Velocity Probability Density Distributions Research Articles

A coupling analysis method of foundation soil dynamic responses induced by metro train based on PDEM and stochastic field theory

Foundation soil is an important medium for vibration wave propagation in the running of metro train. The spatial variability of soil properties has an important influence on vibration response. The parameters of foundation soil are often determined. Based on the probability density evolution method (PDEM) and stochastic field theory, a coupling model of the metro train-track-shield tunnel-foundation soil is established. The stochastic field is expressed by the series of stochastic variables and deterministic space functions by the Karhunen-Loeve Expansion (KLE) method. The stochastic parameters of the cross-section of tunnel-foundation soil are specified to simulate the stochastic field of foundation soil. Based on PDEM, the environmental vibration caused by metro trains in shield tunnels is studied. The results of ground surface vibration displacement under different metro train speeds are analyzed, and the upper and lower limits and probability density information of ground surface vibration displacement are obtained. The results show that the probability density distribution of ground vibration displacement at each time is approximately normal due to the stochastic field of foundation soil. The peak and valley of the vibration displacement curve at the inverted arch of the tunnel are caused by the wheel distance of the metro train. The probability density distribution of velocity and acceleration is more sensitive to the stochastic field of velocity foundation soil and the change in metro train speed. The maximum Z vibration level results under different metro train speeds all meet the requirements of vibration allowable limits in the specification.

Self-diffusion of spherocylindrical particles flowing under non-uniform shear rate.

This work is devoted to study numerically the self-diffusion of spherocylindrical particles flowing down an inclined plane, using the discrete element method (DEM). This system is challenging due to particles being non-spherical and because they are subjected to a non-uniform shear rate. We performed simulations for several aspect ratios and inclination angles, tracking individual particle trajectories. Using the simulation data, we computed the diffusion coefficients D, and a coarse-graining methodology allowed accessing the shear rate spatial profiles (z). This data enabled us to identify the spatial regions where the diffusivity strongly correlates with the local shear rate. Introducing an effective particle size d⊥, we proposed a well-rationalized scaling law between D and . Our findings also identified specific locations where the diffusivity does not correlate with the shear rate. This observation corresponds to zones where  has non-linear spatial variation, and the velocity probability density distributions exhibit asymmetric shapes.

Pore-scale simulation and statistical investigation of velocity and drag force distribution of flow through randomly-packed porous media under low and intermediate Reynolds numbers

Fluid flow through packed porous media and fluid–particle interactions are of importance in various industrial and natural processes. However, the lack of knowledge about the velocity field in the pore space and distribution of drag force on individual particles has been a source of uncertainties in modeling these processes. Therefore, an improved understanding of the velocity field and fluid–particle interactions is a fundamental step for better understanding of these systems. In this article, the pore-scale velocity field and fluid–solid interaction from a single particle to randomly-packed mono-sized porous media are investigated using a 3D GPU-based parallel Lattice Boltzmann model. The packed porous media are generated by means of discrete element method and have a wide range of porosity values. The developed model is first validated by experimental results of fluid flow around single and two interactive particles; the validated model is then used to conduct statistical analysis of velocity in the pore space and drag force on individual particles. The results suggest that the velocity field in porous media can be divided into four zones, namely: zero-velocity zone, low-velocity zone, high-velocity zone, and recirculation zone. Moreover, the probability density distribution of velocity is highly dependent on Reynolds number and porosity and can be bi-modal, depending on a combination of Reynolds number and porosity. The probability density distribution of the drag force always shows a single peak at the mean value with a skewness to the right. Finally, a simpler and more accurate correlation for the mean drag force over a wide range of Reynolds number and porosity is proposed based on the numerical results. The accuracy and reliability of several empirical equations, including the one proposed in this study, for the mean drag force are compared through a statistical analysis.

