Streamwise Turbulence Intensity Research Articles

The logarithmic variance of streamwise velocity and conundrum in wall turbulence

The logarithmic dependence of streamwise turbulence intensity has been observed repeatedly in recent experimental and direct numerical simulation data. However, its spectral counterpart, a well-developed $k^{-1}$ spectrum ( $k$ is the spatial wavenumber in a wall-parallel direction), has not been convincingly observed from the same data. In the present study, we revisit the spectrum-based attached eddy model of Perry and co-workers, who proposed the emergence of a $k^{-1}$ spectrum in the inviscid limit, for small but finite $z/\delta$ and for finite Reynolds numbers ( $z$ is the wall-normal coordinate, and $\delta$ is the outer length scale). In the upper logarithmic layer (or inertial sublayer), a reexamination reveals that the intensity of the spectrum must vary with the wall-normal location at order of $z/\delta$ , consistent with the early observation argued with ‘incomplete similarity’. The streamwise turbulence intensity is subsequently calculated, demonstrating that the existence of a well-developed $k^{-1}$ spectrum is not a necessary condition for the approximate logarithmic wall-normal dependence of turbulence intensity – a more general condition is the existence of a premultiplied power-spectral intensity of $O(1)$ for $O(1/\delta ) < k < O(1/z)$ . Furthermore, it is shown that the Townsend–Perry constant must be weakly dependent on the Reynolds number. Finally, the analysis is semi-empirically extended to the lower logarithmic layer (or mesolayer), and a near-wall correction for the turbulence intensity is subsequently proposed. All the predictions of the proposed model and the related analyses/assumptions are validated with high-fidelity experimental data (Samie et al., J. Fluid Mech., vol. 851, 2018, pp. 391–415).

Self-Preservation of Turbulence Statistics in the Wall-Wake Flow of a Bed-Mounted Horizontal Pipe

This research article analyzed the self-preserving behaviour of wall-wake region of a circular pipe mounted horizontally over a flat rigid sand bed in a shallow flow in terms of mean velocity, RSS, and turbulence intensities. The study aims to investigate self-preservation using appropriate length and velocity scales.in addition to that wall-normal distributions of the third-order correlations along the streamwise direction in the wake region are analyzed. An ADV probe was used to record the three-dimensional instantaneous velocities for four different hydraulic and physical conditions corresponding to four cylinder Reynolds numbers. The results revealed that the streamwise velocity deficits, RSS deficits, and turbulence intensities deficits distributions displayed good collapse on a narrow band when they were non-dimensionalized by their respective maximum deficits. The wall-normal distance was non-dimensionalized by the half velocity profile width for velocity distributions, while the half RSS profile width was used in the case of the RSS deficits and turbulence intensities deficits distributions. The results indicate the self-preserving nature of streamwise velocity, RSS, and turbulence intensities in the wall-wake region of the pipe. The third-order correlations distributions indicate that sweep is the dominant bursting event in the near-bed zone. At the same time, ejection is the dominant bursting event in the region above the cylinder height.

Aeroelastic response of a propulsive rotor blade with synthetic jets

Understanding the aeroelastic response of a propulsive rotor blade is critical to implementing active flow control techniques to mitigate blade structural vibration. In this experimental study, the coupling between rotor blade aerodynamic loading and first flap mode bending and torsion is explored. The three-bladed rotor is 2.58 m in diameter, and contains a NACA 0012 airfoil with zero pre-built twist. Each blade contains 20 high-performance synthetic jet actuators distributed along the span and are activated with a constant mean jet velocity of 66.3 m/s. The rotor was tested at rotor speeds, Ω of 250, 500, 750, and 1000 revolutions per minute (RPM) and collective blade pitch angles, θc of 2, 5, and 8 degrees. Rotor thrust and torque were measured using a high-capacity load cell, and the flow near the blade tip was measured using laser Doppler velocimetry (LDV) techniques. Blade bending and torsion was measured at three equally spaced radial stations on the blade root, middle, tip regions defined by r/R= 0.32, 0.64, and 0.96 respectively using three onboard electronic accelerometers. Synthetic jets reduce the near-wall streamwise velocity deficit and turbulence intensity in the near wall flow, improving the sectional lift coefficient of the blade and delaying flow separation which results in marginally higher thrust and lower torque loading of up to 7.4% and 4.3 % respectively. At higher rotor speeds of 750 and 1000 RPM, there is a pronounced non-linear increase in bending and torsion along blade span. In the blade tip region, the streamwise flow undergoes a significant decrease in velocity and momentum, which contributes to instabilities in the boundary layer with early-stage unsteady flow separation at θc= 8°. This is correlated to a dramatic rise in the baseline power spectral density (PSD) at the blade’s natural frequency along with an increase in root mean square (rms) of bending acceleration and blade pitch angle, where the maximum values measured are arms= 0.74 g and θrms= 1.45°.

