Large eddy simulation of atmospheric flows over the Bolund hill

Transcription

1 Large eddy simulation of atmospheric flows over the Bolund hill Ashvinkumar Chaudhari* 1), Mahdi Ghaderi Masouleh 1), Gábor Janiga 2), Jari Hämäläinen 1), Antti Hellsten 3) 1) Department of Mathematics and Physics, and LUT centre of Computational Engineering and Integrated Design (CEID), Lappeenranta University of Technology (LUT), P.O. Box 20, FI Lappeenranta, Finland 2) Lab. of Fluid Dynamics & Technical Flows, University of Magdeburg Otto von Guericke, Universitätsplatz 2, D Magdeburg, Germany 3) Finnish Meteorological Institute (FMI), P.O. Box 503, FI Helsinki, Finland *) presenting author, ABSTRACT Simulation of local atmospheric flows around a complex topography is important for many wind energy applications. In the present work, Large Eddy Simulations (LES) are performed to reproduce the turbulent wind structures around the Bolund hill located in the Roskilde Fjord, Denmark. In order to develop the inflow turbulence at the upstream boundary the so-called turbulence recycling method is employed and a numerical solver using a fractional step method is utilised to carry out LES in the current work. The simulated results obtained from two different inflow wind directions are compared against the Bolund field measurements, and overall good agreement has been obtained and reported in this paper. The current results show smaller errors for predicting the velocity speed-up and an increase of the turbulent kinetic energy compared to the results reported in the blind comparison especially those of LES and experimental model results. 1 INTRODUCTION A substantial increment of energy production utilising wind farms has made an accurate modelling of Atmospheric Boundary Layer (ABL) flows an interesting topic for many researchers. Nowadays, wind farms are constructed also in areas of a complex topography with intention to produce more energy. Despite the advantages, establishing a turbine over a hill proposes specific difficulties such as a considerable surge in structural loads on wind turbine blades due to inherent flow variability, largescale unsteadiness, and flow separation especially over complex terrains. Therefore, an accurate modelling of ABL flows over a complicated terrain has been a subject of considerable research over the past few decades. Up to now, the Askervein hill project (Taylor and Teunissen, 1985) has been the most well-known field campaign in order to validate numerical codes and to evaluate turbulence models. The steepness of the Askervein hill is below, and it is characterised by a smooth terrain which presents almost two-dimensional flow features (Prospathopoulos et al., 2012). Recently, the Bolund field campaign performed by Berg et al. (2011) over the Bolund hill in Denmark provides a new experimental dataset of the mean flow and the turbulence properties. Although, the Bolund hill is relatively small, it has more challenging topography including a steep slope and cliffs than that of the Askervein hill, and it produces complex three-dimensional flow features. Thus, nowadays the Bolund hill can be considered as an ideal experimental case for validating micro-scale Computational Fluid Dynamics (CFD) models in wind energy applications, and this is the aim of this paper as well. Lately, Bachmann et al. (2011) have reported some interesting results from the blind comparisons of the models over the Bolund case. It was later followed by Prospathopoulos et al. (2012) who performed Reynolds-Averaged Navier-Stokes (RANS) simulations for a wind flow over the Bolund hill. In a more recent work by Diebold et al. (2013), LES was employed with the Immersed

