Three-dimensional Wake Research Articles

High-fidelity simulations of microramp-controlled shock wave/boundary layer interaction

Microvortex generators (MVGs) are a promising solution to control shock wave/turbulent boundary layer interactions (SBLIs), especially in supersonic inlets. In this study, we examine the effects of a microramp vortex generator on an SBLI generated by an oblique shock wave and a turbulent boundary layer using direct numerical simulations (DNSs). Two cases, with and without the presence of a microramp, are compared in terms of their mean and unsteady flow features at free-stream Mach number equal to 2 and friction Reynolds number at the inviscid shock impingement equal to 600. The long integration period allows us to assess how microramps affect the typical low-frequency unsteadiness observed in SBLIs, and the data generated may serve as a reference for simulations of lower fidelity or reduced order models. The analysis shows that the three-dimensional microramp wake alters the interaction region dramatically, inducing a significant spanwise modulation and topology change of the separation. For example, tornado-like structures redistribute the flow in both the spanwise and wall-normal directions inside the recirculation region. The increase in momentum close to the wall by the ramp vortices effectively delays the onset of the separation and, thus, the separation length, but at the same time leads to a significant increase in the intensity of the wall-pressure fluctuations. We then characterise the mutual interaction between the arch-like vortices around the ramp wake and the SBLI. The specific spanwise vorticity shows that these vortices follow the edge of the separation and their intensity, apart from mean compressibility effects, is not affected by the shocks. The shocks, instead, are deformed in shape by the periodic impingement of the vortices, although the spectral analysis did not reveal any significant trace of their shedding frequency in the separation region. These Kelvin–Helmholtz vortices, however, may be relevant in the closure of the separation bubble. Fourier analysis also shows a constant increase, in both value and magnitude, in the low-frequency peak all along the span, suggesting that the motion of the separation shock remains coherent while being disturbed by the arch-like vortices and oscillating at a higher frequency in absolute terms.

Influence of thermal buoyancy on the wake dynamics of a heated square cylinder

Direct numerical simulation of the three-dimensional (3-D) wake transition of a heated square cylinder subjected to horizontal cross-flow is performed in the presence of buoyancy. In order to capture the effects of large-scale heating, a non-Oberbeck–Boussinesq model is utilized, which includes the governing equations for compressible gas flow. All computations are performed at low free stream Mach number $M=0.1$ using air (free stream Prandtl number, $Pr=0.71$ ) as the working fluid. The 3-D instability modes A and B, which correspond to free stream Reynolds numbers of 180 and 250, are observed with longer and shorter spanwise wavelengths, respectively, and the onset of three-dimensionality is triggered at a Reynolds number of 173. In the presence of buoyancy, baroclinic vorticity production in the near-wake plays an important role for streamwise vorticity generation. The chaotic wake of the Mode-A instability bifurcates into periodic and quasiperiodic wakes at various heating levels, expressed by the overheat ratio, $\varepsilon =(T_w-T_\infty )/T_\infty$ , where $T_w$ and $T_\infty$ are the temperature of the cylinder surface and the ambient air, respectively. At low heating ( $\varepsilon =0.2$ ), the 3-D Mode-A instability is suppressed leading to a two-dimensional wake flow. Further increase in heating, again brings back the three-dimensionality in the wake through Mode-E instability. The variation of thermophysical properties and the effective Reynolds number with increase in heating level around the cylinder is examined. It is shown that the effect of thermophysical properties competes with the baroclinic streamwise vorticity generation at higher levels of heating ( $\varepsilon \geqslant 0.4$ ) to control the 3-D modes and wake dynamics.

Development and validation of a three-dimensional wind-turbine wake model based on high-order Gaussian function

Under natural conditions, the wake velocity distribution approximates top-hat shape in the near wake center, and a Gaussian shape in the far wake. To improve the prediction accuracy of the wake distribution, this paper proposes a three-dimensional high-order Gaussian linear entrainment wake model by modifying the wake velocity distribution with high-order Gaussian function. Field tests and wind tunnel tests are then conducted. The obtained results show that the proposed model can accurately describe the radial and vertical spatial distributions of the wake flow. Under different wind speeds, the maximum and minimum radial relative errors are respectively 7.29% and 1.4%, while the maximum and minimum vertical relative errors are respectively 7.64% and 3.87%. This demonstrates that the proposed model can accurately predict the velocity distribution in the whole wake region. The proposed model is simple, has low cost, and exhibits high accuracy. Thus, it can be used in wind farm layout optimization and wake control.

