Statistics Of Velocity Field Research Articles

An artificial neural network model for recovering small-scale velocity in large-eddy simulation of isotropic turbulent flows

Small-scale motions in turbulent flows play a significant role in various small-scale processes, such as particle relative dispersion and collision, bubble or droplet deformation, and orientation dynamics of non-sphere particles. Recovering the small-scale flows that cannot be resolved in large eddy simulation (LES) is of great importance for such processes sensitive to the small-scale motions in turbulent flows. This study proposes a subgrid-scale model for recovering the small-scale turbulent velocity field based on the artificial neural network (ANN). The governing equations of small-scale turbulent velocity are linearized, and the pressure gradient and the nonlinear convection term are modeled with the aid of the ANN. Direct numerical simulation (DNS) and filtered direct numerical simulation (FDNS) provide the data required for training and validating the ANN. The large-scale velocity and velocity gradient tensor are selected as inputs for the ANN model. The linearized governing equations of small-scale turbulent velocity are numerically solved by coupling the large-scale flow field information. The results indicate that the model established by the ANN can accurately recover the small-scale velocity lost in FDNS due to filtering operation. With the ANN model, the flow fields at different Reynolds numbers agree well with the DNS results regarding velocity field statistics, flow field structures, turbulent energy spectra, and two-point, two-time Lagrangian correlation functions. This study demonstrates that the proposed ANN model can be applied to recovering the small-scale velocity field in the LES of isotropic turbulent flows at different Reynolds numbers.

Quantifying the influence of vortex instability on mean velocity field statistics of wingtip vortex

Quantifying the influence of vortex instability on mean velocity field statistics of wingtip vortex

Wind tunnel measurement of pedestrian-level gust wind flow and comfort around irregular lift-up buildings within simplified urban arrays

The implementation of lift-up buildings has demonstrated their practicality in enhancing urban wind comfort in high-density cities. The pedestrian-level wind environment around a central lift-up building surrounded by low-rise buildings was measured using wind tunnel experiments. The time-averaged velocity field and turbulence statistics, including the turbulent kinetic energy, normal component of the Reynolds stresses, gust factor, and gust wind velocity field, were discussed. Based on the results, the pedestrian-level gust wind flow and comfort for two typical building shapes (Arc, V-shaped) were compared with Rectangular lift-up buildings under different wind directions (0∘, 90∘ and 180∘), the pedestrian-level wind environments (PLWEs) were assessed following two wind criteria for weak and windy wind conditions by wind speed thresholds and maximum allowed exceedance probabilities. The results showed that the erection of the high-rise lift-up building modified the pedestrian-level wind environment around the building groups, owing to the interaction between the downwash flow around the building and the surrounding building blocks. A region of high mean and gust wind velocity was observed at the lateral and rear side of the central lift-up building due to the lateral entrained wind and Venturi effect between elevated columns, indicating that lift-up buildings can enhance PLWEs even in the presence of surrounding buildings. The Arc-shaped lift-up building tends to generate a larger “Intolerable” area compared with V- and Rectangular-shaped buildings due to its curved surface. The wind impacts the convex portion of the building, leading to airflow divergence and facilitating downstream ventilation.

