용으로 의해 물질이 빠져나가게 된다.
마지막으로 LES 결과와 실험 데이터를 바탕으로 LES 보다 적은 격자를 가지고 SA/SST DES를 수행하여 그 가능성을 살펴 보았다. 이때 입구 유동에 섭동을 추가한 경우와 그렇지 않은 경우에 대해 그 차이점을 살펴보았다. 난류 섭동을 가지는 SA-DES 의 경우 유동의 난류 특성과 물질 전달 계수를 가장 잘 예측하였다.
