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1 Estimation of Surface Roughness using CFD Simulation Daniel Abdi a, Girma T. Bitsuamlak b a Research Assistant, Department of Civil and Environmental Engineering, FIU, Miami, FL, USA, b Assistant Professor, Department of Civil and Environmental Engineering, FIU, Miami, FL, USA, ABSTRACT: Surface roughness is a critical factor affecting the wind flow and hence loading on structures, dispersion of pollutants, and other atmospheric boundary phenomena. It is characterized by two basic parameters: the roughness length z 0 and the displacement height d. Estimation of these parameters over a large area through full scale tests is typically not feasible. Alternatively, wind tunnel tests could be employed, but they can be costly. Often empirical methods are used for estimating roughness. The Lettau (1969), Counihan (1971), Theurer (1993) and McDonald (1997) models are among the approximate methods used to estimate roughness parameters from data on the planar and frontal areas of obstacles. This paper discusses the limitations of these methods and the benefit of conducting CFD simulations to determine roughness parameters. CFD simulations were conducted for arrays of obstacles arranged in various patterns. The velocity profile estimates at different locations were then used to determine the roughness parameters for the upwind terrain. The performance of the CFD simulations was assessed by comparisons with the approximate methods listed earlier. The CFD simulation showed good agreement with the approximate methods. One obvious advantage of using CFD simulations was that their applicability was not limited to simple arrays of obstacles, albeit prismatic models were used for the sake of comparison. The CFD method may be used on any complex digital surface model obtained from LIDAR (Light Detection and Ranging) or other sources. Although this type of computational effort may become expensive, it only needs to be evaluated once for a particular site. Keywords: Computational fluid dynamics, surface roughness length, displacement height, velocity profile 1 INTRODUCTION The physical meaning of the roughness parameters z 0 and d has not been well established outside of their empirical use in the log-law (DeBruin and Moore 1985). However, z 0 influences the shape of the wind profile and is indicative of the shear force imposed by the surface. The displacement height d roughly indicates the average height of obstacles and is proportional to roughness element height H. A commonly used rule of thumb estimate for d is 0.75H (Gardner 2004). McDonald et al. (1998) has reviewed empirical methods for estimating the surface roughness before providing their own improved method derived from basic principles of fluid dynamics. The roughness parameters were calculated as functions of secondary parameters derived from shape, size and density of roughness elements. For this study, cubes and rectangular prisms of height H were used as roughness elements, where: H = Average height of obstacles A f = frontal area of obstacles λ f = frontal area ratio = A f / A d 1

2 A p = planar area of obstacles λ p = planar area ratio = A p / A d A d = total lot area covered by obstacles. The roughness models are summarized in Table 1 below. The first two methods did not provide formulas for calculating displacement height. For a terrain with high density of obstacles of uniform height, a phenomenon known as skimming flow occurs, where the wind is effectively displaced by the averaged height of obstacles, while the roughness length goes down to zero. The Lettau (1969) and Counihan (1971) model disregarded this effect, hence their use is limited to low area densities usually not more than 30%. Peak values of z 0 occur roughly at an area density ratio of 20% (McDonald 1998). Table 1 Summary of models used for calculating roughness parameters Model Published z 0 / H d/h Lettau λf None Counihan λf None Theurer λf ( λp) 1.67 λp McDonald 1997 z 0 / H = (1 - d/h) exp (-(0.5 * Cd/k2 * (1 - d/h) * λf)-0.5) 1 + A-λ(λ-1) Peterson (1996) compared Lettau (1969) and Counihan (1971) roughness models with a database of wind tunnel measurements of refinery models. The roughness parameters were determined from measurements of wind velocity and turbulence intensity at the downstream end of obstacle arrays. Among the different wind field derived models tested by him, Lo s method (1990) of predicting roughness parameters from wind profiles was found to give the best results. For that method, two measurements of average wind speed inside the inner layer is required, however turbulence intensity measurements are not required. The method is based upon the conservation of mass principle between the original wind speed profile and a displaced log-law profile. This method was used in this paper as well. It was observed that the method is very sensitive to slight fluctuations of measurements in the field or, for this study, computational errors. Peterson also conducted statistical comparisons between different methods and found out Lettau s model gave the best approximation to roughness length when compared with wind tunnel results. When roughness characteristics change from open terrain to suburban, velocity profiles will not automatically adapt to the new roughness condition (Wang et al 2007). Thus, when velocity measurements are taken, the height should be within the zone of influence of the new terrain. For a transition from smooth to rough terrain, the following approximate formula could be used to define the internal boundary layer below which the wind velocity is solely determined by the new roughness. where x measures horizontal distance from the point where transition occurs, z 0 is the new roughness length and z i measures the height of the internal boundary layer. 2 TEST SETUP The test setup used in this paper was similar to the one used by McDonald et al (1998). Regular or staggered arrays of cubes were exposed to an oncoming wind and velocity profiles were recorded at different sections behind the obstacles. The profile showed variations at a given (1) 2

