Modeling, numerical methods, and simulation for particle-fluid two-phase flow problems

In this paper, we study the issues of modeling, numerical methods, and simulation with comparison to experimental data for the particle-fluid two-phase flow problem involving a solid-liquid mixed medium. The physical situation being considered is a pulsed liquid fluidized bed. The mathematical model is based on the assumption of one-dimensional flows, incompressible in both particle and fluid phases, equal particle diameters, and the wall friction force on both phases being ignored. The model consists of a set of coupled differential equations describing the conservation of mass and momentum in both phases with coupling and interaction between the two phases. We demonstrate conditions under which the system is either mathematically well posed or ill posed. We consider the general model with additional physical viscosities and/or additional virtual mass forces, both of which stabilize the system. Two numerical methods, one of them is first-order accurate and the other fifth-order accurate, are used to solve the models. A change of variable technique effectively handles the changing domain and boundary conditions. The numerical methods are demonstrated to be stable and convergent through careful numerical experiments. Simulation results for realistic pulsed liquid fluidized bed are provided and compared with experimental data. (C) 2004 Elsevier Ltd. All rights reserved.

I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10⁵ g. The technique includes bar-coded projectile, sabot-projectile separation, detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10⁵ g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P_max, is linearly scaled with initial projectile energy per unit cross-section area, e_s , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_max(mm) 1.15e_s (J/mm² ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t_max, increases slowly with e_s and does not depend on projectile radius approximately, the dependence of t_max on projectile length is suggested to be described by t_max(μs) = 2.08e_s (J/mm² + 349.0 x m/(πR²), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10⁴, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P_max, and normalized penetration time, t/t_max, as P/P_max = f(t/t_max, where f is a function of t/t_max. After f(t/t_max is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ_f/σ⁰_f = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰_f and έ are reference compressive strength and strain rate, respectively). The non-dispersive Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO₂ were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO₂ to planar shock loading can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ₀ = 3.655 gj cm³ . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge⁺⁴ with O^-2 in vitreous GeO₂ occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO₂ to that on vitreous GeO₂ demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO₂ and fused SiO₂ are found to coincide approximately if pressure in fused SiO₂ is scaled by the ratio of fused SiO₂to vitreous GeO₂ density. This result, as well as the same structure, provides the basis for considering vitreous Ge0₂ as an analogous material to fused SiO₂ under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO₂ decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO₂ decays faster than a linear elastic wave; (2) In vitreous GeO₂ , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^-3.35 , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO₂ and vitreous GeO₂ is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Electrotactile touch surface by using transparent graphene

In this work we present a flexible Electrostatic Tactile (ET) surface/display realized by using new emerging material graphene. The graphene is transparent conductor which successfully replaces previous solution based on indium-thin oxide (ITO) and delivers more reliable solution for flexible and bendable displays. The electrostatic tactile surface is capable of delivering programmable, location specific tactile textures. The ET device has an area of 25 cm 2, and consists of 130 μm thin optically transparent (>76%) and mechanically flexible structure overlaid unobtrusively on top of a display. The ET system exploits electro vibration phenomena to enable on-demand control of the frictional force between the user's fingertip and the device surface. The ET device is integrated through a controller on a mobile display platform to generate fully programmable range of stimulating signals. The ET haptic feedback is formed in accordance with the visual information displayed underneath, with the magnitude and pattern of the frictional force correlated with both the images and the coordinates of the actual touch in real time forming virtual textures on the display surface (haptic virtual silhouette). To quantify rate of change in friction force we performed a dynamic friction coefficient measurement with a system involving an artificial finger mimicking the actual touch. During operation, the dynamic friction between the ET surface and an artificial finger stimulation increases by 26% when the load is 0.8 N and by 24% when the load is 1 N. © 2012 ACM.

