Two-dimensional Hill Research Articles

Impact of a two-dimensional steep hill on wind turbine noise propagation

Abstract. Wind turbine noise propagation in a hilly terrain is studied through numerical simulation in different scenarios. Linearized Euler equations are solved in a moving frame that follows the wavefront, and wind turbine noise is modeled with an extended moving source. We employ large-eddy simulations to simulate the flow around the hill and the wind turbine. The sound pressure levels (SPLs) obtained for a wind turbine in front of a 2D hill and a wind turbine on a hilltop are compared to a baseline flat case. First, the source height and wind speed strongly affect sound propagation downwind. We find that topography influences the wake shape, inducing changes in the sound propagation that drastically modify the SPL downwind. Placing the turbine on the hilltop increases the average sound pressure level and amplitude modulation downwind. For the wind turbine placed upstream of a hill, a strong shielding effect is observed. But, because of the refraction by the wind gradient, levels are comparable with the baseline flat case just after the hill. Thus, considering how terrain topography alters the flow and wind turbine wake is essential to accurately predict wind turbine noise propagation.

Effect of hills on wind turbine flow and power efficiency: A large-eddy simulation study

This study investigates the influence of topography on wind turbine flow and power efficiency. Specifically, a standalone wind turbine is positioned at the top of idealized two-dimensional hills, and the effects of hill geometry and turbine position are systematically investigated. Various parameters are studied, including hill slope, distance between the leeward side of the hill and the turbine, turbine hub height, and hill size. Overall, it is observed that the turbine wake is consistently stronger in the hill cases compared to the flat case. This is attributed to two characteristics of hill flows: (1) the negative streamwise velocity gradients on the leeward side of the hills and (2) the reduced turbulence above the hilltops and hill wake regions. In addition, it is observed that the turbine induction factor is consistently increased in the hill cases compared to the flat case, while the turbine power and thrust coefficients are reduced. In practice, this means that turbines on the hills produce less power output than those on flat terrain for an equivalent wind potential, with the potential decrease in power output reaching more than 20% for certain cases. Altogether, the results offer new insights into the effect of topography on turbine power efficiency. In addition, the study identifies clear relationships between the turbine power coefficient, the induction factor, the overall maximum deficit, and the base flow pressure gradient. These relationships could potentially be used to predict the change in power efficiency based on the wake flow or the base flow. Overall, the results show a clear connection between the turbine power efficiency and the turbine wake development.

The Influence of Topographical Variations on Wind Turbine Wake Characteristics Using LES

A detailed understanding of the characteristics of wind-turbine wakes over complex terrain is crucial for designing efficient wind farms. Complexity of the terrain can be due to changes in elevation (due to, e.g., hills/valley/cliffs), and changes in the surface roughness (due to land types, e.g. fallow/cultivated/forested). We employ large-eddy simulations to study the evolution of a wind-turbine wake sited at different locations on a gradual two-dimensional hill with and without an abrupt transition in its surface aerodynamic roughness. A turbine placed at the foot of the hill, midway between the foot and the peak, and at the hill peak behave very differently when compared against each other. For a homogeneously rough surface, the profile of the velocity deficit normalized by the inflow velocity at the hill peak height shows that the wake recovers fastest for a turbine placed at the midway location. For a heterogeneously rough surface, however, the wake recovery for a turbine at the midway location is not significantly faster than that for a turbine at the hill-foot. The surface heterogeneity accelerates the flow downstream, which affects the wake recovery, due to which the deficits over heterogeneously rough surfaces are typically larger than for homogeneous surfaces. The turbulence intensity as well as the turbulence intensity added due to the presence of the turbine are affected by the position of the turbine as well as the surface roughness heterogeneity. The observed differences between the rates of wake recovery are only partly explained by the pressure gradient of the background flow over the hill in the absence of the wind turbine. The pressure drop over a region from one diameter upstream to five diameters downstream of the turbine explains the wake recovery for the turbines sited on homogeneously rough surface but not on a heterogeneously rough surface.