Three-dimensional wake transition of rectangular cylinders and temporal prediction of flow patterns based on a machine learning algorithm

This study investigates the three-dimensional (3D) wake transition in unconfined flows over rectangular cylinders using direct numerical simulation (DNS). Two different cross-sectional aspect ratios (AR) and Reynolds numbers (Re) are scrutinized: AR = 0.5 at Re = 200 and AR = 3 at Re = 600. The investigation focuses on characterizing the flow patterns and forecasting their temporal evolution utilizing the proper orthogonal decomposition (POD) technique coupled with a long short-term memory (LSTM) network. The DNS results reveal the emergence of an ordered mode A for AR = 3, attributed to the stabilizing effect of the elongated AR. On the other hand, the case with a smaller AR (= 0.5) exhibits a mode-swapping regime characterized by modes A and B's distinct and simultaneous manifestation. The spanwise wavelengths of mode A and mode B are approximately 4.7 and 1.2 D for AR = 0.5, while the spanwise wavelength of mode A is 3.5 D for AR = 3. The POD serves as a dimensionality reduction technique, and LSTM facilitates temporal prediction. This algorithm demonstrates satisfactory performance in predicting the flow patterns, including the instabilities of modes A and B, across both transverse and spanwise directions. The employed algorithm adeptly predicts the pressure time series surrounding the cylinders. The duration for training the algorithm is only about 0.5% of the time required for DNS computations. This research, for the first time, demonstrates the effectiveness of the POD–LSTM algorithm in predicting complex 3D instantaneous wake transition patterns for flow past rectangular cylinders.

Passive control of porous media on the aerodynamic forces and wake structures of wall-mounted short circular cylinders

This paper numerically investigates the aerodynamic forces and the three-dimensional wake characteristics of wall-mounted circular cylinders with and without porous media coatings using large eddy simulation at a Reynolds number of 3.2×104. Short cylinders with aspect ratios of 0.5, 1.0, and 3.0 are considered, with one end fixed to a bottom wall in the current work. The study focuses on aerodynamic coefficients, flow characteristics, and wake structures for cylinders both with and without porous coatings. The statistical results indicate that porous media significantly alter flow patterns behind the cylinders, suppress downwash flow from the free end, and reduce velocity fluctuations and turbulent kinetic energy within the wake. The porous coating enhances the leeward side's base pressure, leading to a reduction in drag on the cylinder surface. The analysis of flow structures reveals that the topology of the arch vortex behind solid cylinders is significantly dependent on the aspect ratio, whereas this dependency is negligible for porous cylinders. Porous coatings diminish the intensity of the tip and trailing vortices behind the cylinder. Finally, based on the time-averaged flow field, we proposed two conceptual models of topological correlation for wall-mounted short cylinders, both with and without porous coatings, which contributes to describing the geometric characteristics and interactions of vortex structures.

On the absence of a secondary vortex street in three-dimensional and turbulent cylinder wakes

On the absence of a secondary vortex street in three-dimensional and turbulent cylinder wakes

Investigation of three-dimensional wake width for offshore wind turbines under complex environmental conditions by large eddy simulation

Abstract The wake of wind turbines is a main concern for offshore wind farms, in which the wake width is a key index and needs to be accurately predicted. However, the existing wake width models have shortcomings in predicting the wake of wind turbines in different offshore environments. In view of this, large eddy simulation (LES) is adopted to simulate offshore wind turbines under various environmental conditions. The analyses show that there are evident differences in wake widths between horizontal and vertical directions. The variations of turbulence intensity and wind speed in the environment have significant effects on the wake width. By fitting the simulation results, a three-dimensional (3-D) wake width model is proposed to predict the wake widths in horizontal and vertical directions, which considers the effects of lateral and vertical turbulence intensities on the wake width in different directions, and uses the thrust coefficient to reflect the effect of wind speed. The proposed 3-D model is then compared with existing models through test cases, indicating that it is more accurate in predicting wake widths in horizontal and vertical directions under different environmental conditions, meanwhile shows good applicability in complex offshore environments.

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.

Three-dimensional wake dynamics of a twisted cylinder

Three-dimensional wake dynamics of a twisted cylinder

Two- and three-dimensional wake transitions of a rectangular cylinder and resultant hydrodynamic effects

Two- and three-dimensional wake transitions of a rectangular cylinder and resultant hydrodynamic effects

Dynamics-augmented cluster-based network model

In this study we propose a novel data-driven reduced-order model for complex dynamics, including nonlinear, multi-attractor, multi-frequency and multiscale behaviours. The starting point is a fully automatable cluster-based network model (CNM) (Li et al., J. Fluid Mech., vol. 906, 2021, A21) that kinematically coarse grains the state with clusters and dynamically predicts the transitions in a network model. In the proposed dynamics-augmented CNM (dCNM) the prediction error is reduced with trajectory-based clustering using the same number of centroids. The dCNM is first exemplified for the Lorenz system and then demonstrated for the three-dimensional sphere wake featuring periodic, quasi-periodic and chaotic flow regimes. For both plants, the dCNM significantly outperforms the CNM in resolving the multi-frequency and multiscale dynamics. This increased prediction accuracy is obtained by stratification of the state space aligned with the direction of the trajectories. Thus, the dCNM has numerous potential applications to a large spectrum of shear flows, even for complex dynamics.

