Boundary layer flow and dispersion over isolated hills and valleys
Application Challenge 5-05 © copyright ERCOFTAC 2004
Flow fields around isolated, nominally two-dimensional hills and valleys were investigated in the low speed meteorological wind tunnel at the US Environmental Protection Agency laboratories. An example of the hill case is shown in figure 1; three hills and a corresponding set of three valleys (not covered in this AC document) were studied. A neutrally stable atmospheric boundary layer of height about 1m was simulated and the hills (or valleys) were located some 7-8m downstream, where the flow was reasonably well developed. For the velocity and turbulence measurements carefully calibrated hot wire and hot film probes were used, with particular attention given to the probes’ yaw responses at low velocities. For the steeper hills, where separation occurred in the lee, use was made of a double-ended pitot probe to assess the size of the separation region; thermal anemometry is inaccurate in such regions.
The experiment was originally designed in the context of pollutant dispersion in the atmosphere. Theoretical models for estimating downwind concentration from sources in the vicinity of isolated topographical features were at that time (and still are) not very reliable so the intention was to obtain data suitable for improving understanding, comparing against theoretical (or computational ) models and, hopefully, thus improving such models. In addition to mean flow and turbulence data, therefore, concentration data was obtained both at ground level and at elevation for cases in which a (scalar) pollutant source was located at x=-a, 0 or a (where a is the hill half-length) and, in each case, at various heights. This allowed determination of ‘terrain amplification factors’ – i.e. the ratio of the maximum surface concentration in the presence of the hill to that in its absence – which is a useful practical measure of the influence of the hill, although not the only one.
These flows were not computed using CFD for a number of years subsequent to the experiments but there have more recently been a number of such attempts (see references). It is suggested here that those performed by Apsley as part of his PhD work and subsequently published in the open literature (see references, particularly Castro & Apsley, 1997, hereafter designated as CA) be used for review, largely because this is the only work which includes computation of the scalar concentration field as well as the flow itself. These computations used a finite-volume, incompressible Navier-Stokes solver employing a cartesian velocity decomposition on a staggered grid. Terrain-fitting, curvilinear meshes were used, along with a variety of turbulence models. These were largely the standard k-ε model along with varients of it, designed to take better account of the effects of streamline curvature and streamwise strains, both of which are known to degrade the adequacy of the standard k-ε model – the latter seriously so. A 2nd order, upwind-biased, flux limiting harmonic advection scheme was used for the convective terms in all equations. This is significantly more accurate than standard upwinding.
This application challenge is a good one for a number of reasons. First, the experimental data is reckoned to be of good quality. Significant care was taken to ensure measurement accuracy both of the velocity and turbulence data and of the concentration data; the smoothed data generated by Trombetti et al (1991) from the original results are particularly convenient.. Secondly, the upstream flow was properly characterised, so that appropriate upstream conditions can be applied in computations. Thirdly, the flow contains difficult features, e.g: rough walls (not easy to model properly); strong adverse pressure gradients (upstream of the steep hills); separation from a curved surface (along with the adverse pressure gradients, a serious test of turbulence models); scalar dispersion (practically important).
Figure 1. Side view of a hill mounted in the simulated atmospheric boundary layer.
Relevance to Industrial Sector
Atmospheric boundary layer flow over hills and valleys is an important problem in the atmospheric sciences, not least because the surface drag, which has a major effect on the atmosphere, is significantly altered by surface topography. Despite considerable study, both in the laboratory and in the field, it remains difficult to compute such flows, particularly for cases of steep-sloped topography. Such surface features significantly affect the mean and turbulence fields and thus have an important influence on pollutant dispersion. Theoretical models for the latter are not well developed for cases in which there is topographical influence and CFD is increasingly being used as an alternative, but with little evidence yet of general adequacy.
Design or Assessment Parameters
There are various design or assessment parameters (DOAPs) which could be used. The major interest may, for example, be essentially in the flow itself. One might then choose parameters appropriate to velocity variations generated by the hill, or the presence of separation, for example. These could be the maximum velocity speed-up at x=0 and the location and size of the lee-side separation region, respectively. On the other hand, if the interest is in the downwind pollutant concentration field, one might choose the terrain amplification factor as a measure of the computational accuracy. However, particularly in this latter case, one should be cautious: it is possible to obtain good prediction of the latter for quite the wrong reasons, as a result of the influence of opposing errors. One would not expect to obtain adequate concentration results if the flow field (including turbulence levels, which influence diffusion characteristics) is inadequately predicted.
Flow Domain Geometry
Figure 1 shows the generic hill geometry; its height (H) was 117mm and its shape was specified parametrically, as given in CA. The flow was nominally two-dimensional, but the spanwise length of each hill was limited by the wind tunnel width and was thus 3.7m. This gave an aspect ratio, defined by the ratio of spanwise width and hill height, of about 32. The hill aspect ratio (half-length divided by height) varied between 3 for the steepest hill, through 5, to 8 for the smallest slope case. The computations assumed two-dimensionality and generally used a domain of ±40H upstream and downstream of the hill summit and 13.7H vertically – the height at which the free stream velocity was measured in the experiments (1.6m). The wind tunnel roof was adjusted so that the velocity at this latter height was independent of fetch.
Flow Physics and Fluid Dynamics Data
Key aspects of the flow physics in this problem are those normally associated with flow of a rough-wall turbulent boundary layer over a surface-mounted obstacle immersed within it and the downwind turbulent dispersion of scalar sources within the flow. Thus, important features include the adverse pressure gradient region upstream of the hill and velocity acceleration on the windward side and deceleration on the downwind side; if the hill slope is large enough, the latter may be strong enough to lead to flow separation. Theoretical considerations suggest that there is an ‘inner layer’ near the surface within which the turbulence perturbations may be in approximate equilibrium (so that eddy viscosity ideas can be used in a linear theory to predict the flow) and an outer flow where the perturbations are essentially inviscid. CFD has been used a number of times to demonstrate the regions of validity of such ideas and this was discussed in CA. But the usefulness of such comparisons (i.e. between CFD data and linear or non-linear theory) rest on the adequacy of the CFD, of course! Major features of the dispersion behavior include the possibility of entrainment into the separation region for certain source locations, the large variations of concentration that can occur within the separation region (in contrast to the common assumption that such a region will be well-mixed), the strong directional variability in effective diffusivities and the large increases in maximum ground level concentration caused by the hill.
© copyright ERCOFTAC 2004
Contributors: Ian Castro - University of Southampton