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A computational and wind tunnel study of particle dry deposition in complex topography
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Atmospheric Environment 38 (2004) 3867–3878
A computational and wind tunnel study of particle dry deposition in complex topography S.T. Parker, R.P. Kinnersley*,1 Division of Environmental Health and Risk Management, School of Geography, Earth and Environmental Sciences, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK Received 1 August 2003; received in revised form 1 March 2004; accepted 10 March 2004
Abstract An understanding of the likely pattern of dry deposition of small particles over a landscape is a key prerequisite to designing strategies for sampling ground contamination following routine or accidental releases to atmosphere. Wind tunnel and computational fluid dynamics studies of flow and particle deposition over landscape features have been carried out. The presence of elevated landscape features showed a strong effect on the pattern of deposition relative to a flat landscape case. A relatively small area of increased deposition occurred on the upwind face, with a larger area of decreased deposition in the wake. The slope of the landscapes affected the magnitude of the effect and the size of the affected region in the wake. The pattern of deposition for a three-dimensional landscape was complex. Good quantitative agreement was seen between the CFD predicted deposition and the wind tunnel results for the twodimensional cases and reasonable qualitative agreement for the three-dimensional case, suggesting that CFD studies might be an appropriate tool to systematically explore the influence of complex topography on particle deposition. r 2004 Elsevier Ltd. All rights reserved. Keywords: Aerosol; CFD; Complex terrain; Hills; Turbulence
1. Introduction Deposition of particulate material from the atmosphere to the ground is a significant transfer pathway for many environmental pollutants. It provides an entry point for contaminants into the food chain, and is one of the factors that govern the rate at which clouds of contaminant become depleted. An understanding of this pathway is important in protecting the population from the adverse effects of airborne contaminants. Of particular concern is the fate of radioactive or toxic *Corresponding author. E-mail address: rob.kinnersley@environment-agency. gov.uk (R.P. Kinnersley). 1 Present address: Air, Land and Water Science, Environment Agency, Olton Court, 10 Warwick Road, Olton, Solihull, West Midlands B92 7HX.
chemical aerosols released over a short period, for example, as a result of an accident at a nuclear installation. Effective emergency management following such a release, including the direction of survey teams and delimiting of restricted land use areas, requires an understanding of the spatial distribution of subsequent deposits of contaminant. Currently, quantification of deposition relies upon deposition velocities that are strictly applicable only to uniform roughness, and do not account for local variations in topography and land cover. Such variations give rise to changes in local wind velocity and turbulence levels that can significantly influence particle deposition rates. The use of such simplifications during emergency exercises has led to operatives deploying finite surveying resources in a less-than-optimal way, and in some cases missing ‘‘hot-spots’’ of contamination (Argyraki et al., 1999).
1352-2310/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2004.03.046
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This work explores the link between landscape topography and spatial variation of particle deposition. A measure of relative deposition rate is required that can be used to derive rules for identifying areas within a real landscape subject to enhanced deposition, so that they can be targeted for sampling. This study is concerned only with dry deposition and the interaction of the flow with the landscape. There has been little work on the dry deposition of environmentally important particles over complex topography. Some study has been made of deposition of dust over complex topography in the field of geomorphology, for example Goossens (1997) and Mason et al. (1999). Direct comparison with such work is difficult because of the larger particle size used in such work, and the importance of resuspension, both direct and due to impaction of larger-sized material. However, comparisons are informative between some of the many published works of Goossens and co-workers (Goossens, 1988, 1996; Offer and Goossens, 1995). These authors found a clear effect on the pattern of deposition, both over hills, and in their wake. The deposition of particles is, of course, linked to the nature of the flow in which they are transported. Belcher and Hunt (1998) reviewed the mechanisms that control turbulent neutral boundary layer flow over hills and noted that turbulence in the flow is greatly influenced by passing over hills, particularly in the wake, and that this has important consequences for the deposition of pollutants. Wind tunnels have been used to model flow over complex topography for some time (Castro and Snyder, 1982; Finnigan et al., 1990; Greeley et al., 1974) and, more recently, computational fluid dynamics (CFD) has become popular for studying such flows (Carpenter and Locke, 1999; Castro and Apsley, 1997; Kim and Boysan, 1999). CFD and wind tunnel studies have also been used for the study of particle dynamics and deposition in particular (Zufall et al., 1999a, b). The combination of CFD of atmospheric flow and particle dynamics is relatively new with some studies of local dispersion and deposition from industrial sources (Ahmadi and Li, 2000). For an introduction to the issues surrounding the use of CFD, Versteeg and Malalasekera (1995) is recommended. The aim of the broader project, to which this work belongs, is to produce a set of ‘‘rules of thumb’’ which can be applied rapidly to any given landscape without the need for computationally intensive calculations. The approach has been to use a combination of CFD and wind tunnel measurements to compare particle deposition for a number of simple landscape shapes and hence to determine how patterns of deposition vary when compared with a flat landscape. The simplified shapes studied are representative of full-scale landscape features. The experimental and modelled boundary layers were similar to a neutral atmospheric boundary layer.
Scaling parameters have been carefully considered to ensure that the deposition variation at model- and fullscale would be similar.
2. Materials and methods 2.1. Wind tunnel experiments The experiments were carried out in an open-return, square cross-section wind tunnel driven by a centrifugal blowing fan. The working section of the tunnel is 2.5 m 2.5 m in cross-section, approximately 10 m long and capable of wind speeds in excess of 10 m s1. Temperature stratification of the air in the wind tunnel is not currently possible, and therefore, only neutral stability flows were simulated. Velocity and turbulence measurements were made using a pulsed wire anemometer as described by Bradbury and Castro (1971), calibrated with a pitot-static tube and a micro-manometer. Vertical and horizontal profiles of streamwise velocity and turbulence were measured at a number of locations. The use of a pulsed wire anemometer allowed the measurement of reversed velocities and the identification of areas of recirculating flow. A turbulent boundary layer was developed in the lower part of the wind tunnel working section, with characteristics representative of a neutral atmospheric boundary layer at a scale of 1:1000. The boundary layer was generated by a series of triangular spires whose dimensions and spacing were calculated using the formula from Irwin (1981) to generate a boundary layer of depth 0.8 m. Five spires were constructed of height 1 m, base 0.12 m and a spacing of 0.5 m between the centres of the spires, placed at a distance of 1.0 m from a large turbulence generating grid at the beginning of the working section. These were followed by a series of roughness elements of decreasing size, to a distance of 2.35 m downwind of the spires. The size and arrangement of the roughness elements was varied by trial and error to achieve a velocity profile consistent with a roughness length of 0.2 mm (model scale). To maintain the developed boundary layer flow, a textured material was applied to the surface of the landscapes and the flat control. This surface was also applied to the floor area upwind and downwind of the model landscapes. The material used was a textured wall covering with an array of uniform raised bumps with a height of approximately 0.5 mm. Three simplified landscapes and a flat control were used in the experiments. Two of the model landscapes were effectively two dimensional, having a uniform cross-section, whilst the third was three dimensional. The two-dimensional landscapes were both flat-sided ridges, of slope 1 in 1 (45 ) and 1 in 3 (18.4 ). The ridges were of height 0.1 m and of lateral width 2.5 m, equal to
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N/A 0 N/A Note that reattachment lengths reported at measured height and at surface for CFD.
