Velocity Correlation Research Articles

Editorial: Celebrating the contributions of Professor Guieppe Marrucci to rheology and non-Newtonian fluid mechanics

Direct numerical simulations (DNS) of generalized Newtonian fluids in a rectangular channel at a friction velocity of 180 are performed using OpenFOAM. The simulations are performed for a Newtonian fluid, a power-law fluid, and a Herschel-Bulkley (HB) fluid. Two-point correlations of the streamwise velocity reveal that a significant increase in the computational domain size is required to avoid statistical correlation due to the shear-thinning and yield stress. The analogous Kolmogorov scale shows that the dissipative structures may be orders of magnitude larger with these two non-Newtonian behaviors. This is demonstrated to be linked to the significant increase in the viscosity. The mean streamwise velocity field integrates to a larger bulk velocity with increased shear-thinning as compared with the Newtonian fluid flow. The addition of the yield stress does the same with respect to the power-law fluid flow. The difference in the velocity profiles is more pronounced in the outer layer. It, however, is observed that the rheology does not play a significant role in the outer layer for the mean streamwise velocity. It is shown that an HB fluid flow does not necessarily show an increase in the fluctuating streamwise velocity with respect to a power-law fluid flow. It is also shown that low power index and high Hedstrom number lead to strong turbulence anisotropy due to the weakening of turbulence. The turbulent kinetic energy (TKE) budget reveals that the studied non-Newtonian behavior mainly affects the inner layer of the flow. The yield stress is also seen to show small variations in the TKE budget in the outer layer. This is attributed to the weakening turbulence as a result of the increased viscosity near the center. It is also demonstrated that the studied HB fluid flow results can be successfully reproduced by under-resolved DNS.

Spectral analysis of turbulence kinetic and internal energy budgets in hypersonic turbulent boundary layers

The spectral transport equations of turbulence kinetic and internal energy (TKE and TIE) are rigorously derived in the compressible turbulent flows, exhibiting a full structural similarity in terms of two-point correlations of velocity and a sound-speed-like variable. The scale dependence of TKE and TIE flow across space and scales, and among components is revealed comprehensively in a similar manner, in hypersonic turbulent boundary layers. Special attention is paid to the effect of wall cooling on the energy evolution, which is observed to exist throughout the boundary layer primarily by means of modifying the small-scale motions.

Evaluation and prediction of rise velocity and drag coefficient of an ascending bubble affected by the impurity in continuous and discrete phases, distinctly and concurrently

Obtaining a deep knowledge about the bubbly flow systems, which are widely applied in various chemical and industrial processes, is crucial for scholars and engineers to achieve more accurate equipment design and processes control. This paper is dedicated to experimentally investigate the distinctly and concurrently effects of fumed silica nanoparticles (NPs) and hexane vapor molecules as impurities in continuous and discrete phases, respectively, on the terminal velocity and drag coefficient of a single rising bubble in aqueous solutions. The obtained experimental data were compared to the calculated data by derived correlations in literatures. As a result, none of those can predict the experimental data and a new correlation for considering the SiO2 NPs as an impurity in liquid is required. As a novelty, this work proposed two new correlations for prediction of terminal velocity and drag coefficient of a rising bubble in NPs solutions as a function of NPs concentration in aqueous solutions. The proposed correlations of terminal velocity and drag coefficient are in excellent agreements with the experimental data over the range of Re <310 and We <1.8, and with the maximum average relative errors of about 0.5% and 1.3%, respectively. Moreover, an interesting synergistic effect at the bubble interface was shown, due to creation of hexane oily layer at the interface and its interaction with rotational and vibrational effects of NPs in 200 ppm solution, where the exerted drag force on the rising bubble was reduced by 12.5% in comparison to the pure water (Air) case.

