Streamwise Turbulence Intensity Research Articles

Impact of blade shape on the aerodynamic performance and turbulent jet dynamics produced by a ducted rotor

A ducted rotor system was used to produce turbulent jets with a Reynolds number up to 5.97 × 105 and Mach number of 0.222 based on mean streamwise velocity. Three rotors with a diameter of 11.8 cm were manufactured and tested inside a duct with a 1 mm tip clearance at a speed up to 30 000 revolutions per minute (rpm). All rotor blades contain the same aspect ratio of 2.2, a National Advisory Committee for Aeronautics 2410 airfoil, and ideal pitch distribution. However, three different blade planform shapes were used including a rectangular shape with constant chord, trapezoidal shape with a taper ratio of 0.5, and elliptical shape where the trailing edge of the blade is expressed with an elliptical function. The rotor thrust and electric power were measured, and the thrust coefficient and figure of merit was computed. The flow-field produced by the ducted rotors was measured in the near-field using laser Doppler velocimetry techniques. The inflow velocity approximately 3 mm upstream of the rotor blade leading edge was acquired and its significance on blade aerodynamics and performance is analyzed. Time-averaged contours of cross-stream vorticity reveal intense hub and blade tip vortex structures, which are impacted by the shape of the blade, particularly in the blade tip region. Tip vorticity as well as streamwise turbulence intensity and turbulent kinetic energy in this region were mitigated for the rotors with trapezoidal and elliptical blades. However, the turbulent structure of the jet produced by all three rotor blade shapes showed similarity at a mere 2.8 rotor diameters downstream of the rotor. This finding emphasizes the importance of blade design on the near-field dynamics of ducted rotor flows for aircraft propulsion.

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.

Time-averaged flow characterisations in a bimodal gravel-bed stream and relative role of sediment depositions on near-bed coherent flow structures

Abstract The present study aims to quantify experimentally the relative role of sediment depositions on near-bed flows and turbulence in a gravel-bed stream. Time-averaged velocity was measured over a sand-filled gravel-bed stream with four cases of sediment depositions and compared with those over a gravel-bed stream without sediment depositions. An acoustic Doppler velocimeter was used to measure the instantaneous velocity of flows. The progressive infilling of void spaces in the gravel-bed stream forms distinct bimodal depositions that alter the mean flows characterised by increasing zero-velocity levels and massive damping in the bed shear stresses. The data plots of turbulent intensity depict enhancement of streamwise turbulent intensity in the near-bed flow region with increasing sand depositions. Moreover, the opposite nature of streamwise and vertical turbulent kinetic energy fluxes in the interfacial sublayer leads to slowing down the time-average Reynolds shear stresses at the vicinity of the gravel-bed surface. At the vicinity of the crest, the ejection and sweep events contributed approximately 86 and 56%, respectively, to the total Reynolds shear stress production in the case of gravel bed under clear-water flow conditions. By contrast, the contributions of turbulent sweep events increased over the sand-filled gravel bed at the same location.

Patterns of turbulent flow structures over dune shaped bed features under the influence of downward seepage

The research presents an experimental investigation on change in streamwise flow velocity and turbulent characteristics over a fixed dune shaped bed feature, in the presence and absence of downward seepage. Streamwise velocity, Reynolds Shear Stress (RSS), turbulent intensities, and third order correlation profiles are presented along the flow depth at eleven locations over the dune. Amplification in the values of streamwise velocities, RSS, and turbulent intensities has been observed at the initial sections on the stoss side as well as at the sections on the lee side of the dune under the influence of downward seepage. At the initial and lee side sections of the dune, average values of the streamwise velocity, RSS, and streamwise turbulent intensity along the depth of flow increase by ∼0.2 %−31 %, ∼9 %−50 %, and ∼2 %−30 % respectively, for the 10 % seepage condition as compared to the no seepage condition. For the 15 % seepage condition, there has been found an increase in these value values by ∼3 %−67 %, ∼52 %−150 %, and ∼35 %−43 % respectively, at the considered sections over the dune. Further, it has also been observed that under the influence of downward seepage, bed shear stress increases at the initialand lee side sectionsof the dune. Through the third order correlation studies, occurrence of rushing flow due to seepage was confirmed at the lee side and initial sections of the dune. Further analysis at the wake zone revealed a reduction in the values of second and third-order moments demonstrating greater streamwise flow of Reynolds stress and diffusion of vertical Reynolds stress in streamwise direction as a result of increased velocity owing to downward seepage. Results indicate that the introduction of seepage leads to the creation of large angled dunes with wake zone stretched in the flow direction as well as the same wake zone was found squeezed in the vertical direction.