Wake steering of wind turbine in the presence of a two-dimensional hill

Wake interference between turbines in wind farms can lead to significant losses in the overall power output from farms. Wake steering is a strategy in which yaw is introduced in the upstream turbines with respect to the incoming flow field to reduce wake interference with downstream turbines. To characterize the effectiveness of wake steering for turbines located on a hilly terrain, an open source simulator for wind farm applications has been used to perform large eddy simulations (LESs) of a 5 megawatt (MW) wind turbine located at the base of a sinusoidal hill. The height and length of the hill, as well as the turbine yaw angle, are systematically varied over a series of 10 simulations in which inflow corresponds to the neutral atmospheric boundary layer. Results from the LES statistics show that, for a given yaw angle, the power output from the turbine is determined primarily by the height of the hill, rather than the length of the hill. The magnitude of the centerline wake deficit and equivalent wake radius are reduced due to the presence of hills and are not very sensitive to the yaw angle. The theoretical prediction of the wake recovery appears to qualitatively agree with the LES statistics. The yaw-induced spanwise wake deflection is not affected by the hill height significantly. Streamwise vorticity distribution within the lower half of the wake intensifies due to the presence of strong mean velocity gradients present near the surface of the hill, which, in turn, leads to a reduction in the distortion of the shape of a wake deficit cross section.

Wake interaction of aligned wind turbines over two-dimensional hills

An experimental investigation was carried out to explore the interaction and wake statistics of model wind turbines operating individually and in pairs over two-dimensional hills with varying heights. The hills shared a sinusoidal shape and extended L/D=20 in the streamwise direction, where D represents the diameter of the turbine rotor. The peak heights of the hills were H/D=0, 0.5, 1, and 1.5. The first turbine was located at the beginning of the hill development, and the second turbine was positioned halfway between the first and the hill's peak, downwind. The flow in the intermediate wake regions was characterized using particle image velocimetry, focusing on the recovery mechanisms of streamwise momentum on the windward side of the hills, ranging from gentle to steep-up slopes. The results indicate that the advection terms play a more significant role than turbulence in the wake recovery mechanism with steeper hill slopes. Associated reduced turbulence levels are attributed to flow acceleration, which led to a higher power availability at the top of the hills.

Large eddy simulation of atmospheric boundary flow over two two-dimensional hills

Understanding turbulent flow over two-dimensional hills is important for microscale meteorology research and application. Most of the existing work focuses on only one hill, and few consider two hills. This Letter adopts the large eddy simulation method to investigate flow and turbulent structures over two two-dimensional hills. In the presence of the second hill, the low-pressure region behind the first hill is extended and recirculated flow in the valley is enhanced. Larger negative velocity forms near the surface before the second hill. Behind the second hill, a reattachment point is closer to the foot of the hill; recirculation is weakened and turbulent kinetic energy is significantly decreased, but the spanwise turbulent fluctuation near the surface is increased.

Adding a simple production term to Reynolds-averaged Navier–Stokes turbulence models for flows over two-dimensional hills

We consider an additional production term for the k,ε turbulence model that is activated by curvature, for turbulent flow over two-dimensional hills of varying steepness. The new term depends on the difference between the strain rate, S, and the rotation, R, which we refer to as the “SR” modification. It is compared to the standard k,ε turbulence model, the Kato–Launder model, and the re-normalization group and realizable versions of the k,ε model. The Kato–Launder model showed the best overall predictions for mean velocity, turbulent kinetic energy, and Reynolds shear stress at most locations before, on, and after the crest of the hills. The SR model was slightly less accurate but uniquely predicted the flow separation in the lee of the steeper hill and was also correctly predicted the flow re-attachment point. This study demonstrates the importance of including a curvature production term in k–ε-based models for flows over hills.

