Two-dimensional Velocity Field Research Articles

Thermodynamic of collapsing cavitation bubble investigated by pseudopotential and thermal MRT-LBM.

The thermodynamic of cavitation bubble collapsing is a complex fundamental issue for cavitation application and prevention. The pseudopotential and thermal multi-relaxation-time lattice Boltzmann method (MRT-LBM) is adopted to investigate the thermodynamic of collapsing cavitation bubble in this paper. The simulation results satisfy the maximum temperature equation of the bubble collapse, which derived from the Rayleigh-Plesset (R-P) equation. The validity of thermal MRT-LBM in simulating the collapse process of cavitation bubble is verified. It shows that the temperature evolution of vapor-liquid phase is well captured. Furthermore, the two-dimensional (2D) temperature, velocity and pressure field of the bubble near a solid wall are analyzed. The maximum temperature inside the bubble and wall temperature under different position offset parameters are discussed in details.

Bimolecular reactive transport in a two-dimensional velocity field in disordered media

The nonlocal-in-time, integro-partial differential equation (iPDE) describing the continuous time random walk (CTRW) is augmented by a nonlinear chemical-species term accounting for migrating bimolecular reactions in disordered media. This augmented form of the iPDE, previously shown to be in excellent agreement with a particle-tracking (CTRW-PT) version of reactive transport, is applied here to a reanalysis of recent experimental results to further establish its validity. The experimental set-up uses an injected solution of a pH indicator (Congo red) as both an inert tracer or a reactant, depending on the pH of the solution. A refraction index-matched, water-saturated porous medium allows tracking of the reacted concentration field, which is modeled by the solutions of the two-species coupled iPDE, whose nonlinear form precludes the use of a Laplace transform. The time-domain solutions are obtained with a finite element method (FEM) and a sum of exponentials representation of the kernel (memory function). The two-dimensional flow field subject to the macroscopic boundary conditions is calculated by solving the Darcy equation. The CTRW is well established for nonreactive transport in disordered media. The fit for the inert tracer in this case provides a reasonable match to these particular experimental data. The comparable, agreeable fit for the reactive case further establishes the validity of the iPDE augmented with a nonlinear, second-order reaction term.

Large-eddy simulation of the effect of distributed plasma forcing on the wake of a circular cylinder

We conducted large-eddy simulation (LES) to investigate the effect of segmented plasma forcing on the wake of a circular cylinder, at a subcritical Reynolds number of 4700. The action of the plasma actuators was simulated by a body-force model developed by Shyy et al. [1]. The main objective of this study was to investigate the changes in the three-dimensionality of the wake, and the nature of separation on the cylinder surface, with the increasing power of segmented forcing. By observing the three-dimensional (3D) structures, and the separating streamlines close to the cylinder surface, we aim to provide more insight on the experimental findings of Bhattacharya and Gregory [2], which contained only two-dimensional (2D) velocity field data. To that end, we used segmented actuators with a spatial wavelength of 5d (d= cylinder diameter), and two separate blowing ratios of 0.2 and 0.7. At the lower blowing ratio (BR=0.2), spanwise vortex shedding was not canceled, although waviness developed in the spanwise vortices. However, there was no considerable difference in the separation angles between two adjacent spanwise locations. Forcing with higher blowing ratio (BR=0.7) completely disrupted the vortex shedding infront of the plasma region. The separation line on the surface of the cylinder developed significant periodicity leading to a spanwise variation of formation length. We show that such spanwise variation created spatially locked streamwise vortices which disrupted regular vortex shedding.

Detailed flow development and indicators of transition in a natural convection flow in a vertical channel

A spatially developing transitional flow in a vertical channel with one side heated uniformly and subjected to random velocity fluctuations at the inlet is investigated in this experimental and numerical study. Two Rayleigh numbers are studied. Experimentally, Particle Image Velocimetry is used to obtain a complete two-dimensional velocity field of the streamwise flow development. A three-dimensional Large-Eddy-Simulation investigation is also performed to obtain a complete streamwise evolution of the flow. The results allow the definition of three transition indicators on the basis of the time-averaged velocities and temperatures fields as well as on the turbulent statistics of the flow. The detailed experimental and numerical spatial development of the transitional natural convective flow is then presented and the ability of the indicators to capture the early and the advanced stages of the transition is assessed. The numerical simulations were performed on the assumptions of a thermally stratified environment, submitted to an environmental noise, and for which wall to wall radiations were considered. These conditions aim at representing realistic experimental conditions.

