Mean Relative Velocity Research Articles

Laser‐Doppler Velocimetry Measurements Inside a Backward Curved Centrifugal Fan

Laser‐Doppler velocimetry (LDV) measurements are presented of relative mean velocity and turbulence intensity components inside the impeller passage of a centrifugal fan with twelve backward curved blades at design, under‐design, and over‐design flow rates. Additional LDV measurements were also performed at the volute outlet to examine the uniformity of the outlet flow for the three selected flow rates. Complementary flow visualization results in the tongue region are further presented. It is found that the number of characteristic flow regions and the average turbulence level increase with decreasing air flow rate. For the case of under‐design flow rate, there are a through‐flow region on the suction side, a reverse flow region on the pressure side, and a shear layer region in between. The corresponding average turbulence intensity is as high as 9.1% of blade tip velocity.

A Critique of Scaling Behavior in Nonlinear Structure Formation Scenarios

Moments of the BBGKY equations for spatial correlation functions of cosmological density perturbations are used to obtain a differential equation for the evolution of the dimensionless function, h = -(v/x), where v is the mean relative pair velocity. The BBGKY equations are closed using a hierarchical scaling Ansatz for the three-point correlation function. Scale-invariant solutions derived earlier by Davis and Peebles are then used in the nonlinear regime, along with the generalized stable-clustering hypothesis (h → const), to obtain an expression for the asymptotic value of h, in terms of the power-law index of clustering, γ, and the tangential and radial velocity dispersions. The Davis-Peebles solution is found to require that tangential dispersions are larger than radial ones, in the nonlinear regime; this can be understood on physical grounds. Finally, stability analysis of the solution demonstrates that the allowed asymptotic values of h, consistent with the stable-clustering hypothesis, lie in the range 0 ≤ h ≤ 1/2. Thus, if the Davis-Peebles scale-invariant solution (and the hierarchical model for the three-point function) is correct, the standard stable-clustering picture (h → 1 as → ∞) is not allowed in the nonlinear regime of structure formation.

Evidence for a low-density universe from the relative velocities of galaxies

The motions of galaxies can be used to constrain the cosmological density parameter Omega and the clustering amplitude of matter on large scales. The mean relative velocity of galaxy pairs, estimated from the Mark III survey, indicates that Omega = 0.35(-0.25)(+0.35). If the clustering of galaxies is unbiased on large scales, Omega = 0. 35 +/- 0.15, so that an unbiased Einstein-de Sitter model (Omega = 1) is inconsistent with the data.

Turbulent Noise Generated by a Centrifugal Fan without Scroll Casing.

Estimation of turbulent noise level with L-weighting and A-weighting functions was proposed to a centrifugal fan without scroll casing. The validity of these formulae was examined experimentally in respect to the effects of parameters ; inlet/outlet area ratio of impeller and five fan types. The agreement between the measured and the predicted values of the width of wake and the mean relative velocity was satisfactory. Moreover the experimental values of the overall turbulent noise with L-weighting and A-weighting functions agreed well with the predicted values. Finally, the effects of slip factor and the inlet/outlet area ratio of the impeller on the relative velocity, the width of wake, the sound pressure level and the specific noise level are shown.

Scale-Invariant Correlation Functions of Cosmological Density Fluctuations in the Strong Clustering Regime and the Stability

We have investigated the scale-invariant solutions of the BBGKY equations for spatial correlation functions of cosmological density fluctuations and the mean relative peculiar velocity in the strongly nonlinear regime. It is found that the solutions for the mean relative physical velocity depend on the three-point spatial correlation function and the skewness of the velocity fields. We find that the stable condition in which the mean relative physical velocity vanishes on the virialized regions is satisfied only under the assumptions which Davis & Peebles took in there paper. It is found, however, that their assumptions may not be general in real. The power index of the two-point correlation function in the strongly nonlinear regime depends on the mean relative peculiar velocity, the three-point correlation function and the skewness. If self-similar solutions exist, then the power index in the strongly nonlinear regime is related to the power index of the initial power spectrum and its relation depends on the three-point correlation function and the skewness through the mean relative peculiar velocity. We also investigate stability of the solutions of the BBGKY equations for two-point spatial correlation functions. In the case that the background skewness is equal to 0, we found that there is no local instability in the strongly non-linear regime.

Dynamics of Pairwise Motions

We propose a simple closed-form expression relating v12(r)—the mean relative velocity of pairs of galaxies at fixed separation r—to the two-point correlation function of mass density fluctuations, ξ(r). Our Ansatz is an interpolation between the perturbative and stable clustering expressions for v12. We compare our analytic model for v12(r) with N-body simulations and find excellent agreement in the entire dynamical range probed by the simulations (0.1 ξ 1000). Our results can be used to estimate the cosmological density parameter, Ω, directly from redshift-distance surveys.

