Simple Hydrodynamic Model Research Articles

CFD simulation of pressure fluctuation characteristics in the gas-solid fluidized bed: Comparisons with experiments

A simple hydrodynamic model based on two-fluid theory, taking into account the effect of discrete particles on both the gas- and solid-phase momentum equations, was used to numerically investigate the pressure fluctuation characteristics in a gas-solid fluidized bed with the aid of CFX 4.4, a commercial CFD software package, by adding user-defined Fortran subroutines. Numerical simulations together with typical experimental measurements show that pressure fluctuations originate above the distributor when a gas pulse is injected into the fluidized bed. The pressure above the bubble gradually increases due to the presence of a rising bubble. When the bubble passes through the bed surface, the pressure near the bed surface gradually decreases to a lower value. Moreover, the pressure signals in the bubbling fluidized beds show obviously periodic characteristics. The major frequency of pressure fluctuations at the same vertical position is affected slightly by the operating gas velocity, and the amplitude of pressure fluctuations is related to both the operating gas velocity and the vertical height. In this study, the influence of the operating gas velocity on the pressure wave propagation velocity can be ignored, and only two peak frequencies in the power spectrum of the pressure fluctuations are observed which are associated with the bubble formation above the distributor and its eruption at the bed surface.

Dynamics of a Tunable Superfluid Junction

We study the population dynamics of a Bose-Einstein condensate in a double-well potential throughout the crossover from Josephson dynamics to hydrodynamics. At barriers higher than the chemical potential, we observe slow oscillations well described by a Josephson model. In the limit of low barriers, the fundamental frequency agrees with a simple hydrodynamic model, but we also observe a second, higher frequency. A full numerical simulation of the Gross-Pitaevskii equation giving the frequencies and amplitudes of the observed modes between these two limits is compared to the data and is used to understand the origin of the higher mode. Implications for trapped matter-wave interferometers are discussed.

Behavior of a train of droplets in a fluidic network with hydrodynamic traps

The behavior of a droplet train in a microfluidic network with hydrodynamic traps in which the hydrodynamic resistive properties of the network are varied is investigated. The flow resistance of the network and the individual droplets guide the movement of droplets in the network. In general, the flow behavior transitions from the droplets being immobilized in the hydrodynamic traps at low flow rates to breaking up and squeezing of the droplets at higher flow rates. A state diagram characterizing these dynamics is presented. A simple hydrodynamic circuit model that treats droplets as fluidic resistors is discussed, which predicts the experimentally observed flow rates for droplet trapping in the network. This study should enable the rational design of microfuidic devices for passive storage of nanoliter-scale drops.

Evolution of the stimulated Raman scattering instability in two-dimensional particle-in-cell simulations

In the following work, we analyze one-dimensional (1D) and two-dimensional (2D) full particle-in-cell simulations of stimulated Raman scattering (SRS) and study the evolution of Langmuir waves (LWs) in the kinetic regime. It is found that SRS reflectivity becomes random due to a nonlinear frequency shift and that the transverse modulations of LWs are induced by (i) the Weibel instability due to the current of trapped particles and (ii) the trapped particle modulational instability (TPMI) [H. Rose, Phys. Plasmas 12, 12318 (2005)]. Comparisons between 1D and 2D cases indicate that the nonlinear frequency shift is responsible for the first saturation of SRS. After this transient interval of first saturation, 2D effects become important: a strong side-scattering of the light, caused by these transverse modulations of the LW and the presence of a nonlinear frequency shift, is observed together with a strong transverse diffusion. This leads to an increase of the Landau damping rate of the LW, contributing to the limiting of Raman backscattering. A model is developed that reproduces the transverse evolution of the magnetic field due to trapped particles. Based on a simple 1D hydrodynamic model, the growth rate for the Weibel instability of the transverse electrostatic mode and magnetic field is estimated and found to be close to the TPMI growth rate [H. Rose et al., Phys. Plasmas 15, 042311 (2008)].

Multi-peak structure of the ion current in laser produced plasma

The experimental multi-peak structure of the transient ion current recorded by a charge-collector probe during the laser produced plasma expansion is reported for Sn and Li targets, and various focusing conditions and laser beam energies. Using a simple hydrodynamic model, the numerical simulations can reproduce well this type of behavior. Theoretically, a fractal hydrodynamic model is developed in a non-differentiable space-time. The solutions of Gaussian wave packet and ‘bouncing’ Gaussian wave packets types are found to explain the plasma expansion and to give a reasonable mathematical description of plasma splitting process.

