LARGE-EDDY SIMULATION OF AN URBAN CANOPY USING A SYNTHETIC TURBULENCE INFLOW GENERATION METHOD

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1 Annual Journal of Hydraulic Engineering, JSCE, Vol.**, 2015, February LARGE-EDDY SIMULATION OF AN URBAN CANOPY USING A SYNTHETIC TURBULENCE INFLOW GENERATION METHOD Tobias GRONEMEIER 1, Atsushi INAGAKI 2, Micha GRYSCHKA 3 and Manabu KANDA 4 1Member of JSCE, M. Sc., Institute of Meteorology and Climatology, Leibniz Universität Hannover (Herrenhäuser Straße 2, Hannover, Germany) 2Member of JSCE, Ph. D., Department of International Development Engineering, Tokyo Institute of Technology (12-1, Ookayama 2, Meguro-ku, Tokyo 152, Japan) 3Ph. D., Institute of Meteorology and Climatology, Leibniz Universität Hannover (Herrenhäuser Straße 2, Hannover, Germany) 4Member of JSCE, Ph. D., Professor, Department of International Development Engineering, Tokyo Institute of Technology (12-1, Ookayama 2, Meguro-ku, Tokyo 152, Japan) When simulating the turbulent flow around urban structures with large-eddy simulation models it is often necessary to use non-cyclic boundary conditions in streamwise direction. In such cases a turbulent inflow condition at the inlet is favored although it is highly difficult to obtain. A synthetic turbulence generator, modelling turbulence statistics and correlations, is used to generate a turbulent inflow for large-eddy simulations. Results are compared with simulations using laminar inflow. An artificial urban canopy consisting of aligned buildings with cubical shape was used. Two simulations contained one additional tall building located at the center of the domain. The turbulence statistics show a well-developed urban boundary layer above the building arrays for each simulation. Higher turbulence intensity was found when using the turbulence inflow method resulting in faster development of an urban boundary layer. Key Words : large-eddy simulation, synthetic turbulence, turbulent inflow, urban canopy 1. INTRODUCTION When using large-eddy simulation (LES) models it is a common technique to use cyclic boundary conditions for the horizontal boundaries of the simulation domain. However, if a structure such as a single building is present in the simulation domain, cyclic boundaries would cause that the simulated flow will see an infinite array of the same building in each horizontal direction rather than a single building. So, if the flow around an isolated structure like a single building or a part of a real urban canopy needs to be simulated, open boundary conditions rather than cyclic conditions have to be used in the LES model. Open boundaries, however, have the disadvantage that the user has to define the inflow. The easiest way to define an inflow condition would be a constant non-turbulent flow. But, to get realistic results for the turbulent motions around the obstacles of interest, the flow has to be turbulent, as it would be the case in a real atmospheric situation, before it hits those obstacles. Therefore, a wide turbulence generation area has to be added to the simulation domain in front of the obstacles of interest where the laminar flow from the inflow boundary forms into a well-developed turbulent flow. Hence, laminar inflow conditions require a distinct larger domain which leads to a significant increase of computation time and cost. In the past many studies were carried out to find a way to provide a realistic turbulent flow at the inflow boundary to minimize the needed simulation domain and therefore the computation time and so the cost of a simulation. In this study a synthetic turbulence inflow generation method designed by Xie and Castro 1) and optimized by Kim et al. 2) will be used to simulate an urban boundary layer over an array of cubes and one tall building in the center of the domain with noncyclic boundary conditions. The objective of this study is to show the advantages of using this synthetic turbulence inflow generator over a laminar inflow.