Measurements of conditional velocities in turbulent premixed flames by simultaneous OH PLIF and PIV

Joint velocity/scalar imaging measurements are performed in turbulent premixed natural-gas/air flames to better characterize the turbulent flux of mean reaction progress variable, ρu″c″ . Simultaneous two-dimensional measurements of the velocity field and the relative OH concentration are obtained by particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) of the OH radical, respectively. The data are used to obtain conditional mean velocities in both reactant and product regions. The relative mean velocity of reactants and products provides an indication of whether turbulent diffusion of the mean progress variable occurs in the gradient or counter-gradient sense. Five flames having different ratios of rms velocity, u′, to laminar flame speed, S L , are considered. The results indicate that a transition from counter-gradient to gradient diffusion occurs as u′/ S L is increased. Such a transition has previously been predicted by direct numerical simulation (DNS) but has not been observed experimentally. The existence of this transition must be taken into account when developing models of turbulent premixed combustion.

Blood Flow in the Human Optic Nerve Head during Isometric Exercise

Investigating blood flow autoregulation in the optic nerve is important to understand the physiopathology of various ocular diseases such as glaucoma. This investigation requires that one establishes the relationship between optic nerve blood flow and perfusion pressure. Previous work has documented the effect of lowering the perfusion pressure on optic nerve blood flow. The purpose of the present study was to investigate the effect of elevated perfusion pressure on blood flow in this tissue.Laser Doppler flowmetry was applied to measure relative mean velocity, volume and flux of red blood cells in the tissue of the optic nerve head. These parameters were measured in 13 subjects during isometric exercise consisting of squatting.In the range of perfusion pressures from 56±4 to 80±5 mmHg (30±8%), there was no significant variation of mean velocity, volume and flux of red blood cells, but vascular resistance increased by about 50%. Intraocular pressure was increased significantly above baseline at the end of squatting and decreased during recovery.The results suggest that the maintenance of constant blood flow is achieved by an increase in vascular resistance taking place either at the arterioles feeding or at the veins draining the blood from the ONH or at the ophthalmic artery and/or vessels between this artery and the site of LDF measurements. Combining the results of this study with those of a previous one where perfusion pressure was decreased by increasing the intraocular pressure, we show the entire relationship between perfusion pressure and optic nerve blood flow in man.

Increase in height during the first year after bone marrow transplantation reflecting nutritional status of children.

We studied the influence of pre-transplant nutritional status on height velocity during the first post-transplant year. Thirty-seven children aged 1.4-12.4 years, 19 males and 18 females, underwent bone marrow transplantation (24 allogeneic, 13 autologous) with fractionated total body irradiation included in the preparative regimen of 25. The underlying diagnoses were leukemia (n = 16), malignant solid tumor (n = 11), and non-malignant hematologic or metabolic disease (n = 10). The serum concentrations of albumin, pre-albumin and transferrin were measured. Anthropometric measurements included weight, mid-arm circumference (MAC) and triceps skinfold thickness, expressed as percentages of the age- and sex-specific standards. The skeletal muscle protein reserve was estimated as muscle index (MI) by ultrasonographic imaging of the femoral quadriceps muscle. Height velocity was expressed as a standard deviation score (SDS) of the age- and sex-specific mean. The mean relative height velocity SDS was -1.6 (95% CI -2.2- -1.0). Height velocity correlated significantly with pre-transplant MI (r = 0.54, P = 0.004), concentration of serum transferrin (r = 0.33, P = 0.05) and MAC (r =0.45, P = 0.04). Our data suggest that pre-transplant nutritional status has an impact on growth in height during the post-transplant period.

Blood flow measurement in the optic nerve head during isometric exercise

Autoregulation of optic nerve head blood flow (Fonh) in response to decreases in perfusion pressure has been demonstrated in animals and humans. The aim of this study was to determine change in Fonh when systemic blood pressure is increased. Blood flow parameters, i.e. relative mean velocity, number, and flux of red blood cells in the ONH tissue (Velonh, Volonh and Fonh, respectively) were measured by laser Doppler flowmetry in one eye of 13 normal subjects (aged 16 to 58 years), at baseline, during, and after isometric exercises consisting of squatting. Brachial artery blood pressure was measured by sphygmomanometry. IOP was measured at baseline and at the end of squatting. During squatting mean arterial pressure increased from 103 +/- 6 mm Hg to 139 +/- 58 mm Hg (average +/- 95% confidence interval), IOP increased from 13 +/- 0.5 to 17 +/- 1 mm Hg. An average increase in PPm from 56 +/- 4 to 80 +/- 7 mm Hg induced no significant (p > 0.05) change in the blood flow parameters. The sensitivity (detection threshold) of the blood flow changes was 8%. This study shows for the first time in human autoregulation of Fonh when PPm is increased by increasing the systemic blood pressure.

