Fluctuating Velocity Components Research Articles

Parametric study of large-eddy simulation to capture scaling laws of velocity fluctuations in neutral atmospheric boundary layers

The development of digital twins for wind farms often involves the use of large-eddy simulation (LES) to model atmospheric boundary layers. Existing LES solvers primarily focus on accurately capturing streamwise fluctuations. They, however, overlook the less energetic cross-stream fluctuations, which play a crucial role in wind turbine wake evolution. In this study, we conduct a systematic parametric study and incorporate changes in an open-source LES solver. The improved solver is able to predict all three components of velocity fluctuations in alignment with the scaling laws derived from the attached-eddy hypothesis. In particular, we examine the impact of (i) the subgrid-scale model, (ii) the wall model, (iii) the von Kármán constant, and (iv) the grid-cell aspect ratio. We find that although all these factors influence the prediction of velocity fluctuations, the grid-cell aspect ratio has the greatest effect on the spanwise and vertical velocity components. Notably, utilizing nearly isotropic grid cells leads to the best alignment of all three velocity component fluctuations with the scaling laws. Spectral analysis further demonstrates that the present LES solver accurately predicts the characteristic length scales for all velocity fluctuation components, making it a reliable tool for obtaining turbulent inflow conditions for wind farm modeling.

The impact of operating temperatures on the fluctuating flow field and precessing vortex core in cyclone separator using large-eddy simulations

The present study evaluates numerically the impact of the operating temperature of gas on the cyclone performance viz. the pressure drop, collection efficiency, and flow field details at an inlet velocity, Uin=15 m/s. The gas temperature in a range of 273–1073 K is considered to significantly vary the fluid density and viscosity. For an in-depth analysis, we use advanced closure large-eddy simulation (LES) with the standard Smagorinsky model for treating the unresolved scales. LES can accurately provide additional details on the precessing vortex core phenomena that give rise to enhanced fluctuations in the core region of the cyclone. Apart from the traditional fast Fourier transformation analysis to evaluate the periodicity in the signal, we also perform continuous wavelet transformation and empirical mode decomposition operation on the temporal velocity signals for a better understanding of the flow instabilities—the signals reveal variations of frequency components with time, indicating a non-stationary behavior. It has been observed that an increase in the gas temperature causes lateral contraction of the inner vortex followed by the reduction in its precessional frequency about the cyclone axis with a significantly increased level of noise in the spectra. Furthermore, both pressure losses and collection efficiency largely reduce due to the weakening of swirling strength and enhancement in the fluctuating velocity components with an increase in the gas temperature.

Multiscale analysis of turbulence in horizontal pipes: Liquid and particle-liquid flow investigation

An experimental–theoretical methodology is developed to investigate the characteristics of turbulence in horizontal particle-liquid pipe flows. Using a discrete wavelet transform, the three-dimensional Lagrangian trajectories of the liquid phase experimentally determined by positron emission particle tracking are decomposed into their deterministic and stochastic sub-trajectories, which are then utilized to construct profiles of local fluctuating velocity components and turbulent kinetic energy. The results for a single-phase flow are independently validated using computational fluid dynamic simulation and the analysis parameters are fine-tuned using direct numerical simulation data from the literature. In a particle-liquid flow, the investigation explores the influence of various factors including particle size, density, and concentration on turbulence intensity. Remarkably, the results demonstrate significant effects of the particle size and density on liquid turbulence. The enhanced understanding gained regarding turbulence intensity helps to advance our fundamental interpretation of the dynamics of particle-liquid flows, thus potentially aiding the rational design of such complex flows and associated equipment.

