Turbulence modeling of atmospheric boundary layer flow over complex terrain: a comparison of models at wind tunnel and full scale

The aim of this work is to evaluate the performance of two popular k ? ? turbulence closure schemes for atmospheric boundary layer (ABL) flow over hills and valleys and to investigate the effect of using ABL‐modified model constants. The standard k ? ? and the RNG k ? ? models are used to simulate flow over the two‐dimensional analytical shapes from the RUSHIL and RUSHVAL wind tunnel experiments. Furthermore, the mean turbulent flow over the real complex terrain of Blashaval hill is simulated and the results verified with a data set of full‐scale measurements. In general, all models yield similar results. However, use of ABL‐modified constants in both models tends to decrease the predicted velocity and increase the predicted turbulent kinetic energy. Copyright © 2010 John Wiley & Sons, Ltd.     

The k‐ϵ‐fP model applied to wind farms

The recently developed k‐?‐f_P eddy‐viscosity model is applied to one on‐shore and two off‐shore wind farms. The results are compared with power measurements and results of the standard k‐? eddy‐viscosity model. In addition, the wind direction uncertainty of the measurements is used to correct the model results with a Gaussian filter. The standard k‐? eddy‐viscosity model underpredicts the power deficit of the first downstream wind turbines, whereas the k‐?‐f_P eddy‐viscosity model shows a good agreement with the measurements. However, the difference in the power deficit predicted by the turbulence models becomes smaller for wind turbines that are located further downstream. Moreover, the difference between the capability of the turbulence models to estimate the wind farm efficiency reduces with increasing wind farm size and wind turbine spacing. Copyright © 2014 John Wiley & Sons, Ltd.     

An improved k‐ ϵ model applied to a wind turbine wake in atmospheric turbulence

An improved k‐ ? turbulence model is developed and applied to a single wind turbine wake in a neutral atmospheric boundary layer using a Reynolds averaged Navier–Stokes solver. The proposed model includes a flow‐dependent C_μ that is sensitive to high velocity gradients, e.g., at the edge of a wind turbine wake. The modified k‐ ? model is compared with the original k‐ ? eddy viscosity model, Large‐Eddy Simulations and field measurements using eight test cases. The comparison shows that the velocity wake deficits, predicted by the proposed model are much closer to the ones calculated by the Large‐Eddy Simulation and those observed in the measurements, than predicted by the original k‐ ? model. Copyright © 2014 John Wiley & Sons, Ltd.     

Trailing edge serrations effects on the aerodynamic performance of a NACA 643418

A study of the aerodynamic performance of a NACA 64₃418 airfoil with trailing edge serrations is presented. For the prediction of the changes in lift due to the serration installation, an empirical law is derived that can be extended to typical cambered airfoils for wind turbine applications. The law is deduced from 2D and 3D Reynolds‐averaged Navier–Stokes simulations (RANS) of the flow over the airfoil. Lift and drag together with the changes in the wake flow due to the presence of the serrated edges are investigated. An additional study of the sensitivity of the results at Re_c = 3·10⁶ with respect to the turbulence modeling is carried out by using three different RANS models: Spalart–Allmaras, k‐omega SST, and Transition SST. Results show that the changes in lift due to trailing‐edge extensions are approximated by the effect of a split plate with reduced length.     

Impact of different forest densities on atmospheric boundary‐layer development and wind‐turbine wake

The aim of this work is to investigate the atmospheric boundary‐layer (ABL) flow and the wind turbine wake over forests with varying leaf area densities (LAD). The forest LAD profile used in this study is based on a real forest site, Ryningsnäs, located in Sweden. The reference turbine used to model the wake is a well‐documented 5‐MW turbine, which is implemented in the simulations using an actuator line model (ALM). All simulations are carried out with openFOAM using the Reynolds averaged Navier‐Stokes (RANS) approach. Twelve forest cases with leaf area index (LAI) ranging from 0.42 to 8.5 are considered. Results show that the mean velocity decreases with increasing LAI within the forest canopy, but increases with LAI above the hub height. Meanwhile, the turbulent kinetic energy (TKE) varies nonmonotonically with forest density. The TKE increases with forest density and reaches to its maximum at an average LAI of 1.70, afterwards, it decreases gradually as the density increases. It is also observed that the forest density has a clear role in the wake development and recovery. Comparisons between no‐forest and forest cases show that the forest characteristics help in damping the added turbulence from the turbine. As a consequence, the forest with the highest upstream turbulence has the shortest wake downstream of the turbine.     