3 section from location to location. Therefore, sample points were taken and results were averaged to get a representative velocity profile for that particular section. This approximation is acceptable for regular arrays of cubes, but may be inaccurate for irregular obstacles. Close to the ground and right behind an obstacle, negative velocity profiles may be developed due to wake interference, while at locations close to the gap center line the velocity is usually positive. Average values that remove these variations close to the ground were used, and positive values were expected there as well. The area density ratio for the configurations considered can be easily approximated by the following formula. For example, a spacing S = 1.5H between blocks gives λ = The Lettau (1969) model predicts a roughness length z 0 = 0.5λH = 0.08H. One of the objectives of this paper was to evaluate predictions of roughness length and displacement height by using CFD simulations. From velocity profile measurements at the five locations shown in Figure 1, the corresponding roughness parameters were estimated using Lo s equations. To begin, the displacement height was determined by iteration using equation 3, which is based on normalized values of velocity and height. While the value of d obtained was satisfactory, the approximation z 0 was very sensitive to the selected reference heights in the inner layer. (2) (a) (b) Figure 1 (a) Plan for regular array of cubes with height H and spacing of S = 1.5H. Velocity profile measurements are taken at 5 locations mid-way between blocks, (b) OpenFOAM mesh for staggered array of obstacles.. 3

4 (a (b) (c) Figure 2 Symmetric sections used for (a) Staggered array of blocks (b) Regular array of blocks (c) 45 0 wind angle of attack. Hatched sides represent planes of symmetry. (3) The test was conducted for various configurations of obstacles with different spacing, staggered placement, rectangular obstacle shapes, and different angles of attack as shown in Figure 2. Other shapes of obstacles may be considered for the CFD simulation but the calculation of planar and frontal areas gets complicated. Symmetry of arrangement of obstacles was exploited to significantly cut the computational effort needed. Models were prepared for six area density ratios (0.05, 0.11, 0.16, 0.2, 0.33, and 0.5) for every configuration of obstacles considered. A series of 32 blocks of 20 m height were arranged in different ways, and a steady state solution of the flow problem was sought. The choice of steady state solution allowed for more cases to be considered because the amount of time required for a solution was significantly reduced compared to a transient solution. However, it excluded wind field derived models which make use of turbulence intensity measurements. The CFD software used for this study was the open source software OpenFOAM. Scripts were written for generation of the required surface model in stereographic format (STL), for a given spacing, shape, placement and angle of attack. Arbitrary models could also be generated from LIDAR measurements, having xyz coordinates of obstacles. The computational domain was constructed using the surface model as a base. Meshes were generated with more refinement closer to the wall. On the inlet side of the computational domain a parabolic wind profile was applied with small z 0 and no displacement height. Symmetry boundary conditions were set at the sides and top of the computational domain. Then, a steady state solution was carried out and velocity profiles were sampled at different fetch lengths. It should be noted that the ultimate objective of this work was to gauge performance of CFD simulation for roughness estimation of a large area on an arbitrary 3D digital terrain model. Among the models considered in this study, McDonald s model is the only model that accounts for the shape effect by the use of the drag coefficient C d. The Lettau (1969) and Counihan (1971) model are more suited to rounded elements with low drag coefficients. 4

5 3 RESULTS AND DISCUSSION A sample actual and best fit log-law velocity profile is shown in Figure 3a. The idea behind conservation of mass (COM) derived models, such as Lo s method, is to get equal area under both curves. A mass flow is subtracted from the log-law profile and added to the bottom layer resulting in the same mass flow under both curves. (a) Figure 3 (a) Sample recorded and best-fit log-law velocity profile (b) Typical profile showing wake-interference between blocks. (b) (a) Figure 4 (a) Variation of averaged velocity profiles with fetch length (b) Five different velocity profiles sampled at a section before averaging. y = 0 m is right behind the middle of block. (b) 5

6 Sometimes this is difficult to achieve if the selected points do not fall within the inner layer. Peterson (1996) modified Lo s method to improve the accuracy of estimation of roughness length. In this paper, the two heights in the inner layer were selected manually by looking at the goodness of fit to the log-law profile. As the area density ratio increases the behavior of the flow changes from isolated to wake interference, and finally to skimming flow. This behavior is clearly observed at larger area densities considered in this paper. Some roughness models disregard this behavior thereby overpredicting the actual roughness length. Figure 5 Roughness length plots for different models (a) (b) Figure 6 (a) Roughness lengths plots for staggered and regular arrays (b) displacement height comparison of CFD result with Theurer s approximation. 6

