Actuator Disk Model Research Articles

Comparing and validating intra-farm and farm-to-farm wakes across different mesoscale and high-resolution wake models

Abstract. Numerical wind resource modelling across scales from the mesoscale to the turbine scale is of increasing interest due to the expansion of offshore wind energy. Offshore wind farm wakes can last several tens of kilometres downstream and thus affect the wind resources of a large area. So far, scale-specific models have been developed but it remains unclear how well the different model types can represent intra-farm wakes, farm-to-farm wakes as well as the wake recovery behind a farm. Thus, in the present analysis the simulation of a set of wind farm models of different complexity, fidelity, scale and computational costs are compared among each other and with SCADA data. In particular, two mesoscale wind farm parameterizations implemented in the mesoscale Weather Research and Forecasting model (WRF), the Explicit Wake Parameterization (EWP) and the Wind Farm Parameterization (FIT), two different high-resolution RANS simulations using PyWakeEllipSys equipped with an actuator disk model, and three rapid engineering wake models from the PyWake suite are selected. The models are applied to the Nysted and Rødsand II wind farms, which are located in the Fehmarn Belt in the Baltic Sea. Based on the performed simulations, we can conclude that both WRF + FIT (BIAS = 0.52 m s−1) and WRF + EWP (BIAS = 0.73 m s−1) compare well with wind farm affected mast measurements. Compared with the RANS simulations, baseline intra-farm variability, i.e. the wind speed deficit in between turbines, can be captured reasonably well with WRF + FIT using a resolution of 2 km, a typical resolution of mesoscale models for wind energy applications, while WRF + EWP underestimates wind speed deficits. However, both parameterizations can be used to estimate median wind resource reduction caused by an upstream farm. All considered engineering wake models from the PyWake suite simulate peak intra-farm wakes comparable to the high fidelity RANS simulations. However, they considerably underestimate the farm wake effect of an upstream farm although with different magnitudes. Overall, the higher computational costs of PyWakeEllipSys and WRF compared with those of PyWake pay off in terms of accuracy for situations when farm-to-farm wakes are important.

A wall-modeled approach accounting for wave stress in Large Eddy Simulations of offshore wind farms

In the context of offshore wind farms, accurate predictions of surface fluxes in the marine atmospheric boundary layer are critical for Large Eddy Simulations (LES) of airflow over waves. The effect of the waves on the airflow is often modeled by prescribing the roughness length in the framework of Monin-Obukhov similarity theory. However, such approaches lack generalizability over different wave conditions due to reliance on model coefficients tuned to specific datasets. Wave phase-resolving simulations on the other hand have higher accuracy but also a higher computational cost. In this work, a sea surface-based hydrodynamic drag model is applied to model the pressure-based surface drag felt by the wind due to the waves. An offshore wind farm configuration is simulated using a wall-modeled LES, with the effect of the waves represented using the wave-drag model and the wind turbines represented by an actuator disk model. The approach is validated with data from high fidelity wave-resolving Large Eddy Simulations. The effect of the waves and the farm configuration on the mean velocity profiles power production, and kinetic energy budget are quantified.

Ground effect for ducted wind turbines: A computational study

Ducted wind turbines (DWTs) can take the advantage of ground effect (GE) when installed close to urban areas. To this aim, a parametric study to investigate the aerodynamic performance of DWTs in relation to three different ground distances are investigated. The flow around a commercial DWT model using a simplified duct actuator disc (AD) model based on Reynolds Averaged Navier-Stokes (RANS) equations is performed. The results indicate that DWTs placed close to the ground will lead to increased mass flow rate the turbine plane, and thereby improving the aerodynamic performance. However, the additional ground force leads to an asymmetric flow-field at the turbine plane, which will ultimately induce unsteady forces on the DWT system. The present analysis will serve as a strong recommendation to address siting issues for DWT manufacturers.

