Turbulent Wake Flow Research Articles

Vortex simulations of wind turbines operating in atmospheric conditions using a prescribed velocity‐vorticity boundary layer model

AbstractA prescribed velocity‐vorticity boundary layer model for the vorticity transport equation is proposed, which corrects the unphysical upward deflection of the wake seen in a simpler prescribed velocity shear approach. A Lagrangian implementation of the boundary layer model has been investigated using our in‐house vortex solver MIRAS. The MIRAS code contains both an aerodynamic part and a structural‐mechanical part taking into account aeroelastic phenomena. The solver is employed to simulate flows around wind turbines and uses a combination of filaments and particles in order to mimic the vorticity released by the wind turbine blades. The vorticity is interpolated onto a uniform Cartesian mesh, where the interaction is efficiently calculated by an fast Fourier transform‐based method. Simulations of wind turbines operating in an atmospheric boundary layer flow are carried out and analysed in detail for a range of scenarios. The manuscript focuses on studying the influence of wind shear and turbulence, which is varied to mimic natural atmospheric conditions. A traverse virtual probe up to 30 diameters downstream of the rotor plane is used to investigate the properties of the turbulent wake flow for the different cases. This includes mean and standard deviation of the streamwise velocity component, wake deficit, Reynolds stresses, and power spectral density of the velocity signal. The results show that combining a prescribed boundary layer approach with a vortex method gives consistent and physically correct results if properly implemented.

A 3D common-refinement method for non-matching meshes in partitioned variational fluid–structure analysis

We present a three-dimensional (3D) common-refinement method for non-matching unstructured meshes between non-overlapping subdomains of incompressible turbulent fluid flow and nonlinear hyperelastic structure. The fluid flow is discretized using a stabilized Petrov–Galerkin method, and the large deformation structural formulation relies on a continuous Galerkin finite element method. An arbitrary Lagrangian–Eulerian formulation with a nonlinear iterative force correction (NIFC) coupling is achieved in a staggered partitioned manner by means of fully decoupled implicit procedures for the fluid and solid discretizations. To begin, we first investigate the accuracy of common-refinement method (CRM) to satisfy the traction equilibrium condition along the fluid-elastic interface with non-matching meshes. We systematically assess the accuracy of CRM against the matching grid solution by varying grid mismatch between the fluid and solid meshes over a tubular elastic body. We demonstrate the second-order accuracy of CRM through uniform refinements of fluid and solid meshes along the interface. We then extend the error analysis to transient data transfer across non-matching meshes between the fluid and solid solvers. We show that the common-refinement discretization across non-matching fluid–structure grids yields accurate transfer of the physical quantities across the fluid–solid interface. We next solve a 3D fluid–structure interaction (FSI) problem of a cantilevered hyperelastic plate behind a circular bluff body and verify the accuracy of coupled solutions with respect to the available solution in the literature. By varying the solid interface resolution, we generate various non-matching grid ratios and quantify the accuracy of CRM for the nonlinear structure interacting with a laminar flow. We illustrate that the CRM with the partitioned NIFC treatment is stable for low solid-to-fluid density ratio and non-matching meshes for the 3D FSI problem. Finally, we demonstrate the 3D parallel implementation of the common-refinement with the NIFC method for a realistic engineering problem of drilling riser undergoing complex vortex-induced vibration with strong added mass effects and turbulent wake flow.

