Streamwise Length Scale Research Articles

Effects of multi-scale turbulent motions on aerodynamic performance of wind turbine under sand-laden conditions

Wind turbine installation in the desert and Gobi regions offers a promising approach for meeting long-term energy demands. However, the effect of multi-scale characteristics in sand-laden atmosphere flows on wind turbine aerodynamic performance has not been evaluated. In this study, wind velocity data collected from the Qingtu Lake Observation Array (QLOA) were employed to address this gap. Results show that up to 58% of the total turbulent kinetic energy (TKE) is accounted for by very large-scale motions (VLSMs), which make up a considerable portion of the TKE. The contributions of the large-scale motions (LSMs) and the small-scale motions (SSMs) to TKE are 36% and 6%, respectively. The contribution of multi-scale turbulent motions to the aerodynamic loads of wind turbine under sand-laden conditions has been quantified for the first time. The comparison demonstrates that while LSMs and SSMs exhibit a rapid drop in their contributions to wind turbine loads with height, VLSMs show a rapid increase. Wavelet analysis revealed a strong correlation between VLSMs and power, thrust, and blade root flapwise moment at periods ranging from 256 to 1024 s. This correlation weakens as the streamwise length scale of the turbulent coherent structure decreases. This study provides essential insights for optimizing wind turbine design and site selection in sand-laden environments.

Effects of streamwise-elongated and spanwise-periodic surface roughness arrays on supersonic boundary-layer instability

We investigate the influence of streamwise-elongated and spanwise-periodic roughness arrays on the supersonic boundary-layer instability under the assumption of a high Reynolds number. The main focus is on the lower-branch viscous instability modes, and the spanwise spacing of the roughness arrays is taken to be comparable to the characteristic wavelength of the modes (which is on the triple-deck scale), so that most significant effects can be generated. The streamwise length scale of the elements is much greater than the spanwise length scale. The roughness height is determined by requiring the change of the wall shear to be O(1). The equations governing the nonlinear roughness-induced streaky flow are deduced from the standard triple-deck theory. These equations are parabolic in the streamwise direction and are solved using a streamwise marching method to characterize the evolution of streaky structures. The linear stability of the streaky flow is analyzed. By exploiting the asymptotic structure, the bi-global eigenvalue problem is reduced to a one-dimensional one, where the stability is found to be controlled by the spanwise-dependent wall shear. The reduced eigenvalue problem is solved numerically. The results show that roughness arrays inhibit instability modes with moderate frequencies but promote high-frequency modes. Roughness elements of greater height have stronger effects on the linear stability. The shape of roughness elements plays an important role. A significant feature, different from the subsonic case, is that fundamental and superharmonic resonance modes radiate sound waves spontaneously into the far field.

Impact of large-scale free-stream turbulence on a pitching airfoil

This paper investigates the impact of large-scale turbulence on the aerodynamic characteristics of a pitching wind turbine blade at Reynolds number 135 000, whose cross-section is a NACA0012 airfoil with constant chord length. Large-eddy simulations at reduced frequencies, $k_{red} = 0.05$ and 0.1, were validated against reference data from the literature. An efficient method capable of generating synthetic large-scale turbulence at the inlet was applied by using two streamwise integral length scales $L_{x} = 1c$ and 1.5 $c$ , which represent energetic turbulence eddies at the height where the wind turbine operates. For $k_{red}= 0.1$ , the change in the maximum lift coefficient at the dynamic stall angle near the maximum angle of attack is on average 20 % lower and during the downstroke it is on average 22 % lower, compared with the smooth inflow. A higher reduced frequency ( $k_{red} = 0.2$ ) apparently does not further change the lift, drag and moment coefficients, and the inflow turbulence disordered leading-edge vortices. The turbulent shear stress and the phase-averaged dispersive shear stress in the wake are of the same magnitude, but with negative and positive signs, respectively, suggesting that the large-scale phase-averaged fluctuations transfer momentum in the opposite direction compared with the turbulent fluctuations, reducing the drag on the suction-side flow, and subsequently increasing the averaged lift coefficient. This demonstrates the critical importance of the large-scale non-turbulent unsteadiness in the wake of a pitching wing.