A novel three-dimensional analytical model of the added streamwise turbulence intensity for wind-turbine wakes

Accurate prediction of the streamwise turbulence intensity in turbine wakes is of great significance to the layout of wind turbines. However, significant knowledge gaps exist on how the streamwise turbulence intensity changes in the turbine wakes, and we still lack an accurate model to predict the added turbulent intensity in the wakes. To this end, the wakes of a single turbine with different thrust coefficients and ground roughness heights are studied via large-eddy simulation under neutral atmospheric condition. To the best of our knowledge, it is the first time that we find that, like the velocity deficit of the wakes, the added streamwise turbulence intensity (ΔIu) also exhibits a self-similar characteristic and expands linearly with the downstream. Based on the findings, a novel three-dimensional analytical model of ΔIu is proposed. Considering the ground effect, a new correction function is also constructed to superpose on the proposed model. Data from both wind tunnel experiments and large-eddy simulations are introduced to validate the proposed model. The results demonstrate that the proposed model can accurately predict the variation of the streamwise turbulence intensity in both the vertical and horizontal directions, and the prediction accuracy is higher than that of the existing models.

Design and construction of an open loop subsonic high temperature wind tunnel for investigation of SCR dosing systems

The requirement of high-fidelity experimental data of microscopic properties as well as the whole spray development is fundamental since they are determinant in the understanding of atomization and evaporation process in a variety of multiphase flows. The Selective Catalytic Reduction (SCR) system is one of the industrial applications where understanding the whole spray atomization and development process is essential in developing new systems to cope with stringent emission regulations. A new subsonic heated open-loop wind tunnel has been designed and manufactured specifically with a 0.25 × 0.25 m cross-section and 1.59 m long optically accessible quartz glass side panels. The purpose of the wind tunnel was to investigate Selective Catalytic Reduction (SCR) sprays using Phase Doppler Anemometry (PDA). The wind tunnel is capable of reaching a flowrate equating to 50 m/s in the test section when operating at standard room conditions (25°C and 101,325 kPa). A 145 kW heater is mounted downstream the blower to achieve air temperatures of up to 400°C with maximum air mass flow of 1200 kg/h. The diffuser, flow conditioning and contraction cone sections of the wind tunnel have been designed to minimize velocity and temperature gradients within the test section while minimizing flow disturbances. A diffuser with a cone angle of 5° and an area ratio of 3.95 and a contraction cone with a contraction ratio of 4.05 was selected. The test section has been designed to give complete visible access through top and both sides, while the bottom is made of stainless steel. The two sides are made of quartz glass to provide the best signal transmission quality for usage with any optical equipment e.g. PDA. The top of the test section has sections made of Robax glass with detachable windows for easy mounting and dismounting of any equipment subject to be tested in the flow section. The streamwise turbulence intensity in the test section was found to be less than 2% in the core with similar values for the cross-stream turbulence intensities. The complete design and construction of each section of the wind tunnel has been presented and discussed in this paper.

