Effect Of Wind Shear Research Articles

Research on three-dimensional wake model of horizontal axis wind turbine based on Weibull function

In wind turbine wake models, Gaussian models depend on multidimensional integration to ascertain the distribution of wake velocity deficits. These integrations, which often involve complex boundary conditions, significantly enhance the complexity of mathematical computations. Due to the difficulty of obtaining analytical solutions, numerical integration methods such as Monte Carlo or other numerical integration techniques are commonly employed. This study presents a three-dimensional wake model (3DJW) for horizontal axis wind turbines, utilizing the Weibull function to simplify wake deficit characterization instead of traditional Gaussian distribution methods. The 3DJW model considers wind shear effects and mass conservation laws to enhance predictions of vertical wake velocities. By integrating incoming wind conditions and turbine parameters, the model efficiently computes downstream wake velocities, improving computational efficiency. To enhance predictions in the ultra-far wake region, an improved three-dimensional Weibull wake model is proposed using the exponential fitting method. Validation through wind tunnel experiments and wind farm data demonstrates the model's accuracy in predicting wake deficits at the hub height, with relative errors in horizontal and vertical profiles mostly within 5% and 3%, respectively. The proposed model enables accurate and rapid calculation of wake velocities at any spatial location downstream, facilitating enhanced energy utilization and reduced costs.

The Indirect Bang-Singular Algorithm (IBSA) for singular control problems with state-inequality constraints

In this study, we present the Indirect Bang-Singular Algorithm (IBSA), a straightforward computational framework developed to solve a wide range of Singular Optimal Control Problems (SOCP) with state-inequality constraints. The algorithm is a type of arc-classification technique which reformulates the SOCP as a nonlinear programming problem over the switching times, and possibly some other parameters such as the co-states’ initial values at the entry time to a singular interval. We derive the singular control feedback using the Pontryagin’s maximum principle and analyze the possibility of an interval where multiple controls are simultaneously singular. Furthermore, we incorporate the state-inequality constraints using the direct-adjoining method. Owing to the linear property of the co-state dynamics, the co-state variables and consequently, the singular controls are computed automatically using MATLAB’s symbolic platform. The nonlinear programming is constructed in a manner to circumvent the challenges posed by state-inequality constraints in more intricate scenarios involving singular controls expressed in terms of incomplete state-feedback functions. We also present several theorems that are integral to devising a straightforward computational approach for solving SOCPs. To assess the effectiveness of the proposed algorithm, we solve the following novel problems: (1) time–fuel-optimal commercial aircraft cruise flight in a vertical plane (i.e., with state-inequality constraint, a scalar singular control, and wind shear effects), and (2) the free-routing time–fuel-optimal commercial aircraft flight in a vertical plane (i.e., with state-inequality constraint, a dual-entry singular control, and wind shear effects). Notably, the optimality of the graphed results has been carefully inspected through first and second-order optimality conditions.

Factors contributing to the minimum water column stability and timing of the winter turnover in the Ogouchi reservoir

Turnover in lakes and reservoirs causes circulation in the water column from the bottom to the surface when the water column stability becomes low. Previous studies commonly mentioned that turnover occurs when stratification indices become small, but the threshold is rarely discussed. While turnover phenomena have been extensively studied by evaluating changes in bottom dissolved oxygen (DO), the relationship between the disappearance of hypoxia and water temperature indices has not been determined. This study focused on the factors influencing the minimum thermal gradient (TG) and Schmidt Stability Index (SSI), and the timing of turnover events using DO as an indicator of mixing in the Ogouchi reservoir from 1992 to 2001. The results showed that the occurrence of minimum TG and SSI is mainly driven by inflow retention time and average maximum wind speed. Moreover, minimum air temperature and outflow retention time have few contributions to minimum SSI. It was found that 7 out of 10 years exhibited full winter turnover, while the remaining years showed incomplete mixing with persistent hypoxia at the reservoir bottom. This study identifies four cases based on onset thresholds of 0.0035 °C m−1 for TG and 30 J m−2 for SSI to explain turnover event: Case 1: an ideal state with stratification indices below the threshold, resulting in the disappearance of hypoxia; Case 2: indices above the threshold sustain hypoxia; Case 3: an irregular state where the indices exceed the threshold, yet hypoxia disappears; and Case 4: an unexpected persistence of hypoxia despite being below the threshold. The majority of the years (70 percent) were explained by thresholds. The multiple regression analysis indicated the importance of wind speed on the turnover event. Therefore, the effect of wind shear was analyzed for 30 percent of the years that cannot be explained by thresholds (cases 3 and 4). Case 3 shows turnover occurrence due to strong accumulated wind shear, despite exceeding thresholds. Conversely, Case 4 reveals weak wind shear preventing bottom water upwelling, even below thresholds. In conclusion, the precise TG and SSI thresholds for the onset of turnover event were determined using DO data. The thresholds explained the occurrence and non-occurrence of turnover event in most of the years and wind speed clarified unexplained cases by thresholds. The presented method successfully evaluated the timing of turnover and can be applicable elsewhere.