The influence of rotor downwash on spray distribution under a quadrotor unmanned aerial system

• Computational Fluid Dynamics model of sprays interaction with propeller airflow. • CFD model for multi nozzle/propeller crop sprayer, crosswind and forward flight. • Experimental validation of CFD model using a spray pattonator. • CFD model can be used to model the distribution of the spray’s impact with the crop. • Modelled distributions can be used for spray mission planners. • Spray distribution heavily effected by propeller downwash. • Higher propeller thrust leads to a peakier and less uniform distribution. This paper investigates how sprays are influenced by rotor downwash produced by a quadrotor Unmanned Aerial System when crop spraying. Computational Fluid Dynamics simulations, using RANS modelling for the flow field and Lagrangian particle tracking for the spray, are conducted for several single-rotor and multi-rotor cases with the spray injected underneath the centre of the rotor. The rotor is modelled using a Blade Element actuator disc model. The accuracy of the computational approach is demonstrated by good agreement with experiment for both thrust and deposited spray pattern for a single rotor in an indoor environment. Both the experimental and computational results show that the peak in the spray distribution under a single rotor increases as rotor thrust increases, whilst increasing the rotor height above the ground causes this peak to decrease. The validated Computational Fluid Dynamics method is then used to simulate flight conditions for single-rotor and multi-rotor cases. These show the existence of a critical flight speed, above which the spray impinging on the ground no longer contains a notable peak. This behaviour is seen to be due to the streamtube detaching from the ground and no longer carrying the spray directly to the ground plane. Above this critical speed the spray is seen to become suspended in the air behind the Unmanned Aerial System. This behaviour makes realistic simulation more difficult, as details of the ambient turbulence conditions would be needed to model the subsequent spray transport. The reliance on turbulence to transport the spray is undesirable from a practical point of view due to the increased likelihood of significant spray drift.

Handling Individual Pitch Control within an Actuator Disk framework: verification against the Actuator Line method and application to wake interaction problems

The present study aims at assessing the Actuator Disk (AD) method supplemented with an Individual Pitch Control (IPC) strategy, at a resolution appropriate for the Large Eddy Simulation of large wind farms. The IPC scheme is based on a state-of-the art individual pitch control, generalized to be applied to an AD approach. This procedure also requires an accurate recovery of the flapwise bending moment on each blade, which is not trivial for a disk-type model. In order to compute flapwise moments on each blade, blade trajectories are reproduced through the disk and the AD aerodynamic forces are interpolated onto these virtual blades at each time step. We verify the AD model with IPC in simulations of an isolated wind turbine, for different wind speeds and turbulence intensities, and in a configuration with two rotors. We compare the AD statistics with those obtained using an Actuator Line (AL) method. The comparison done in terms of equivalent moment shows that the AD and AL simulations produce very similar results.

Effects of the Parameter C4ε in the Extended k-ε Turbulence Model for Wind Farm Wake Simulation Using an Actuator Disc

The actuator disc model (ADM) incorporated into the k-ε turbulence model of EI Kasmi is able to simulate the wind farm wakes with high fidelity, which is essential for layout optimization and the evaluation of power production in modern wind farms. However, the effects of the parameter C4ε in the k-ε model of EI Kasmi on turbulent kinetic energy (TKE) in the superposition areas and the recovery of wind farm wake velocity have rarely been studied. To this end, the k-ε model of EI Kasmi is coupled with the advanced ADM in PHOENICS to investigate the influence of the parameter C4ε on the wake simulation of wind farms (e.g., two offshore wind farms, one onshore wind farm). It is concluded that a decreased parameter C4ε makes the generation range of TKE in the vicinity of the rotor smaller, but the TKE near the rotor becomes larger, and the wake recovery rate of the downstream turbine is less affected by the near wake. As the interwind turbine spacing increases, the influence area of TKE in the wake region of each downstream machine gradually reduces, and atmospheric turbulence plays a dominant role in wake recovery. A decreased parameter C4ε can effectively promote the inflow wind velocity and power output of downstream turbines. The power output simulated compares well with the measured power value when the parameter C4ε = 0.15.

Pseudo-2D RANS: A LiDAR-driven mid-fidelity model for simulations of wind farm flows

Next-generation models of wind farm flows are increasingly needed to assist the design, operation, and performance diagnostic of modern wind power plants. Accuracy in the descriptions of the wind farm aerodynamics, including the effects of atmospheric stability, coalescing wakes, and the pressure field induced by the turbine rotors are necessary attributes for such tools as well as low computational costs. The Pseudo-2D RANS model is formulated to provide an efficient solution of the Navier–Stokes equations governing wind-farm flows installed in flat terrain and offshore. The turbulence closure and actuator disk model are calibrated based on wind light detection and ranging measurements of wind turbine wakes collected under different operative and atmospheric conditions. A shallow-water formulation is implemented to achieve a converged solution for the velocity and pressure fields across a farm with computational costs comparable to those of mid-fidelity engineering wake models. The theoretical foundations and numerical scheme of the Pseudo-2D RANS model are provided, together with a detailed description of the verification and validation processes. The model is assessed against a large dataset of power production for an onshore wind farm located in North Texas showing a normalized mean absolute error of 5.6% on the 10-min-averaged active power and 3% on the clustered wind farm efficiency, which represent 8% and 24%, respectively, improvements with respect to the best-performing engineering wake model tested in this work.

