Hydrodynamic Velocity Research Articles

A Systematic and Integrative Sequence Approach (SISA) for mastery learning: Anchoring Bloom's Revised Taxonomy to student learning

In this contribution, a methodical and student-based learning sequence entitled Systematic and Integrative Sequence Approach (SISA) is introduced. Primarily utilized within STEM disciplines, SISA is inspired by instructivist and constructivist approaches to learning and ultimately seeks to help students reach mastery learning levels regarding complex concepts within these fields. By organizing and anchoring lesson plans concerning these concepts to the cognitive objectives outlined by Bloom's Revised Taxonomy (Krathwohl, 2002), SISA facilitates students’ preparedness to contribute to the creation of technological developments and innovation in STEM fields. Offering an example of its application, this paper outlines how SISA has been integrated into the instruction of hydrodynamic velocity profiles in viscous flows. In addition, this effort highlights exploratory data collected from students taught by the SISA approach. Analysis of this study and implications for future work are also discussed.

Sound Modes of a Bose–Fermi Mixture Superfluid at Finite Temperatures

We study the sound modes of a Bose–Fermi mixture superfluid at finite temperatures in the collisional hydrodynamic regime. We extend Landau’s hydrodynamic theory to deal with a Bose–Fermi mixture superfluid and show the existence of three sound modes. We calculate the hydrodynamic sound velocities numerically using the Nozieres and Schmitt-Rink theory at unitarity. The three-sound-modes hybrid in Bose–Fermi mixture superfluids contrasts with the two sound modes exhibited by 3He and 4He superfluids.

Determination and impact factor analysis of hydrodynamic dispersion coefficient within a gravel layer using an electrolyte tracer method

Hydrodynamic dispersion is a measure for describing the process of solute transport in porous media. Characterizing the dispersion of water flow within gravel is essential for the prediction of solute transport especially nonpoint source pollutants migration in alpine watersheds where the land surface is typically covered with gravel. In this study, an integrated model and experimental method using an electrolyte tracer is proposed for determination of the hydrodynamic dispersion coefficient. Two experimental scenarios were designed to measure electrolyte tracer transport processes in both free water flow and gravel layer flow under different slope gradients and transport distances. Subsequently, the measured data were used to simultaneously calculate both the hydrodynamic dispersion coefficient and flow velocity by fitting the experimental data with the mathematical model. Dispersivity, as a critical feature of hydrodynamic dispersion, was determined as well under the two specified scenarios. Finally, the impact mechanisms of the gravel layer and factors related to the dispersion processes were comprehensively analyzed. The results indicate that the presence of a gravel layer significantly reduces flow velocity and the hydrodynamic dispersion coefficient, but increases solute dispersivity. For the flow within gravel layers, with much lower velocity, the positive effect of the gravel layer on dispersivity may be neutralized or even surpassed by the negative effect of flow velocity. The results should be helpful in characterizing the dispersion processes of water flow within gravel layer and hence in predicting solute transport, especially in nonpoint source pollutants migration in alpine watersheds where the land surface is richly covered with gravel.

Solitary Nanostructures Produced by Ultrashort Laser Pulse.

Laser-produced surface nanostructures show considerable promise for many applications while fundamental questions concerning the corresponding mechanisms of structuring are still debated. Here, we present a simple physical model describing those mechanisms happened in a thin metal film on dielectric substrate irradiated by a tightly focused ultrashort laser pulse. The main ingredients included into the model are (i) the film–substrate hydrodynamic interaction, melting and separation of the film from substrate with velocity increasing with increase of absorbed fluence; (ii) the capillary forces decelerating expansion of the expanding flying film; and (iii) rapid freezing into a solid state if the rate of solidification is comparable or larger than hydrodynamic velocities. The developed model and performed simulations explain appearance of microbump inside the focal spot on the film surface. The model follows experimental findings about gradual transformation of the bump from small parabolic to a conical shape and to the bump with a jet on its tip with increasing fluence. Disruption of the bump as a result of thinning down the liquid film to a few interatomic distances or due to mechanical break-off of solid film is described together with the jetting and formation of one or many droplets. Developed theory opens door for optimizing laser parameters for intended nanostructuring in applications.