Control of vortex-induced motion in multi-column offshore platform by near-wake jets

Vortex-induced motion (VIM) poses a serious challenge in many engineering applications such as offshore structures, floating wind turbines, and high rise buildings. In particular, significant aspects of VIM have to be considered in offshore platforms subjected to high currents. The objective of this numerical study is to investigate the VIM suppression of multi-column floating platforms by injecting steady near-wake jets at the wake side of the columns. Before proceeding to the blowing-jet based flow control method, the transverse VIM amplitude of floating platform is validated with the model test data. We perform a systematic investigation of 3D scaled model with and without prescribed jet flows for varying reduced velocity (Ur) at a fixed mass ratio m*=0.83, the damping ratio ζ=0.01 and the Reynolds number Re=20,000. The numerical investigations are carried out for different near-wake jet configurations at reduced velocity Ur=10. We assess the response characteristics and flow profile patterns to identify a suitable configuration of blowing jet along the columns. We demonstrate that the semi-submersible with elongated near-wake jet configuration is efficient in suppressing VIM in comparison to other near-wake jet configurations and the uncontrolled no-jet case. The vibration amplitudes, the force coefficients and the flow patterns of semi-submersible with the blowing-based control technique are further examined for various mass flow rate coefficients. From our studies, we observe approximately 30% reduction of forces and the amplitudes for the offshore system with the prescribed jet flow compared to the system without near-wake jets. The optimal Vjet/U is estimated to be in the range of 2.5–5, for the effective VIM suppression, where Vjet and U are the prescribed jet flow speed and the free-stream speed, respectively. To understand the underpinning of VIM suppression mechanism, the vortex dynamics and flow patterns in the near-wake region of a freely vibrating semi-submersible platform with the near-wake jet are explored. For this numerical study, we employ a stabilized finite element formulation with an explicit dynamic subgrid-scale model to simulate the fluid-structure interaction subjected to a turbulent wake flow.

Challenges in Scale-Resolving Simulations of turbulent wake flows with coherent structures

The objective of this work is to investigate the challenges encountered in Scale-Resolving Simulations (SRS) of turbulent wake flows driven by spatially-developing coherent structures. SRS of practical interest are expressly intended for efficiently computing such flows by resolving only the most important features of the coherent structures and modelling the remainder as stochastic field. The success of SRS methods depends upon three important factors: i) ability to identify key flow mechanisms responsible for the generation of coherent structures; ii) determine the optimum range of resolution required to adequately capture key elements of coherent structures; and iii) ensure that the modelled part is comprised nearly exclusively of fully-developed stochastic turbulence. This study considers the canonical case of the flow around a circular cylinder to address the aforementioned three key issues. It is first demonstrated using experimental evidence that the vortex-shedding instability and flow-structure development involves four important stages. A series of SRS computations of progressively increasing resolution (decreasing cut-off length) are performed. An a priori basis for locating the origin of the coherent structures development is proposed and examined. The criterion is based on the fact that the coherent structures are generated by the Kelvin–Helmholtz (KH) instability. The most important finding is that the key aspects of coherent structures can be resolved only if the effective computational Reynolds number (based on total viscosity) exceeds the critical value of the KH instability in laminar flows. Finally, a quantitative criterion assessing the nature of the unresolved field based on the strain-rate ratio of mean and unresolved fields is examined. The two proposed conditions and rationale offer a quantitative basis for developing “good practice” guidelines for SRS of complex turbulent wake flows with coherent structures.

Modelling yawed wind turbine wakes: a lifting line approach

Yawing wind turbines has emerged as an appealing method for wake deflection. However, the associated flow properties, including the magnitude of the transverse velocity associated with yawed turbines, are not fully understood. In this paper, we view a yawed turbine as a lifting surface with an elliptic distribution of transverse lift. Prandtl’s lifting line theory provides predictions for the transverse velocity and magnitude of the shed counter-rotating vortex pair known to form downstream of the yawed turbine. The streamwise velocity deficit behind the turbine can then be obtained using classical momentum theory. This new model for the near-disk inviscid region of the flow is compared to numerical simulations and found to yield more accurate predictions of the initial transverse velocity and wake skewness angle than existing models. We use these predictions as initial conditions in a wake model of the downstream evolution of the turbulent wake flow and compare predicted wake deflection with measurements from wind tunnel experiments.

