Turbulence Integral Length Scale Research Articles

Influence of freestream turbulence and porosity on porous disk-generated wakes

This study aims to evaluate the effect of freestream turbulence (FST) on wakes produced by disks with different porosity. The wakes are exposed to various freestream turbulence “flavors,” where turbulence intensity and integral length scale are independently varied. The turbulent wakes are interrogated through hot-wire anemometry from 3 to 15 diameters downstream of the disks. It is found that disks with low porosity behave similarly to a solid body, in terms of both entrainment behavior and scaling laws for the centerline mean velocity evolution. Far from the disks, the presence of FST reduces both the wake growth rate and entrainment rate, with a clear effect of both turbulence intensity and integral length scale. As porosity increases, these “solid body” FST effects gradually diminish and are reversed above a critical porosity. The entrainment behavior in disk-generated wakes is significantly influenced by the presence of large-scale coherent structures, which act as a shield between the wake and the surrounding flow, thus impeding mixing in the near wake. We found that higher porosity, turbulence intensity, or integral length scale weakens the energy content of these structures, thereby limiting their influence on wake development to a shorter distance downstream of the disk. This, in turn, potentially reduces the influence of large-scale engulfment on the overall entrainment mechanism to a shorter distance downstream of the disks as well. For low-porosity disks, freestream turbulence intensity initially promotes near-wake growth through the suppression of large-scale structures; however, farther downstream, the wakes grow faster when the background is nonturbulent. Published by the American Physical Society 2024

Impact of freestream turbulence integral length scale on wind farm flows and power generation

The impact of freestream turbulence integral length scale on wind farm flow and power production is investigated by conducting Large Eddy Simulations on wind farms with two spacings, Sx=8R and Sx=12R (turbine radius R). The integral length scale of inflow turbulence Lu is varied, Lu∈[3.2R,12.0R], while maintaining identical turbulence intensity and velocity. Shorter integral length scales lead to a faster near wake breakdown and improved wake recovery in the wake of the first turbine, causing substantial increases in the second turbine power output; 42% and 18% for the two spacings. Over the first four turbines, total power output increases by 8.6% and 6.0% respectively. Spectra, cross-correlations and entrainment scales are also examined and show that the first turbine breaks down inflow scales and wake-generated turbulence dominates the inflow to the second turbine. Further into the turbine row, dominant flow structures and entrainment scales are associated with both wake turbulence and larger wind farm-generated structures matching the turbine spacing. These results show that the freestream turbulence integral length scale has a significant impact on wind farm flows and power generation, mainly by impacting the development of wakes in the farm entrance.

Impacts of inflow turbulence on the flow past a permeable disk

A permeable disk serves as a simplified model for the conversion of wind energy by a horizontal axis wind turbine. In this study, we investigate how inflow turbulence intensity (TI), $I_\infty$ , and inflow turbulence integral length scale, $L_\infty$ , influence the flow recovery in the wake, the capability of a permeable disk in extracting turbulence kinetic energy (TKE) of the incoming flow, and the statistics of wake-added turbulence using large-eddy simulation. The simulated inflows include various TIs (i.e. $I_\infty =2.5\,\%$ – $25\,\%$ ) and integral length scales (i.e. $L_\infty / D =0.5$ – $2.0$ ) for two thrust coefficients. Simulation results show that both inflow TI and integral length scale influence flow recovery via enhanced ejections and sweeps across the wake boundary, with the former strongly affecting the position where the wake starts to recover and the latter mainly on the recovery rate. Moreover, it is shown that increasing $I_\infty$ and $L_\infty$ increases the TKE extraction by the disk, occurring mainly at scales ( $s$ ) greater than $0.5D$ and frequencies depending on the inflow integral length scale. As for the wake-added TKE, the inflow TI mainly affects its intensity, while the inflow integral length scale affects both its intensity and the sensitive frequencies, with the spectral distributions in scale space ( $s$ ) being similar and the peak located around $s/D=1.0$ for the considered inflows.