Spatio-temporal linear stability analysis of stratified planar wakes: Velocity and density asymmetry effects

This paper explores the hydrodynamic stability of bluff body wakes with non-uniform mean density, asymmetric mean density, and velocity profiles. This work is motivated by experiments [S. Tuttle et al., “Lean blow off behavior of asymmetrically-fueled bluff body-stabilized flames,” Combust. Flame 160, 1677 (2013)], which investigated reacting wakes with equivalence ratio stratification and, hence, asymmetry in the base flow density profiles. They showed that highly stratified cases exhibited strong, narrowband oscillations, suggestive of global hydrodynamic instability. In this paper, we present a local hydrodynamic stability analysis for non-uniform density wakes that includes base flow asymmetry. The results show that increasing the degree of base density asymmetry generally has a destabilizing effect and that increasing base velocity asymmetry tends to be stabilizing. Furthermore, we show that increasing base density asymmetry slightly decreases the absolute frequency and that increasing the base velocity asymmetry slightly increases the absolute frequency. In addition, we show that increasing the degree of base density asymmetry distorts the most absolutely unstable hydrodynamic mode from its nominally sinuous structure. This distorted mode exhibits higher amplitude pressure and velocity oscillations near the interface with the smaller density jump than near the one with the bigger density jump. This would then be anticipated to lead to strongly non-symmetric amplitudes of flame flapping, with much stronger flame flapping on the side with lower density ratio. These predictions are shown to be consistent with experimental data. These comparisons support the analytical predictions that increased base density asymmetry are destabilizing and that hydrodynamic velocity fluctuation amplitudes should be greatest at the flame with the lowest density jump.

Numerical and experimental study of field synergy analysis in water jet impingement based on minimum entropy generation method

Most detailed reviews of field synergy principle FSP are mainly focused on numerical approaches, while validating first deduction of FSP experimentally is very rare. Therefore, an experimental analysis is carried out on a simple heated plate surface. Experiments are conducted using infrared thermal-vision system and a professional high-speed camera. The field study concerns the hydrodynamic and water jet velocity ratio based on four different configurations under relatively low jet Reynolds number ranging from 2602 to 6505 and to be optimized by FSP. New analytical equations are developed to verify experimentally the synergy between velocity streamline and temperature field as well as synergy number especially in the mid integral areas where images have clear appearance along the lateral direction of the heated plate. Laminar heat flow field synergy equation is developed based on the minimum entropy generation MEG method, and it is treated for relatively low Reynolds number in order to reduce computational effort and time cost. The new proposed laminar heat synergy optimization equation is deduced by setting irreversibility of heat transfer process under the additional assumption that constraint of thermal generation by mechanism of viscous dissipation is considered. The variation principles with respect to velocity give new Navier–Stokes equation with additional volume force, which is constructed through functional variation of Lagrange multipliers to numerically simulate convective heat transfer. Solving simultaneously the field synergy equations (Fx​, Fy​, Fz) for input constant related to viscous dissipation equal to −1.0E05 will give several synergy flow fields which are followed by gradual increase of entropy generation rate as ratio of H/D increases.

Consistent Hydrodynamics for Phase Field Crystals.

We use the amplitude expansion in the phase field crystal framework to formulate an approach where the fields describing the microscopic structure of the material are coupled to a hydrodynamic velocity field. The model is shown to reduce to the well-known macroscopic theories in appropriate limits, including compressible Navier-Stokes and wave equations. Moreover, we show that the dynamics proposed allows for long wavelength phonon modes and demonstrate the theory numerically showing that the elastic excitations in the system are relaxed through phonon emission.