Damping of MHD turbulence in a partially ionized medium

ABSTRACT The coupling state between ions and neutrals in the interstellar medium plays a key role in the dynamics of magnetohydrodynamic (MHD) turbulence, but is challenging to study numerically. In this work, we investigate the damping of MHD turbulence in a partially ionized medium using 3D two-fluid (ions + neutrals) simulations generated with the athenak code. Specifically, we examine the velocity, density, and magnetic field statistics of the two-fluid MHD turbulence in different regimes of neutral-ion coupling. Our results demonstrate that when ions and neutrals are strongly coupled, the velocity statistics resemble those of single-fluid MHD turbulence. Both the velocity structures and kinetic energy spectra of ions and neutrals are similar, while their density structures can be significantly different. With an excess of small-scale sharp density fluctuations in ions, the density spectrum in ions is shallower than that of neutrals. When ions and neutrals are weakly coupled, the turbulence in ions is more severely damped due to the ion-neutral collisional friction than that in neutrals, resulting in a steep kinetic energy spectrum and density spectrum in ions compared to the Kolmogorov spectrum. We also find that the magnetic energy spectrum basically follows the shape of the kinetic energy spectrum of ions, irrespective of the coupling regime. In addition, we find large density fluctuations in ions and neutrals and thus spatially inhomogeneous ionization fractions. As a result, the neutral-ion decoupling and damping of MHD turbulence take place over a range of length-scales.

Large-eddy simulations of compressible Rayleigh–Taylor turbulence with miscible fluids using spatial gradient model

Large-eddy simulations (LES) and implicit LES (ILES) of three-dimensional compressible Rayleigh–Taylor turbulence with miscible fluids are performed and compared with direct numerical simulation (DNS) at the Atwood number At=0.5 and stratification parameters Sr = 1.0 and 4.0. Three sub-grid-scale (SGS) models including constant-coefficient spatial gradient model (CSGM), dynamic Smagorinsky model (DSM), and dynamic mixed model (DMM) are considered. The CSGM model achieves a high accuracy by using the velocity gradients at the neighboring LES grids. The a priori tests show that the CSGM model has significantly higher correlation coefficients and lower relative errors than traditional SGS models. In the a posteriori tests, the probability density functions of SGS terms predicted by the CSGM model are consistent with the filtered DNS results. The CSGM model can accurately predict the small bubble and spike structures, resulting in good predictions of mixing heights and concentration fields. The instantaneous structures, spectra, and statistics of velocity and vorticity fields are also examined, showing the excellent performance of the CSGM model compared to the ILES, DSM, and DMM models. Moreover, the predictions of the temperature and pressure fields by the CSGM model are significantly better than the traditional SGS models and ILES.

Incompressible energy spectrum from wave turbulence

Bose–Einstein condensates with their superfluidity property provide an interesting parallel to classical fluids. Due to the Kolmogorov spectrum of homogeneous turbulence the statistics of the incompressible velocity field is of great interest, but in superfluids obtaining quantities such as the statistics of the velocity field from the macroscopic wavefunction turns out be a complicated task; therefore, most of the work up to now has been numerical in nature. We made use of the Weak Wave Turbulence (WWT) theory, which provides the statistics of the macroscopic wavefunction, to obtain the statistics of the velocity field, which allowed us to produce a semi analytical procedure for extracting the incompressible energy spectrum in the WWT regime. This is done by introducing an auxiliary wavefunction that preserves the relevant statistical and hydrodynamical properties of the condensate but with a homogeneous density thus allowing for a simpler description of the velocity field.

Extreme wave statistics of surface elevation and velocity field of gravity waves over a two-dimensional bathymetry

This paper presents the effects of two-dimensional bathymetry on the evolution of skewness and kurtosis of the surface elevation and velocity field in long-crested irregular waves propagating over a circular shoal and a submerged bar with a semicircular step. For a circular shoal, we show that the surface elevation has a local maximum of skewness and kurtosis on top of the shoal. We find that the skewness of the horizontal velocity field has similar behaviour to the surface elevation, but the kurtosis of the horizontal velocity field has two local maxima at different locations on the lee side of the shoal. For a semicircular step, which acts similar to a converging lens, we find that refraction contributes to the statistical properties of the surface elevation and horizontal velocity field to deviate from Gaussian statistics.