Effects of turbulence intensity and integral length scale on wind-induced vibrations of a three-dimensional aeroelastic square cylinder

Despite a wealth of prior research on the effects of free-stream turbulence (FST) on the aerodynamics of square cylinders, there is limited knowledge about their aeroelasticity such as characteristics of wind-induced vibrations that vary with the FST properties. This paper focuses on the investigation of the effects of FST properties including longitudinal turbulence intensity and integral length scale on the wind-induced vibrations of a three-dimensional (3D) aeroelastic square cylinder with an aspect ratio of 10 (a super-tall building model). Through wind tunnel testing, displacements of the aeroelastic model are measured in smooth flow and four turbulent flows to experimentally investigate its characteristics of fluid-solid interaction, including along- and across-wind vibrations, especially vortex-induced vibration and galloping. The effects of the turbulence intensity with a higher-level than previous studies are also investigated. The results show that the root-mean-square (RMS) displacements of the along-wind responses increase with the increase of turbulence intensity and are not affected by integral length scale. For the across-wind responses, in the non-lock-in region, the RMS displacements generally increase with the increase of turbulence intensity. In the lock-in region, the RMS displacements remain unchanged with the increase of turbulence intensity, while increase with the increase of integral length scale. This paper aims to improve the comprehension of the effects of FST on the wind-induced vibrations of 3D square cylinders and to furnish valuable insights for the wind-resistant design of slender structures, such as supertall buildings.

Requirements for partial turbulence simulations using nondimensional turbulence energy contributions

Quantifying turbulence effects is crucial for understanding building aerodynamics and for ensuring accurate wind tunnel test methods. This is especially important in wind tunnel methods that require post-experiment adjustments because approximate wind fields are used, such as the Partial Turbulence Simulation (PTS) approach. Understanding and analyzing these effects enables load adjustments since the PTS method only requires matching the high frequency portions of the upstream spectra of the longitudinal velocity component in model and full-scale. However, the limits for which the PTS method is applicable are unclear in terms of the allowable range of wind field characteristics that can be used in the wind tunnel simulation. To address this, the paper utilizes two nondimensional parameters, one representing the small-scale turbulence energy, ES, and the other the large-scale turbulence energy, EL, to elaborate the aerodynamic effects of turbulence intensity and integral length scales in the upstream wind. The results show that the maximum allowable mismatch ratio of integral length scales and of Jensen numbers between model and full-scale simulations depend on the target small-scale turbulence energy and the maximum allowable deviation of small-scale energy. By quantifying the effects of ES and EL on area-averaged pressure coefficients, the allowable limits are identified for wind tunnel test parameters that lead to negligible differences in the resultant pressure coefficient statistics in regions of separated-reattaching flow on the roof of a low-rise building.

Isolating effects of large and small scale turbulence on thermodiffusively unstable premixed hydrogen flames

Lean turbulent premixed hydrogen/air flames have substantially increased flame speeds, commonly attributed to differential diffusion effects. In this work, the effect of turbulence on lean hydrogen combustion is studied through Direct Numerical Simulation using detailed chemistry and detailed transport. Simulations are conducted at six Karlovitz numbers and four integral length scales. A general expression for the burning efficiency is proposed which depends on the conditional mean chemical source term and gradient of a progress variable, and the amount of superadiabatic burning. At a fixed Karlovitz number, the normalized turbulent flame speed and area both increase almost linearly with the integral length scale ratio. The effect on the mean source term profile is minimal, indicating that the increase in flame speed can solely be attributed to the increase in flame area. At a fixed integral length scale, both the flame speed and area first increase with Karlovitz number before decreasing. The qualitative observations and trends do not change when Soret effects are neglected. Specifically, neglecting Soret diffusion is shown to reduce the flame speed, area, and burning efficiency. At higher Karlovitz numbers, the diffusivity is enhanced due to penetration of turbulence into the reaction zone, significantly dampening differential diffusion effects.Novelty and SignificanceLean premixed hydrogen flames are subject to thermodiffusive instabilities, which can lead to system level instabilities such as flashback. A comprehensive study of the thermodiffusively unstable turbulent flames with detailed chemistry and detailed transport (including Soret diffusion) was conducted across a wide range of turbulent intensities and integral length scales. Varying these two parameters independently was necessary to isolate the effects of large- and small-scale turbulence. Using these results, we propose a general expression for the burning efficiency to explain the relationship between the turbulence intensity, flame speed, and flame area. This work is an important step in developing predictive models which can aid in the design of practical combustion devices.

