scholarly journals Monin–Obukhov Similarity Theory for Modeling of Wind Turbine Wakes under Atmospheric Stable Conditions: Breakdown and Modifications

2019 ◽  
Vol 9 (20) ◽  
pp. 4256
Author(s):  
Xingxing Han ◽  
Deyou Liu ◽  
Chang Xu ◽  
Wenzhong Shen ◽  
Linmin Li ◽  
...  
Keyword(s):  
Side Effects ◽  
Wind Turbine ◽  
Velocity Gradient ◽  
Similarity Theory ◽  
Turbulence Models ◽  
Disk Model ◽  
Similarity Functions ◽  
Stable Conditions ◽  
Flow Similarity ◽  
Wake Modeling

Monin–Obukhov similarity theory (MOST) overestimates the mean vertical velocity gradient in some atmospheric stable conditions, i.e., Richardson number R f < 0 . 25 . To obtain a given hub-height inflow velocity for a certain roughness length, this overestimated velocity gradient underpredicts the friction wind speed and the turbulence intensity, potentially influencing wake modeling of a wind turbine. This work investigates the side effects of the breakdown of MOST on wake modeling under stable conditions and makes some modifications to the flow similarity functions to eliminate these side effects. Based on a field measurement in a wind farm, we first show that MOST predicts a larger velocity gradient for the atmospheric stability parameter ζ > 0 . 1 and proposes new flow similarity functions without constraining R f to limit the overestimated velocity gradient. Next, different turbulence models based on MOST and a modified one based on the new similarity functions are investigated through numerical simulations. These turbulence models are combined with the actuator disk model (AD) and Reynolds-averaged Navier–Stokes equations (RANS) to model wind turbine wakes under stable conditions. As compared to measurements, numerical results show that turbulence models based on MOST result in a larger wake deficit and a slower wake recovery rate with a root-mean-squared error (RSME) of wake deficit in the range of 0.07 to 0.20. This overestimated wake effect is improved by applying the new similarity functions, and the RSME of wake deficit is reduced by 0.05 on average.

scholarly journals Monin-Obukhov Similarity Theory for Modeling of Wind Turbine Wakes under Atmospheric Stable Conditions: Breakdown and Modifications

2019 ◽  
Author(s):  
Xing Xing Han ◽  
De You Liu ◽  
Chang Xu ◽  
Wen Zhong Shen ◽  
Lin Min Li ◽  
...  
Keyword(s):  
Wind Turbine ◽  
Turbulence Intensity ◽  
Wind Shear ◽  
Similarity Theory ◽  
Turbulence Models ◽  
Wake Effect ◽  
Similarity Functions ◽  
Stable Conditions ◽  
Flow Similarity ◽  
Ambient Turbulence

Monin-Obukhov similarity theory (MOST) overestimates wind shear in some atmospheric stable conditions, i.e. Richardson number $R_f&lt;0.25$. The overestimated wind shear that leads to an under-predicted friction wind speed and a lower ambient turbulence intensity for a given hub-height reference wind speed and a given roughness length, could influence wake modeling of a wind turbine. This work investigates the side effects of the breakdown of MOST on wake modeling under stable conditions and makes some modifications to the flow similarity functions to eliminate these side effects. Based on a field measurement in a wind farm, we firstly show that MOST predicts a larger wind shear for the atmospheric stability parameter $\zeta&gt;0.1$ and proposes new flow similarity functions without constraining $R_f$ to limit the overestimated wind shear by MOST. Next, different turbulence models based on MOST and a modified one based on the new similarity functions are investigated through numerical simulations. These turbulence models are combined with the actuator disk model (AD) and Reynolds-averaged Navier&ndash;Stokes equations (RANS) to model wind turbine wakes under stable conditions. As compared to measurements, numerical results show that turbulence models based on MOST result in larger wake deficits and slower wake recovery rate with a square root of the mean-squared-error (RSME) of wake deficit in the range of 0.07-0.18. This overestimated wake effect is improved by applying the new similarity functions and the RSME of wake deficit is averagely reduced by 0.05. Finally, we check the role of the under-predicted turbulence intensity playing in the larger wake deficit predicted by models based MOST. Additional numerical simulations using the modified turbulence model are carried out, in which the roughness length is reduced to impose a hub-height ambient turbulence intensity equivalent to the MOST case. Simulation results show that reducing turbulence intensity enhances wake effects, however, it cannot reproduce the large wake deficit predicted by models based on MOST, which suggests that the overestimated wake effect by MOST could be also related to the overestimated wind shear.