Investigation into wind turbine wake effect on complex terrain

In complex-terrain wind fields, the wind speed-up phenomenon is pronounced on highlands, which has huge impact on wake development. This paper comprehensively investigates the wind speed-up and the wake effect in complex terrains. The objective is to develop an advanced process to reveal the complex wake characteristics. Both theoretical and experimental methods are used to the study. First, the wind speed-up characteristics caused by topography are discussed, and the wind speed-up over escarpments with different shapes is numerically studied. Based on the results, the impact of wind speed-up on average wind speed of wind turbine is investigated. Next, a three-dimensional wake model for complex terrains is developed, and the model is applicable for the terrain with slope of less than 0.3. Then, a wind field experiment is conducted on a two-dimensional hill, and the wake model is validated and further improved for application to escarpments. From this research, both large aspect ratio and small rotor diameter have significant influence on the average wind speed. Even in the wake area, the wind speed on highland is stronger than that on flat terrain, and the wind speed increment is the largest at the height of 0.25D. In complex-terrain wind fields, the wind speed-up effect must be carefully considered at least within the 5D downwind distance.

Experimental Study on the Influence of a Two-Dimensional Cosine Hill on Wind Turbine Wake

The accurate prediction of wind energy distribution on the terrain has been of great significance for wind farm selection. Therefore, this paper evaluated the influence of a two-dimensional hill with a relatively large slope (i.e., 0.83) on wind turbine wake. Firstly, the wakes on flat terrain and wind characteristics around a single hill were investigated by using a hot-wire anemometer. Subsequently, wake distributions combined with the hill were measured when the turbine was located 2D in front and on the hilltop. The results of the hill showed that a flow separation was formed within 6D of the leeward side (where D is the rotor diameter). The turbulence intensity increased initially and then decreased as height increased, leading to a high turbulence region 2.28 times the hill height, according to the experiment of a wind turbine combined with the hill. In conclusion, wake recovery was promoted on the windward side and 4D behind the hilltop. As the longitudinal coordinate increased, the intensity of the turbulence changed to a single peak, and the peak value was more than twice as high as on flat terrain. Based on this, it may be possible to optimize the design of wind turbines for better performance.

Large-eddy simulation of wind-turbine wakes over two-dimensional hills

Wind-turbine wakes over two-dimensional (2D) hills with different slope gradients are systematically investigated using large-eddy simulation with wind turbine parameterized as actuator disk model and hilly terrain modeled by immersed boundary method. The chosen hill models represent typical hilly terrains with and without flow recirculation in the wake of the hills. The flow characteristics of wind-turbine wakes [including mean velocity, wake-center trajectory, turbulence statistics, and mean kinetic energy (MKE) budgets] and the power performance are analyzed, and the related flow mechanisms are elucidated in our study. It is found that the velocity deficit in turbine wakes cannot be acceptably represented by the Gaussian model in the wake of the steep hill until at a further distance. It is also found that the assumption that the wake-center trajectory maintains a nearly constant elevation downwind of the hilltop proposed by Shamsoddin and Porté-Agel [“Wind turbine wakes over hills,” J. Fluid Mech. 855, 671–702 (2018)] may not be applicable in particular for the steep hill cases. Furthermore, the hilltop is the optimal location for turbine placement because the turbine harvests more wind energy due to the speed-up effect and suffers less fatigue loading due to the lower turbulence levels. Both the turbulence levels and the magnitude of vertical turbulent flux are found to drop below those of the flat ground case on the windward side of the hills, and they also decrease within the hill wake region compared with the no-turbine cases. A detailed analysis of MKE budgets reveals that the budgets of pressure transport and mean convection are mainly responsible for balancing the MKE in turbine wakes over hilly terrain.