N/A 0 0 0 0 0 Flat
0
45 1.25 1.5 400 400 200 0.4 0.2 Cone
0.4
18.43 1.25 1.1 600 600 100 2.5 0.1 Ridge 1 in 3
0.6
0.30 (z ¼ 0:02 m)
0.81 (z ¼ 0:05 m) 1.13 (z ¼ 0:00 m) 0.59 (z ¼ 0:02 m) 0.70 (z ¼ 0:00 m) 0.32 (z ¼ 0:02 m) 0.32 (z ¼ 0:00 m) N/A 0.90 (z ¼ 0:05 m) 45 1.25 1.1 200 200 100 2.5 0.2 0.1 Ridge 1 in 1
Y (m) X (m) Length (m) Width (m) Height (m) Width (m)
Length (m) Height (m)
0.50 (z ¼ 0:02 m)
CFD (m)
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Wind tunnel (m)
Gradient (deg) Location of peak Full-scale Model Geometry
Table 1 Model geometry dimensions at model and full-scale, and reattachment lengths
the width of the wind tunnel. The three-dimensional landscape was conical in shape and of height 0.2 m with a slope of 45 . The shapes of the model landscapes were chosen to be representative of sections of real hilly or mountainous topography and to possess sharp changes in gradient so that the effect of flow separation could be examined. The Reynolds numbers of the flows, using the height as the characteristic length, were 33,000 for the ridges and 66,000 for the cone. Snyder (1972) quotes a value of 11,000 for sharp-edged buildings, for Reynolds number independence. Chatzipanagiotidis and Olivari (1996) used a value of 11,000 for a wind tunnel study of a two-dimensional ridge, quoting a critical Reynolds number of 5000 for rough sharp objects. Therefore, the Reynolds numbers of the features studied here are thought to ensure similarity between model and fullscale. Thermal effects are neglected because the boundary layer is of neutral stability. The area covered by the experiment is small enough (o5 km) that the effect of the Coriolis force at full-scale can be neglected using the criteria of Snyder (1972). A summary of the model landscapes is included in Table 1. Kind (1986), Xuan and Robins (1994) and Goossens and Offer (1990) discuss similarity criteria for modelling snowdrifting, dust emission and deposition, and dust deposition, respectively. Based on the approach used by these authors the following criteria were equal between model and full-scale: density ratio (particle:air), terminal velocity ratio, and reference velocity ratio. The roughness-height Reynolds number was equal to 40 and greater than the criterion of 30 (Kind, 1986). Because of the small particle size in this case, neither resuspension nor saltation are significant mechanisms affecting net deposition patterns. Therefore criteria regarding emission velocity can be neglected. The Froude number is not equal between model and full-scale, but can be neglected because of the very shallow fall angle for the small particles studied and absence of saltation. The above criteria should ensure similarity between patterns of particle deposition at model-and full-scale. For the deposition part of the experiment, Fluorescein particles were generated using a medical nebuliser containing an aqueous solution of 25 g l1 Sodium Fluorescein. The flow rate of air through the nebuliser was approximately 5.7 l min1. The output from the nebuliser was fed into a 25 mm diameter tube leading downwind from the nebuliser and entering the boundary layer at a point located 0.21 m from the end of the boundary layer development section, with its centre 0.0125 m from the floor of the wind tunnel. The tube allowed the source to be located close to the model landscapes (B0.9 and 1.3 m upwind of the peak of the ridges and cone, respectively) without the body of the nebuliser disrupting the flow. In addition, it allowed some time for the generated particles to equilibrate with the air before release.
Reattachment lengths at model scale
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The particles released were characterised with a GRIMM light-scattering particle monitor. Approximately 90% of the particle volume was in the size fraction from 0.75 to 1 mm diameter and 10% was in the size range 1–2 mm diameter. Although the particles were not monodisperse, a nebuliser was used in preference to aerosol generators with a narrower range of particle sizes because of the higher aerosol concentrations attainable. Particle concentrations at the plume centreline, immediately upwind of the landscapes, were in the order of 160,000 particles l1. To measure the deposition of particles, 25 mm GFA filters were placed on the textured surface at intervals along the centreline of the wind tunnel, and also across the width of the tunnel at several locations. Once the filters were positioned, the flow within the wind tunnel was started and allowed to stabilise for a period of 10 min. The particles were then released from the source for 30 min. Following exposure the filters were collected and extracted into pH7 buffer and quantified by fluorimetric analysis with a Perkin Elmer 1000 M fluorimeter. 2.2. CFD studies The flows over the landscapes were modelled using a commercial CFD solver, Fluent 5.5.14. The flows were solved using steady-state Reynolds-averaged Navier– Stokes equations. A number of turbulence models were tested, including standard k–epsilon, Renormalisation Group (RNG) k–epsilon and Reynolds stress model. Preliminary studies showed that the RNG k–epsilon approach predicted the position of the reattachment point of the recirculating area with the most accuracy. The RNG k–epsilon turbulence model has also been shown to perform well by other workers for studies of flow over complex topography (Kim et al., 2000; Maurizi, 2000). This turbulence model was therefore chosen for the remaining studies. Flow over each landscape and the flat control case were modelled at wind tunnel scale. The modelled domain was equal in width to the wind tunnel (2.5 m), had a length of 6 m and a height of 1 m (a height of 1 m was chosen rather than the full height of the wind tunnel for computational efficiency). The grids were constructed with hexahedral cells of horizontal spacing 0.01 m close to the area of the ridges and cone and increasing to 0.05 m away from this area. The vertical spacing started at a size of 0.005 m at the surface, increasing geometrically by a factor of 1.1 with each cell. This is equivalent to a y+ value of just under 35 for the lowest cell, slightly above the lower limit and in the range recommended for CFD solvers (ERCOFTAC, 2000; Fluent, 1999). The total number of cells for each domain ranged from approximately 390,000 to 645,000. An earlier series of model runs were carried out with
larger y+ values and approximately 110,000 cells. The results from these runs showed slight differences in the predicted flow and some areas of significant difference to the deposition rate, and these differences are discussed below. The upwind boundary was defined as a velocity inlet, with a log law profile having uand z0 parameters as determined from experimental measurements (0.23 m s1 and 0.22 mm, respectively). The turbulent kinetic energy and dissipation rate were assigned profiles based on the value of u, using relationships recommended by Richards and Hoxey (1993). These were used in preference to experimental values to allow an evaluation of the use of CFD for generic studies of flow and deposition over hills where wind tunnel data are not available. The initial turbulent kinetic energy is relatively small compared to that generated by the model landscapes and therefore the final deposition results should not be very sensitive to the inlet turbulence parameters provided they are of the correct order. The sides of the wind tunnel were defined as smooth no-slip walls. The floor of the wind tunnel was defined as a noslip wall with a roughness height of 0.001 m and a roughness constant of 0.5, equivalent to the textured roughness used on the surface. (Note that the roughness height is the actual height of the roughness element as opposed to the aerodynamic roughness length, z0 ; of the surface). The top of the modelled domain was defined as a symmetry boundary (effectively a slip wall). The downwind boundary was defined as an outflow boundary. Following solution of the flow, the deposition of particles was modelled using the CFD software’s discrete phase model option. The trajectories of the particles were calculated from the point of release according to the modelled forces acting upon them. These forces include aerodynamic drag due to the flow, gravity, Brownian motion and Saffman lift force. The actual flow affecting the particle motion was determined by the mean flow and the calculated turbulent kinetic energy at each point in the domain. The turbulent velocity in each direction was modelled as a random Gaussian probability distribution multiplied by the RMS velocity in that direction. Because of the isotropic nature of the RNG k–epsilon model, the RMS of the velocity fluctuations is equal in each direction and is proportional to the square root of the turbulent kinetic energy. The pattern of deposition was calculated using a stochastic approach. Particle trajectories were calculated repeatedly using the randomised turbulence until an average pattern of deposition was established. For these studies the number of particles tracked was 1 106. A particle diameter of 1 mm was used, particle density was 1000 kg m3 and the Cunningham slip correction factor used was 1.16632. The source of particles was defined as
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a point source at the location of the centre of the release. The lower surface of the domain was defined such that particles coming within one radius distance were trapped and recorded as deposited. Resuspension of deposited particles was not considered.
3. Results and discussion 3.1. Flow measurements In the following section all distances are given as distance downwind from the peak height, with the exception of the flat case where they are given from the particle source. The velocity profile for the developed boundary layer (at X ¼ 0:33 m) was in reasonable agreement with a log law of surface roughness 0.22 mm as shown in Fig. 1(a). This surface roughness at model scale is typical of atmospheric boundary layer flow over rural terrain at full-scale (Counihan, 1975). The roughness length was slightly longer than that expected from the surface roughness of the textured material alone, but profiles taken further downwind
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(X ¼ 1:42 m, 2.68 m) showed little change in the boundary layer. The vertical profile of turbulence intensity is shown in Fig. 1(b) and the values in the lower part of the boundary agreed well with typical streamwise turbulence values for the lower part of atmospheric boundary layers (Stull, 1988). The range of turbulence intensities at a full-scale height of 50 m were 18% in this study compared with a range of approximately 14–28% reported by Farell and Iyengar (1999) for a slightly larger roughness length. Figs. 2(a)–(f) show the effect of the landscapes on the velocity profiles at varying downwind distances. The vertical profile at the peak of the hills and in the immediate wake show a region of increased velocity in the upper part of the boundary layer. This is more pronounced for the ridges which extended across the width of the tunnel than for the three-dimensional cone. In the wake behind the hill the velocity above the hill height is higher than the upstream value, but changes rapidly towards the surface, with a region of recirculating flow close to the surface, the extent of which is shown in Figs. 3(a)–(c). The velocity profiles further downwind show a recovery to the upwind profile.