Assessing atmospheric stability and its impacts on rotor‐disk wind characteristics at an onshore wind farm

As the average hub height and blade diameter of new wind turbine installations continue to increase, turbines typically encounter higher wind speeds, which enable them to extract large amounts of energy, but they also face challenges due to the complex nature of wind flow and turbulence in the planetary boundary layer (PBL). Wind speed and turbulence can vary greatly across a turbine's rotor disk; this variability is partially due to whether the PBL is stable, neutral or convective. To assess the influence of stability on these wind characteristics, we utilize a unique data set including observations from two meteorological towers, a surface flux tower and high‐resolution remote‐sensing sound detection and ranging (SODAR) instrument. We compare several approaches to defining atmospheric stability to the Obukhov length (L). Typical wind farm observations only allow for the calculation of a wind shear exponent (α) or horizontal turbulence intensity (I_U) from cup anemometers, whereas SODAR gives measurements at multiple heights in the rotor disk of turbulence intensity (I) in the latitudinal (I_u), longitudinal (I_v) and vertical (I_w) directions and turbulence kinetic energy (TKE). Two methods for calculating horizontal Ifrom SODAR data are discussed. SODAR stability parameters are in high agreement with the more physically robust L,with TKE exhibiting the best agreement, and show promise for accurate characterizations of stability. Vertical profiles of wind speed and turbulence, which likely affect turbine power performance, are highly correlated with stability regime. At this wind farm, disregarding stability leads to over‐assessments of the wind resource during convective conditions and under‐assessments during stable conditions. Copyright © 2011 John Wiley & Sons, Ltd.     

Thermal transport phenomena of turbulent jet diffusion flames by means of anisotropic k–ϵ–t2–ϵt model

A numerical study is performed on transport phenomena in a turbulent jet diffusion flame of hydrogen from a vertical circular nozzle. An anisotropic k–ϵ–t² –ϵ_t model and the eddy‐dissipation model are employed to simulate thermal fluid flow and combustion phenomena, respectively. The governing boundary‐layer equations are discretized by means of a control volume finite‐difference technique and are numerically solved. The model predicts the experimental data in the existing literature. It is found from the study that (i) the model employed here can be applied to combustion phenomenon, and (ii) the presence of flame enhances the anisotropy of turbulence and causes a substantial attenuation in the turbulent kinetic energy, that is, most turbulent kinetic energy in the flame in the downstream part is laden exclusively in the streamwise fluctuation. Copyright © 1999 John Wiley & Sons, Ltd.     

Study of aerodynamical interference for a wind turbine

A two-dimensional interference model of upwind wind turbine, based on NREL Phase VI, was simulated by an available Navier–Stokes solver under parallel process. The simulation domain was divided into a stationary tower domain and a sliding blade domain with varying geometric factors, including blade chord to tower diameter ratio and tower-blade gap to tower diameter ratio, to figure out the unsteady problem. The turbulence model was treated with SST k–ω turbulence model and the boundary layers around the solid walls were refined by the y⁺ value. The simulated results of velocity field were compared with the potential cylinder flow, and some phenomena were exhibited, including the movement of stagnation point of tower, the skewed wake of tower and the excess of velocity in the field. The lift force coefficient of blade was different from the ideal angle of attack for the blade passing in front of the potential cylinder flow.     

Blade‐resolved simulations of a model wind turbine: effect of temporal convergence

Simulations of a model wind turbine at various tip‐speed‐ratios were carried out using Tenasi, a node‐centered, finite volume unstructured flow solver. The simulations included the tunnel walls, tower, nacelle, hub and the blades. The effect of temporal convergence on the predicted thrust and power coefficients is evaluated and guidelines for best practices are established. The results presented here are for tip‐speed‐ratios of 3, 6 and 10, with 6 being the design point. All simulations were carried out at a freestream velocity of 10 m s^?1 with an incoming boundary layer present and the wind turbine RPM was varied to achieve the desired tip‐speed‐ratio. The performance of three turbulence models is evaluated. The models include a one‐equation model (Spalart–Allmaras), a two‐equation model (Menter SST) and the DES version of the Menter SST. Turbine performance as well as wake data at various locations is compared to experiment. All the turbulence models performed well in terms of predicting power and thrust coefficients. The DES model was significantly better than the other two turbulence models for predicting the mean and fluctuating components of the velocity in the wake. Copyright © 2015 John Wiley & Sons, Ltd.     