Application of the Convective Diffusion Equation with Potential-Dependent Boundary Conditions to the Charge Transfer Problem in Four-Electrode Electrochemical Cell on the Condition of Small Hydrodynamic Velocity

Application of the Convective Diffusion Equation with Potential-Dependent Boundary Conditions to the Charge Transfer Problem in Four-Electrode Electrochemical Cell on the Condition of Small Hydrodynamic Velocity

Breatherlike defects and their dynamics in the one-dimensional roll structure of twisted nematics

The dynamics of the nonsingular defects in the periodic structures of the rolls that appear in π/2-twisted nematic liquid crystals during electroconvection is studied experimentally and theoretically. The roll structures in twisted nematics are characterized by the presence of an axial component of the hydrodynamic flow velocity with opposite directions in neighboring rolls. The critical oscillation frequency of structural defects is quantitatively estimated using a nonlinear equation of motion for roll displacements. It is found that a pair of edge dislocations with topological charges of +1 and–1 nucleates and annihilates periodically during the oscillations of a defect with a nonsingular core. Oscillating defects with a zero topological charge is shown to correspond to the solution of the sine-Gordon equation in the form of standing breathers. Asymmetry is detected in the full oscillation cycle of a breather defect, and it is related to the twist symmetry of a twist nematic. This asymmetry is taken into account as effective anisotropic friction. The behavior of a breather on a trap, namely, a classical defect (dislocation), is investigated. Dislocation motion is shown to be anisotropic in the oscillation cycle: in one direction, a dislocation moves regularly; in the second phase, the transition into the initial state proceeds via the decay of the breather into a dipole pair of dislocations of opposite signs followed by their annihilation.

Temperature dependence of the velocity-density relation for liquid metals under high pressure: Implications for the Earth’s outer core

The relationship between the sound velocity, density, and temperature of liquid metals is important when one tries to interpret the seismic velocity profile and infer the chemical compositions of the Earth’s outer core. We, therefore, have experimentally measured the longitudinal acoustic (LA) velocity of liquid indium under high P-T conditions. Also, we examined a Hugoniot data of liquid iron by comparing with an existing equation of state (EoS). The LA velocities of liquid and solid indium at pressures up to 6.7 GPa and temperatures mostly at 710 K were measured using inelastic X-ray scattering (IXS) to probe samples in an externally heated diamond-anvil cell. A thermal EoS for liquid indium derived from existing literature was used to calculate the density for the IXS measurements and to provide an independent check on the sound velocities. The IXS data are consistent with the hydrodynamic LA velocity derived from the liquid EoS, implying that the positive dispersion is minimal in liquid indium. The velocity-density relation for liquid indium derived from the EoS has temperature dependence, implying that Birch’s law does not hold for the liquid phase. Similarly we calculated the temperature-velocity-density relation of liquid iron over the Earth’s core range from a recently reported EoS. The resulting velocity-density relation is also temperature dependent, indicating that liquid iron thus does not follow Birch’s law. The violation of Birch’s law implies that the Hugoniot data cannot be directly compared with seismological observations because of the different temperature ranges. Formulation of the temperature-velocity-density of liquid iron-alloys supported by experimental measurements provides better understanding of the thermodynamic state of the Earth’s core.

Evaluation of the physical parameters of gas in the neutral atmospheres of comets: Method of isophots

A new method of isophots is considered in application to the evaluation of the physical parameters of gas in the neutral atmospheres of comets. It is compared to the method of circular diaphragms. The use of the method of isophots in the photometric observations of comet 2009/P1 (Garradd) has shown that it is completely applicable to the retrieving of the hydrodynamic velocity of the gas outflow and the lifetime of molecules in the neutral atmospheres of comets.

2D-CFD Analysis of the Fluid Pressure and Velocity Distribution of Experimentally Machine Hammer Peened Surface Structures in Hydrodynamic Applications

Machine hammer peening is an incremental forming process for high frequency surface finishing of technical components. Recently, machine hammer peening has attracted automotive industry’s attention for the surface finishing and structuring of deep drawing tools. Deep drawing tools surface structured by machine hammer peening are characterized by beneficial friction and wear characteristics in lubricated sliding contacts. However, the physics of hydrodynamic effects in machine hammer peened structures is yet insufficiently researched. Therefore, this work investigates the hydrodynamic effects in surface structures generated by machine hammer peening using a two-dimensional computational fluid dynamic analysis. The effects of structure geometry, structure arrangement and selected sliding parameters on the hydrodynamic fluid pressure and velocity distribution within the structures are analysed. It was observed, that the sliding direction and the structure arrangement have a significant influence on the hydrodynamic fluid pressure maximum.