Effects of Distance Uncertainties on Determinations of the Galaxy Peculiar Velocity Field

Galaxy distance indicators are subject to different uncertainties and biases, which may be reflected in the peculiar velocity field. In this work, we present different statistical analysis applied to the peculiar velocities of samples of galaxies and mock catalogs taken from numerical simulations considering these observational effects. Our statistical studies comprise the mean relative velocity and velocity correlation for pairs of galaxies as a function of separation, and a bulk flow analysis of spheres of 10 h-1 Mpc radius. In order to test the statistical analysis, we use COBE-normalized cold dark matter (CDM) numerical simulations with different density parameters and cosmological constant, and take into account the Tully-Fisher (TF) scatter and a possible TF zero-point offset, as well as variations in the results of the simulations arising from different observer positions. We compare the results of the mock catalogs with samples of spiral galaxies taken from the Mark III catalog. The results of our analysis indicate the importance of errors in deriving the density parameter Ω from statistics applied to the observational data, and it is found that large values of Ω ≥ 0.8 may be derived from the analysis if errors are not taken into account. However, the observed value of the TF scatter (0.35 mag) produce CDM models with Ω > 0.6, inconsistent with the statistical tests involving relative velocities. A suitable agreement is found for models with Ω ≤ 0.6, although this requires a TF zero-point offset on the order of a tenth of a magnitude to provide consistency with the observed flow coherence.

Oscillatory alignment phenomena in Rydberg-atom–rare-gas collisions

Retention of orbital alignment during near-resonant energy transfer collisions of rare-gas projectiles with excited alkaline-earth-metal atoms is explored theoretically for scattering of Xe from Rydberg states of Ca. For such collisions, conventional interpretations of alignment phenomena, which are based on potential curves for a transient molecule thought to form during the collision, are not relevant. Theoretical partial magnetic sublevel cross sections for Ca**(4s17d D2→4s18p P1) transitions confirm the existence of alignment effects, as demonstrated experimentally by Spain et al. @J. Chem. Phys. 102, 9532 ~1995!#, at a mean relative velocity of 914 m/s. Theory further predicts heretofore unobserved oscillatory structures in these cross sections as a function of relative velocity and that these oscillations depend strongly on the initial magnetic quantum number of the Rydberg electron. @S1050-2947~98!50301-0#

Scale‐invariant Correlation Functions of Cosmological Density Fluctuations in the Strong‐clustering Regime

We investigate the scale-invariant solutions of the BBGKY equations for spatial correlation functions of cosmological density fluctuations and the mean relative peculiar velocity in the strongly nonlinear regime. It is found that the solutions for the mean relative physical velocity depend on the three-point spatial correlation function and the skewness of the velocity fields. We find that the stability condition, in which the mean relative physical velocity vanishes on the virialized regions, is satisfied only under the assumptions that Davis & Peebles made in their 1977 paper. It is found, however, that their assumptions may not be general in real systems. The power index of the two-point correlation function in the strongly nonlinear regime depends on the mean relative peculiar velocity, the three-point correlation function, and the skewness. If self-similar solutions exist, then the power index in the strongly nonlinear regime is related to the power index of the initial power spectrum, and its relation depends on the three-point correlation function and the skewness through the mean relative peculiar velocity.

Autoregulation of human optic nerve head blood flow in response to acute changes in ocular perfusion pressure.

Studies in animals have demonstrated that optic nerve head (ONH) blood flow (F(onh)) is autoregulated, but there is a lack of evidence for such a process in humans. Therefore, we investigated the relationship between F(onh) and mean ocular perfusion pressure (PPm) in normal volunteers when PPm is decreased through elevation of the intraocular pressure (IOP). Laser Doppler flowmetry (LDF) was used to measure relative mean velocity (Velohn), volume (Volonh) and F(onh) of blood at sites of the ONH away from visible vessels, while PPm was decreased in two ways: (1) rapidly, by IOP increments of 15 s duration, and (2) slowly, by IOP increments of 2 min duration, both by scleral suction cup in one eye of each of nine subjects. A rapid and large decrease of PPm of more than 100% induced a decrease of more than 80% in F(onh). With the slower decrease in PPm, F(onh) remained constant down to a PPm of approximately 22 mm Hg (IOP = 40 mm Hg) and then decreased, predominantly due to a decrease in Velohn. Immediately after removal of the suction cup, F(onh) increased transiently by 44% above baseline. This study demonstrates efficient blood flow autoregulation in the OHN, which is probably brought about by an increase in vascular capacitance. The magnitude of the reactive hyperaemia agrees with the compensatory decrease in ONH vascular resistance during IOP elevation. The time scale of the autoregulatory process and the dependence of the hyperaemia upon duration of IOP elevation suggest a metabolic mechanism of autoregulation.

