Numerical simulation of topographic effects on wind flow fields over complex terrain

The Eighth Asia-Pacific Conference on Wind Engineering, December 10 14, 2013, Chennai, India Numerical simulation of topographic effects on wind flow fields over complex terrain B.W. Yan 1, Q.S. LI 2, Y.C. HE 3, P.W. CHAN 4 1 PhD candidate of Dept. of Civil and Architectural Engineering, City University of Hong Kong, Hong Kong, boyan2@student.cityu.edu.hk 2 Professor of Dept. of Civil and Architectural Engineering, City University of Hong Kong, Hong Kong, bcqsli@ cityu.edu.hk 3 PhD candidate of Dept. of Civil and Architectural Engineering, City University of Hong Kong, Hong Kong, heyuncheng2009@gmail.com 4 Senior Research Scientist of Hong Kong Observatory, Kowloon, Hong Kong, pwchan@hko.gov.hk ABSTRACT This study addresses the issues pertinent to both the topographic effects on wind flow fields over complex terrain and the accuracy of computational fluid dynamics (CFD). The numerical simulations using isotropic eddy viscosity and wall functions are conducted based on the numerical solutions of the incompressible, nonisothermal, steady-state turbulent flows, in which a regional computational model of a hilly island in Hong Kong has been constructed and the computational results are compared with the experimental data of a boundary layer wind tunnel testing and the in-situ measurements from a remote sensing facility (Doppler radar wind profiler system) at Cheung Chau (CCH) weather station in the island. KEYWORDS: CFD, RANS, TOPOGRAPHIC EFFECTS, WIND SPEED, FRACTIONAL SPEED-UP RATIO (FSR) Introduction Numerical simulation of wind flows in the atmospheric boundary layer (ABL) over complex terrains using CFD techniques represents a major breakthrough for furthering researches in a number of wind engineering fields for the so-called micro-scale phenomena, such as wind power generation, dispersion of pollutants in the atmosphere, prediction of wind loads on structures, analysis of wind flow patterns in urban environments and the air ventilation assessment (AVA) for new residential areas. In this study, to address the issues pertinent to both the topographic effects and the accuracy of the computational fluid dynamics(cfd), a numerical procedure is presented for simulating the Atmospheric Boundary Layer flows over complex terrains. The numerical analysis using isotropic eddy viscosity and wall functions are conducted by the numerical solutions of the incompressible, non-isothermal, steady-state turbulent flows over twodimensional models and real terrains, in which a regional computational model of a hilly island in Hong Kong has been constructed and the computational results are compared with the tested results of a scale model of the island in the boundary layer wind tunnel of City University of Hong Kong (CityU) and the field measurement results from a remote sensing facility (Doppler radar wind profiler system) at Cheung Chau (CCH) weather station, which is located at 71.9 m height above sea level (a.s.l). In the first part of this paper, a grid refinement study has been carried out on turbulent flow over a steep ridge and the numerical results are compared with the experimental data available in the literature, in order to find out the proper grid size both in vertical and horizontal directions and to determine the most appropriate RANS (Reynolds-averaged Navier-Stokes equations) model for the numerical simulations. Then, the updated methodology is applied to the simulation of the topographic effects on the wind flow field over complex terrain. Finally, the predictions are compared with the wind speed data recorded by a Doppler radar to verify the accuracy of the numerical simulations. Proc. of the 8th Asia-Pacific Conference on Wind Engineering Nagesh R. Iyer, Prem Krishna, S. Selvi Rajan and P. Harikrishna (eds) Copyright c 2013 APCWE-VIII. All rights reserved. Published by Research Publishing, Singapore. ISBN: 978-981-07-8011-1 doi:10.3850/978-981-07-8012-8 083 541