Turbulent planar wakes under pressure gradient conditions

Accurate prediction of the spatial evolution of turbulent wake flows under pressure gradient conditions is required in some engineering applications such as the design of high-lift devices and wind farms over topography. In this paper, we aim to develop an analytical model to predict the evolution of a turbulent planar wake under an arbitrary pressure gradient condition. The model is based on the cross-stream integration of the streamwise momentum equation and uses the self-similarity of the mean flow. We have also made an experimentally supported assumption that the ratio of the maximum velocity deficit to the wake width is independent of the imposed pressure gradient. The asymptotic response of the wake to the pressure gradient is also investigated. After its derivation, the model is successfully validated against experimental data by comparing the evolution of the wake width and maximum velocity deficit. The inputs of the model are the imposed pressure gradient and the wake width under zero pressure gradient. The model does not require any parameter tuning and is deemed to be practical, computationally fast, accurate enough, and therefore useful for the scientific and engineering communities.

Large-eddy simulation and experimental study on the turbulent wake flow characteristics of a two-bladed wind turbine

Large-eddy simulation (LES) with fully resolved rotor method (FRM) is applied to explore the turbulent wake flow characteristics and vortex evolution laws of a two-bladed horizontal-axis wind turbine. Relevant wind tunnel experiments have been done based on time resolved particle image velocimetry (TRPIV) technique. The simulation results are validated by the experimental data and they are in good agreement. The axial average velocity, turbulent kinetic energy, shear Reynolds stress, and vortex structure of the wind turbine wake are analyzed based on the comparison of LES results and experimental data. It is observed that the wake diameter of wind turbine enlarges with the increase of tip speed ratio (TSR). Turbulent kinetic energy meets its minimum value when x / R =2.0. Shear Reynolds stress appears a positive peak in the near wake when x / R <2.0, and the value of shear Reynolds stress decreases along the axial direction. The blade tip vortex dissipates more quickly than the central vortex in the wind turbine wake, and the gradient of the relationship curve between the blade tip vortex core position and the vortex age decreases as the TSR increases. With the increase of TSR, the thrust coefficient increases, and the power coefficient increases first and then decreases. The present work proves that LES with FRM could calculate wind turbine turbulent wake flow with a high accuracy.

Optimization of planar PIV-based pressure estimates in laminar and turbulent wakes

The performance of four pressure estimation techniques using Eulerian material acceleration estimates from planar, two-component Particle Image Velocimetry (PIV) data were evaluated in a bluff body wake. To allow for the ground truth comparison of the pressure estimates, direct numerical simulations of flow over a circular cylinder were used to obtain synthetic velocity fields. Direct numerical simulations were performed for $$Re_\mathrm{D} = 100$$ , 300, and 1575, spanning laminar, transitional, and turbulent wake regimes, respectively. A parametric study encompassing a range of temporal and spatial resolutions was performed for each $$Re_\mathrm{D}$$ . The effect of random noise typical of experimental velocity measurements was also evaluated. The results identified optimal temporal and spatial resolutions that minimize the propagation of random and truncation errors to the pressure field estimates. A model derived from linear error propagation through the material acceleration central difference estimators was developed to predict these optima, and showed good agreement with the results from common pressure estimation techniques. The results of the model are also shown to provide acceptable first-order approximations for sampling parameters that reduce error propagation when Lagrangian estimations of material acceleration are employed. For pressure integration based on planar PIV, the effect of flow three-dimensionality was also quantified, and shown to be most pronounced at higher Reynolds numbers downstream of the vortex formation region, where dominant vortices undergo substantial three-dimensional deformations. The results of the present study provide a priori recommendations for the use of pressure estimation techniques from experimental PIV measurements in vortex dominated laminar and turbulent wake flows.

Self-Similarity Analysis of Turbulent Wake Flows

This paper investigates the self-similarity properties in the far downstream of high Reynolds number turbulent wake flows. The growth rate of the wake layer width, dδ/dx; the decaying rate of the maximum velocity defect, dUs/dx; and the scaling for the maximum mean transverse (across the stream) velocity, Vmax, are derived directly from the self-similarity of the continuity equation and the mean momentum equation. The analytical predictions are validated with the experimental data. Using an approximation function for the mean axial flow, the self-similarity analysis yields approximate solutions for the mean transverse velocity, V, and the Reynolds shear stress, T=−〈uv〉. Close relations among the shapes of U, V, and T are revealed.