Effect of Induction and Blade Elasticity Modelling on Wind Turbine Rotor Performance Predictions

This study investigates the impact of blade induction modelling on the accuracy of wind turbine rotor aeroelastic predictions. It extends the capabilities of AEOLIAN (AErOeLastic sImulAtioN), a Fluid Structure Interaction (FSI) solver based on Blade Element Momentum Theory (BEMT) coupled with a Lumped Mass approach to represent the blade structure. Herein, AEOLIAN’s analytical wake induction engineering model is replaced with the outcomes of a physically-consistent three-dimensional Free-Vortex Wake (FVW) formulation initially employed in AeroROTOR. This versatile aeroelastic simulation tool is implemented within the framework of MATLAB Simulink/Simscape-Multibody©, a modular environment suitable for industry analysts, researchers, and academic users focusing on wind turbine aero-servo-elastic applications. Furthermore, it serves to lay the groundwork for the development of advanced control laws for multi-megawatt rotors, fostering innovation in the design and optimization of the next-generation wind turbines. The presented analyses focus on predicting the aeroelastic behavior of the bottom-fixed NREL 5MW rotor in uniform axial flow over the operating range, complemented by more detailed investigations at the rated condition undergoing inflow with/without wind misalignment (yaw). The study on key performance parameters is conducted by comparing with the higher-fidelity data from available Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD) coupled with CFD.

The onset of instability and bifurcations in the transitional wake of two tandem square cylinders

Unsteady three-dimensional simulations are performed to elucidate the hidden transitional flow dynamics and Hopf bifurcations along the topological corelines of the created von Kármán streets behind a pair of square cylinders positioned in tandem. Our simulations provide significant new insight into the three-dimensional wake evolution and governing flow physics. We explain how pressure, velocity, and vorticity fluctuation along the Kármán vortex corelines in the increasingly unstable wake amplify, facilitating the growth of various modal instability patterns. The existing knowledge of wake transition through the intertwining of modes A, B, and C instabilities and associated linear stability analysis helped to gain some insight into the overall wake feature. The current study explains how exactly the transitional disturbances physically spread behind a pair of inline and tandem cylinders through the self-excited spanwise-periodic oscillation of the wake and created a sequence of variable length scaled Hopf bifurcations and their swapping for varied gaps between the cylinders and Reynolds number. The growth of a slow mode of the spectral frequency at the bifurcation points seemed crucial in initiating the near-transitional flow irregularity.

Multi-objective layout optimization for wind farms based on non-uniformly distributed turbulence and a new three-dimensional multiple wake model

Wind farm layout optimization (WFLO) can reduce the turbulence intensity on the wind turbines while maximizing power generation. To accurately compute turbulence intensity distribution in the wind farm, we utilize the innovative three-dimensional cosine-shaped turbulence intensity (3D-COTI) model. By integrating the three-dimensional cosine-shaped linear entrainment (3DCLE) wake model previously developed by the authors, we introduce a new multiple wind turbine wake model (3DCLE-M). This model considers the wake superposition effect, enabling precise calculation of power generation. Building upon the 3D-COTI and 3DCLE-M models, we propose a multi-objective WFLO approach to maximize power generation and minimize streamwise turbulence intensity in the wind-turbine-swept area. The results indicate that under maximized power generation, this approach significantly reduces turbulence intensity and its non-uniform distribution in the wind-turbine-swept area. In two ideal cases, the maximum turbulence intensity in all wind-turbine-swept areas of the optimized layout is 25 % and 3.8 % lower than that of the selected benchmark layout. By optimizing the layout of the Horns Rev offshore wind farm, a new layout can be obtained with increased total power output by 1.58 % and the reduced total duration of high-fatigue-load wind turbines under high turbulence intensity by 25 % compared to the benchmark.

Reconstructing Three-Dimensional Bluff Body Wake from Sectional Flow Fields with Convolutional Neural Networks

Reconstructing Three-Dimensional Bluff Body Wake from Sectional Flow Fields with Convolutional Neural Networks

Synchronized optimization of wind farm start-stop and yaw control based on 3D wake model

In existing wind farms, the overall power output can be increased through yaw control. However, the cooperative control of start/stop, yaw and turbines positions is often overlooked, leading to wake superposition to downstream wind turbines and suboptimal power output. This paper proposes a synchronized optimized method that considers start/stop, yaw and turbines positions control based on a three-dimensional wake model and yaw flow superposition model. The objective function of the proposed strategy is to maximize the power output of the Chapman Ranch (CR) wind farm. Four cases are considered: start-stop, yaw control, start-stop & yaw control and start-stop & yaw & turbines positions control. The particle swarm algorithm is introduced to optimize the wind farm layout. According to the results, considering start-stop, yaw and turbines positions optimization can not only increase the annual power output of the wind farm by 8.85 %, but also avoid the colliding wake in the CR wind farm. However, the other three cases will cause colliding wake in some fields of the CR wind farm. This study provides important guidance on improving the overall power output of existing wind farms.