1 0.9 Log law z0=0.22mm
0.8 0.7
X=0.33m
z (m)
0.6 0.5
X=1.42m
0.4 0.3
X=2.68m
0.2 0.1 0 0
1
2
3
4
5
6
U (ms-1)
(a) 1 0.9 0.8 0.7
z (m)
0.6 0.5 0.4 0.3 0.2 0.1 0 0
(b)
0.05
0.1
0.15
0.2
Turbulence Intensity
Fig. 1. Wind tunnel without model landscapes, vertical profiles of (a) streamwise velocity, experimental data are represented by points, fitted log law by continuous line, (b) streamwise turbulence intensity.
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-0.35m
0.6
0.00m
1.95m 0.2
(a)
X = - 0.35m
0.8
0.65m
0.4
X = 0.00m
1 z (m)
z (m)
1 0.8
X = 0.65m
X = 1.95m
0.6 0.4 0.2 0
0 -2
0
2
4
6
-1
(d)
2
1
0
3
1
1 -0.35m
0.8
0.6
0.25m
0.6
0.4
1.95m
z (m)
z (m)
0.8
X = 1.95m
0.4 0.2
0.2
0
0
(b)
X = - 0.35m X = 0.25m
-2
0
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4
6
(e)
-1
0
2
1
3
1
1
-0.75m
0.6
0.25m
0.4
1.55m
0.2
X = 0.25m
X = 1.55m
0.6 0.4 0.2 0
0 -2
(c)
X = - 0.75m
0.8 z (m)
z (m)
0.8
0
2
4
-1
6
U (ms-1)
(f)
0
1
2
3
Distance downwind of peak (m)
Fig. 2. Wind tunnel vertical streamwise velocity profiles at varying downwind distances, (a) ridge of 1 in 1 slope, (b) ridge of 1 in 3 slope and (c) cone of 1 in 1 slope. Normalised profiles of the same data indicating location within wind tunnel, (d) ridge of 1 in 1 slope, (e) ridge of 1 in 3 slope and (f) cone of 1 in 1 slope.
Figs. 3(a)–(c) show the streamwise velocity measured at 0.05 m above the surface, along the centreline of the wind tunnel for each case. There is a clear region of speed-up on the upwind face of the slope, followed by a sudden reduction in velocity and reversal in flow direction in the wake of the hill before the velocity returns to a positive value further downwind. The recirculating region is smaller for the ridge of shallower slope although further measurements at 0.02 m above the surface identified the reattachment point was at 0.54 m from the peak, suggesting a shallow, elongated region of recirculating flow. Note that the velocity in the wake of the cone recovers more quickly than that of the ridges despite the extra height of the cone (0.2 m) because of its limited extent across the width of the wind tunnel. The results for the shallower ridge show good agreement with results from Finnigan et al. (1990) for flow over a shallower sinusoidal ridge, with a velocity minimum upwind of the ridge, followed by a maximum close to the peak and a larger minimum in the wake. Figs. 3(d)–(f) show the profiles of r.m.s. streamwise turbulent velocity also measured at 0.05 m above the surface. All three show an increase of turbulence in the wake, with the more steeply sloped ridge and cone showing a small region of reduction in the immediate wake. Again, the results for the shallower ridge agree
well with those of Finnigan et al. (1990), showing a maximum 4–8 ridge heights downwind of the peak. Comparison of the CFD and experimental profiles of velocity showed that the CFD predicted the flow field reasonably well. The modelled flows all showed regions of reversed flow of similar proportions to the experimental flow. The points of reattachment also compared well, and these are presented in Table 1. The CFD model was used to produce values for reattachment lengths at the same height as measured in the wind tunnel (slightly above the surface) and also at the surface itself. It is clear that there is a significant difference between the two. The values agree with values summarised in Kim et al. (2000) from a number of experimental and computational sources, for flow over a two-dimensional 45 triangular ridge, varying from 9.8 to 16.5 ridge heights. Fig. 4(a) compares the vertical profiles of streamwise velocity between the CFD and the wind tunnel measurements for the cone of slope 1 in 1 and the CFD does well in achieving the same profiles. The CFD overpredicts the vertical extent of the recirculation region in the immediate wake and the velocity further downwind is affected by this discrepancy. Fig. 4(b) compares the longitudinal profile of streamwise velocity. The general pattern and the maxima and minima of the velocity coincide for the experimental and modelled case.
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6 5
3
σu (ms-1)
U (ms-1)
4
2 1 0 -1 -1
-0.5
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0.5
1
1.5
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2.5
3
-2
(a)
1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0
(d)
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4
2 1 0 -1 -1
(b)
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0.5
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3
-2
(e)
1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0
6
1.8 1.6 1.4
5
3
σu (ms-1)
U (ms-1)
4
2 1 0 -1 -1
-0.5
0
0.5
1
1.5
2
2.5
0.4 0.2 0
3
-2
(c)
Distance downwind of peak (m)
1.2 1 0.8 0.6
(f)
2
2.5
3
Distance downwind of peak (m)
Fig. 3. Wind tunnel longitudinal profiles of streamwise velocity (a–c) and streamwise turbulent velocity (d–f). (a, d) Ridge of 1 in 1 slope, (b, e) ridge of 1 in 3 slope and (c, f) cone of 1 in 1 slope. Measured at 0.05 m above surface.
1.2 1
Height (m)
However, there is some difference in the magnitude of the velocity, which appears to grow with distance downwind. This is likely to be due to the overprediction of the vertical extent of the recirculating region by the CFD. 3.2. Particle deposition measurements
WT
X= - 0.75m
X = 0.25m
0.8
X = 1.55m
CFD
0.6 0.4 0.2 0 -1
0
-0.5
(a)
1
0.5
2
1.5
2.5
Distance downwind of peak (m) 5 4 3
-1
Velocity (ms )
Experimental deposition for the flat case showed a very strong decay in deposition rate with increasing distance from the source due to the reduction in concentration as the aerosol dispersed. Lateral samples also showed the deposition falling off strongly with distance from the centreline. This flat case was used as a baseline against which to compare the deposition to the model landscapes. Figs. 5(a)–(c) show the ratio of deposition rate relative to the flat case for the three landscape cases. For all three cases there is a similar pattern: a small reduction in deposition upwind of the landscape feature, a significant maximum on the windward face (a factor of 0.9–1.7 times the flat case) and a reduction in the immediate wake which recovers back to the upwind value with further distance downwind. The recovery is quicker for the shallower ridge, returning to
2
WT CFD
1 0 -1 -2
-1.5
(b)
Z=0.05m
-1
-0.5
0
0.5
1
1.5
2
2.5
Distance downwind of peak (m)
Fig. 4. Comparison of vertical (a) and longitudinal (b) profiles of streamwise velocity for CFD and wind tunnel, for cone of slope 1 in 1, (b) Measured at 0.05 m above surface.
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Deposition relative to flat
3 WT
2.5
CFD 2 1.5 1 0.5 0
(a)
-1
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3
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Deposition relative to flat
3
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WT CFD
2
1.5
1
0.5
0
-1
(c)
0
1
2
3
4
5
Distance downwind of peak (m)
Fig. 5. Deposition ratio relative to flat case for wind tunnel and CFD. Ridge of slope 1 in 1 (a), ridge of 1 in 3 slope (b) and cone of 1 in 1 slope (c).