Numerical method and turbulence model For the neutrally stratified atmosphere, the Reynolds-averaged equations of continuity and momentum for steady, incompressible and viscous flow are expressed as follows: Conservation of mass: U j = 0, x j (1) Momentum: ( UU ) i j 1 p Ui = + ( ν uu ) + F. i j x ρ x x x j i i j (2) where the subscripts i and j = 1, 2, and 3 correspond to the streamwise (x), spanwise (y), and vertical (z) directions, respectively. In the above equations, U i is the mean velocity component in the i-direction, p is the mean pressure, is the air density. In Eq. (2), F is related to the external forces, such as the buoyancy and rotation of the earth. The Coriolis force is neglected in this study and the Reynolds stress uu i j is related to the mean flow by the Boussinesq approximation of linear and isotropic eddy viscosity as follows: 2 τ = 2μ S ρkδ ij T ij ij (3) 3 2 where S is the mean strain-rate tensor and μ = ρck / ij T μ ε is the eddy viscosity, where k = 0.5( uu i i), C is the dimensionless constant and δ is the Kronecker delta. ij The eddy viscosity in Eq. (3) is obtained by the RNG based k -ε model (Yakhot and Orszag, 1986). In order to avoid too much computational efforts for capturing the rough-wall induced turbulence in the viscous sub-layer, the wall function is used, in which u z U = ln( ), κ z 0 2 u k=, 1/2 C μ 3 u ε =. κ z where u is the friction velocity, z 0 is the roughness length parameter, z is the distance from surface, and κ is the Karman constant (=0.41). The first grid is located in the logarithm region, y + + <30 ( y = u y/ v ) (Wilcox, 1993). Discretization The control volume has been discretized using the block-structured grid with refined boundary layers attached to the hilly surfaces, to achieve a reduction of the calculation resources and increase of the computational efficiency and accuracy. And the Semi-Implicit Method for Pressure-Linked Equations Consistent (SIMPLEC) algorithm was used to couple pressure and velocity on a non-staggered grid. The second order upwind schemes were used for velocity and turbulence, and the Pressure Staggering Option (PRESTO) Scheme was applied for pressure interpolation. Some numerical simulations presented divergence when the SIMPLEC method for pressure-velocity coupling was employed. Therefore, the relaxation parameters were set to the value of 0.2 for pressure, and of 0.1 for the other prognostic variables, which resulted in satisfactory solutions that reached the full convergence. Boundary conditions Based on the field measurements of vertical profiles of wind speed during tropical cyclones (He et al., 2010), the gradient height in the present simulation was chosen as 700 m, (4) 542

and the inlet boundary conditions were set up as same as the oncoming wind characteristics simulated in the wind tunnel test. A symmetry condition (vanishing vertical derivatives of the streamwise and spanwise velocity components, as well as vanishing vertical velocity) at the top boundary of the computational domain was adopted. For the Large Eddy Simulation (LES), the outflow boundary conditions are less troublesome, and the familiar zero gradient boundary condition was used for all the variables normal to the outflow boundary. For the hilly surfaces, the boundary conditions were set to be no-slip wall boundary (u=v=0) which is appropriate for the velocity components at solid walls. Wind flow over a triangular ridge Turbulent flow over a two-dimensional hill is investigated first in this study by simulating the flow field over a steep ridge. The dimensions of the triangular ridge with a slope of 40 o are of height (H) 40 mm and width (B) 95 mm. Several turbulence models are adopted with the standard wall function to simulate the neutral atmospheric flow over the triangular ridge, and the models are assessed by comparison with available wind tunnel testing data. Two block-structured grid systems for the numerical simulation are employed as shown in Figure 1, and the mesh arrangements for the standard case and the refined case are of 226 (x) 80 (y) 40 (z), and 336 (x) 80 (y) 40 (z), respectively. The grid independency of the computational results is verified based on the comparison of the numerical results of the standard and refined grid systems. Special care is taken in assigning the inflow information at the inlet, such as the vertical profiles of horizontal component including mean wind velocity and turbulent intensity which are determined based on the experimental results and wind load codes. Table 1: Measured and predicted reattachment lengths behind the triangular ridge. shows the reattachment locations predicted with different turbulence models along with the experimental observations. The reattachment distance is measured from the center of the ridge, (x, y) = (0, H) being the peak of the ridge to the reattachment point. The simulated results with various turbulence models are compared with the experimental data and the existing computational results. ` Fig.1 Block-structured mesh arrangements for the simulation of flow over a steep ridge (a) Standard grid system; (b) Refined grid system Velocity contour and streamline at vertical plane z=0 m by four different turbulence models including RNG based k -ε model (RNG), standard k -ε model (std), k-ω sst model and realizable k -ε model are shown in Fig.2. Fig.3 shows the vertical profiles of horizontal velocity at various locations behind the ridge. It is noteworthy that the vertical profiles of horizontal velocity calculated by various turbulence models at x/h= -4 near the inlet boundary agree quite well with those measured in the boundary layer wind tunnel testing as shown in 543