The five main influencing factors for lidar errors in complex terrain

Abstract. Lidars have become a valuable technology to assess the wind resource at hub height of modern wind turbines. However, because of the assumption of homogeneous flow in their wind vector reconstruction algorithms, common wind profile Doppler lidars suffer from errors at complex terrain sites. This study analyses the impact of the five main influencing factors for lidar measurement errors in complex terrain, i.e. orographic complexity, measurement height, surface roughness and forest, atmospheric stability, and half-cone opening angle, in a non-dimensional, model-based parameter study. In a novel approach, the lidar error ε is split up into a part εc, caused by flow curvature at the measurement points of the lidar, and a part εs, caused by the local speed-up effects between the measurement points. This approach allows for a systematic and complete interpretation of the influence of the half-cone opening angle φ of the lidar on the total lidar error ε. It also provides information about the uncertainty in simple lidar error estimations that are based on inflow and outflow angles at the measurement points. The model-based parameter study is limited to two-dimensional Gaussian hills with hill height H and hill half-width L. H/L and z/L, with z being the measurement height, are identified as the main scaling factors for the lidar error. Three flow models of different complexity are used to estimate the lidar errors. The outcome of the study provides various findings that enable an assessment of the applicability of these flow models. The study clearly shows that orographic complexity, roughness and forest characteristics, and atmospheric stability have a significant influence on lidar error estimation. Based on the error separation approach it furthermore allows for an in-depth analysis of the influence of reduced half-cone opening angles, explaining contradiction in the previously available literature. The choice and parameterization of flow models and the design of methods for lidar error estimation are found to be essential to achieve accurate results. The use of a Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics (CFD) model in conjunction with an appropriate forest model is highly recommended for lidar error estimations in complex terrain since forest (and roughness) tends to reduce the lidar error. If atmospheric stability variation at a measurement site plays a vital role, it should also be considered in the modelling. When planning a measurement campaign, an accurate estimation of the predicted lidar error should be carried out in advance to choose a reasonable measurement location. This will decrease measurement uncertainties and maximize the value of the measurement data.

An Elliptic Blending Turbulence Model-Based Scale-Adaptive Simulation Model Applied to Fluid Flows Separated from Curved Surfaces

On the basis of a previously developed elliptic blending turbulence model (SST–k–ω–φ–α model), a scale-adaptive simulation (SAS) model is developed by following Menter and Egorov’s SAS concept. An SAS source term, which is related to the ratio of the modeled turbulence scale to the von Kármán length scale, is introduced into the corresponding length-scale determining equation. The major motivation of this study is that the conventional unsteady Reynolds-averaged Navier–Stokes (URANS) models provide only large-scale unsteadiness. The introduction of the SAS term allows the proposed SAS model to dynamically adjust to resolved structures in a URANS framework because this term is sensitive to resolved fluctuations. The predictive capabilities of the proposed SAS model are demonstrated by computing the complex flow configurations in three cases with flow separation from curved surfaces, namely, three-dimensional (3D) diffuser flow, two-dimensional (2D) periodic hills flow, and 2D U-turn duct flow. For comparison, the results predicted by the SST–k–ω–φ–α model and the Menter and Egorov’s SAS model (SST–SAS) are provided. The results are also compared with the relevant experimental, direct numerical simulation, and large eddy simulation data. The results show that the SST–k–ω–φ–α model cannot capture the critical features for all three flows, and that the SST–SAS model is able to predict the results reasonably well. The proposed SAS model is capable of resolving more portions of the turbulence structures, and it yields the best results in all the cases.

NUMERICAL SIMULATION OF THE PROPAGATION OF A HARFULL EMISSIONS PASSIVE IMPURITY OVER A TWO-DIMENSIONAL MODEL OF THE TERRAIN

High concentrations of pollutants are caused not only by strong emissions, but also by a decrease in dispersion, especially in the atmospheric layer adjacent to the surface, where most of the pollutants are emitted. In this paper, the forecast of wind flow and dispersion of pollutants over a two-dimensional hilly terrain is considered by numerical methods. The experimental data were used to verify the reliability of the numerical results of modeling the propagation of a passive impurity over a two-dimensional uneven terrain. The numerical data agree quite satisfactorily with the profiles of the average velocity and turbulence characteristics measured in the experiment. The hypothesis about the independence of the flow of the boundary layer of the atmosphere over an aerodynamically uneven terrain from the Reynolds number is confirmed by numerical methods. The influence of two-dimensional hills on the dispersion of pollutants from continuously or temporarily operating sources of different heights and locations of emissions is also studied. Concentrations of harmful impurities at the level of the earth's surface significantly decrease as the height of the source of their emissions increases. In addition, the numerical values of the concentration at ground level are somewhat overestimated. This is probably due to large deviations in the wind direction near the ground during the field experiment, which lead to a change in the direction of propagation and low concentrations of harmful emissions at ground level.