Nanostructure and mechanical measurement of highly oriented lamellae of melt-drawn HDPE by scanning probe microscopy

Scanning probe microscopy was used to simultaneously determine the molecular chain structure and intrinsic mechanical properties, including anisotropic elastic modulus and friction, for lamellae of highly oriented high-density polyethylene (HDPE) obtained by the melt-drawn method. The molecular-scale image of the highly oriented lamellae by friction force microscopy (FFM) clearly shows that the molecular chains are aligned parallel to the drawing direction, and the periodicities along and perpendicular to the drawing direction are 0.26 and 0.50 nm, respectively. The results indicate that the exposed planes of the lamellae resulting from the melt-drawn method are (200), which is consistent with results of transmission electron microscopy and electron diffraction. Because of the high degree of anisotropy in the sample, coming from alignment of the molecular chains along the drawing direction, the measured friction force, F, determined by FFM is strongly dependent on the angle, theta, between the scanning direction and the chain axis. The force increases as theta is increased from 0 degrees (i.e., parallel to the chain axis) to 90 degrees (i.e., perpendicular to the chain axis). The structural anisotropy was also found to strongly influence the measurements of the transverse chain modulus of the polymer by the nanoindentation technique. The measured value of 13.8 GPa with transverse modulus was larger than the value 4.3 GPa determined by wide-angle X-ray diffraction, which we attributed to anisotropic deformation of the lamellae during nanoindentation measurements that was not accounted for by the elastic treatment we adopted from Oliver and Pharr. The present approach using scanning probe microscopy has the advantage that direct correlations between the nanostructure, nanotribology, and nanomechanical properties of oriented samples can be determined simultaneously and simply.

Correlated electron-ion dynamics in metallic systems

In this paper we briefly discuss the problem of simulating non-adiabatic processes in systems that are usefully modelled using molecular dynamics. In particular we address the problems associated with metals, and describe two methods that can be applied: the Ehrenfest approximation and correlated electron-ion dynamics (CEID). The Ehrenfest approximation is used to successfully describe the friction force experienced by an energetic particle passing through a crystal, but is unable to describe the heating of a wire by an electric current. CEID restores the proper heating.

Scattering theory of cooling and heating in optomechanical systems

We present a one-dimensional scattering theory which enables us to describe a wealth of effects arising from the coupling of the motional degree of freedom of scatterers to the electromagnetic field. Multiple scattering to all orders is taken into account. The theory is applied to describe the scheme of a Fabry-Perot resonator with one of its mirrors moving. The friction force, as well as the diffusion, acting on the moving mirror is derived. In the limit of a small reflection coefficient, the same model provides for the description of the mechanical effect of light on an atom moving in front of a mirror.

Proposal of a floating mechanism based on magnetic levitation method toward EEG-driven robotic system

We discussed a floating mechanism based on quasi-magnetic levitation method that can be attached at the endpoint of a robot arm in order to construct a novel redundant robot arm for producing compliant motions. The floating mechanism can be composed of magnets and a constraint mechanism such that the repelling force of the magnets floats the endpoint part of the mechanism stable for the guided motions. The analytical and experimental results show that the proposed floating mechanism can produce stable floating motions with small inertia and viscosity. The results also show that the proposed mechanism can detect small force applied to the endpoint part because the friction force of the mechanism is very small.

