Implicit Large Eddy Simulation of Wind Flow Over Rough Terrain

Implicit Large eddy simulation of wind flow over rough terrain

Bofu Wang1, Fei Chen2, Hui Xu3, Xuerui Mao1*

Abstract TATI RO NG N M Atmospheric boundary layer (ABL) ow over a rough terrain is studied numerically. A drag force O A A C I H S model is employed to represent surface roughness. e spectral vanishing viscosity (SVV) method I

O N

M is adopted for implicit large eddy simulation (ILES). ese techniques enable us to capture the

Y Y

S dominant features of turbulent ow over non-smooth terrain with inhomogeneous roughness at high Reynolds number without resolving the very ne scale turbulence near the wall. We then run a test case of wind resource assessment on rough terrain, namely ABL ow over a hill with ISROMAC 2017 small-scale surface roughness at Re = 106 (Re is dened based on hill height). e instantaneous ow, mean ow and Reynolds stress are analysed in order to interprete the obtained turbulent ow. International Symposium on e eect of roughness length and associated drag coecient are also evaluated. Transport Phenomena Keywords and Large eddy simulation — Rough terrain — Wind energy — Spectral element method — Spectral Dynamics of Rotating vanishing viscosity. Machinery 1Faculty of Engineering, University of Noingham, Noingham, NG7 2RD, UK Maui, Hawaii 2Xinjiang Goldwind Science & Technology Co., Ltd., Beijing, 100176, China 3Department of Aeronautics, Imperial College London, London SW7 2AZ, UK December 16-21, 2017 *Corresponding author: xuerui.mao@noingham.ac.uk