The Correlation of Gyroscope Axial Velocities

In engineering, all movable expanse revolving objects manifest gyroscopic effects. These effects are created by the action of the outer load on the revolving items whose rotating mass originates eight inertial torques about two axes. Two torques of centrifugal forces, one torque of the Coriolis force originated by the rotating distributed mass, and the torque of the change in the angular momentum of the center mass act about each axis. The inertial torques activate rotations of the gyroscope by the determined correlation. Inertial torques depend on their geometry and orientation at the spatial coordinate system. The known analytical model for the rotation of the revolving disc about axes contains a mechanical error. This error was obtained by the incorrect integration of the centrifugal inertial torque. The corrected inertial torque yields the accurate expression for the interacted rotations of the revolving disc about axes.

Spin and velocity correlations in a confined two-dimensional fluid of disk-shaped active rotors

We study the velocity autocorrelations in an experimental configuration of confined two-dimensional active rotors (disks). We report persistent small scale oscillations in both rotational and translational velocity autocorrelations, with their characteristic frequency increasing as rotational activity increases. While these small oscillations are qualitatively similar in all experiments, we found that, at strong particle rotational activity, the large scale particle spin fluctuations tend to vanish, with the small oscillations around zero persisting in this case, and spins remain predominantly and strongly anti-correlated at longer times. For weaker rotational activity, however, spin fluctuations become increasingly larger, and angular velocities remain de-correlated at longer times. We discuss in detail how the autocorrelation oscillations are related to the rotational activity and why this feature is, generically, a signal of the emergence of chirality in the dynamics of a particulate system.

Non-equilibrium extension of the explicit algebraic subgrid-scale stress model with application to turbulent channel flow at low Reynolds numbers

An extension of the explicit algebraic subgrid-scale (SGS) stress model (EASSM) of Marstorp et al. [J. Fluid Mech. 639, 403–432 (2009)] is proposed to account for the non-local equilibrium between the production, P, and viscous dissipation, ϵ, of the SGS turbulent kinetic energy in its formulation. The original derivation of the EASSM uses the equilibrium assumption P=ϵ, whereas in the current new derivation, a cubic algebraic equation is extracted for P/ϵ from the modeled transport equation for the SGS stress anisotropy, which can be solved to improve the EASSM predictions with less than 4% additional computational costs per time step. The performance of the extended EASSM is assessed in large-eddy simulation of plane turbulent channel flow at Reτ=587 and 179 for a wide range of resolutions, where deviations from the local equilibrium assumption are expected at the vicinity of the walls. The enhanced EASSM formulation lowers resolution dependence of the model predictions and improves its predictions at low resolutions. The improvements affected major one-point turbulence statistics of interest, such as the wall shear stress, mean velocity, Reynolds stresses, and SGS dissipation as well as the two-point velocity correlations and premultiplied spanwise spectra of the streamwise velocity. The predicted mean P/ϵ also reasonably agrees with the filtered direct numerical simulation data.

Anomalous scaling in kinematic magnetohydrodynamic turbulence: Two-loop anomalous dimensions of leading composite operators.

Using the field theoretic formulation of the kinematic magnetohydrodynamic turbulence, the explicit expressions for the anomalous dimensions of leading composite operators, which govern the inertial-range scaling properties of correlation functions of the weak magnetic field passively advected by the electrically conductive turbulent environment driven by the Navier-Stokes velocity field, are derived and analyzed in the second order of the corresponding perturbation expansion (in the two-loop approximation). Their properties are compared to the properties of the same anomalous dimensions obtained in the framework of the Kazantsev-Kraichnan model of the kinematic magnetohydrodynamics with the Gaussian statistics of the turbulent velocity field as well as to the analogous anomalous dimensions of the leading composite operators in the problem of the passive scalar advection by the Gaussian (the Kraichnan model) and non-Gaussian (driven by the Navier-Stokes equation) turbulent velocity field. It is shown that, regardless of the Gaussian or non-Gaussian statistics of the turbulent velocity field, the two-loop corrections to the leading anomalous dimensions are much more important in the case of the problem of the passive advection of the vector (magnetic) field than in the case of the problem of the passive advection of scalar fields. At the same time, it is also shown that, in phenomenologically the most interesting case with three spatial dimensions, higher velocity correlations of the turbulent environment given by the Navier-Stokes velocity field play a rather limited role in the anomalous scaling of passive scalar as well as passive vector quantities, i.e., that the two-loop corrections to the corresponding leading anomalous dimensions are rather close to those obtained in the framework of the Gaussian models, especially as for the problem of scalar field advection. On the other hand, the role of the non-Gaussian statistics of the turbulent velocity field becomes dominant for higher spatial dimensions in the case of the kinematic magnetohydrodynamic turbulence but remains negligible in the problem of the passive scalar advection.

