Flow over surface-mounted cube/rectangular obstacles

Underlying Flow Regime 3-14 © copyright ERCOFTAC 2004

Description

Introduction

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 will 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-ε) 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.

Review of UFR studies and choice of test case

The first detailed study of boundary layer flow over a surface-mounted cube was that of Castro & Robins (1977). They demonstrated the significant affects of the upstream turbulence and shear, by comparing cases for which h/d was 0.1 and 40, where h is the cube height and d is the upstream boundary layer thickness. Comprehensive cube surface pressure and mean velocity and turbulence data in the wake were obtained. Less extensive data were collected for intermediate values of h/d and these suggested that if the turbulence level in the upstream flow at the cube height exceeded about 10% then the separated shear layer reattached onto the roof of the cube. In the h/d=0.1 case (having an upstream intensity of around 35%) this occurred well upstream of the centre of the roof.

Similar experiments were performed later by Sakamoto & Arie (1982) and Ogawa et al (1983); the latter included field studies and very recently there have been some further field measurements, reported by Hoxey et al (2002a). Some of these various experiments have provided the basis for CFD comparisons. For example, Baethe et al (1990) provided the first LES computations of the Castro & Robins experiments although, a little earlier, Murakami et al (1987) described a similar calculation of their own experiment. In fact, Murakami has undertaken extensive CFD for this case, with reviews given in Murakami (1997) for example, but unfortunately their wind tunnel experiments have never been comprehensively presented in the literature so, in terms of a test case, their experiment is not satisfactory from a QNET-CFD perspective. (The experiment was described in four lines only in the Murakami et al, 1990, paper and this is more than in any other related publication, as far as this reviewer can determine!). Most recently, Hoxey et al (2002b) have reported RANS computations of their field experiments. Other computations can be found in Paterson & Apelt (1990), He & Song (1992), Delauney et al (1995), Lee & Bienkiewicz (1997) and Thomas & Williams (1997), for example. In some respects many of these computations have not been entirely satisfactory. This is often because the upstream flow characteristics were not sufficiently well characterised to allow adequate inflow boundary conditions to be set up for the computations. The Castro & Robins experiment is certainly less than ideal in this respect and, for this reason, there have been more recent experiments undertaken specifically to provide the necessary data for comparison with the results of numerical simulations. Tamura et al (1997), for example, report studies conducted for the Architectural Institute of Japan, but in this case for a 'low-rise' building with relative dimensions (length/width/height) of 1/1/0.5.

Since in all these cases the entire boundary layer has to be modelled and also, ideally, a reasonable depth of free stream, the computational demands are more severe than they are for the flow studied by Martinuzzi & Tropea (1993). In this case, the cube was mounted on the wall in a fully developed, smooth-wall channel flow and had a height of one half of the channel depth. So the flow is in detail rather different from those mentioned above, but nonetheless embodies many of the important physical effects. Although the experiments were not originally designed to produce data specifically for comparison with CFD results, a wider range of turbulence quantities were measured than in any of the previous studies and, given also the well-characterised nature of the upstream flow, it is thus particularly well suited to comparisons with detailed numerical modelling. This is no doubt why it has been the subject of considerable attention. A workshop which focussed particularly on Large-Eddy Simulation (LES) for bluff bodies was held in 1995 and the results have been reported by Rodi et al (1997). This 'cube-in-a-channel' flow was one of the test cases and the results for this case, obtained using various (steady) RANS methods as well as LES, have been recently reviewed again by Rodi (2002). Shah & Ferziger (1997) provided one of the most comprehensive and useful comparisons (using LES) and one of the better (unsteady) RANS simulations has been given by Iaccarino & Durbin (2000).

The major disadvantage of this 'cube-in-a-channel' case in the wind engineering context is that cube surface pressures were not measured or, at least, seem not to be available. It is well known that computing accurate values for these can be difficult, particularly if the body is orientated at an angle to the free stream - the common case is a 45° angle, when the two delta-wing-type vortices generated along the top leading edges can lead to very large suction pressures close to the edges. And it is these pressures (and, often, their fluctuating values) which are of major concern in terms of wind loading. However, it is possible to compute the overall pressure field reasonably (even if localised peaks are not captured) whilst missing the velocity field by a wide margin, as Shah & Ferziger (1997) have pointed out. They have suggested that to 'validate a method solely by its ability to predict the velocity distribution about a single object may be dangerous; relying on the pressure distribution alone is almost surely of no value whatever'. Despite the limitation (no measured surface pressures) it is this 'cube-in-a-channel' case which is therefore chosen as the specific test case to be reviewed here. It also has the advantage of having been the subject of a workshop which, although not very recent (1995 - see above) included comparisons between a variety of turbulence models - mostly k-ε based - as well as LES.

Contributors: Ian Castro - University of Southampton