1. INTRODUCTION include detachment and recirculation under gentle slope as- sumption, and it reproduces quite satisfactorily the measured Modelling atmospheric turbulent ow over a complex terrain speed-up on Askervein at the hill top [3] but performs less with roughness is of great interest for many engineering, successfully on the lee side. Another prominent measure- environmental, and geophysics applications, such as wind ment is the Bolund eld campaign [4, 5, 6] over Bolund Hill energy assessment; weather predictions; wind eects on agri- in Denmark which provided new experimental datasets of culture and forest; and transport and dispersion of pollutants the mean ow and the turbulence properties. e hill has a in the atmospheric environment. Specially, for wind energy elatively smaller scale (12 m high) than Askervein Hill, but it application, accurate wind resource assessment is critical oers a challenging topography with steep slopes and a cli in the early stage development of wind farms. Inland wind (90°). e selection of Bolund Hill is justied by the three turbines are usually sited on complex rough terrains with dimensional nature of the hill and by the ow separations grass, forests, hills and mountains which make the evalua- induced by the cli that make it more challenging to model tion of wind resources extremely challenging as the height of than gentler terrains. Up to now, these two measurements roughness is commensurate with the turbines. Moreover, the have been widely used as complex-terrain benchmark cases Reynolds number of turbulent Atmospheric boundary layer 8 for validating experimental and numerical implementations (ABL) is very high (up to 10 ), imposing extra challenges to as well as evaluating turbulence models. numerical assessment of wind resources and wind turbine performances. During the past decades, serious aempts Regarding surface roughness, in early times, some model have been made to predict the ow over complex terrain experiments were performed in wind-tunnel to obtain tur- with roughness through conducting eld experiments, em- bulent ow elds within and above a model plant canopy. ploying physical models in wind-tunnel experiments, and Finnigan and Brunet [7] carried out a ”Furry hill” experiment carrying out numerical simulations. e most widely studied with a two-dimensional ridge using and provided a rst view case is ow over forested hills. of the main features of canopy ow over a hill. Ne and e area with forested hills is commonly dicult to ac- Meroney [8] conducted single-hot lm anemometer mea- cess, which prevents eld measurements by either masts or surements to evaluate how hill and vegetation aect wind LiDAR. A well-known hill experiment was conducted by an power availability. More recently, Poggi and Katul [9, 10, 11] international group on the Askervein Hill in the UK [1, 2]. conducted a series laser Doppler anemometry measurements e slope of this hill is relatively smooth and the mean wind over a train of gentle and narrow forested hills in a ume proles are extensively used for research with particular in- facility. eir results conrmed the theoretically predicted terest in the so-called linearised model. is model does not intermient recirculation region downstream of a hill cov- LES of flow over rough terrain — 2/6 ered by a dense canopy. ey also observed sweep motions 2. METHODS dominating momentum transfer within and near the canopy e governing equations for the current problem are the top all along the hill, while ejections dominating further incompressible NS equations with a volume force term rep- above. Teunissen et al. used two wind tunnels and constant- resenting the force induced by the roughness, temperaturehot-wire anemometry to study the Askervein −1 2 hill at three scales: 1/800, 1/1200, and 1/2500. Turbulence ∂t u+(u·∇)u = −∇p+Re ∇ u+F with ∇·u = 0, (1) statistics gave more scaer compared to eld observations with more than 50% error [12]. Discrepancies observed were where u, p and F are velocity, pressure and volume force, higher in the wake and weaker at the location of the maxi- respectively. Re is the Reynolds number dened based on mum speed-up. Recently, Yeow et al. [13, 14, 15] performed the free-stream velocity and the height of the hill. Re = 106 a series of wind-tunnel analyses with hot-wire anemometry is used throughout this work if not otherwise specied. and particle image velocimetry to study ow around the Bol- und island with a 1/115 scale model and gave details on the 2.1 Spectral element method unsteady ow behaviour. ere are also some other exper- A majority of numerical tools for wind ow simulation are iments with complex topographies inducing complex ow based on nite volume methods. ere are also some ex- phenomena, such as Chock and Cochran [16]. amples of successful applications of element-based Galerkin methods in numerical weather prediction [27]. In this study, we adopt the open-source soware Nektar++ [28] which is Measurement from meteorological towers and model designed to support the development of high-performance experiments are currently indispensable in industrial prac- scalable solvers for partial dierential equations using the tices, but not sucient to analyse the intricate wind pro- spectral/hp element method. As a high order nite element le on complex terrains. Numerical models have the poten- method, it can deal with arbitrary geometric complexity, tial to oer insight with high delity information in this and are capable of local mesh adaption by either increasing regard. Wind ow in complex terrains exhibits complex the number of elements or increasing the polynomial order phenomenons such as ow stagnation, rapid acceleration de- within elements. Moreover, it has excellent scalability for celeration, recirculation-reaachment, vortex shedding, etc. parallel simulation and is scalable to more than one million Such micro-scale events occur at higher frequencies as well processor cores. as at smaller spatial scales compared to meteorologic scale events, which imposes challenges to numerical simulation. 2.2 Roughness model Many eorts have been devoted to the behavior of the ow In LES applied in oshore wind energy, the roughness (waves) phenomena over terrain hills using Reynolds averaged mod- is considered to be sub-scale of the computational grid, and els [17, 18], which predict the mean ow elds using far less therefore can be modelled using wall turbulence models, computational resoures. However, such models are based on which are commonly in the form of the boundary condition a variety of assumptions and intrinsically ignore the ow un- for shear stress. However regarding the deployment of wind steadiness; they are also known to be inaccurate in the ow turbines on rough terrains, the scale of the roughness ele- separation region. In recent years, due to the development ments, e.g. buildings and forest, is commensurate with the of numerical techniques and high-performance computing turbine and these elements cannot be considered as sub-grid. facilities, more advanced CFD methods, e.g. large-eddy sim- In the present work, a drag force approach is introduced to ulation (LES) and direct numerical simulation (DNS) [19, 20] model roughness. e drag term can be expressed as: are employed in wind energy. It has been demonstrated that √ the LES techniques are able to reproduce many observed fea- Fi = Cd Af ujujui, (2) tures of turbulent ow over at terrain with homogeneous roughness [21] and downwind of forest leading edges [22]. where i=1, 2, 3 refers to streamwise, lateral and vertical com- ere are investigations applying LES to ow over a rough ponents respectively, Cd is the mean drag coecient of the hill (see [23] and references therein). Recently, developing roughness, Af is the density of roughness, and ui is the wind- LES models in the open source soware OpenFOAM [24] velocity component. Furthermore, the dimensionless rough- becomes very popular for wind energy application [25, 26]. ness length is dened as z0. Both Cd and Af are assumed to be ree dimensional calculations for the Bolund hill case have independent on wind velocity. In our following simulations, been performed for validations. Improved comparison with we set Af = 1, Cd = 0.4 and z0 = 0.1 if not otherwise speci- measurements [4,5] were obtained. ed. Without loss of generality, the roughness is assumed to be with a uniform height.