A new k‐epsilon model consistent with Monin–Obukhov similarity theory

A new k‐? model is introduced that is consistent with Monin–Obukhov similarity theory (MOST). The proposed k‐? model is compared with another k‐? model that was developed in an attempt to maintain inlet profiles compatible with MOST. It is shown that the previous k‐? model is not consistent with MOST for unstable conditions, while the proposed k‐? model can maintain MOST inlet profiles over distances of 50km. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical investigation of airflow through a Savonius rotor

The aim of this report is to present a model of a rigid‐rotor system based on computational fluid dynamics (CFD), which is applied on a vertical axis wind turbine (VAWT) research. Its originality results from the use of the average value of the variable rotational speed method taken in a periodic steady‐state (PSS) of the VAWT rotor instead of the classical fixed rotational speed method. This approach was chosen in order to determine the mechanical and aerodynamic parameters of the wind turbine. The modeling method uses an implicit Euler iterative solution strategy, which resolves the coupling between fixed and moving rotor domains. The main methods that were adopted are based on the three‐dimensional modeling of the interaction of the fluid flow with a rigid‐rotor. The strategy consists of using the Reynolds averaged Navier Stokes (RANS) equations with the standard k‐ ? and SST k‐ ω models to solve the fluid flow problem. To perform the rigid‐rotor motion in a fluid, the one degree of freedom (1‐DOF) method was applied. In the present study, the steady‐state and dynamic CFD simulations of the Savonius rotor are adopted to contribute to the validation elements of the VAWT models that are used. The dynamic study allows the investigation of the rotor behavior and the relation between velocity, pressure, and vorticity fields in and around the rotor blades. The flow fields generated by the rotation of the Savonius rotor were investigated in the half revolution period of the rotor angle θ from 0° to 180°. In this range of θ, the focus is on generating and dissipating vortices. Copyright © 2013 John Wiley & Sons, Ltd.     

A study on the prediction of aerofoil trailing‐edge noise for wind‐turbine applications

This paper presents a comparative study between the so‐called BPM and TNO models for the prediction of aerofoil trailing‐edge noise with particular emphasis on wind‐turbine applications (the BPM model is named after Brooks, Pope and Marcolini who first proposed the model, and the TNO model is named after the TNO institute of Applied Physics where it was first proposed). In this work, two enhanced versions of the BPM model are proposed, and their performances are compared against two recent anisotropic TNO models that require more detailed boundary‐layer information than the BPM‐based models. The two current enhanced models are denoted as BPMM‐PVII and BPMM‐BLkω, where the former uses a panel method with viscous‐inviscid interaction implemented (PVII) for boundary‐layer calculations, the latter estimates the boundary‐layer (BL) properties using a two‐dimensional k‐ω turbulence model (kω), and BPMM stands for BPM‐Modified. By comparing the predicted sound spectra with existing measurement data for seven different aerofoils tested in the current study, it is shown that the BPMM‐PVII model exhibits superior results to those by the other models for most cases despite the simplicity without considering anisotropy. The BPMM‐PVII model is then combined with Prandtl's nonlinear lifting‐line theory to calculate and investigate three‐dimensional rotor noise characteristics of an NREL UAE Phase‐VI wind turbine (NREL UAE stand for the National Renewable Energy Laboratory Unsteady Aerodynamic Experiment). It is demonstrated that the current approach may provide an efficient solution for the prediction of rotor aerodynamics and noise facilitating industrial design and development for low‐noise wind turbines. Copyright © 2016 John Wiley & Sons, Ltd.     

The k‐ε‐fP model applied to double wind turbine wakes using different actuator disk force methods

The newly developed k‐ε‐f_P eddy viscosity model is applied to double wind turbine wake configurations in a neutral atmospheric boundary layer, using a Reynolds‐Averaged Navier–Stokes solver. The wind turbines are represented by actuator disks. A proposed variable actuator disk force method is employed to estimate the power production of the interacting wind turbines, and the results are compared with two existing methods: a method based on tabulated airfoil data and a method based on the axial induction from 1D momentum theory. The proposed method calculates the correct power, while the other two methods overpredict it. The results of the k‐ε‐f_P eddy viscosity model are also compared with the original k‐ε eddy viscosity model and large‐eddy simulations. Compared to the large‐eddy simulations‐predicted velocity and power deficits, the k‐ε‐f_P is superior to the original k‐ε model. Copyright © 2014 John Wiley & Sons, Ltd.     