From random sphere packings to regular pillar arrays: Analysis of transverse dispersion

We study the impact of microscopic order on transverse dispersion in the interstitial void space of bulk (unconfined) chromatographic beds by numerical simulations of incompressible fluid flow and mass transport of a passive tracer. Our study includes polydisperse random sphere packings (computer-generated with particle size distributions of modern core–shell and sub-2μm particles), the macropore space morphology of a physically reconstructed silica monolith, and computer-generated regular pillar arrays. These bed morphologies are analyzed by their velocity probability density distributions, transient dispersion behavior, and the dependence of asymptotic transverse dispersion coefficients on the mobile phase velocity. In our work, the spherical particles, the monolith skeleton, and the cylindrical pillars are all treated as impermeable solid phase (nonporous) and the tracer is unretained, to focus on the impact of microscopic order on flow and (particularly transverse) hydrodynamic dispersion in the interstitial void space. The microscopic order of the pillar arrays causes their velocity probability density distributions to start and end abruptly, their transient dispersion coefficients to oscillate, and the asymptotic transverse dispersion coefficients to plateau out of initial power law behavior. The microscopically disordered beds, by contrast, follow power law behavior over the whole investigated velocity range, for which we present refined equations (i.e., Eq. (13) and the data in Table 2 for the polydisperse sphere packings; Eq. (17) for the silica monolith). The bulk bed morphologies and their intrinsic differences addressed in this work determine how efficient a bed can relax the transverse concentration gradients caused by wall effects, which exist in all confined separation media used in chromatographic practice. Whereas the effect of diffusion on transverse dispersion decreases and ultimately disappears at increasing velocity with the microscopically disordered chromatographic beds, it dominates in the pillar arrays. The pillar arrays therefore become the least forgiving bed morphology with macroscopic heterogeneities and the engendered longitudinal dispersion in chromatographic practice. Wall effects in pillar arrays and the monolith caused by their confinement impact band broadening, which is traditionally observed on a macroscopic scale, more seriously than in the packings.

Characteristics of Hyperconcentrated Sediment-Laden Flows

Microscopic and macroscopic characteristics of hyperconcentrated sediment-laden flows are investigated using kinetic theory for differing concentrations of non-cohesive sediment particles. Variations in the microscopic particle velocity distribution function and in derived macroscopic variables such as the particle mean velocity, particle fluctuating velocity, and particle number per unit volume are discussed. Analysis of the microscopic characteristics shows that the peak value of the particle velocity probability density distribution function decreases with increasing vertically averaged volumetric (or mean) particle concentration Cv¯, particularly when Cv¯ exceeds a certain threshold. A case study indicates that the characteristic velocity uc is hardly influenced by the particle concentration, but the standard deviation σ is significantly affected. For given particle concentrations, both uc and σ tend to become larger with increasing relative elevation from the bottom. From the derived macroscopic char...

An equation for the particle velocity probability density function in inhomogeneous turbulent flow

The Eulerian continuum description of a gas dispersion (two-phase) turbulent flow is considered on the basis of the particle velocity probability density distribution method. A refined variant of the kinetic equation for the probability density distribution in inhomogeneous turbulent flow is presented, a chain of equations for the velocity moments of the dispersed phase is constructed, and the reverse influence of the particles on the characteristics of the carrier flow is determined.

Modeling of particle motion in a turbulent flow with allowance for collisions

On the basis of the kinetic equation for the colliding-particle velocity probability density distribution in a turbulent flow, a model for calculating the dispersed phase motion is constructed for a broad range of variation of the number density and particle size.

The kinetic theory for dilute solid/liquid two-phase flow

On the basis of a brief review of the continuum theory for macroscopic descriptions and the kinetic theory for microscopic descriptions in solid/liquid two-phase flows, some suggestions are presented, i.e. the solid phase may be described by the Boltzmann equation and the liquid phase still be described by conservation laws in the continuum theory. Among them the action force on the particles by the liquid fluid is a coupling factor which connects the phases. For dilute steady solid/liquid two-phase flows, the particle velocity distribution function can be derived by analogy with the procedures in the kinetic theory of gas molecules for the equilibrium state instead of being assumed, as previous investigators did. This done, more detailed information, such as the velocity probability density distribution, mean velocity distribution and fluctuating intensity etc. can be obtained directly from the particle velocity distribution function or from its integration. Experiments have been performed for dilute solid/liquid two-phase flow in a 4 × 6 cm 2 sized circulating square pipe system by means of laser Doppler anemometry so that the theories can be examined. The comparisons show that the theories agree very well with all the measured data.