Analytical solutions of incompressible laminar channel and pipe flows driven by in-plane wall oscillations

Emerging flow control strategies have been proposed to tackle long-lasting problems, for instance, precise mixing of chemicals and turbulent drag reduction. Employing actuators imposing in-plane wall oscillations are particularly popular. This paper investigates incompressible laminar rectangular channel and circular pipe flows driven by uniform and traveling wave in-plane wall oscillations. A comprehensive set of exact analytical solutions are presented describing parallel and concentric flows. Dimensionless groups are identified, and it is described how they characterize the one- and two-dimensional time-dependent velocity and pressure fields. The solutions enable to compute the oscillating boundary layer thickness. It is demonstrated that the dimensionless groups and the boundary layer thickness narrows the region of interest within the parameter space. In particular, the oscillating boundary layer thickness obtained from these laminar flows estimates a “radius of action” within which flow features can be altered to boost mixing or reduce turbulent friction drag. The results are suitable for software validation and verification, may open the way to promising complex wall oscillations, and ease the optimization task that delays the industrial application of flow controls.

Flow visualisation in swimming practice using small air bubbles

A non-harmful system to visualize the flow around an entire swimmer in a regular swimming pool is developed. Small air bubble tracers are injected through the bottom of the swimming pool in a prescribed measurement area. The motion of these bubbles, which will be largely induced by the swimmer’s motion, is captured by a camera array. The two-dimensional velocity field of the water at arbitrary planes of interest can be resolved using a refocussing method in combination with an optical visualisation method, based on particle image velocimetry, which is commonly used in fluid dynamics research. Using this technique, it is possible to visualize coherent flow structures produced during swimming; it is demonstrated here for the dolphin kick.

Modeling of rolling force of ultra-heavy plate considering the influence of deformation penetration coefficient

The deformation characteristic of an ultra-heavy plate in thickness direction is described by introducing a parameter, called deformation penetration coefficient, and the rolling force model taking this parameter into account in the broadside stage is established. In this paper, the deformation penetration coefficient is defined as the ratio of the actual deformation depth to the overall plate thickness, which is shown as the function of the initial thickness, the pass reduction and the critical shape factor. Since the plate width speard can be neglected during broadside rolling, a two-dimensional velocity field is constructed by simplifying a classical three-dimensional velocity field. For the purpose of solving the problem of functional integration originated from the nonlinear Mises specific plastic power, the simplified velocity field is analyzed by the geometric approximation (GA) yield criterion, and the internal deformation power is obtained. Moreover, the friction power and the shear power are obtained by the inner product method of the strain vector and the mean velocity intergral method, respectively. The analytical solution of rolling force is obtained by the variational method, and its value for each pass is compared with the measured data from a domestic factory. The comparison result shows that the rolling force model in this paper has a high predictive accuracy, since the maximum error is less than 8.6%. The rolling parameter analysis shows that the deformation penetration coefficient, the pass reduction and the ratio of plate thickness to diameter affect the rolling force of the ultra-heavy plate apparently.

Analytic reconstruction of a two-dimensional velocity field from an observed diffusive scalar

Inverting an evolving diffusive scalar field to reconstruct the underlying velocity field is an underdetermined problem. Here we show, however, that for two-dimensional incompressible flows, this inverse problem can still be uniquely solved if high-resolution tracer measurements, as well as velocity measurements along a curve transverse to the instantaneous scalar contours, are available. Such measurements enable solving a system of partial differential equations for the velocity components by the method of characteristics. If the value of the scalar diffusivity is known, then knowledge of just one velocity component along a transverse initial curve is sufficient. These conclusions extend to the shallow-water equations and to flows with spatially dependent diffusivity. We illustrate our results on velocity reconstruction from tracer fields for planar Navier–Stokes flows and for a barotropic ocean circulation model. We also discuss the use of the proposed velocity reconstruction in oceanographic applications to extend localized velocity measurements to larger spatial domains with the help of remotely sensed scalar fields.

