Radial Velocity Distribution Research Articles

Qualitative analysis on the electrohydrodynamic flow equation

<abstract><p>In this paper, we present a comprehensive analysis of the lower and upper bounds of solutions for a nonlinear second-order ordinary differential equation governing the electrohydrodynamic flow of a conducting fluid in cylindrical conduits. The equation describes the radial distribution of the flow velocity in an "ion drag" configuration, which is affected by an externally applied electric field. Our study involves the establishment of rigorous analytical bounds on the radial distribution, taking into account the Hartmann number $ H $ and a parameter $ \alpha. $ An analytic approximate solution is obtained as an improvement of the a priori estimates and it is found to exhibit strong agreement with numerical solutions, particularly when considering small Hartmann numbers. Further, estimates for the central velocity $ w(0) $ of the fluid occurring at the center of the cylindrical conduit were also established, and some interesting relationships were found between $ H $ and $ \alpha. $ These findings establish a framework that illuminates the potential range of values for the physical parameter within the conduit.</p></abstract>

Water-based Fe2 O3 Ferrofluid Flow over a Rotatable Plate

In the current work, the influence of rotational viscosity as a result of an external magnetic field on water-based Fe2O3 ferrofluid flow over a rotating plate is investigated. The governing equations of the physical model are transformed into a set of ordinary differential equations. The numerical solution of the differential equations is obtained by using the finite element method. The findings of the radial, tangential, and axial velocity distributions are descriptively presented for the different range of rotational viscosity The outcomes of this research demonstrate that the magnetic field has an important role in controlling the velocity profiles in the flow. A comparative study of velocity distributions is presented for COFe2O4, Fe2O3, NiO, and CO nanoparticles.

An experimental study of steam turbulent jet condensation & upward propagation of thermal plume into sub-cooled water pool

Supersonic steam’s axial injection into water in a cylindrical vessel (1 m high and 24 cm in diameter) was achieved through a nozzle of 6 mm diameter, located at the center of the vessel. Optical examinations were determined through a steam jet to find out condensation rate, which was allied with the steam mass flux (295–672 kg/m2/s) while leaving the nozzle’s exit. The Reynolds number (i.e., 41,000–73,610) has been estimated based on most swollen section of the steam’s jet. Further beyond the condensation zone, the steam, that has been condensed, progresses into a condensed steam plume, which is surrounded by the sub-cooled water. Particle Image Velocimetry (PIV) has been applied to focus region through the mid axis of the heated water plume along a vertical plane of 100 mm × 100 mm cross sections till 400 mm from the nozzle. Central upward averaged velocity profile of the condensed water thermal plume has been evaluated at 295 and 672 kg/m2s, both have hinted the exponential decrease of mean axial velocity when the plume travels vertically upward. The radial velocity distribution of the mean axial velocity across the radial dispersal of the jet, has been obtained as self-preservable and the mean axial velocity attained the Gaussian profile by incorporating appropriate grading of axial distance and mean velocity. Other significant aspect of the current work is to apply the buoyant scaling evolved from the single-phase non-condensing upward thermal plumes to the condensed upward plume through the relations of volume flow, momentum and buoyant being computed from the steam jet operating conditions. The source values of physical dimensionless parameters such as Reynolds number (Reo), Plume Richardson number (Ripo), entrainment coefficient (αo), buoyant vertical scale (Bo) have been evaluated. Based on the radial spread of the velocity profiles along the vertical distance from the condensation region, the dynamics of the thermal and the jet propagation has been highlighted through the evaluation of the dimensionless buoyant parameters along the downstream of the plume. The present experimental measurements obtained for condensed single-phase plume are compared with the experimental results of the non-condensed single-phase thermal plume to signify the vitality of the dimensionless parameters derived from non-condensed plumes.