Experimental study on characteristics of methane-coal dust explosions and the spatiotemporal evolution of flow field in early flame

To understand the explosion characteristics of methane-lignite coal dust mixtures and the spatiotemporal evolution of the early flame flow field, explosion pressure, OH* emission spectra, and early flame schlieren images were captured in a 60L constant volume combustion bomb. Schlieren image velocimetry was used to obtain the instantaneous velocity distribution of the methane-coal dust flame front. The results indicate that adding coal dust causes a nonlinear increase in explosion pressure, particularly at low methane concentrations. At a 5 % methane concentration, adding coal dust can increase the maximum explosion pressure by up to 39 % (190 kPa). The trend of the OH* emission spectra corresponds with the maximum explosion pressure. A slight increase in coal dust significantly enhances the OH* emission spectra, especially at lower concentrations, potentially increasing it by nearly five times. However, at higher coal dust concentrations, the OH* emission spectra are significantly reduced. Additionally, within the considered concentration range (≤58.14 g/m³), larger turbulent integral length scales in initial conditions consistently result in the fastest flame acceleration. These findings provide experimental evidence for further exploration of the explosion mechanisms of methane-coal dust mixtures and the development of chemical reaction kinetic models.

Effects of turbulence integral length scales on aerodynamic characteristics and displacement responses of a square prism

This paper investigates the influence of the inflow turbulence integral length scales on the aerodynamic forces on a surface-mounted finite-length square prism and its displacement responses by computational fluid dynamics simulations. Four turbulent inflow conditions with the same mean wind speed and turbulence intensity but different longitudinal and transverse turbulence integral length scales are generated for the simulations. First, the wind pressures and forces on a rigid square prism model and the shear layer characteristics are simulated by large eddy simulations. The simulation results show that the mean characteristics of the wind pressures and shear layers are not sensitive to the turbulence integral length scales. However, the root mean square (RMS) wind pressures on side faces and RMS across-wind forces are increased with the longitudinal turbulence integral length scale, and the mechanism is analyzed by the proper orthogonal decomposition. Second, the displacement responses at the mean wind speed of vortex-induced resonance are computed based on an aeroelastic square prism model by fluid–solid interaction simulations. The RMS displacements of the model are observed to be more sensitive to the transverse turbulence integral length scale rather than the longitudinal turbulence integral length scale. Finally, the influence of the turbulence integral length scales on the Reynolds stresses around the square prism is presented and discussed.

Onsite measurements of pedestrian-level wind and preliminary assessment of effects of turbulence characteristics on human body convective heat transfer

Wind is an important factor affecting outdoor thermal comfort in urban environment, but its turbulence characteristics at the pedestrian level and effects on convective heat transfer (hc) from a human body remain poorly understood. Previous studies were only conducted in wind tunnels with low turbulence intensity, small turbulence integral length scale, and fixed prevailing wind direction. To address this knowledge gap, this field study was conceived to monitor the pedestrian level wind in actual outdoor settings and to measure the hc of a thermal manikin at the same time. The results show that both longitudinal and lateral turbulence intensity significantly enhance whole body hc. It remains to be examined whether the small-scale wind direction variation can be included in the lateral turbulence intensity or vice versa. The integral length scale found at the two sites were larger than a typical manikin dimension, and the whole body hc peaked when these two scales were comparable. As the first major field study to quantify convection heat loss of a thermal manikin exposed to real-life urban boundary layer wind, it is demonstrated crucial to consider realistic turbulence characteristics in the field when evaluating hc over a human body for urban microclimate design.

The lidar probe volume averaging effect: A wind tunnel investigation in streamwise turbulence with continuous-wave lidar

The main limitation of lidars to capture the turbulence is the filtering of small-scale fluctuations within the probe volume, which is far less significant with conventional anemometers. In this study, the probe volume averaging effect on the streamwise turbulence statistics is investigated in the wind tunnel. Different turbulent flows, which exhibit distinct turbulence intensities and integral length scales are generated and subsequently captured using a short-range continuous-wave WindScanner with different probe volumes. Hot wire measurements are performed as a reference. The results indicate that the turbulence intensity (TI) is underestimated using conventional lidar methods compared to the hot wire measurements. The relative error increases with the increasing ratio of probe volume over integral length scale (l p /L) which is the indication of probe volume averaging. The TI is underestimated by 4 % at l p /L = 0.5 and by 63 % at the largest tested l p /L = 11.3 with the conventional lidar method. However, the TI estimated from the averaged Doppler spectrum of the lidar compensates for the probe volume averaging effect and shows a better agreement with the hot wire measurements with an average overestimation of 7.8 %. This study shows that the continuous-wave lidars have the potential to estimate the TI under different flow conditions using the averaged Doppler spectrum method.