On the Breakup of Patterned Nanoscale Copper Rings into Droplets via Pulsed-Laser-Induced Dewetting: Competing Liquid-Phase Instability and Transport Mechanisms

Nanolithographically patterned copper rings were synthesized, and the self-assembly of the rings into ordered nanoparticle/nanodrop arrays was accomplished via nanosecond pulsed laser heating above the melt threshold. The resultant length scale was correlated to the transport and instability growths that occur during the liquid lifetime of the melted copper rings. For 13-nm-thick rings, a change in the nanoparticle spacing with the ring width is attributed to a transition from a Raleigh-Plateau instability to a thin film instability because of competition between the cumulative transport and instability timescales. To explore the competition between instability mechanisms further, we carried out experiments with 7-nm-thick rings. In agreement with the theoretical predictions, these rings break up in both the azimuthal and radial directions, confirming that a simple hydrodynamic model captures the main features of the processes leading to the breakup.

Quantitative Experimental Study on the Transition between Fast and Delayed Coalescence of Sessile Droplets with Different but Completely Miscible Liquids

Quantitative experimental data on the coalescence behavior of sessile droplets with different but completely miscible liquids are presented. The liquids consist of various aqueous mixtures of different nonvolatile diols and carbon acids with surface tensions ranging from 33 to 68 mN/m, contact angles between 9 degrees and 20 degrees, and viscosities from 1 to 12 cP. Two distinctly different coalescence behaviors, a delayed and a fast regime, are found. The transition between the two behaviors is remarkably sharp. It is found that the coalescence mode depends predominantly on the differences in the surface tensions of the two droplets. If the surface tension difference exceeds approximately 3 mN/m, the coalescence is delayed. If it is less, droplet fusion occurs fast. Within the investigated parameter space, the transition seems independent from droplet size, absolute values of the surface tensions, and viscosity. Certain aspects of the experimental findings are explained with the simple hydrodynamic model presented in a recent publication.

Parameters identification for ship motion model based on particle swarm optimization

PurposeThe purpose of this paper is to identify the Nomoto ship model parameters accurately, in order to produce a very close match between the predictions based on the model and the full‐scale trials.Design/methodology/approachVarious ship maneuvering mathematical models have been used when describing the ship dynamics behavior. The Nomoto ship model is a class of simplified hydrodynamic derivative type models which are the most widely used, accepted and perhaps well developed. To determine the model parameters accurately, particle swarm optimization (PSO) is chosen as an evolution algorithm in this paper. This arithmetic can guarantee the convergence and global optimization ability, and avoid sinking into a local optimal solution.FindingsThe process of PSO for identifying the Nomoto ship model parameters is given.Research limitations/implicationsAvailability of the full‐scale trial data are the main limitations.Practical implicationsThe ship model parameters provide very useful advice in ship's autopilot process.Originality/valueThe paper presents a new parameter identification method for the second‐order Nomoto ship model based on PSO.

Adhesion Assays of Endothelial Cells on Nanopatterned Surfaces within a Microfluidic Channel

We present a simple analytical method to measure adhesion of human umbilical vein endothelial cells (HUVECs) and calf pulmonary artery endothelial cells (CPAEs) using nanopatterned, biodegradable poly(lactic-co-glycolic acid) (PLGA) surfaces for potential applications to artificial tissue-engineered blood vessel. Various nanostructured PLGA surfaces (350 nm wide ridges/350 nm grooves, 350 nm ridges/700 nm grooves, 350 nm ridges/1750 nm grooves, 700 nm ridges/350 nm grooves, 1050 nm ridges/350 nm grooves, 1750 nm ridges/350 nm grooves) and flat (unpatterned) surfaces were fabricated on the bottom of polydimethylsiloxane (PDMS) microfluidic channel of 2 mm width and 60 microm height by using thermal imprinting and irreversible channel bonding. To measure adhesion strength of HUVECs and CPAEs, the cells were exposed to a range of shear stress (12, 40, and 80 dyn/cm(2)) within the channels for 20 min after a preculture for 3 days and the remaining cells were counted under each condition. The highest adhesion strength was found on the surface of 700 nm wide ridges, 350 nm wide grooves for both cell types. The enhanced adhesion on nanopatterned surfaces can be attributed to two aspects: (i) contact guidance along the line direction and (ii) clustered focal adhesions. In particular, the contact guidance induced cell alignment along the line directions, which in turn lowers wall shear stress applied to the cell surface, as supported by a simple hydrodynamic model based on cell morphology.

Mean steady granular force on a wall overflowed by free-surface gravity-driven dense flows

We studied free-surface gravity-driven recirculating flows of cohesionless granular materials down a rough inclined plane and overflowing a wall normal to the incoming flow and to the bottom. We performed two-dimensional spherical particle discrete element simulations using a linear damped spring law between particles with a Coulomb failure criterion. High-frequency force fluctuations were observed. This paper focuses on the mean steady force exerted by the flow on the obstacle versus the macroscopic inertial number of the incoming flow, where the inertial number measures the ratio between a macroscopic deformation time scale and an inertial time scale. A triangular stagnant zone is formed upstream of the obstacle and sharply increases the mean force at low incoming inertial numbers. A simple hydrodynamic model based on depth-averaged momentum conservation is proposed. This analytical model predicts the numerical data fairly well and allows us to quantify the different contributions to the mean force on the wall. Beyond this model, our study provides an example of the ability of simple hydrodynamic approaches to describe the macroscopic behavior of an assembly of discrete particles not only in terms of kinematics but also in terms of forces.