CFD-based hydrodynamic analyses of ship course keeping control and turning performance in irregular waves

Ship manoeuvrability studies are usually carried out in calm and regular seas; however, an irregular sea state can better present the real operational conditions at sea, compared to both calm and regular seas. In this study, the manoeuvrability of a well-known benchmarking ship in an irregular sea state was investigated using a fully nonlinear unsteady RANS model. The JONSWAP spectrum was used to generate long-crested irregular seas with a significant wave height of 5m and a peak period of 12.4s in full scale, representing sea state 6. Comparisons with the ship manoeuvrability in both calm and regular seas were also made with a view to identifying the changes in the manoeuvring characteristics of the ship. The generated regular waves were characterised by the height and period equivalent to the average height and period of the irregular waves applied in this work. The ship is equipped with a single propeller with a semi-balanced horn rudder, and the propeller is simulated by an actuator disk model based on the body force method. In analysing the correlations between the ship manoeuvrability and the irregular waves, the findings of this study have demonstrated that the irregular waves may cause substantial changes in the course keeping capability and turning performance when compared to the inherent manoeuvring qualities in calm water. It is expected that the results of this work can provide a deeper insight into ship manoeuvrability in irregular waves as well as help masters and navigation officers in decision-making for ship handling actions in real sea states.

Predictive capability of actuator disk models for wakes of different wind turbine designs

To evaluate the predictive capability of the actuator disk (AD) models in simulating wakes of different wind turbine designs, we compare the results of the AD simulation with those of the actuator surface (AS) simulation for the EOLOS, NREL and a variant of the NREL (i.e., NREL-V) wind turbine designs. Two types of AD models are considered, i.e., the AD-R and AD-NR models corresponding to the AD model with and without rotational effects, respectively. For the AD models, the force coefficients are both obtained from the corresponding AS simulations. The results from the AD simulation are compared with those of AS simulations. It is observed that the velocity profiles predicted by the AD models agree well with the AS predictions. For the turbulent kinetic energy and the Reynolds shear stress, differences appear at far wake locations (7D, and 9D downwind of the turbine where D is the rotor diameter) for both the EOLOS and the NREL-V turbines. In case of the NREL turbine, on the other hand, there is an overall good agreement except in 3D downwind to the turbine. Furthermore, the modes obtained by using the proper orthogonal decomposition from the AD and AS simulations are also presented and compared with each other, indicating that the distribution of the mode energy, and the location and features of the mode patterns differ for different turbine designs.

Blade-Resolved CFD Simulations of a Periodic Array of NREL 5 MW Rotors with and without Towers

A fully resolved (FR) NREL 5 MW turbine model is employed in two unsteady Reynolds-averaged Navier–Stokes (URANS) simulations (one with and one without the turbine tower) of a periodic atmospheric boundary layer (ABL) to study the performance of an infinitely large wind farm. The results show that the power reduction due to the tower drag is about 5% under the assumption that the driving force of the ABL is unchanged. Two additional simulations using an actuator disc (AD) model are also conducted. The AD and FR results show nearly identical tower-induced reductions of the wind speed above the wind farm, supporting the argument that the AD model is sufficient to predict the wind farm blockage effect. We also investigate the feasibility of performing delayed-detached-eddy simulations (DDES) using the same FR turbine model and periodic domain setup. The results show complex turbulent flow characteristics within the farm, such as the interaction of large-scale hairpin-like vortices with smaller-scale blade-tip vortices. The computational cost of the DDES required for a given number of rotor revolutions is found to be similar to the corresponding URANS simulation, but the sampling period required to obtain meaningful time-averaged results seems much longer due to the existence of long-timescale fluctuations.