Estimation of upper bounds for the applicability of non-linear similarity functions for non-dimensional wind and temperature profiles in the surface layer in very stable conditions

2010 ◽  
Vol 467 (2126) ◽  
pp. 473-494 ◽  
Author(s):  
Maithili Sharan ◽  
Pramod Kumar
Keyword(s):  
Surface Layer ◽  
Similarity Theory ◽  
Upper Bounds ◽  
Surface Fluxes ◽  
Similarity Function ◽  
Temperature Profiles ◽  
Similarity Functions ◽  
Surface Exchange ◽  
Stable Conditions ◽  
Non Linear

The computation of surface fluxes by Monin–Obukhov similarity theory with different linear/non-linear similarity functions for non-dimensional wind and temperature profiles becomes limited to specific ranges of ζ = z / L (where z is the height above ground and L is the Obukhov length) and bulk Richardson number ( Ri B ) under very stable conditions. A systematic mathematical analysis is carried out to estimate the upper bounds of ζ and Ri B for the extent of applicability of different non-linear similarity functions in the surface layer under these conditions. A generalized methodology is proposed on the basis of momentum drag coefficient ( C D ) and heat exchange coefficient ( C H ) and applied to various non-linear similarity functions available in the literature. A theoretically derived criterion for the applicability of each of the non-linear similarity function is evaluated with observations from Cooperative Atmosphere-Surface Exchange Study-99 and UK Meteorological Office’s Cardington datasets. The evaluation with both datasets for each non-linear similarity function confirms the validity of proposed theoretical results under very stable conditions.

scholarly journals A BEM-Based Actuator Disk Model for Wind Turbine Wakes Considering Atmospheric Stability

2019 ◽  
Author(s):  
Xing Xing Han ◽  
De You Liu ◽  
Chang Xu ◽  
Wen Zhong Shen ◽  
Lin Min Li ◽  
...  
Keyword(s):  
Wind Turbine ◽  
Wind Farm ◽  
Atmospheric Stability ◽  
Stability Conditions ◽  
High Fidelity ◽  
Thrust Coefficient ◽  
Disk Model ◽  
Similarity Functions ◽  
Actuator Disk ◽  
Blade Element

Atmospheric stability affects wind turbine wakes significantly. High-fidelity approaches such as large eddy simulations (LES) with the actuator line (AL) model which predicts detailed wake structures, fail to be applied in wind farm engineering applications due to its expensive cost. In order to make wind farm simulations computationally affordable, this paper proposes a new actuator disk model (AD) based on the blade element method (BEM) and combined with Reynolds-averaged Navier&ndash;Stokes equations (RANS) to model turbine wakes under different atmospheric stability conditions. In the proposed model, the upstream reference velocity is firstly estimated from the disk averaged velocity based on the one-dimensional momentum theory, and then is used to evaluate the rotor speed to calculate blade element forces. Flow similarity functions based on field measurement are applied to limit wind shear under strongly stable conditions, and turbulence source terms are added to take the buoyant-driven effects into consideration. Results from the new AD model are compared with field measurements and results from the AD model based on the thrust coefficient, the BEM-AD model with classical similarity functions and a high-fidelity LES approach. The results show that the proposed method is better in simulating wakes under various atmospheric stability conditions than the other AD models and has a similar performance to the high-fidelity LES approach however in much lower computational cost.

scholarly journals Measurements of Momentum and Heat Transfer across the Air–Sea Interface