Figure 3 (a). However, the predicted horizontal velocity profiles with different turbulence models significantly deviate with each other at the locations behind the steep triangular ridge. As shown in Fig.3 (b), (c), the profile predicted by the standard k -ε model differs largely from those predicted by other turbulence models. However, its horizontal velocity profile close to the outlet boundary (x/h = 30) shows better agreement with the reference velocity profile than those predicted by other models, which proves that the effects of the triangular ridge has been diminished near the location, corresponding to its lowest value of reattachment length (9.0H). The prediction by the RNG based k -ε model is in excellent agreement with the experimentally determined reattachment point at 11H by Lee and Park (1997). Generally speaking, the differences predicted among various turbulence models indicate their different performances in simulating the shear layer flow and flow separation behind the ridge. Table 1: Measured and predicted reattachment lengths behind the triangular ridge. Classification Source Reattachment Point Experiment Lee and Park (1998) 11.0H k -ω sst model 12.5H Realizable k -ε model Present computation 12.0H Standard k -ε model 7.0H RNG based k -ε model 10.5H Fig.2 Velocity contours and streamlines at vertical plane z=0 m. (a) RNG k -ε model (present); (b) Standard k -ε model (present); (c) k -ω sst model (present); (d) Realizable k -ε model (present). Several turbulence models were applied with the standard wall functions to simulate the neutrally stratified atmospheric flows over the triangular ridge, and the models were assessed by comparisons with the available wind tunnel data. It is found that the result accomplished by the RNG k -ε model shows the best overall performance. 544

a b x/h = 8 x/h = -4 c d x/h = 15 x/h = 30 Fig.3 Vertical profiles of horizontal velocity at various locations behind the ridge (a) at X/H=-4; (b) at X/H=8; (c) at X/H=15; (d) X/H=30 Wind flows over complex terrain The same numerical procedure as illustrated above is adopted to simulate the turbulent flows over complex terrain to predict the topographic effects on the wind flow fields. A regional computational model of a hilly island in Hong Kong has been constructed based on Geographic information system (GIS) data with the resolution of 2 m. The computational results are compared with the wind speed data recorded at the CCH weather station in the island and those measured from a 1:400 scale model study conducted in the boundary layer wind tunnel at CityU. From the previous analysis of the long-term field measurements (He et al., 2011), the height of 700 m a.s.l was chosen as the gradient height, and in the present study, a neutrally stratified ABL has been supposed and a geostrophic plane was set at 700 m a.s.l. The computational domain is of 1.6 km length (x), 1.4 km width (y) and 0.7 km height (z) as illustrated in Figure 3; the two buffer zones located behind the inflow and in front of the outflow are divided by 25 and 15 non-uniform grids with stretching ratio of 1.05, respectively, for the purpose of stabilizing the calculations. Two computational domains using different grid schemes were generated to compare the computational results and check the grid independency. The standard surface mesh resolution is 8 m composed of 35,000 quadrangular cells and the refined surface mesh resolution is 5m with 89,600 quadrangular cells, while horizontal grid spacing gradually increases at stretching ratios of 1.05 towards the inlet and of 1.15 towards outlet. Vertical grid spacing increases at a stretching ratio of 1.05 along the elevation, starting from a near ground cell height of 0.5m with the total vertical grids of 51. For the wind tunnel study, the physical models constructed for the wind tunnel test is shown. Fig.5 presents the elevation contours 545