Two-dimensional dam-break wave analysis: particle image velocimetry versus optical flow

Dam-break waves have been the focus of a number of research papers; next to analytical investigations, scaled experimental models and numerical simulations are used to determine dam-break wave propagation. Experimental models and data analysis tools are necessary to generate calibration data for numerical models. Often, particle image velocimetry (PIV) algorithms are used to calculate two-dimensional velocity fields of propagating dam-break waves. This paper deals with a visual analysis method called optical flow (OF). An experimental model was built to identify the initial stage of dam-break waves. A comparison between results using the PIV method and the OF method is given to identify flow velocities for two-dimensional dam-break waves. It can be shown that the OF method is able to predict resulting velocity profiles accurately. The mean relative error for the comparison of manually observed data and OF results is less than 6%, while for the PIV comparison an error of 11% can be calculated. Since velocity vectors are produced for all image pixels, the resulting information density is high compared to results produced by the PIV method.

Quantitative visualization of fluid mixing in slug flow for arbitrary wall-shaped microchannel using Shannon entropy

Micro-reactors based on slug flow are among the most promising developments for improving the efficiencies of chemical reactions and unit operations in chemical engineering. Quantitative understanding of the local and global fluid dynamics and their effects on fluid mixing is required for designing effective slug flow micro-reactors. This paper proposes a new method for quantitative two-dimensional assessment of fluid mixing in slug flow. Pixel-wise calculation of local entropy inside a slug is discussed. The proposed method is based on two-phase simulation using the volume of fraction (VOF) algorithm and is thus applicable to the flow pattern in arbitrary wall-shaped micro-reactors. The method consists of three steps. (1) Flow analysis using two-phase VOF algorithm: A series of two-dimensional velocity fields inside the slug along time is obtained for a certain duration. (2) Backward particle tracking from the target image to the initial image: The slug in the initial image is divided into small regions, and each region is assigned a different label. Accumulation of backward particle tracking results reveals a two-dimensional distribution of labels in the target image. (3) Pixel-wise calculation of entropy on the obtained distribution of labels: The resulting image is a quantitative two-dimensional mixing pattern inside the slug. The proposed method was applied to three types of microchannels with different bumps on the walls. The results could quantitatively distinguish the differences in fluid mixing capability among the systems.

Nonaxisymmetric models of galaxy velocity maps

Galaxy velocity mapsoften show the typical pattern of a rotating disk, consistent with the dynamical model where emitters rotate in circular orbits around the galactic center. The simplest template used to fit these maps consists in the rotating disk model (RDM) where the amplitude of circular velocities is fixed by the observed velocity profile along the kinematic axis. A more sophisticated template is the rotating tilted-ring model (RTRM) that takes into account the presence of warps and allows a radius-dependent orientation of the kinematic axis. In both cases, axisymmetry is assumed and residuals between the observed and the model velocity fields are interpreted as noncircular motions. We show that if a galaxy is not axisymmetric, there is an intrinsic degeneracy between a rotational and a radial velocity field. We then introduce a new galaxy template, the radial ellipse model (REM), that is not axisymmetric and has a purely radial velocity field with an amplitude that is correlated with the major axis of the ellipse. We show that best fits to the observed two-dimensional velocity fields of 28 galaxies extracted from the THINGS sample with both the REM and the RDM give residuals with similar amplitudes, where the REM residuals trace nonradial motions. Best fits obtained with the RTRM, because of its larger number of free parameters, give the smallest residuals: however, we argue that this does not necessarily imply that the RTRM gives the most accurate representation of a galaxy velocity field. Instead, we show that this method is not able to disentangle between circular and radial motions for the case of nonaxisymmetric systems. We then discuss a refinement of the REM, able to describe the properties of a more heterogeneous velocity field where circular and radial motions are respectively predominant at small and large distances from the galaxy center. Finally, we consider the physical motivation of the REM, and discuss how the interpretation of galactic dynamics changes if one assumes that the main component of a galaxy velocity field is modeled as a RDM/RTRM or as a REM.

Unsteadiness control of laminar junction flows on pressure fluctuations

Smoke-wire flow visualization is conducted carefully in a laminar junction to explore the physical behavior of laminar junction flows. The two-dimensional (2D) velocity fields in the 30° plane of a laminar junction flow are acquired by a time-resolved particle image velocimetry (PIV) system at a frame rate of 1 kHz, based on which the unsteady fluctuating pressure fields can be calculated by the multi-path integration method proposed in the literature (GAND, F., DECK, S., BRUNET,V., and SAGAUT, P. Flow dynamics past a simplified wing body junction. Physics of Fluids, 22(11), 115111 (2010)). A novel control strategy is utilized to attenuate the unsteadiness of the horseshoe vortices of the laminar junction flow, and the consequent effect on pressure fields is analyzed.