Constant stress layer characteristics in simulated stratified air flows: Implications for aeolian transport

Varying thermal atmospheric stability conditions and their effects on shearing flows has long been a subject of interest for researchers working in atmospheric science. The development of new instrument technologies now offers an opportunity to study flows with high spatial and temporal resolutions in wind tunnel atmospheric boundary layers. In the presented study, we use a laser Doppler anemometer within the Trent Environmental Wind Tunnel Laboratory to investigate the influence of thermal stratification on the constant stress layer. Analyses of the thermal stratification represented by the gradient Richardson number and the apparent von Kármán parameter, shear velocity, and the slope of the streamwise velocity profiles reveal strong linear relationships. An exponential relationship between thermal stability and the apparent roughness length is also revealed. Profiles of the streamwise and vertical velocity and turbulence intensity, as well as the dimensionless Reynolds stress, are influenced by the gradient Richardson number. These findings have implications for producing accurate models of sediment entrainment and transport by wind in non-neutral conditions.

Characteristics of turbulent boundary layers generated by different tripping devices

In this study, we employ a high-fidelity flow visualisation technique to investigate the resemblance between a turbulent boundary layer generated in a lab environment with a limited development length by different tripping devices and a naturally developed canonical turbulent boundary layer. Furthermore, we aim to provide statistics of the wall-normal velocity fluctuation of the tripped boundary layers and analyse them compared with the canonical turbulent boundary layer. This is achieved by conducting two-dimensional particle image velocimetry measurements to acquire the velocity components in the stream-wise wall-normal plane downstream of the tripping location. Different criteria including integral parameters, diagnostic plot, stream-wise and wall-normal turbulence intensities, and mean velocity deficit profiles are employed to compare the boundary layer profiles generated by different trips with well-behaved turbulent boundary layers presented in the literature. The generation of Reynolds shear stress in tripped boundary layers is analysed using quadrant analysis, and suitably sized trips are shown to have contributions of sweeps and ejections in a similar manner to a well-behaved turbulent boundary layer. Furthermore, through the detection of uniform momentum zones, the presence of coherent structures in the logarithmic and outer layers of these well-behaved tripped boundary layers is shown. The findings of this study identify the blockage created by trips as the main factor affecting the turbulence statistics at a certain downstream distance. The results also suggest that the investigation of inner-scaled mean stream-wise velocity is recommended as a simple yet reliable and rapid assessment of the impact of a trip on the turbulent boundary layer development in short test sections.

Effect of void space arrangement on wind power potential and pressure coefficient distributions for high-rise void buildings

High-rise void building complexes can augment the permeation of airflows over buildings, and thereby strengthen urban wind energy harvesting for realization of the sustainable development goals (SDGs). This paper considers the wind over a typical 2×2 compact high-rise building array with the openings to analyze the wind power potential at varying void sizes, locations of voids, and direction of incoming wind. The predicted mean wind speeds and turbulence intensities are compared against the measured data with 4 generic high-rise building models having voids in an atmospheric boundary layer wind tunnel for validation of the computational model. Based on the comparative results from four common Reynolds-averaged Navier-Stokes (RANS) turbulence models including the standard, realizable, renormalization group (RNG) k-ε, and shear-stress transport (SST) k-ω models as well as the Reynolds stress model (RSM), the RSM approach can provide the most accurate predictions of streamwise mean velocity and turbulence intensity. The present study then conducts CFD simulations to explore the effects of opening configuration and wind direction on the wind field around high-rise void buildings. Considering the variations of void sizes of 10 × 10 m2, 12.5 × 12.5 m2, 15 × 15 m2, void heights of z/H = 0.25, 0.5, 0.75 and wind directions of 0°, 45°, respectively, the simulated results indicate elevated wind power densities with acceptable turbulence intensities over the upstream gap passage and void channels to achieve prospective urban wind power harvest and mitigate wind load on structures of high-rise void buildings.