Scaling of global properties of fluctuating and mean streamwise velocities in pipe flow: Characterization of a high Reynolds number transition region

We study the global, i.e., radially averaged, high Reynolds number (asymptotic) scaling of streamwise turbulence intensity squared defined as I2=u2¯/U2, where u and U are the fluctuating and mean velocities, respectively (overbar is time averaging). The investigation is based on the mathematical abstraction that the logarithmic region in wall turbulence extends across the entire inner and outer layers. Results are matched to spatially integrated Princeton Superpipe measurements [Hultmark et al., “Logarithmic scaling of turbulence in smooth- and rough-wall pipe flow,” J. Fluid Mech. 728, 376–395 (2013)]. Scaling expressions are derived both for log- and power-law functions of radius. A transition to asymptotic scaling is found at a friction Reynolds number Reτ∼11 000.

Field measurements of crestal flow direction and turbulent flow over two transverse dune ridges

Turbulent airflow is a fundamental factor that controls the geomorphology of sand dune systems, especially dune expansion and sandy desertification. However, little is known about turbulent air flow in dune systems, and this limits efforts to control dune expansion and sandy desertification. To obtain some of the missing information, we calculated the turbulent airflow characteristics over a transverse dune in the Tengger Desert in southeastern China. We found that the angle of airflow at the dune crest controls flow angles at middle of the dune's stoss slope and at the toe of the leeward slope, and also controls the turbulent flow characteristics over the dune surface. The critical wind direction was from the NW (wind directions ranged from 355° to 45° to the crest perpendicular line [CPL]) and SE (wind directions ranged from 65° to 165° with respect to the CPL), and about 20° and25° with respect to the CPL for northwesterly winds and southeasterly winds, respectively. The kinematic Reynolds' stress (RSk), streamwise turbulence intensity (CVu), and total kinetic energy (TKE) were largest close to the critical wind direction for winds from the NW, indicating that dune movement was mainly controlled by the critical wind direction. However, TKE, RSk, and CVu differed between southeast and northwest winds; for southeasterly winds, they were largest for wind directions from 65° to 115° with respect to the CPL and similar to the values for wind directions from 115° to 165° with respect to the CPL, indicating asymmetrical sand movement. We conclude that, for closely spaced transverse dunes, sand transport is controlled by the critical wind directions; this indicates that efficient control of sand movement and sandy desertification will benefit from sand-control structures that block airflow from the critical wind directions.

Scaling of turbulence intensities up to Reτ=106 with a resolvent-based quasilinear approximation

Scaling of near-wall turbulence intensities has been a subject of many investigations over several decades. Emerging evidence suggests that the near-wall streamwise turbulence intensity may not precisely depend on the logarithm of the friction Reynolds number, challenging the scaling obtained with Towsend's attached eddy model. Here, we present new mathematical evidence that it is instead proportional to the inverse of the outer velocity scale using a novel quasilinear approximation made to the Navier-Stokes equations.

Experimental Investigation on Effects of Elastic Agitator to Turbulence Enhancement

The conventional method to promote mass, momentum and energy transport between fluid particles is to introduce a disturbance to the flow. An ultrasonic velocity profiler, UVP experiment was used to study the mean and fluctuating flow properties in the near wake of the rigid and flexible protruding surface in a water tunnel under the Reynolds number of 4000, 6000 and 8000. In the current study, circular finite cylinders (cantilevers) with various aspect ratios (AR = 10, 12, 14 and 16) and materials were used as the geometry of the rigid and protruding surface. The motion of the cylinder alters the fluid flow significantly. The increment of the wake region (~10 larger in the flexible cylinder compared to the rigid case, for AR = 16) is due to the weakening of the influence of downwash caused by the stream-wise deflection of the flexible cylinder. As a mean to quantify turbulence, the turbulent intensity, Ti, was studied. In general, the flexible cylinders show better capability in augmenting the turbulence than the rigid cylinder. The stream-wise turbulent intensity for AR = 16 and Re = 8000 can be as high as 97 for the flexible cylinder compared to only 26 for the rigid case. The normalized amplitude response graph, which records the cross-flow oscillation of the flexible cylinder was also analyzed. Under the same Reynolds number, the turbulence enhancement increases with the structural velocity. An organized oscillating motion is in favor of a higher performance of turbulence enhancement. © 2020 All Rights Reserved