Large-scale motions in a turbulent natural convection boundary layer immersed in a stably stratified environment

This study investigates the coherence of turbulent fluctuations in a turbulent vertical natural convection boundary layer immersed in a stably stratified medium (turbulent buoyancy layer). A turbulent buoyancy layer of a fluid having a Prandtl number of $0.71$ at a Reynolds number of $800$ is numerically simulated using direct numerical simulation. The two-point correlations reveal that the streamwise velocity fluctuations are coherent over large streamwise distances, with the length scale of the streamwise coherence being greater than the boundary layer thickness. This is due to large-scale motions (LSMs), similar to the LSMs observed in canonical wall-bounded turbulence despite the stark differences in flow dynamics. Both high-speed (positive) and low-speed (negative) streamwise velocity fluctuations form LSMs, with their streamwise length scales increasing with increasing wall-normal distance. High-speed LSMs are composed of upwash flow with high temperatures, while low-speed LSMs are composed of downwash flow with low temperatures. Both high-speed and low-speed LSMs meander appreciably in the streamwise direction, with the degree of meandering being correlated with the sign of the spanwise velocity fluctuations. The LSMs exhibit coherence across significant wall-normal distances and contribute significantly to the turbulence production in the outer layer. Examining the one-dimensional energy spectra of the turbulent buoyancy layer shows that the LSMs are the dominant energy-containing motions, implying that the length scale of the energy-containing range is of the order of boundary layer thickness. Notably, wall-normal velocity, spanwise velocity and buoyancy fluctuations do not form LSMs with streamwise length scales comparable to streamwise velocity fluctuations.

Lift alleviation in travelling vortical gusts

AbstractLift alleviation by a mini-spoiler on aerofoils, unswept and swept wings encountering an isolated counter-clockwise vortical gust was investigated by means of force and velocity measurements. The flow separation region behind the spoiler remains little affected during the gust encounter. The maximum lift reduction is found for the static stall angle of attack. The change in the maximum lift during the gust encounter is approximately equal to that in steady freestream. The comparison with plunging aerofoils reveals that, for the same maximum gust and plunge velocity, the effectiveness of the mini-spoiler is much better in travelling gusts. This reveals the importance of the streamwise length scale of the incident gust. For the unswept wing, there is some three-dimensionality of the flow separation induced by the mini-spoiler near the wing tip. The magnitude of the lift reduction can be estimated using the aerofoil data and by making an aspect ratio correction for the reduced effective angle of attack. For the swept wing, the mini-spoiler can disrupt the formation of a leading-edge vortex induced by the incident vortex on the clean wing and can still reduce the maximum lift.

Influence of synthetic jet on uniform momentum zones

Based on a set of streamwise-wall-normal experimental databases of turbulent boundary layer (TBL) acquired by time-resolved particle image velocimetry (TR-PIV) system at the Reynolds number Reτ=537, which includes the velocity fields with and without synthetic jet, the influence of the synthetic jet on uniform momentum zones (UMZs) was studied. The turbulent/non-turbulent (T/NT) interface of each instantaneous frame was identified by local turbulent kinetic energy (L-TKE) method and the area below the interface was divided into UMZs by probability density function (P.d.f.) histogram of streamwise velocity. The relationship between the T/NT interface average height EYi and the UMZs number NUMZ is analyzed. The spatial position and velocity of UMZs are extracted by centroid method, and the basic statistical characteristics within UMZs under two working conditions are investigated. After processing the velocity fields corresponding to each NUMZ separately, it is found that NUMZ is highly correlated with Q events. The synthetic jet reduces the streamwise and wall-normal length scales of the fluid induced by Q events, and under the same externa conditions, the two scales are also positively related to the intensity of Q events. The shear stress in the flow field promotes the generation of the forward vortices, which drives the stratification of UMZs. The hairpin vortices generated by synthetic jet result in a large number of forward vortices in the region with y/δ<0.3, and the turbulent kinetic energy (TKE) and Reynolds shear stress are input into the vortex region in varying degrees.

Spectral analysis on dissimilarity between turbulent momentum and heat transfers in plane Couette turbulence

Nonlinear interactions between different scales in turbulence result in both interscale and spatial transport of turbulent energy, and their role in the turbulent heat transfer mechanism is also of practical importance from an engineering viewpoint. In this study, we investigate a turbulent plane Couette flow with passive-scalar heat transfer at the Prandtl number of 0.71 to discuss the similarity/difference between scale interactions in velocity and temperature fields. The constant-temperature-difference boundary condition is used so that the mean velocity and temperature profiles are similar, and then, the roles of interscale and spatial transports are compared for the spectral transport budgets of turbulent energies and temperature-related statistics. We show that turbulent heat transfer occurs at relatively small streamwise length scales compared to momentum transfer, although molecular diffusion is more significant in the temperature field as the Prandtl number is less than 1. Detailed analysis on the transport budgets of temperature-related spectra shows that scale interactions in the temperature field supply more energy to small scales than those in the velocity field. This significant temperature cascade causes more energetic temperature fluctuation at small scales, resulting in the spectral dissimilarity between turbulent heat and momentum transfers.