2 The following chapter will give a short introduction to the used LES model and the synthetic turbulence inflow generator. In chapter 3 the simulation setup is described and the results of four cases differing in inflow conditions and topography are shown. At the end the conclusions will be drawn in chapter SIMULATION TECHNIQUE (1) PALM The parallelised LES model PALM 3), version 3.10 revision 1466, was used to carry out the simulations for this study. PALM is open source software and the code can be accessed under palm.muk.uni-hannover.de/browser/?rev=1466. The model solves the non-hydrostatic incompressible Boussinesq equations using a fifth-order advection scheme of Wicker and Skamarock 4) and a third-order Runge-Kutta 5) scheme for time step. Topography is added by using a masking method based on the method of Kanda et al. 6). At first the prognostic equations are solved without considering the topography and in a second step the wall-normal velocities at the edge of the obstacles are set to zero 7). (2) Inflow method A synthetic turbulence inflow generation method developed by Xie and Castro 1) is used for the inflow boundary condition. At the inlet unscaled turbulent disturbances u i containing correlations in space and time are added to the mean wind velocity profiles U i u i = U i + a ij u j, (1) where i, j {1,2,3}, u i is the instantaneous wind velocity, and a ij is the amplitude tensor derived from the Reynolds stress tensor R ij by a transformation after Lund et al. 8) a ij = (2) 0.5 R ( 1 R 21 a 11 (R 22 a 2 21 ) ). 1 1 R 31 a 11 (R 32 a 21 a 31 )a 22 (R 33 a 2 31 a 2 32 ) 0.5 The turbulent disturbances were derived using a filter function 2n 0.5 b i = b i ( 2 b k ), (3a) k= 2n b k = exp ( π k ), (3b) n where n = L / Δx, Δx is the grid size, and L is the length scale. A spatial correlation for a two dimensional slice at the inlet is then generated by 2n 2n ψ m,l = b j b k r m+j,l+k, (4) j= 2n k= 2n where r m,l is a set of random number with zero mean and unit variance. The two dimensional data ψ m,l is then correlated in time with the disturbance of the previous time step forming the new velocity disturbance u i (t + t) = u i (t) exp ( π t 2T ) + ψ i (t) [1 exp ( π t T )] 0.5, (5) where T is the Lagrangian time scale. The modification Kim et al. 2) provided for this method is the mass flux correction, so that the bulk velocity will not change throughout the simulation. This is important for models using incompressible assumptions such as PALM does. The velocity at the inflow is corrected with the ratio of the prescribed bulk velocity u b and u b,t = S 1 S u n,t ds, (6) which is the bulk velocity calculated with the uncorrected velocity normal to the inlet u n,t at the inlet, where S is the surface area of the inlet. The corrected velocity at the inlet follows as u b u i = u u i,t, (7) b,t where u i,t is the uncorrected velocity. The synthetic turbulence inflow generator needs in total 18 profiles as input profiles, which are the six components of R ij, the mean velocity profiles U i, and the length scale for each of the three velocity components in both orthogonal directions of the flow direction as well as the Lagrangian time scale along the flow direction. These input profiles can be derived from a precursor simulation or even by measurements. 3. SIMULATIONS WITH AND WITHOUT SYNTHETIC TURBULENCE (1) Simulation setup Four cases were simulated and will be presented in this study. Two cases using a homogeneous building array consisting of aligned cubes. A single tall building was added to the building array for the other two cases. In either case a laminar inflow condition and for the other case the synthetic turbulence inflow generator was applied for each urban canopy. The setup for each simulation contains a strict neutral stratified atmosphere without heating from the