Effects of wind shear and thrust coefficient on the induction zone of a porous disk: A wind tunnel study

AbstractNeglecting the velocity reduction in the induction zone of wind turbines can lead to overestimates of power production predictions, and, thus, of the annual energy production for a wind farm. An experimental study on the induction zone associated with wind turbine operations is performed in the boundary‐layer test section of the BLAST wind tunnel at UT Dallas using stereo particle image velocimetry. This experiment provides a detailed quantification of the wind speed decrease associated with the induction zone for two different incoming flows, namely, uniform flow and boundary layer flow. Operations of wind turbines in different regions of the power curve are modeled in the wind tunnel environment with two porous disks with a solidity of 50.4% and 32.3%, which correspond to thrust coefficients of 0.71 and 0.63, respectively. The porous disks are designed to approximate the wake velocity profiles previously measured for utility‐scale wind turbines through scanning wind LiDARs. The results show that the streamwise velocity at one rotor diameter upwind of both disks decreases 1% more for the boundary layer flow than for the uniform flow. Further, the effect of shear in front of the disk with a higher thrust coefficient can be observed until 1.75 rotor diameter upwind of the disk, whereas for the disk with a lower thrust coefficient, the effect of shear becomes negligible at 1.25 rotor diameter upwind. It is found that at one rotor diameter upwind, for both incoming flows, the disk having a higher thrust coefficient has 2% more velocity reduction than the lower‐thrust‐coefficient disk. The results suggest that the variability in wind shear and rotor thrust coefficient, which is encountered during typical operations of wind turbines, should be considered for the development of improved models for predictions of the rotor induction zone, the respective cumulative effects in the presence of multiple turbines, namely, wind farm blockage, and more accurate predictions of wind farm power capture.

Numerical investigation of dynamic icing of wind turbine blades under wind shear conditions

In the wind shear icing environment, the periodically varying inflow conditions experienced by wind turbine blades can significantly enhance the dynamic icing characteristics, which poses a great challenge to wind turbine icing research. To investigate this phenomenon, the Improved Multi-Shot Icing Computational Model (IMSICM) is utilized. In IMSICM, an efficient dynamic icing computational frame is designed by using the 3D Free Wake Lifting Line method coupled with the 2D Viscous and Inviscid Interaction method to calculate the flow field. Meanwhile, the Lagrangian method is applied to compute the water droplet impingement information and the Messinger Model is used to simulate the ice growth. After validation of IMSICM by the icing wind tunnel experimental results, the wind shear icing processes of the NREL 5 MW wind turbine under different wind shear conditions are analyzed. The results show that different from the linear growth behavior of Rime ice, the nonlinear features of Glaze ice development are significant. The wind shear effect has a greater impact on the Glaze ice shape, mainly manifested as the ice protrusions behind the main ice horn are suppressed. This phenomenon is mainly due to the combined effect of water impingement shadowing and heat transfer reduction.

Updates in the NCEP GFS PBL and Convection Models with Environmental Wind Shear Effect and Modified Entrainment and Detrainment Rates and Their Impacts on the GFS Hurricane and CAPE Forecasts

Abstract To reduce hurricane intensity bias, the NCEP Global Forecast System (GFS) planetary boundary layer (PBL) and convection schemes have been updated with a new parameterization for environmental wind shear and enhanced entrainment and detrainment rates with increasing PBL or subcloud mean turbulent kinetic energy (TKE) in their updraft and downdraft mass-flux schemes. Tests with the GFS show that the updated schemes significantly reduce the hurricane intensity bias by reducing the momentum transport in the mass-flux schemes. Along with the reduced intensity bias, the hurricane intensity and track errors have also been reduced. On the other hand, to reduce the PBL overgrowth over areas with a higher vegetation fraction or larger surface roughness, the entrainment rate in the PBL mass-flux scheme has also been increased with increasing vegetation fraction or increasing surface roughness. This entrainment rate increase has increased near-surface moisture, and as a result, helped to increase the underestimated convective available potential energy (CAPE) forecasts over the continental United States.