Blind test comparison of the performance and wake flow between two in-line wind turbines exposed to different turbulent inflow conditions

Abstract. This is a summary of the results of the fourth blind test workshop that was held in Trondheim in October 2015. Herein, computational predictions on the performance of two in-line model wind turbines as well as the mean and turbulent wake flow are compared to experimental data measured at the wind tunnel of the Norwegian University of Science and Technology (NTNU). A detailed description of the model geometry, the wind tunnel boundary conditions and the test case specifications was published before the workshop. Expert groups within computational fluid dynamics (CFD) were invited to submit predictions on wind turbine performance and wake flow without knowing the experimental results at the outset. The focus of this blind test comparison is to examine the model turbines' performance and wake development with nine rotor diameters downstream at three different turbulent inflow conditions. Aside from a spatially uniform inflow field of very low-turbulence intensity (TI = 0.23 %) and high-turbulence intensity (TI = 10.0 %), the turbines are exposed to a grid-generated highly turbulent shear flow (TI = 10.1 %).Five different research groups contributed their predictions using a variety of simulation models, ranging from fully resolved Reynolds-averaged Navier–Stokes (RANS) models to large eddy simulations (LESs). For the three inlet conditions, the power and the thrust force of the upstream turbine is predicted fairly well by most models, while the predictions of the downstream turbine's performance show a significantly higher scatter. Comparing the mean velocity profiles in the wake, most models approximate the mean velocity deficit level sufficiently well. However, larger variations between the models for higher downstream positions are observed. Prediction of the turbulence kinetic energy in the wake is observed to be very challenging. Both the LES model and the IDDES (improved delayed detached eddy simulation) model, however, consistently manage to provide fairly accurate predictions of the wake turbulence.

Effect of Upstream Turbine Tip Speed Variations on Downstream Turbine Performance

A wake study and combined power output analysis of an array of two model wind turbines is presented. In a wind farm arrangement wakes behind the upstream turbines directly affect the performance and structural loads of the downstream turbines. In this analysis the characteristics of the mean and turbulent wake flow behind an upstream model turbine is directly related to the performance characteristics of a downstream rotor located at three different downstream locations. First the influence of the upstream turbine's tip speed ratio variation from design conditions on the wake flow and the downstream turbine performance is analyzed. Thereafter, also the turbulence intensity level at the wind tunnel inlet is varied from low (laboratory conditions, TI=0.23%) to high (atmospheric conditions, TI=10.0%). Finally, the combined power output of the two turbine array is evaluated for a matrix of the different scenarios.A significant influence of the background turbulence level on the wake recovery is observed, especially for the intermediate separation distance of x/D=5. Controlling the upstream turbine's tip speed ratio away from its design point does not result in a significant increase in combined power output. Only for the case of low turbine separation distance (x/D=3) and low background turbulence the added kinetic energy in the wake can be recovered by the downstream turbine. For higher turbine separation distances and higher background turbulence, the added kinetic energy diffuses into the freestream flow and cannot be recovered anymore. In average, the combined efficiency is observed to increase by about 2.5% with every additional rotor diameter of turbine separation distance. Thus, this analysis suggests an accurate management of the upstream turbine tip speed ratio in dependence of background turbulence and turbine separation distance when optimizing the power output of a wind farm.