Computational Fluid Dynamics model of stratified atmospheric boundary‐layer flow

For wind resource assessment, the wind industry is increasingly relying on computational fluid dynamics models of the neutrally stratified surface‐layer. So far, physical processes that are important to the whole atmospheric boundary‐layer, such as the Coriolis effect, buoyancy forces and heat transport, are mostly ignored. In order to decrease the uncertainty of wind resource assessment, the present work focuses on atmospheric flows that include stability and Coriolis effects. The influence of these effects on the whole atmospheric boundary‐layer are examined using a Reynolds‐averaged Navier–Stokes k‐ ε model. To validate the model implementations, results are compared against measurements from several large‐scale field campaigns, wind tunnel experiments, and previous simulations and are shown to significantly improve the predictions. Copyright © 2013 John Wiley & Sons, Ltd.     

Evaluation of the effects of turbulence model enhancements on wind turbine wake predictions

The modelling of wind turbine wakes is investigated in this paper using a Navier–Stokes solver employing the k–ω turbulence model appropriately modified for atmospheric flows. It is common knowledge that even single‐wind turbine wake predictions with computational fluid dynamic methods underestimate the near wake deficit, directly contributing to the overestimation of the power of the downstream turbines. For a single‐wind turbine, alternative modelling enhancements under neutral and stable atmospheric conditions are tested in this paper to account for and eventually correct the turbulence overestimation that is responsible for the faster flow recovery that appears in the numerical predictions. Their effect on the power predictions is evaluated with comparison with existing wake measurements. A second issue addressed in this paper concerns multi‐wake predictions in wind farms, where the estimation of the reference wind speed that is required for the thrust calculation of a turbine located in the wake(s) of other turbines is not obvious. This is overcome by utilizing an induction factor‐based concept: According to it, the definition of the induction factor and its relationship with the thrust coefficient are employed to provide an average wind speed value across the rotor disk for the estimation of the axial force. Application is made on the case of five wind turbines in a row. Copyright © 2010 John Wiley & Sons, Ltd.     

Laminar‐turbulent flow simulation for wind turbine profiles using the γ– transition model

The accurate prediction of the laminar‐turbulence transition process is fundamental in predicting the aerodynamic performance of wind turbine profiles. Fully turbulent flow simulations have been shown to over‐predict the aerodynamic performance and thereby negatively impacting the design of airfoils in flow regimes where the possible presence of laminar flow could be exploited to improve the performance of wind turbine rotors. Correlation‐based transition modelling offers a fully computational fluid dynamics compatible approach, where the model integrates completely with the existing turbulence model, allows for the prediction of various transition mechanisms, is applicable to three‐dimensional flows and compatible to adjoint‐based design optimization frameworks. The present paper addresses several modifications necessary for a robust transition model and investigates the accuracy of the model for a wide range of angles of attack and Reynolds numbers, which are necessary for a thorough validation of the correlation‐based transition model for wind turbine profiles. The transition model was employed to predict the transition locations; and an assessment of the various transition mechanisms, Reynolds number effects, sectional characteristics and aerodynamic performance for the NLF(1)‐0416 and S809 airfoils is presented with comparisons to experimental data and numerical solutions. Copyright © 2013 John Wiley & Sons, Ltd.     

Parabolic RANS solver for low‐computational‐cost simulations of wind turbine wakes

A numerical framework for simulations of wake interactions associated with a wind turbine column is presented. A Reynolds‐averaged Navier‐Stokes (RANS) solver is developed for axisymmetric wake flows using parabolic and boundary‐layer approximations to reduce computational cost while capturing the essential wake physics. Turbulence effects on downstream evolution of the time‐averaged wake velocity field are taken into account through Boussinesq hypothesis and a mixing length model, which is only a function of the streamwise location. The calibration of the turbulence closure model is performed through wake turbulence statistics obtained from large‐eddy simulations of wind turbine wakes. This strategy ensures capturing the proper wake mixing level for a given incoming turbulence and turbine operating condition and, thus, accurately estimating the wake velocity field. The power capture from turbines is mimicked as a forcing in the RANS equations through the actuator disk model with rotation. The RANS simulations of the wake velocity field associated with an isolated 5‐MW NREL wind turbine operating with different tip speed ratios and turbulence intensity of the incoming wind agree well with the analogous velocity data obtained through high‐fidelity large‐eddy simulations. Furthermore, different cases of columns of wind turbines operating with different tip speed ratios and downstream spacing are also simulated with great accuracy. Therefore, the proposed RANS solver is a powerful tool for simulations of wind turbine wakes tailored for optimization problems, where a good trade‐off between accuracy and low‐computational cost is desirable.     