2 Boundary Method (IBM), that is, a numerical technique to incorporate terrain topography into CFD simulation. However, more research and investigation are necessary to have a better vision of LES modelling over complicated terrains, and therefore, the current paper concentrates on three main goals. The initial purpose is to study and reproduce the flow over the Bolund hill which is an interesting topic for many researchers. Secondly, to illustrate that LES is potential to predict the speed-up in a complicated terrain with rather small errors compared to RANS models which have attracted substantial attentions in recent years. And finally, this study also aims to validate our LES code over the Bolund case so that it can be used to predict flows over other complicated terrains where field measurements are missing and are too expensive to perform. The current paper focuses on scrutinising the atmospheric flow by using a LES model for mainly two westerly wind directions: and out of the four wind directions established in the Bolund experiment (Berg et al., 2011). In the present work, the Bolund hill is briefly described, and then the numerical model and computational details of LES are explained in the following section. Finally, the simulated results are compared against the Bolund field measurements provided by Berg et al. (2011). It is shown that the present LES can reproduce the complex turbulent wind flow structures over a complicated terrain such as the Bolund hill. The simulated results are in good agreement with the field measurements. Furthermore, the present LES reports the better prediction of the turbulent kinetic energy (TKE) increase with the smaller error compared to other results reported in the past for the Bolund case. 2 THE BOLUND HILL EXPERIMENT The Bolund hill is a natural and relatively small hill located in the Roskilde Fjord, Denmark, and north of Risø DTU (Technical University of Denmark). The hill is m high, roughly m long, and 75 m wide. It is surrounded by a sea thoroughly except the east side which is connected to the mainland by a narrow isthmus (see Figure 1(a)). Thus, the hill is experiencing free wind inflow from the west side. Furthermore, the field measurements were carried out at the surface level due to the low hill height (12 m). It is assumed that the ABL is neutrally stratified (Bechmann et al., 2011). However, despite the advantages of the well-defined case, simulation of the Bolund hill can be considerably challenging owing to the shape of the hill which consists almost a vertical escarpment. (a) (b) Figure 1 (a): A photo of the Bolund hill, (b) positions of masts installed around the hill. (Pictures are taken from Bechmann et. al., 2011 and Berg et. al., 2011). During the field campaign, 23 sonic and 12 cup anemometers were simultaneously employed to measure the wind velocity and their variances from 10 different mast locations. As it can be seen in Figure 1(b), the measuring masts referred as M1 to M8 were placed on two lines: Line A and Line B. In addition, two more masts M0 and M9 were utilised to provide undistributed wind conditions for westerly and easterly winds, respectively. At each mast, the data were recorded for four different wind directions, in which three westerly winds were originating from the sea side (, and ),

3 and one easterly wind was originating from the land ( ). According to Berg et al. (2011), the mean wind speed during the measurements was around m/s, which leads to a Reynolds number of, and thus, the flow can be considered to be independent of the Re. More detailed information about the Bolund field experiment can be found in Berg et al. (2011), Bechmann et al. (2009) and Bechmann et al. (2011). 3 NUMERICAL MODEL AND COMPUTATIONAL DETAILS In the present work, the computational domain is extended from -810 m to 400 m in the wind-wise ( ) direction to be ensured the fully developed upstream flow before it reaches to the reference mast M0. The vertical height ( ) of the domain is set to 120 m and the boundary-layer depth is also 120 m which is approximately 10 times higher than the height of the Bolund hill (i.e. ). The computational domain is also extended from -205 m to 185 m in the cross-wind ( ) direction in order to avoid the periodic effects on the hill part as the periodic boundary conditions are applied in the cross-wind direction. The centre of the hill is located at. The computational domain is then discretised using a block-structured hexahedron mesh with finer grid resolution on the hill surface. The grid is non-isotropic with the finest grid spacing of m and m is used on a region containing the vertical escarpment (see Figure 2). On the rest of the hill part, varies from m to m and from m to m depending on the local details of the hill shape. After the hill part, grid sizes in both horizontal directions are relaxed up to m. The vertical grid spacing also varies gradually from m to m at the top boundary. The whole computational grid consists of hexahedron cells in each LES calculation. In the present LES, the filtered Navier-Stokes equations for the incompressible fluid are solved using the unstructured finite volume method based on the open-source code OpenFOAM (OpenFOAM, 2013). Recently, Vuorinen et al. (2012) have developed a new type of a numerical solver using a fractional step method and the solver has been validated on various problems including LES of the turbulent channel flow at. The same solver is employed here to carry out LES for atmospheric flows over the Bolund topography. The solver uses the classical 4th order Runge-Kutta (RK) scheme for the time integration and a projection step where the velocity field is corrected using the pressure gradient in-between the RK sub-steps. A pressure field is obtained by solving the Poisson equation. Since LES does not resolve eddies smaller than the grid size, they need to be modelled using a Sub-Grid Scale (SGS) model. Here, the one-equation eddy viscosity SGS model is employed to model the smaller eddies. The one-equation model is time-integrated numerically using the second order backward implicit method and it is solved after the fourth (last) RK sub-step. All the governing equations are discretised in space using the central difference scheme. 3.1 Boundary conditions Figure 2: Closer look on the Bolund hill model and the grid resolutions. The most accurate way of generating the genuine inflow turbulence is to run a so-called precursor simulation, either before the main simulation or simultaneously with it. For the present case, the

