Abstr:Flow over surface-mounted cube/rectangular obstacles

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Semi-Confined Flows

Underlying Flow Regime 3-14

Abstract

Fluid flow past bluff obstacles - i.e. those whose geometry ensures that at all practical Reynolds numbers flow separation will occur somewhere on the surface - is ubiquitous. In the QNET-CFD context and, in particular, within the TA4 and TA5 themes, there are a number of Application Challenges which include flow past obstacles. For example, 4.02 concerns the atmospheric wind flow over an airport terminal building. If the obstacle has sharp-edges and corners - a common situation in the environmental field - issues of Reynolds number dependence are less significant than they are for the more classical case of, for example, flow over a circular cylinder. On the other hand, in this field the upstream flow is usually both sheared and turbulent and the obstacle is normally attached to the surface (the ground). The flow is consequently very complex, even if the geometry is not.

Boundary layer flow over one of the simplest (isolated) obstacles possible, a cube, can be thought of as the most elemental of flows typical of those that occur in practice. Even this flow could be broken down conceptually into underlying flow regimes like, for example, a boundary separating from a flat surface, curved mixing layers, 3D wakes, etc. But it is helpful to consider the whole as a UFR, particularly as there have now been a few detailed experimental studies of such a situation and an increasing number of corresponding CFD investigations.

We consider here only cases in which the scale of the vertical shear is not small compared to the height of the body (e.g. the latter is a small fraction of the upstream boundary layer height). There are many features of such a flow which provide severe tests for CFD modelling. Some of these are outlined now; we reserve detailed discussion until later. First, there is the upstream region embodying a turbulent boundary layer responding to the 3D adverse pressure gradient generated by the presence of the obstacle. It is well known that standard RANS models (like k-e) do not react properly to strong adverse pressure gradients, so one expects the separation process upstream of the obstacle and, in fact, the entire region upstream of the front face of the body, to be difficult to capture accurately. Secondly, there is substantial mean flow curvature not only upstream but in the wake region also. This, too, could tax standard models. Thirdly, the interactions between the small-scale turbulence in the shear layers separating from the leading edges (assuming this process is itself captured adequately) and the distorted, larger scale structures advected from the upstream region and 'seen' by these shear layers at their outer boundaries, is quite subtle. Such interactions can determine whether or not the shear layers reattach onto the body surfaces and are thus important even for the mean flow. Fourthly, although there is no genuine periodic unsteadiness (like Karman vortex shedding), the flow is nonetheless very unsteady and some experiments have suggested a bi-modal behaviour in the wake. This would clearly not be captured at all by standard RANS methods. Fifthly, in the environmental context, the ground plane would normally be aerodynamically rough. Given that local values of surface stress (and thus friction velocity) will vary widely around the body - and indeed be zero at mean separation or attachment points - this requires considerable care in applying wall boundary conditions. The surface of the body itself may well be smooth but, in any case, there is little likelihood of genuine log-law regions being present in the region immediately upstream or in the near wake; it is not yet really clear how much inappropriate boundary conditions affect the overall accuracy of the computations.

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Contributors: Ian Castro - University of Southampton

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