Statistics Of Velocity Fluctuations Research Articles

Statistics of velocity fluctuations in a homogeneous liquid fluidized bed

A liquid-solid fluidized bed is investigated by means of optical techniques involving index matching. Statistics of velocity fluctuations of both phases are determined. A physical model distinguishing between interstitial and wake regions is introduced. It reproduces the velocity fluctuation distributions up to the third-order-moment, explaining the reversal of the skewness when increasing the solid concentration.

Structure function tensor equations in inhomogeneous turbulence

Exact budget equations for the second-order structure function tensor ⟨𝛿u$_{i}$𝛿u$_{j}$⟩, where 𝛿u is the difference of the i th fluctuating velocity component between two points, are used to study the two-point statistics of velocity fluctuations in inhomogeneous turbulence. The anisotropic generalised Kolmogorov equations (AGKE) describe the production, transport, redistribution and dissipation of every Reynolds stress component occurring simultaneously among different scales and in space, i.e. along directions of statistical inhomogeneity. The AGKE are effective to study the inter-component and multi-scale processes of turbulence. In contrast to more classic approaches, such as those based on the spectral decomposition of the velocity field, the AGKE provide a natural definition of scales in the inhomogeneous directions, and describe fluxes across such scales too. Compared to the generalised Kolmogorov equation, which is recovered as their half-trace, the AGKE can describe inter-component energy transfers occurring via the pressure–strain term and contain also budget equations for the off-diagonal components of ⟨𝛿u$_{i}$𝛿u$_{j}$⟩. The non-trivial physical interpretation of the AGKE terms is demonstrated with three examples. First, the near-wall cycle of a turbulent channel flow at a friction Reynolds number of Re$_{𝜏}$ = 200 is considered. The off-diagonal component ⟨-𝛿u𝛿υ⟩, which cannot be interpreted in terms of scale energy, is discussed in detail. Wall-normal scales in the outer turbulence cycle are then discussed by applying the AGKE to channel flows at Re$_{𝜏}$ = 500 and 1000. In a third example, the AGKE are computed for a separating and reattaching flow. The process of spanwise-vortex formation in the reverse boundary layer within the separation bubble is discussed for the first time.

Effects of aspect ratio on higher-order moments, conditional statistics, TKE budget and anisotropy in narrow open channel flow

The purpose of the present study is to investigate the influence of aspect ratio on the higher- order statistics of velocity fluctuations, conditional statistics, turbulent kinetic energy (TKE) fluxes, TKE budget, and Reynolds stress anisotropy in hydraulically rough narrow open channel flow (OCF). In the experiments, the aspect ratios were maintained low and varied between 2.5 and 4. The velocities were measured with an acoustic Doppler velocimeter (ADV). The higher-order moments, quadrant analysis, and TKE budget from the present experiments were compared with available literature data in wide and narrow OCFs to elucidate the effect of the aspect ratio. In this analysis, the third-order moments of velocity fluctuations were found to be sensitive to the aspect ratio in the outer region. The fractional contributions of all quadrant events are approximately equal in magnitude in lower aspect ratio flows, whereas ejections and sweeps are the dominant events as the aspect ratio increases. The upward transfer of TKE flux increases in the outer layer with increase in aspect ratio. In the inner layer, the TKE production and rate of dissipation are found to be increasing with decreasing aspect ratio. Therefore, the production and dissipation of TKE are dependent on the aspect ratio of the flow. The analysis of Reynolds stress AIM reveals that for low aspect ratio flows turbulence tends to attain rod-like axisymmetric turbulence only in the intermediate layer whereas for higher aspect ratio, turbulence attains rod-like axisymmetric turbulence throughout the depth.