is paper is oriented towards applying LES for ABL 2.3 Spectral vanishing viscosity method ows over complex terrains at very large Reynolds number. e spectral vanishing viscosity (SVV) method is adopted e boundary layer ow over an idealistic hilly terrain is stud- to account the small-scale turbulence. e SVV dene a ied. is work paves the way for wind resource assessment viscosity in the spectral space that reaches a maximum at over an area with a mixed scale of roughnesses. high wave numbers, but vanishes for wave numbers below a LES of flow over rough terrain — 3/6 resolution-dependent threshold [29]. In this approach, one 50 adds an additional reaction term of the form to equations (1) Farfield

∂ ˆ ∂u SVV (Q ∗ ), (3) 1 ∂x ∂x High order outflow y where SVV is a constant, * denotes the convolution operator, 0.5 and Qˆ is a kernel dictating which modes receive damping. U=1 0 is approach has been widely applied as a tool for implicit •1 0 1 U=(z/ )(1/7) Rough wall large eddy simulation (ILES). e key point in SVV ltering 0 •500 50 is that due to the shape of the kernel Qˆ(k), x

2  (N − k) Figure 2. Mesh in each x − y plane. exp(− ), M < k ≤ N Qˆ(k) = (M − k)2 (4)  0, k ≤ M  4. RESULTS AND DISCUSSION articial viscosity for any mode number k is only applied above a cuto mode M. For these damped modes, the total 4.1 Instantaneous flow field viscosity can thus be expressed as 1/Re + SVV .

50 Farfield (a)

1 (b) High order Hill outflow y H 0.5 (c) W U=1 0 •1 0 1 (d) U=(z/ )(1/7) Rough wall 0 •50 0 50 x (e)

Figure 1. Schematic of the computational domain. Figure 3. Instantaneous contours of the streamwise velocity on horizontal cross sections (x-z planes) at (a) y=0.05, (b) y=0.1, (c) y=0.5, (d) y=1 and (e) y=2. 3. DISCRETIZATION e model of ABL ow over a small hill with uniform rough- We rst evaluate the instantaneous ow elds. Figure ness near the wall is shown in Figure1. e hill is quasi- 3 shows contours of streamwise velocity at various heights. three-dimensional (the spanwise direction is assumed to be Due to the roughness eect, upstream has already devel- homogeneous and discretised by Fourier transformation) and oped to turbulence. When this turbulent ow past the hill a only a two-dimensional (2d) plane is shown here. e shape turbulent wake region develops, the wind speed is reduced. of the hill is sinusoidal with height H = 1 and width W = 2. e upstream streamwise velocity is characterised by longi- At inow, a power law velocity prole is applied. In order to tudinal paerns which can be regarded as the signature of trigger transition, a random perturbation with 5% turbulence coherent structures induced by the boom roughness. With intensity is applied at y < 2 in most of our calculations. A increasing height, these structures increase in size and look high order outow condition is used at outlet [30]. At the like coherent streaks as usually observed in boundary layers. boom, no-slip wall condition is applied combined with a With further increasing height, uctuations gradually de- uniform roughness with length z0. Far eld condition is used crease and the laminar ambient ow is recovered. e eect at the top. e computational domain spans from -60 to 50, of the hill on instantaneous wind ow velocity is strong at 0 to 50 and 0 to π in the streamwise, vertical and spanwise the near wall region as shown in Figure3 (a). When reaching directions, respectively. the hill, the longitudinal paern is almost eliminated in the Figure2 shows the mesh generated by gmsh. ere are wake and then regenerated further downstream as shown in 2815 quadrilateral elements in each 2d plane, and at least one Figure3 (b), (c), (d). e eect of the hill diminishes with in- element is set within the rough region near boom. In each creasing height which can be seen from the contrast between element, a spectral method is used to further decompose the upwind and downwind velocity. In Figure3 (d) which shows element to a (P+1)×(P+1)grid, where P represents a polyno- the contour at y=1 (hill height), stronger uctuation can be mial order. P = 6 is adopted in all our following simulations. observed manifesting higher turbulence intensity there. At In the homogeneous direction, a Fourier decomposition is y=2, the eect of the hill on instantaneous wind ow is no adopted and 32 Fourier modes are computed . longer observable (see Figure3 e). LES of flow over rough terrain — 4/6 (a)