Experimental and numerical investigation of turbulent wake flow around wall-mounted square cylinder of aspect ratio 2

The turbulent wake velocity fields around a short wall-mounted square cylinder of aspect ratio 2 fully immersing into a thick turbulent boundary layer are obtained experimentally with PIV and numerically with LES. Comparison between the two sets of data is made on the time-averaged mean velocities, turbulent fluctuating velocities, and the detailed characteristics of energetic large-scale coherent structures. It is noted that a good comparison of the low-order statistics of velocity fields does not guarantee a satisfactory reproduction of the coherent structures. These flow structures show great similarities in the spatial patterns and dynamic performance between PIV and LES, but apparent differences in turbulent kinetic energy contribution. On the horizontal plane parallel to the wall, the dominant antisymmetric spatial mode pair illustrates the evolution process of Karman vortex shedding with a clear spectral peak around the characteristic frequency while three extra frequency peaks are found in the symmetric spatial modes. Further investigation on the velocity field on the central vertical plane reveals the connection between the unsteadiness of shear layer flow at the free end and the spanwise symmetric vortex shedding activities. It is confirmed that the flapping motion and vortex convection mechanisms observed for the present cylinder could modulate the symmetric wake dynamics. The three-dimensional extreme wake patterns, available from LES results, are related to the most energetic Karman vortex shedding demonstrate upward flow in the vortex weakening side. Meanwhile, the downwash flow at the extreme time instants is found to become stronger always for this kind of short cylinder with a dipole wake pattern.

X-raying molecular clouds with a short flare: probing statistics of gas density and velocity fields

ABSTRACT We take advantage of a set of molecular cloud simulations to demonstrate a possibility to uncover statistical properties of the gas density and velocity fields using reflected emission of a short (with duration much less than the cloud’s light-crossing time) X-ray flare. Such a situation is relevant for the Central Molecular Zone (CMZ) of our Galaxy where several clouds get illuminated by an ∼110 yr-old flare from the supermassive black hole Sgr A* . Due to shortness of the flare (Δt ≲ 1.6 yr), only a thin slice (Δz ≲ 0.5 pc) of the molecular gas contributes to the X-ray reflection signal at any given moment, and its surface brightness effectively probes the local gas density. This allows reconstructing the density probability distribution function over a broad range of scales with virtually no influence of attenuation, chemo-dynamical biases, and projection effects. Such a measurement is key to understanding the structure and star formation potential of the clouds evolving under extreme conditions in the CMZ. For cloud parameters similar to the currently brightest in X-ray reflection molecular complex Sgr A, the sensitivity level of the best available data is sufficient only for marginal distinction between solenoidal and compressive forcing of turbulence. Future-generation X-ray observatories with large effective area and high spectral resolution will dramatically improve on that by minimizing systematic uncertainties due to contaminating signals. Furthermore, measurement of the iron fluorescent line centroid with sub-eV accuracy in combination with the data on molecular line emission will allow direct investigation of the gas velocity field.

Experimental and numerical investigation of the hydrodynamic characteristics of Autonomous Underwater Vehicles over sea-beds with complex topography

Improved designs for Autonomous Underwater Vehicles (AUV) are becoming increasingly important due to their utility in academic and industrial applications. However, a majority of such testing and design is carried out under conditions that may not reflect the operating environment of shallow water AUVs. This may lead to imprecise estimations of the AUV's performance and sub-optimal designs. This article presents experimental and numerical studies carried out in conjunction, to investigate the hydrodynamic characteristics of AUV hulls at different Reynolds numbers over sloped channel-beds. We carry out experiments to measure the velocity field and turbulent statistics around the AUV with quantified uncertainty. These are contrasted against corresponding flat bed experiments to gauge the effect of test bed topography on AUV performance. The experimental data was used to validate Reynolds Stress Model predictions. Hydrodynamic parameters such as drag, pressure and skin friction coefficients were predicted from the RSM simulations at different test bed slopes, angles of attack and drift angles of the AUV hull, to analyze the hydrodynamic performance of the AUV. The results presented in this article offer avenues for design improvement of AUVs operating in shallow environments, such as the continental slope and estuaries.