A new 3D asymmetric double-Gaussian wake analytical model for horizontal-axis wind turbines

A new three-dimensional analytical model named 3DADG that is able to describe asymmetric evolution of wind turbine wake is proposed in this paper. Due to the combined effects of wind wheel rotation and wind shear effects wake attenuation shows asymmetric properties. However, existing wake analytical models fail to describe such unique properties. To solve this problem, spatial dependencies of the wake expansion rate and deficit coefficient are revealed to successfully present horizontal attenuations of the wake varying from asymmetric-double-Gaussian in the near and transition wake regions, and then to single-Gaussian in the far wake region. The wind shear effect is also considered in the model to include asymmetric vertical wake speed attenuation. This model is derived from the laws of mass and momentum conservation. It is verified through comparisons with the results of wind tunnel “blind test” and LES simulation. The model proposed is capable to show spatial evolution of wind turbine wake from a three-dimensional perspective. Sensitivities of thrust coefficient and turbulence intensity to the model are also investigated. It not only promotes development of wake analytical model but also provides a useful tool for power prediction and wake control of wind farms under wake effects.

An advanced three-dimensional analytical model for wind turbine near and far wake predictions

Most existing analytical wake models have been designed to represent the velocity distribution of the far wake region behind a wind turbine, but fail to reproduce the trend of the near wake. In order to meet the demand for both near and far wake velocity predictions, a concise three-dimensional dual-cosine shape (3D-COU) model is proposed. Moreover, by taking into account the wind shear and ground effects in the vertical direction, this model is capable of describing the anisotropic property of the 3-D wake field and is much closer to the reality. The proposed model is then calibrated and validated through a series of test cases, including different scales of turbines that are operating under a wide range of inflow conditions, and meanwhile the reference data resource is diverse. Overall, the results demonstrate that the 3D-COU model can accurately predict the variations of the wake velocity in both the vertical and horizontal directions throughout the whole wake region. Given its good accuracy, simplicity and applicability, this model provides the potential to effectively address practical problems in wind energy projects.

Two three-dimensional super-Gaussian wake models for hilly terrain

With the increase in wind farms in hilly terrain, it is particularly important to explore the downstream wake expansion of wind turbines in hilly terrains. This study established two complex terrain-applicable super-Gaussian wake models based on the Coanda effect and the wind speed-up phenomenon. Then, by considering the wind shear effect and the law of mass conservation, two three-dimensional (3D) super-Gaussian wake models were obtained. The 3D super-Gaussian models were used to describe the shape of the wake deficit and could reflect the wake changes in the full wake region. The introduction of the Coanda effect could reflect the sinking of the wind turbine wake on the top of a hilly terrain. And considering that the wind speed-up phenomenon could better reflect the incoming velocity distribution of the actual hilly terrain. The validation results demonstrated that the prediction results of the 3D super-Gaussian wake models had negligible relative errors compared to the measured data and could better describe the vertical and horizontal expansion changes of the downstream wake. The models established in this study can assist with the development of complex terrain models and super-Gaussian models, as well as providing guidance for power prediction and wind turbine control strategies in complex terrain.

Effects of Wind Shear and Aerosol Conditions on the Organization of Precipitating Marine Stratocumulus Clouds

AbstractThis study examines how wind shear affects precipitating marine stratocumulus clouds under different cloud droplet number concentrations (Nd). We performed a series of large eddy simulations (LES) of nocturnal marine stratocumulus clouds using Cloud Model 1 (CM1). The simulations show that Nd is the dominant factor for cloud cellular organization in this cloud regime rather than wind shear. Low Nd characterizes the open cellular structure with a high in‐cloud liquid water path (LWP). When wind shear is increased, the cloud fraction tends to decrease along with LWP, suggesting the cloud top region is significantly influenced by the entrainment and mixing of dry air from the free troposphere. We also examine cold pools in open and closed cellular clouds. Open‐cell clouds produce larger and deeper cold pools compared to closed‐cell clouds. Interestingly, cold pools can exist without surface precipitation and are produced by evaporation of light precipitation (drizzle) below the cloud base with weak downdrafts. The evaporation of raindrops and drizzle play an important role in initiating new convection, particularly where colliding outflows occur downstream of the cloud. This secondary convection contributes to the development and maintenance of the cloud cellular organization and formation.