A Numerical Renormalization Solution for Self‐similar Cosmic Structure Formation

We present results of a numerical renormalization approximation to the self-similar growth of clustering of a collisionless pressureless fluid out of a power-law spectrum of primeval Gaussian mass density fluctuations, P(k) ∝ kn, in an Einstein-de Sitter cosmological model. The self-similar position two-point correlation function, ξ(r), seems to be well established. The renormalization solutions for ξ(r) show a satisfying insensitivity to the parameters in the method, and at n = -1 and n = 0 they are quite close to the Hamilton et al. formula for interpolation between the large-scale perturbative limit and stable small-scale clustering. Self-similar behavior is tested by the comparison of the mean relative peculiar velocity vij of particle pairs (ij) and the velocity derived from ξ(r) under the assumption of self-similar evolution. Both the renormalization and a comparison conventional N-body solution are in reasonable agreement with the test, although the conventional approach does slightly better at large separations, and the renormalization approach does better at small separations. Other comparisons of renormalization and conventional solutions are more demanding and the results much less satisfactory. Maps of the particle positions in redshift space in the renormalization solutions show more nearly empty voids and fewer prominent walls than do comparison conventional N-body solutions. The rms relative velocity dispersion is systematically smaller in the renormalization solution; the difference approaches a factor of 2 on small scales. This is related to substantial differences in the frequency distributions of clump masses in the renormalization and conventional solutions. The third moment S3 from the distribution of mass within cells is in reasonable agreement with second-order perturbation theory on large scales, while on scales less than the clustering length S3 is roughly consistent with hierarchical clustering, but is heavily affected by shot noise.

Properties and Averaged Equations for Flows of Bubbly Liquids

Averaged properties of bubbly liquids in the limit of large Reynolds and small Weber numbers are determined as functions of the volume fraction, mean relative velocity, and velocity variance of the bubbles using numerical simulations and a pair interaction theory. The results of simulations are combined with those obtained recently for sheared bubbly liquids [19] and the mixture momentum and continuity equations to propose a complete set of averaged equations and closure relations for the flows of bubbly liquids at large Reynolds and small Weber numbers.

Interplanetary Neutral Particle Fluxes Influencing the Earth's Atmosphere and the Terrestrial Environment

It is well known that the Solar System is swept over by neutral interstellar gases, primarily hydrogen and helium, entering the heliosphere from the upwind side and penetrating inward, even up to the orbit of the Earth. The Earth on its orbit is thus moving through this density field and is intercepting time-variable hydrogen and helium fluxes. Quantitatively, this is associated with a sensitive reaction of the density fields to time-dependent conditions of the solar radiation pressure and the ionizing solar radiations during the solar activity cycle. As we shall show, the density distribution of interstellar hydrogen along the orbit of the Earth is strongly varying during the solar cycle. In connection with the variation of the mean relative velocity of this gas with respect to the orbiting Earth a highly variable hydrogen inflow into the Earth's atmosphere will be induced. There is also an additional source of hydrogen influencing the Earth's environment due to the fact that neutral interstellar hydrogen and helium are neutralizing solar wind protons by charge exchange inside the orbit of the Earth, thereby producing an antisolar flux of keV-energetic hydrogen atoms impinging onto the Earth's atmosphere. These time-variable fluxes could be directly monitored by gas detectors of an advanced technology. They might also be indicated by indirect terrestrial effects. We are investigating the question of whether and how these time-variable inflows could be recognized by careful studies of relevant upper atmospheric reactions. We study particle-induced energy inputs and ionization rates in the upper atmosphere and analyze influences on the hydrogen geocorona. We also study the process of relaxation of the inflowing hydrogen within the terrestrial atmosphere and investigate the reaction of atmospheric hydrogen densities to these variable inflows. While it is shown that the induced short-period variation of upper atmospheric hydrogen densities is of negligible amplitude at the present epoch, long-periodic variations of the hydrogen inflow like those connected with the entrance of the Solar System into a region of increased interstellar density at earlier or later eons clearly give their imprints even at lower heights and could even be reflected in ozone depletions induced by increased hydrogen densities at heights of around 50 km. At present anomalous variations of the geocoronal H-1216 A and He-584 A glows uncorrelated with the solar resonance line illumination indicate a breathing of the geocorona under variable interplanetary gas inflows.