Investigation of the wake propagation behind wind turbines over hilly terrain with different slope gradients

In this study, a Reynolds-averaged Navier-Stokes (RANS) numerical simulation with wind turbine simulated through actuator disk model was conducted to quantify the characteristics of wind turbine wake over two-dimensional Gaussian hills with different slope gradients. The simulated flow characteristics in the wind turbine wake, such as velocity deficit, wake expansion and wake centerline, were compared with those given by the Jensen wake model to quantitatively evaluate the accuracy of the current engineering wake model for the optimal design of wind turbine layout over complex terrain. For the gentle slope hill, the topography behind the wind turbine has a significant effect on the wake characteristics, which is not taken into account in the Jensen wake model. A new method for calculating wake velocity is proposed based on the local speed-up factor and the simulated velocity in the wake of wind turbine sited on flat terrain that can more reasonably predict the wake velocity over complex terrain. For the steep slope hill, the propagation of wind turbine wake is not related to the hill shape in the region behind the hilltop. The assumption that the wake centerline follows the surface of the hill in the Jensen wake model is no longer applicable. The recovery of wind turbine wake in the far wake region was always faster for the steep slope hill compared with the gentle slope hill case. This acceleration of wake recovery is thought to be closely related to the separation flow at the lee side of the hill, which highly restricts the downward deflection and expansion of the wind turbine wake.

Statistical properties of a model of a turbulent patch arising from a breaking internal wave

The turbulent patch arising from internal gravity wave breaking is investigated with direct numerical simulation of a stably stratified flow over a two-dimensional hill. The turbulent patch is distinguished from the non-turbulent wave region with potential vorticity. The turbulent patch is highly intermittent, and its location fluctuates with space and time. The buoyancy Reynolds number slowly decays with time in the turbulent patch and the mixing efficiency stays around 0.2. The turbulent patch is separated from the non-turbulent wave region by a turbulent/non-turbulent interfacial (TNTI) layer, whose thickness is about five times the Kolmogorov scale. The kinetic energy dissipation rate also sharply decreases from the turbulent to the wave region while the potential energy dissipation rate has a large peak within the TNTI layer. Both shear and stable stratification are strong in the upper area of the turbulent patch. On the other hand, the lower area has a small mean density gradient, i.e., weak stratification, which is related to the strong intermittency of the turbulent patch in the lower area. Furthermore, weak stratification in the lower area results in a low gradient Richardson number, which is below the critical value for the shear instability, and the roller vortex appears. The outer edge of the turbulent patch aligns with the perimeter of the roller vortex, and the vortex affects the spatial distribution of the turbulent patch.

Experimental investigation of wind flow characteristics over hills and escarpments - A review

A comprehensive knowledge of the wind flow in hilly terrains is of great interest in many engineering applications, be it wind energy distribution for suitable site selection for wind farms, pollution dispersion, forest fire propagation or agro-meterological studies. Several researchers have shown that wind flow over a hilly terrain may be significantly different when compared with the wind flow over a flat terrain. Complex hilly terrains may alter the wind speed to a great extent. Therefore, this effect of terrain must be properly assessed by designers and planners to arrive at a proper wind flow distribution. This paper reviews the work done in this area over the past three decades. Wind flow over two-dimensional hills and two-dimensional escarpments investigated in wind tunnels by various researchers is presented in this paper.

Study of wind-direction effects on flow fields over two-dimensional hills using large eddy simulations

Numerous studies have been performed to investigate the characteristics of flow fields over simplified topographies to understand the basic trend of the flow field evolution as a function of hill shapes, hill slopes, ground roughness, and oncoming flow stratifications. However, wind direction, which has a key function in determining flow structures, has rarely been examined. Accordingly, the effects of wind direction on flow fields over two-dimensional (2D) hills are investigated in this study using large eddy simulations. It is found that when the approaching wind direction is not normal to the ridge line, the wind direction behind the 2D hill is not parallel to the approaching wind direction. The recirculation bubble downstream of the hill is weakened, and a significant spanwise velocity behind the hill is observed as the wind direction angle increases. The main direction of the streamwise correlation is found to be normal to the ridge line when the wind direction is 45° rather than parallel with the oncoming wind. A distinct peak in the spectrum of streamwise velocity is identified when the wind direction is 45°. This spectral peak is caused by the periodic shedding of an organized spiral flow structure.