Experimental Investigation of Near-Field Aeroacoustic Characteristics of a Pre- and Post-Stall NACA 65-410 Airfoil

The present study reports an experimental investigation of the near-field aeroacoustic characteristics of a cambered NACA 65-410 airfoil. The experiments were performed in an aeroacoustic wind tunnel facility at a moderate chord-based Reynolds number of 4.2×105. Detailed static and dynamic surface pressure information was recorded to reveal the pre- and post-stall dynamics. By varying the angle of attack from 7° to 15°, a stall behavior similar to thin airfoil stall is observed from the evolution of the static and dynamic surface pressure spectra at different chordwise locations. Moreover, while the surface pressure spectra show a monotonic decrease with constant gradients after entering full stall, the pre-stall behavior shows a different trend and partly resembles the attached and stalled flows. Furthermore, the unsteady surface pressure spectra are compared to those obtained from a NACA 0012 airfoil, showing notable differences in the near-field stall dynamics. A scaling formula proposed by a previous study is applied to the present pressure spectra and found to scale well except for measurements close to the leading edge. The present near-field measurements and the streamwise and spanwise length scales can be useful input to the modeling of airfoil separation and stall noise for cambered airfoils.

Study of coherent structures and heat flux transportation under different stratification stability conditions in the atmospheric surface layer

A field experiment was carried out on a dry flat bed of Qingtu Lake in Minqin, China to measure the velocity and temperature in the atmospheric surface layer at high Reynolds number. The facility, the Qingtu Lake Observation Array, permits synchronous multi-point measurements of three-dimensional wind velocity and temperature at different wall-normal and spanwise positions. Data were selected to analyze the characteristics of the large-scale coherent structures under different stratification stability conditions. The results confirm the previous findings that the positive buoyancy can be considered as a wall-normal force to have a “lifting” effect increasing the size of large-scale structures and further illustrate that negative buoyancy in the stable condition has an opposite effect leading to small structures with less wall-normal coherence. The stability dependence of structure inclination angles for all three velocity components is built by a parametric model indicating a log-linear trend under near-neutral and unstable conditions. In addition, the unique measurement array at this facility also permits us to study the three-dimensional form of these features and the associated temperature fluctuations. By computing the space average for momentum and heat flux, we found that the threshold stability parameter z/L=−0.1, where z = 2.5 m and L is the Obukhov length scale, can act as a role to determine the dominant flow by shear-driven and buoyancy-driven, respectively. Last, the streamwise length scales for temperature component are investigated where a smaller length scale corresponds to a stronger buoyancy condition, but with larger values at higher heights.

Eigensolutions of the unsteady boundary-layer equations revisited (with extensions to three-dimensional modes)

Abstract

On the effects of anisotropic turbulence on leading edge noise

This paper presents an investigation on the broadband noise produced by the interaction of anisotropic turbulence with isolated aerofoils. Computational aeroacoustic simulations are performed using a synthetic turbulence method with a linearised Euler solver. A comprehensive and fundamental parameter study on leading edge noise is presented to assess the effects of aerofoil thickness, mean flow Mach number, and angle of attack in the presence of moderately anisotropic turbulence. To this end, the streamwise-to-transverse length scale ratio is varied from 0.33 to 3, which can be representative of the anisotropy in the fan wakes from aero-engines, grid-generated turbulence in open-jet wind tunnel experiments, and rotors ingesting turbulent boundary layers. Anisotropic turbulence presents a significant redistribution of the energy in the turbulence spectra in comparison with an isotropic baseline, which affects the resulting noise spectra. It has been found that the noise spectra are mainly influenced by the transverse velocity component for the examined anisotropic flows. The frequency at which the noise spectrum is at a maximum only relies on the mean flow speed and the axial length scale of the anisotropic turbulent flow. Noise reduction due to aerofoil thickness at high frequencies follows a linear trend, but the amount of noise reduction is sensitive to the anisotropy in the flow. It is shown that the contribution of the streamwise disturbances and length scale become increasingly important for thick aerofoils at high Mach numbers and for aerofoils at non-zero angle of attack.