Buffeting characteristics of cable-stayed box beam bridge based on pressure measurement test of full bridge aeroelastic model

The aim of this study is to explore the buffeting characteristics of cable-stayed box beam bridge based on pressure measurement test of full bridge aeroelastic model. The study includes the influence of turbulence integral length scale and wind yaw angle on the magnitude of buffeting force, spatial distribution of buffeting force, and buffeting displacement response. Under larger turbulence integral length scale, the buffeting force of the box beam and it’s spanwise correlation are larger, which verifies the three-dimensional effect of the buffeting force. It is worth mentioning that, unlike traditional section models, there are differences in the pressure values of the pressure strips in the aeroelastic model at the flow separation point, which may be influenced by the cables. The experimental results of different wind yaw angles show that there is little difference in the buffeting force of the box beam section under the condition of 0°∼15° wind yaw angle, indicating that the maximum buffeting response will occur in the range of 0°∼15° wind yaw angle, which is consistent with the displacement results measured by the aeroelastic model. In addition, by fixing the model with a steel wire, the static and vibration states of the model were achieved. However, due to the high stiffness of the model, it can only generate small buffeting displacement, and the self-excited force component can be almost ignored. There is no significant difference in the results between the static and vibration states.

Broadband Noise Reduction of a Two-Stage Fan with Wavy Trailing-Edge Blades

In this paper, a numerical investigation is performed to study the broadband noise of a fan stage with wavy trailing-edge blades. A study of the wavelength and ratio of amplitude to wavelength (H/L) is conducted to better understand the noise reduction effect of wavy trailing-edge blades. A rotor–stator interaction broadband noise prediction method based on the result of a Reynolds-averaged Navier–Stokes equation is used. The results show that all wavy trailing-edge configurations reduce the sound power level of the fan stage. The noise reduction effect of H20L10 is the best among all the wavy trailing-edge configurations, and the sound power level is reduced by 2.4 dB at 1000 Hz. When the H/L remains unchanged, the noise reduction effect of the wavy trailing-edge configuration increases with the increase in wavelength. When the wavelength remains unchanged, the noise reduction effect of the wavy trailing-edge configuration with an H/L of 2 is the best. The use of wavy trailing-edge configurations reduces the turbulent kinetic energy and turbulent integral length scale upstream of the stator by changing the wake of the rotor, thereby reducing the rotor–stator interaction broadband noise of the fan stage.

A numerical framework to investigate isotropic turbulent inflow interacting with an airfoil’s leading edge

This paper presents a numerical framework to study the interaction of isotropic turbulence with airfoils. Specifically, the developed numerical framework is used to investigate the distortion of the turbulent structures interacting with an airfoil’s leading edge. For turbulence modeling, Large Eddy Simulation (LES) is used. The isotropic turbulent inflow for the Computational Fluid Dynamics (CFD) simulations is synthetically generated using the turbulent digital filter method. The case studied with the numerical framework is a NACA 0012 airfoil with a chord-based Reynolds number of Rec=2×105 and an angle of attack of α=5°. The numerical simulation results are compared to high-speed particle image velocimetry (PIV) measurements performed for a NACA 0012 airfoil at the equivalent chord-based Reynolds number and turbulent inflow conditions. The CFD results of the numerical framework compare well with the experiments in terms of velocity spectra and RMS values upstream of the airfoil’s leading edge. The spectra and correlations of the velocity field generated by the turbulent digital filter demonstrate its ability to generate isotropic turbulent inflow. Instantaneous velocity fields show that the airfoil suppresses large-scale turbulent structures of the incoming turbulent flow. The size of the incoming turbulent structures decreases as they approach the leading edge due to the presence of the airfoil. The pre-multiplied spectra of the different velocity components show that downstream of the airfoil’s leading edge, the turbulent structures are stretched in the streamwise direction. The streamwise turbulent integral length scales and the velocity RMS values upstream of the airfoil’s leading edge indicate that the velocity components most affected by distortion are the streamwise and wall-normal components.