Computational study of combined effects of tip leakage jets and wetness on the performance of steam turbine exhaust system using actuator disc model

A numerical model to study the individual and combined effects of the tip clearance jets and the presence of wetness on the performance of the steam turbine exhaust hood has been developed. The Eulerian-Eulerian wet steam flow equations along with mass, momentum, energy, and k- ε model equations are solved in the present study. An increase in inlet wetness level improves the pressure recovery capacity of the steam turbine exhaust hood by reducing the total pressure loss. The presence of moisture causes a turbulence attenuation which in turn reduces the vortex strength. The combined effect of the tip leakage jets and the presence of inlet wetness improve the performance of the exhaust system further. However, the presence of a non-uniform condenser pressure gradient caused by the temperature variation of the cooling water flow increases the level of complexity of the flow in the exhaust system deteriorating the performance.

Computational study of combined effects of tip leakage jets and wetness on the performance of steam turbine exhaust system using actuator disc model

Computational study of combined effects of tip leakage jets and wetness on the performance of steam turbine exhaust system using actuator disc model

풍력터빈의 후류 우회를 위한 요각도 분석

The wake deficit from wind turbines is a major factor in reducing the performance of wind farms. Numerous studies have been performed on yaw angle control for the wind turbine rotor to mitigate the wake effect. It is necessary to establish a physical understanding of wake deflection and deformation at various yaw angles. In the present study, the turbine wake development at various yaw angles(-30° ~ 30°) and inflow wind speeds(7 ~ 9m/s) were analyzed via Large-Eddy Simulation coupled with Actuator Disk Model. Simulations were performed under uniform inflow conditions with the NREL 5MW wind turbine model placed at the center. The center, width, and shape of wake deficit profiles were calculated based on the velocity field and the vorticity of the wake. It shows that as the wake center deflection did not increase linearly with the yaw angle, and the slope of the wake deflection varied from the starting point to the end. In addition, the asymmetry of the wake distributions was analyzed based on the vorticity field which evolved into a kidney-shaped wake profile. Lastly, it was found that the wake deficit distribution held a self-similarity profile for the given range of uniform inflows.

Towards multi-fidelity simulation of flows around an underwater vehicle with appendages and propeller

Flow around a real-life underwater vehicle often happens at a high Reynolds number with flow structures at different scales from the boundary layer around a blade to that around the hull. This poses a great challenge for large-eddy simulation of an underwater vehicle aiming at resolving all relevant flow scales. In this work, we propose to model the hull with appendages using the immersed boundary method, and model the propeller using the actuator disk model without resolving the geometry of the blade. The proposed method is then applied to simulate the flow around Defense Advanced Research Projects Agency (DARPA) suboff. An overall acceptable agreement is obtained for the pressure and friction coefficients. Complex flow features are observed in the near wake of suboff. In the far wake, the core region is featured by a jet because of the actuator disk, surrounded by an annular region with velocity deficit due to the body of suboff.

How far the wake of a wind farm can persist for?

With the increased penetration of wind energy in our nation’s energy portfolio, wind farms are placed in a way close to each other. Thus, their wakes have to be fully considered in the design and operation of a wind farm. In this study, we investigate the wake of a wind farm using large-eddy simulation with wind turbine rotor modelled by the actuator disk model. The simulated results show that the wake of a wind farm can persist for a long distance in its downstream. For the considered wind farm layout, the velocity in the wake recovers 95% of that of the undisturbed inflow at 55 rotor diameters downstream from its last row, suggesting that the wake of a wind farm should be fully considered in the optimal design and operation for its downstream wind farms.

Double-Ducted Fan as an Effective Lip Separation Control Concept for Vertical-Takeoff-and-Landing Vehicles

This paper describes a novel inlet flow conditioning concept that significantly improves ducted fans’ performance and controllability. High angle-of-attack operation of ducted fans is very common in vertical-takeoff-and-landing systems. The new concept named double-ducted fan (DDF) uses a secondary shroud to control inlet lip-separation-related momentum deficit at the inlet of the fan rotor during edgewise flight. The DDF is helpful in a wide edgewise flight velocity range, and its corrective aerodynamic effect becomes more pronounced with increasing flight velocity. A conventional baseline duct operating at 90 deg angle of attack is compared to other novel double-ducted fan designs via three-dimensional, viscous, and turbulent flow computations. A custom actuator-disk model replaces the zonal computation of the complex and three-dimensional rotor flowfield in the rotating frame of reference. Both hover and edgewise flight conditions are considered around the ducted fan unit and inside the ducts. Significant improvements from several novel ducted fan designs are in the areas of vertical thrust enhancement, nose-up pitching moment reduction, and recovery of fan through-flow mass flow rate in a wide horizontal flight range. A variable DDF design, a partial DDF design, and a fan-in-wing implementation of the DDF are introduced.