Wire mesh fences for manipulation of turbulence energy spectrum

Manipulation of turbulence within an atmospheric boundary layer flow by application of woven wire mesh fences is investigated. Turbulence properties behind fences of different porosities and mesh opening widths were determined from velocity measurements in a wind tunnel. It is found that with the application of a fence with a porosity of 0.46, the streamwise turbulence intensity can be reduced from the inflow level of 12.5%–8.8% and the integral length scale can be reduced from 380 to 270 mm. The results show that behind the mesh fences turbulence kinetic energy decays as a power law function of the downstream distance for all wire mesh fences tested in the wind tunnel. The decay rate of turbulence kinetic energy is faster, and a larger reduction in the integral length scale is achieved for fences with porosities between 0.46 and 0.64 compared to higher porosities of between 0.73 and 0.75. Porosity of the woven wire meshes is found to be the key parameter which influences their turbulence reduction performance. In the end, application of the wire mesh fences for reduction of wind loads on solar panels and heliostats is discussed. Evaluation of wind loads based on the reduction of turbulence intensity and integral length scale shows that up to 48% and 53% reduction in peak drag and lift forces on a heliostat, respectively, can be achieved with application of mesh fences.

Swirling turbulent pipe flows: Inertial region and velocity–vorticity correlations

Swirling pipe flows are studied here with an aim towards understanding the onset of the inertial region — where the turbulent-inertia term in the mean momentum equation is balanced by pressure gradient and viscous term is sub-dominant — as well as the clarifying the velocity–vorticity correlations that make up the turbulent inertia. To this end, we first manipulate the mean momentum equation in both axial and azimuthal directions and find some exact results in the inertial region, and carry out direct numerical simulations of swirling pipe flows at axial friction Reynolds numbers of 170 and 500. The swirl number considered in our simulations is S≈0.3, and we compare our results to non-swirling pipe flows at similar Reynolds numbers. We find that swirling produces a drag increase and an influence on the turbulence statistics similar to increasing the Reynolds number except for the streamwise turbulence intensity. An analysis on the axial and azimuthal mean momentum equations shows that swirling shifts the beginning of the inertial region wall-normal location closer to the wall. The turbulent inertia decomposition reveals that the near-wall region the velocity–vorticity correlations of the axial direction are similar to a 2D channel flow and interpreted as vorticity stretching/reorientation and dispersion, whereas in the new correlations in the azimuthal direction can also be given a similar physical meaning in the near-wall region. In the outer-region, however, the pipe axial correlations are different to the 2D-channel, and so are the azimuthal correlations. We find that the pipe has new a ‘geometric’ contribution in both axial and azimuthal directions that play an important role in contributing towards vorticity dispersion in the outer core region of a swirling pipe flow.

An in-flight investigation of a turbulent boundary layer at Reynolds numbers up to hbox {Re}_{theta }=49,400

The ongoing attempts to gain access to the realm of high Reynolds number turbulence have resulted in the dedicated development of major experimental facilities and novel diagnostic methodologies as well as in the probing of atmospheric surface flows. In contrast to this, the presented study discusses the feasibility of an in-flight laboratory for Reynolds number investigations up to rm {Re}_{theta },le ,49,400. The underpinning velocity data were obtained in flight tests by two moveable differential pressure probes and a stereo Particle Image Velocity (sPIV) system. The region of interest was located far downstream of the aircraft’s nose within the fuselage boundary layer. The pressure probes scanned the full boundary layer while the sPIV system remained fixed at certain wall-normal locations. The velocity data acquired exhibits distinct characteristics within the defect layer that deviate from Coles’ classical description of the wake. Furthermore, the streamwise turbulence intensities show a pronounced ‘outer peak’ further away from the wall at y^{+}=2000-5000 . The measurements were conducted under authentic flight conditions with an increased level of free-stream turbulence. These boundary conditions enabled an analysis of turbulent flows that are of relevance for various aeronautical applications. The manuscript elaborates on the main findings of this experimental study by presenting the velocity profiles captured by the moveable pressure probe system and samples of sPIV data. The capabilities and limitations of a flying laboratory for the investigation of high Reynolds number turbulence are discussed in detail.Graphic