Impact of High-Pressure-Turbine Purge Flow on the Evolution of Turbulence in a Turbine Vane Frame

Abstract This paper describes the measurement and postprocessing of turbulence data. The experiments were carried out in a two-stage, two-spool transonic turbine test rig at the Institute for Thermal Turbomachinery and Machine Dynamics at the Graz University of Technology, which includes relevant purge and turbine rotor tip leakage flows. The test setup consists of a high-pressure turbine (HPT) stage, a turbine vane frame (TVF) with turning struts and splitters, and a counter-rotating low-pressure turbine (LPT) to allow engine realistic measurements. Time-resolved area traverse measurements have been performed for three different operating conditions in three measurement planes downstream of the HPT rotor, which enable the measurement of the turbulence quantities at the TVF inlet and outlet as well as the LPT outlet. The turbulence quantities are evaluated using triaxial- and single hot-film probes by means of Constant-Temperature-Anemometry, and their results were validated with five-hole probe (FHP) measurements. Ensemble- and time-averaging, as well as Fourier transforms, were applied for data reduction. It is shown how the turbulence intensity and integral length scale vary over different purge flowrates (PFR). The acquired measurement data illustrate that the interaction of the ejected purge flow with mean flow enhances the turbulent mixing in the secondary flow structures at the TVF inlet and TVF outlet, respectively. Furthermore, the flow downstream of the LPT rotor is affected by TVF and LPT rotor secondary flow structures, which are identified as high turbulence regions. These regions strongly depend on the purge flowrate. These results acquired under engine realistic rig flow conditions enable a deeper understanding of the relationship between loss and turbulence quantities and will help improve the application of computational fluid dynamics turbulence models to turbomachinery modeling.

Experimental Study of Wake Evolution under Vertical Staggered Arrangement of Wind Turbines of Different Sizes

During the expansion of a wind farm, the strategic placement of wind turbines can significantly improve wind energy utilization. This study investigates the evolution of wake turbulence in a wind farm after introducing smaller wind turbines within the gaps between larger ones, focusing on aspects such as wind speed, turbulence intensity, and turbulence integral length scale. The flow field conditions are described using parameters like turbulence critical length and power spectral density, as determined through wind tunnel experiments. In these experiments, a single large wind turbine model and nine smaller wind turbine models were used to create a small wind farm unit, and pressure distribution behind the wind turbines was measured under various operating conditions. The results indicate that downstream wind speed deficits intensify as the number of small wind turbines in operation increases. The impact of these smaller turbines varies with height, with a relatively minor effect on the upper blade tip and increasingly adverse effects as you move from the upper blade tip to the lower blade tip. Through an analysis of power spectral density, the contribution of vortex motion to wake turbulence kinetic energy is further quantified. In the far wake region, the number of small wind turbines has a relatively small impact on wind speed fluctuations.

Measurements of Turbulence in Compressible Low-Density Flows at the Inlet of a Transonic Linear Cascade With and Without Unsteady Wakes

Abstract In the present work, hot-wire anemometry was employed for the characterization of the turbulent field at the inlet of a high-speed low-pressure turbine cascade, in terms of turbulence intensity and integral length scales. This work addresses two major topics relevant to the turbomachinery field: the application of hot-wire anemometry in transonic and rarefied flow regimes and the decoupling of the deterministic and the stochastic fluctuations when measuring unsteady phenomena. In compressible and rarefied flows, a hot-wire is strongly sensitive to both density and velocity fluctuations, and the commonly used Nusselt–Reynolds correlations are not valid. In this article, a nondimensional calibration methodology, based on Nusselt, Reynolds, and Knudsen numbers, was coupled with a sensitivity analysis and employed to postprocess the experimental dataset, allowing to decouple the fluctuations of density and velocity and to compute the turbulence parameters. In the presence of unsteady wakes generated upstream of the cascade, two different phase-locked averaging techniques were employed to distinguish the wake deterministic fluctuations from the background turbulence intensity.