Using 2DVD technology to explore droplet characteristic variations of sprinkler irrigation as affected by a maize canopy

Canopy cover influences the water distribution and droplet characteristics of sprinkler irrigation, creating uncertainty in the design optimization of sprinkler irrigation systems. To evaluate the effects of canopy cover on water distribution and droplet characteristics of sprinkler irrigation, the radial distribution of droplet diameters, velocities, impact angles, shear stresses, and kinetic energies were investigated by an indoor experiment using a two-dimensional video disdrometer (2DVD) with Nelson R33LP low-pressure sprinklers at three operating pressures (100, 200, and 300 kPa), three nozzle diameters (4.4, 4.8, and 5.2 mm), and two growing stages of the maize canopy. Additionally, the water application rates were measured by catch-can devices for each treatment. The results show that small droplets passing through the canopy converge into larger-diameter droplets and large droplets passing through the canopy break up into smaller-diameter droplets. The canopy cover significantly affected droplet kinetic energy and velocity and reduced shear stress by 2.48–96.09 %, which could minimize the risk of soil erosion. Meanwhile, an increase in the leaf area index (LAI) reduced the kinetic energy by 0.26–99.00 %. Canopy cover also had an obvious effect on the irrigation uniformity coefficients (CU). The CU without the canopy exhibited a significant linear correlation with the CU with the canopy. When the irrigation CU without the canopy was 62.00 %, the maize canopy at the jointing stage improved it by 16.62 %, and when the CU without the canopy was 88.47 %, the maize canopy cover at the jointing stage reduced it by 4.68 %. An increase in operating pressure improved the uniformity of the sprinkler by 0.57–151.58 % and reduced shear stress by 2.80–95.11 %. An increasing nozzle size increased the application rate and specific power. This study provides technical support for the design of sprinkler irrigation systems.

Mixing tank hydrodynamics and mixing efficiency for propeller impellers

In this study, the distribution of axial and radial velocities with the use of a PIV laser system was determined and the mixing power in a mixing tank with narrow and wide propeller impellers was measured. The pumping capacity and secondary circulation values in the mixing tank were calculated and on this basis, the energy efficiency of the operation of both types of propeller impellers was determined and compared with the efficiency of turbine impellers with inclined blades. It turned out that propeller impellers with wide blades are most effective as regards the amount of energy that should be supplied to the mixing tank to achieve the required mixing time. It was found that the share of pumping capacity in the total secondary circulation is almost twice as high as the share of induced circulation. Correlation equations for the dependence of the mixing power and dimensionless flow numbers on the pitch of the propeller blade were also formulated. All the results obtained were compared with the works of other authors. The paper also found that propeller impellers with a variable angle of inclination of the blade α depending on the current radius do not meet the theoretical assumption of a constant axial velocity of the liquid flowing out from of the impeller zone. For small radii of the impeller the explanation for this observation is the presence of the hub and shaft in the axis of the mixer and the effect of liquid slip for the steep agitator blades near the hub. For radii close to the radius of the stirrer, the reason is generation of induced circulation as the expense of the kinetic energy of the liquid flowing out of the impeller area.

Rotational movement analysis based on Fourier-rectangular function transform for cylindrical plasma

This article presents a method to estimate the rotational velocity of a cylindrical plasma from its two-dimensional images by an extended use of the Fourier-rectangular function transform, which was proposed to analyze the structure and dynamics of a cylindrical plasma [K. Yamasaki etal., J. Appl. Phys. 126, 043304 (2019)]. The proposed method is applied to tomography images of plasmas produced in a linear cylindrical device and succeeds in obtaining the radial distribution of rotational velocity and its fluctuations, providing an interesting finding, that is, the existence of flow modulation associated with m=1 mode fluctuations.

Inversion of radial formation velocity distribution based on monopole acoustic logging while drilling

