Turbulence Integral Length Scale Research Articles

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.

Experimental study of turbulent thermal diffusion of particles in an inhomogeneous forced convective turbulence

We investigate experimentally the phenomenon of turbulent thermal diffusion of micrometer-size solid particles in an inhomogeneous convective turbulence forced by one vertically oriented oscillating grid in an air flow. This effect causes the formation of large-scale inhomogeneities in particle spatial distributions in a temperature-stratified turbulence. We perform detailed comparisons of the experimental results with those obtained in our previous experiments with an inhomogeneous and anisotropic stably stratified turbulence produced by a one oscillating grid in the air flow. Since the buoyancy increases the turbulent kinetic energy for convective turbulence and decreases it for stably stratified turbulence, the measured turbulent velocities for convective turbulence are larger than those for stably stratified turbulence. This tendency is also seen in the measured vertical integral turbulent length scales. Measurements of temperature and particle number density spatial distributions show that particles are accumulated in the vicinity of the minimum of the mean temperature due to the phenomenon of turbulent thermal diffusion. This effect is observed in both convective and stably stratified turbulence, where we find the effective turbulent thermal diffusion coefficient for micrometer-size particles. The obtained experimental results are in agreement with theoretical predictions.

Large Eddy Simulation Inflow Generation Using Reduced Length Scales for Flows Past Low-Rise Buildings

When undertaking wind assessment around buildings using large eddy simulation (LES), the implementation of the integral length scale at the inlet for inflow generation is controversial, as real atmospheric length scales require huge computational domains. While length scales significantly influence inflow generation in the domain, their effect on the downstream flow field has not, as yet, been investigated. In this paper, we validate the effectiveness and accuracy of implementing a reduced turbulence integral length scale for inflow generation in LES results at the rooftop of low-rise buildings and develop a technique to estimate the real local length scales using simulation results. We measure the wind locally and calculate the turbulence length scales from the energy spectrum of the wind data and simulation data. According to these results, there is an excellent agreement between the length scale from simulation and measurement when they are scaled with their corresponding freestream/inlet value. These results indicate that a reduced integral length scale can be safely used for LES to provide a reliable prediction of the energy spectrum as well as the length scales around complex geometries. The simulation results were confidently employed to obtain the best location for a wind turbine installation on low-rise buildings.

Effects of turbulence on variations in early development of hydrogen and iso-octane flame kernels under engine conditions

The understanding and prediction of the early development of flame kernels are of high practical importance for the robust relight of aviation gas turbines and the control of cycle-to-cycle variations (CCV) of spark-ignition engines. CCV are known to correlate strongly with early flame kernel development and complicate the optimization of such engines in terms of safety, thermal efficiency, and engine emissions. The flame kernel initiated by a spark is initially small, in the very early combustion phase typically smaller than the size of the turbulent integral length scales. Therefore, the development of the flame kernel is dominated by local, intermittent flow fluctuations and can vary under the same nominal conditions. In this study, the effects of turbulence on the early development of premixed iso-octane and hydrogen turbulent flame kernels under realistic engine conditions are investigated through direct numerical simulations. Multiple realizations were simulated under the same nominal conditions for both fuels. Significant variations in flame kernel interactions with turbulence can be identified among different realizations. The fuel consumption rate varies by a factor of two, which is remarkable considering that only statistical differences in the local flow field are present between different realizations. Effects of different flow features of the initial flow fields on the flame kernel development were analyzed. It was found that the flow motion on the scale of the ignition radius, specifically the fluid deformation, which is characterized by the invariants of the strain rate tensor, determines the global shape of the kernel, while the variations of the kernel growth rate are mostly driven by the variations of the smallest turbulent scales. In particular, turbulence influences the flame surface area growth mainly through the tangential strain rate at the flame surface, which is shown to result from the small-scale turbulent motion. Due to differential diffusion effects, hydrogen and iso-octane exhibit significantly different flame responses to curvature, which is comprehensively studied for both fuels. The findings in this study will guide the development of combustion models that are capable to capture variations of the early flame kernels based on the local turbulence dissipation rate.