On the rotation of a Savonius turbine at low Reynolds numbers subject to Kolmogorov cascade of turbulence

With an increasing demand for small energy generation in urban areas, small-scale Savonius wind turbines are growing their share rapidly. In such an environment, Savonius turbines are exposed to low mean velocity with highly turbulent flows made by complex geographies. Here, we report the flow-induced rotation of a Savonius turbine in a highly turbulent flow (18% turbulence intensity). The high turbulence is realized by using the far-field of an open-jet. Compared to low turbulence inflow (1% turbulence intensity), the turbine rotates 4% faster in high turbulence since the torque/power increases with turbulence intensity. The wake measurement by hot-wire anemometry and particle image velocimetry reveals the suppression of vortex shedding in high turbulence. In addition, a newly developed semi-empirical low-order model, which can include the effect of turbulence intensity and integral length scale, also confirms high turbulence intensity contributes to the rotation of the turbine. These results will boost more installation of small Savonius turbines in urban areas in the future.

Integral Turbulent Length and Time Scales of Higher Order Moments

Turbulent length and time scales represent a fundamental quantity for analysing and modelling turbulent flows. Although higher order statistical moments have been conveniently used for decades to describe the mean behaviour of turbulent fluid flow, the definition of the integral turbulent scales seems to be limited to the velocity or its fluctuation itself (i.e. the first moment). Higher order moments are characterized by smaller integral scales and a framework is proposed for estimating autocorrelation functions and integral turbulent length or time scales of higher order moments under the assumption that the probability distribution of the velocity field is Gaussian. The new relations are tested for synthetic turbulence as well as for DNS data of a turbulent plane jet at Reynolds number 10000. The present results in particular suggest that the length or time scales of higher order moments can be markedly smaller than those of the turbulent variable itself, which has implications for statistical uncertainty estimates of higher order moments.

Effects of integral length scale variations on the stall characteristics of a wing at high free-stream turbulence conditions

The effect of variations in the integral length scale of incoming free-stream turbulence on a NACA0012 wing is investigated with the use of force, moment and particle image velocimetry measurements. At a chord-based Reynolds number ( $Re = U_\infty c/\nu$ where c is the chord length, $U_\infty$ is the free-stream velocity and $\nu$ is the kinematic viscosity) of $2\times 10^5$ , an active grid generates turbulence intensities of 15 % at normalised integral length scales ranging from 0.5 $c$ to 1 $c$ . The introduction of turbulence improves the time-averaged performance characteristics of the wing by delaying stall and increasing the peak lift coefficient. It is found that for half-chord integral length scales, the magnitude of the fluctuations in forces and moments is larger than that of full-chord integral length scales, as the former amplifies the naturally occurring unsteadiness in the flow (when there is no free-stream turbulence). The increase in magnitude is ascribed to a larger density of smaller-scale vortices within the separated flow and wake region of the wing.

A generalized k−ϵ model for turbulence modulation in dispersion and suspension flows

A large amount of published data show that particles with diameter above 10% of the turbulence integral length scale (D/l>0.1) tend to increase the turbulent kinetic energy of the carrier fluid above the single-phase value, and smaller particles tend to suppress it. We attempted to remove limitations in earlier modelling efforts for solids on the coupling between the particles and turbulence, and better fits to the turbulence modulation amplitude as function of D/l was achieved for a number of data sets. Explicit algebraic forms of the full model were derived using asymptotic analysis, and these are general enough for application to emulsions, bubbles and solids in bulk regions of multiphase turbulent flow. Rigorous particle-kinetic theory was used to derive the work exchanged between the particles and the fluid due to both drag and added mass forces, where the latter is essential for low or moderate particle/fluid density ratios, enabling a well justified model also for emulsions and bubbles. A novel sub-model for turbulence production by vortex shedding due to turbulence-generated slip velocity was incorporated, where earlier models took the slip velocity as an input parameter. The correct asymptotic limit of vanishing turbulence modulation for small tracer particles was also provided, giving better fit to the data for small particles. We found that turbulence augmentation for large diameter solids is due to vortex shedding, and turbulence suppression for small diameters is due to mainly to turbulent drag forces and extra fluid dissipation – a conclusion that agrees with earlier models for solids, despite their possible shortcomings. An important finding is that the mechanisms for turbulence suppression for bubbles and emulsion droplets are similar to those of solids, but with the addition of added mass scaling factors. Another important observation is that augmentation may not occur at all for bubbles or emulsion droplets since the larger diameters require moderate turbulence levels to prevent breakup, so that vortex shedding may be insignificant.