Chain of kinetic equations for the distribution functions of particles in simple liquid taking into account nonlinear hydrodynamic fluctuations

Chain of kinetic equations for non-equilibrium single, double and s-particle distribution functions of particles is obtained taking into account nonlinear hydrodynamic fluctuations. Non-equilibrium distribution function of non-linear hydrodynamic fluctuations satisfies a generalized Fokker–Planck equation. The method of non-equilibrium statistical operator by Zubarev is applied. A way of calculating the structural distribution function of hydrodynamic collective variables and their hydrodynamic velocities (above Gaussian approximation) contained in the generalized Fokker–Planck equation for the non-equilibrium distribution function of hydrodynamic collective variables is proposed.

Spontaneous Flows in Suspensions of Active Cyclic Swimmers

Many swimming cells rely on periodic deformations to achieve locomotion. We introduce in this work a theoretical model and numerical simulations in order to elucidate the impact of these cyclic strokes on the emergence of mesoscale structures and collective motion in swimmer suspensions. The model extends previous kinetic theories for populations of identical swimmers to the case of self-propelled particles undergoing transitions between pusher and puller states, and is applied to quantify how the unsteadiness of the hydrodynamic velocity field, to which each swimmer population contributes, affects the onset and characteristics of spontaneous flows. A linear stability analysis reveals that the sign of the population-averaged dipole determines the stability of the uniform isotropic state, with suspensions dominated by pushers being subject to growing nematic bend fluctuations. Stochastic transitions, however, are also seen to provide an additional damping mechanism. To investigate the population dynamics above the instability threshold, we also perform direct particle simulations based on a slender-body model, where the growth or decay of the active power generated by the swimmers is found to be a robust measure of the structural and dynamical instability.

Anomalous sea surface structures as an object of statistical topography.

By exploiting ideas of statistical topography, we analyze the stochastic boundary problem of emergence of anomalous high structures on the sea surface. The kinematic boundary condition on the sea surface is assumed to be a closed stochastic quasilinear equation. Applying the stochastic Liouville equation, and presuming the stochastic nature of a given hydrodynamic velocity field within the diffusion approximation, we derive an equation for a spatially single-point, simultaneous joint probability density of the surface elevation field and its gradient. An important feature of the model is that it accounts for stochastic bottom irregularities as one, but not a single, perturbation. Hence, we address the assumption of the infinitely deep ocean to obtain statistic features of the surface elevation field and the squared elevation gradient field. According to the calculations, we show that clustering in the absolute surface elevation gradient field happens with the unit probability. It results in the emergence of rare events such as anomalous high structures and deep gaps on the sea surface almost in every realization of a stochastic velocity field.

Spectral Analysis of Velocity Fluctuations in the Vicinity of a Bias Flow Liner With Respect to the Damping Efficiency

Bias flow liners are perforated walls with an additional bias flow through the perforation. A common application is their integration in walls of hot gas areas, e.g. in combustion chambers of aero engines, for cooling. It is wellknown for a long time that the bias flow additionally provides a substantial amount of acoustic damping. However, until now the detailed damping mechanisms are not fully understood. Therefore, this study takes a closer look at the energy transfer from a propagating acoustic wave to the flow velocity field, which can be measured in the vicinity of the perforated wall. Two laser-optical measurement techniques, Doppler global velocimetry with sinusoidal laser frequency modulation (FM-DGV) and acoustic particle image velocimetry (A-PIV), were applied to a bias flow liner. The time-continuous velocity signal measured by FM-DGV was used to perform a spectral analysis of the fluctuating velocity components above the liner surface. This was done for different acousticexcitation frequencies, where the liner exhibits different dissipation rates. After removal of the acoustic Content from the power spectral density, the hydrodynamic velocity components feature a spectral augmentation in the vicinity of the excitation frequency. The effect appears downstream of the holes. The amount of spectral Augmentation correlates to the dissipation rate of the liner at the different excitation frequencies. Consequently, a certain transfer of acoustic energy into turbulent velocity fluctuations occurs in different frequency regimes. This energy transfer is, as a matter of fact, a function of the dissipation rate of the liner. Moreover, it has a strong dependence on the spatial location with respect to the orifice of the bias flow liner.