Effects of compressional waves on the response of quartz crystal microbalance in contact with silicone oil droplets

Droplet quartz crystal microbalance has been demonstrated to be a promising tool for accessing material properties of fluids as well as the diverse solid-fluid interface phenomena. However, a microliter droplet localized on the surface of the electrodes of finite lateral size may cause a nonuniform distribution of the plane velocity, which may lead to surface normal fluid flow and generate the compressional waves above the crystal surface. In the present article, we report systematical investigation on both resonance frequency and dissipation measurements with reference to the small droplets of silicone oils spreading on the surface of the quartz crystal microbalance. Significant cyclical variations in the resonant frequency and resistance of the crystal have been observed as the characteristic sizes of the silicone oil droplets are close to specific values known to favor compressional wave generation. The experimental results have been compared with the theoretical values predicted by the finite element computation associated with a simple hydrodynamic model. Good agreement between theory and experiment has been obtained. The finding indicates that the small droplets on the crystal surface can act as resonant cavities for the compressional wave generation and that the greatest propensity to exhibit periodical resonance behavior in the frequency and dissipation measurements is at droplet height of λc/2 above the crystal surface.

The viscous overstability, nonlinear wavetrains, and finescale structure in dense planetary rings

This paper addresses the fine-scale axisymmetric structure exhibited in Saturn's A and B-rings. We aim to explain both the periodic microstructure on 150–220 m, revealed by the Cassini UVIS and RSS instruments, and the irregular variations in brightness on 1–10 km, reported by the Cassini ISS. We propose that the former structures correspond to the peaks and troughs of the nonlinear wavetrains that form naturally in a viscously overstable disk. The latter variations on longer scales may correspond to modulations and defects in the wavetrains' amplitudes and wavelength. We explore these ideas using a simple hydrodynamical model which captures the correct qualitative behaviour of a disk of inelastically colliding particles, while also permitting us to make progress with analytic and semi-analytic techniques. Specifically, we calculate a family of travelling nonlinear density waves and determine their stability properties. Detailed numerical simulations that confirm our basic results will appear in a following paper.

Nanoparticle assembly via the dewetting of patterned thin metal lines: Understanding the instability mechanisms

Nanosecond pulsed laser heating was used to control the assembly of spatially correlated nanoparticles from lithographically patterned pseudo-one-dimensional nickel lines. The evolution of the nickel line instabilities and nanoparticle formation with a correlated size and spacing was observed after a series of laser pulses. To understand the instabilities that direct the nanoparticle assembly, we have carried out nonlinear time-dependent simulations and linear stability analysis based on a simple hydrodynamic model. We find that the simulated time scales and length scales agree well with the experimental results. Interestingly, in both experiments and simulations, the instabilities associated with the line edge, and with the surface perturbation-driven mechanism, are found to result in similar particle sizes and spacings.

Soft microflow sensors

We present a rapid prototyping method for integrating functional components in conventional PDMS microfluidic devices. We take advantage of stop-flow lithography (D. Dendukuri, S. S. Gu, D. C. Pregibon, T. A. Hatton and P. S. Doyle, Lab Chip, 2007, 7, 818)(1) to achieve the in situ fabrication of mobile and deformable elements with a controlled mechanical response. This strategy is applied to the fabrication of microflow sensors based on a deformable spring-like structure. We show that these sensors have a large dynamic range, typically 3 to 4 orders of magnitude, and that they can be scaled down to measure flows in the nl per min range. We prepared sensors with different geometries, and their flow-elongation characteristics were modeled with a simple hydrodynamic model, with good agreement between model and experiments.

Purification of liquid indium by electric current-induced impurity migration in a static transverse magnetic field

We have developed an original method for indium purification. Our approach is based on the directional transfer of impurities by applying crossed electric and magnetic fields to the melting volume. The method reduced the concentration of nickel and tin by a factor of 10 while copper was reduced by a factor of 3. A simple hydrodynamic mass transport model describing the process was also derived.