Intrinsic alignment statistics of density and velocity fields at large scales: Formulation, modeling, and baryon acoustic oscillation features

The kinematic Sunyaev-Zel'dovich effect enables us to directly probe the density-weighted velocity field up to very large cosmic scales. We investigate the effects of intrinsic alignments (IAs) of dark-matter halo shapes on cosmic density and velocity fields on such large scales. In the literature IAs have been detected up to $\sim 100~h^{-1}{\rm Mpc}$ using the gravitational shear-intrinsic ellipticity correlation and the alignment correlation function. In this paper we introduce the corresponding various velocity statistics: the (density-weighted) velocity-intrinsic ellipticity correlation as well as the alignment pairwise infall momentum, momentum correlation function, and density-weighted pairwise velocity dispersion. We derive theoretical expressions for these velocity alignment statistics for the first time based on the assumption that the density fluctuation is a Gaussian random field. Using large-volume, high-resolution $N$-body simulations, we measure the alignment statistics of density and velocity fields. The behaviors of IAs in the velocity statistics are similar to those in the density statistics, except that the halo orientations are aligned with the velocity field up to scales larger than those with the density field, $r\gg 100~h^{-1}{\rm Mpc}$, because of a factor of the wave number in the linear relation between the density and velocity fields in Fourier space, $v\propto \delta/k$. We show that the detected IAs of the velocity field can be well predicted by the linear alignment model. We also demonstrate that the baryon acoustic oscillation features can be detected in both the conventional and alignment velocity statistics. Our results indicate that observations of IAs with the velocity field on large scales can provide additional information on cosmological models, complementary to those with the density field.

Analysis of the isothermal transition process in wide aspect ratio rectangular channels

This work is aiming at extending the understanding of the transition process from a laminar gas flow to a turbulent gas flow in wide aspect ratio rectangular channels under isothermal conditions. The role of the inlet geometry and its impact on the transition process have been studied. Three inlet geometries have been used to influence the transition process, each geometry having a different critical Reynolds number at which the flow is becoming turbulent. The geometries are named bellmouth, square edged and undulated geometry. Multiple measurement techniques were applied: Laser Doppler Anemometry was applied to measure the inlet boundary conditions in terms of mean and fluctuating velocity field statistics. Static pressure measurements were applied to measure the friction diagram in between 2000 < ReDh < 10,000. Double frame Particle Image Velocimetry was applied to measure velocity correlations between the stream-wise velocity component and the velocity component perpendicular to the wall and its connection to the friction diagram. Furthermore, Time Resolved Particle Image Velocimetry was applied to visualize the generation of coherent vortical structures originating at the inlet into the rectangular channel.

Propelled microprobes in turbulence

The temporal statistics of incompressible fluid velocity and passive scalar fields in developed turbulent conditions is investigated by means of direct numerical simulations along the trajectories of self-propelled point-like probes drifting in a flow. Such probes are characterised by a propulsion velocity which is fixed in intensity and direction; however, like vessels in a flow they are continuously deviated by their intended course as the result of local sweeping of the fluid flow. The recorded time-series by these moving probes represent the simplest realisation of transect measurements in a fluid flow environment. We investigate the non trivial combination of Lagrangian and Eulerian statistical properties displayed by the transect time-series. We show that, as a result of the homogeneity and isotropy of the flow, the single-point acceleration statistics of the probes follows a predictable trend at varying the propulsion speed, a feature that is also present in the scalar time-derivative fluctuations. Further, by focusing on two-time statistics we characterize how the Lagrangian-to-Eulerian transition occurs at increasing the propulsion velocity. The analysis of intermittency of temporal increments highlights in a striking way the opposite trends displayed by the fluid velocity and passive scalars.

Atmospheric effects on acoustic vector sensing

Two-dimensional acoustic particle velocity and acoustic pressure, concurrent with atmospheric data, were collected during a series of field tests. It was found that for short propagation distances, the particle velocity field remained unsaturated (little variation in amplitude and phase) for higher frequencies than did the pressure field. Theoretical comparisons are made to examine the physical effects of the propagation environment on the particle velocity field statistics.