Transient Flow Evolution of a Hypersonic Inlet/Isolator with Incoming Windshear

In this paper, a novel flow perturbation model meant to investigate the effects of incoming wind shear on a hypersonic inlet/isolator is presented. This research focuses on the transient shock/boundary layer interaction and shock train flow evolution in a hypersonic inlet/isolator with an on-design Mach number of 6.0 under incoming wind shear at high altitudes, precisely at an altitude of 30 km with a magnitude speed of 80 m/s. Despite the low intensity of wind shear at high altitudes, the results reveal that wind shear significantly disrupts the inlet/isolator flowfield, affecting the shock wave/boundary layer interaction in the unthrottled state, which drives the separation bubble at the throat to move downstream and then upstream. Moreover, the flowfield behaves as a hysteresis phenomenon under the effect of wind shear, and the total pressure recovery coefficients at the throat and exit of the inlet/isolator increase by approximately 10% to 12%. Furthermore, this research focuses on investigating the impact of wind shear on the behavior of the shock train. Once the inlet/isolator is in a throttled state, wind shear severely impacts the motion of the shock train. When the downstream backpressure is 135 times the incoming pressure (p0), the shock train first moves upstream and gradually couples with a cowl shock wave/boundary layer interaction, resulting in a more significant separation at the throat, and then moves downstream and decouples from the separation bubble at the throat. However, if the downstream backpressure increases to 140 p0, the shock train enlarges the separation bubble, forcing the inlet/isolator to fall into the unstart state, and it cannot be restarted. These findings emphasize the need to consider wind shear effects in the design and operation of hypersonic inlet/isolator.

Dynamic analysis of offshore triceratops supporting wind turbine: Preliminary studies

Offshore triceratops, the recent innovation in deep water compliant platforms, is primarily designed to withstand lateral forces through its geometric shape. The uniqueness of the platform is the presence of the ball joints between the legs and deck, which partially restrain the transfer of rotations from the legs to the deck and vice-versa. However, displacements such as surge, sway, and heave motions are transferred, ensuring a rigid connection between the legs and the deck. Efficient operations of offshore wind turbines are more dependent on the support systems on which they are mounted. Increased stability and reduction in stress concentration in rigid connections are desirable. Nonlinear dynamic response analysis is carried out in FAST by coupling the frequency response of the platform obtained in ANSYS AQWA with that of the HydroDyn module of FAST. The current study investigates a fully coupled three-dimensional hydro-aerodynamic model of triceratops mounted with a horizontal axis wind turbine. Unsteady Blade Element Momentum theory (BEM) is used to estimate the aerodynamic loads, which encompasses the effect of wind shear using a power law and spatially coherent turbulence. In contrast, Morison equations are used to estimate the hydrodynamic loads on the platform. After the preliminary proportioning of the platform, Response Amplitude Operator (RAO) plots are drawn to illustrate the partial motion transfer between the deck and the buoyant legs. Based on the preliminary studies, it is seen that the environmental loads do not impose instability, reinforcing the dynamic stability of the platform. Frequency responses for operating and parked conditions illustrate the coupling between the degrees of freedom and the influence of the rotor motion of the wind turbine on the platform deck. Tether tension variation is assessed in all three legs for the operational sea states to check the safety standards for a compliant system to avoid tether pull-out. The presented study is prima facie to encourage the suitability of triceratops as floaters to support the wind turbine under moderate sea states. Highlights This study is focused on new-generation offshore triceratops as support system for wind turbine Prelimiary dynamic anlaysis of coupled action of the supprting system and wind turbine are presented Use of ball joints help partial isolation of the deck and restrain transfer of moment from the turbine shaft to the supporting system, which is a novelty Infleunce of rotor motion of the triceratops is illustarted to highlight the advantage of complinacy of trirceratops This study disucsses only the performance assessment and not the design perspectives

A three-dimensional wake model for wind turbines based on a polynomial distribution of wake velocity