Measurement and analysis of unsteady flow structures in rotor blade wakes

Time-variant data are obtained to investigate the exit flow field from a rotor in a research compressor. In the free-stream region, the instantaneous data are analogous to one another and to the ensemble averaged free-stream results. However, in the wake region, some of the instantaneous signals are similar to one another and to the ensemble averaged wake, but others differ significantly. These variations in the instantaneous data are interpreted and shown to be due to a vortex street structure in the wake. This is accomplished by: (1) developing a mathematical model of the rotor blade exit flow field based on a wake vortex street structure analogous to the unsteady flow field behind bluff bodies due to classical von Karman vortex shedding; and (2) correlating predictions of both the ensemble averaged and instantaneous rotor blade exit flow fields as well as the velocity probability density distributions from this vortex wake flow field model with the corresponding data. The correlation of the ensemble averaged rotor blade exit flow fields is very good and the flow angle distribution correlation excellent. The predicted instantaneous rotor blade exit flow field exhibits many of the flow features found in the data. Also, the probability density distributions for the data and the vortex wake flow field model are analogous to one another.

Two-Component Phase-Averaged Turbulence Statistics Downstream of a Rotating Spoked-Wheel Wake Generator

Measurements of the axial and tangential components of the unsteady turbulent flow downstream of a rotating spoked-wheel wake generator have been obtained. The results of this study have implications for the use of this type of wake generator to produce simulated turbine guide vane wakes. Instantaneous velocity information was phase averaged based on a signal synchronized with the bar-passing frequency. Mean velocity profiles and phase-averaged Reynolds stress results were found to be consistent with measurements obtained behind a stationary cylinder. Reynolds stresses were significantly higher than corresponding measurements obtained in large-scale research turbomachines, however. Phase-averaged triple velocity correlations, also calculated from the digital velocity records, reveal the sign and magnitude of skewness in the velocity probability density distributions for the two components. Large crossflow gradients observed in the triple correlations in the wake indicate the importance of the tangential-component fluctuations in the net turbulent transport of turbulent energy across the wake. Streamwise-component wake velocity spectra for low values of reduced bar-passing frequency include a peak associated with vortex shedding from the cylindrical wake-generating bars at a shedding Strouhal number of 0.2. For higher bar-passing frequencies, the energy associated with vortex shedding is shifted to lower frequencies and becomes broadband from the stationary reference frame viewpoint.

Estimation of the conduction velocity of muscle action potentials using phase and impulse response function techniques.

Two new techniques are described for calculating the conduction velocity of action potentials in muscle fibres from surface EMG recordings in human subjects. In the first method the conduction velocity is determined from the impulse response function calculated from the two EMG signals. The peak of this function onsists of a single peak located at the delay between the signals. The velocity probability density distribution is then estimated from this impulse response function. The mode of this distribution occurred at 5 m s−1. The second technique uses the phase part of the frequency response function relating the two EMG signals to determine the conduction velocity. These two new approaches overcome some of the limitations associated with estimating conduction velocity from the maximum absolute value of the cross-correlation function, and provide additional information about the conduction velocity.

