Turbulent Wake Research Articles

An empirical mean-field model of symmetry-breaking in a turbulent wake.

Improved turbulence modeling remains a major open problem in mathematical physics. Turbulence is notoriously challenging, in part due to its multiscale nature and the fact that large-scale coherent structures cannot be disentangled from small-scale fluctuations. This closure problem is emblematic of a greater challenge in complex systems, where coarse-graining and statistical mechanics descriptions break down. This work demonstrates an alternative data-driven modeling approach to learn nonlinear models of the coherent structures, approximating turbulent fluctuations as state-dependent stochastic forcing. We demonstrate this approach on a high–Reynolds number turbulent wake experiment, showing that our model reproduces empirical power spectra and probability distributions. The model is interpretable, providing insights into the physical mechanisms underlying the symmetry-breaking behavior in the wake. This work suggests a path toward low-dimensional models of globally unstable turbulent flows from experimental measurements, with broad implications for other multiscale systems.

Turbulent flow over a cylinder confined in a channel at Re = 3,900

This paper presents data from numerical simulation of the flow over a cylinder confined in a channel at Reynolds number of 3,900. Direct numerical simulation (DNS) of the flow field from blockage ratio of 0 (i.e. the canonical flow over an unconfined cylinder) up to blockage ratio of 0.7 have been performed. At large blockage ratios, an adverse pressure gradient develops and the boundary layer on the channel walls separates and interacts with the cylinder wake. It is observed that the interaction gives rise to complex flow dynamics, affecting the size of the wake, making the wake asymmetric and also resulting in a decrease in the intensity of the turbulent fluctuations in the shear layer. Analysis of the spectra of the turbulent near wake shows an increase of the shedding frequency of the Kármán vortices as blockage ratio is increased. This occurs up to around blockage ratio of 0.7 where it is observed that the formation and shedding of coherent Kármán vortices no longer occur. For all except the blockage ratio of 0.5 case, the frequency of the shear layer is well approximated by the natural frequency of the shear layer instabilities obtained from linear stability theory. In all of these cases, there is a peak of energy associated with subharmonics of the shear layer frequency indicating pairing of the Kelvin–Helmholtz vortices in the shear layer.

Optimum storage sizing in a hybrid wind-battery energy system considering power fluctuation characteristics

Power dispatching is one of the important requirements for wind power systems. Using energy storage systems, especially the battery energy storage system (BESS) is one of the more effective solutions for overcoming this problem. The required battery capacity depends on the fluctuation level of the output power, which is affected by several factors. In this paper, the object is to estimate the required battery capacity based on wind speed data and turbines position in the design phase of a wind farm. An analytical method is presented to estimate the short-term fluctuation of wind farm power considering wake effect, turbulence, and spatial smoothing. Then, a method for estimating the optimum battery capacity, based on the statistical characteristics of wind farm power including average value and standard deviation over a long-term period, is presented. In addition, a new model is presented to estimate the battery lifetime in the case of non-uniform charge/discharge cycles. The numerical results for a case study, over one-year wind speed data, are presented and the results show the effectiveness of the proposed approach in determining the optimum battery capacity.

A new wake detection methodology to capture wind turbine wakes using adaptive mesh refinement and Large Eddy Simulation

The development of turbulent vortical wakes released downstream of wind turbines is crucial as it presents many technological implications for wind farm design and exploitation. The numerical prediction of these wakes constitutes a challenging problem as they involve the shedding of fine vortical structures, their instabilities, and interactions with a turbulent ambient flow. A Large Eddy Simulation (LES) approach allows capturing such flow phenomena, which implies a suitable mesh. Adaptive Mesh Refinement (AMR) is used to refine the mesh in the wind turbine wake to limit the computational cost. A methodology is developed to define and capture the wake envelope adequately. Three main parts of this methodology can be identified: The wind turbine wake detection, the target cell size required and adaptation frequency. The target cell size needed to properly capture the wind turbine wake is investigated in previous work [1], while this paper focuses on wind turbine wake detection. A strategy based on a progress variable with a source term in the rotor region is used to capture the wake. This variable is transported by the flow and thus defines the wake envelope. AMR is used to refine the mesh within this region. To validate the method, a comparison between an adaptive mesh case and a reference mesh case has been performed on a single rotor and a two aligned rotor configuration. For both, the wind turbine wake tracking method is effective. The progress variable is transported correctly and leads to a well-defined wake area. The mesh is refined adequately within it. The physical comparison between cases showed similar results, while the performance comparison showed a computational cost reduction of 30% in the single turbine configuration and 50% in the two turbines configuration. Therefore, our methodology coupled with adaptive mesh refinement can adequately capture wind turbine wake, define an accurate wake envelope and decrease the computational cost for the same physical precision.