Response of a supersonic turbulent boundary layer to different streamwise adverse pressure gradients

An adverse pressure gradient (APG) has an impact on the boundary layer, increasing the turbulent intensity of the layer. The mean and turbulent properties of the turbulent boundary layer on a flat plate with different APGs were investigated at Mach 2.7 in the present work utilizing the particle image velocimetry and nanoparticle-based planar laser scattering techniques. According to analysis, the changing trends of boundary layer parameters are different depending on whether the local mainstream velocity or freestream velocity of the wind tunnel is used to normalize. Using the former might make the enhanced effect of the rising APG more visible. With the rise in APG, the principal strain rate, turbulent fluctuation, Reynolds stress, and turbulence production in the boundary layer all increased, while the turbulent boundary layer's thickness dropped. Furthermore, the heightened upward ejection and downward sweep events caused the streamwise turbulence intensity to reach its outer peak under the influence of strong APG. The characteristics of the spanwise vortex in the boundary layer are investigated in conjunction with the probability density function analysis. The growing APG, which primarily promote negative vorticity, can strengthen the rotational strength of spanwise vortices, which are a component of hairpin vortices. As APG rises, the number of small-scale vortices in the boundary layer increases and the fractal dimension grows. The increase in small-scale vortices tends to induce strong transportation and promotes turbulence intensity. Further investigation reveals that the increased volume change caused by the enhanced compression effect with increasing APG exacerbated the vorticity.

The Barnacle: A low-cost marine turbulence sensor

The Barnacle is a new form of marine sensor, which offers a low-cost alternative to the Acoustic Doppler Velocimeter (ADV) for turbulence measurements in oceanographic applications, including tidal power sites. This new device measures flow velocity from pressure differences between slanted faces, and is estimated to cost five to ten times less than an ADV. The Barnacle is of interest to tidal turbine developers because accurate quantification of the unsteady inflow is vital for determining fatigue loads.In this work, results are presented from a benchmarking campaign against an ADV in the Strangford Narrows (County Down, Northern Ireland). When the Vector performs optimally (i.e., with minimal noise), good agreement is seen between the Barnacle and the ADV in the streamwise direction: mean flow measurements are typically within 5%.The Barnacle is less susceptible to random noise than the ADV: the noise floor is up to two decades lower. Good agreement is observed in unsteady flow measurements, and the streamwise turbulence intensity estimates from the two devices are consistently within 3 percentage points.Overall, the novel approach outlined here offers a robust, low-cost alternative to traditional techniques for oceanographic turbulence measurements, in particular directional flows and tidal power sites.

A novel superposition method for streamwise turbulence intensity of wind-turbine wakes

A novel superposition method for streamwise turbulence intensity of wind-turbine wakes

Characterisation of flow dynamics within and around an isolated forest, through measurements and numerical simulations

The case study of ‘Bosco Fontana’, a densely-vegetated forest located in the north of Italy, is analysed both experimentally and numerically to characterise the internal ventilation of a finite forest with a vertically non-homogeneous canopy. Measurements allow for the evaluation of the turbulent exchange across the forest canopy. The case study is then reproduced numerically via a two-dimensional RANS simulation, successfully validated against experimental data. The analysis of the internal ventilation leads to the identification of seven regions of motion along the predominate-wind direction, for whose definition a new in-canopy stability parameter was introduced. In the vertical direction, the non-homogeneity of the canopy leads to the separation of the canopy layer into an upper foliage layer and a lower bush layer, characterised respectively by an increasing streamwise velocity and turbulence intensity, and a weak backflow. The conclusions report an improved description of the dynamic layer and regions of motion presented in the literature.

Estimation of wavenumber–frequency spectra of wall pressure due to turbulent flow over a flat plate using large-eddy simulation