Accurate and fast prediction of wake is essential for power generation prediction of wind farms. This paper proposes a three-dimensional wake model that considers the effect of wind shear and the mass loss caused by such shear. The model simplifies the wake velocity distribution by assuming a straightforward polynomial shape rather than a complex Gaussian distribution, which makes the model simpler and more intuitive. To be close to reality, it incorporates the anisotropic expansion of the wake boundary and provides expressions for crossflow and vertical wake expansion rates. By solely possessing information regarding the incoming wind conditions and wind turbine parameters, wake velocity at any position can be calculated in a fast way. This model's prediction accuracy is demonstrated by four cases including three experimental as well as large eddy simulation (LES) data. Compared to conventional Gaussian models, it can maintain a higher level of accuracy in all cases. The model is quite simple and offers high accuracy and low cost. It can be used in wind farm layout optimization and wake control.

Effects of wind shear and aerosol conditions on the organization of precipitating marine stratocumulus clouds

Effects of wind shear and aerosol conditions on the organization of precipitating marine stratocumulus clouds

Wind and Turbulence Effects on Raindrop Fall Speed

Abstract Wind and turbulence effects on raindrop fall speeds were elucidated using field observations over a 2-yr time period. Motivations for this study include the recent observations of raindrop fall speed deviations from the terminal fall speed predictions (Vt) based upon laboratory studies and the utilizations of these predictions in various important meteorological and hydrological applications. Fall speed (Vf) and other characteristics of raindrops were observed using a high-speed optical disdrometer (HOD), and various rainfall and wind characteristics were observed using a 3D ultrasonic anemometer, a laser-type disdrometer, and rain gauges. A total of 26 951 raindrops were observed during 17 different rainfall events, and of these observed raindrops, 18.5% had a subterminal fall speed (i.e., 0.85Vt ≥ Vf) and 9.5% had a superterminal fall speed (i.e., 1.15Vt ≤ Vf). Our observations showed that distributions of sub- and superterminal raindrops in the raindrop size spectrum are distinct, and different physical processes are responsible for the occurrence of each. Vertical wind speed, wind shear, and turbulence were identified as the important factors, the latter two being the dominant ones, for the observed fall speed deviations. Turbulence and wind shear had competing effects on raindrop fall. Raindrops of different sizes showed different responses to turbulence, indicating multiscale interactions between raindrop fall and turbulence. With increasing turbulence levels, while the raindrops in the smaller end of the size spectrum showed fall speed enhancements, those in the larger end of the size spectrum showed fall speed reductions. The effect of wind shear was to enhance the raindrop fall speed toward a superterminal fall.

Study on Typical Aerodynamic Faults of Variable Pitch Wind Turbine

The variable-speed variable-pitch wind turbine is an important part of China's power and energy systems, and is also the main conversion form of wind energy utilization. Aiming at the problem that the traditional blade element-momentum theory cannot achieve the modeling and simulation of wind turbine plane wind unbalance caused by wind shear and tower shadow effect, the modeling and simulation numerical calculation method of aerodynamic load of wind turbine actuation disk with different blade wind unbalance pitch angles is proposed, This method can derive the analytical expressions for solving the key variables of load calculation, axial induction factor and tangential induction factor, and realize the aerodynamic load solution. At the same time, it is also verified that the characteristic vibration component of 3 times the low speed shaft rotation frequency (3P) is a typical dynamic load feature of tower shadow effect, and is also the most important aerodynamic load fluctuation feature of variable-speed variable-pitch wind turbine, However, under normal conditions, the wind shear effect has little effect on the wind turbine load fluctuation.

Investigation of the accuracy of the transient wind forcing model applied for a shear-driven LES

We examine the effectiveness of the Transient Wind Forcing (TWF), previously validated with field and wind tunnel experiments, using LES in large-scale and small-scale cyclic domains. The small domain includes only a part of the atmospheric boundary-layer height, so the effect of wind shear is modeled near its upper boundary with the TWF coupling method. It is essentially a time-dependent volume source of momentum, which is controlled using velocity time series extracted from a point in the large domain. Surface roughness is explicitly modeled in both domains. The dispersion of atmospheric pollutants is investigated by the Lagrange method. The model error of TWF coupling is quantitatively evaluated in the case of atmospheric boundary layers with different Coriolis parameters, atmospheric stability, and surface roughness. The results of the small model driven by the TWF method showed good agreement with the reference results obtained from the large domain based on the average wind speed and turbulence profiles between and directly above the buildings, as well as the concentration of air pollutants emitted at ground level. For this, it was also necessary to consider the pressure gradient corresponding to the geostrophic wind and the effect of the Coriolis force in the small domain.