Characteristics of vertical turbulent velocities in the urban convective boundary layer

Turbulence measurements of the vertical velocity component were obtained by an instrumented aircraft under fair weather conditions in the St. Louis, Missouri, metropolitan area. Time series of vertical velocity fluctuations from horizontal flight segments made in the lower part of and near the middle of the convective boundary layer (CBL) over the urban area and surrounding region were subjected to various statistical and objective analyses. Higher order vertical velocity moments, and positive and negative velocity statistics, were computed. The horizontal dimensions of updrafts and downdrafts, and related properties of these turbulent eddies were derived by conditional sampling analysis. Emphasis is on a comparison of the results from urban and selected rural measurements from the lower part of the CBL. The vertical velocity probability density distribution for each segment was positively skewed and the mode was negative. The means and standard deviations of positive and negative velocity fluctuations were greater over the urban area. The urban vertical velocity variance was 50% greater than rural values, and power spectra revealed greater production of vertical turbulent energy in the urban area over a wide frequency range. The mean and maximum widths of downdrafts were generally larger than the corresponding values for updrafts. Differences between urban and rural eddy sizes were not statistically significant. The widths of the largest updraft and downdraft are comparable to the boundary-layer depth, Z i, and the mean value of the ratio of spectral peak wavelength to Z iwas about 1.3 and 1.1 for urban and rural areas, respectively. Convective similarity scaling parameters appeared to order both the urban and rural measurements.

Sinusoidal and random whole-body vibration: comparative effects on visual performance : M. J. Moseley, C. H. Lewis and M. J. Griffin 1982. Aviation, Space and Environmental Medicine53, 1000–1005. (6 pages, 4 figures, 4 tables, 15 references)

An experimental comparison of the effect of whole-body sinusoidal and one-third octave-band random vibration on the performance of a display reading task is described. The findings indicate that one-third octave-band random vibration has significantly less effect on performance. Subsequent measurements of rotational head motion demonstrated that this finding may be due to differences in the velocity probability density distributions produced by the different motions. Subjects also performed the visual task during exposure to several broad-band random motions. Predicted error values were obtained by averaging the frequency weighted time histories of these motions. It was found that both R.M.S. and R.M.Q. averaging procedures applied to the broad-band frequency weighted time histories gave accurate error predictions when compared with the measured error scores. Practical implications of the experimental findings and recommendations for future research are discussed.

Measurement of local size and velocity probability density distributions in two-phase suspension flows by Laser-Doppler technique

A technique is presented for the simultaneous measurement of the local number and velocity probability densities of a dilute two-phase suspension which has a distribution of particle sizes and a predominate direction of flow orientation such as in the cases of pipe and boundary-layer flows. It is shown that by a suitable scheme of discrimination on the amplitude as well as the residence time and frequency of the individual Laser-Doppler bursts, one can obtain the statistics on the size number density distribution and, for each size range, velocity distribution of the particulate phase together with the velocity probability distribution of the fluid phase. Results have been obtained for experiments conducted on a laminar uniform flow and a turbulent shear flow of a dilute glass particle-water suspension having a particle size distribution. Calibration needed for the scheme was accomplished by analyzing particle size and number density distribution data obtained from a Coulter particle sizing counter on a sample taken with an isokinetic probe.

Low-altitude turbulence model for estimating gust loads on aircraft.

The development of a low-altitude turbulence model for estimating aircraft gust loads within the friction layer of the atmosphere Is described. The development of the model is based largely on the gust data obtained from the B-66 low-level gust program arid climatological wind data provided by the National Weather Records Center, Asheville, N. C. In developing the model, the B-66 vertical gust spectra are used to determine a spectrum function relating spectrum shape to the height above ground arid terrain roughness. From the standard deviations of the vertical gust velocities and mean wind speed estimates, empirical standard deviation vs mean wind speed functions are estimated for smooth and rough terrain conditions. Climatological wind data analyses for both smooth arid rough terrains are used to provide wind probability density distribution characteristics. From these results, estimates of the standard deviation of vertical gust velocity probability density distribution functions are obtained on the basis of specified confidence limits for the empirical standard deviation gust velocity functions. Finally, the procedure for obtaining probability estimates of the vertical gust velocity is presented for assumed climatic mean wind speed conditions for both smooth and rough terrains. Application of the model to estimating aircraft gust loads is also discussed.