The wavenumber–frequency spectra (WFS) of turbulent wall pressure fluctuations are used to design underwater acoustic systems, and a method is presented to determine them for flat plate flow using large-eddy simulations (LES). First, the Reynolds averaged Navier–Stokes (RANS) analysis is carried out for flow over the plate using k–ω shear-stress transport model. Flow parameters are extracted from the output of this analysis and used to impose boundary conditions for large-eddy simulations using a smaller domain with finer mesh. Mesh convergence studies are done to establish the adequacy of the proposed meshing scheme for estimating the turbulent boundary layer wall pressures. The stream-wise velocity profiles, turbulence intensities, and power spectra obtained using LES are compared with other computational and experimental results. The time history of fluctuating pressure on the wall at various stream-wise locations is used to estimate the WFS. Estimations are made of the convective ridge as well as sub-convective and low wavenumber portions of the spectrum. The computations are performed at momentum thickness-based Reynolds numbers (Rθ) of 5761, 7988, and 7709. The effect of downstream distance on the WFS is studied by computing it at three downstream locations and shown that the downstream distance has little effect on the WFS once the flow has become fully turbulent. The use of a desktop workstation for the estimation of WFS has not been reported earlier. The results show that the WFS of turbulent pressure due to flow over more complex geometries can be estimated using a similar method.

Experimental and numerical characterization of the airflow in the wake of a heavy truck

The wake flow of a heavy truck model is investigated at Re=8.5×104 using particle image velocimetry measurements combined with computational fluids dynamics-simulations. Experimental measurements are carried out on a 1:28-scale model, focusing exclusively on the central longitudinal plane, in the rear of the truck model. Numerical simulations are performed based on the URANS (unsteady Reynolds averaged Navier–Stokes) approach using two statistical turbulence models, i.e., the shear stress transport k–ω and the baseline Reynolds stress (BSL-RSM) models. A comparison between the numerical and experimental results of the mean velocity profiles in the wake of the heavy truck is found to be relatively consistent. The BSL-RSM model, however, gives a better prediction of experiments, with a deviation of 6% in the near wake, against 13% for the SST k–ω. Both URANS models undervalue the streamwise and spanwise turbulence intensity components with a deviation around 24%, compared with the experimental results. The characteristic feature of the wake flow topology is the formation of a recirculation bubble resulting from the shear layers separated from the truck surfaces. Different identification methods, including visualization of closed streamlines, vorticity magnitude, and the Q-invariant criterion, are considered and highlight the existence of two particular vortex regions in the mean flow: a vortex-shedding area in the upper recirculation region and a back-truck attached vortical structure. It is found that the Q criterion-based technique is a relevant indicator of the vortex cores regions.

The turbulence development of a vertical natural convection boundary layer

Results from direct numerical simulations of a vertical natural convection boundary layer (NCBL) with $Pr=0.71$ reveal that the turbulence development of such a thermally driven convective flow has two distinct stages: at relatively low Grashof number, the bulk flow is turbulent while the near-wall region is laminar-like or weakly turbulent; at sufficiently high Grashof number, the entire flow becomes turbulent in the sense of von Kármán (cf. Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56, for the ultimate turbulent regime). Investigations on the turbulence statistics show that the near-wall Reynolds shear stress is negligible in the weakly turbulent regime but will grow in magnitude as the flow transitions to the ultimate regime at higher Grashof number. Similar behaviour is also seen in the streamwise turbulence intensity, where it develops from a mono-peak profile into a dual-peak structure as the Grashof number increases. At higher Grashof number, the near-wall energetic site is shown to have an energy distribution similar to that of a canonical wall-bounded turbulence (e.g. Hutchins & Marusic, Phil. Trans. R. Soc.A, vol. 365, 2007, pp. 647–664), with a peak centred at fixed location and wavelength ( $y^+=18$ and $\lambda ^+_x=1000$ ) in viscous coordinates. Investigation on the spanwise spectra also suggests that the turbulent near-wall streaks emerge only at sufficiently high Grashof number, with constant spacing $\lambda _z^+\approx 130$ . The extent of the weakly turbulent regime is identified using the maximum velocity location $\delta_m$ and a laminar length scale $\delta_u$ . The development of near-wall turbulence is also investigated by examining the turbulence kinetic energy budget. In the weakly turbulent regime, the near-wall turbulence is sustained predominantly by the pressure transport in addition to the shear production. At higher Grashof number, the flow becomes fully turbulent, and both turbulent transport and shear production become stronger, while the pressure transport is decreased. These results also reveal that the production–dissipation ratio $P/\varepsilon$ of the NCBL would follow a fundamentally different trend to the canonical wall-bounded flows, which further supports that the near-wall turbulence generation is affected by the bulk flow.