7 The effect of fetch length on the velocity profile is duly noted as shown in Figure 4a. As the fetch length becomes larger, the flow stabilizes. In other words, the internal boundary layer grows until it becomes equal or greater than the height of the computational domain adopted for the present study. Stabilization of flow is usually achieved much earlier than the last row of blocks is reached. The average velocity within the viscous layer increases with fetch length, while the velocity in the inner and outer layers decreases. This is in accordance with the COM principle as discussed previously. The roughness length and displacement height obtained from averaged velocity profile measured at the last row of series of blocks is plotted in Figure 5 along with predictions from different roughness models. The McDonald roughness model was tried in two ways. One way was to determine roughness length from displacement height calculated using Lo s equation (shown as McDonald 1 in Figure 5). The other option was to use d calculated from Theurer s equation (shown as McDonald 2 in Figure 5). The first option gave the best fit to the CFD calculated data. The Theurer model also showed good fit up to an area density ratio of 20%. The Lettau and Counihan models grossly underestimated the roughness for area density below 20% and overestimate it for area density larger than 20%. The staggered obstacle arrays and regular arrays with a 45 wind angle of attack resulted in higher roughness compared to the simple case of regular arrays. Literature also suggests staggered placement of obstacles increases roughness due to relatively larger exposure of faces of the cubes to incoming wind. A regular array of cubic obstacles exposed to a 45 oncoming wind is basically a staggered array of triangular obstacles as shown in Figure 2c. Also, it is observed that the deviation of the Lettau and Counihan model from the CFD model was less pronounced for the staggered array compared to the case of regular arrays. This is reasonable due to much less wake interference for staggered arrays with large spacing (small λ), in which case the flow effectively becomes isolated for each block. However, the Lettau and Counihan model still showed significant deviations from the CFD model partly explained by larger drag imposed by the cubic obstacles (C d = 1.2). Figure 7 Digital model extracted from LIDAR data. 7

8 4 CONCLUSIONS AND FUTURE STUDY In this paper, CFD simulation was presented as an alternative method to determine roughness parameters of obstacle arrays arranged in different manners. The results obtained from simulation were compared with existing models, and good agreement was found. Also, the problems associated with some of the models (Lettau and Counihan) at higher area density ratios were avoided by using direct simulation of the situation. The simulation was conducted only on rectangular prisms for the sake of comparison with existing methods; but, it may be done on arbitrary digital models of a large area (Figure 7) at much lower costs than wind tunnel or full scale tests. Research is being done to use CFD simulations over a model prepared from LIDAR measurements to determine roughness parameters. Both the model preparation and the simulation usually take a very long time for an arbitrary area with buildings, trees, hills and other obstacles. To reduce the computational load, a narrow strip of the area is taken to evaluate roughness from a certain angle. This procedure is suitable, for example, if a multi-story building is to be built and the performance of the building for different wind angles of attack is required. Near the area of interest the model should be refined to correctly replicate the shapes and sizes of adjacent buildings because wake interference effects can significantly alter the wind load on the building. 5 ACKNOWLEDGEMENTS This material is based in part upon work supported by the National Science Foundation CA- REER project under Grant Numbers Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. The feedback given by James Erwin is gratefully acknowledged. 6 REFERENCES Counihan J. (1971), Wind tunnel determination of the roughness length as a function of the fetch and roughness density of three dimensional roughness elements, Atmospheric Environment, 5, De Bruin, H.A.R. and C.J. Moore (1984), Zero-plane displacement and roughness length vegetation, derived from a simple mass conservation hypothesis, Boundary Layer Meteorology, 31, Gardner, A.G. (2004), A full scale investigation of roughness lengths in inhomogeneous terrain and a comparison of wind prediction models for transitional flows, PhD thesis, Texas Tech University. Lettau H. (1969), Note on aerodynamic roughness parameter estimation on the basis of roughness element description, Journal of Applied Meteorology 8, MacDonald R.W., Griffiths, R.F. and Hall, D.J. (1998), An improved method for estimation of surface roughness of obstacle arrays, Atmospheric Environment 32, MacDonald R.W, Carter Schofield S., Slawson P.R (2002), Physical modeling of urban roughness using arrays of regular elements, Water, Air, and Soil Pollution: Focus 2: Petersen R. L (1994), A wind tunnel evaluation of methods for estimating roughness length at industrial facilities, Atmospheric Environment, Theurer, W (1993), Dispersion of ground level emissions in complex built-up areas, PhD thesis. University of Karlsruhe, Germany. Wang K., Stathopoulos T. (2007), Exposure model for wind loading of buildings, Journal of Wind Engineering and Industrial Aerodynamics, 95,

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