Study on the operation of small rooftop wind turbines and its effect on the wind environment in blocks

Rooftop wind turbine is a typical utilization form of urban wind power. However, knowledge gaps still exist in the understanding on the wind resources of an urban district, the operation of small rooftop turbines and its effect on the block wind environment. To add new knowledge on this subject, the operation of rooftop wind turbines in an urban district is numerically studied via large-eddy simulation. The turbines are modeled by the actuator disk model and the urban district is represented by 16 idealized cube-shaped buildings. We find that flow above the urban district shows an obvious speedup due to the crowding-out effect of the urban district, and the turbulence intensity is dramatically enhanced. Above the first two rows of buildings, flow adjusts intensely and quickly evolves to a quasi-fully developed regime downstream. Due to the flow characteristics above the rooftop, the relative power increment of the rooftop turbines increases first and then decreases with the hub height, the power and the load fluctuations of the turbines are significantly aggrandized near the rooftop and diminished far away from the rooftop. For the small turbines investigated in this study, the impacts of small rooftop turbines on the wind environment are almost negligible in the blocks.

Numerical investigation of wind turbine wakes under high thrust coefficient

AbstractWe study wind turbine wakes of rotors operating at high thrust coefficients (CT > 24/25) using large‐eddy simulations with a rotating actuator disk model. Wind turbine wakes at high thrust coefficients are different from wakes at low thrust coefficients. Wakes behave differently at high thrust, with increased turbulence and faster recovery. Lower induction in the wake is achieved because wakes in high‐thrust conditions recover much faster than in normal operating conditions. This enhanced recovery is possible thanks to the turbulence generated in the near wake. We explore the mechanism behind this behavior and propose a simple model to reproduce it. We also propose a Gaussian fit for the wakes under high‐thrust conditions and use it use it to initialize an Ainslie type model within the FAST.Farm framework.

Definition and Validation of Cavitating Rocket Turbopump Transmission Matrices for Modular Multi Actuator Disk Approach

Abstract Cavitation-induced instabilities are a critical issue to face in the design process of rocket turbopumps, and reduced-order linear methods still represent a powerful tool to evaluate their onset. The modular multi-actuator disk approach is a successful method developed to study the dynamic behavior of compressors. Recently, it has also been proposed for the assessment of the dynamics of cavitating turbopumps. In this paper, the modular multiactuator disk approach was used as the mathematical framework to implement and validate a well-established model of a cavitating inducer developed in the 90 s for the assessment of azimuthal instabilities with a particular focus on rotating cavitation. The matching between the obtained results and the available data in the open literature for a tapered inducer validated the dynamic model of the cavitating inducer implemented in the new mathematical framework. The flexibility introduced by the new modular approach represents a step toward the study of complex hydrodynamic systems that are not limited to the simplified configuration studied by the actuator disk model proposed in the 1990s.

Maximal power per device area of a ducted turbine

Abstract. The aerodynamic design of a ducted wind turbine for maximum total power coefficient was studied numerically using the axisymmetric Reynolds-averaged Navier–Stokes equations and an actuator disc model. The total power coefficient characterizes the rotor power per total device area rather than the rotor area. This is a useful metric to compare the performance of a ducted wind turbine with an open rotor and can be an important design objective in certain applications. The design variables included the duct length, the rotor thrust coefficient, the angle of attack of the duct cross section, the rotor gap, and the axial location of the rotor. The results indicated that there exists an upper limit for the total power coefficient of ducted wind turbines. Using an Eppler E423 airfoil as the duct cross section, an optimal total power coefficient of 0.70 was achieved at a duct length of about 15 % of the rotor diameter. The optimal thrust coefficient was approximately 0.9, independent of the duct length and in agreement with the axial momentum analysis. Similarly independent of duct length, the optimal normal rotor gap was found to be approximately the duct boundary layer thickness at the rotor. The optimal axial position of the rotor was near the rear of the duct but moved upstream with increasing duct length, while the optimal angle of attack of the duct cross section decreased.