Acoustic logging is an effective solution to obtain the radial formation velocity profile near a borehole, and it is critical for borehole stability evaluation and production performance monitoring. Herein, the responses of monopole acoustic logging while drilling (LWD) in a fluid-filled borehole surrounded by homogeneous and heterogeneous formations are numerically simulated using the finite difference algorithm in a cylindrical coordinate system. A stepwise inversion method is proposed to determine radial formation velocity distributions near the borehole based on the acoustic LWD data as follows. The heterogeneous formation around the borehole is approximated as multi-layered media with different elastic parameters, and then the slowness time correlation (STC) algorithm is applied to determine the compressional (P) and shear (S) wave velocities corresponding to different offsets. Finally, the thickness of each layer is determined according to the ray theory. Influences of measurement environment parameters, such as the central frequency of the source, thickness of the formation variation zone and elastic parameter changes of the formation variation zone, on the inversion results are evaluated to confirm the applicability of the proposed stepwise inversion method. The numerical simulation results demonstrate that refracted P-, refracted S- and Stoneley waves exhibit specific responses to the heterogeneity of the near-borehole formation, whereas collar waves are minimally influenced by the formation properties. The formation velocities do not change with the offset in the homogeneous formation models, although stepped changes are observed in the heterogeneous formation models. Short-offset waveforms are affected by the properties of the formation close to the borehole wall, whereas long-offset waveforms are primarily affected by the properties of the original formation. Relationships between the formation velocities and the offset can be converted into the radial formation velocity distributions by calculating the arrival times of waves propagating along different ray paths. Under common survey conditions, the inversion result of each model is similar to its real velocity distribution, which confirms the effectiveness of the proposed stepwise inversion method. This study thus provides a theoretical basis for developing 3D acoustic LWD tools.

Numerical analysis of solid phase hydrodynamics in a continuous precipitator relevant for plutonium reconversion

The extensive application of solid-liquid flow in various industries, has made it important to comprehend the hydrodynamics inside different process equipment and optimize their operation. In the present work, solid phase hydrodynamics in a continuous precipitator relevant for plutonium (Pu) reconversion has been investigated numerically. Euler-Euler two-fluid simulations were performed to analyse the performance by varying the solid concentration (5, 10, 15, and 20 g/l), impeller speed (500 and 700 rpm) and overflow outlet height (0.65, 0.75 and 0.85 m). The solid phase behaviour in precipitator is analysed by comparing the solid volume fraction and pressure distributions along the height. To enable easy handling of precipitator inside glove-box, the solid mass, volume rate and pressure distributions through overflow outlet at different height is thoroughly investigated. Further, the effect of solid concentration and rotating speed of impeller on radial velocity distribution is analysed. The results show that overflow of solid phase is dependent on dispersed phase concentration and rotating speed of the impeller. Further, the increase in overflow outlet height increases the overflow time. However, the volume fraction of solid remains constant during the steady operation. The study will be helpful to design a glove-box adaptable precipitator for continuous plutonium reconversion.

Hydrodynamic behavior of liquid flow in a rotating packed bed

Rotating Packed Bed (RPB) technology has emerged as a promising technology for reducing carbon footprint of various petrochemical processes by leveraging the HiGee field-induced mass transfer enhancement and allow for better capture of greenhouse gases. Despite its potential, there are still significant challenges that hinder the effective utilization of RPB technology in process intensification. Specifically, the hydraulics of liquid and gas phases within RPB packings present a significant challenge. In this study, 2D – VOF approach is employed to study the behavior of liquid droplets impacting on single rotating wire and on a whole rotating wire mesh within a Rotating Packed Bed (RPB). A comprehensive computational fluid dynamics (CFD) model is developed to analyze the influence of rotating speed, liquid velocity, and droplet diameter on the dynamics of liquid droplets. The boundaries of splashing – no splashing and dripping – capture breakup modes were validated for a single rotating wire and identified for wire mesh in RPBs by constructing the corresponding regime maps. This is achieved thanks to a new data processing algorithm that applies the principle of neighborhood aggregation. The proposed data processing algorithm helps reconstruct the regime maps for the various breakup phenomena within RPBs. The results show that the splashing mechanism reproduces higher-velocity detached daughter droplets, while the momentum-induced dripping mechanism results in low velocity daughter droplets. The results also reveal that the deposited liquid film with the wires has a key role in enhancing the splashing phenomena in RPBs. The radial distribution of diameter and velocity of liquid droplets in RPB is also analyzed in light of the droplet impact dynamics. The increase in the average liquid velocity with radial direction was attributed to the increase of splashed drops, which led to a bigger number of high-velocity droplets. The conclusions of this study can be used to help improve the dynamics of the two-phase flow within RPBs through a better packing design and flow conditions.