Wind tunnel experiments for investigating wake effects in atmospheric boundary layers using a simplified miniature model wind turbine

The clustering of wind turbines within a prospective site is prone to significant wake interactions, which have a negative impact in terms of loads and plant performance. Further improvements in the design and control of wind farms can be achieved through a detailed assessment of wake effects under site-specific conditions. The aim of this paper was to investigate wake effects in atmospheric boundary layer (ABL) flows using a simplified model wind turbine. First, we performed experiments under smooth- and turbulent-uniform inflows to highlight the wake features of the model. Second, we evaluated the interactions with two different neutrally stratified ABL: i) ABL Type-I (α = 0.11, TI = 6 %), ii) ABL Type-II (α = 0.23, TI = 13 %), where α is the incident wind shear and TI is the turbulence intensity. For each case, hot-wire anemometry was used to obtain wake mean velocity, turbulence intensity and power spectrum profiles at four different downstream positions. We also included a comparison with three analytical wake models to get further indications on the experimental measurements. First results showed that the simplified model is well-suited for its intended purpose. The largest discrepancies between experiments and model predictions were in the near-wake region and in cases with lower background turbulence. We also corroborated a strong influence of the incoming wind profile on how fast the wake recovers to the undisturbed conditions. Furthermore, this study provided an initial framework to explore the ABL wind tunnel at Universidade Federal do Rio Grande do Sul (UFRGS) as a viable tool for research in wind energy.

Wake rotation impacts on wake decay

This study considers the behavior of a well-conditioned swirling turbulent wake. A custom swirling wake generator was used to produce a swirling wake absent of a tower that complicates the flow regime. Four swirling wakes were studied with swirl numbers ranging from 0.19 to 0.37 and compared to a non-swirling counterpart. Two-component Laser-Doppler Anemometry was used to measure mean and turbulent quantities in the wake. Measured profiles were analyzed based on similarity theory applied to a swirling wake. The results show that wake behavior was impacted by the initial swirl strength. Generally, wake growth rate and axial deficit decay rate increased with higher levels of swirl, and tangential velocity decay rate increased with lower levels of swirl. However, the wake that diffused fastest was the case with a swirl number of 0.27.

Low Reynolds Number Effects on the Separation and Wake of a Compressor Blade

Abstract This paper investigates the surface boundary layer and wake development of a compressor blade at a range of low Reynolds number from 45,000 to 120,000. Experiments in a miniature linear compressor cascade facility have been performed with detailed surface pressure measurements and flow visualization to track variations in the separation bubble size. These have been combined with high-resolution pneumatic pressure and hot-wire probe traverses in the downstream wake. High-fidelity direct numerical simulations have been completed on the same compressor blade section across the same range of operating conditions. The results show that large laminar separation bubbles exist on both blade surfaces. As Reynolds number increases, these separation bubbles shorten in length and reduce in thickness. Correspondingly, the downstream wake narrows, although the peak wake loss coefficient remains approximately constant. As the Reynolds number is increased from 45,000 to 120,000, the bubble length on the suction side reduced from 48% to 28% chord and on the pressure side reduced from 35% to 20% chord, while the loss coefficient reduced from 9% to 5%. The flow features are examined further within the high-fidelity computations, which reveal the dependence of the wake turbulence on the laminar separation bubbles. The separation bubbles are found to generate turbulent kinetic energy, which convects downstream to form the outer part of wake. As Re increases, a shorter bubble produces less turbulence in the outer part of the boundary layer leading to a narrower wake. However, the trailing edge separation is largely independent of Reynolds number, leading to the constant peak loss coefficient observed. The overall loss is shown to vary linearly with the total turbulence production, and this depends on the size of the separation bubbles. Overall, this research provides new insight into the connection between the blade surface flow field and the wake characteristics at low Reynolds number. The findings suggest that changes that minimize the extent of the blade separation bubbles could provide significant improvements to both the steady and unsteady properties of the wake.