2008 ◽  
Vol 38 (5) ◽  
pp. 1054-1072 ◽  
Author(s):  
Gregory P. Gerbi ◽  
John H. Trowbridge ◽  
James B. Edson ◽  
Albert J. Plueddemann ◽  
Eugene A. Terray ◽  
...  
Keyword(s):  
Similarity Theory ◽  
Turbulence Models ◽  
Wave Band ◽  
Langmuir Circulation ◽  
Rigid Boundary ◽  
Length Scales ◽  
Stability Functions ◽  
Stable Conditions ◽  
Momentum And Heat Transfer ◽  
Boundary Turbulence

Abstract This study makes direct measurements of turbulent fluxes in the mixed layer in order to close heat and momentum budgets across the air–sea interface and to assess the ability of rigid-boundary turbulence models to predict mean vertical gradients beneath the ocean’s wavy surface. Observations were made at 20 Hz at nominal depths of 2.2 and 1.7 m in ∼16 m of water. A new method is developed to estimate the fluxes and the length scales of dominant flux-carrying eddies from cospectra at frequencies below the wave band. The results are compared to independent estimates of those quantities, with good agreement between the two sets of estimates. The observed temperature gradients were smaller than predicted by standard rigid-boundary closure models, consistent with the suggestion that wave breaking and Langmuir circulation increase turbulent diffusivity in the upper ocean. Similarly, the Monin–Obukhov stability function ϕh was smaller in the authors’ measurements than the stability functions used in rigid-boundary applications of the Monin–Obukhov similarity theory. The dominant horizontal length scales of flux-carrying turbulent eddies were found to be consistent with observations in the bottom boundary layer of the atmosphere and from laboratory experiments in three ways: 1) in statically unstable conditions, the eddy sizes scaled linearly with distance to the boundary; 2) in statically stable conditions, length scales decreased with increasing downward buoyancy flux; and 3) downwind length scales were larger than crosswind length scales.

Performance enhancement of Savonius wind turbine by blade shape and twisted angle modifications

2021 ◽  
pp. 095765092098794
Author(s):  
Ahmed M Nagib Elmekawy ◽  
Hassan A Hassan Saeed ◽  
Sadek Z Kassab
Keyword(s):  
Wind Turbine ◽  
Performance Enhancement ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Vertical Axis ◽  
Cfd Simulations ◽  
Sliding Mesh ◽  
Blade Shape ◽  
Rotor Shape ◽  
Twisting Angle

Three-dimensional CFD simulations are carried out to study the increase of power generated from Savonius vertical axis wind turbines by modifying the blade shape and blade angel of twist. Twisting angle of the classical blade are varied and several proposed novel blade shapes are introduced to enhance the performance of the wind turbine. CFD simulations have been performed using sliding mesh technique of ANSYS software. Four turbulence models; realizable k -[Formula: see text], standard k - [Formula: see text], SST transition and SST k -[Formula: see text] are utilized in the simulations. The blade twisting angle has been modified for the proposed dimensions and wind speed. The introduced novel blade increased the power generated compared to the classical shapes. The two proposed novel blades achieved better power coefficients. One of the proposed models achieved an increase of 31% and the other one achieved 32.2% when compared to the classical rotor shape. The optimum twist angel for the two proposed models achieved 5.66% and 5.69% when compared with zero angle of twist.

scholarly journals Estimation of wind turbine blade aerodynamic performances computed using different numerical approaches

2018 ◽  
Vol 45 (1) ◽  
pp. 53-65 ◽  
Author(s):  
Jelena Svorcan ◽  
Ognjen Pekovic ◽  
Toni Ivanov
Keyword(s):  
Wind Turbine ◽  
Thrust Force ◽  
Turbulence Models ◽  
Turbine Rotor ◽  
Momentum Balance ◽  
Horizontal Axis Wind Turbine ◽  
Ansys Fluent ◽  
Force Coefficients ◽  
Aerodynamic Performances ◽  
Numerical Approaches