4 inflow turbulence is generated by using the so-called recycling (or mapping) method in which the precursor simulation is combined with the main domain. The method is earlier proposed by Baba- Ahmadi and Tabor (2009). In this method, the flow variables are sampled on a cross-wind plane which is sufficiently far downstream of the inflow plane, and the sampled data are then recycled back to the inflow plane at each time step. By recycling the flow data from further downstream a recycling section is created in which the flow is forced to become fully developed and at the same time the flow within this section is automatically fed into the main domain. The method has earlier been validated over the flat terrain situations in order to estimate the recycling-distance between the inflow plane and the recycling plane, and it was found that should be at least more than to ensure that this distance is larger than the wind-wise length of the largest turbulent structure. Here, is the boundary layerdepth. Furthermore, the velocity flux is fixed at the inflow boundary in order to maintain the same amount of volumetric flow throughout the simulation. The static pressure is fixed to a constant value on the outlet plane and a Neumann boundary condition is used for the rest of the flow variables. The slip boundary condition is used for all the flow variables at the top boundary. The periodic boundary conditions are set in the cross-wind direction. A roughness-length based wall function is utilised to determine the ground surface fluxes on the lower boundary. Two LES calculations for two different wind directions and were performed up to the physical time of s. After the flow development the results are time averaged over the last s which is approximately more than 6.5 advection times along the whole computational domain or 32 advection times along the hill length. 4 RESULTS AND DISCUSSIONS Figure 3 depicts the iso-surfaces of the second invariant of the velocity gradient tensor with the velocity magnitude around the Bolund hill from the LES computation of the direction in order to show the resolved small-scale turbulent motions. coloured wind Figure 3: Iso-surfaces of the second invariant of the velocity gradient tensor coloured with the velocity magnitude around the Bolund hill for wind direction. Next, the simulated results from two LES calculations performed each for and wind directions are presented and compared with the Bolund field measurements provided by the Berg et al. (2011). The ratio of the LES results to the field data for the normalised velocity magnitude and the normalised turbulent kinetic energy (TKE) is shown in Figures 4 and 5, respectively. Here, is the frictional velocity at the reference mast M0. The results from both wind directions are shown as a function of the height above the ground level (a.g.l.) and the mast locations. According to Figure 4(a), the results are much scattered for m and showing more than 200% of overestimation at mast M2. Moreover, the velocity prediction is underestimated at mast M8. Above

5 m, the prediction accuracy is improved with the heights and the results look much accurate. The masts M2 and M6 were located approximately m from the steep vertical escarpment where a small zone of the detached flow near the surface with an intermittent negative wind velocity is observed in the field measurements (Berg et al., 2011). This kind of a flow is perhaps difficult to be predicted by most of the numerical models. The mast M8 was located in the lee of the Bolund, where the flow separation occurs. Although LES captures the flow separation well, the mean velocity is mostly under-predicted below m in both cases. The overall prediction of TKE is comparatively poor in both cases compared to that of velocity prediction, although the level of overestimation is much reduced at m height. However, the accuracy does not seem to be improved with the height from m to m (see Figure 5(a)). It is also interesting to note that the velocity is predicted slightly better in the case of, whereas the prediction of TKE is much better in the case of. Figure 4: Ratio of LES to Field data for the normalised velocity magnitude. The results from both wind directions: and are sorted with respect to (a) the height above the ground level (a.g.l.) and (b) the mast measurement locations. Figure 5: Ratio of LES to Field data for the normalised turbulent kinetic energy. The results from both wind directions: and are sorted with respect to (a) the height above the ground level (a.g.l.) and (b) the mast measurement locations. Figures 6(a) and 6(b) show the vertical profiles of the velocity speed-up and the TKE increase for all the masts except the reference masts M0 and M9 only for the wind direction. The speedup and the TKE increase are defined as follows (1)