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.

Dynamics and dispersion of inertial particles in circular cylinder wake flows: A two-way coupled Eulerian–Lagrangian approach

In this paper, the motion of inertial particles in three-dimensional (3D) unsteady cylindrical wake flow is investigated by a two-way coupled Eulerian–Lagrangian approach. At different flow Reynolds numbers (Re), the corresponding striking dynamic property and dispersion mechanism of four particle classes have been studied, with inertia parameterized by means of Stokes number (Sk). It is found that inertial particles with lower Stokes number are expelled from vortex cores, and coherent voids encompass the local Kármán vortex cells. As Stokes number increases, a low velocity particle channel could be formed, which almost coincides with the results in the literature. Moreover, with the increase of Reynolds number, numerous irregular coherent voids are observed in the cylinder wake, and the high-speed particles follow the fluid flow closely when they are contained in the vortices. Although the centrifugal force of Kármán vortex cells significantly affects the dynamics of inertial particles, the fluid flow modulation is believed to be responsible for the distinctive particle dispersion patterns in the vortex streets. For particles with medium inertia, the two-way coupled modulation weakens the centrifugal effect of vortex structures on the particles. This trend declines with the increase of Reynolds number, and vanishes with light particles, while both two-way coupled modulation and the centrifugal effect of vortex structures are almost equally effective with heavy particles. The investigations contribute to a better understanding of the particle-laden flows in practical applications, which will benefit the optimized design of certain machinery and equipment for the industry.

Large eddy simulations of flow past an inclined circular cylinder: Insights into the three-dimensional effect

The flow past an inclined cylinder is simulated using large eddy simulations to study the three-dimensional wake flow effects on the forces on the cylinder at Re = 3900. Four inclination angles of α = 0°, 30°, 45°, and 60° are considered. The validity of the independence principle (IP) at the four investigated angles is examined. The results suggest that IP can predict the vortex shedding frequency at 0° ≤ α ≤ 60°, while it fails to predict the drag, lift, and pressure coefficients variations because the three-dimensional effect is neglected for IP. A comprehensive analysis is performed to provide insights into the three-dimensional effects on the drag and lift forces caused by α. The flow velocities, the Reynolds stress, and the spanwise characteristic length of the flow structures are discussed in detail. It is found that the recirculation length reaches its maximum at α = 45°, which results in the smallest drag coefficient and lift force amplitudes. The spanwise characteristic lengths of the vortices are similar for all cases, while spanwise traveling patterns are observed only for α > 0°. A force partitioning analysis is performed to quantify the correlations between the forces and the spanwise and cross-spanwise vortices. It reveals that for α = 30°, the drag force becomes dominated by the cross-spanwise vorticity. With the increasing α, the dominant contribution gradually changes from the cross-spanwise to the spanwise vorticity, and the cross-spanwise vorticity contribution to the drag force further becomes negative at α = 60°.

Research on the dynamic characteristics of wind turbine gearboxes under the spatiotemporal inhomogeneous in the wake

In response to the problem of increasing fatigue load and frequent faults caused by the wake effect, the dynamic characteristics and fatigue life analysis of wind turbine gearbox under the Spatial-temporal non-uniformity of wake region were carried out in this paper. A rigid-flexible coupling model of gears transmission system for a 2 MW wind turbine was established. Based on the three-dimensional Station-temporal inhomogeneous wake model proposed in our previous work, the wind speed distribution of six typical locations in the wake region was obtained. Results show that, the spatiotemporal inhomogeneous effects of the wake expansion have great impact on the dynamic characteristics of the gearboxes for the downwind turbines located in different positions. Vibration energy representing the magnitude of impact energy during the operation of the gearbox is significantly higher under wake conditions than under upstream conditions; meanwhile, the gearbox vibration signal contains more impact component in the wake. The velocity deficit and increased turbulence intensity results in less intense but more complex vibration non-smoothness in the turbine transmission system. As the downwind distance downwind increases, the vibration frequency distribution of the transmission system at each moment is larger, but the vibration energy is reduced. Under the 3D spatiotemporal inhomogeneous effects of the wake expansion, the downstream turbine with staggered arrangement is less affected by wake and has a smoother vibration than the tandem arrangement. At the same downstream distance, the gear life is better in a tandem arrangement than in a staggered arrangement (a maximum value happens at the downstream distance of 6D). Research in this paper can provide references for the study of the dynamic characteristics of large wind turbine transmission systems under the wake effects as well as for the micro-siting of wind farms.