50% of the flat case within 2.5 ridge heights from the ridge, compared with 6.5 ridge heights for the steeper ridge. There is good agreement for the pattern of deposition between the CFD and the wind tunnel results. The two-dimensional cases show very good agreement although there is some overprediction by the CFD on the windward face of the ridges, which is more apparent for the steeper slope. There is also a slight divergence in results at large distances for the 1 in 3 slope ridge and this is believed to be due to increasing experimental error in fluorescence measurements with distance in the wind tunnel case, because of reduced deposition with distance from the source. To achieve a
high enough concentration to perform the experiment in a reasonable time, it was necessary to use a point source close to the ground and close to the model landscape. As a result the concentration field, and therefore the deposition rate, fell sharply with distance. The actual, rather than the relative, changes in deposition rate at large distances downwind became comparable with the measurement uncertainty. Further experiments are planned with a stronger and more diffuse source further upwind from the region of interest to alleviate this problem. Direct comparison of these results with those in the literature is difficult because of the influence of
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resuspension and saltation in many reported studies. The strong dependence on the location of the particle source also prevents equivelence between reported work and this study. However, it is informative to compare the results for the ridges to wind tunnel deposition of larger-sized dust (25 mm median diameter, 65 mm maximum diameter) to a symmetrical ridge (Goossens, 1988). The results appear to be in qualitative agreement, with an increase on the windward face and a decrease on the leeward face and in the immediate wake. The present data do not match the rise in the wake because of the different source characteristics. A point source close to the ridges was used in these experiments, compared with a much broader source representative of a ‘dust storm’ in Goossens (1988). Quantitative comparison is also prevented because the reported results are given as difference in deposition from the flat case without a reference value. The two-dimensional results are also in broad agreement with wind tunnel, and CFD studies, to wave surfaces (Zufall et al., 1999a, b). The graph for centreline deposition for the 1 in 1 cone shares the same general features as the two-dimensional landscapes. However, the increased deposition to the upwind face is significantly increased and the reduction in the immediate wake in the experimental results is less than for either of the ridges. It should be remembered that the cone is twice the height of the ridges, which may account for the increased upwind deposition. The less significant region of reduced deposition behind the cone may be due to particles travelling around the sides of the cone and the smaller region of recirculation (in three dimensions) compared to the two-dimensional cases. In addition to the samples taken along the centreline of the cone, a number were also taken on the cone surface and in the wake up to a distance of 1 m from the centreline. The resulting deposition rates at these locations are presented in Fig. 6, which shows that there are areas of increased deposition to the sides and base of
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the windward face of the cone in addition to the peak. Note that this graph shows actual deposition rather than the ratio to the flat case. In the wake, the centreline deposition values are lower than those to each side. The results from Offer and Goossens (1995) for deposition of larger particle sizes to a conical hill show a similar pattern of deposition. The authors of that paper also discuss the presence of horseshoe vortices shed from the sides of the cone. These are thought to be related to the pattern of increased deposition. There is some asymmetry in the pattern of deposition rate, with those at negative Y values showing slightly increased deposition relative to positive Y values. This is supported by several lateral samples taken for the flat and two-dimensional cases that show a slight bias towards the same direction, which becomes apparent at distances of more than 2 m from the peak of the ridges. It is believed that this is due to some slight asymmetry in the flow in the wind tunnel. The influence of such an asymmetry will be expected to be more significant for the three-dimensional case, where the plume of released material is split as it passes the cone. Agreement between the CFD and experiment is not as precise for the cone as it is for the ridges, although the key features are similar. As with the two ridges, deposition to the upwind face is slightly overpredicted by the CFD on the lower part of the cone, but the main difference from the two-dimensional cases is that the deposition in the wake region is consistently underpredicted by approximately 50%. It is believed that this is due to a combination of two reasons. Firstly, the overprediction of deposition to the windward face removes a significant proportion of particles from the flow that are then unavailable to deposit further downwind. Secondly, there is evidence of slight asymmetry in the wind tunnel flow and therefore in the pattern of deposition. The CFD predicted pattern of deposition showed that deposition to a narrow region
Fig. 6. Contour plot of wind tunnel deposition rate (mg m2 s1) to cone and area in immediate wake of cone.
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along the centreline was reduced by 20–50% compared to that on either side. Asymmetry in the flow would cause this region to be offset and higher deposition from the area to the side to result. As mentioned in the CFD method section above, an earlier series of runs were carried out at a coarser resolution and the results from these showed some differences in the pattern of deposition. The principle difference was a larger overprediction on the windward face, with ratios as high as 4.5 for the cone case. However for the other areas, including the wake, there was relatively little difference. In order to examine the effect of the specificity of the results to the location of the particle source, a number of CFD models were run in which the height of the source was varied. Heights from 0.01 to 0.30 m were modelled and the pattern of deposition remained similar with the peak concentration on the upwind face increasing with the height of release. The reduction in the wake became less pronounced with height and eventually increased, showing a maximum increase of 50% for a release at twice the ridge height and approximately 70% for a release height at three times the ridge height. These values become comparable with the deposition increase to the windward face, which agree with the results of Goossens (1988). It is clear that there is a variation in deposition caused by the model landscapes in these experiments. However, it is well known that the presence of the complex topography will also affect the dispersion and hence the concentration field resulting from a point source (Castro and Apsley, 1997; Castro and Snyder, 1982; Castro et al., 1988). It was not possible to measure the concentration of the experimental particles concurrently with the measurement of deposition. However, the results for deposition to the surface and for the concentration immediately above the surface from the CFD were examined. The large rise in deposition to the surface of the cone, both windward and leeward, was not accompanied by a rise in concentration. Deposition in the wake followed the concentration more closely and was most likely a result of mixing of concentration at height down to the surface because of the increased turbulence in the wake. The pattern of deposition is therefore not easily predicted by the concentration alone, supporting our hypothesis that the influence of the landscape arises through locally increased turbulence as well as through the changes in concentration that are a secondary result of increased dispersion due to landscape generated turbulence.
3.3. Result summary The model landscapes had a significant influence on deposition of particles from a point source relative to a
flat landscape case. A number of general features were identifiable: *
*
*
*
a slight decrease in deposition upwind of the raised topography; a maximum in deposition increase on the upwind face close to the peak; a region of decreased deposition on the leeward face, extending into the immediate wake and gradually recovering with distance to upwind levels; In the case of the three-dimensional cone, there is a more complex pattern of deposition on the leeward face, with a minimum at the centreline in the lateral cross-section of deposition in the wake and enhancement at the edge of the wake region.
The CFD predictions of deposition agreed remarkably well for the two-dimensional cases and reasonably well for the three-dimensional case. However, even for the three-dimensional case, the predicted pattern of deposition was in good qualitative agreement with the experiment. The differences in the three-dimensional case are believed to be due to slight asymmetry in the wind tunnel flow. The results serve to validate the use of CFD for studying the influence of landscape on deposition, allowing a greater range of landscape geometries to be investigated than would be practical if physical modelling were always necessary. While it remains impractical to carry out CFD modelling for real landscapes within the timeframe needed for emergency response, the generation of guidelines on the likely modification of deposition patterns in complex terrain offers a means of improving the ability of emergency controllers and sampling strategists to make best use of the sampling resources at their disposal. Note that these results apply only to dry deposition of particles. Clearly under certain meteorological conditions, and with the influence of orographic factors, wet deposition may be an important mechanism.
4. Conclusions The wind tunnel experiments of particle deposition to different topographies indicate that there is a significant effect on particle deposition compared to the flat control case. Areas of increased and decreased deposition relative to the flat were recorded. Using a commercial CFD solver (Fluent 5.5.14), the flows in the wind tunnel were modelled and particle deposition was predicted using stochastic particle tracking in these flows. The resulting predictions were in general in good agreement with experiment suggesting that this approach is of practical use for predicting particle deposition to
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complex geometries giving at least qualitatively correct results. Careful consideration of wind tunnel scaling parameters suggests that the wind tunnel results are applicable to the full-scale case of a neutral atmospheric boundary layer flow over such landscape features. CFD appears to have significant potential for predicting relative deposition effects due to landscape features. More recent work has begun to reap the benefits of this approach for a range of landscape shapes.
Acknowledgements The authors would like to thank T. Huggins for his help with the wind tunnel work. This work was supported by the School of Geography, Earth and Environmental Sciences, University of Birmingham, and by a grant from the Nuffield Foundation.