Large-Eddy Simulation of Wakes of Waked Wind Turbines

The wake dynamics of a wind turbine are influenced by the atmospheric turbulence and the wake of its upwind turbine. In this work, we investigate the wake characteristics of a waked wind turbine for four different downwind spacings and three different inflows using large-eddy simulation with a turbine parameterized using the actuator surface model. The wake statistics of the waked turbine are compared with those of the stand-alone wind turbine under the same inflow. The results show that the oncoming wake significantly affects the near wake of the waked turbine, where it accelerates the wake recovery by increasing the turbulent convection, and increases the turbulence kinetic energy. The velocity deficit and turbulence kinetic energy in the far wake, on the other hand, are fairly similar with each other for the considered different turbine spacings, and are close to those of the stand-alone wind turbine. As for the wake meandering of the waked wind turbines, it is initiated quickly and enhanced by the oncoming wake turbulence, as shown by the meandering amplitudes and the power spectral density of the instantaneous wake positions. The growth rates of the wake meandering from the waked wind turbines, on the other hand, are close to that of the stand-alone wind turbine, indicating the critical role of the atmospheric turbulence on wake meandering. The present work details how the oncoming wake influences the wake dynamics of the downwind turbine, and provides physical insights on developing engineering models to take into account such effects.

Toward a high performance and strong resilience wind energy harvester assembly utilizing flow-induced vibration: Role of hysteresis

Wind energy harvester utilizing flow-induced vibration (FIV-WEH) has attracted much attention because of its ability to capture low-speed wind energy. This study is motivated to design a reliable FIV-WEH assembly in a wind farm, and to understand the altered environmental flow and disturbed output performance through large-eddy simulations and wind tunnel experiments, for the sake of harnessing fluctuating near-ground wind energy efficiently. The results demonstrates that the proposed eco-friendly FIV-WEH assembly has less impact on the surroundings due to the fast recovery of turbulent wake. Moreover, it is equipped with remarkable hysteresis caused by the delay of wake transition from 2P to C mode, which can enhance the output power, effective wind band, and more importantly, resilience. The resilience guarantees that the FIV-WEH assembly can harvest the fluctuating wind resources optimally even under strong turbulence intensity. Specifically, compact FIV-WEH assembly (l ≤ 1.5, where l is dimensionless streamwise span) based on extended-body regime has a low cut-in speed (3 m/s), showing great potential to harvest breeze energy in a near-ground residential environment. Loose FIV-WEH assembly (1.5 < l < 5) based on reattachment regime has a large cut-in speed (9 m/s) and low span-sensitivity, which can be flexibly adjusted to extract the wind energy in spacious wind-abundant areas. Finally, two strategies developed by modifying surfaces of FIV-WEH assembly can further enhance the resilience and conversion efficiency by approximately 200%.

POD analysis of spatiotemporal characteristics of wake turbulence over hilly terrain and their relationship to hill slope, hill shape and inflow turbulence