NUMERICAL INVESTIGATION OF TURBULENCE CHARACTERISTICS AND SELF-SIMILARITY IN A HIGHLY AERATED STABLE HYDRAULIC JUMP USING LARGE EDDY SIMULATION

This work presents a numerical study of a stable hydraulic jump at Froude number 4.25 and Reynolds number 1.15×105 inside a horizontal and rectangular channel with a length of 3.2 m, a width of 0.5 m and a height of 0.4 m using large eddy simulation (LES). Classical hydraulic jump characteristics are obtained, such as conjugate depths, jump length, void fraction and velocity profiles. The hydraulic jump maximum streamwise velocity decay and shear layer spreading rate are simulated and compared with experimental data. For these parameters, numerical results demonstrate that is possible to stablish an analogy with other shear flows, such as the horizontal plane wall jet. Profiles of streamwise and vertical components of mean velocity are simulated, and self-similarity is observed for cross-sections located at the recirculation region of the jump. Self-similarity is also observed in terms of turbulent fluctuations, insofar as LES simulations indicate a high level of turbulence in the recirculation region. The simulated root mean square of streamwise velocity fluctuations, , ranges from 0.5 to 0.7 of the maximum cross-sections velocity, whereas the root mean square of vertical component of velocity fluctuations, , stays around 0.5 of the maximum cross-sections velocitiy. All validation comparisons show good agreement with the selected experimental data of Kramer and Valero (2020) and Wang (2014), presenting average deviations always lesser than 5%.

Modeling wind-driven seed dispersal using a coupled Lagrangian particle tracking and 1-D [formula omitted]-[formula omitted] turbulence model

We present a one-dimensional k-ɛ model and a Markov chain stochastic Lagrangian particle tracking model to study wind-driven dispersal of forest and grassland seeds. The turbulence model within and above the canopy is implemented for transient winds so that time series of profiles of mean velocity, turbulence kinetic energy, dissipation rate, and the root-mean-square of fluctuating velocity components can be modeled. We validate the model for steady state conditions using observations in a wide range of canopies, and apply the model for predicting time series of seed dispersal of Andropogon gerardii in a tall grass prairie in Missouri, United States. The stochastic seed dispersal model is validated against experimental data from a Quercus-Carya (oak-hickory) forest where seeds were released from different heights for a range of wind speeds. Using the model, we explore the detailed seed movement trajectories, instantaneous velocities, and investigate the relationship between dispersal distance and the seed falling duration and the mean fluctuating velocity during the falling. Moreover, examining the role of individual turbulent velocity components, we elucidate the different roles of horizontal and vertical velocity fluctuations, i.e., the horizontal component mainly contributes to the seed spreading in the wind direction, while the vertical component enhances the long tail of the distribution in the downstream direction, i.e., promoting long-distance-dispersal of seeds by wind.

Effects of wave direction on ship turning in regular waves

In this study, we focused on the drift motion of a ship during turning in regular waves and investigated the effects of wave direction on ship turning and drifting. First, turning tests in regular waves were conducted using a bulk carrier model by systematically changing the wave direction and wavelength to capture drifting characteristics. Subsequently, long-duration turning simulations were performed to capture the drifting characteristics with a large heading angle change over 2000° in waves using the two-time scale method (Yasukawa, 2006b; Skejic and Faltinsen, 2008). The simulation results indicated that the ship constantly drifted in a particular direction with respect to the incident wave direction during turning when sufficient time had passed. This phenomenon can be understood analytically using new formulas derived for the drifting indices (drifting distance and drifting direction). According to the formulas, the ship turning trajectory is deformed in waves drifting in proportional to time. The drifting velocity and drifting direction were determined by combining the average velocity components (ship surge velocity, lateral velocity, and yaw rate) and the first-order velocity fluctuation components with turning circular frequency. The formulas for the drifting indices were verified through comparison with the simulation results.

Experimental analysis of a propeller noise in turbulent flow

This paper presents a comprehensive experimental aeroacoustic investigation of a propeller under turbulence ingestion. Two turbulence-generating passive grids were utilized to quantify the effect of turbulence intensity on the aeroacoustic characteristics of the propeller. A two-component hot-wire anemometry was employed to study the flow field. The flow field results demonstrate a substantial increase in fluctuating velocity components in both axial and radial directions, concentrated at the mid-span of the blade and near the tip, respectively. Energy spectral analysis in the vicinity of the propeller blade shows significantly higher broadband energy levels with multiple haystacking peaks at the harmonics of the blade passage frequency. Far-field noise and load measurement results show that turbulence ingestion has a strong effect on the aerodynamic loading and acoustic response at the blade passage frequency. The directivity of noise radiation at low frequency shows a significant tonal noise contribution. Meanwhile, broadband noise radiation is more dominant at a higher range of frequency, especially when the propeller is operated with turbulence ingestion and at higher advance ratio settings. The far-field noise results revealed the haystacking trends in the low frequency domain of the spectra and are most significant for propellers operating in turbulent inflows.