of the hilly island and the height of the crest is 70 m a.s.l with the discrepancy of approximately 2% compared with the peak of the real terrain (71.9 m a.s.l). Fig.4 Physical model of CCH island in the wind tunnel test Fig.5 Elevation contours of complex terrain Four flow field cases with different incident wind directions have been simulated and analyzed herein, where the wind direction of 0 o corresponds to the north wind, 90 o represents the east wind, 180 o stands for the south wind, and 270 o denotes the west wind. Special care was taken for the implementation of the inflow conditions. The vertical profile of the mean wind velocity follows the power law as follows: α U() z = Uref ( z/ zref ) (5) where the exponential value is 0.12 in this study. 546

a Fig.6 Vertical profiles of mean streamwise wind component and turbulence intensity b c d Fig.7 Velocity contours of horizontal plane at 5 m height from the surface of the terrain for various oncoming flow directions (a) N (0 o or 360 o ); (b) S (180 o ) (c) W (270 o )and (d) E (90 o ) (exaggerated vertical height) For the turbulence intensity profile of the oncoming flow, the power law recommended in AIJ-2004 is adopted: α 0.05 I( z) 0.1( z/ z G ) = (6) 547

where, z G stands for the gradient height, andα is the same power exponent as in Eq.(5), z is the height from the ground. Fig.7 shows the velocity contours of horizontal plane at 5 m height from the terrain under various wind directions of N, S, W, and E. It is found that the wind velocity was obviously increased near the peak zones of CCH. In the windward and leeward areas, the velocity was greatly decreased due to the vortices induced by the obstacle effects of the hill. As indicated in Fig.5 (b), there is a shallow valley near the northern face of CCH between two peaks. For the wind in the valley, the lower wind zone was observed in the lee side of the hill under various wind directions, which indicated that the wind flow was obstructed by the vortices stirred up from the interference of the dual-peak terrain. Moreover, it is revealed that the downslope wind velocity magnitude was increased as indicated by Duran (1990) and Smith (1985). According to the velocity contours, the topographic effects of the mountainous terrain were observed and verified. a b Fig.8 Pathlines of the stable astmospheric flow near ground under various wind directions (a) N (0 o or 360 o ); (b) W (270 o ) As depicted in are the pathlines of the atmospheric flow near the terrain suface under northern and western winds. In particular the vortices induced by the flow separation were not reproduced, which are consistent with the field measurements, indicating that the separation phenomenon by the numerical simulations was not typically observed in the neighborhood of the complex terrain. The Fractional speed-up ratios (FSR) at the peak of the hilly island where the anemometer is installed were compared with the results from the wind tunnel study. The same inflow conditions of both the mean wind speed and turbulence intensity were adopted and reproduced in the numerical simulations. As depicted in Figure 9, the predicted FSRs are in good agreement with those from the wind tunnel study, especially for the wind directions of 0 o or 360 o and E (90 o ), while the similar distributions, but larger discrepancies of the FSRs compared to the experimental results were revealed under wind directions of S (180 o ) and W (270 o ) and the average difference ratios are approximately 8% for both cases. The discrepancy between the numerical results and the experimental data of the wind tunnel study increases with the decrease of the height from the hilly surface. 548