Atmospheric Turbulent Characteristics Under Summer Shamal in Coastal Qatar

AbstractSummer Shamal, a strong low‐level northwesterly wind in the Middle Eastern, is the major trigger for dust storm activity with a broad impact on regional transport and human safety. However, near‐ground turbulent mixing analysis under Shamal is still rare due to the lack of available high frequency data. The present study explores the near‐surface turbulence characteristics under summer Shamal, compared with those of non‐Shamal, in the coastal region of Qatar (26.08°N, 51.36°E). The results show that Shamal prevents the development of summer sea breezes in the Persian Gulf. A “Shamal day” (SD) is commonly defined as a day with a strong, continuous, north‐northwesterly wind. Compared to non‐Shamal days (NSD), SDs are characterized by higher surface sensible heat flux and turbulent kinetic energy (TKE) with lower humidity, especially around noon time. At night, the wind turbulence energy is contained in smaller eddies for SD due to the more stable atmospheric conditions. The streamwise velocity spectra analysis displays a power‐law trend with a coefficient of −1.53 as compared to the traditional Kolmogorov −1.67 (−5/3) power law, indicating a higher TKE dissipation rate for SD. The smaller scatter of the normalized TKE dissipation rate observed for SD is related to lower streamwise turbulence intensity. A Weibull distribution is observed for probability distribution of TKE dissipation rate under SD in log scale for both stable and unstable conditions. This distribution for TKE dissipation rate is different than the results from other field measurements due to Shamal.

Secondary motions and wall-attached structures in a turbulent flow over a random rough surface

Large-eddy simulations (LESs) are performed to explore the effects of roughness on the secondary motions (SMs) and wall-attached structures in a turbulent open-channel flow over a random rough surface at a friction Reynolds number of Reτ≈1000. Turbulent flow over two groups of rough walls – a homogeneous random arrangement and a clustered arrangement – is considered, and the results are compared with the turbulence over a smooth wall. The results show that the two roughness arrangements exhibit minor differences in the variation of mean streamwise velocity. The rough surfaces of a clustered arrangement can generate large-scale SMs, resulting in spanwise-alternating high-momentum pathways (HMPs) and low-momentum pathways (LMPs) in the time-averaged velocity. Because of SMs, the streamwise turbulence intensity is enhanced in the outer region and a larger-scale spectral peak occurs in the turbulence energy spectra. On the other hand, the outer-layer similarity is still satisfied for the homogeneous random arrangement. The wall-attached structures of streamwise velocity fluctuations in the presence of roughness are extracted through a three-dimensional clustering identification approach. The wall-attached structures retain their geometric self-similarity for both rough surfaces, whereas the length and width of these structures decreases and increases, respectively. The population density scales inversely with the height, reflecting the hierarchical nature of the structures. In addition, when the streamwise velocity fluctuations within the wall-attached structures are conditionally averaged, the profile exhibits logarithmic behavior in the logarithmic region for the homogeneous random arrangement; in the case of the clustered arrangement, the reconstructed profile is affected by the SMs. A new identification approach is applied to decompose the secondary flow structures into wall-detached structures, and the logarithmic behavior of the streamwise turbulence intensity is reconstructed on the basis of the new wall-attached structures. The present results provide evidence of the presence of the wall-attached structures in instantaneous flow fields of rough-wall turbulence, for both homogeneous and heterogeneous roughness arrangements.

A scale-based study of the Reynolds number scaling for the near-wall streamwise turbulence intensity in wall turbulence

Very recently, a defect model which depicts the growth tendency of the near-wall peak of the streamwise turbulence intensity has been developed (Chen and Sreenivasan, 2021). Based on the finiteness of the near-wall turbulence production, this model predicts that the magnitude of the peak will approach a finite limit as the Reynolds number increases. In the present study, we revisit the basic hypotheses of the model, such as the balance between the turbulence production and the wall dissipation in the region of peak production, the negligible effects of the logarithmic motions on the wall dissipation, and the typical time-scale that the outer-layer flow imposes on the inner layer. Our analyses show that some of them are not consistent with the characteristics of the wall-bounded turbulence. Moreover, based on the spectral stochastic estimation, we develop a framework to assess the wall dissipation contributed by the energy-containing eddies populating the logarithmic region, and uncover the linkage between its magnitude and the local Reynolds number. Our results demonstrate that these multi-scale eddies make a non-negligible contribution to the formation of the wall dissipation. Based on these observations, we verify that the classical logarithmic model, which suggests a logarithmic growth of the near-wall peak of the streamwise turbulence intensity with regard to the friction Reynolds number, is more physically consistent, and still holds even with the latest high-Reynolds-number database.