Impact of Water-Sediment Exchange on Underwater Terrain Shaping Process for a Tide-Influenced Waterfront Lake

AbstractThis study selected a typical waterfront lake, the Inner Lake, as the research area. Based on field measurements and laboratory experiments, the basic properties of sediment particles were analyzed, including size, bulk and dry bulk density, and hydrostatic and hydrodynamic settling velocity. With the finite-volume method, the flux vector splitting (FVS) scheme was employed to establish a two-dimensional unsteady flow and sediment mathematical model. The underwater terrain shaping processes in the short term (2017), middle term (2020), and long term (2025) were predicted. The results showed that sediment deposition thickness will significantly increase in the Inner Lake, reaching 13.5 cm in the short term (January 2017), 28.6 cm in the middle term (January 2020), and 55.2 cm in the long term (January 2025). Owing to the strong hydrodynamic condition of the Leading Channel, sediment deposition there is the lowest, with the lake bed elevating rate at 3.92 cm·a−1 on average. The elevating rate at th...

The hydrodynamic description for the system of self-propelled particles: Ideal Viscek fluid

We use the method of the microscopic phase density to get the kinetic equation for the system of self-propelled particles with Vicsek-like alignment rule. The hydrodynamic equations are derived for the ordered phase taking into account the mean-field force only. The equation for the hydrodynamic velocity plays the role of the Euler equation for the self-propelled Vicsek fluid. The hydrodynamics of such ideal self-propelled fluid demonstrates the dynamical transition from disordered initial state to the completely ordered motion. To take the noise into account we consider how the framework of the local equilibrium approximation affects the hydrodynamic equations and the viscous tensor and show that in such approximation the shear viscosity vanishes.

Particle dynamics and rapid trapping in electro-osmotic flow around a sharp microchannel corner

We study here the curious particle dynamics resulting from electro-osmotic flow around a microchannel junction corner whose dielectric walls are weakly polarizable. The hydrodynamic velocity field is obtained via superposition of a linear irrotational term associated with the equilibrium zeta potentials of both the microchannel and particle surfaces and the nonlinear induced-charge electro-osmotic flow which originates from the interaction of the externally applied electric field on the charge cloud it induces at the solid-liquid interface. The particle dynamics are analyzed by considering dielectrophoretic forces via the addition of a mobility term to the flow field in the limit of Stokes drag law. The former, non-divergence free term is responsible for migration of particles towards the sharp microchannel junction corner, where they can potentially accumulate. Experimental observations of particle trapping for various applied electric fields and microparticle size are rationalized in terms of the growing relative importance of the dielectrophoretic force and induced-charge contributions to the global velocity field with increasing intensity of the externally applied electric field.

A novel design of brush scrubbing in post-CMP cleaning

Concentric and eccentric brush scrubbing behaviors of the hard disk drive (HDD) substrates in post-chemical mechanical polishing (CMP) process have been investigated with kinetic brush–disk contact trajectory analysis and hydrodynamic fluid velocity simulation as well as experimental studies. The adhesion forces as well as the hydrodynamic drag force for particle removal are also discussed. The brush nodules–disk contact trajectories with eccentric scrubbing cover the full surface of the disk, however, the trajectories with concentric scrubbing only accumulate on several concentric circular bands aligned along the discrete distribution of brush nodules. The fluid hydrodynamic force with eccentric scrubbing is larger than that with concentric scrubbing. The experimental results have found that the disk surfaces with eccentric scrubbing have approximately 40% lower particle count than that with concentric scrubbing. The modeling analysis and experimental results have found that the eccentric scrubbing has higher particle removal efficiency for the work piece with a hole at the center.