In this study, the turbulent wake flow fields over isolated 2-D ridges and 3-D hills with different slopes and oncoming flow conditions are predicted by large-eddy simulations (LES). The coupling effects of hill slopes, hill shapes and inflow turbulence on the spatiotemporal characteristics of wake turbulence over hilly terrain are clarified in terms of turbulent statistics and unsteady flow patterns. The snapshot-based proper orthogonal decomposition (POD) technique is then adopted to elucidate the physical meaning of wake turbulence over hilly terrain. The numerical results show that the vertical distributions of turbulent statistics and the unsteady flow patterns in the wake of hilly terrain are jointly determined by hill slopes, hill shapes and oncoming flow conditions. Additionally, the snapshot-based POD method is capable of reconstructing a large amount of fluctuating kinetic energy in the wake of hilly terrain with a few low-order POD modes. Moreover, the primary wake patterns and their relations to hill slopes, hill shapes and oncoming flow conditions are identified. On the horizontal plane, the wake turbulence structures of 3-D gentle/steep hill are dominated by the asymmetric elongated streak structures and a pair of counter-rotating vortices, respectively. On the vertical plane, the main patterns of hill wake are often featured by the recirculating flow, and the size of recirculation bubble is highly dependent on hill slopes and hill shapes.

Large Eddy Simulation of wind turbine fatigue loading and yaw dynamics induced by wake turbulence

A coupled Large Eddy Simulation (LES) and aeroelastic code was used to evaluate control responses and fatigue loading of a four-inline wind turbine array. Neutral and unstably stratified atmospheric boundary layers with hub-height wind speeds of 7 and 15 m/s were used for wind farm inflows. These cases operate in different control regions. It was found that for both incoming wind speeds, atmospheric stability has no significant impact on the fatigue loads of the front-row wind turbines. However, stability affected wake characteristics which caused differences in control response and fatigue experienced by downstream turbines. The most distinctive difference was observed at a downstream turbine in the above-rated condition where the shaft torsional load in neutral stability condition was up to 50% higher than the unstable case. A baseline active yaw controller was implemented in the below-rated condition, which caused higher fatigue on turbines in the wake compared to the fixed yaw turbine case, without any power output gain.

Numerical analysis of wake turbulence between hybrid tidal turbine and hypothetical actuator cylinder for shallow water with low velocity conditions

Towards modernisation of the technological era, electricity demands have been an issue. Although the supply of electrical energy from the renewable sources are increasing, it is still not sufficient to offset the carbon production. Malaysia as a developing country needs ample of supply of electrical energy. As most of the current electrical energy for the country are being produced by non renewable sources, the Malaysian government have started looking into renewable options to produce electrical energy. There are various sources of energy that are available in Malaysia such as solar, natural gas, petroleum, ocean energy and many more. This paper is focused on the tidal energy which is an ocean energy that can produce electrical energy by using the power of tide. This research explores the hybrid turbine design which is a type of vertical-axis tidal turbine that combines two distinct type of devices, namely Savonius and H-Darrieus turbines. Hybrid turbine is useful as it helps to overcome the limitation of individual turbine and also be able to produce energy at a low water velocity. Numerical analysis is employed to investigate the wake recovery behaviour and turbulent mixing due to the positioning of the device using Ansys CFD Fluent. By understanding the general wake characteristics produced by each device, proper planning can be done to configure these devices in an array for future planning. The simulation result shows that the hybrid turbine utilising NACA0015 and NACA0018 with nested configuration demonstrates faster velocity recovery compared to NACA0021. The turbulence wake results also provides a promising output which shows the acceleration of flow at the downstream region for hybrid nested NACA0015 and NACA0018 are more narrow compared to NACA0021. The result of this simulation has also been validated with published data. In a nutshell, the NACA blade design not only affects the performance of the turbine but can also influence the velocity recovery downstream of the device.

High fidelity numerical simulations on the unsteady flow field of low-pressure turbine cascades with and without upstream disturbance at moderate Reynolds number

This paper numerically investigates the aerodynamic performance of the T106A low-pressure turbine based with different inflow conditions at moderate Reynolds number by using high performance computing based on high order unstructured methods. Two different inflow conditions respectively of uniform and disturbed are considered, while for the latter a small circular cylinder is placed upstream of the cascade to generate wake turbulence as a long-standing disturbance. A high order Fourier-spectral/hp element method is employed to solve the flow dynamics in the cascade of high complex geometries. Flow transition characteristics are quantified in terms of the distribution of cascade wall surface pressure and friction coefficient, the distribution of wake profile pressure loss and the evolution characteristics of boundary layer flow structures as well. The numerical results show that the current numerical simulations accurately predict the flow transition performance of low-pressure turbine cascades and capture the effects of wake-generated disturbance on the cascade, which is shown to effectively modify the flow transition performance as compared with the uniform inflow case.