Úlceras de pressão: um estudo com pacientes de unidade de terapia intensiva

To characterize patients according to gender, age category, internment time, diagnostical hypothesis and location of the pressure ulcer; to identify the susceptibility conditions, intrinsical and extrinsical factors present on ICU patients and to verify on the existence of association between the susceptibility conditions and the intrinsecal and extrinsecal factors on the occurrence of PU. Methods: It is a descriptive study, of longitudinal design of the panel type, with quantitative approach, performed on two ICU s of a private hospital located in Natal/RN, with 40 patients interned at these units. The data collection was performed on all three shifts through a structured observation and physical exam of the patients' skin form seeking to identify the presence of PU. Results: The greatest occurence of PU was on individuals of the male gender (70%) when compared to the female gender (30%), that difference being statistically significant (p=0,0267), with the male gender presenting 4,3 times greater chance of developing PU than the female; the predominant age category was from 60 years of age on (85%), 60,0% presented 1 to 2 PU s after 7 (seven) days of permanence in the ICU s, the predominant diagnostical hypothesis on the patients with PU were the respiratory diseases (42,3%) and the most frequent locations of PU were the sacral region (40,0%) and heels (36,0%). 25 PU s of stage I were diagnosed on 50,0% of the followed patients, with general incidence of 50,0% on both ICUs. from the 88 variables researched, 75 were identified on the patients from the study, being the predominant conditions (anemia, hypotension, leukocytosis, other diseases hypertension blood pressure, cardiac insuffience, pneumonia - and ansiolythic), the intrinsecal factors (diminished muscular strenght and/or mass, discrete edema, totally compromised mobile coordination and total inability for movement on the bed) and the extrinsecal factors (inadequate mattress type, permanence on a single position for >2 hours, shearing/friction force, bed clothes with folds that leave marks on the body, pressure force) predominated on patients with PU. The male gender variables (p=0,0267,OR=4,3), sedation (p=0,0006,OR=4,1), psychomotive agitation (p=0,0375,OR=5,8) and leukocytosis (p=0,0285,OR=5,0) presented a significant statistical diference when analyzed independently. We verified an association of 17,3%, statistically significant (p=0,0384), between the susceptibility conditions (anemia, leukocytosis and hypotension), the intrinsecal factors (age equal or above 60 years, diminished/absent pain sensibility and smooth, fine or delicate skin) and the extrinsecal factors (inadequate mattress, pressure forces, shearing/friction force, permanence on a single position for more than 2 hours, elevation between 30 to 45 degrees and inadequate bed clothes' conditions), with a chance ratio of 4,6 times the risk of occurrence of PU on the patients that presented the referred association. Conclusion: The incidence of PU detected on the ICU-interned patients was high and we made evident the existence of association between the susceptibility conditions, the intrinsecal and extrinsecal factors on the occurrence of PU s on the ICUinterned patients, and thus we accept the alternative hypothesis proposed on the study

Análise tribológica de um sistema de acionamento alternativo de pigs para a indústria do petróleo

It is analyzed through the concepts of tribology and mechanical contact and damage the suggestion of implementing a backup system for traction and passage of Pipeline Inspection Gauge (Pig) from the inside of pipelines. In order to verify the integrity of the pipelines, it is suggested the possibility of displacement of such equipment by pulling wires with steel wires. The physical and mechanical characteristics of this method were verified by accelerated tests in the laboratory in a tribological pair, wire versus a curve 90. It also considered the main mechanisms of wear of a sliding system with and without lubricant, in the absence and presence of contaminants. To try this, It was constructed a test bench able to reproduce a slip system, work on mode back-and-forth ("reciprocation"). It was used two kinds of wires, a galvanized steel and other stainless steel and the results achieved using the two kinds of steel cables were compared. For result comparative means, it was used steel cables with and without coating of Poly Vinyl Chloride (PVC). The wires and the curves of the products were characterized using metallographic analysis, microhardness Vickers tests, X-ray diffraction (XRD), X-Ray Refraction (XRF) and tensile tests. After the experiments were analyzed some parameters that have been measurable, it demonstrates to the impracticality of this proposed method, since the friction force and the concept of alternating request at the contact between the strands of wire and the inner curves that are part ducts caused severe wear. These types of wear are likely to cause possible failures in future products and cause fluid leaks

Competition between suppression and production of Fermi acceleration

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

O uso da análise de Fourier, de Wavelets e dos expoentes de Lyapunov no estudo de um sistema dinâmico não-ideal com atrito seco e excitação externa

Pós-graduação em Física - IGCE

Abordagem experimental da força de atrito em aulas de Física do Ensino Médio

In this paper we propose and describe the performance of an experimental activity to address the concept of friction in High School Physics practical classes. We use a low-cost and simple construction device that enables the determination of the coefficient of static friction between two materials through three different procedures. The results were coherent, with small percentage deviation, which gives reliability to the activity and can stimulate discussions in class. The activity also allows greater contextualization of concepts that are usually discussed only theoretically, requiring a higher abstraction level of the students. This can stimulate discussions and greater interaction between teacher and students.