Micro-flow investigation on laying process in Al2O3 stereolithography forming

When printing Al2O3 parts by stereolithography technology, the laying process is an extremely important part. In the current work, the referred flow analysis was numerically investigated. The rheological behavior was measured to determine the rheological type of the slurry. According to the fitting analysis, a Sisko model was available to describe the non-Newtonian behavior. Then, the modified multiple relaxation time lattice Boltzmann method was proposed and validated to effectively improve the stability of the simulation. Based on the proposed method, the situations without and with printed solids in the previous layer were investigated by a series of simulations. The laying velocity and layer thickness were considered as two important factors on the laying process. When the situation without printed solids in the previous layer is analyzed, the streamlines and flow velocities curves were almost horizontal. With different laying velocities, the flow velocities show obvious differences at the same thickness. With different layer thicknesses, the difference is mainly embodied in the vertical velocity component. When the printed solid is considered, the solid seriously affected the smooth flow. The vortices appeared near the printed solid, which also caused the disturbance in both horizontal and vertical velocity components. The mentioned interfering factors indicated different actions on the flow. The research will contribute to understanding the flow of the laying process. It can help to select suitable laying velocity and layer thickness to avoid severe flow velocity fluctuation and redundant vertical velocity components.

Influence of curvature distribution smoothing on the reduction of aerofoil self-noise

PurposeThis paper aims to investigate the influence of smooth curvature distributions on the self-noise of a low Reynolds number aerofoil and to unveil the flow mechanisms in the phenomenon.Design/methodology/approachIn this paper, large Eddy simulation (LES) approach was performed to investigate the unsteady aerodynamic performance of both the original aerofoil E387 and the redesigned aerofoil A7 in a time-dependent study of boundary layer characteristics at Reynolds number 100,000 and angle of attack (AoA) 4-degree. The aerofoil A7 is redesigned from E387 by removing the irregularities in the surface curvature distributions and keeping a nearly identical geometry. Flow vorticity magnitude of both aerofoils, along with the spectra of the vertical fluctuating velocity component and noise level, are analysed to demonstrate the bubble flapping process near the trailing edge (TE) and the vortex shedding phenomenon.FindingsThis paper provides quantitative insights about how the flapping process of the laminar separation bubble (LSB) within the boundary layer near the TE affects the aerofoil self-noise. It is found that the aerofoil A7 with smooth curvature distributions presents a 10% smaller LSB compared to the aerofoil E387 at Reynolds number 100,000 and AoA 4-degree. The LES results also suggest that curvature distribution smoothing leads to a 6.5% reduction in overall broadband noise level.Originality/valueThis paper fulfils an identified need to reveal the unknown flow structure and the boundary layer characteristics that resulted in the self-noise reduction phenomenon yielded by curvature distribution smoothing.

ACOUSTIC ADMITTANCE OF AN ALUMINIZED COMPOSITE SOLID PROPELLANT BY LASER DOPPLER VELOCIMETRY AT LOW PRESSURE

The present study involves the use of laser Doppler velocimetry (LDV) to determine the acoustic admittance of an aluminized composite solid propellant at low mean chamber pressure. The aim of this study is to measure the fluctuating velocity component perpendicular to the burning surface of the particles in the gaseous phase above the burning surface of the aluminized composite solid propellant for the imposed acoustic pressure oscillations. To check the accuracy and precision of the mini-LDV used in this study the acoustic mode shape was generated for the imposed acoustic oscillations with amplitudes of 215 and 6 Pa. The results obtained are very satisfying; they show that the predicted acoustic velocity mode shape matches with the generated mode shape using the LDV. The response function of a solid propellant indicates the inclination of the propellant to cause acoustic combustion instability. Both velocity fluctuations and imposed pressure fluctuations are measured experimentally and used to determine the acoustic admittance of the solid propellant and hence deducing the pressure coupled response function from acoustic admittance. The probe volume of the laser is maintained at a constant distance of 800-900 μm from the burning surface by a servomechanism using a linear actuator. The incorporation of the linear actuator dramatically increases the number of particles passing through the laser probe volume. The linear actuator is controlled using a microcontroller and the servomechanism is operated under an open loop system. A high-pressure window bomb is designed and fabricated. Low-frequency ranges (140-280 Hz) of the longitudinal acoustic modes are investigated in this paper. Tests were conducted at a mean chamber pressure of 0.5 MPa. To generate the acoustic pressure oscillations a rotary valve is designed and fabricated. The rotary valve generates a standing wave of the characterizing frequency depending upon the length of the chamber. Tests are conducted for two aluminized composite solid propellants. The results obtained are in good agreement with the literature for the pressure coupled response function at these mean chamber pressures.