3 ground. The atmosphere was assumed to be dry, so no humidity effects were considered. Surface conditions were non-slip for the surface and each wall boundary while the top boundary condition of the domain was slip. Cyclic boundary conditions were used in spanwise (y) direction while in streamwise (x) direction the synthetic turbulence inflow generator at the inflow and an open boundary at the outflow were used. The domain size was set to 1440m in streamwise and 480m in spanwise direction and 240m in vertical (z) direction (see Fig. 1). An isotropic grid was used with a grid spacing of 2m. The topography consists of an aligned array of cubes with an edge length of h = 24m and a distance between cubes of also h in x and y direction. The first and last row of cubes have a distance of 6h and 7h to the inlet and outlet, respectively, which corresponds to the absence of the first and last 3 rows of buildings. This results into a homogeneous grid of building cubes as shown in figure 1. For the latter two cases, one tall building with a horizontal width and depth of 3h and a height of 4h was added at the center of the domain. These cases will therefore be named TB_l (tall building case, laminar inflow) and TB_t (tall building case, turbulent inflow) while the other two cases without the tall building will be named HB_l (homogeneous building case, laminar inflow) and HB_t (homogeneous building case, turbulent inflow) hereafter. Results obtained from a simulation with cyclic boundaries with flat topography were used for the input of the turbulence generator. The domain height in this preliminary simulation was set to 200m and the profiles were later set to constant values above this height to match the new domain height. Only the mean wind profile was used as input for HB_l and TB_l. The simulation time was set to two hours. A dynamic time-step was used, which fulfilled the Courant-Friedrichs-Levy criterion. After the first hour of simulation time the flow reached a quasisteady state and therefore only the second hour of each simulation is used for analysis. (2) Results First results of the two cases with homogeneous buildings will be compared. Both cases HB_l and HB_t show the development of an urban boundary layer. Figure 2 shows the vertical profile of the wind speed component in x direction (u), averaged over the last hour of the simulation and spatially averaged over the building area as indicated in figure 1. The solid line represents the HB_l case while the longdashed line shows the HB_t case. Also the input profile for the turbulence generator (stars) and the profile for the TB_t case, which will be discussed later, are shown. The height is normalized by the domain height H. The building layer reaching up to 0.1H is clearly visible in the HB_l and HB_t case by the decelerating of the wind speed. On top of the buildings the wind speed accelerates faster with height than the input profile. Similar behavior of u was also observed by Kanda et al. 6) for a flow over a homogeneous cubical array. However, the flow inside the building layer is slightly faster for HB_t than for HB_l and above the building layer HB_t is slightly slower until 0.4H. Figure 3 shows the normalized and time averaged profiles of u 2 and w 2, which are the variances of wind speed in x and z direction, respectively, as well as the vertical momentum flux w u. Profiles were normalized by the friction velocity u. The shape of the variance profiles and also of the vertical momentum flux are comparable between both cases and also to those reported by Kanda et al. 6) giving confidence in the turbulence produced by the new inflow method. However, w 2 and w u reach higher values Fig.1 Domain specifications. The grey shaded tall building is only included in the TB cases. The averaging area shows the area used for horizontal averaging of profiles. Fig.2 Spatially and time-averaged u profiles.

4 Fig.3 Normalized spatially and time-averaged profiles of u, 2 (b) u, 2 and (c) w. u (a) for HB_t than for HB_l indicating a higher turbulence intensity inside the canopy layer and the urban boundary layer developing on top of the canopy layer. This differences indicate a higher vertical mixing for the HB_t case which causes also the reduced wind speed inside the boundary layer found in figure 2. A vertical slice in streamwise direction of the vertical velocity is shown in figure 4 for HB_l and HB_t. It is clearly visible that in the HB_t case the atmosphere above the canopy layer is turbulent while in the HB_l case it remains laminar above the urban boundary layer. In past studies these turbulent motions above the boundary layer were identified to have a significant influence of the turbulence inside the boundary layer 9) which is also the case in this study as shown in figure 3. Note that the high vertical velocities at the edge of the first building row are caused by the decelerating of the flow due to the buildings. The development of the urban boundary layer along the streamwise direction is shown in figure 5. The boundary layer height (BLH) is defined as the height where the vertical gradient w / z u reaches a value of ms -2. The BLH develops reasonably faster in the HB_t case compared to the HB_l case and the largest values for the HB_l case are reached about 350m further upstream in the HB_t case. This shows that a larger domain size would be necessary to simulate the same BLH with laminar inflow than with the turbulence inflow method. After showing the differences between the cases with homogeneous buildings now the cases including the tall building will be analyzed. The mean wind profile for the TB_t case (fig. 2) is accelerating slower over the small buildings compared to the HB_t case until the rooftop of the tall building at 0.4H, where u reaches higher values for the TB_t case than for the HB_t case. This shows the decelerating effect of the tall building on the flow. Also the turbulence is affected by the single tall building as shown by the profiles in figure 3. In the TB_t case w u (fig. 3c) is equal to the HB_t case inside the canopy layer. However, the profile of u 2 is slightly decreased. This decrease is then compensated of an increase of w 2 inside the canopy layer resulting in equal values for w. u The influence of the tall building causes the profiles of the TB_t case to differ from those of the HB_t case above the lower buildings. However, w u is nearly equal for both cases until 0.27H from whereon the rooftop of the tall building causes stronger turbulent motions in vertical direction and w u increases again. This effect at the rooftop is also visible in the u 2 and w 2 profiles creating another boundary layer. At about 0.6H the profiles of the TB_t case follow those at the input again