CFD simulations to study bed characteristics in gas–Solid fluidized beds with binary mixtures of Geldart-B particles: A qualitative analysis

The bed dynamics of unary and binary fluidized beds play a key role in understanding the pressure drop and hence provides an opportunity for performance improvement of the beds. In the present work, characteristics of fluidized beds with binary mixtures of Geldart-B particles were investigated using CFD simulations. The phenomena of segregation and mixing using simulations were studied, both qualitatively and quantitatively, at a range of superficial gas velocities (0.3–0.6 m/s) and two different bed heights. The study was divided into two parts. In Part I, the current study, a qualitative analysis of flow patterns for seven different binary mixtures, is presented. The quantitative analysis, including particle and gas velocity profiles, particle volume fraction profiles, and correlations for minimum fluidization velocity and pressure drop, will be presented in Part II of this work. A mathematical model consisting of an Eulerian-Eulerian model with RNG k-ε model and KTGF model to capture the bubble dynamics was used. The standardized values of coefficients and plastic stresses have been used for all simulations. The CFD model was validated using experimental data from the literature. Qualitative predictions of volume fraction profiles of small-sized particles showed that, for mixtures within a range of 40%–60% Geldart-B type large particles, the bubble and solid particle dynamics were different from those of single particles of the superficial gas velocities considered. In contrast to the single particles in the given superficial gas velocity range that were in bubbling regime, the binary particles showed a transition from bubbling to slugging to turbulent regime, as demonstrated by qualitative analysis. A homogeneous regime was observed for lower superficial gas velocities for mixtures consisting of 0%–20% large particles.

Deep learning-based prediction of intra-cardiac blood flow in long-axis cine magnetic resonance imaging

Purpose: We aimed to design and evaluate a deep learning-based method to automatically predict the time-varying in-plane blood flow velocity within the cardiac cavities in long-axis cine MRI, validated against 4D flow. Methods: A convolutional neural network (CNN) was implemented, taking cine MRI as the input and the in-plane velocity derived from the 4D flow acquisition as the ground truth. The method was evaluated using velocity vector end-point error (EPE) and angle error. Additionally, the E/A ratio and diastolic function classification derived from the predicted velocities were compared to those derived from 4D flow. Results: For intra-cardiac pixels with a velocity > 5 cm/s, our method achieved an EPE of 8.65 cm/s and angle error of 41.27°. For pixels with a velocity > 25 cm/s, the angle error significantly degraded to 19.26°. Although the averaged blood flow velocity prediction was under-estimated by 26.69%, the high correlation (PCC = 0.95) of global time-varying velocity and the visual evaluation demonstrate a good agreement between our prediction and 4D flow data. The E/A ratio was derived with minimal bias, but with considerable mean absolute error of 0.39 and wide limits of agreement. The diastolic function classification showed a high accuracy of 86.9%. Conclusion: Using a deep learning-based algorithm, intra-cardiac blood flow velocities can be predicted from long-axis cine MRI with high correlation with 4D flow derived velocities. Visualization of the derived velocities provides adjunct functional information and may potentially be used to derive the E/A ratio from conventional CMR exams.

Experimental study of H2/air turbulent expanding flames over wide equivalence ratios: Effects of molecular transport