Particle-scale analysis of thermophysical behaviors of coaxial gas swirling jets with binary-size particle mixture

Understanding the multi-physics coupling of coaxial-jet gas-particle swirling flow is crucial for practical applications. In this study, computational fluid dynamics coupled with the discrete element method is utilized to investigate the flow behavior of a coaxial jet composed of powder and coal within an annular pipe. The influence of particle diameter on particle-scale information is examined. When powder diameter is 450 μm, large particles display high Reynolds and Nusselt numbers, whereas small coal particles demonstrate elevated velocities and temperature. The variation in particle diameter affects momentum and energy exchanges at specific locations, but has a negligible impact on the radial velocity distribution and Nusselt number of powder particles. Specifically, increasing the particle diameter from 50 to 450 μm leads to a reduction in swirling velocity at the outlet of the annular pipe from 15.43 m/s to 9.57 m/s for binary mixtures, and from 18.49 m/s to 7.03 m/s for powders.

Numerical study of the coalescence-induced droplet jumping with macrotexture based on single-phase model

The low energy conversion efficiency in coalescence-induced droplet jumping limits its potential for various applications, such as self-cleaning, anti-icing, and energy harvesting. Fortunately, it has been proven that this efficiency can be significantly increased through a sophisticated macrotexture design. In this study, we propose a single-phase model with a moving mesh to simulate the self-jumping process under a ridge. The effect of the ridge is realized by adopting a pointwise constraint on several surface nodes. This effective model is validated by experimental results of droplet velocity. In comparison with volume-of-fluid, a single-phase flow method enhances computational efficiency by at least 33.3%. The kinematics and dynamics of the self-jumping process have been investigated with respect to the influences of ridge height and Ohnesorge number. With the help of the radial distributions of velocity and internal pressure, the self-propelled process can be divided into coalescence-induced and lobe-induced stages. The high ridge brings more symmetry-breaking, accelerating the droplet in the coalescence-induced stage. In the lobe-induced stage, the slingshot effect is weakened under high Ohnesorge number due to the prolate shape caused by viscous dissipation. Moreover, the study's findings demonstrate promising application prospects for other ridge shapes, thereby expanding the potential practical applications of this research.

Spatial Transformations for Reacting Gas Shock Tube Experiments

Shock tube flows can be used to investigate nonequilibrium thermochemistry and radiative processes found in hypersonic flows. The flow in a shock tube contains many flow nonuniformities, in particular boundary-layer effects. For the purpose of studying the properties of the test slug, the flow behind the shock is usually considered analogous to the stagnation line flow over a blunt body. In reality, radial and longitudinal velocity distributions in the two flows are different, and so a coordinate transformation is needed to match time-of-flight profiles. This work develops a method to approximately transform the postshock distance for normal and blunt body shocks to a shock tube flow using a Mirels analysis. The effects of shock tube diameter and shock speed variation are highlighted along with the importance of postshock temperature and density rises. This is then applied to blunt body simulations of NASA EAST data for air and Titan tests. This showed that minimal difference is encountered for fast reacting flows. However, large differences can be seen in the slower reacting Titan tests, which to date have been misinterpreted when compared to blunt body simulations.

Study on Radial Distribution of Fragments Velocity of D-shaped Fragmentation Warhead

For the asymmetric D-shaped fragmentation warhead with high charging coefficient and space efficiency, we simulate the driving process of fragments under typical eccentric initiation by using the fluid-structure interaction algorithm, and obtained the change rule of the fragment velocity radial distribution with the central angel, the thickness and material of the upper end cap. The results of numerical simulation show that the fragment velocity of D-shaped warhead increases gradually from the reverse to the forward direction, the velocity of fragment in forward direction increases by about 10% under single-point eccentric initiation compared with the cylindrical casing under center initiation, and the fragment velocity under double-point eccentric initiations is higher than single-point eccentric initiation; The initial velocity of the fragment has a positive correlation with the thickness and density parameters of the upper end cap; the mass of the warhead and the total kinetic energy of the fragments in the forward area increase with the increase of the central angle, but their ratio increases first and then decreases with the increase of the central angle. The results can be applied to structural optimization design and power evaluation of the warhead.