Wind turbine CFD modeling using a correlation-based transitional model

This paper describes the development of a Horizontal Axis Wind Turbine 3D CFD model using the Ansys Fluent solver. The model was developed to predict wind turbine performance and evaluate the capabilities of the 1D model (based on BEM Theory) developed by the authors. The two models were compared in terms of accuracy, predictability and calculation time.The strategy of generating a high quality mesh and optimizing the turbulence models (two equations SST k–ω fully turbulent and four equations Transitional SST models) is presented. In particular, a high quality unstructured 3D grid was generated to optimize spatial discretization and meet turbulence model requirements. The mesh was subsequently converted from a tetrahedral into a polyhedral geometry to considerably reduce the number of cells and better align the cell faces and flow. Polyhedral cells also reduce interpolation errors and false numerical diffusion. The empirical correlations of the Transitional SST turbulence model were modified to improve it for wind turbine applications. A significant number of numerical 2D airfoil tests were implemented to calibrate the turbulence model. The results of these tests were applied to the turbulence model by modifying the local correlation parameters. The same parameters were used in the 3D wind turbine model. A Moving Reference Frame model was used to simulate rotation and evaluate 3D flow along the rotor blades.The numerical results were compared to the fully turbulent SST k–ω simulation data to demonstrate the superior capabilities of the modified Transitional model.The 3D CFD model was validated using NREL PHASE VI experimental data available from scientific literature.An application of the 3D model to a new micro wind turbine is presented at the end of this paper. The micro rotor was designed and optimized using the 1D code and actually built.     

Modelling of stratified gas–liquid two-phase flow in horizontal circular pipes

This paper reports numerical and experimental investigation of stratified gas–liquid two-phase flow in horizontal circular pipes. The Reynolds averaged Navier–Stokes equations (RANS) with the k–ω turbulence model for a fully developed stratified gas–liquid two-phase flow are solved by using the finite element method. A smooth interface surface is assumed without considering the effects of the interfacial waves. The continuity of the shear stress across the interface is enforced with the continuity of the velocity being automatically satisfied by the variational formulation. For each given interface position and longitudinal pressure gradient, an inner iteration loop runs to solve the non-linear equations. The Newton–Raphson scheme is used to solve the transcendental equations by an outer iteration to determine the interface position and pressure gradient for a given pair of volumetric flow rates. Favorable comparison of the numerical results with available experimental results indicates that the k–ω model can be applied for the numerical simulation of stratified gas–liquid two-phase flow.     

Evaluation of Turbulence Models in the Prediction of Heat Transfer Due to Slot Jet Impingement on Plane and Concave Surfaces

The performance of several turbulence models in the prediction of convective heat transfer due to slot jet impingement onto flat and concave cylindrical surfaces is evaluated against available experimental data. The candidate models for evaluation are (1) the standard k – ε model, (2) the RNG k – ε model, (3) the realizable k – ε model, (4) the SST k – ω model, and (5) the LRR Reynolds stress transport model. Various near-wall treatments such as equilibrium wall function and two-layer enhanced wall treatment are used in combination with these turbulence models. The computations are performed using the commercial computational fluid dynamics (CFD) code Fluent. From the validation exercises, it is found that when the impingement surface is outside the potential core of the jet, most of the turbulence models predict reasonably accurate thermal data (local Nusselt number variation along the impingement surface). When the impingement surface is within the potential core of the jet, the turbulence models grossly overpredict the Nusselt number in the impingement region, but in the wall jet region the Nusselt number prediction is fairly accurate. Overall, the RNG k – ε model with the enhanced wall treatment and the SST k – ω model predict the Nusselt number distribution better than the other models for the flat plate as well as for the concave surface impingement cases. However, the hydrodynamic data such as the mean velocity profiles are not accurately predicted by the SST k – ω model for the concave surface impingement case, whereas the RNG k – ε model predictions of the velocity profiles agree very well with the experiment. The Reynolds stress model does not show any distinctive advantage over the other eddy viscosity models.