Proper orthogonal decomposition of large-eddy simulation data over real urban morphology

Proper orthogonal decomposition (POD) is implemented to the atmospheric surface layer (ASL) over real urban morphology based on the data of large-eddy simulation (LES) with explicitly resolved buildings. Turbulence structures with different scales in the inertial (ISLs) and roughness (RSLs) sublayers are unveiled by decomposing the fluctuating velocity components into a range of spatial eigenmodes ψm(x) and time coefficients am(t). POD spatial modes, which are ranked according to their turbulence kinetic energy (TKE), are visualized to contrast their sizes. These dominant structures illustrate the footprints of most energetic eddies at the ground level which could modify the dynamics locally. Moreover, their temporal behaviors are examined by energy spectrum and Lissajous curve, elucidating the existence of large-scale traveling structures. It is also shown that around 80 and 100 modes (out of 1000) are able to retrace 90% of the original TKE and momentum flux, respectively. The aforementioned remarkable data reduction demonstrates the capability of POD for flow characteristic extraction and city-scale, reduced-order model (ROM) development. Besides, dominant modes transport more efficiently especially in ISLs. With proper urban planning, such as building height and orientation, these energy-carrying eddies would sweep into street canyons, improving pedestrian-level air quality as well as city ventilation. (200 words)

Nonlinear dynamics of traveling beam with longitudinally varying axial tension and variable velocity under parametric and internal resonances

In this investigation, the nonlinear dynamics of an axially accelerating viscoelastic beam on a pully mounting system have been analyzed. The axial tension of the beam is modeled as a function of the traveling velocity, support stiffness parameter as well as spatial coordinate. Geometric cubic nonlinearity in the equation of motion is due to elongation in the neutral axis of the beam. The integro-partial differential equation of motion of the axially accelerating beam associated with the simply supported end conditions is solved analytically by adopting the direct perturbation method of multiple time scales. As a result, a set of complex variable modulation equations is generated, which governs the modulation of amplitude and phase. This set of modulated equations is numerically solved to explore the influence of the support stiffness parameter upon the stability and bifurcation of the beam which has not been addressed in the existing literature. Apart from this, the impact of fluctuating velocity component, viscoelastic coefficient, longitudinal stiffness parameter, internal and parametric frequency detuning parameters on the stability and bifurcation analysis is studied, revealing significant dynamic characteristics of the traveling system. The fourth-order Runge–Kutta method is applied is to find the dynamic solution of the system. The system displays stable periodic, quasi-periodic, and mixed-mode dynamic responses along with the unstable chaotic behavior for a specific set of system parameters. The results obtained through an analytical–numerical approach may help the design and operation of an axially moving beam.

Parametrically excited axially accelerating viscoelastic beam subjected to time-varying axial speed, longitudinally varying axial tension and internal resonance

The present work investigates the nonlinear characteristics of an axially moving viscoelastic beam of the Kelvin–Voigt model on a pulley mounting system. The equation of motion is developed by including the terms like external and internal damping, geometric cubic nonlinearity, Coriolis, time-dependent axial speed, and longitudinally varying axial tension. The direct perturbation method of multiple time scales (MMS) is adopted to get an approximate solution for the nonlinear integro-partial differential equation of motion which leads to a set of complex variable modulation equations. These modulated equations are solved numerically to study the trivial state stability plot considering the effect of the support stiffness parameter for the first time. In addition to this, the impact of material, and viscous damping parameters on stability boundary is also studied. Continuation algorithm is implemented to analyse the influence of the support stiffness parameter, internal and parametric detuning parameters, fluctuating velocity component, and longitudinal stiffness parameter on the stability and bifurcation of the steady state solutions. Variation in internal frequency detuning parameter and variable axial speed component reveals different kinds of equilibrium solution curves in the nonlinear travelling system. The stability and bifurcation features observed in the present nonlinear system with change in the above control parameters are interesting and also not available in the existing literature.