5 but are still slightly increased. The boundary layer height caused by the tall building is, therefore, around 0.6H. Figure 6 shows a vertical slice in xz-direction of time-averaged u for case TB_l and TB_t at y = 240m. The different inflow methods used in these two cases cause different influences of the tall building on the flow field. Especially in the leeward area of the building the velocity field is changed significantly. In case TB_l (fig. 6a) a rectangular shaped area of negative u values is located at the leeward side of the building reaching to the first edge of the second small building behind the tall building. When using the more realistic turbulence inflow method this area of negative u velocity has a more triangular shape and reaches slightly farther in x direction close to the ground including the first two building rows behind the tall building. These differences occur because of the higher vertical mixing in case TB_t compared to TB_l. Such significant differences cannot be neglected especially when focusing on the effect of tall buildings on the flow field. 4. CONCLUSIONS The results shown in this paper revealed the feasibility of using the synthetic turbulence inflow method for LES of urban canopies. The shape of the received profiles from the turbulent inflow case were in good agreement with other studies such as Kanda et al. 6) who, used cyclic boundary conditions in their LES, and Nozawa and Tamura 10), who used a turbulence recycling method instead of cyclic boundary conditions along the mean flow to simulate an urban boundary layer over a staggered grid of buildings. Also the advantages of the turbulence inflow method over a laminar inflow were shown. When using the turbulence inflow method stronger turbulent motions Fig.4 Vertical slice of w averaged along y for (a) the HB_l case and (b) the HB_t case at the end of each simulation. Black cubes indicate the positions of buildings. Fig.5 Development of the boundary layer height along the streamwise direction for cases HB_l and HB_t.

6 Fig.6 Time-averaged vertical slice of u at y = 240m for case (a) TB_l and (b) TB_t. developed inside the boundary layer and the BLH grew faster compared to the laminar case. As a benefit simulation domains can be smaller reducing the time and cost of simulations. When comparing the two TB cases a change of the influence of tall buildings on the flow field was found which can have a high influence on the interpretation of the effects of tall buildings on their surroundings. Simulated pollution emissions adjacent to such a building or calculations of the wind chill might be significantly changed when using laminar instead of turbulent inflow conditions. In the future this synthetic turbulence inflow generation method will be applied to simulations using different urban canopy layers. The influence of tall buildings on the velocity field will be further investigated by a case study with different canopy setups. This case study would highly benefit from the use of the synthetic turbulence inflow generator by reducing the required time for each simulation making it possible to enlarge the number of cases. ACKNOWLEDGMENT: We would like to thank Prof. Satoru Iizuka, Nagoya University, for supporting us in the early beginning of our research. The first author was supported by a grant of the DAAD (German Academic Exchange Service). All computations presented in this study were performed on TSU- BAME2.5 at the Tokyo Institute of Technology, Tokyo, Japan. conditions for large eddy simulation of street-scale flows, Flow Turbulence Combust, Vol.81, pp , ) Kim, Y., Castro, I. P. and Xie, Z.-T.: Divergence-free turbulence inflow conditions for large-eddy simulations with incompressible flow solvers, Computers & Fluids, Vol.84, pp.56-68, ) Raasch, S. and Schröter, M.: Palm a large-eddy simulation model performing on massively parallel computers, Meteorol. Z., Vol.10, pp , ) Wicker, L. J. and Skamarock, W. C.: Time-splitting methods for models using forward time schemes. Mon. Wea. Rev., Vol.130, pp , ) Williamson, J. H.: Low-storage runge-kutta schemes, J. Comput. Phys., 35, pp.48-56, ) Kanda, M., Moriwaki, R. and Kasamatsu, F.: Large eddy simulation of turbulent organized structures within and above explicitly resolved cube arrays, Boundary-Layer Meteorol., Vol.112, pp , ) Letzel, M. O., Krane, M. and Raasch, S.: High resolution urban large-eddy simulation studies from street canyon to neighborhood scale, Atmos. Environ., Vol.42, pp , ) Lund, T., Wu, X. and Squires, D.: Generation of turbulent inflow data for spatially developing boundary layer simulation, J. Comput. Phys., Vol.140, pp , ) Thole, K. A. and Bogard, D. G.: High freestream turbulence effects on turbulent boundary layers, J. Fluids Eng., Vol.118, pp , ) Nozawa, K. and Tamura, T.: Large eddy simulation of the flow around a low-rise building immersed in a rough-wall turbulent boundary layer, J. Wind Eng. Ind. Aerodyn., Vol.90, pp , REFERENCES 1) Xie, Z.-T. and Castro, I. P.: Efficient generation of inflow (Received September 30, 2014)

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