On the effect of streamwise and spanwise spacing to height ratios of three-dimensional sinusoidal roughness on turbulent boundary layers

A developing zero pressure gradient (ZPG) turbulent boundary layer (TBL) over different three-dimensional (3D) sinewave roughnesses is investigated experimentally using single hot-wire anemometry. Seven different sinewave profiles are fabricated with the same amplitude and with different wavelengths in the streamwise (sx) and spanwise (sz) directions. The effects of varying sx and sz on turbulence statistics and the drag coefficient (Cf) are assessed. The wall-unit normalized streamwise mean velocity profile is shifted downward compared with the smooth wall profile for all roughnesses. The streamwise spacing to height ratio sx/k has a more significant effect on the roughness function ΔU+ and Cf compared with the spanwise spacing to height ratio sz/k. However, sz/k has a large impact on the streamwise turbulence intensities in the log and outer layer. An excellent collapse is observed among the mean streamwise velocity profiles plotted in defect form in the outer region. However, a lack of similarity between TBLs over different rough surfaces is observed in the outer region for the turbulence intensities profiles. For isotropic 3D sinusoidal roughness (equal streamwise and spanwise spacing to height ratios), the contours of premultiplied streamwise turbulent energy spectrograms show an increase in energy in the outer layer with increasing spacing to height ratios. For anisotropic 3D sinusoidal roughness (unequal streamwise and spanwise spacing to height ratios), the contours of premultiplied streamwise turbulent energy spectrograms show an increase in energy in the outer layer with increasing sz/sx from half to two in this study.

On the application of statistical turbulence models to the simulation of airflow inside a car cabin

Computational fluid dynamics simulations of airflow inside a full-scale passenger car cabin are performed using the Reynolds averaged Navier–Stokes equations. The performance of a range of turbulence models is examined by reference to experimental results of the streamwise mean velocity and turbulence intensity profiles, obtained using the hot-wire anemometry technique at different locations inside the car cabin. The models include three linear eddy-viscosity-based variants, namely, the realizable k–ε, the renormalization group k–ε, and the shear-stress transport k–ω models. The baseline Reynolds stress model (BSL-RSM), a second-moment-closure variant, and an Explicit Algebraic Reynolds Stress Model (BSL-EARSM) are also investigated. Visualization of velocity vectors and streamlines in different longitudinal planes shows a similar airflow pattern. The flow topology is mainly characterized by jet flows developing from the dashboard air vents and extending to the back-seats compartment resulting in a large vortex structure. Additionally, a comparison between numerical and experimental results shows a relatively good agreement of the mean velocity profiles. However, all models exhibit some limitations in predicting the correct level of turbulence intensity. Moreover, the realizability of the modeled Reynolds stresses and the structure of turbulence are analyzed based on the anisotropy invariant mapping approach. All models reveal a few amounts of non-realizable solutions. The linear eddy-viscosity-based models return a prevailing isotropic turbulence state, while the BSL-RSM and the BSL-EARSM models display pronounced anisotropic turbulence states.

Large-eddy simulation and analytical modeling study of the wake of a wind turbine behind an abrupt rough-to-smooth surface roughness transition

The evolution of a wind turbine wake situated downstream of an abrupt change in surface roughness is investigated using large-eddy simulations (LES). The results are compared with the evolution of the wake of a turbine sited on a homogeneously rough surface, and with the flow over a surface undergoing an abrupt roughness transition without a turbine. The changed surface roughness affects the turbulent statistics such as streamwise velocity, turbulence intensity, and shear stress. Different velocity deficits can be constructed based on different definitions of “background” velocity. The usual definition, that is, the difference between the velocity upstream and downstream of a turbine, attains negative values over a significant portion of the turbine wake, rendering it difficult to model using the usual Gaussian radial shape-based framework. An alternative definition, that is, the difference between the velocity over a heterogeneous surface in the absence and in the presence of a turbine, has mostly positive values and is amenable to modeling. A new model accounting for streamwise and vertical variations of the background velocity profile is developed. The new model yields more accurate predictions of the LES results than the existing Gaussian wake-shape model, which is applicable only for turbines sited on homogeneously rough surfaces.