6 and (2) where is the LES simulated mean wind speed at any mast location and is the mean wind speed at the reference mast M0. In the same way, and are the TKE at some particular mast and at the mast M0, respectively. It can be seen that the present LES is able to capture both the speed-up and a TKE increase at most of the masts installed around the hill and the overall agreement with the field data is very good excluding a few locations at lower heights. The LES results over-perform the speed-up at masts M2 and M6 only at m. This is because the local flow contains a very small region of the intermittent flow separation close to the surface. Due to this, the TKE is suddenly increased at those locations and clear peaks in the profiles of the TKE increase can be seen. These peaks are well captured in the present results, especially at mast M6 (Figure 6(b)). The similar results are also obtained from the LES calculation of wind direction. Bechmann et al. (2011) gathered the results from the Bolund blind comparison of the micro-scale flow models. They reported that most of the models were capable to predict the speed-up and the TKE increase at M1. However, the linearised models started to show inaccurate prediction after M1. Only few LES and RANS models satisfactory captured the low wind speeds at M2. At M3 and M4, RANS models appeared to have most accurate speed-up predictions. Using the experimental methods, the prediction of the speed-up was reasonable. However, expect for M4 position, the experimental results unexpectedly underestimate the TKE increase at all locations. LES models were capable to predict the extreme gradient of TKE at only M2 location; elsewhere they underestimate the TKE increase. In the blind comparison, however the RANS models overall performed well and reported less error for the speed-up and the TKE increase even compared to LES and experimental model results at most of the locations. Figure 6: Vertical profiles of (a) the velocity speed and (b) the TKE increase at masts M1 to M8 compared with the Bolund field measurements of the wind direction. After the Bolund experiment, Prospathopoulos et al. (2012) carried out RANS simulations of the Bolund flows. Their predictions of the velocity and the TKE increase also show slight discrepancies

7 especially at m and m of M2 and M6 locations. Elsewhere, the result accuracy is improved compared to the blind comparison. Recently, Diebold et al. (2013) performed the first LES over the Bolund hill after the blind comparison. The prediction of the speed-up is very good and indeed better than the present results. However, their LES results of the turbulence quantities are worsen than the present LES results. For example, their prediction of the variances of the wind-wise and the crosswind components of the velocity is much over predicted at M8 and under predicted at M6 locations. Also, the results are more scattered at m and m heights. This is perhaps because of the insufficient time averaging applied over the results to calculate the flow statistics. Their averaging time of 200 s might be sufficient to calculate the mean flow statistics, however the second order statistics such as the variance or the TKE sometime require much longer time. In addition to the vertical profiles of the speed-up and the TKE increase, the simulation error is also calculated here in order to compare the present results with other results reported in the past. Table 1 shows the mean absolute errors for predicting the speed-up and the TKE increase from the present LES calculations of two wind directions of and. The error from the best performing model for each model type is shown in parentheses. The errors of and are calculated using the equations provided by Bechmann et al. (2011). Table 1: Mean absolute speed-up and TKE increase errors for all sonic measurements reported in the past and from the present LES of the wind directions and. Values are in percent (%). Model Mean error of (best) Mean error of (best) Reference RANS 2 eq (14.4) 47.0 (29.9) Bechmann et al. (2011) RANS 1 eq (13.8) 44.7 (42.7) Bechmann et al. (2011) Experiment 14.7 (13.3) 61.4 (59.4) Bechmann et al. (2011) LES 17.3 (14.1) 48.0 (41.6) Bechmann et al. (2011) Linearised 23.7 (20.6) 76.7 (71.4) Bechmann et al. (2011) LES-EPFL 9.6 (7.1) - Diebold et al. (2013) Present LES 10.3 (9.7) 24.1 (19.3) Table 1 illustrates that the mean error of the present LES is 10.3% and 24.1% for the prediction of the speed-up and the TKE increase, respectively. The present results, especially of the TKE increase, show a clearly smaller error compared to those reported by Bechmann et al. (2011) from the blind comparison. The speed-up error of our LES is slightly higher than the value reported by Diebold et al. (2013), which is being the best performing LES model for predicting the speed-up over the Bolund hill so far. On the other hand, they did not report the error for the TKE increase at all. In the qualitative comparison, the present LES results are likely to have much less error for predicting the TKE increase compared to the results by Diebold et al. (2013). Furthermore, the smallest error of the TKE increase from the present work is 19.3% which is calculated in the case of wind direction. This prediction is the best results of the TKE increase among all the model results reported in the past. 5 CONCLUSIONS In this paper, we have carried out LES to investigate the atmospheric flow over the complicated Bolund hill. The LES calculations have been performed for two different inflow wind directions of and. The roughness-length based wall model has been implemented into the LES model to estimate the ground-surface fluxes. Even more importantly, the estimation of the upstream boundary conditions for LES especially over real terrains has been probably the largest source of