References Ahmadi, G., Li, A., 2000. Computer simulation of particle transport and deposition near a small isolated building. Journal of Wind Engineering and Industrial Aerodynamics 84 (1), 23–46. Argyraki, A., Kinnersley, R.P., Ramsey, M.H., 1999. Optimising emergency sampling strategy following a release of radioactive material into the environment. MAFF Research Contract No. RP 0249. Belcher, S.E., Hunt, J.C.R., 1998. Turbulent flow over hills and waves. Annual Review of Fluid Mechanics 30, 507–538. Bradbury, L.J.S., Castro, I.P., 1971. A pulsed-wire technique for velocity measurements in highly turbulent flows. Journal of Fluid Mechanics 49 (4), 657–691. Carpenter, P., Locke, N., 1999. Investigation of wind speeds over multiple two-dimensional hills. Journal of Wind Engineering and Industrial Aerodynamics 83 (1–3), 109–120. Castro, I.P., Apsley, D.D., 1997. Flow and dispersion over topography: a comparison between numerical and laboratory data for two-dimensional flows. Atmospheric Environment 31 (6), 839–850. Castro, I.P., Snyder, W.H., 1982. A wind-tunnel study of dispersion from sources downwind of 3-dimensional hills. Atmospheric Environment 16 (8), 1869–1887. Castro, I.P., Snyder, W.H., Lawson, R.E., 1988. Wind direction effects on dispersion from sources downwind of steep hills. Atmospheric Environment 22 (10), 2229–2238. Chatzipanagiotidis, A., Olivari, D., 1996. Pollutant dispersal downstream of a hill in different wind conditions. Journal of Wind Engineering and Industrial Aerodynamics 64, 233–248. Counihan, J., 1975. Adiabatic atmospheric boundary layers: a review and analysis of data from the period 1880–1972. Atmospheric Enviornment 9, 871–905. ERCOFTAC, 2000. The ERCOFTAC Best Practice Guidelines for Industrial Computational Fluid Dynamics. European Research Community on Flow, Turbulence and
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Combustion, Special Interest Group on ‘‘Quality and Trust in CFD’’ Best Practice Guidelines Version 1.0. Internet resource http://imhefwww.epfl.ch/lmf/ERCOFTAC/SIGs/ BPG.html, accessed 18th July 2003. Farell, C., Iyengar, A.K.S., 1999. Experiments on the wind tunnel simulation of atmospheric boundary layers. Journal of Wind Engineering and Industrial Aerodynamics 79 (1–2), 11–35. Finnigan, J.J., Raupach, M.R., Bradley, E.F., Aldis, G.K., 1990. A wind tunnel study of turbulent flow over a twodimensional ridge. Boundary-Layer Meteorology 50, 277–317. Fluent, 1999. 9.8.1 Near-wall mesh guidelines for wall functions. In: Fluent 5 User’s Guide. Fluent Inc., Lebanon, New Hampshire, USA. Goossens, D., 1988. Sedimentation characteristics of natural dust in the wake of symmetrical hills. Zeitschrift fur Geomorphologie 32 (4), 499–502. Goossens, D., 1996. Wind tunnel experiments of aeolian dust deposition along ranges of hills. Earth Surface Processes and Landforms 21, 205–216. Goossens, D., 1997. Long-term aeolian loess accumulation modelled in the wind tunnel: the Molenberg case (central loess belt, Belgium). Zeitschrift fur Geomorphologie 41 (1), 115–129. Goossens, D., Offer, Z.I., 1990. A wind tunnel simulation and field verification of desert dust deposition (Avdat Experimental Station, Negev Desert). Sedimentology 37, 7–22. Greeley, R., Iversen, J.D., Pollack, J.B., Udovich, N., White, B., 1974. Wind tunnel studies of Martian aeolian processes. Proceedings of the Royal Society of London Series A—Mathematical Physical and Engineering Sciences 341, 331–360. Irwin, H.P.A.H., 1981. The design of spires for wind simulation. Journal of Wind Engineering and Industrial Aerodynamics 7, 361–366. Kim, S.E., Boysan, F., 1999. Application of CFD to environmental flows. Journal of Wind Engineering and Industrial Aerodynamics 81, 145–158. Kim, H.G., Patel, V.C., Lee, M.L., 2000. Numerical simulation of wind flow over hilly terrain. Journal of Wind Engineering and Industrial Aerodynamics 87, 45–60. Kind, R.J., 1986. Snowdrifting: a review of modelling methods. Cold Regions Science and Technology 12, 217–228. Mason, J.A., Nater, E.A., Zanner, C.W., Bell, J.C., 1999. A new model of topographic effects on the distribution of loess. Geomorphology 28, 223–236. Maurizi, A., 2000. Numerical simulation of turbulent flows over 2-D valleys using three versions of the kappa–epsilon closure model. Journal of Wind Engineering and Industrial Aerodynamics 85 (1), 59–73. Offer, Z.Y., Goossens, D., 1995. Wind tunnel experiments and field measurements of aeolian dust deposition on conical hills. Geomorphology 14, 43–56. Richards, P.J., Hoxey, R.P., 1993. Appropriate boundary conditions for computational wind engineering models using the k–epsilon turbulence model. Journal of Wind Engineering and Industrial Aerodynamics 46 and 47, 145–153.
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Snyder, W.H., 1972. Similarity criteria for the application of fluid models to the study of air pollution meteorology. Boundary-Layer Meteorology 3, 113–134. Stull, R.B., 1988. An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers, Dordrecht. Versteeg, H.K., Malalasekera, W., 1995. An Introduction to Computational Fluid Dynamics. The Finite Volume Method. Longman, Harlow. Xuan, J., Robins, A., 1994. The effects of turbulence and complex terrain on dust emissions and depositions from
coal stockpiles. Atmospheric Environment 28 (11), 1951–1960. Zufall, M.J., Dai, W., Davidson, C.I., Etyemezian, V., 1999a. Dry deposition of particles to wave surfaces: I. Mathematical modeling. Atmospheric Environment 33 (26), 4273–4281. Zufall, M.J., Dai, W.I., Davidson, C., 1999b. Dry deposition of particles to wave surfaces: II. Wind tunnel experiments. Atmospheric Environment 33 (26), 4283–4290.
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A computational and wind tunnel study of particle dry deposition in complex topography S.T. Parker, R.P. Kinnersley*,1 Division of Environmental Health and Risk Management, School of Geography, Earth and Environmental Sciences, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK Received 1 August 2003; received in revised form 1 March 2004; accepted 10 March 2004
Abstract An understanding of the likely pattern of dry deposition of small particles over a landscape is a key prerequisite to designing strategies for sampling ground contamination following routine or accidental releases to atmosphere. Wind tunnel and computational fluid dynamics studies of flow and particle deposition over landscape features have been carried out. The presence of elevated landscape features showed a strong effect on the pattern of deposition relative to a flat landscape case. A relatively small area of increased deposition occurred on the upwind face, with a larger area of decreased deposition in the wake. The slope of the landscapes affected the magnitude of the effect and the size of the affected region in the wake. The pattern of deposition for a three-dimensional landscape was complex. Good quantitative agreement was seen between the CFD predicted deposition and the wind tunnel results for the twodimensional cases and reasonable qualitative agreement for the three-dimensional case, suggesting that CFD studies might be an appropriate tool to systematically explore the influence of complex topography on particle deposition. r 2004 Elsevier Ltd. All rights reserved. Keywords: Aerosol; CFD; Complex terrain; Hills; Turbulence
1. Introduction Deposition of particulate material from the atmosphere to the ground is a significant transfer pathway for many environmental pollutants. It provides an entry point for contaminants into the food chain, and is one of the factors that govern the rate at which clouds of contaminant become depleted. An understanding of this pathway is important in protecting the population from the adverse effects of airborne contaminants. Of particular concern is the fate of radioactive or toxic *Corresponding author. E-mail address: rob.kinnersley@environment-agency. gov.uk (R.P. Kinnersley). 1 Present address: Air, Land and Water Science, Environment Agency, Olton Court, 10 Warwick Road, Olton, Solihull, West Midlands B92 7HX.
chemical aerosols released over a short period, for example, as a result of an accident at a nuclear installation. Effective emergency management following such a release, including the direction of survey teams and delimiting of restricted land use areas, requires an understanding of the spatial distribution of subsequent deposits of contaminant. Currently, quantification of deposition relies upon deposition velocities that are strictly applicable only to uniform roughness, and do not account for local variations in topography and land cover. Such variations give rise to changes in local wind velocity and turbulence levels that can significantly influence particle deposition rates. The use of such simplifications during emergency exercises has led to operatives deploying finite surveying resources in a less-than-optimal way, and in some cases missing ‘‘hot-spots’’ of contamination (Argyraki et al., 1999).
1352-2310/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2004.03.046
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This work explores the link between landscape topography and spatial variation of particle deposition. A measure of relative deposition rate is required that can be used to derive rules for identifying areas within a real landscape subject to enhanced deposition, so that they can be targeted for sampling. This study is concerned only with dry deposition and the interaction of the flow with the landscape. There has been little work on the dry deposition of environmentally important particles over complex topography. Some study has been made of deposition of dust over complex topography in the field of geomorphology, for example Goossens (1997) and Mason et al. (1999). Direct comparison with such work is difficult because of the larger particle size used in such work, and the importance of resuspension, both direct and due to impaction of larger-sized material. However, comparisons are informative between some of the many published works of Goossens and co-workers (Goossens, 1988, 1996; Offer and Goossens, 1995). These authors found a clear effect on the pattern of deposition, both over hills, and in their wake. The deposition of particles is, of course, linked to the nature of the flow in which they are transported. Belcher and Hunt (1998) reviewed the mechanisms that control turbulent neutral boundary layer flow over hills and noted that turbulence in the flow is greatly influenced by passing over hills, particularly in the wake, and that this has important consequences for the deposition of pollutants. Wind tunnels have been used to model flow over complex topography for some time (Castro and Snyder, 1982; Finnigan et al., 1990; Greeley et al., 1974) and, more recently, computational fluid dynamics (CFD) has become popular for studying such flows (Carpenter and Locke, 1999; Castro and Apsley, 1997; Kim and Boysan, 1999). CFD and wind tunnel studies have also been used for the study of particle dynamics and deposition in particular (Zufall et al., 1999a, b). The combination of CFD of atmospheric flow and particle dynamics is relatively new with some studies of local dispersion and deposition from industrial sources (Ahmadi and Li, 2000). For an introduction to the issues surrounding the use of CFD, Versteeg and Malalasekera (1995) is recommended. The aim of the broader project, to which this work belongs, is to produce a set of ‘‘rules of thumb’’ which can be applied rapidly to any given landscape without the need for computationally intensive calculations. The approach has been to use a combination of CFD and wind tunnel measurements to compare particle deposition for a number of simple landscape shapes and hence to determine how patterns of deposition vary when compared with a flat landscape. The simplified shapes studied are representative of full-scale landscape features. The experimental and modelled boundary layers were similar to a neutral atmospheric boundary layer.