Analysis of characteristic wake flow modes on a generic transonic backward-facing step configuration

To gain insight into characteristic wake flow modes, which among others are responsible for asymmetrical loads on the engine extensions of space launchers at transonic speeds, combined experimental and numerical investigations of a turbulent wake flow are performed at Ma∞=0.8 and Reh=1.8⋅105. The experiments are conducted at the Bundeswehr University Munich using planar PIV and wall pressure measurements, while the numerical investigations are performed by the Institute of Aerodynamics at RWTH Aachen University using a zonal RANS–LES approach and dynamic mode decomposition (DMD). The analysis is done on a planar space launcher configuration that consists of a backward-facing step with a long shock-free forebody avoiding undesired shock-boundary-layer interactions upstream of the analyzed wake flow region. The investigated wake flow is characterized by a highly unsteady behavior of the shear layer shedding from the forebody and subsequently reattaching onto the splitter plate. The strong variation of the reattachment positions in the spanwise and the streamwise direction leads to pronounced wall pressure oscillations and consequently, structural loads. By means of a classical statistical analysis, i.e., spatial and temporal Fourier transforms and two-point correlations of experimental and numerical data, one spatial coherent scale with a spanwise wavelength of λz≈2h and two characteristic frequencies of Srh≈0.01 and Srh≈0.07 have been obtained for the investigated wake flow problem. To clarify the coherent fluid motion dominating the detected spatio-temporal behavior, a DMD algorithm is applied to the time-resolved three-dimensional streamwise velocity field. The frequencies of the first two extracted stable sparsity DMD modes closely coincide with the characteristic peaks in the wall pressure spectra. The analysis of the three-dimensional shape of the extracted DMD modes reveals that the detected wake flow behavior is caused by a pronounced low-frequency cross-pumping motion of the recirculation region and a high-frequency cross-flapping motion of the shear layer, respectively. Both wake flow modes feature a pronounced nearly-periodical variation in the spanwise direction with an approximate spanwise wavelength of two step heights. Thus, the extracted underlying wake modes clearly explain the occurrence of corresponding peaks in the wall pressure spectra, the periodical formation of wedge-shaped reattachment regions on the splitter plate, and the detection of finger-like structures in the PIV experiments.

Time-resolved and time-averaged stereo-PIV measurements of a unit-ratio cavity

An experimental setup was developed to perform wind tunnel measurements on a unit-ratio, 2D open cavity under perpendicular incident flow. The open cavity is characterized by a mixing layer at the cavity top, that divides the flow field into a boundary layer flow and a cavity flow. Instead of precisely replicating a specific type of inflow, such as a turbulent flat plate boundary layer or an atmospheric boundary layer, the setup is capable of simulating a wide range of inflow profiles. This is achieved by using triangular spires as upstream turbulence generators, which can modify the otherwise laminar inflow boundary layer to be moderately turbulent and stationary, or heavily turbulent and intermittent. Measurements were performed by means of time-resolved stereo PIV. The cavity shear layer is analyzed in detail using flow statistics, spectral analysis, and space–time plots. The ability of the setup to generate typical cavity flow cases is demonstrated for characteristic inflow boundary layers, laminar and turbulent. Each case is associated with a distinct shear layer flow phenomena, self-sustained oscillations for the former and Kelvin–Helmholtz instabilities for the latter. Additionally, large spires generate a highly turbulent wake flow, resulting in a significantly different cavity flow. Large turbulent sweep and ejection events in the wake flow suppress the typical shear layer and sporadic near wall sweep events generate coherent vortices at the upstream edge.

Experimental and numerical investigations of the turbulent wake flow of a generic space launcher at $$M_\infty =3$$ M ∞ = 3 and $$M_\infty =6$$ M ∞ = 6