Self-similar propagation and flame acceleration of hydrogen-rich syngas turbulent expanding flames

In order to investigate the flame self-similar propagation and flame acceleration characteristics of hydrogen-rich syngas turbulent expanding flames, the turbulent combustion experimental studies of H2/CO/air mixtures with XH2 = 55%-95%, φ = 0.6–1.0, P = 1 bar-3 bar, u’=0.809–2.533 were conducted in a fan-stirred turbulent combustion chamber with an inner diameter of 380 mm. Results show that the normalized flame propagation speed ST/SL and turbulent flame Reynolds number ReT,flame could be represented by power-law correlations. With the increase of hydrogen fraction from 55% to 95%, the power exponent decreases from 0.413 to 0.301. The increase of hydrogen fraction makes the flame acceleration weaker because that the enhancing of laminar flame speed is more obvious than the differential-diffusion effect by decreasing Le. With the decrease of equivalence ratio from 1.0 to 0.6, the power exponent increases from 0.304 to 0.411 in this study. The relative high power exponent under low equivalence ratio is due to the coupling between differential-diffusion and the flame stretch on the local wrinkled flame structures. In addition, the influence of turbulence and flame intrinsic instabilities on flame acceleration propagation process of hydrogen-enriched syngas were studied. The acceleration exponent was extracted to quantitatively investigate the flame self-acceleration propagation in the transition stage, and the relationships between acceleration exponent and turbulence intensity (u’), Kovasznay number (Kz), turbulence integral length scale (LT), flame thickness (δ), thermal expansion ratio (ρu/ρb), effective Lewis number (Leeff) were analyzed

Production and transport of turbulent kinetic energy from premixed flames subjected to mean pressure gradients

The influence of mean favorable pressure gradients on the production and transport of turbulent kinetic energy is experimentally investigated in a premixed bluff-body combustor. The combustor wall geometry is modified into converging, straight, or diverging configurations to experimentally alter the mean pressure gradient in the reacting flow field. For each configuration, turbulent kinetic energy production and transport dynamics are characterized with high-speed particle image velocimetry and simultaneous CH* chemiluminescence imaging. For all cases, the premixed reaction increases the turbulent kinetic energy and integral length scales in the flow. However, increasing the magnitude of the mean favorable pressure gradient increases the turbulent kinetic energy produced by the flame. The source of increased turbulent fluctuations from reactants to products is first investigated with a steady flow energy analysis, and is accompanied with a Reynolds decomposed investigation of the kinetic energy in the flow. As the mean pressure gradient increases, the turbulent kinetic energy in the flow increases due to stronger magnitudes of flame-generated turbulence in the form of baroclinic torque. The evolution of the flame-generated turbulence is examined by decomposing the transport equation of turbulent kinetic energy. Increasing the mean favorable pressure gradient augments the largest magnitude transport terms, and the budget of turbulent kinetic energy is primarily driven by pressure gradient work and viscous dissipation. The results here differ from previous direct numerical simulation (DNS) studies, and should ultimately motivate additional research to aid the development of computational models which can better predict turbulent flame-flow dynamics in confined environments with mean pressure gradients.

Effects of turbulence intensity and integral length scale on the surface pressure on a rectangular 5:1 cylinder

This paper presents the LES of the turbulence effects on the flow over a two-dimensional rectangular 5:1 cylinder. The homogeneous and isotropic inflow turbulence fields are generated by the Iterating-Reshaping based Consistent Discrete Random Flow Generation (IRCDRFG) technique. A total of nine numerical cases with the inflow turbulence intensity equal to 5.0%, 7.5%, and 10.0%, and the ratio of integral length scale to cylinder depth (L/D) equal to 1, 2, and 4 are simulated respectively. The LES tool well reproduces both the instantaneous and time-averaged flow structures in the near cylinder area. The sizes of the mean separation bubble on the cylinder surface are noticed to decrease and be closer to the leading edge with the higher turbulence intensity and the lower L/D, which contributes to the shift of location with the minimum mean value and that with the maximum RMS value of the surface pressure. Besides, the consistent drag force results with different inflow conditions are obtained, which have strong connection with the following correlation results of surface pressure in different directions. Additionally, the PSD analysis shows that the low-frequency energy of the fluctuating pressure is significantly increased with the presence of the incoming large-scale turbulence field.

Inflow turbulence distortion for airfoil leading-edge noise prediction for large turbulence length scales for zero-mean loading.

Turbulence distortion due to airfoil finite thickness is an important but not fully understood phenomenon that affects the airfoil radiated noise, resulting in inaccurate noise predictions. This study discusses the turbulence distortion in the leading edge (LE) region of an airfoil aiming to obtain more accurate LE noise predictions. Wind tunnel experiments were performed for National Advisory Committee for Aeronautics (NACA) 0008 and NACA 0012 airfoils at zero angle of attack subjected to large turbulence length scales (between 10 and 43 times the airfoil LE radius) generated by a grid and a rod. Hot-wire and surface pressure measurements were performed in the LE region. Results show that the root mean square of the velocity fluctuations urms and the turbulence integral length scale Λf at the stagnation line decrease considerably as the LE is approached. Rod-airfoil radiated noise was measured and compared with Amiet's model. The predicted noise overestimates the LE noise for high frequencies. However, the prediction agrees well with measurements when the turbulence spectrum based on the rapid distortion theory is used in Amiet's model, with as inputs the urms and Λf values measured close to the LE. This work's main contribution is to demonstrate that more accurate noise predictions are obtained when the inputs to the model consider the turbulence distortion effects.