Scaling parameters have been carefully considered to ensure that the deposition variation at model- and fullscale would be similar.
2. Materials and methods 2.1. Wind tunnel experiments The experiments were carried out in an open-return, square cross-section wind tunnel driven by a centrifugal blowing fan. The working section of the tunnel is 2.5 m 2.5 m in cross-section, approximately 10 m long and capable of wind speeds in excess of 10 m s1. Temperature stratification of the air in the wind tunnel is not currently possible, and therefore, only neutral stability flows were simulated. Velocity and turbulence measurements were made using a pulsed wire anemometer as described by Bradbury and Castro (1971), calibrated with a pitot-static tube and a micro-manometer. Vertical and horizontal profiles of streamwise velocity and turbulence were measured at a number of locations. The use of a pulsed wire anemometer allowed the measurement of reversed velocities and the identification of areas of recirculating flow. A turbulent boundary layer was developed in the lower part of the wind tunnel working section, with characteristics representative of a neutral atmospheric boundary layer at a scale of 1:1000. The boundary layer was generated by a series of triangular spires whose dimensions and spacing were calculated using the formula from Irwin (1981) to generate a boundary layer of depth 0.8 m. Five spires were constructed of height 1 m, base 0.12 m and a spacing of 0.5 m between the centres of the spires, placed at a distance of 1.0 m from a large turbulence generating grid at the beginning of the working section. These were followed by a series of roughness elements of decreasing size, to a distance of 2.35 m downwind of the spires. The size and arrangement of the roughness elements was varied by trial and error to achieve a velocity profile consistent with a roughness length of 0.2 mm (model scale). To maintain the developed boundary layer flow, a textured material was applied to the surface of the landscapes and the flat control. This surface was also applied to the floor area upwind and downwind of the model landscapes. The material used was a textured wall covering with an array of uniform raised bumps with a height of approximately 0.5 mm. Three simplified landscapes and a flat control were used in the experiments. Two of the model landscapes were effectively two dimensional, having a uniform cross-section, whilst the third was three dimensional. The two-dimensional landscapes were both flat-sided ridges, of slope 1 in 1 (45 ) and 1 in 3 (18.4 ). The ridges were of height 0.1 m and of lateral width 2.5 m, equal to
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N/A 0 N/A Note that reattachment lengths reported at measured height and at surface for CFD.
N/A 0 0 0 0 0 Flat
0
45 1.25 1.5 400 400 200 0.4 0.2 Cone
0.4
18.43 1.25 1.1 600 600 100 2.5 0.1 Ridge 1 in 3
0.6
0.30 (z ¼ 0:02 m)
0.81 (z ¼ 0:05 m) 1.13 (z ¼ 0:00 m) 0.59 (z ¼ 0:02 m) 0.70 (z ¼ 0:00 m) 0.32 (z ¼ 0:02 m) 0.32 (z ¼ 0:00 m) N/A 0.90 (z ¼ 0:05 m) 45 1.25 1.1 200 200 100 2.5 0.2 0.1 Ridge 1 in 1
Y (m) X (m) Length (m) Width (m) Height (m) Width (m)
Length (m) Height (m)
0.50 (z ¼ 0:02 m)
CFD (m)
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Wind tunnel (m)
Gradient (deg) Location of peak Full-scale Model Geometry
Table 1 Model geometry dimensions at model and full-scale, and reattachment lengths
the width of the wind tunnel. The three-dimensional landscape was conical in shape and of height 0.2 m with a slope of 45 . The shapes of the model landscapes were chosen to be representative of sections of real hilly or mountainous topography and to possess sharp changes in gradient so that the effect of flow separation could be examined. The Reynolds numbers of the flows, using the height as the characteristic length, were 33,000 for the ridges and 66,000 for the cone. Snyder (1972) quotes a value of 11,000 for sharp-edged buildings, for Reynolds number independence. Chatzipanagiotidis and Olivari (1996) used a value of 11,000 for a wind tunnel study of a two-dimensional ridge, quoting a critical Reynolds number of 5000 for rough sharp objects. Therefore, the Reynolds numbers of the features studied here are thought to ensure similarity between model and fullscale. Thermal effects are neglected because the boundary layer is of neutral stability. The area covered by the experiment is small enough (o5 km) that the effect of the Coriolis force at full-scale can be neglected using the criteria of Snyder (1972). A summary of the model landscapes is included in Table 1. Kind (1986), Xuan and Robins (1994) and Goossens and Offer (1990) discuss similarity criteria for modelling snowdrifting, dust emission and deposition, and dust deposition, respectively. Based on the approach used by these authors the following criteria were equal between model and full-scale: density ratio (particle:air), terminal velocity ratio, and reference velocity ratio. The roughness-height Reynolds number was equal to 40 and greater than the criterion of 30 (Kind, 1986). Because of the small particle size in this case, neither resuspension nor saltation are significant mechanisms affecting net deposition patterns. Therefore criteria regarding emission velocity can be neglected. The Froude number is not equal between model and full-scale, but can be neglected because of the very shallow fall angle for the small particles studied and absence of saltation. The above criteria should ensure similarity between patterns of particle deposition at model-and full-scale. For the deposition part of the experiment, Fluorescein particles were generated using a medical nebuliser containing an aqueous solution of 25 g l1 Sodium Fluorescein. The flow rate of air through the nebuliser was approximately 5.7 l min1. The output from the nebuliser was fed into a 25 mm diameter tube leading downwind from the nebuliser and entering the boundary layer at a point located 0.21 m from the end of the boundary layer development section, with its centre 0.0125 m from the floor of the wind tunnel. The tube allowed the source to be located close to the model landscapes (B0.9 and 1.3 m upwind of the peak of the ridges and cone, respectively) without the body of the nebuliser disrupting the flow. In addition, it allowed some time for the generated particles to equilibrate with the air before release.
Reattachment lengths at model scale
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The particles released were characterised with a GRIMM light-scattering particle monitor. Approximately 90% of the particle volume was in the size fraction from 0.75 to 1 mm diameter and 10% was in the size range 1–2 mm diameter. Although the particles were not monodisperse, a nebuliser was used in preference to aerosol generators with a narrower range of particle sizes because of the higher aerosol concentrations attainable. Particle concentrations at the plume centreline, immediately upwind of the landscapes, were in the order of 160,000 particles l1. To measure the deposition of particles, 25 mm GFA filters were placed on the textured surface at intervals along the centreline of the wind tunnel, and also across the width of the tunnel at several locations. Once the filters were positioned, the flow within the wind tunnel was started and allowed to stabilise for a period of 10 min. The particles were then released from the source for 30 min. Following exposure the filters were collected and extracted into pH7 buffer and quantified by fluorimetric analysis with a Perkin Elmer 1000 M fluorimeter. 2.2. CFD studies The flows over the landscapes were modelled using a commercial CFD solver, Fluent 5.5.14. The flows were solved using steady-state Reynolds-averaged Navier– Stokes equations. A number of turbulence models were tested, including standard k–epsilon, Renormalisation Group (RNG) k–epsilon and Reynolds stress model. Preliminary studies showed that the RNG k–epsilon approach predicted the position of the reattachment point of the recirculating area with the most accuracy. The RNG k–epsilon turbulence model has also been shown to perform well by other workers for studies of flow over complex topography (Kim et al., 2000; Maurizi, 2000). This turbulence model was therefore chosen for the remaining studies. Flow over each landscape and the flat control case were modelled at wind tunnel scale. The modelled domain was equal in width to the wind tunnel (2.5 m), had a length of 6 m and a height of 1 m (a height of 1 m was chosen rather than the full height of the wind tunnel for computational efficiency). The grids were constructed with hexahedral cells of horizontal spacing 0.01 m close to the area of the ridges and cone and increasing to 0.05 m away from this area. The vertical spacing started at a size of 0.005 m at the surface, increasing geometrically by a factor of 1.1 with each cell. This is equivalent to a y+ value of just under 35 for the lowest cell, slightly above the lower limit and in the range recommended for CFD solvers (ERCOFTAC, 2000; Fluent, 1999). The total number of cells for each domain ranged from approximately 390,000 to 645,000. An earlier series of model runs were carried out with
larger y+ values and approximately 110,000 cells. The results from these runs showed slight differences in the predicted flow and some areas of significant difference to the deposition rate, and these differences are discussed below. The upwind boundary was defined as a velocity inlet, with a log law profile having uand z0 parameters as determined from experimental measurements (0.23 m s1 and 0.22 mm, respectively). The turbulent kinetic energy and dissipation rate were assigned profiles based on the value of u, using relationships recommended by Richards and Hoxey (1993). These were used in preference to experimental values to allow an evaluation of the use of CFD for generic studies of flow and deposition over hills where wind tunnel data are not available. The initial turbulent kinetic energy is relatively small compared to that generated by the model landscapes and therefore the final deposition results should not be very sensitive to the inlet turbulence parameters provided they are of the correct order. The sides of the wind tunnel were defined as smooth no-slip walls. The floor of the wind tunnel was defined as a noslip wall with a roughness height of 0.001 m and a roughness constant of 0.5, equivalent to the textured roughness used on the surface. (Note that the roughness height is the actual height of the roughness element as opposed to the aerodynamic roughness length, z0 ; of the surface). The top of the modelled domain was defined as a symmetry boundary (effectively a slip wall). The downwind boundary was defined as an outflow boundary. Following solution of the flow, the deposition of particles was modelled using the CFD software’s discrete phase model option. The trajectories of the particles were calculated from the point of release according to the modelled forces acting upon them. These forces include aerodynamic drag due to the flow, gravity, Brownian motion and Saffman lift force. The actual flow affecting the particle motion was determined by the mean flow and the calculated turbulent kinetic energy at each point in the domain. The turbulent velocity in each direction was modelled as a random Gaussian probability distribution multiplied by the RMS velocity in that direction. Because of the isotropic nature of the RNG k–epsilon model, the RMS of the velocity fluctuations is equal in each direction and is proportional to the square root of the turbulent kinetic energy. The pattern of deposition was calculated using a stochastic approach. Particle trajectories were calculated repeatedly using the randomised turbulence until an average pattern of deposition was established. For these studies the number of particles tracked was 1 106. A particle diameter of 1 mm was used, particle density was 1000 kg m3 and the Cunningham slip correction factor used was 1.16632. The source of particles was defined as
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a point source at the location of the centre of the release. The lower surface of the domain was defined such that particles coming within one radius distance were trapped and recorded as deposited. Resuspension of deposited particles was not considered.