The turbulent expanding flames of hydrogen/air mixtures are investigated over a wide range of equivalence ratios (ϕ = 0.4–5.0) using the fan-stirred combustion chamber. The effects of molecular transport on turbulent flame propagation are interpreted over a wide Lewis number range, including turbulent flame morphology, turbulent burning velocity, and its general correlation. The wrinkled degree of turbulent flame surface becomes strengthened at fuel-lean conditions than that of fuel-rich conditions at the same normalized turbulence intensity (u’/SL), and the flame morphology becomes more wrinkled with the flame propagating outwardly. The equivalence ratio of peak turbulent burning velocity is shifted towards fuel-lean side compared to that of laminar burning velocity. At fuel-lean conditions (ϕ = 0.6–1.0), the normalized turbulent burning velocity (ST/SL) decreases sharply with the equivalence ratio, while at fuel-rich conditions it first decreases slowly (ϕ = 1.0–2.0) and then nearly unchanged (ϕ = 2.0–5.0). The general correlations of turbulent burning velocity under different Lewis numbers can be obtained in different u’/SL ranges, and the effects of molecular transport on turbulent burning velocity are strengthened at the intense turbulent field. All of these indicate that the molecular transport has significant effects on hydrogen turbulent flames.

Alpha tensor and dynamo excitation in turbulent fluids with anisotropic conductivity fluctuations

AbstractA mean‐field theory of the electrodynamics of a turbulent fluid is formulated under the assumption that the molecular electric conductivity is correlated with the turbulent velocity fluctuation in the (radial) direction, . It is shown that for such homogeneous fluids a strong turbulence‐induced field advection anti‐parallel to arises almost independently of rotation. For rotating fluids, an extra effect appears with the known symmetries and with the expected maximum at the poles. Fast rotation, however, with Coriolis number exceeding unity suppresses this term. Numerical simulations of forced turbulence using the nirvana code demonstrate that the radial advection velocity, , always dominates the term. We show finally with simplified models that dynamos are strongly influenced by the radial pumping: for the solutions become oscillatory, while for they become highly exotic if they exist at all. In conclusion, dynamo models for slow and fast solid‐body rotation on the basis of finite conductivity–velocity correlations are unlikely to work, at least for dynamos without strong shear.

Beads, bubbles and drops in microchannels: stability of centred position and equilibrium velocity

Understanding and predicting the dynamics of dispersed micro-objects in microfluidics is crucial in numerous natural, industrial and technological situations. In this paper, we experimentally characterized the equilibrium velocity $V$ and lateral position $\varepsilon$ of various dispersed micro-objects, such as beads, bubbles and drops, in a cylindrical microchannel over an unprecedentedly wide range of parameters. By varying the dimensionless object size ( $d \in [0.1; 1]$ ), the viscosity ratio ( $\lambda \in [10^{-2}; \infty [$ ), the density ratio ( $\varphi \in [10^{-3}; 2]$ ), the Reynolds number ( $Re \in [10^{-2}; 10^2]$ ) and the capillary number ( $Ca \in [10^{-3}; 0.3]$ ), we offer an exhaustive parametric study exploring various dynamics from the non-deformable viscous regime to the deformable inertial regime, thus enabling us to highlight the sole and combined roles of inertia and capillary effects on lateral migration. Experiments are compared and agree well with a steady three-dimensional Navier–Stokes model for incompressible two-phase fluids, including the effects of inertia and possible interfacial deformations. This model enables us to propose a correlation for the object velocity $V$ as functions of $d$ , $\varepsilon$ and $\lambda$ , obtained in the ${Re}={Ca}=0$ limit, but valid for a larger range of values of ${Re}$ and ${Ca}$ delimited by the validity of the linear regime. Next, we present stability maps for the centred position showing that non-deformable objects dominated by inertial effects are only stable if large enough, typically for $d \gtrsim 0.7$ , whereas deformable objects dominated by capillary effects can be stable for much smaller sizes, provided the viscosity ratio is outside the range $0.7 \lesssim \lambda \lesssim 10$ , in which deformability also plays a destabilizing effect, as for inertia.

Anomalous fluctuations in homogeneous fluid phase of active Brownian particles

Giant number fluctuations (GNF) are an anomaly universally observed in active fluids with polar or nematic order. In this paper, we show that GNF arise in the fluid phase of active Brownian particles (ABP), where the polar order is absent. GNF in ABP extends over a large but finite length which characterizes the growing velocity correlations. To suppress unwanted phase separation and allow ones to explore the disordered fluid phase at large activities, we impart the inertia, or the mass, to the ABP. A linearized hydrodynamic theory captures our findings, but only qualitatively. We find numerically a nontrivial scaling relation for the density correlation function, which the linearized theory cannot explain. The results suggest ubiquitousness of the anomalous fluctuations even in the disordered homogeneous fluid phase in the absence of the directional order.