Near Wake Development Behind Marine Propeller Model in Presence of Freestream Turbulence

Abstract Three-dimensional particle image velocimetry (PIV) experiments were conducted in the immediate near wake and up to seven diameters downstream of a three-bladed marine propeller model operating in two different inflow conditions: one with imposed freestream turbulence with intensity of 7% and streamwise integral length scale comparable to propeller geometry, and the second experiment with a quiescent inflow conditions as a reference. The resulting Reynolds number based on propeller chord and relative velocity is Re0.7R = 4.7 × 105. All components of radial transport of mean flow kinetic energy are analyzed and the largest contributor to the fluxes is found to be correlated to Reynolds shear stresses, resulting in radially outward flux in the wake. Two regions of the near wake are distinguishable with downstream extent dependent on the level of external turbulence. In the first region, immediately behind the propeller, shed tip vortices are very coherent and undergo grouping and roll-up around each other and the second region where the vortex merger process is complete and characterized by breakdown of vortices into small-scale turbulence. The latter region was found to occur earlier in the experiment with external turbulence. Conditional statistics of velocity fluctuations were employed and they show that outward interactions and sweep events contribute the most to the transfer of mean flow kinetic energy from the inner wake to the freestream.

Large Eddy Simulation of boundary layer transition over an isolated ramp-type micro roughness element

Boundary layer transition over an isolated surface roughness element is investigated by means of numerical simulation. Large Eddy Simulation (LES) flow-modeling approach is employed to study flow characteristics and transition phenomenon past a roughness element immersed within an incoming developing boundary layer, at a height-based Reynolds number of 1170. LES numerical results are compared to experimental data from literature showing the time-averaged velocity distribution, the velocity fluctuation statistics and the instantaneous flow topology.Despite slight difference in the intensity of streamwise velocity fluctuations, the present LES results and experimental data show very good agreement. The mean flow visualization shows streamwise counter-rotating vortices pairs formation downstream of the obstacle. The primary pair induces an upwash motion and a momentum deficit that creates a Kelvin-Helmholtz type flow instability. The instantaneous flow topology reveals the formation of coherent K-H vortices downstream that produce turbulent fluctuations in the wake of the roughness element. These vortices are streched and lifted up when moving downstream. The velocity fluctuations results show that the onset of the turbulence is dominated by the energy transfer of large-scale vortices.

Stresses and Drag in Turbulent Bed Load From Refractive Index‐Matched Experiments

AbstractWe report steady open‐channel flow experiments that resolve the internal dynamics of turbulent bed load layers at subgrain diameter resolution. Optical access is gained by using materials of matched refractive index, and a laser light sheet is scanned across the medium to capture both the solid and liquid motions over a 3‐D volume. The imaging measurements yield vertical profiles of granular concentration, solid and liquid mean velocity, and velocity fluctuation statistics including the granular temperature and the Reynolds stress. This makes it possible to determine all principal contributions to the momentum balance of each phase. In particular, experimental profiles are obtained for the stresses and interphase drag force. They are used to test constitutive relationships derived from kinetic theory, turbulence theory, and fluidization cell experiments.

Turbulence features in a wall-wake flow downstream of a wall-mounted vertical cylinder

Characteristics of turbulent kinetic energy (TKE) fluxes and budget, conditional Reynolds shear stress (RSS) and Reynolds stress anisotropy in the near- and far-wake flows downstream of a wall-mounted vertical circular cylinder are studied. The TKE fluxes exhibit that the near-wake flow is characterized by an accelerating effect and the far-wake flow by a retarding effect. The TKE budget is explained by using the principle of the TKE conservation. The profiles of TKE budget show that the wall-shear layer of the wall-wake flow is governed by a high negative pressure energy diffusion rate in addition to a high TKE dissipation rate. The conditional statistics of velocity fluctuations were studied to examine the turbulent bursting events by using the quadrant analysis. The conditional RSS profiles illustrate that the near-wake flow is characterized by inward interactions, while the far-wake flow is characterized by sweeps. In the wall-wake flow, the mean duration of bursting events is shorter than their mean interval of occurrence. The Reynolds stress anisotropy reveals that the anisotropic invariant maps appear to be a closed looping trend in the near-wake flow and an open looping trend in the far-wake flow. However, all the profiles, for example, TKE fluxes and budget, conditional RSS and turbulence anisotropy, regain their uninterrupted upstream profiles with an increase in downstream distance.