The turbulent wake of a generic space launcher wind tunnel model with an underexpanded nozzle jet is investigated experimentally and numerically to gain insight into the variation of intricate wake flow phenomena of space vehicles at higher stages of the flight trajectory with increasing Mach number. The experiments are carried out at $$M_\infty =3$$ and $$M_\infty =6$$ in the Ludwieg tube test facility at the Institute of Fluid Mechanics at the Technische Universitat Braunschweig, while the corresponding time-resolved computations are performed by the Institute of Aerodynamics at RWTH Aachen University using a zonal RANS–LES approach. A strong alteration of the wake topology with increasing Mach number due to the changing pressure ratio at the nozzle exit is found. At $$M_\infty =3$$ the moderate underexpansion rate of $$p_\mathrm{e}/p_\infty \approx 5$$ leads to a formation of a recirculation region with an elongated triangular cross-section reaching to the nozzle exit. At $$M_\infty =6$$ a substantially stronger afterexpansion of the jet plume ( $$p_\mathrm{e}/p_\infty \approx 100$$ ) causes the formation of a cavity region with a quadrangular cross-section. The stronger deflection towards the nozzle at $$M_\infty =3$$ results in lower mean and rms wall pressure ratios than at $$M_\infty =6$$ . However, due to the higher freestream pressure value at the lower Mach number the relation of absolute values is reciprocal, making the lower supersonic regime more critical with respect to dynamic structural loads. This observation is confirmed by an overall good agreement between numerical and experimental data at characteristic positions on the base and nozzle wall. Furthermore, it was shown that undesired effects of the strut support in the wake are present along the whole circumference. For $$M_\infty =3$$ the strut influence is found to be particularly intense. The spectral analysis of wall pressure fluctuations reveals fundamental differences in the dynamic behavior of the two investigated wake flow regimes. At $$M_\infty =3$$ , a dominant frequency range around $$Sr_\mathrm{D}\approx 0.2$$ associated with the inner dynamics of the recirculation bubble is found at the base, while on the nozzle a broad-band low-frequency content of substantially higher amplitudes is detected, which is a footprint of the graduate realignment of the turbulent shear layer along the nozzle wall. The spectra at $$M_\infty =6$$ are characterized by several high-frequency sharp peaks at $$Sr_\mathrm{D}\geqslant 0.8$$ . A strong correlation between the supported wind tunnel configuration and the axisymmetric free-flight case is found for the peaks at $$Sr_\mathrm{D}\approx 0.85$$ known to be caused by the radial flapping motion of the shear layer along the cavity.

VELOCITY MEASUREMENTS OF TURBULENT WAKE FLOW OVER A CIRCULAR CYLINDER

There are two general concerns in the velocity measurements of turbulence. One is the temporal characteristics which governs the turbulent mixing process. Turbulence is rotational and is characterized by high levels of fluctuating vorticity. In order to obtain the information of vorticity dynamics, the spatial characteristics is the other concern. These varying needs can be satisfied by using a variety of diagnostic techniques such as invasive physical probes and non-invasive optical instruments. Probe techniques for the turbulent measurements are inherently simple and less expensive than optical methods. However, the presence of a physical probe may alter the flow field, and velocity measurements usually become questionable when probing recirculation zones. The non-invasive optical methods are mostly made of the foreign particles (or seeding) instead of the fluid flow and are, thus, of indirect method. The difference between the velocities of fluid and foreign particles is always an issue to be discussed particularly in the measurements of complicated turbulent flows. Velocity measurements of the turbulent wake flow over a circular cylinder will be made by using two invasive instruments, namely, a cross-type hot-wire anemometry (HWA) and a split-fiber hot-film anemometry (HFA), and a non-invasive optical instrument, namely, particle image velocimetry (PIV) in this study. Comparison results show that all three employed diagnostic techniques yield similar measurements in the mean velocity while somewhat deviated results in the root-mean-squared velocity, particularly for the PIV measurements. It is demonstrated that HFA possesses more capability than HWA in the flow measurements of wake flow. Wake width is determined in terms of either the flatness factor or shear-induced vorticity. It is demonstrated that flow data obtained with the three employed diagnostic techniques are capable of yielding accurate determination of wake width.