Although much employed, wind energy systems still present an open, contemporary topic of many research studies. Special attention is given to precise aerodynamic modeling performed in the beginning since overall wind turbine performances directly depend on blade aerodynamic performances. Several models different in complexity and computational requirements are still widely used. Most common numerical approaches include: i) momentum balance models, ii) potential flow methods and iii) full computational fluid dynamics solutions. Short explanations, reviews and comparison of the existing computational concepts are presented in the paper. Simpler models are described and implemented while numerous numerical investigations of isolated horizontal-axis wind turbine rotor consisting of three blades have also been performed in ANSYS FLUENT 16.2. Flow field is modeled by Reynolds Averaged Navier-Stokes (RANS) equations closed by two different turbulence models. Results including global parameters such as thrust and power coefficients as well as local distributions along the blade obtained by different models are compared to available experimental data. Presented results include fluid flow visualizations in the form of velocity contours, sectional pressure distributions and values of power and thrust force coefficients for a range of operational regimes. Although obtained numerical results vary in accuracy, all presented numerical settings seem to slightly under- or over-estimate the global wind turbine parameters (power and thrust force coefficients). Turbulence can greatly affect the wind turbine aerodynamics and should be modeled with care.

Evaluation of Boundary Layer Similarity Theory for Stable Conditions in CASES-99

2007 ◽  
Vol 135 (10) ◽  
pp. 3474-3483 ◽  
Author(s):  
Kyung-Ja Ha ◽  
Yu-Kyung Hyun ◽  
Hyun-Mi Oh ◽  
Kyung-Eak Kim ◽  
Larry Mahrt
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Similarity Theory ◽  
Unknown Origin ◽  
Strong Stability ◽  
Surface Exchange ◽  
Stability Functions ◽  
Stable Conditions ◽  
Mean Wind Speed ◽  
Strong Winds

Abstract The Monin–Obukhov similarity theory and a generalized formulation of the mixing length for the stable boundary layer are evaluated using the Cooperative Atmosphere–Surface Exchange Study-1999 (CASES-99) data. The large-scale wind forcing is classified into weak, intermediate, and strong winds. Although the stability parameter, z/L, is inversely dependent on the mean wind speed, the speed of the large-scale flow includes independent influences on the flux–gradient relationship. The dimensionless mean wind shear is found to obey existing stability functions when z/L is less than unity, particularly for the strong and intermediate wind classes. For weak mean winds and/or strong stability (z/L &gt; 1), this similarity theory breaks down. Deviations from similarity theory are examined in terms of intermittency. A case study of a weak-wind night indicates important modulation of the turbulence flux by mesoscale motions of unknown origin.

scholarly journals A Clustering Method to Characterize Intermittent Bursts of Turbulence and Interaction with Submesomotions in the Stable Boundary Layer

2015 ◽  
Vol 72 (4) ◽  
pp. 1504-1517 ◽  
Author(s):  
Nikki Vercauteren ◽  
Rupert Klein
Keyword(s):  
Thermal Stratification ◽  
Factor Model ◽  
Similarity Theory ◽  
Stable Stratification ◽  
Small Scale ◽  
Clustering Method ◽  
Atmospheric Boundary Layers ◽  
Optimal Sequence ◽  
Stable Conditions ◽  
Turbulence Data

Abstract Atmospheric boundary layers with stable stratification include a variety of small-scale nonturbulent motions such as waves, microfronts, and other complex structures. When the thermal stratification becomes strong, the presence of such motions could affect the turbulent mixing to a large extent, and common similarity theory that is used to describe weakly stable conditions may become unreliable. The authors apply a statistical clustering methodology based on a bounded variation, finite-element method (FEM-BV) to characterize the interaction between small-scale nonturbulent motions and turbulence. The clustering methodology achieves a multiscale representation of nonstationary turbulence data by approximating them through an optimal sequence of locally stationary multivariate autoregressive factor model (VARX) processes and some slow hidden process switching between them. The clustering method is used to separate periods with different influence of the nonturbulent motions on the vertical velocity fluctuations. The methodology can be used in a later stage to derive a stochastic parameterization for the interactions between nonturbulent and turbulent motions.