The vorticity equation on a rotating sphere and the shallow fluid approximation

The material conservation of vorticity in fluid flows confined to a thin layer on the surface of a large rotating sphere, is a central result of geophysical fluid dynamics. In this paper we revisit the conservation of vorticity in the context of global scale flows on a rotating sphere. Starting from the vorticity equation instead of the Euler equation, we examine the kinematical and dynamical assumptions that are necessary to arrive at this result. We argue that, in contrast to the planar case, a two-dimensional velocity field does not lead to a single component vorticity equation on the sphere. The shallow fluid approximation is then used to argue that only one component of the vorticity equation is significant for global scale flows. Spherical coordinates are employed throughout, and no planar approximation is used.

Effect of gas flow velocity on convection in a horizontal evaporating liquid layer

The structure of convective flows in a horizontal evaporating layer of liquid (ethanol) was studied experimentally depending on the velocity of gas (air) flowing near the interface. Using the PIV method, we measured distribution of the two-dimensional velocity field and visualized the convective flows in a liquid layer. The existence of a vortex flow structure in an evaporating liquid layer, when the interface moves towards the gas flow, was proved.

Wall-Normal Variation of Spanwise Streak Spacing in Turbulent Boundary Layer With Low-to-Moderate Reynolds Number.

Low-speed streaks in wall-bounded turbulence are the dominant structures in the near-wall turbulent self-sustaining cycle. Existing studies have well characterized their spanwise spacing in the buffer layer and below. Recent studies suggested the existence of these small-scale structures in the higher layer where large-scale structures usually receive more attention. The present study is thus devoted to extending the understanding of the streak spacing to the log layer. An analysis is taken on two-dimensional (2D) wall-parallel velocity fields in a smooth-wall turbulent boundary layer with = 440∼2400, obtained via either 2D Particle Image Velocimetry (PIV) measurement taken here or public Direct Numerical Simulation (DNS). Morphological-based streak identification analysis yields a -independent log-normal distribution of the streak spacing till the upper bound of the log layer, based on which an empirical model is proposed to account for its wall-normal growth. The small-scale part of the spanwise spectra of the streamwise fluctuating velocity below = 100 is reasonably restored by a synthetic simulation that distributes elementary streak units based on the proposed empirical streak spacing model, which highlights the physical significance of streaks in shaping the small-scale part of the velocity spectra beyond the buffer layer.

Kinematics and Dynamics of the Galactic Halo from RR Lyrae Variable Stars

Based on a sample of RR Lyrae variable stars including more than 9000 objects with proper motions and distances, we have investigated the kinematics of the Galactic halo from the two-dimensional velocity field. We have used both the proper motions deduced independently by us from the positional data taken from all-sky catalogues in a time interval up to 65 years and the proper motions taken from the Gaia DR2 catalogue. In addition, we have also studied the halo kinematics from the three-dimensional velocity field of ~850 RR Lyrae variables with distances, proper motions, and line-of-sight velocities. The kinematic parameters describing the velocity field have been estimated by the maximum-likelihood method; their change with Galactocentric distance has been investigated. The radial velocity dispersion in spherical coordinates σr ≈ 160−170 km s−1 exceeds its values from previous papers approximately by 20 km s−1, while the anisotropy parameter β ≈ 0.68−0.72 agrees satisfactorily with previous studies. When estimating the rotation velocity of the population of RR Lyrae stars, we identified the inner and outer halos with weak prograde and retrograde rotations, respectively.

Two-dimensional flow visualization and velocity measurement in natural convection near indoor heated surfaces using a thermal image velocimetry method

Indoor velocity measurement techniques are categorized into point-wise and global-wise measurement techniques. Currently, measurements are either intrusive or restricted to the measurement area. This study presents a thermal image velocimetry (TIV)-based flow measurement method that is suitable for visualizing indoor two-dimensional velocity fields near indoor heated surfaces. The proposed technique uses only an infrared camera for mapping the surface temperature fluctuations. Image processing steps that are used to recover the velocity distribution include the decomposition of the video files into individual frames, the application of filtering to remove background noise, cross-calculation to estimate the velocity, and a final velocity correction based on the continuity equation. To investigate the feasibility of this method, natural convection was studied close to a heated vertical surface in a rectangular cavity. Thermal image velocimetry and particle image velocimetry (PIV) were used to visualize the flow field above a heating unit. The results indicate that the airflow field can be visualized by TIV, and the results measured by TIV are shown to be similar to those for the surface of 6 mm away from the heated surface measured by PIV. A linear correlation is established between TIV and PIV.