Bubble velocimetry using the conventional and CNN-based optical flow algorithms

In the present study, we introduce new bubble velocimetry methods based on the optical flow, which were validated (compared) with the conventional particle tracking velocimetry (PTV) for various gas–liquid two-phase flows. For the optical flow algorithms, the convolutional neural network (CNN)-based models as well as the original schemes like the Lucas-Kanade and Farnebäck methods are considered. In particular, the CNN-based method was re-trained (fine-tuned) using the synthetic bubble images produced by varying the density, diameter, and velocity distribution. While all models accurately measured the unsteady velocities of a single bubble rising with a lateral oscillation, the pre-trained CNN-based method showed the discrepancy in the averaged velocities in both directions for the dilute bubble plume. In terms of the fluctuating velocity components, the fine-tuned CNN-based model produced the closest results to that from PTV, while the conventional optical flow methods under- or over-estimated them owing to the intensity assumption. When the void fraction increases much higher (e.g., over 10%) in the bubble plume, the PTV failed to evaluate the bubble velocities because of the overlapped bubble images and significant bubble deformation, which is clearly overcome by the optical flow bubble velocimetry. This is quite encouraging in experimentally investigating the gas–liquid two-phase flows of a high void fraction. Furthermore, the fine-tuned CNN-based model captures the individual motion of overlapped bubbles most faithfully while saving the computing time, compared to the Farnebäck method.

Compressibility effect on interaction of shock wave and turbulent boundary layer

The compressibility effect when an oblique shock wave impinges on a turbulent boundary layer was analyzed with a direct numerical simulation using Helmholtz decomposition. The turbulent intensity near the impinging region is significantly enhanced by the interaction of the shock wave and boundary layer. In particular, the interaction behavior can enhance the dilatational components of the Reynolds stress and velocity fluctuations. This also enhances the negative correlation between the dilatational components of streamwise and normal velocity fluctuations. The dilatation fluctuation in the impinging region increases significantly. Moreover, in the impinging region, the dilatational components of the production term and transport term contribute to the production and transport terms of the kinetic energy equation mainly in the vicinity of the interface. This simulation shows that the interaction behavior of an oblique shock wave and turbulent boundary layer can enhance flow compressibility significantly. In the interaction region, the turbulent intensity of the flow field is stronger than those upstream and downstream. This study provides a theoretical basis for the improvement of other simulation methods and turbulence modeling for the interaction of an oblique shock wave and turbulent boundary layer.

Investigations of Turbulence in the IIAEM Wind Tunnel Using Computational Fluid Dynamics

Turbulence is important to be assessed in the design of wind tunnels. Undesired turbulence levels undermine the quality of fluid flow and accordingly the quality of scientific data. At the test section, the level of turbulence is critical. The amount of turbulence present in the test section of a subsonic wind tunnel has not been investigated in earlier researches. In the present research, a subsonic open-section wind tunnel installed at the authors’ facility is used as a testbed for turbulence investigation. Computational Fluid Dynamics that solves Reynolds Averaged Navier Stokes equations (RANS) is used as the scientific method for calculating the turbulent flow parameters. RANS instead of Large Eddy Simulation or Direct Numerical Simulation is adopted as a first step to identify large-scale eddies. The characterization of turbulence is performed though decomposition of fluctuating velocity components (u and v) in two-dimension.