Asteroid Collisions: Estimating Their Probabilities and Velocity Distributions

A new method of estimating the collisional probabilities and velocities of asteroids is elaborated, differing substantially from previous methods. It is argued that the distance from a target asteroid to the nearest asteroid of an ambient population must be distributed over time according to the Weibull distribution. An empirical distribution of such distances may be generated efficiently by a novel type of computer simulation of the long-term statistical mechanics of large sets of asteroids, a simulation entailing no orbit propagation. The simulation yields distributions of both minimum distances and relative velocity vectors. By estimating the two parameters of this distribution and the mean relative velocity, it is possible to estimate the intrinsic collisional probability of the target asteroid with the ambient asteroid population. The distribution of relative velocities can be estimated directly from the simulation data. Some initial results determined by the new method are, for the mean intrinsic collisional probabilities of 243 Ida, 2 Pallas, and 951 Gaspra with ambient asteroid populations numbering 799, 680, and 533, respectively: 5.34 × 10−18, 5.96 × 10−18, and 2.28 × 10−18km−2year−1. The new method affords an alternative pathway for solving problems in asteroid interactions, a pathway that is fundamentally statistical in nature. It is easy to implement and offers a great deal of flexibility in its basic simulation for quantitatively studying many aspects of collisions and near-collisions involving asteroids, planets, and comets.

Patterns in Nonlinear Gravitational Clustering: A Numerical Investigation

The nonlinear clustering of dark matter particles in an expanding universe is usually studied by N-body simulations. One can gain some insight into this complex problem if simple relations between physical quantities in the linear and nonlinear regimes can be extracted from the results of N-body simulations. Hamilton et al. (1991) and Nityananda and Padmanabhan (1994) have made an attempt in this direction by relating the mean relative pair velocities to the mean correlation function in a useful manner. We investigate this relation and other closely related issues in detail for the case of six different power spectra: power laws with spectral indexes $n=-2,-1$, cold dark matter (CDM), and hot dark matter models with density parameter $\Omega=1$; CDM including a cosmological constant ($\Lambda$) with $\Omega_{CDM}=0.4$, $\Omega_{\Lambda}=0.6$; and $n=-1$ model with $\Omega=0.1$. We find that: (i) Power law spectra lead to self-similar evolution in an $\Omega=1$ universe. (ii) Stable clustering does not hold in an $\Omega=1$ universe to the extent our simulations can ascertain. (iii) Stable clustering is a better approximation in the case of $\Omega<1$ universe in which structure formation freezes out at some low redshift. (iv) The relation between dimensionless pair velocity and the mean correlation function, $\bar\xi$, is only approximately independent of the shape of the power spectrum. At the nonlinear end, the asymptotic value of the dimensionless pair velocity decreases with increasing small scale power, because the stable clustering assumption is not universally true. (v) The relation between the evolved $\bar\xi$ and the linear regime $\bar\xi$ is also not universal but shows a weak spectrum dependence. We present simple theoretical arguments for these conclusions.

A simple description of some inertia effects in the behaviour of heavy particles in a turbulent gas flow

The effects of some inertia parameters and the influence of non-linear drag in the behaviour of heavy particles in a turbulent gas flow are investigated by examining th properties of their streamwise fluctuating motion. The particles are suspended in a stationary homogeneous turbulent gas flow, under the influence of an external body force field, which implies a non-zero mean slip velocity between the two phases. Two kinds of methods, the results of which are compared, are used. The first method is based on a simplified kinematic simulation of the fluid velocity fluctuation in the streamwise direction, according to a known turbulence spectrum. The second method is a classical Lagrangian tracking technique. The presence of an external body force field makes the particle turbulent response depend on three dimensionless parameters, among them the conventional Stokes number St and the particle Reynolds number Re p , based on the mean relative velocity between the fluid and the particle, are found to be the most influential ones for heavy particles. A particle response diagram is built, leading to an approximate expression for the particle-to-fluid turbulent intensity ratio in terms of a modified Stokes number which embodies the effects of both St and Re p . Numerical predictions are provided in the case of an upward vertical flow, in a large range of particle mean Reynolds numbers exceeding unity. A significant influence of the drag non-linearity can be observed. The main conclusion is that the effect of non-linear drag may surpass the well-known crossing-trajectory effect, in causing the particle mean-square velocity to increase with increasing mean relative velocity, contrary to what is generally expected for small inertia particles.