Multivariate and conditioned statistics of velocity and wall pressure fluctuations induced by a jet interacting with a flat plate

The increasing size of aircraft engines is leading to reconsideration of their conventional integration in the under-wing configuration due to the strong interaction between the jet and the airframe components. As a consequence, more insight is needed into the complex mechanisms underlying the interaction phenomenon between the jet flow and a surface. The objective of this paper is to carry out a series of experimental tests on a simplified laboratory-scale model to approach/deepen the problem. This analysis is the continuation of a previous study (Di Marco et al., J. Fluid Mech., vol. 770, 2015, pp. 247–272) on a rigid flat plate installed tangentially to the axis of an incompressible jet. In the present work, the velocity and wall pressure fields were simultaneously measured for different radial distances of the plate from the nozzle axis. Pointwise hot-wire anemometer measurements were carried out to characterize the effect of the plate on the velocity field statistics up to the fourth-order moment. The analysis revealed that the presence of the plate brings about a deflection of the mean aerodynamic field over the surface and a reduction of the turbulence intensity. Wall pressure fluctuations induced by the jet flow over the plate were measured by a linear array of cavity-mounted microphones placed along the streamwise direction. The velocity/pressure cross-statistics are achieved in the time and frequency domains using cross-correlations and Fourier analysis. A wavelet-based conditional sampling procedure is applied as well to characterize the flow signatures related to the velocity and wall pressure fluctuations, revealing that the surface induces the breakdown of the large-scale turbulent structures. The dependence of the multivariate and conditioned statistics on the plate distance from the jet as well as on the streamwise and crosswise probe positions is extensively discussed. Different organized flow motions over the surface are found based on the wall pressure events detected. A scaling criterion for velocity signatures is also presented addressing the governing parameters of the jet–plate interaction phenomenon.

Stochastic Analysis of Natural Convection in Vertical Channels with Random Wall Temperature

This study attempts to derive the statistics of temperature and velocity fields of laminar natural convection in a heated vertical channel with random wall temperature. The wall temperature is expressed as a random function with respect to time, or a random process. First, analytical solutions of the transient temperature and flow velocity fields for an arbitrary temporal variation in the channel wall temperature are obtained by the integral transform and convolution theorem. Second, the autocorrelations of the temperature and velocity are formed from the solutions, assuming a stationarity in time. The mean square values of temperature and velocity are computed under the condition that the fluctuation in the channel wall temperature can be considered as white noise or a stationary Markov process. Numerical results demonstrate that a decrease in the Prandtl number or an increase in the correlation time of the random process increases the level of mean square velocity but does not change its spatial distribution tendency, which is a bell-shaped profile with a peak at a certain horizontal distance from the channel wall. The peak position is not substantially affected by the Prandtl number or the correlation time.

Validation of four LES and a vortex model against stereo-PIV measurements in the near wake of an actuator disc and a wind turbine

In this paper we report the results of a workshop organised by the Delft University of Technology in 2014, aiming at the comparison between different state-of-the-art numerical models for the simulation of wind turbine wakes. The chosen benchmark case is a wind tunnel measurement, where stereoscopic Particle Image Velocimetry was employed to obtain the velocity field and turbulence statistics in the near wake of a two-bladed wind turbine model and of a porous disc, which mimics the numerical actuator used in the simulations. Researchers have been invited to simulate the experimental case based on the disc drag coefficient and the inflow characteristics. Four large eddy simulation (LES) codes from different institutions and a vortex model are part of the comparison. The purpose of this benchmark is to validate the numerical predictions of the flow field statistics in the near wake of an actuator disc, a case that is highly relevant for full wind farm applications. The comparison has shown that, despite its extreme simplicity, the vortex model is capable of reproducing the wake expansion and the centreline velocity with very high accuracy. Also all tested LES models are able to predict the velocity deficit in the very near wake well, contrary to what was expected from previous literature. However, the resolved velocity fluctuations in the LES are below the experimentally measured values.