Numerical Simulation and Experimental Verification of Wind Field Reconstruction Based on PCA and QR Pivoting

Short-term wind forecasting is critical for the dispatch, controllability and stability of a power grid. As a challenging but indispensable work, short-term wind forecasting has attracted considerable attention from researchers. In this paper, Principal Component Analysis (PCA) is applied to Computational Fluid Dynamics (CFD) calculation results for feature extraction and then combined with sparse sensing to achieve the rapid reconstruction of a three-dimensional wind speed field and pressure field. Before reconstruction, the relationship between the reconstruction error and the noise level, and a number of the basis vectors is systematically studied. In the simulation, the wind shear effect is introduced into the inlet boundary condition, and the reconstruction errors of the uniform inlet are 0.21% and 6.46%, respectively, while the maximum reconstruction errors including the wind shear effect are 1.21% and 6.41%, respectively, which verifies the feasibility of applying a PCA-based reconstruction algorithm to a 3D wind field reconstruction. In addition, to solve the time-consuming problem of most optimization algorithms based on a brute-force combinatorial search, an innovative optimization algorithm based on the QR pivoting is investigated to determine the sparse sensor placements. Simulation results show that when the number of sensors is equal to the number of basis vectors, the error of random placement is even 20 times of the optimal placement, which illustrates that QR pivoting is a powerful optimization algorithm. Finally, a wind tunnel experiment of velocity field reconstruction is performed, to verify the practicability of the optimized method based on QR pivoting, and the results indicate that a reasonably high accuracy 3D wind field can be obtained with only 10 sensors (the error of most points is less than 5% and the minimum error is only 0.74%). In general, the proposed algorithm incorporating PCA, sparse sensing and QR pivoting can quickly reconstruct the 3D velocity and pressure fields with reduced measurement costs, which is of great significance for the development of short-term wind forecasting methods.

A new three-dimensional entrainment model for wind-turbine wakes

A linear entrainment (LE) wake model can maintain both mass conservation and momentum conservation, improving wake prediction accuracy. However, its key parameter entrainment coefficient E determines the exchange of fluids inside and outside the wake region, which significantly affects its prediction accuracy and requires further testing and correction. Also, its assumed top-hat shape can cause large errors. This work first establishes the best value of E (E = 0.12) based on experimental data and numerical simulation. Then we construct the three-dimensional cosine-shaped wake model by correcting the radial velocity distribution of the LE model with the cosine function and considering the wind shear effect. In addition, different from the two-parameter turbulence intensity model used in the previous models, the recently proposed three-parameter turbulence-intensity model is used to correct the E value in order to integrate the effects on downstream distance, thrust coefficient, and ambient turbulence intensity. Comparisons with two field measurements and three wind tunnel test cases demonstrate the accuracy of this model, which provides predictions of wake velocity loss in both the lateral and vertical directions that are more accurate than those of the conventional models.

The effect of vertical arrangement on performance and wake characteristics of two tandem offshore wind turbines under various operating conditions

Apart from streamwise and lateral distances, a vertical distance may also be imposed for adjacent wind turbines to achieve performance improvement of downstream turbines. Previous research was primarily devoted to wind farm layout optimisation using simplified analytical wake models, while impacts of operating conditions were ignored for studies using more advanced Large-Eddy Simulation (LES) methods. In this paper, the effect of vertical arrangement on performance and wake characteristics of two tandem offshore wind turbines under various operating conditions is investigated using an LES approach coupled with an actuator line technique. Results show that vertically arranging turbines can improve downstream turbine performance, but its effects vary with the operating conditions. If turbines typically operate below or at the rated condition, due to deflection of upstream turbine wake associated with shaft tilt, raising the upstream turbine can result in greater improvement in power output, with a considerable rise of 50% for a relatively small height difference of 0.1 times rotor diameter. For above-rated operating conditions, the wind shear effect becomes important and it is preferable to increase the hub height of the downstream turbine to take advantage of higher wind speed. Wake characteristics of both turbines are analysed to support the results.