3. Results and discussion 3.1. Flow measurements In the following section all distances are given as distance downwind from the peak height, with the exception of the flat case where they are given from the particle source. The velocity profile for the developed boundary layer (at X ¼ 0:33 m) was in reasonable agreement with a log law of surface roughness 0.22 mm as shown in Fig. 1(a). This surface roughness at model scale is typical of atmospheric boundary layer flow over rural terrain at full-scale (Counihan, 1975). The roughness length was slightly longer than that expected from the surface roughness of the textured material alone, but profiles taken further downwind
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(X ¼ 1:42 m, 2.68 m) showed little change in the boundary layer. The vertical profile of turbulence intensity is shown in Fig. 1(b) and the values in the lower part of the boundary agreed well with typical streamwise turbulence values for the lower part of atmospheric boundary layers (Stull, 1988). The range of turbulence intensities at a full-scale height of 50 m were 18% in this study compared with a range of approximately 14–28% reported by Farell and Iyengar (1999) for a slightly larger roughness length. Figs. 2(a)–(f) show the effect of the landscapes on the velocity profiles at varying downwind distances. The vertical profile at the peak of the hills and in the immediate wake show a region of increased velocity in the upper part of the boundary layer. This is more pronounced for the ridges which extended across the width of the tunnel than for the three-dimensional cone. In the wake behind the hill the velocity above the hill height is higher than the upstream value, but changes rapidly towards the surface, with a region of recirculating flow close to the surface, the extent of which is shown in Figs. 3(a)–(c). The velocity profiles further downwind show a recovery to the upwind profile.
1 0.9 Log law z0=0.22mm
0.8 0.7
X=0.33m
z (m)
0.6 0.5
X=1.42m
0.4 0.3
X=2.68m
0.2 0.1 0 0
1
2
3
4
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Fig. 1. Wind tunnel without model landscapes, vertical profiles of (a) streamwise velocity, experimental data are represented by points, fitted log law by continuous line, (b) streamwise turbulence intensity.
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-0.35m
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X = - 0.35m
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z (m)
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2
4
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6
U (ms-1)
(f)
0
1
2
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Distance downwind of peak (m)
Fig. 2. Wind tunnel vertical streamwise velocity profiles at varying downwind distances, (a) ridge of 1 in 1 slope, (b) ridge of 1 in 3 slope and (c) cone of 1 in 1 slope. Normalised profiles of the same data indicating location within wind tunnel, (d) ridge of 1 in 1 slope, (e) ridge of 1 in 3 slope and (f) cone of 1 in 1 slope.
Figs. 3(a)–(c) show the streamwise velocity measured at 0.05 m above the surface, along the centreline of the wind tunnel for each case. There is a clear region of speed-up on the upwind face of the slope, followed by a sudden reduction in velocity and reversal in flow direction in the wake of the hill before the velocity returns to a positive value further downwind. The recirculating region is smaller for the ridge of shallower slope although further measurements at 0.02 m above the surface identified the reattachment point was at 0.54 m from the peak, suggesting a shallow, elongated region of recirculating flow. Note that the velocity in the wake of the cone recovers more quickly than that of the ridges despite the extra height of the cone (0.2 m) because of its limited extent across the width of the wind tunnel. The results for the shallower ridge show good agreement with results from Finnigan et al. (1990) for flow over a shallower sinusoidal ridge, with a velocity minimum upwind of the ridge, followed by a maximum close to the peak and a larger minimum in the wake. Figs. 3(d)–(f) show the profiles of r.m.s. streamwise turbulent velocity also measured at 0.05 m above the surface. All three show an increase of turbulence in the wake, with the more steeply sloped ridge and cone showing a small region of reduction in the immediate wake. Again, the results for the shallower ridge agree
well with those of Finnigan et al. (1990), showing a maximum 4–8 ridge heights downwind of the peak. Comparison of the CFD and experimental profiles of velocity showed that the CFD predicted the flow field reasonably well. The modelled flows all showed regions of reversed flow of similar proportions to the experimental flow. The points of reattachment also compared well, and these are presented in Table 1. The CFD model was used to produce values for reattachment lengths at the same height as measured in the wind tunnel (slightly above the surface) and also at the surface itself. It is clear that there is a significant difference between the two. The values agree with values summarised in Kim et al. (2000) from a number of experimental and computational sources, for flow over a two-dimensional 45 triangular ridge, varying from 9.8 to 16.5 ridge heights. Fig. 4(a) compares the vertical profiles of streamwise velocity between the CFD and the wind tunnel measurements for the cone of slope 1 in 1 and the CFD does well in achieving the same profiles. The CFD overpredicts the vertical extent of the recirculation region in the immediate wake and the velocity further downwind is affected by this discrepancy. Fig. 4(b) compares the longitudinal profile of streamwise velocity. The general pattern and the maxima and minima of the velocity coincide for the experimental and modelled case.
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6 5
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Fig. 3. Wind tunnel longitudinal profiles of streamwise velocity (a–c) and streamwise turbulent velocity (d–f). (a, d) Ridge of 1 in 1 slope, (b, e) ridge of 1 in 3 slope and (c, f) cone of 1 in 1 slope. Measured at 0.05 m above surface.
1.2 1
Height (m)
However, there is some difference in the magnitude of the velocity, which appears to grow with distance downwind. This is likely to be due to the overprediction of the vertical extent of the recirculating region by the CFD. 3.2. Particle deposition measurements
WT
X= - 0.75m
X = 0.25m
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0.6 0.4 0.2 0 -1
0
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-1
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Experimental deposition for the flat case showed a very strong decay in deposition rate with increasing distance from the source due to the reduction in concentration as the aerosol dispersed. Lateral samples also showed the deposition falling off strongly with distance from the centreline. This flat case was used as a baseline against which to compare the deposition to the model landscapes. Figs. 5(a)–(c) show the ratio of deposition rate relative to the flat case for the three landscape cases. For all three cases there is a similar pattern: a small reduction in deposition upwind of the landscape feature, a significant maximum on the windward face (a factor of 0.9–1.7 times the flat case) and a reduction in the immediate wake which recovers back to the upwind value with further distance downwind. The recovery is quicker for the shallower ridge, returning to
2
WT CFD
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Z=0.05m
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-0.5
0
0.5
1
1.5
2
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Distance downwind of peak (m)
Fig. 4. Comparison of vertical (a) and longitudinal (b) profiles of streamwise velocity for CFD and wind tunnel, for cone of slope 1 in 1, (b) Measured at 0.05 m above surface.