Why Do Chromospheric Oscillations in Sunspot Umbrae Appear to Propagate Downward?

Umbral oscillations constitute the most noticeable chromospheric feature of sunspot umbrae—large-amplitude oscillations of intensity (umbral flashes, if very strong) and line-of-sight velocity, with periods of about 3 minutes. These umbral oscillations are usually interpreted as acoustic waves propagating upward under the effect of gravity. However, there have been observational reports that intensity peaks tend to occur in downflowing phases of umbral oscillations, and this appears to be more compatible with downward propagation. We investigate whether this intensity–velocity correlation occurs persistently or not, by determining the vertical flux of the wave energy, based on Hα line measurements of the temperature and velocity. As a result, we find that the wave flux is persistently negative in sunspot umbrae, confirming the discrepancy specified above. We attribute this discrepancy to the nonzero fluctuation of net radiative heating. We find that when this effect is taken into account in the energy equation, the pressure is peaked during upflowing phases, being compatible with the notion of upward propagation. We conclude that temperature (and intensity) peaks occur during downflowing phases, not because of downward propagation, but because of radiative heat transport.

Experimental investigation on the influence of longitudinal fire location on critical velocity in a T-shaped tunnel fire

A series of fire experiments were performed in a reduced-scale T-shaped bifurcated tunnel to explore the influence mechanism of longitudinal fire location on critical velocity. The smoke temperature and critical velocity characteristics were recorded and identified. The results show that in the current experimental range, the change in critical velocity with the parameter L denoting the longitudinal location of the fire can be separated into two regions: the increasing region and the stable region. When -0.2 m≤L<0.7 m, that is, the fire source is located at the T-junction or near upstream of the T-junction, the critical velocity increases with L. When 0.7 m≤L≤1.3 m, that is, the fire source is located at downstream of the T-junction, the critical velocity almost remains constant. Based on the application of Bernoulli's equation, a proportionality coefficient kl/kc is proposed to normalize the critical velocity at different fire source locations, and an empirical correlation of the critical velocity of the T-shaped bifurcated tunnel is proposed. By comparing current experimental data and previous scholars’ test results, the effectiveness of the proposed empirical correlation for critical velocity in bifurcated tunnel fire scenario is well verified. The current study can serve as a reference for the ventilation and smoke control of fire scenarios in complex-branch tunnel structures.

Steady state correlations and induced trapping of an inertial AOUP particle

We study the dynamics of an inertial active Ornstein–Uhnlenbeck particle self-propelling in a confined harmonic well. The transport behavior of the particle is investigated by analyzing the particle trajectories, steady state correlations and mean square displacement (MSD). The steady state correlation functions for the position as well as velocity are exactly calculated using different methods. We explore how the inertia affects the dynamical behavior, when the particle is confined in a harmonic trap as well as when it is set free. From the exact calculation of MSD, it is observed that the initial time regimes are ballistic for both harmonically confined particle and free particle, whereas the long time regimes are diffusive for a free particle and nondiffusive for a harmonically confined particle. One of our interesting observations is that the harmonically confined particle gets more and more confined with increase in the self-propulsion time or activity time of the dynamics and finally it gets trapped for very large value of the self-propulsion time. For a free particle, the velocity correlation decays by the complex interplay between the inertial time scale and the self-propulsion time scale of the dynamics. Moreover, decorrelation in velocity happens only when these two time scales are of equal order.

Evidence of validity and reliability of Jumpo 2 and MyJump 2 for estimating vertical jump variables.