Effect of aspect ratio on higher order moments of velocity fluctuations in hydraulically rough open channel flow

The effect of aspect ratio on the higher order statistics of velocity fluctuations in a hydraulically rough turbulent open channel flow is investigated. In this regard, an experiment was conducted in a rough bed narrow open channel flow of aspect ratio equal to three and the instantaneous flow velocities were measured using a Nortek Vectrino+ Acoustic Doppler Velocimeter. To understand the effect of aspect ratio, the results obtained from the present study are compared with the literature data of approximately same Reynolds number and bed roughness in a wide open channel flow for turbulence intensities and higher order statistics of velocity fluctuations. Comparison of turbulence intensities between Narrow OCF and Wide OCF shows occurrence of higher streamwise and vertical turbulence intensities in the outer region of Narrow OCF. The results of third order moments of velocity fluctuations are sensitive to aspect ratio in the outer region.

Statistics of velocity fluctuations of Geldart A particles in a circulating fluidized bed riser

Particle velocity fluctuations in a large-scale circulating fluidized bed are observed to be anisotropic and non-Maxwellian. Interfacial drag acting on high-density configurations lead to excursions resulting in Levy flight of particles.

Surface‐sampled simulations of turbulent flow at high Reynolds number

SummaryA new approach to turbulence simulation, based on a combination of large eddy simulation (LES) for the whole flow and an array of non–space‐filling quasi‐direct numerical simulations (QDNS), which sample the response of near‐wall turbulence to large‐scale forcing, is proposed and evaluated. The technique overcomes some of the cost limitations of turbulence simulation, since the main flow is treated with a coarse‐grid LES, with the equivalent of wall functions supplied by the near‐wall sampled QDNS. Two cases are tested, at friction Reynolds number Reτ=4200 and 20000. The total grid point count for the first case is less than half a million and less than 2 million for the second case, with the calculations only requiring a desktop computer. A good agreement with published direct numerical simulation (DNS) is found at Reτ=4200, both in the mean velocity profile and the streamwise velocity fluctuation statistics, which correctly show a substantial increase in near‐wall turbulence levels due to a modulation of near‐wall streaks by large‐scale structures. The trend continues at Reτ=20000, in agreement with experiment, which represents one of the major achievements of the new approach. A number of detailed aspects of the model, including numerical resolution, LES‐QDNS coupling strategy and subgrid model are explored. A low level of grid sensitivity is demonstrated for both the QDNS and LES aspects. Since the method does not assume a law of the wall, it can in principle be applied to flows that are out of equilibrium.

Time-resolved stereo PIV measurements in the far-field of a turbulent zero-net-mass-flux jet

This paper presents time-averaged and temporally evolving mean flow and turbulence statistics for a turbulent zero-net-mass-flux (ZNMF) jet at high Reynolds and Strouhal numbers in the far-field in a plane perpendicular to the jet axis. The measurements have been obtained using time-resolved stereo particle image velocimetry (TR-SPIV). The jet is generated by the oscillation of a piston, which discharges filtered water to the quiescent fluid in a tank through a round orifice. A multigrid cross correlation digital particle image velocimetry algorithm (MCCDPIV) has been used to compute the images from each camera that subsequently have been combined to obtain the three components of the velocity. Velocity and turbulence statistics are in good agreement with results obtained in previous work. A comparative study has been performed to determine the contribution to the spreading rate due to the displacement of the center of the jet as rigid body. Different criteria to define the instantaneous jet center have been considered. For the different cases carried out for this study it has been observed that subtracting the movement as a rigid body the width of the jet becomes similar to that of a continuous jet. Velocity fluctuation statistics are also influenced by this restriction. The image series have also been analyzed to determine the temporal evolution of the velocity field and its fluctuations. The fast Fourier transforms (FFT) have been used to calculate the power spectra of these variables.