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Deposition relative to flat
3 WT
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Fig. 5. Deposition ratio relative to flat case for wind tunnel and CFD. Ridge of slope 1 in 1 (a), ridge of 1 in 3 slope (b) and cone of 1 in 1 slope (c).
50% of the flat case within 2.5 ridge heights from the ridge, compared with 6.5 ridge heights for the steeper ridge. There is good agreement for the pattern of deposition between the CFD and the wind tunnel results. The two-dimensional cases show very good agreement although there is some overprediction by the CFD on the windward face of the ridges, which is more apparent for the steeper slope. There is also a slight divergence in results at large distances for the 1 in 3 slope ridge and this is believed to be due to increasing experimental error in fluorescence measurements with distance in the wind tunnel case, because of reduced deposition with distance from the source. To achieve a
high enough concentration to perform the experiment in a reasonable time, it was necessary to use a point source close to the ground and close to the model landscape. As a result the concentration field, and therefore the deposition rate, fell sharply with distance. The actual, rather than the relative, changes in deposition rate at large distances downwind became comparable with the measurement uncertainty. Further experiments are planned with a stronger and more diffuse source further upwind from the region of interest to alleviate this problem. Direct comparison of these results with those in the literature is difficult because of the influence of
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resuspension and saltation in many reported studies. The strong dependence on the location of the particle source also prevents equivelence between reported work and this study. However, it is informative to compare the results for the ridges to wind tunnel deposition of larger-sized dust (25 mm median diameter, 65 mm maximum diameter) to a symmetrical ridge (Goossens, 1988). The results appear to be in qualitative agreement, with an increase on the windward face and a decrease on the leeward face and in the immediate wake. The present data do not match the rise in the wake because of the different source characteristics. A point source close to the ridges was used in these experiments, compared with a much broader source representative of a ‘dust storm’ in Goossens (1988). Quantitative comparison is also prevented because the reported results are given as difference in deposition from the flat case without a reference value. The two-dimensional results are also in broad agreement with wind tunnel, and CFD studies, to wave surfaces (Zufall et al., 1999a, b). The graph for centreline deposition for the 1 in 1 cone shares the same general features as the two-dimensional landscapes. However, the increased deposition to the upwind face is significantly increased and the reduction in the immediate wake in the experimental results is less than for either of the ridges. It should be remembered that the cone is twice the height of the ridges, which may account for the increased upwind deposition. The less significant region of reduced deposition behind the cone may be due to particles travelling around the sides of the cone and the smaller region of recirculation (in three dimensions) compared to the two-dimensional cases. In addition to the samples taken along the centreline of the cone, a number were also taken on the cone surface and in the wake up to a distance of 1 m from the centreline. The resulting deposition rates at these locations are presented in Fig. 6, which shows that there are areas of increased deposition to the sides and base of
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the windward face of the cone in addition to the peak. Note that this graph shows actual deposition rather than the ratio to the flat case. In the wake, the centreline deposition values are lower than those to each side. The results from Offer and Goossens (1995) for deposition of larger particle sizes to a conical hill show a similar pattern of deposition. The authors of that paper also discuss the presence of horseshoe vortices shed from the sides of the cone. These are thought to be related to the pattern of increased deposition. There is some asymmetry in the pattern of deposition rate, with those at negative Y values showing slightly increased deposition relative to positive Y values. This is supported by several lateral samples taken for the flat and two-dimensional cases that show a slight bias towards the same direction, which becomes apparent at distances of more than 2 m from the peak of the ridges. It is believed that this is due to some slight asymmetry in the flow in the wind tunnel. The influence of such an asymmetry will be expected to be more significant for the three-dimensional case, where the plume of released material is split as it passes the cone. Agreement between the CFD and experiment is not as precise for the cone as it is for the ridges, although the key features are similar. As with the two ridges, deposition to the upwind face is slightly overpredicted by the CFD on the lower part of the cone, but the main difference from the two-dimensional cases is that the deposition in the wake region is consistently underpredicted by approximately 50%. It is believed that this is due to a combination of two reasons. Firstly, the overprediction of deposition to the windward face removes a significant proportion of particles from the flow that are then unavailable to deposit further downwind. Secondly, there is evidence of slight asymmetry in the wind tunnel flow and therefore in the pattern of deposition. The CFD predicted pattern of deposition showed that deposition to a narrow region
Fig. 6. Contour plot of wind tunnel deposition rate (mg m2 s1) to cone and area in immediate wake of cone.
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along the centreline was reduced by 20–50% compared to that on either side. Asymmetry in the flow would cause this region to be offset and higher deposition from the area to the side to result. As mentioned in the CFD method section above, an earlier series of runs were carried out at a coarser resolution and the results from these showed some differences in the pattern of deposition. The principle difference was a larger overprediction on the windward face, with ratios as high as 4.5 for the cone case. However for the other areas, including the wake, there was relatively little difference. In order to examine the effect of the specificity of the results to the location of the particle source, a number of CFD models were run in which the height of the source was varied. Heights from 0.01 to 0.30 m were modelled and the pattern of deposition remained similar with the peak concentration on the upwind face increasing with the height of release. The reduction in the wake became less pronounced with height and eventually increased, showing a maximum increase of 50% for a release at twice the ridge height and approximately 70% for a release height at three times the ridge height. These values become comparable with the deposition increase to the windward face, which agree with the results of Goossens (1988). It is clear that there is a variation in deposition caused by the model landscapes in these experiments. However, it is well known that the presence of the complex topography will also affect the dispersion and hence the concentration field resulting from a point source (Castro and Apsley, 1997; Castro and Snyder, 1982; Castro et al., 1988). It was not possible to measure the concentration of the experimental particles concurrently with the measurement of deposition. However, the results for deposition to the surface and for the concentration immediately above the surface from the CFD were examined. The large rise in deposition to the surface of the cone, both windward and leeward, was not accompanied by a rise in concentration. Deposition in the wake followed the concentration more closely and was most likely a result of mixing of concentration at height down to the surface because of the increased turbulence in the wake. The pattern of deposition is therefore not easily predicted by the concentration alone, supporting our hypothesis that the influence of the landscape arises through locally increased turbulence as well as through the changes in concentration that are a secondary result of increased dispersion due to landscape generated turbulence.
3.3. Result summary The model landscapes had a significant influence on deposition of particles from a point source relative to a
flat landscape case. A number of general features were identifiable: *
*
*
*
a slight decrease in deposition upwind of the raised topography; a maximum in deposition increase on the upwind face close to the peak; a region of decreased deposition on the leeward face, extending into the immediate wake and gradually recovering with distance to upwind levels; In the case of the three-dimensional cone, there is a more complex pattern of deposition on the leeward face, with a minimum at the centreline in the lateral cross-section of deposition in the wake and enhancement at the edge of the wake region.
The CFD predictions of deposition agreed remarkably well for the two-dimensional cases and reasonably well for the three-dimensional case. However, even for the three-dimensional case, the predicted pattern of deposition was in good qualitative agreement with the experiment. The differences in the three-dimensional case are believed to be due to slight asymmetry in the wind tunnel flow. The results serve to validate the use of CFD for studying the influence of landscape on deposition, allowing a greater range of landscape geometries to be investigated than would be practical if physical modelling were always necessary. While it remains impractical to carry out CFD modelling for real landscapes within the timeframe needed for emergency response, the generation of guidelines on the likely modification of deposition patterns in complex terrain offers a means of improving the ability of emergency controllers and sampling strategists to make best use of the sampling resources at their disposal. Note that these results apply only to dry deposition of particles. Clearly under certain meteorological conditions, and with the influence of orographic factors, wet deposition may be an important mechanism.
4. Conclusions The wind tunnel experiments of particle deposition to different topographies indicate that there is a significant effect on particle deposition compared to the flat control case. Areas of increased and decreased deposition relative to the flat were recorded. Using a commercial CFD solver (Fluent 5.5.14), the flows in the wind tunnel were modelled and particle deposition was predicted using stochastic particle tracking in these flows. The resulting predictions were in general in good agreement with experiment suggesting that this approach is of practical use for predicting particle deposition to
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complex geometries giving at least qualitatively correct results. Careful consideration of wind tunnel scaling parameters suggests that the wind tunnel results are applicable to the full-scale case of a neutral atmospheric boundary layer flow over such landscape features. CFD appears to have significant potential for predicting relative deposition effects due to landscape features. More recent work has begun to reap the benefits of this approach for a range of landscape shapes.
Acknowledgements The authors would like to thank T. Huggins for his help with the wind tunnel work. This work was supported by the School of Geography, Earth and Environmental Sciences, University of Birmingham, and by a grant from the Nuffield Foundation.
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