Tomographic particle image velocimetry flow structures downstream of a dynamic cylindrical element in a turbulent boundary layer by multi-scale proper orthogonal decomposition

This study reports the modification of large and small scales in a turbulent boundary layer (TBL) perturbed by a dynamic cylindrical element (DCE). Tomographic particle image velocimetry (Tomo-PIV) was utilized to measure the flow fields downstream of the dynamic perturbation. By the approach of multi-scale proper orthogonal decomposition (mPOD), the coherent modes relevant to the predefined frequency bands were extracted from the Tomo-PIV dataset. Then, a method was developed to construct the large- and small-scale structures and the DCE-perturbed structure based on the mPOD modes. The DCE impact on the large- and small-scale structures was elaborated by comparing with the unperturbed TBL case. The two-point correlation analysis indicated that large-scale structures appear downstream of the DCE perturbation in a short streamwise length scale. More importantly, the scale rearrangements were further examined by presenting the modulation coefficients between the large scales and small-scale energy. It revealed that even though the DCE perturbation alters the level of correlation, three different types of interaction scenario can still be observed. In the near-wall region, the large-scale structures have an amplitude modulation effect on the small-scale energy with the lower positive coefficients. The reversal scale arrangement was observed at the wall-normal height around the DCE amplitude, which could be attributed to the fluid exchange caused by the new-generated turbulent structures. In the log region, it confirmed that the inclined shear layer resides along the low-speed regions, which supported the robustness of the conceptual model of hairpin packets in the current DCE-perturbed TBL.

On the near-wall structures and statistics of fluctuating pressure in compressible turbulent channel flows

The near-wall structures and statistics of fluctuating pressure (p′) in compressible turbulent channel flows (CTCF) with isothermal walls have been investigated by direct numerical simulations. Two typical cases for high bulk Mach number Ma = 3.83 and low one Ma = 1.56 are considered. A novel type of near-wall pressure structures named “alternating positive and negative structures (APNS)” is found in the high-Ma case based on the comprehensive analysis of spectra and dynamic mode decomposition of p′. These APNS of p′ are identified to have the streamwise and spanwise length scales of (λx/h, λz/h) ≈ (0.9, 1.5), where h is the channel half-height, and prefer to inhabit the low-speed wall streaks. It is also verified via a pressure splitting method that the APNS of p′ are dominated by the compressibility effects. Based on the linear stability analysis, the APNS of p′ can be intimately related to a linear stability eigenmode of the high-Ma CTCF and are sustained by the transient growth mechanism as the disturbances of the APNS length scales. Furthermore, these APNS of p′ offer an extra mechanism to generate the near-wall p′ for the high-Ma case. Moreover, it is found that the APNS of p′ have a dominating effect on the pressure-dilatation correlation and the production of Reynolds shear stress. The present study may provide a reliable way to achieve a better understanding and modeling of compressibility effects in the wall-bounded turbulence of high Ma.

Large scale structures of turbulent flows in the atmospheric surface layer with and without sand

Field measurements at the Qingtu Lake Observation Array site were performed to explore the features of large scale structures relevant to very large scale motions (VLSMs) and large scale motions (LSMs) in the atmospheric surface layer during dust weather events. The three velocity components, PM10 concentrations (particles with size less than 10 μm), and sand saltation fluxes at different heights were measured synchronously. By comparing with the results in clean-air flows, the influences of sand particles on the VLSMs were investigated. The present results indicate that the streamwise turbulent kinetic energy across all scales is enhanced in the sand-laden flows. However, the energy enhancement of small-scale motions is more pronounced than that of large scale structures, resulting in a decreased energy fraction of the large scale structures in the sand-laden flows. The inclination angles of the large scale structures are found to increase with sand concentration, owing to the decreased velocity gradient. The streamwise length scale of large scale structures and the size of the most energetic turbulent structures are found to be unchanged in the sand-laden flows relative to those in the clean-air flows. This is the study on the particle-laden wall turbulence at the largest Reynolds number to date, and the results demonstrate that the dispersed tiny particles in very dilute particle–gas flows can affect the turbulence even for the large scale structures.

Spatial characteristics of turbulent organized structures within the roughness sublayer over idealized urban surface with obstacle-height variability

The effects of obstacle-height variability on spatial characteristics of turbulent organized structures were investigated with the use of a large-eddy simulation technique for airflows over roughness obstacles. Two-types simulation cases were considered: one is uniform-height case in which uniform-height obstacles are aligned in streamwise direction, the other is height-variability case with staggered higher-height obstacles. Streaky structures were observed above the roughness sublayer (RSL) regardless of obstacle-height variability. When obstacles are uniform, flow fields within the RSL contain low- and high-speed regions along the streamwise streets. When obstacle heights vary, airflow within the RSL collides with the front-facing surfaces of taller obstacles. The statistical features of low- and high-speed structures were examined using the spatial correlations of flow fields centering on strong ejection and sweep, respectively. The ejection– and sweep–center spatial correlations extend forward and backward in the streamwise direction, respectively. Length scales were obtained from the ejection–center and sweep–center spatial correlations. The streamwise lengths vary significantly below the canopy height when obstacles are uniform. In contrast, the streamwise length scales remain nearly constant when obstacle heights vary. The horizontal aspect ratios below the canopy heights indicate that turbulent organized structures over obstacles with variable heights are more isotropic than those over uniform obstacles. The inclination angles of the organized structures were also deduced using the spatial correlations. The angles of sweep–center structures are steeper than those of the ejection–center structures. The angles of the ejection–center structures at the RSL heights become larger with obstacle-height variability.