Waves and turbulence in katabatic winds

The measurements taken during the Vertical Transport and Mixing Experiment (VTMX, October, 2000) on a northeastern slope of Salt Lake Valley, Utah, were used to calculate the statistics of velocity fluctuations in a katabatic gravity current in the absence of synoptic forcing. The data from ultrasonic anemometer-thermometers placed at elevations 4.5 and 13.9 m were used. The contributions of small-scale turbulence and waves were isolated by applying a high-pass digital (Elliptical) filter, whereupon the filtered quantities were identified as small-scale turbulence and the rest as internal gravity waves. Internal waves were found to play a role not only at canonical large gradient Richardson numbers $$(\overline{\hbox {Ri}_\mathrm{g} } >1)$$ , but sometimes at smaller values $$(0.1 < \overline{\hbox {Ri}_\mathrm{g}}<1)$$ , in contrast to typical observations in flat-terrain stable boundary layers. This may be attributed, at least partly, to (critical) internal waves on the slope, identified by Princevac et al. [1], which degenerate into turbulence and help maintain an active internal wave field. The applicability of both Monin-Obukhov (MO) similarity theory and local scaling to filtered and unfiltered data was tested by analyzing rms velocity fluctuations as a function of the stability parameter z/L, where L is the Obukhov length and z the height above the ground. For weaker stabilities, $$\hbox {z/L}<1$$ , the MO similarity and local scaling were valid for both filtered and unfiltered data. Conversely, when $$\hbox {z/L}>1$$ , the use of both scaling types is questionable, although filtered data showed a tendency to follow local scaling. A relationship between z/L and $$\overline{\hbox {Ri}_\mathrm{g} }$$ was identified. Eddy diffusivities of momentum $$\hbox {K}_\mathrm{M}$$ and heat $$\hbox {K}_\mathrm{H}$$ were dependent on wave activities, notably when $$\overline{\hbox {Ri}_\mathrm{g} } > 1$$ . The ratio $$\hbox {K}_{\mathrm{H}}/\hbox {K}_{\mathrm{M}}$$ dropped well below unity at high $$\overline{\hbox {Ri}_\mathrm{g} }$$ , in consonance with previous laboratory stratified shear layer measurements as well as other field observations.

Statistics of turbulent fluctuations in counter-rotating Taylor-Couette flows

The statistics of velocity fluctuations of turbulent Taylor-Couette flow are examined. The rotation rates of the inner and outer cylinders are varied while keeping the Taylor number fixed to 1.49×10(12) [O(Re)=10(6)]. The azimuthal velocity component of the flow is measured using laser Doppler anemometry. For each experiment 5×10(6) data points are acquired and carefully analyzed. Using extended self-similarity [Benzi et al., Phys. Rev. E 48, R29 (1993)] the longitudinal structure function exponents are extracted and are found to weakly depend on the ratio of the rotation rates. For the case where only the inner cylinder rotates the results are in good agreement with results measured by Lewis and Swinney [Phys. Rev. E 59, 5457 (1999)] using hot-film anemometry. The power spectra show clear -5/3 scaling for the intermediate angular velocity ratios -ω(o)/ω(i)∈{0.6,0.8,1.0}, roughly -5/3 scaling for -ω(o)/ω(i)∈{0.2,0.3,0.4,2.0}, and no clear scaling law can be found for -ω(0)/ω(i)=0 (inner cylinder rotation only); the local scaling exponent of the spectra has a strong frequency dependence. We relate these observations to the shape of the probability density function of the azimuthal velocity and the presence of a neutral line.

Turbulent mixing in a Richtmyer–Meshkov fluid layer after reshock: velocity and density statistics