A simplified semi-empirical model for long-range low-frequency noise propagation in the turbulent atmosphere

We present a semi-empirical long-range low-frequency acoustic propagation model, which accounts for atmospheric turbulence. Ostashev and Wilson’s scattering model is combined with a ray-theory based refraction model to account for turbulent scattering and refraction via a turbulent absorption coefficient. The coefficient is ascertained via integration of scattered energy. The model is formulated, calibrated, and validated via corresponding experiments conducted within the National Science Foundation Boundary Layer Wind Tunnel. The predictions of the newly proposed ‘bridging model’ match the wind tunnel experimental data with an average error of 11.9%. Example predictions are shown to quantify the effect of turbulent kinetic energy and turbulent integral length scale on long-range infrasound propagation. To demonstrate the approach, we present predictions of the propagation of noise from a tornado and a nonlinear wave.

Effects of incoming free-stream turbulence on the flow dynamics of a square finite wall-mounted cylinder

This study attempts to describe associated fluid dynamics of a square finite wall-mounted cylinder (FWMC) immersed within free-stream turbulent flow characterized by different turbulence intensities and integral length scales. An improved delayed detached eddy simulation method is adopted to numerically reproduce the fully developed turbulent flow fields. The results reveal that both the turbulence intensities and integral length scales have a significant effect on the separated shear layers, base pressure, and associated aerodynamic forces of the cylinder. Constrained streamlines along with critical point techniques are employed to further illustrate the influence of parameters of interest on a time-averaged flow pattern, including horseshoe vortex, surface flow, and wake topology. Distribution of second-order statistics within the wake region shows a shorter longitudinal length of the reversed flow region and enhanced vortex strength when background turbulence intensity increases. The time-dependent interaction between background turbulence and separated flow around the square FWMC is illustrated based on the phase difference between pressure of opposing side faces and the evolution of the reverse-flow region. In the end, the spectral proper orthogonal decomposition technique is employed to further investigate the effects of incoming flow turbulence on characteristics of the free-end shear flow and Von Kármán vortex shedding in the wake.

Control of airfoil broadband noise through non-uniform sinusoidal trailing-edge serrations

This study provides experimental and analytical investigations on the use of non-uniform sinusoidal trailing edge (TE) serrations as a passive means for the control of airfoil broadband noise over a wide range of frequencies. Combinations of sharper/wider non-uniform TE serrations provide higher noise reductions up to about 5 dB over the uniform ones. The normalized sound power reductions (ΔPWL/) of non-uniform sinusoidal TE serrated airfoils show linear dependence with the corrected Strouhal number, i.e., ΔPWL/ = a Stm + b, where a and b are the arbitrary constants and Stm is the modified Strouhal number. It reveals that the presence of non-uniform wavy TE serrations shows superior noise reduction performance over uniform ones from mid to high frequencies when λ2 (wide) > λ1 (narrow), which is indicated by the good coalesce of ΔPWL/ with Stm. Furthermore, the modified Strouhal number scaling law for non-uniform sinusoidal TE serrated airfoils indicates the universal behavior of the noise reduction performance. The highest overall noise reductions provided by the non-uniform wavy TE serrations occur when the transverse turbulence integral length scale (Λt) is 0.5 times the geometric mean of the wavelengths of two individual serrations. The flow visualization clearly shows the breakup of eddies by the tip of serrations, and the pairing of the vortices evolved from the root/tip of the serrations. The presence of higher span-wise de-coherence/phase interference provided by the non-uniform TE serrated airfoils leads to higher noise reductions over uniform ones.

New method to separate turbulence statistics of fan rotor wakes from background flow

The separation of turbulence parameters such as turbulence intensity and integral length scale of fan rotor wakes from background flow from unsteady velocity data is a challenge. The two processes are overlapped, and typically, very few samples of the data are taken inside the rotor wakes, making it hard to perform any spectral analysis. This work proposes a new time domain approach to separate the two processes by using two suitable data tapers. The unsteady velocity cyclic variance distribution is used as reference to establish the border between the blade wakes and the background flow. Results indicate an increase in wake turbulence levels and a slight increase in background turbulence levels with the increase in fan blade loading. The integral length scale of the rotor wakes did not change considerably among the different fan loading analyzed. This contrasts with the values observed for the background flow, which decreased with increasing of fan loading. The rotor wakes seem to be anisotropic, regardless of the fan operating point.Graphical abstract