Experimental and numerical investigation of impinged water jet effects on heated cylinders for convective heat transfer

Effect of jet flow structures impinged on a heated cylinder has been investigated experimentally and numerically in this study. The FLUENT 6.3.26 was used to simulate this numerical problem. In the numerical section, the influence of some variables such as the distance between cylinder and jet on the fluid flow characteristics has been analyzed. The distance between the cylinders and jet has been varied as H/S = 4, 6, and 10. The flow characteristics around the heated cylinder with a diameter of 30 mm were obtained in the range of 5000≤ReD ≤ 20000. Variations of velocity and temperature profiles on the cylinder have been determined for increasing Reynolds Number. Techniques of high image velocimetry will be employed throughout the investigations to obtain two-dimensional velocity field distributions. Rectangular nozzle jet flow is achieved with a size of 30 mm × 390 mm. The experiments are performed in a large scale water channel and obtained experimental results are compared numerical results for three different Reynolds number of 5000, 7500, and 10000 based on cylinder diameter. The results showed that the heat transfer decreased with the increase in the H/S value. Especially the decline in high H/S values took place linearly. The increase in H/S values decreased the impact of the first cylinder on the second cylinder. The increase in Reynolds number also increases the heat transfer.

The extended Planetary Nebula Spectrograph (ePN.S) early-type galaxy survey: The kinematic diversity of stellar halos and the relation between halo transition scale and stellar mass

Context. In the hierarchical two-phase formation scenario, the halos of early type galaxies (ETGs) are expected to have different physical properties from the galaxies’ central regions. Aims. The ePN.S survey characterizes the kinematic properties of ETG halos using planetary nebulae (PNe) as tracers, overcoming the limitations of absorption line spectroscopy at low surface brightness. Methods. We present two-dimensional velocity and velocity dispersion fields for 33 ETGs, including fast (FRs) and slow rotators (SRs). The velocity fields were reconstructed from the measured PN velocities using an adaptive kernel procedure validated with simulations, and extend to a median of 5.6 effective radii (Re). We complemented the PN kinematics with absorption line data from the literature, for a complete description of the kinematics from the center to the outskirts. Results. ETGs typically show a kinematic transition between inner regions and halo. Estimated transition radii in units of Re anti-correlate with stellar mass. SRs have increased but still modest rotational support at large radii. Most of the FRs show a decrease in rotation, due to the fading of the inner disk in the outer, more slowly rotating spheroid. 30% of the FRs are dominated by rotation also at large radii. Most ETGs have flat or slightly falling halo velocity dispersion profiles, but 15% of the sample have steeply falling profiles. All of the SRs and 40% of the FRs show signatures of triaxial halos such as kinematic twists or misalignments. We show with illustrative photometric models that this is consistent with the distribution of isophote twists from extended photometry. Conclusions. ETGs have more diverse kinematic properties in their halos than in the central regions. FRs do contain inner disk components but these frequently fade in outer spheroids which are often triaxial. The observed kinematic transition to the halo and its dependence on stellar mass is consistent with ΛCDM simulations and supports a two-phase formation scenario.

Numerical and Experimental Investigation of Newtonian Flow around a Confined Square Cylinder

The confined flow of a Newtonian fluid around a square cylinder mounted in a rectangular channel was investigated both numerically and experimentally. Ratio between the pipe and channel height, the blockage ratio, is kept constant at 1/4. The flow variables including streamlines, vorticity and drag coefficients were calculated at 0 ≤ Re ≤ 50 using finite volume method. The velocity terms in the momentum equations are approximated by a higher-order and bounded scheme of Convergent and Universally Bounded Interpolation Scheme for the Treatment of Advection (CUBISTA). Particle Image Velocimetry (PIV) was also used to obtain the two-dimensional velocity field. The flow measurements were conducted for 1 ≤ Re ≤ 50. Streamline and vorticity results obtained by PIV are compared with those of the numerical simulation. Based on this comparison, good agreement is found between the numerical and experimental results in a qualitative manner.