Data-Driven Analysis of Final Separation Between Successive Landing Aircraft

In recent years, with the development of air traffic in China, airspace resources cannot keep up with the growth of traffic demand. Therefore, enhancement of runway capacity by reducing wake turbulence separation has become a research hotspot in the air traffic management field. As there are gaps between theory and practice, many scholars are doing practical operation-based evaluations, focusing on the final separations (intervals) between two successive aircraft. However, few studies have considered the impact of different controllers and the evolution of separations over time. This paper is dedicated to analyzing the final separations between leading and trailing aircraft based on the aircraft trajectories. This study carries out the final separation analysis from static and dynamic perspectives, considering the final separations under different traffic pressures, by different controllers, and in the different segregated and mixed operations. Guangzhou Baiyun International Airport (ZGGG) is taken as an experimental case. The results indicate that the final separation buffer decreases over time. Moreover, under the same high traffic pressures, the final separations could be used to compare the effectiveness of different controllers.

Scalings of scale-by-scale turbulence energy in non-homogeneous turbulence

A theory of non-homogeneous turbulence is developed and applied to boundary-free shear flows. The theory introduces assumptions of inner and outer similarity for the non-homogeneity of two-point statistics, and predicts power-law scalings of second-order structure functions that have some similarities with but also some differences from Kolmogorov scalings. These scalings arise as a consequence of these assumptions, of the general interscale and interspace energy balance, and of an inner–outer equivalence hypothesis for turbulence dissipation. They reduce to the usual Kolmogorov scalings in stationary homogeneous turbulence. Comparisons with structure function data from three qualitatively different turbulent wakes provide support for the theory's predictions but also raise new questions for future research.

Dynamic inflow model for a floating horizontal axis wind turbine in surge motion

Abstract. Floating offshore wind turbines may experience large surge motions, which can cause blade–vortex interaction if they are similar to or faster than the local wind speed. Previous research hypothesized that this blade–vortex interaction phenomenon represented a turbulent wake state or even a vortex ring state, rendering the actuator disc momentum theory and the blade element momentum theory invalid. This hypothesis is challenged, and we show that the actuator disc momentum theory is valid and accurate in predicting the induction at the actuator in surge, even for large and fast motions. To accomplish this, we develop a dynamic inflow model that simulates the vorticity–velocity system and the effect of motion. The model's predictions are compared to other authors' results, a semi-free-wake vortex ring model, other dynamic inflow models, and CFD simulations of an actuator disc in surge. The results show that surge motion and rotor–wake interaction do not result in a turbulent wake or vortex ring state and that the application of actuator disc momentum theory and blade element momentum theory is valid and accurate when applied correctly in an inertial reference frame. In all cases, the results show excellent agreement with the higher-fidelity simulations. The proposed dynamic inflow model includes a modified Glauert correction for highly loaded streamtubes and is accurate and simple enough to be easily implemented in most blade element momentum models.

Aerodynamics of a wing in turbulent bluff body wakes

The aerodynamics of a stationary wing in a turbulent wake are investigated. Force and velocity measurements are used to describe the unsteady flow. Various wakes are studied with different dominant frequencies and length scales. In contrast to the pre-stall angles of attack, the time-averaged lift increases substantially at post-stall angles of attack as the wing interacts with the von Kármán vortex street and experiences temporal variations of the effective angle of attack. At an optimal offset distance from the wake centreline, the time-averaged lift becomes maximum despite of small amplitude oscillations in the effective angle of attack. The stall angle of attack can reach 20° and the maximum lift coefficient can reach 64 % higher than that in the freestream. Whereas large velocity fluctuations at the wake centreline cause excursions into the fully attached and separated flows during the cycle, small-amplitude oscillations at the optimal location result in periodic shedding of leading edge vortices. These vortices may produce large separation bubbles with reattachment near the trailing-edge. Vorticity roll-up, strength and size of the vortices increase with increasing wavelength and period of the von Kármán vortex street, which also coincides with an increase in the spanwise length scale of the incident wake, and all contribute to the remarkable increase in lift.