8 x=•25 x=•20 x=•15 x=•10 x=•5 x=3 y (z/ )(1/7) 4 (c)

0 0 0.4 0.8 1.2 U

Figure 4. Mean streamwise velocity proles.

Figure 6. Averaged contour plots for (a) streamwise velocity and (b) spanwise velocity. 8 x=•25 x=•20 x=•15 x=•10 can be found in Figure5. We can see that there is a small x=•5 zone with concentrated stream which forms low-level jet like x=3 y prole. In meteorological studies, low-level jets are caused 4 by a lot of mechanisms which is beyond the scope of current study. Figure6 presents x-y slices of time- and z-averaged velocity components. From Figure6 (a), the streamlines are distorted by the presence of the hill and a separated region on 0 the lower lee side of the hill is generated as can be expected. 0 0.4 0.8 1.2 e ow reacts as if the hill and its separation region were a U single smooth obstacle. In Figure6 (b), the average spanwise Figure 5. Mean streamwise velocity proles with inow velocity has a relative small magnitude and shows coherent perturbation applied at y < 4. structure similar in instantaneous eld. is distribution suggests that the ow in spanwise direction is dominated by small scale structures. 4.2 Mean flow e average pressure led is presented in Figure7 (a). Figure4 gives streamwise velocity prole sliced at dierent A large-scale horizontal pressure gradient appears due to streamwise positions x=-25, x=-20, x=-15, x=-10, x=-5 and topography, inducing the distortion of the mean ow. e x=3 as well as the 1/7 power law velocity prole. We can minimum pressure is located in wake region followed by an see the velocity prole does not have much variation with adverse pressure gradient. e surface pressure shown in upstream position (from x=-25 to x=-5), which is remarkably Figure7 (b) also has a maximum before the hill. A minimum dierent from turbulent boundary layer ow. e extracted in surface pressure occurs as the ow passes the hill summit, proles deviate from the power law prole in the near wall and large-magnitude oscillation is observed near hill top. e region where the velocity decreases a lile due to the surface variation of surface pressure is qualitative in agreement with roughness. e velocity prole indicates the boundary layer the wind tunnel measurement [32]. does not grow until near the hill side, a feature resulting from the uniform roughness. e prole at x=3 shows an inection 4.3 Reynolds stress point near boundary which is caused by the inverse pressure Figure8 shows the distribution of spanwise averaged stream- π T < u0u0 >= 1 1 ∫ ∫ u0u0dzdt gradient in that region. From this prole, it is also observed wise normal Reynolds stress, π T 0 0 , that the velocity above the hill is slightly larger than free where u0 is perturbation from the time averaged streamwise stream velocity due to the speed up. Note that one important velocity. It can be seen that the wake turbulence exhibit feature so called low-level jet [31] usually observed in ABL is plume-like structure [33]. e region of maximum produc- not captured in this case. We then increase the perturbation tion is some distance along the downstream of the hill. e region at inow to y < 4. e streamwise velocity proles structure extends downwind above the region of reversed LES of flow over rough terrain — 5/6 (a) 0.00012

z0=0.1, Cd=0.4 z =0.05, C =0.4 8E•05 0 d z0=0.1, Cd=0.2

4E•05 Wall shear stress shear Wall

0 0.2 •40 0 40 (b) x

Pressure Figure 9. Wall shear stress.

P 0 and drag coecient can strongly increase the wall shear stress.

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