AbstractThe properties of turbulent mixing in a Richtmyer–Meshkov (RM) unstable fluid layer are studied under the impact of a single shock followed by a reshock wave using simultaneous velocity–density measurements to provide new insights into the physics of RM mixing. The experiments were conducted on a varicose ${\mathrm{SF} }_{6} $ fluid layer (heavy fluid) interposed in air (light fluid) inside a horizontal shock tube at an incident Mach number of 1.21 and a reflected reshock Mach number of 1.14. The light–heavy–light fluid layer is observed to develop a nonlinear growth pattern, with no transition to turbulence upon impact by a single shock (up to $tU/ \lambda = 23. 4$). However, upon reshock, enhanced mixing between the heavy and light fluids along with a transition to a turbulent state characterized by the generation of significant turbulent velocity fluctuations (${\sigma }_{u} / U\ensuremath{\sim} 0. 3$) is observed. The streamwise and spanwise root-mean-squared velocity fluctuation statistics show similar trends across the fluid layer after reshock, with no observable preference for the direction of the shock wave motion. The measured streamwise mass flux ($ \overline{{\rho }^{\ensuremath{\prime} } {u}^{\ensuremath{\prime} } } $) shows opposing signs on either side of the density peak within the fluid layer, consistent with the turbulent material transport being driven along the direction of the density gradient. Measurements of three of the six independent components of the general Reynolds stress tensor (${R}_{ij} = \overline{\rho { u}_{i}^{\ensuremath{\prime} \ensuremath{\prime} } { u}_{j}^{\ensuremath{\prime} \ensuremath{\prime} } } $) show that the self-correlation terms ${R}_{11} $ and ${R}_{22} $ are similar in magnitude across much of the fluid layer, and much larger than the cross-correlation term ${R}_{12} $. Most importantly, the Reynolds stresses (${R}_{ij} $) are dominated by the mean density, cross-velocity product term ($ \overline{\rho } \hspace{0.167em} \overline{{ u}_{i}^{\ensuremath{\prime} } { u}_{j}^{\ensuremath{\prime} } } $), with the mass flux product and triple correlation terms being negligibly smaller in comparison. A lack of homogeneous mixing (and, possibly, a long-term imprint of the initial conditions) is observed in the spanwise turbulent mass flux measurements, with important implications for the simulation and modelling of RM mixing flows.

Statistics of velocity fluctuations observed by SuperDARN under steady interplanetary magnetic field conditions

A study of velocity fluctuations observed by the Super Dual Auroral Radar Network (SuperDARN) HF radar network is presented. The study was undertaken with the goals of determining the level of fluctuation due to internal magnetospheric processes, and to examine the probability of observing a significant velocity fluctuation within any given time interval. The study included 6 years of observations from periods when the interplanetary magnetic field (IMF) was moderately southward and steady. It was assumed that the IMF that encounters the magnetosphere is the same as that observed at a spacecraft located upstream from the Earth and that all variability of the plasma convection is due either to variability of the IMF driver or to internal magnetospheric processes. IMF variability away from the satellite was examined statistically by comparing the distributions of observations for the ACE and Wind satellites. The distribution of velocity fluctuations and their waiting time distribution were examined over a grid of latitude and local time. It was found that the waiting time is scale free over the range of times that could be examined. From the waiting time distributions, the probability of observing fluctuations within various time intervals was determined over the grid. It was found that the probability of observing a significant velocity fluctuation is high for all local times in the high‐latitude region.

Using digital holographic microscopy for simultaneous measurements of 3D near wall velocity and wall shear stress in a turbulent boundary layer

A digital holographic microscope is used to simultaneously measure the instantaneous 3D flow structure in the inner part of a turbulent boundary layer over a smooth wall, and the spatial distribution of wall shear stresses. The measurements are performed in a fully developed turbulent channel flow within square duct, at a moderately high Reynolds number. The sample volume size is 90 × 145 × 90 wall units, and the spatial resolution of the measurements is 3–8 wall units in streamwise and spanwise directions and one wall unit in the wall-normal direction. The paper describes the data acquisition and analysis procedures, including the particle tracking method and associated method for matching of particle pairs. The uncertainty in velocity is estimated to be better than 1 mm/s, less than 0.05% of the free stream velocity, by comparing the statistics of the normalized velocity divergence to divergence obtained by randomly adding an error of 1 mm/s to the data. Spatial distributions of wall shear stresses are approximated with the least square fit of velocity measurements in the viscous sublayer. Mean flow profiles and statistics of velocity fluctuations agree very well with expectations. Joint probability density distributions of instantaneous spanwise and streamwise wall shear stresses demonstrate the significance of near-wall coherent structures. The near wall 3D flow structures are classified into three groups, the first containing a pair of counter-rotating, quasi streamwise vortices and high streak-like shear stresses; the second group is characterized by multiple streamwise vortices and little variations in wall stress; and the third group has no buffer layer structures.