Whole-wavelength description of a wave boundary layer over permeable wall

This paper describes the whole-wavelength, highly resolved velocity field statistics in an oscillatory boundary layer driven by gravity waves, evolving on both impermeable and permeable beds. Velocity data from PTV measurements are acquired in a small window and then extended to the whole wavelength by means of a new phase-locked slotting technique. This technique increases the robustness of statistics and resolution by improving the number of the data samples available for each spatial cell in the Eulerian representation of the oscillatory boundary layer. The into- and out-of-bed volume flux is evaluated and its effects on the velocity field are reported, together with its influence on vorticity evolution. The presence of coherent structures embedded in a shear-dominated scenario is emphasized. The Lagrangian flow features extracted by PTV are presented in the context of the generalized Lagrangian-mean theory. The Stokes drift vertical profile is estimated by comparing the Eulerian and Lagrangian velocities. A critical height-separating region where the volume flux due to ventilation has different effects on both orbital amplitudes and Stokes drift is found. This distance corresponds to the maximum height of the still-attached vorticity layer.

Direct numerical simulation of turbulent flow with an impedance condition

DNS solutions for a pipe/jet configuration are re-computed with the pipe alone to investigate suppression of previously identified internal noise source(s) with an acoustic liner, using a time domain acoustic liner model developed by Tam and Auriault (AIAA Journal, 34 (1996) 913–917). Liner design parameters are chosen to achieve up to 30dB attenuation of the broadband pressure field over the pipe length without affecting the velocity field statistics. To understand the effect of the liner on the acoustic and turbulent components of the unsteady wall pressure, an azimuthal/axial Fourier transform is applied and the acoustic and turbulent wavenumber regimes clearly identified. It is found that the spectral component occupying the turbulent wavenumber range is unaffected by the liner whereas the acoustic wavenumber components are strongly attenuated, with individual radial modes being evident as each cuts on with increasing Strouhal number.

Tracking of large-scale structures in turbulent channel with direct numerical simulation of low Prandtl number passive scalar

Channel flow DNS (Direct Numerical Simulation) at friction Reynolds number 180 and with passive scalars of Prandtl numbers 1 and 0.01 was performed in various computational domains. The “normal” size domain was ∼2300 wall units long and ∼750 wall units wide; size taken from the similar DNS of Moser et al. The “large” computational domain, which is supposed to be sufficient to describe the largest structures of the turbulent flows was 3 times longer and 3 times wider than the “normal” domain. The “very large” domain was 6 times longer and 6 times wider than the “normal” domain. All simulations were performed with the same spatial and temporal resolution. Comparison of the standard and large computational domains shows the velocity field statistics (mean velocity, root-mean-square (RMS) fluctuations, and turbulent Reynolds stresses) that are within 1%-2%. Similar agreement is observed for Pr = 1 temperature fields and can be observed also for the mean temperature profiles at Pr = 0.01. These differences can be attributed to the statistical uncertainties of the DNS. However, second-order moments, i.e., RMS temperature fluctuations of standard and large computational domains at Pr = 0.01 show significant differences of up to 20%. Stronger temperature fluctuations in the “large” and “very large” domains confirm the existence of the large-scale structures. Their influence is more or less invisible in the main velocity field statistics or in the statistics of the temperature fields at Prandtl numbers around 1. However, these structures play visible role in the temperature fluctuations at low Prandtl number, where high temperature diffusivity effectively smears the small-scale structures in the thermal field and enhances the relative contribution of large-scales. These large thermal structures represent some kind of an echo of the large scale velocity structures: the highest temperature-velocity correlations are not observed between the instantaneous temperatures and instantaneous streamwise velocities, but between the instantaneous temperatures and velocities averaged over certain time interval.