The parameters of electron avalanches and the runaway of electrons in strong electric fields

A simple hydrodynamic model is suggested for the calculation of parameters of electron avalanches in a strong field, where the mean energy of electrons exceeds the ionization energy; this model is used to calculate the electron drift velocities and the coefficient of ionization and intensity of electric fields for cesium, helium, and xenon atoms in a wide range of variation of the mean energy of electron flow. It is demonstrated that, in a strong field, inelastic collisions make a determining contribution both to the loss of energy by electrons and to the loss of momentum. A criterion is suggested for the determination of the conditions of runaway of electrons. The dependence is obtained of the voltage, at which the runaway of electron with mean energy occurs, on the field intensity, mean energy, and the value of pd.

A Giant Metrewave Radio Telescope Multifrequency Radio Study of the Isothermal Core of the Poor Galaxy Cluster AWM 4

We present a detailed radio morphological study and spectral analysis of the wide-angle tail radio source 4C +24.36 associated with the dominant galaxy in the relaxed galaxy cluster AWM 4. Our study is based on new high-sensitivity GMRT observations at 235, 327, and 610 MHz and on literature and archival data at other frequencies. We find that the source major axis is likely oriented at a small angle with respect to the plane of the sky. The wide-angle tail morphology can be reasonably explained by adopting a simple hydrodynamical model in which both ram pressure (driven by the motion of the host galaxy) and buoyancy forces contribute to bend the radio structure. The spectral index progressively steepens along the source major axis from α ~ 0.3 in the region close to the radio nucleus to beyond 1.5 in the lobes. The results of the analysis of the spectral index image allow us to derive an estimate of the radiative age of the source of ~160 Myr. The cluster X-ray-emitting gas has a relaxed morphology and short cooling time, but its temperature profile is isothermal out to at least 160 kpc from the center. Therefore, we seek evidence of energy ejection from the central AGN to prevent catastrophic cooling. We find that the energy injected by 4C +24.36 in the form of synchrotron luminosity during its lifetime is far less than the energy required to maintain the high gas temperature in the core. We also find that it is not possible for the central source to eject the requisite energy in the intracluster gas in terms of the enthalpy of buoyant bubbles of relativistic fluid, without creating discernible large cavities in the existing X-ray XMM-Newton observations.

Hydrodynamic instabilities in the solar tachocline

Aims. We consider the stability of simple hydrodynamic models of the solar tachocline. This study addresses only the non-magnetic instabilities. In our model there is a strong radial shear, which because of the rotation is coupled to a latitudinal temperature gradient. We also assume there is a strong stable stratification, appropriate for the slow tachocline. Methods. These instabilities are calculated by finding the eigenvalues and eigenfunctions using a matrix-based collocation method. We also find analytic expressions for the key instabilities in the relevant asymptotic limits of strong stable stratification and small Prandtl number. Results. We find two distinct types of instability, axisymmetric modes of the Goldreich-Schubert type, and three-dimensional Eadytype modes. Both types of mode are affected by thermal diffusion. We find that the axisymmetric modes considered by Knobloch & Spruit (1982, A&A, 113, 261) are likely to dominate in the slow tachocline. The non-axisymmetric baroclinic instability of Eady-type may be important in the layers closer to the base of the convection zone.

Numerical prediction of MODUs drift during Hurricane Katrina

Severe hurricanes, such as Katrina, broke the mooring lines of a number of mobile offshore drilling units (MODU) deployed in the Gulf of Mexico and some of those MODUs went adrift. A drifting MODU may damage other critical elements of the offshore oil and gas infrastructure by colliding with floating or fixed production systems and transportation hubs, or by rupturing pipelines owing to their dragging anchors over the seabed. To avoid or mitigate the damage caused by a drifting MODU, it is desirable to understand the mechanics of the drift of a MODU under the impact of severe wind, wave and current and have the capability of predicting the trajectory of the drift. To explore the feasibility and accuracy of predicting the trajectory of a drifting MODU based on hindcast met-ocean conditions and limited knowledge of the condition of the drifting MODU, this study employed a simplified equation describing only the horizontal (surge, sway and yaw) motions of a MODU under the impact of steady wind, current and wave forces. The simplified hydrodynamic model neglects the first- and second-order oscillatory wave forces, unsteady wind forces (owing to wind gustiness), wave drift damping, and the effects of the body oscillation on the steady wind and current forces. It was assumed that the net effects of the oscillatory forces on the steady motion are insignificant. To verify the accuracy and feasibility of our simplified approach, the predicted drifting trajectories of two MODUs were compared with the corresponding measurements recorded by the global positioning system (GPS).

Lifetime of a two-dimensional air bubble

Air bubbles created in many viscous liquids rise up to the liquid-air interface and stay there for a while before exploding and disappearing. The lifetimes of such bubbles are governed by the thinning dynamics of the hemispherical liquid film separating the bubble from bulk air. Here, the lifetime of bubbles confined by two separated wetting plates is experimentally studied as the distance apart, viscosity, and bubble size are changed. Although the film is not hemispherical but takes a nontrivial shape, a relatively simple hydrodynamic model accounts for the observations.