Effects of streamwise-elongated and spanwise-periodic surface roughness elements on boundary-layer instability

Abstract

Three‐dimensional antidunes coexisting with alternate bars

AbstractAntidunes are fluvial bedforms that form in rivers with supercritical flows. The water surface over antidunes is strongly in phase with the bed surface, and the water surface is amplified to produce large surface waves. Many experimental studies have addressed antidunes; however, the shapes of three‐dimensional antidunes in a wide channel with alternate bars have not yet been appropriately understood. In this study, we experimentally investigated the streamwise and transverse length scales of antidunes under conditions with a large width–depth ratio. Our experimental results provide evidence for the coevolution of antidunes and free alternate bars, and show for the first time that the development of free bars greatly alters the three‐dimensional shape of water surface waves over antidunes. In the absence of free bars in a wide channel, multiple longitudinal wave trains form, and the number of wave trains counted in the transverse direction increases with increases in the width–depth ratio. However, the presence of free bars affects the local flow characteristics, resulting in a decrease of the number of wave trains in the transverse direction. Therefore, we propose a simple model for predicting the reduction in the number of wave trains by combining two previous theories for antidunes and free bars. Results obtained by the model were found to largely agree with experimental observations. © 2020 The Authors. Earth Surface Processes and Landforms published by John Wiley &amp; Sons Ltd

Interaction of viscous free-surface flows with topography

The interaction of gravitationally driven, free-surface flows of viscous fluid with topographic features is investigated theoretically. The motion is studied in the regime where the depth of the flow is much smaller than the streamwise extent of the topography. A lubrication model of the motion is developed, integrated numerically and analysed asymptotically. For small mounds, it is shown that the flow surmounts the obstacles, but for larger mounds the flow is deflected around it and can form dry zones in its wake into which fluid does not flow, as well as forming deeper ponded regions upstream. Which of these phenomena prevails is shown to depend upon the amplitude of the mound height and the thickness of the oncoming flow relative to the streamwise length scale over which the topography varies. By using numerical and asymptotic results, we demonstrate that relatively wide mounds lead to the development of deep ponds of material upstream, which may lead to flow overtopping if the mound is not sufficiently high. These insights can be used to inform the design of barriers that defend built infrastructures from lava flows, and it is shown how this model can also provide an upper bound on the force exerted by the flow on them.

Coherent large-scale structures from the linearized Navier–Stokes equations

The wall-normal extent of the large-scale structures modelled by the linearized Navier–Stokes equations subject to stochastic forcing is directly compared to direct numerical simulation (DNS) data. A turbulent channel flow at a friction Reynolds number of $Re_{\unicode[STIX]{x1D70F}}=2000$ is considered. We use the two-dimensional (2-D) linear coherence spectrum (LCS) to perform the comparison over a wide range of energy-carrying streamwise and spanwise length scales. The study of the 2-D LCS from DNS indicates the presence of large-scale structures that are coherent over large wall-normal distances and that are self-similar. We find that, with the addition of an eddy viscosity profile, these features of the large-scale structures are captured by the linearized equations, except in the region close to the wall. To further study this coherence, a coherence-based estimation technique, spectral linear stochastic estimation, is used to build linear estimators from the linearized Navier–Stokes equations. The estimator uses the instantaneous streamwise velocity field or the 2-D streamwise energy spectrum at one wall-normal location (obtained from DNS) to predict the same quantity at a different wall-normal location. We find that the addition of an eddy viscosity profile significantly improves the estimation.

Effect of drag reducing riblet surface on coherent structure in turbulent boundary layer

The characteristics of turbulent boundary layer over streamwise aligned drag reducing riblet surface under zero-pressure gradient are investigated using particle image velocimetry. The formation and distribution of large-scale coherent structures and their effect on momentum partition are analyzed using two-point correlation and probability density function. Compared with smooth surface, the streamwise riblets reduce the friction velocity and Reynolds stress in the turbulent boundary layer, indicating the drag reduction effect. Strong correlation has been found between the occurrence of hairpin vortices and the momentum distribution. The number and streamwise length scale of hairpin vortices decrease over streamwise riblet surface. The correlation between number of uniform momentum zones and Reynolds number remains the same as smooth surface.