8 uncertainty in general. In the present work, the so-called turbulence recycling method is employed at the upstream boundary in order to develop the inflow turbulence. The LES results at different heights above the ground levels are compared against the field measurements recorded at different positions across the hill. The prediction of the velocity speed-up and the TKE increase are in good agreement with the measurements at the most of the locations. The present results show smaller errors for predicting the speed-up and the TKE increase compared to the results reported in the blind comparison especially those of LES and experimental model results. The error seems to decrease with the height above the ground level for both the speed-up and the TKE increase at every mast location. The simulation error for predicting the speed-up is found to be slightly higher than the value reported in the more recent work by Diebold et al. (2013). On the other hand, the present LES reports the best results of the TKE increase with the smallest error compared to the results by any other numerical or experimental studies reported for the Bolund case. From the overall prediction obtained in the present work, it can be concluded that the present LES model is able to reproduce the complex turbulent flow structures of the local atmospheric wind flows over a complicated terrain such as the Bolund hill. It is therefore possible to employ the same LES methodology to analyse the wind structures over other real terrains. Acknowledgements The authors would like to thank to the CSC, the Finnish IT Centre for Science Ltd, Espoo (Finland) for their valuable computational resources. The work presented here is part of the RENEWTECH project which aims for the development of wind power technology and business in South-East Finland. The work is funded by the European Regional Development Fund (ERDF). References Baba-Ahmadi, M., Tabor, G. (2009). Inlet conditions for LES using mapping and feedback control. Comp. & Fluids, 38, p Bechmann, A., Sørensen, N.N., Berg, J., Mann, J., Rethore, P.E. (2011). The Bolund Experiment, Part II: Blind comparison of microscale flow models. Boundary-Layer Meteorol., 141, p Bechmann, A., Berg, J., Courtney, M.S., Jørgensen, H.E., Mann, J., Sørensen, N.N. (2009). The Bolund experiment: overview and background. Technical report, Risø DTU, National Laboratory for Sustainable Energy, Denmark. Berg, J., Mann, J., Bechmann, A., Courtney, M.S., Jørgensen, H.E. (2011). The Bolund Experiment, Part I: flow over a steep, three-dimensional hill. Boundary-Layer Meteorol., 141, p Diebold, M., Higgins, C., Fang, J., Bechmann, A., Parlange, M. (2013). Flow over hills: A Large-Eddy Simulation of the Bolund case. Boundary-Layer Meteorol., 148, p OpenFOAM. (2013). OpenFOAM User Guide. OpenFOAM Foundation. Prospathopoulos, J.M., Politis, E.S., Chaviaropoulos, P.K. (2012). Application of a 3D RANS solver on the complex hill of Bolund and assessment of the wind flow predictions. J. Wind Eng. Ind. Aerodyn., , p Taylor, P.A., Teunissen, H.W. (1985). The Askervein Hill Project: Report on the Sept./Oct.1983, Main Field Experiment. Research Report MSRB-84-6, Technical Report, Meteorological Services Research Branch Atmospheric Environment Service 4905 Dufferin Street, Downsview, Ontario, Canada. Vuorinen, V., Larmi, M., Schlatter, P., Fuchs, L., Boersma, B. (2012). A low-dissipative, scale-selective discretization scheme for the Navier - Stokes equations. Comp. & Fluids, 70, p