Reconstructing Synoptic Maps of Solar Wind Radial Velocity between 20 and 60 R ⊙ Based on STEREO/HI1 Images

Previously, we developed a correlation-aided reconstruction method to recognize and locate solar wind transients observed by the Heliospheric Imager-1 (HI1) on board the Solar Terrestrial Relations Observatory and then developed a technique to infer the radial velocity distribution in each solar wind transient. Considering that the common field of view of HI1 may cover the full longitudes through the solar rotation, we further apply these methods to small-scale transients (STs) in a complete Carrington rotation to reconstruct a synoptic map of the solar wind radial velocity. Our test suggests that the reconstructed synoptic map is in agreement with the preset synthetic STs in latitude, longitude, and radial velocity. Then, Carrington rotation 2095 between 2010 March 26 and April 22 is selected to demonstrate the new technique. The derived synoptic map shows that the solar wind radial velocity corresponding to STs is in the range of 250–550 km s−1 between 20 and 60 R ⊙ in the low-to-middle latitudes. We extrapolate the in situ observation near 1 au to 20 R ⊙ and find that it matches the synoptic velocity map well. The magnetohydrodynamic simulations of the solar wind radial velocity are consistent with the synoptic map near the heliospheric current sheet (HCS) but usually overestimate the velocity values for STs far away from the HCS. We expect that this technique will be a powerful tool to learn about and monitor the solar wind in the inner heliosphere, where the number of human probes is limited.

Influence of internal components on the hydrodynamic properties of the scrubbing-cooling chamber

The bubble-breaking plate is a crucial internal component in the scrubbing-cooling chamber. The study of hydrodynamics under its influence is the basis for designing and scaling up industrial installations. Experimental measurements of characteristic bubble parameters and liquid phase structure parameters at local locations were carried out using a conductivity probe and a pitot tube, respectively, to investigate the effects of five types of bubble-breaking plate installation on the hydrodynamic properties of the annular gap bubble bed. The experimental results show that the staggered placement of two plates is the most favorable for increasing the gas holdup, reducing the bubble size, increasing the gas–liquid interface area, improving the liquid velocity distribution and suppressing the turbulence fluctuations. In addition, a dimensionless mathematical model predicted the radial distribution of local gas holdup and axial time-averaged liquid velocity, and the expected results agreed with the experimental values.

Optimization of capsule diameters in cascade packed-bed thermal energy storage tank with radial porosity oscillations based on genetic algorithm

The packed-bed thermal energy storage system (PBTES) has broad application prospects in renewable energy, such as for solar, hydraulics, biomass, and geothermal. This study varied the capsule diameter arrangement of the PBTES using a genetic algorithm (GA) to optimize the thermal performance of the cascaded three-layer PBTES during charging. When considering the oscillatory distribution of the radial porosity, the thermal energy storage (TES) rate density was used as an objective function to evaluate the system’s thermal performance. The TES rate density of PBTES was calculated for more than 4000 capsule diameter arrangements. The results indicate that the tank-to-capsule diameter ratio significantly affects the radial porosity distribution, velocity, and temperature distribution of PBTES. The optimal capsule diameter arrangement in the range of 15 mm ≤d≤ 40 mm was obtained as d1 = 15.58 mm, d2 = 21.78 mm, and d3 = 27.68 mm. Compared with the original model, the optimal model’s charging time was reduced by 33.90%, the TES rate density improved by 37.07%, and the cost per unit of heat storage increased by 92.41%. The results show that the GA is a powerful tool for optimizing PBTES structures.

Cross-correlating radial peculiar velocities and CMB lensing convergence

We study, for the first time, the cross correlation between the angular distribution of radial peculiar velocities (PV) and the lensing convergence of cosmic microwave background (CMB) photons. We derive theoretical expectations for the signal and its covariance and assess its detectability with existing and forthcoming surveys. We find that such cross-correlations are expected to improve constraints on different gravitational models by partially breaking degeneracies with the matter density. We identify in the distance-scaling dispersion of the peculiar velocities the most relevant source of noise in the cross correlation. For this reason, we also study how the above picture changes assuming a redshift-independent scatter for the PV, obtained for example using a reconstruction technique. Our results show that the cross correlation might be detected in the near future combining PV measurements from DESI and the convergence map from CMB-S4. Using realistic direct PV measurements we predict a cumulative signal-to-noise ratio of approximately 3.8σ using data on angular scales 3 ≤ ℓ ≤ 200. For an idealized reconstructed peculiar velocity map extending up to redshift z = 0.15 and a smoothing scale of 4 Mpc h -1 we predict a cumulative signal-to-noise ratio of approximately 27σ from angular scales 3 ≤ ℓ ≤ 200. We conclude that currently reconstructed peculiar velocities have more constraining power than directly observed ones, even though they are more cosmological-model dependent.