The Atmospheric Boundary Layer Above Generic Hills: Computational Model of a Unidirectional Body Force-Driven Flow

A computational steady Reynolds-averaged Navier–Stokes model is developed for a neutrally-stratified unidirectional flow in the atmospheric boundary layer (ABL) over generic two-dimensional cosine-shaped hills. Simulations are performed for a hill of a constant height and three different hill slopes. The hill surface is treated as smooth and aerodynamically rough. Atmospheric-boundary-layer inflow profiles for computations of the flow over a hill are generated from the precursor two-dimensional simulations with applied Neumann boundary conditions and an additional body force (wind-source term) introduced into the momentum equation, which value varies with increasing height. This body force ensures the appropriate momentum transport along an empty computational domain and its physical meaning is put in perspective regarding the realistic twisted ABL. The results obtained using the standard constants of the standard k−e turbulence model are compared to the results obtained using several sets of modified constants of this same turbulence model, to evaluate the influence of the inactive turbulence. The results generally indicate good agreement with the characteristics of strong flow over hills. While the modified turbulence constants yield better results for the ABL flow over flat terrain, the flow characteristics over a hill are more accurate when the standard constants of the standard k−e turbulence model are used.

Effects of Two-Dimensional Steep Hills on the Performance of Wind Turbines and Wind Farms

We use large-eddy simulations with an immersed boundary method to study the performance of wind turbines and wind farms in hilly terrain. First, we analyze the performance of wind turbines in the vicinity of a two-dimensional hill. For turbines that are significantly taller than the hill, the performance improves as the flow speeds up over the hill. For turbines that have approximately the same or a smaller height than the hill, the impact of the hill on the turbine performance depends on the positioning of the turbine in relation to the hill. For these turbines, the performance is better at the hilltop. However, the power production of these turbines is reduced due to blockage effects when they are placed at the base of the hill. The performance of turbines placed on the windward side of the hill is well predicted by superimposing the wind-turbine wake profile for the flat terrain on the hilly-terrain flow field. In contrast, we show that this approach is invalid when the turbine is placed on the leeward side of the hill where flow separation occurs. Subsequently, we consider wind farms with a hill in the middle. The hill wake is very pronounced due to which the performance of turbines located behind and close to the hill is mainly determined by the flow dynamics induced by the hill instead of the wind-turbine wakes. Finally, we study a wind farm located between two hills. We find that, for this particular configuration, there is a unique turbine spacing that maximizes the wind-farm power production in the valley.

Flux Reconstruction Implementation of an Algebraic Wall Model for Large-Eddy Simulation

In the present study, an algebraic equilibrium wall model is implemented and tested for a large-eddy simulation (LES) solver based on the flux reconstruction (FR) method. One of the objectives of the present paper is to verify the main results of Frère et al. (“Application of Wall Models to Discontinuous Galerkin LES,” Physics of Fluids, Vol. 29, No. 8, 2017, Paper 085111) under the FR framework. In addition, the influence of the mesh growth ratio in the wall-normal direction and the mesh resolutions in the wall-parallel directions are investigated, as well as the size of the first element in the wall-normal direction. In the present wall model, the wall shear stress is computed according to the wall tangential velocity at the interface between the first and second cells from the wall. The stress is then used to update the solution unknowns. Various strategies are evaluated using a turbulent channel flow at a high Reynolds number. A comparison between a wall-modeled LES and implicit LES (ILES) without a wall model on a coarse mesh shows that the wall-modeled approach produces better results than the ILES. The wall model is then evaluated with the two-dimensional periodic hill problem to assess its capability of capturing flow separation and reattachment. The equilibrium wall model fails to capture turbulent flow separation and reattachment, indicating the need for nonequilibrium wall models for such problems.