Turbulent channel flow of generalized Newtonian fluids at a low Reynolds number

Abstract

A Study of The Turbulent Flows behind A Rectangular Sharp Crested Weir in Open Channel Using Laser Doppler Velocimetry (Dept.C)

This paper describes the experimental investigation using laser Doppler velocimetry) (LDV) in the downstream of .be rectangular sharp crested weir in a horizontal rectangular channel of constant width. The study was carried out for flows on smooth and rough weir. For precise and accurate measurements of mean and fluctuating a ting flow characteristics such as streamwise and vertical turbulence intensity components and streamwise and vertical mean velocity components. The depthwise measurements were carried out for different heights of the weir along to e centerline at different cross sections downstream of weir in the wake region . The results show that, the measured values of turbulence intensities are found to have high level of turbulence in the Dear wake region but are low in the far wake region. The turbulence intensities depict the occurrence of a constant turbulence close to the wall in the far wake region. The roughness was found to increase the turbulence. Also, it can be seen that with increasing weir height, the turbulence intensities are Increased.

High Frequency Characteristics of the Near Wake and Vortex Past a Triangular Cylinder

Abstract The flow past a triangular cylinder is one of the fundamental flows and widely utilized in flame stabilization and heat transfer. In this study, the near wake and vortex characteristics of the flow past an equilateral triangular cylinder are experimentally measured by a high frequency particle image velocimetry (PIV) system at 3 kHz. The triangular cylinder is installed in a wind tunnel with Reynolds numbers ranging from 10,700 to 17,700. The Reynolds-averaged and phase-averaged methods are utilized to analyze the flow field. Based on the flow fields, the length of the vortex formation region is about 1.5 times of the length of the equilateral triangle side. The residence time of a vortex in the vortex formation region is equal to a vortex shedding period. The stream wise velocity of the vortex core center downstream the vortex formation is about 0.8 times of the freestream velocity, which is slightly larger than the value about 0.7 for the flow past a circular cylinder at the same Reynolds number. The maximum tangential velocity at the periphery of the vortex core maybe occurs slightly in advance of the vortex reaching the boundary of the vortex formation region. The normalized lengths of the recirculation zone of the triangular cylinder keep nearly unchanged and are about 1.55 to 1.9 times of those of the circular cylinder at the same Reynolds number. The normalized normal wise instead of stream wise turbulence intensity has stronger effects on the distribution of the normalized turbulent kinetic energy.

Statistical behaviour of self-similar structures in canonical wall turbulence

Abstract

Information measures through velocity time series in a seepage affected alluvial sinuous channel

Alluvial channels with sinuosity follow an altered flow behavior, contradictory to straight flows. At the interface of surface water and groundwater, seepage is a significant phenomenon occurring at the boundary of alluvial channels. The study of turbulence in seepage affected sinuous alluvial channels would thus provide us with a better insight into their hydro-morphological behavior. To address the nature of turbulence in sinuous channel with downward seepage an experimental framework was design. The paper reports the structure of turbulence in the sinuous channel for no seepage and seepage flow. With downward seepage, there is a noticeable shift of Reynolds shear stress at near-bed, which reports more momentum transport. The average streamwise and transverse turbulence intensity increased by 3.8–18.5% and 4–10.6%, respectively with downward seepage. Calculation of Kolmogorov complexity and the Kolmogorov complexity spectrum suggests higher randomness in the outer region, which can be associated with excess momentum transport. In the lower flow depth $$ \left( {{\text{z}}/{\text{h}}} = 0.2 \right)$$ , the randomness in the transverse velocities is higher in the outer region of the bend for about 25% and 38% compared to the central and inner region of the bend, respectively. With downward seepage, randomness increased especially in the outer region. This increase in randomness may report the erosive action in the outer part of the bend. Permutation entropy provided an informative measure to study the complex behavior of the transverse velocity time-series, which we found to be higher in the outer flow zone. For downward seepage, mean of entropy increased across the bend. The turbulent flow alterations and increase in randomness with seepage may be helpful to understand the flow in seepage affected sinuous alluvial channels.