TR-PIV measurements of turbulent confined impinging twin-jets in crossflow

In this work, time-resolved particle image velocimetry (TR-PIV) measurements have been carried out to study the flow structure and flow dynamics of submerged transverse impinging twin-jet flows discharged into a confined laminar crossflow. A parametric study has been carried out for fixed spacing ratio between the jets of s=L/D=3, fixed jet-to-target spacing ratio of H/D=6.73, fixed crossflow Reynolds number of Re=3500, and two jet Reynolds numbers based on the outlet velocities and jet diameter D of Rej=8670 and 9933 that correspond to jet-to-cross-flow velocity ratios of r=vj/u0=10 and 11.46, respectively. Flow measurements in several different planes of the test section are acquired to assess the confinement effect of the bounded jets. Flow visualization images of the mean velocity, vorticity, strain rate distributions, turbulence kinetic energy, and Reynolds stresses have been obtained. The results reveal the dependence of Rej on the trajectory, penetration, crossflow entrainment and lateral spreading of the twin jets. Spectral analysis of the fluctuating velocity components shows the characteristic frequencies related to vortex pairing and vortex breakup, and the shedding frequencies of the upstream and downstream wall jets have also been obtained. The swirling strength criteria has been applied to identify coherent structures, and their development confirms that these structures undergo two or three stages of vortex pairing prior to the vortex breakdown activity. The experimental data has been analyzed using proper orthogonal decomposition (POD), and the most energetic modes, the relative and cumulative energy contributions, dominant POD modes, and temporal POD coefficients have been obtained. The results show that the for Rej=8670, the first two POD modes account for 16.50% of the total kinetic energy, and the cumulative energy of the first 20 POD modes is 55.10%. For Rej=9933, the first two POD modes account for 17.98% of the total energy, and the sum of energies of the first 20 POD modes is 57.13%.

Physics-based model for boundary layer transition prediction in a wide speed range

A new physics-based model employing three transport equations is developed for the simulation of boundary layer transitions in a wide speed range. The laminar kinetic energy is used to represent pretransitional streamwise velocity fluctuations, taking account of different instability modes. The fluctuation velocity components normal to the streamwise direction are modeled by another transport equation. Transition is triggered automatically with the development of the pretransitional velocity fluctuations. In the fully turbulent region, the model reverts to the k-ω turbulence model. Different test cases, including subsonic, supersonic and hypersonic flows around flat plates, airfoils and straight cones, are numerically simulated to validate the performance of the model. The results demonstrate the excellent predictive capabilities of the model in different paths of transition. The model can serve as a basis for the extension of additional transition mechanisms, such as rotation and curvature effects, roughness-induced transition and crossflow-induced transition.

PIV Measurements of Turbulent Airflow in a Channel with Trapezoidal Ribs on One Wall

This paper presents the results of PIV measurements of turbulent airflow in a channel with a single ribbed wall. The rough elements had the form of evenly spaced trapezoids. The ratio of the height of a single rib to the height of the measurement channel was 0.1. The ratio of the distance between adjacent ribs to the height of a single rib (i.e., the w/k ratio) was 5, which suggests a transitional region within the airflow structure between the d- and k- types. The measurements were carried out for the inlet velocity, at which the Reynolds number (Re) was equal to 32,500. The distance to the first rib, at which the turbulent velocity profile is fully developed, was determined. The distribution of the average velocity components, the velocity fluctuation components, turbulent shear stress, as well as the turbulence kinetic energy between two adjacent ribs was presented. The analysis of average streamlines indicated the existence of two vortex structures between the ribs.

Revisiting the Reynolds-averaged Navier–Stokes equations

Abstract This study revisits the Reynolds-averaged Navier–Stokes (RANS) equations and finds that the existing literature is erroneous regarding the primary unknowns and the number of independent unknowns in the RANS. The literature claims that the Reynolds stress tensor has six independent unknowns, but in fact the six unknowns can be reduced to three that are functions of the three velocity fluctuation components, because the Reynolds stress tensor is simply an integration of a second-order dyadic tensor of flow velocity fluctuations rather than a general symmetric tensor. This difficult situation is resolved by returning to the time of Reynolds in 1895 and revisiting Reynolds’ averaging formulation of turbulence. The study of turbulence modeling could focus on the velocity fluctuations instead of the Reynolds stress. An advantage of modeling the velocity fluctuations is, from both physical and experimental perspectives, that the velocity fluctuation components are observable whereas the Reynolds stress tensor is not.