A unified theory for turbulent wake flows described by eddy viscosity

In this paper, we consider the conservation laws for the far downstream wake equations described by eddy viscosity. A basis of conserved vectors is constructed. The well-known conserved quantities for the turbulent classical wake and the turbulent wake of a self-propelled body are obtained by integrating the corresponding conservation law across the wake and imposing the boundary conditions. For the wake of a self-propelled body the additional condition that the drag on the body is zero and is required to obtain the conserved quantity. A third conservation law, which possibly belongs to another type of wake, is discovered. The Lie point symmetry associated with the conserved vector is used to obtain the invariant solution and a typical velocity profile for this wake is provided. This wake appears to have common properties with the other two well-known wakes. We then analyse the invariant solutions to all three wake problems and prove that a simple mathematical relationship exists between them thus unifying the theory for turbulent wake flows.

On the bubble rise velocity of a continually released bubble chain in still water and with crossflow

The rise velocities of in-chain bubbles continually released from a single orifice in still water with and without crossflow are investigated in a series of laboratory experiments for wobbling ellipsoidal bubbles with moderate Reynolds number. For the limiting case in still water, that is, crossflow velocity = 0, the theoretical turbulent wake model correctly predicts the in-chain bubble rise velocity. In this case, the bubble rise velocities VB are enhanced compared to the terminal velocities of the isolated bubbles V0 due to wake drafting and are scaled with flow rate Q and bubble diameter D. Here, we also derive an updated wake model with consideration of the superposition of multiple upstream bubble wakes, which removes the nonlinear behavior of the non-distant (i.e., local) wake model. For the cases with crossflow, the enhancement of the in-chain bubble rise velocity can be significantly reduced, and imaging of the experiments shows very organized paring and grouping trajectories of rising bubbles not observed in still water under different crossflow velocities. The in-chain bubble rise velocities in crossflow are described by two models. First, an empirical model is used to correct the still-water equation for the crossflow effect. In addition, a semi-theoretical model considering the turbulent wake flow and the crossflow influence is derived and used to develop a theoretical normalization of bubble rise velocity, crossflow velocity, and the released bubble flow rate. The theoretical model suggests there are two different regimes of bubble-bubble interaction, with strong interaction occurring for the non-dimensional crossflow velocity Uc+=πUc3D3V0/(18gβQ2) less than 0.06 and weaker interaction occurring for Uc+ greater than 0.06, where Uc is the crossflow velocity, g is the acceleration of gravity, and β is the mixing length coefficient.

Revised Prandtl mixing length model applied to the two-dimensional turbulent classical wake

Previous applications of Prandtl׳s mixing length model to turbulent wake flows, which neglect the kinematic viscosity of the fluid, have underestimated the width of the boundary layer. In this paper, we present a revised Prandtl mixing length model by including the kinematic viscosity of the fluid. We show that this model predicts a boundary that lies outside the one predicted by Prandtl. We also prove that the results for the two models converge for very large Reynolds number wake flows.

Diffusive dynamics and stochastic models of turbulent axisymmetric wakes

A modelling methodology to reproduce the experimental measurements of a turbulent flow in the presence of symmetry is presented. The flow is a three-dimensional wake generated by an axisymmetric body. We show that the dynamics of the turbulent wake flow can be assimilated by a nonlinear two-dimensional Langevin equation, the deterministic part of which accounts for the broken symmetries that occur in the laminar and transitional regimes at low Reynolds numbers and the stochastic part of which accounts for the turbulent fluctuations. Comparison between theoretical and experimental results allows the extraction of the model parameters.

Characterizing Wake Turbulence with Staring Lidar Measurements

Lidar measurements in the German offshore wind farm Alpha Ventus were performed to investigate the turbulence characteristics of wind turbine wakes. In particular, we compare measurements of the free flow in the surroundings of the wind turbines with measurements in the inner region of a wake flow behind one turbine. Our results indicate that wind turbines modulate the turbulent structures of the flow on a wide range of scales. For the data of the wake flow, the power spectrum as well as the multifractal intermittency coefficient reveal features of homogeneous isotropic turbulence. Thus, we conjecture that on scales of the rotor a new turbulent cascade is initiated, which determines the features of the turbulent wake flow quite independently from the more complex wind flow in the surroundings of the turbine.