Quantifying copepod kinematics in a laboratory turbulence apparatus

We describe application of a new apparatus that permits simultaneous detailed observations of plankton behavior and turbulent velocities. We are able to acquire 3D trajectories amenable to statistical analyses for comparisons of copepod responses to well-quantified turbulence intensities that match those found in the coastal ocean environment. The turbulence characteristics consist of nearly isotropic and homogeneous velocity fluctuation statistics in the observation region. In the apparatus, three species of copepods, Acartia hudsonica, Temora longicornis, and Calanus finmarchicus were exposed separately to stagnant water plus four sequentially increasing levels of turbulence intensity. Copepod kinematics were quantified via several measures, including transport speed, motility number, net-to-gross displacement ratio, number of escape events, and number of animals phototactically aggregating per minute. The results suggest that these copepods could control their position and movements at low turbulence intensity. At higher turbulence intensity, the copepods movement was dominated by the water motion, although species-specific modifications due to size and swimming mode of the copepod influenced the results. Several trends support a dome-shaped variation of copepod kinematics with increasing turbulence. These species-specific trends and threshold quantities provide a data set for future comparative analyses of copepod responses to turbulence of varying duration as well as intensity.

Competing Broadband Noise Mechanisms in Low-Speed Axial Fans

This paper compares two broadband noise mechanisms, the trailing-edge noise or self-noise, and the leading-edge noise or turbulence-ingestion noise, in several blade technologies. Two previously developed analytical models for these broadband contributions are first validated with well-defined measurements on several airfoils embedded in an homogeneous flow at low-Mach number. Each instrumented airfoil is placed at the exit of an open jet anechoic wind tunnel with or without a grid generating turbulence upstream of it. Sound is measured in the far field at the same time as the wall-pressure fluctuations statistics close to the airfoil trailing edge and the inlet velocity fluctuation statistics impacting the airfoil leading edge. The models are then compared in some practical cases representative of airframes, wind turbines, and automotive engine cooling modules. The airfoil models of the two mechanisms are then extended to a full rotating machine in open space. The model predictions of both mechanisms are compared with in-flight helicopter measurements and automotive engine cooling modules measurements. In both instances, the turbulence-ingestion noise is found to be a dominant source over most of the frequency range. The self-noise only becomes a significant contributor at high angles of attack close to flow separation.

Experimental and numerical investigation of premixed acetylene flame

In this paper, the mean velocity, turbulence intensity and temperature profiles in different cross-sections of premixed acetylene flame are given. A mathematical model for prediction of velocity, temperature and concentration fields of axisymmetric free premixed turbulent flame is presented in this paper. A second-order closure for turbulent reacting flows is used. Special attentions is paid to model behavior with the respect to the prediction correlation coefficients of turbulent diffusion of the scalar components. Conditional and unconditional statistics of the LDA signals were performed using jet and/or air seed. Compared to commonly used unconditional statistics, conditional statistics of velocity fluctuations can give us more data about intensity of turbulent mixing in the flame.

Effective velocity created by a point vortex in two-dimensional hydrodynamics.

We complete previous investigations on the statistics of velocity fluctuations arising from a random distribution of point vortices in two-dimensional hydrodynamics. We show that, in a statistical sense, the velocity created by a point vortex is shielded by cooperative effects on a distance Lambda approximately n(-1/2), the intervortex separation. For R>>Lambda, the "effective" velocity decays as R-2 instead of the ordinary law R(-1) recovered for R<<Lambda. These results are similar to those obtained by Agekyan [Sov. Astron. 5, 809 (1962)] in his investigations on the fluctuations of the gravitational field. They give further support to our previous observation that the statistics of velocity fluctuations are (marginally) dominated by the contribution of the nearest neighbor.