We investigated the concurrent validity and test-retest reliability of the Jumpo 2 and MyJump 2 apps for estimating jump height, and the mean values of force, velocity, and power produced during countermovement (CMJ) and squat jumps (SJ). Physically active university aged men (n=10, 20±3 years, 176±6 cm, 68±9 kg) jumped on a force plate (i.e., criterion) while being recorded by a smartphone slow-motion camera. The videos were analyzed using Jumpo 2 and MyJump 2 using a Samsung Galaxy S7 powered by the Android system. Validity and reliability were determined by regression analysis, typical error of estimates and measurements, and intraclass correlation coefficients. Both apps provided a reliable estimate of jump height and the mean values of force, velocity, and power. Furthermore, estimates of jump height for CMJ and SJ and the mean force of the CMJ were valid. However, the apps presented impractical or poor validity correlations for velocity and power. Compared with criterion, the apps underestimated the velocity of the CMJ. Therefore, Jumpo 2 and MyJump 2 both provide a valid measure of jump height, but the remaining variables provided by these apps must be viewed with caution since the validity of force depends on jump type, while velocity (and as consequence power) could not be well estimated from the apps.

Charge–velocity correlation transport equations in gas–solid flow with triboelectric effects

This paper is dedicated to the development of particle charge and velocity second-order moment transport equations for monodisperse particles in gas flow with a tribocharging effect. The full transport equations for the particle charge–velocity covariance and the charge variance are derived in the framework of the kinetic theory of granular flow assuming that the electrostatic interaction does not modify the collision dynamics. The collision integrals are solved without presuming the form of the electric part for the particle probability density function. The full second-order transport equation model is tested in a one-dimensional periodic domain. The results show that this model is able to capture more important physical mechanisms that are neglected by simple algebraic models proposed in the past. An in-depth analysis of the transport equations is also performed. This study reveals that, for sufficiently small covariance characteristic destruction time scales, the transient and third-order moments terms can be safely neglected. In addition, two different reduced-order models are proposed: a more general algebraic model that takes into account the variance effect and a semi-algebraic model that only resolves a transport equation for the charge variance coupled with an algebraic model for the covariance. The former could, however, lead to non-physical predictions in many cases, while the latter can be a suitable alternative only for a sufficiently small interparticle collision time. Finally, a simple chart based on test case simulations is proposed to show under which conditions a semi-algebraic model could be considered as a suitable alternative.

Mode-coupling theory for the dynamics of dense underdamped active Brownian particle system.

We present a theory to study the inertial effect on glassy dynamics of the underdamped active Brownian particle (UABP) system. Using the assumption of the nonequilibrium steady-state, we obtain an effective Fokker-Planck equation for the probability distribution function (PDF) as a function of positions and momentums. With this equation, we achieve the evolution equation of the intermediate scattering function through the Zwanzig-Mori projection operator method and the mode-coupling theory (MCT). Theoretical analysis shows that the inertia of the particle affects the memory function and corresponding glass transition by influencing the structure factor and a velocity correlation function. The theory provides theoretical support and guidance for subsequent simulation work.

Experimental study on temperature profile and critical velocity in bifurcated tunnel fire with inclined transverse cross-passage

A series of model-scaled bifurcated tunnel fire tests were conducted to explore the effect mechanism of branch slope. Different fuel pool sizes and a range of branch slopes between -6°∼9° were considered. The temperature profiles, velocity data and critical velocity were measured and analyzed. Results show that within the current test range of -6°≤slope≤9° and 6.63 kW≤HRR≤35.53 kW, as the branch slope changes from negative to positive, the thermal smoke entering branch tunnel and the corresponding high-temperature region obviously increase. And the amount of thermal smoke diverted by branch tunnel also affects the critical velocity of main tunnel, which is mainly attributed to the stack effect induced by the inclined branch tunnel. For the fire scenario with positive branch slope, stack effect is conducive to the discharge of thermal smoke, and the critical velocity of main tunnel shows a decrease tendency with the increase of slope. For the fire scenario with negative branch slope, the pressure difference caused by stack effect prevents the spread of thermal smoke inside branch tunnel to some extent, and the critical velocity of main tunnel increases with the increase of branch slope. Theoretically, there may be a critical slope for the fire scenario with negative slope, at which the thermal smoke cannot diffuse out from branch tunnel. Finally, an empirical correlation for the critical velocity considering the effect mechanism of branch slope was proposed for current experiment. This work is expected to provide some reference for the fire safety issue in bifurcated tunnel structures.