Fig.9 Fractional speed-up ratios (FRS) at the peak of complex terrain (a) N (0 o or 360 o ); (b) S (180 o ) (c) W (270 o ) and (d) E (90 o ) As demonstrated in Table, FSRs under various wind directions are compared with those measured from the wind tunnel test, which shows satisfactory consistence between them and the maximum discrepancy ratio is approximately 16% under wind direction of 270 (W), while the minimum discrepancy ratio is approximately 1.5% under the wind direction of 90 (E). According to the field records, the FSRs at 10 m height away from the terrain surface is 1.42-1.63 in the azimuth section of about 90 o (E) and the corresponding numerical result is 1.49, which falls in the measurement range. Although, the overall performance of the numerical simulation is fairly satisfactory, obvious discrepancy is observed under several incident wind directions, which may be attributed to the difference between the computational terrain model and the real terrain, the adoption of the standard wall function attached to the rough wall and the implementation of the inflow boundary conditions. These issues may need further verifications and clarifications. Direction Table 2: Directional FSRs for mean wind speed FSR (wind tunnel) Fractional Speed Ratio (FSR) FSR (CFD) 98.6m 26.7m 10m 98.6m 26.7m 10m 0 (N) 0.93 1.12 1.28 1.11 1.32 1.43 90 (E) 1.06 1.28 1.47 1.09 1.32 1.49 180 (W) 0.99 1.19 1.35 1.14 1.39 1.54 270 (S) 0.92 1.11 1.27 1.12 1.35 1.52 Conclusions In this study, a procedure is presented for simulating the Atmospheric Boundary Layer (ABL) flow over complex terrain to predict the topographic effects on the wind flow fields. The numerical simulations using isotropic eddy viscosity and wall functions were conducted by the numerical solutions of the incompressible, non-isothermal, steady-state turbulent flows over two-dimensional models and real complex terrain of an island in Hong Kong, and the computational results were compared with the wind tunnel testing results and the field measurements from a weather station in the island. The following conclusions are summarized based on the combined study of numerical simulation, wind tunnel testing and field measurements: 549

1. The wind velocity was obviously increased near the peak zones of the complex terrain. In the windward and leeward areas, the velocity was decreased due to the vortices induced by the obstacle effects of the hill. 2. For the wind in the valley, the lower wind zone was observed in the lee side of the hill under various wind directions, which indicated that the wind flow was obstructed by the vortices stirred up from the interference of the dual-peak terrain. 3. The vortices induced by the flow separation were not reproduced, which also consists with the results from the field measurements, indicating that the separation phenomenon was not typically generated near the complex terrain. 4. The fractional speed ratio (FSR) was in a good agreement with the results from the wind tunnel test, and the average difference ratios are approximately 8%. Furthermore, the discrepancy between the numerical results and the experimental results decreased with the height. 5. The overall performances of the numerical simulations were fairly satisfactory, while obvious discrepancy was also observed, which should be verified and clarified in the further study. Acknowledgement The authors would like to express their gratitude to Hong Kong Observatory for the provision of the wind data records and the permission of using the data for this study. The work described in this paper was supported by a grant from the Research Grants Council of Hong Kong Special Administrative Region, China (Project No: CityU 117709) and a grant from the National Natural Science Foundation of China (Project No: 51278439). References Durran, D.R. (1990), Mountain waves and downslope winds, Meteorological Monographs. 23, 59-62. He Y.C., Chan P.W, Li Q.S. (2011), Monitoring of vertical profiles of wind speed during tropical cyclones, Proceedings of the 13th International Conference on Wind Engineering, pp.427-434. Lee, S.J., Park, C.W. (1998), Surface pressure variations on a triangular prism by porous fences in a simulated atmospheric boundary layer., Journal of Wind Engineering and Aerodynamics. 73, 45-58. Smith R.B. (1985), On severe downslope winds, Journal of Atmospheric Science. 42, 2597-2603. Wilcox, D.C. (1993), Turbulence modeling for CFD, DCW Industries, Inc., La Canada, CA, 126. Yakhot, V., Orszag, S.A. (1986), Renormalization group analysis of turbulence. I. basic theory, Journal of Scientific Computing. 1, 3-51 550