The circulation growth of non-impulsive starting jet

An analytical model that can be used to predict the circulation growth process for non-impulsive starting jets has been developed by extending the over-pressure correction model for impulsive starting jets. Only the jet velocity function U0(t) is needed to obtain the circulation growth process of non-impulsive starting jet. The non-impulsive starting jets generated by nozzle and orifice configurations are performed numerically with two acceleration schemes (represented by two kinds of velocity functions) and different acceleration stage stroke ratios LaD (modifying the acceleration time ta in each velocity function to obtain LaD=0.05:0.2:1.25) to verify the accuracy of the proposed analytical model. The influence of radial velocity distribution in the jet inflow boundary is ignored in the process of constructing this model, but this has been proven to be reasonable. The time-averaged relative error with the growth process of the total circulation predicted by this model is about 11% to 26%, which is smaller than the 44% to 88% obtained by the classical slug model. For the range of LaD from 0.05 to 1.25, the relative error with the prediction of the total circulation at the end of the acceleration stage is from 4% to 28%, as compared to the 39% to 96% for the slug model.

On Liquid Flow Maldistribution through Investigation of Random Open-Structure Packings

The optimal design of packed columns for separation processes is strongly dependent on an accurate prediction of the fluid flows in the packing. Insufficient knowledge about the complex factors and mechanisms governing hydrodynamic effects is compensated for by empirical information. The present study fills the gap in experimental data about the liquid phase distribution in plastic Raschig Super-Ring (RSRP) packing and plastic Ralu–Flow (RF) packing. These belong to the family of widely used random packings with an open lattice structure characterized by high mass transfer efficiency and a low pressure drop. The study was performed using the liquid collection method with a device with concentric annular collection sections at the packing outlet. Large-scale liquid maldistribution in the central and peripheral zones of the packed bed were evaluated in comparison data on competing random and structured packings. The effects of the packing size and the liquid load on the radial distribution of the superficial liquid velocity, wall flow formation and the maldistribution factor were investigated and analyzed. The results contribute to deepening the knowledge about the phenomenon of large-scale liquid flow maldistribution in packed columns, as well as to design enhancement.

The LMC impact on the kinematics of the Milky Way satellites: clues from the running solar apex

ABSTRACT Dwarf galaxies provide a unique opportunity for studying the evolution of the Milky Way (MW) and the Local Group as a whole. Analysing the running solar apex based on the kinematics of the MW satellites, we discovered an unexpected behaviour of the dipole term of the radial velocity distribution as a function of the Galactocentric distance. The nearby satellites (<100 kpc) have a bulk motion with an amplitude of 140–230 km s−1, while the more distant ones show an isotropic distribution of the radial velocities. Such strong solar apex variations cannot be explained by the net rotation of the satellites, as it would require an enormously high rotation rate (≈970 km s−1). If we exclude the Large and Magellanic Clouds (LMC) and its most closely related members from our sample, this does not suppress the bulk motion of the nearby satellites strongly enough. Nevertheless, we have demonstrated that the observed peculiar kinematics of the MW satellites can be explained by a perturbation caused by the first infall of the LMC. First, we ‘undone’ the effect of the perturbation by integrating the orbits of the MW satellites backwards (forwards) with (without) massive LMC. It appears that the present-day peculiar enhancement of the solar apex in the inner halo is diminished the most in the case of 2 × 1011 M⊙ LMC. Next, in self-consistent high-resolution N-body simulations of the MW–LMC interaction, we found that the solar apex shows the observed behaviour only for the halo particles with substantial angular momentum, comparable to that of the MW satellites.