A new three-dimensional analytical model for wind turbine wake turbulence intensity predictions

In wind farm design, accurately predicting the wake turbulence level is crucial for turbine power and load evaluation. However, a knowledge gap still exists on the characteristics of wake turbulence, meanwhile there has been little work on the development of related engineering models. In view of this, firstly, one-dimensional analytical models that can estimate the wake width and maximum wake turbulence level at any streamwise positions are proposed and validated. Based on these, a highly simple three-dimensional cosine shape (3D-COTI) model is proposed for estimating the wake turbulence intensity in an effective way. Moreover, by taking into account the wind shear and ground effects, this proposed model is capable of describing the anisotropic property of the 3-D wake field. Afterwards, model evaluations are performed through several test cases consisting various types of turbines operating under a wide range of inflow conditions. Overall, the proposed model shows a good agreement with the measurements about the spatial distribution of turbulence enhancement within the wake flow. Because of its good accuracy, simplicity and universality, the present model has potential for large-scale wind farm applications.

A parametric and feasibility study for data sampling of the dynamic mode decomposition: Spectral insights and further explorations

The present work extends the parametric investigation on the sampling nuances of dynamic mode decomposition (DMD) under Koopman analysis. Through turbulent wakes, the study corroborated the generality of universal convergence states for all DMD implementations. It discovered implications of sampling range and resolution—determinants of spectral discretization by discrete bins and the highest resolved frequency range, respectively. The work reaffirmed the necessity of the convergence state for sampling independence, too. Results also suggested that the observables derived from the same flow may contain dynamically distinct information, thus altering the DMD output. Surface pressure and vortex fields are optimal for characterizing the structure and the flow field, respectively. Pressure, velocity magnitude, and turbulence kinetic energy also suffice for general applications, but Reynolds stresses and velocity components shall be avoided. Mean-subtraction is recommended for the best approximations of Koopman eigen tuples. Furthermore, the parametric investigation on truncation discovered some low-energy states that dictate a system's temporal integrity. The best practice for order reduction is to avoid truncation and employ dominant mode selection on a full-state subspace, though large-degree truncation supports fair data reconstruction with low computational cost. Finally, this work demonstrated synthetic noise resulting from pre-decomposition interpolation. In unavoidable interpolations to increase the spatial dimension n, high-order schemes are recommended for better retention of original dynamics. Finally, the observations herein, derived from inhomogeneous anisotropic turbulence, offer constructive references for DMD on fluid systems, if not also for others beyond fluid mechanics.

Machine-learning identification of the variability of mean velocity and turbulence intensity for wakes generated by onshore wind turbines: Cluster analysis of wind LiDAR measurements

Light detection and ranging (LiDAR) measurements of isolated wakes generated by wind turbines installed at an onshore wind farm are leveraged to characterize the variability of the wake mean velocity and turbulence intensity during typical operations, which encompass a breadth of atmospheric stability regimes and rotor thrust coefficients. The LiDAR measurements are clustered through the k-means algorithm, which enables identifying the most representative realizations of wind turbine wakes while avoiding the imposition of thresholds for the various wind and turbine parameters. Considering the large number of LiDAR samples collected to probe the wake velocity field, the dimensionality of the experimental dataset is reduced by projecting the LiDAR data on an intelligently truncated basis obtained with the proper orthogonal decomposition (POD). The coefficients of only five physics-informed POD modes are then injected in the k-means algorithm for clustering the LiDAR dataset. The analysis of the clustered LiDAR data and the associated supervisory control and data acquisition and meteorological data enables the study of the variability of the wake velocity deficit, wake extent, and wake-added turbulence intensity for different thrust coefficients of the turbine rotor and regimes of atmospheric stability. Furthermore, the cluster analysis of the LiDAR data allows for the identification of systematic off-design operations with a certain yaw misalignment of the turbine rotor with the mean wind direction.