Characterization of the vertical evolution of the three-dimensional turbulence for fatigue design of tidal turbines.

A system of two coupled four-beam acoustic Doppler current profilers was used to collect turbulence measurements over a 36-h period at a highly energetic tidal energy site in Alderney Race. This system enables the evaluation of the six components of the Reynolds stress tensor throughout a large proportion of the water column. The present study provides mean vertical profiles of the velocity, the turbulence intensity and the integral lengthscale along the streamwise, spanwise and vertical direction of the tidal current. Based on our results and considering a tidal-stream energy convertor (TEC) aligned with the current main direction, the main elements of turbulence prone to affect the structure (material fatigue) and to alter power generation would likely be: (i) the streamwise turbulence intensity (Ix), (ii) the shear stress, [Formula: see text], (iii) the normal stress, [Formula: see text] and (iv) the vertical integral lengthscale (Lz). The streamwise turbulence intensity, (Ix), was found to be higher than that estimated at other tidal energy sites across the world for similar height above bottom. Along the vertical direction, the length (Lz) of the large-scale turbulence eddies was found to be equivalent to the rotor diameter of the TEC Sabella D10. It is considered that the turbulence metrics presented in this paper will be valuable for TECs designers, helping them optimize their designs as well as improve loading prediction through the lifetime of the machines. This article is part of the theme issue 'New insights on tidal dynamics and tidal energy harvesting in the Alderney Race'.

A Calibration Procedure for an Analytical Wake Model Using Wind Farm Operational Data

Wind energy is one of the fastest growing renewable energy sources in the U.S. Wind turbine wakes change the flow field within wind farms and reduce power generation. Prior research has used experimental and computational methods to investigate and model wind farm wake effects. However, these methods are costly and time-consuming to use commercially. In contrast, a simple analytical approach can provide reasonably accurate estimates of wake effects on flow and power. To reducing errors in wake modeling, one must calibrate the model based on a specific wind farm setting. The purpose of this research is to develop a calibration procedure for wind farm wake modeling using a simple analytical approach and wind turbine operational data obtained from the Supervisory Control And Data Acquisition (SCADA) system. The proposed procedure uses a Gaussian-based analytical wake model and wake superposition model. The wake growth rate varies across the wind farm based on the local streamwise turbulence intensity. The wake model was calibrated by implementing the proposed procedure with turbine pairs within the wind farm. The performance of the model was validated at an onshore wind farm in Iowa, USA. The results were compared with the industry standard wind farm wake model and shown to result in an approximate 1% improvement in sitewide total power prediction. This new SCADA-based calibration procedure is useful for real-time wind farm operational optimization.

Modified mixing coefficient for the crossflow between sub-channels in a 5 × 5 rod bundle geometry

We performed experiments to measure a single-phase upward flow in a 5 × 5 rod bundle with spacer grids using a particle image velocimetry, focusing on the crossflow. The Reynolds number based on the hydraulic diameter and the bulk velocity is 10,000. The ratio of pitch between rods and rod diameter is 1.4 and spacer grid is installed periodically. The turbulence in the rod bundle results from the combination of a forced mixing and natural mixing. The forced mixing by the spacer grid persists up to 10Dh from the spacer grid, while the natural mixing is attributed to the crossflow between adjacent sub-channels. The combined effects contribute to a sinusoidal distribution of the time-averaged streamwise velocity along the lateral direction, which is relatively weak right behind the spacer grid as well as in the gap. The streamwise and lateral turbulence intensities are stronger right behind the spacer grid and in the gap. Based on these findings, we newly defined a modified mixing coefficient as the ratio of the lateral turbulence intensity to the time-averaged streamwise velocity, which shows a spatial variation. Finally, we compared the developed model with the measured data, which shows a good agreement with each other.