Nonlinear ball and beam control system identification

The Ball and Beam system is a common didactical experiment in control laboratories that can be used to illustrate many different closed-loop control techniques. The plant itself is subjected to many nonlinear effects, which the most common comes from the relative motion between the ball and the beam. The modeling process normally uses the lagrangean formulation. However, many other nonlinear effects, such as non-viscous friction, beam flexibility, ball slip, actuator elasticity, collisions at the end of the beam, to name a few, are present. Besides that, the system is naturally unstable. In this work, we analyze a subset of these characteristics, in which the ball rolls with slipping and the friction force between the ball and the beam is non-viscous (Coulomb friction). Also, we consider collisions at the ends of the beam, the actuator consists of a (rubber made) belt attached at the free ends of the beam and connected to a DC motor. The model becomes, with those nonlinearities, a differential inclusion system. The elastic coefficients of the belt are experimentally identified, as well as the collision coefficients. The nonlinear behavior of the system is studied and a control strategy is proposed.

Model for the Dynamics of the Cytoskeleton.

Particle tracking of microbeads attached to the cytoskeleton (CSK) reveals an intermittent dynamic. The mean squared displacement (MSD) is subdiffusive for small Δt and superdiffusive for large Δt, which are associated with periods of traps and periods of jumps respectively. The analysis of the displacements has shown a non-Gaussian behavior, what is indicative of an active motion, classifying the cells as a far from equilibrium material. Using Langevin dynamics, we reconstruct the dynamic of the CSK. The model is based on the bundles of actin filaments that link themself with the bead RGD coating, trapping it in an harmonic potential. We consider a one- dimensional motion of a particle, neglecting inertial effects (over-damped Langevin dynamics). The resultant force is decomposed in friction force, elastic force and random force, which is used as white noise representing the effect due to molecular agitation. These description until now shows a static situation where the bead performed a random walk in an elastic potential. In order to modeling the active remodeling of the CSK, we vary the equilibrium position of the potential. Inserting a motion in the well center, we change the equilibrium position linearly with time with constant velocity. The result found exhibits a MSD versus time ’tau’ with three regimes. The first regime is when ‘tau’ < ‘tau IND 0’, where ‘tau IND 0’ is the relaxation time, representing the thermal motion. At this regime the particle can diffuse freely. The second regime is a plateau, ‘tau IND 0’ < ‘tau’ < ‘tau IND 1’, representing the particle caged in the potential. Here, ‘tau IND 1’ is a characteristic time that limit the confinement period. And the third regime, ‘tau’ > ‘tau IND 1’, is when the particles are in the superdiffusive behavior. This is where most of the experiments are performed, under 20 frames per second (FPS), thus there is no experimental evidence that support the first regime. We are currently performing experiments with high frequency, up to 100 FPS, attempting to visualize this diffusive behavior. Beside the first regime, our simple model can reproduce MSD curves similar to what has been found experimentally, which can be helpful to understanding CSK structure and properties.

Computersimulationen zur Dynamik von verdünnten und halbverdünnten Polymerlösungen

Diese Arbeit legt eine neue Methode zur Simulation derDynamik vonPolymeren in verdünnter und halbverdünnterLösung vor. Die Effizienz der Methode und derAnstieg der Computerleistung in den letzten Jahren erlaubenes, weitaus komplexere Systeme als bisher zu betrachten.Die neue Methode modelliert die Polymere als Kugel-Feder-Ketten, die mittels Molekulardynamik simuliertwerden. Die Flüssigkeit wird durch die numerischeLösung der Kontinuitätsgleichungund der Navier-Stokes-Gleichung mit derLattice-Boltzmann-Methodemodelliert. Die Flüssigkeit wird über eineReibungskraft an die Monomere des Kugel-Feder-Modellsgekoppelt. Die Methode wird auf das Problem einer flexiblen EinzelketteimLösungsmittel angewendet. Der Vergleich derErgebnisse mit einer existierenden reinenMolekulardynamik-Simulationergibt Übereinstimmung innerhalb weniger Prozent,während die neueMethode um etwa einen Faktor 20 weniger CPU-Zeitbenötigt. Eine semiflexible Kette zeigt völliganderes Verhalten: Die Hydrodynamik spielt im Gegensatz zur flexiblen Ketteeineuntergeordnete Rolle. Simulationen von halbverdünntenLösungen flexibler Kettenbestehend aus insgesamt 50000 Monomeren zeigen zum erstenMal direkt dieAbschirmung sowohl der Volumenausschluss-Wechselwirkung alsauch derHydrodynamik.