A Review of Wind Turbine Polar Data and its Effect on Fatigue Loads Simulation Accuracy

2015 ◽  
Author(s):  
Matthew Lennie ◽  
Georgios Pechlivanoglou ◽  
David Marten ◽  
Christian Navid Nayeri ◽  
Oliver Paschereit
Keyword(s):  
Wind Turbine ◽  
Turbine Blades ◽  
Turbulence Models ◽  
Leading Edge ◽  
Sensitivity Study ◽  
Wind Turbine Blades ◽  
Simulation Code ◽  
Simulation Accuracy ◽  
Inflow Turbulence ◽  
Lift And Drag

To certify a Wind Turbine the standard processes set out by the GL guidelines and the IEC61400 demand a large number of simulations in order to justify the safe operation of the machine in all reasonably probable scenarios. The result of this rather demanding process is that the simulations rely on lower fidelity methods such as the Blade Element Momentum (BEM) method. The BEM method relies on a number of simplified inputs including the coefficient of lift and drag polar data (usually referred to as polars). These polars are usually either measured experimentally, generated using tools such as XFoil or, in some cases obtained using 2D CFD. It is typical to then modify these polars in order to make them suitable for aeroelastic simulations. Some of these modifications include 360° angle of attack extrapolation methods and polar modifications to account for 3D effects. Many of these modifications can be perceived to be a black art due to the manual selection of coefficients. The polars can misrepresent reality for many reasons, for example, inflow turbulence can affect measurements obtained in wind tunnels. Furthermore, on real wind turbine blades leading edge erosion can reduce performance. Simulated polars can even vary significantly due to the choice of turbulence models. Stack these effects on top of the uncertainties caused by yaw error, pitch error and dynamic stall and one can clearly see an operating environment hostile to accurate simulations. Colloquial evidence suggests that experienced designers would account for all of these sources of errors methodically, however, this is not reflected by the certification process. A review of experimental data and literature was performed to identify some of the inaccuracies in wind turbine polars. Significant variations were found between a range of 2D polar techniques and wind tunnel measurements. A sensitivity study was conducted using the aeroelastic simulation code FAST (National Renewable Energy Laboratory) with lift and drag polars sourced using different methods. The results were post-processed to give comparisons the rotor blade fatigue damage; variations in accumulated damages reached levels of 164%. This variation is not disastrous but is certainly enough to motivate a new approach for certifying the aerodynamic performance of wind turbines. Such an approach would simply see the source of polar data and all post-processing steps documented and included in the checks performed by certification bodies.

Developing the Actuator Disk Model to Predict the Fluid–Structure Interaction in Numerical Simulation of Multimegawatt Wind Turbine Blades

2019 ◽  
Vol 142 (3) ◽  
Author(s):  
Ali Behrouzifar ◽  
Masoud Darbandi
Keyword(s):  
Numerical Methods ◽  
Wind Turbine ◽  
Fluid Structure Interaction ◽  
Cone Angle ◽  
Disk Model ◽  
Fluid Structure ◽  
Aerodynamic Loads ◽  
Structure Interaction ◽  
Actuator Disk ◽  
Analytical Approaches

Abstract The fluid–structure interaction (FSI) is generally addressed in multimegawatt wind turbine calculations. From the fluid flow perspective, the semi-analytical approaches, like actuator disk (AD) model, were commonly used in wind turbine rotor calculations. Indeed, the AD model can effectively reduce the computational cost of full-scale numerical methods. Additionally, it can substantially improve the results of pure analytical methods. Despite its great advantages, the AD model has not been developed to simulate the FSI problem in wind turbine simulations. This study first examines the effect of constant (rigid) cone angle on the performance of the chosen benchmark wind turbine. As a major contribution, this work subsequently extends the rigid AD model to nonrigid applications to suitably simulate the FSI. The new developed AD-FSI solver uses the finite-volume method to calculate the aerodynamic loads and the beam theory to predict the structural behaviors. A benchmark megawatt wind turbine is simulated to examine the accuracy of the newly developed AD-FSI solver. Next, the results of this solver are compared with the results of other researchers, who applied various analytical and numerical methods to obtain their results. The comparisons indicate that the new developed solver calculates the aerodynamic loads reliably and predicts the blade deflection very accurately.

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