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## Über dieses Buch

The book presents a collection of selected papers from the I Workshop of the Venezuelan Society of Fluid Mechanics held on Margarita Island, Venezuela from November 4 to 9, 2012. Written by experts in their respective fields, the contributions are organized into five parts: - Part I Invited Lectures, consisting of full-length technical papers on both computational and experimental fluid mechanics covering a wide range of topics from drops to multiphase and granular flows to astrophysical flows, - Part II Drops, Particles and Waves - Part III Multiphase and Multicomponent Flows - Part IV Atmospheric and Granular Flows - and Part V Turbulent and Astrophysical Flows. The book is intended for upper-level undergraduate and graduate students as well as for physicists, chemists and engineers teaching and working in the field of fluid mechanics and its applications. The contributions are the result of recent advances in theoretical and experimental research in fluid mechanics, encompassing both fundamentals as well as applications to fluid engineering design, including pipelines, turbines, flow separators, hydraulic systems and biological fluid elements, and to granular, environmental and astrophysical flows.

## Inhaltsverzeichnis

### Environmental Fluid Mechanics: Applications to Weather Forecast and Climate Change

Virtually all economic sectors as well as many public and private activities are affected in some measure by changes in weather and climate. Uncertainties in the scope and severity of these changes pose financial and social risks for individuals, businesses, and government agencies, with direct influence on food security and production, transport, health, electricity generation, and water resources. The vulnerability of human settlement to extreme weather and climate episodes is a further aspect that must be emphasized. Hence, achieving accurate weather and climate forecasts has important implications to modern society. In this chapter, we present an overview of the basic fluid-mechanical principles that govern the behaviour of weather and climate. We shall mainly focus on the numerical modelling of weather prediction and climate projections, spanning the range from the very first attempts, based on simple barotropic models, to the development of general circulation models of the atmosphere and ocean to the most recent multi-model ensemble forecasting systems.

Leonardo Di. G. Sigalotti, Eloy Sira, Jaime Klapp, Leonardo Trujillo

### Turbulent Diffusion of Heat at High Rayleigh Numbers

Thermal convection is observed in controlled laboratory experiments at very high Rayleigh numbers using a relatively large apparatus filled with low temperature helium gas. The low temperature environment offers two advantages toward the study of turbulent convection; namely the favorable properties of the working fluid in achieving very high Rayleigh numbers and the low thermal mass of the heated metallic surfaces at cryogenic temperatures. The latter property is exploited in order to provide a means of measuring an effective thermal diffusion coefficient of the buoyancy-driven turbulence by propagating thermal waves into the bulk and observing the damping of their amplitude with distance. The diffusivity measured directly in this way compares well with values inferred from the time-independent measurements of the global turbulent heat transfer at Rayleigh numbers of order

$$10^{9}$$

10

9

but are significantly different at Rayleigh numbers of order

$$10^{13}$$

10

13

which can be interpreted as a consequence of the formation of well developed bulk turbulence decoupled from the thermal boundary layers at the heated horizontal surfaces.

Joseph J. Niemela

### Numerical Simulation of Sliding Drops on an Inclined Solid Surface

We consider numerical simulations of drops sliding on an inclined solid surface. The simulations are performed using our in house research code JADIM based on the Volume of Fluid formulation of the mass and momentum equations. Special algorithms have been developed for the simulation of the hysteresis of the contact line as well as for the description of moving contact lines. The onset of motion is analyzed and the effect of the contact line hysteresis is studied. The critical angle of inclination, as well as the corresponding drop shape, are discussed and compared with previous experiments. The sliding velocity for a constant angle of inclination is also considered and compared with experiments. The different shapes observed in experiments (rounded, corner, cusp, or pearling drop) are recovered depending on both the fluid properties and the angle of inclination. The drop sliding velocity is then considered for larger values of the hysteresis.

Marco Maglio, Dominique Legendre

### Fluids in Cosmology

We review the role of fluids in cosmology by first introducing them in General Relativity and then by applying them to a FRW model of the Universe. We describe how relativistic and non-relativistic components evolve in the background dynamics.We also introduce scalar fields to show that they are able to yield an inflationary dynamics at very early times (inflation) and late times (quintessence). Then, we proceed to study the thermodynamical properties of the fluids and, lastly, its perturbed kinematics. We make emphasis on the constrictions of parameters by recent cosmological probes.

Jorge L. Cervantes-Cota, Jaime Klapp

### Fluid Mechanics and Systems Biology for Understanding the Cosmic Distribution of Life: A Review

Due to progress in instrumentation both in cryogenics and in space exploration, the 20th century witnessed the extension of fluid mechanics applications in two novel systems. While the major aim for the first of these two cases—low temperature physics—was to understand the underlying microscopic theory, in the second case of fluid mechanics in the outer Solar System the major problem was, and still is, one of instrumentation, rather than theory. This second kind of environments may provide hints regarding the central problem of astrobiology, namely the search for life outside our own planet. The Galileo Mission (1995–2003) allowed closer probing of the Jovian satellite Europa, both with imaging techniques, as well as with spectroscopy of its icy surface over a deep ocean that is covered with chemical elements. Other examples of oceans are found in Ganymede and Callisto, two other icy Galilean moons, but possibly these oceans are not in contact with a silicate core, as in the cases of the life-friendly world: the Earth. In addition, Europa, with possibly the same internal geological structure as our planet, is also potentially a life-friendly world. These appealing phenomena are currently the source of plans for the next European mission to Europa that will provide a baseline for the search of life. For this purpose knowledge of our oceans will guide us in the search of life in other solar system oceans. These possibilities have encouraged underlining technologically feasible proposals for delivering small missiles (“penetrators”) with appropriate instrumentation. Whenever compatible with the available payloads, one objective of these instruments has been to identify bioindicators. We are interested essentially in understanding the surficial sulfur stains of Europa’s icy surface. Although not included in the most recent approved mission for Europa, penetrators remain a valid alternative in lunar research that we have shown to be relevant to the basis of astrobiology. In this context we have argued that already existing miniaturized mass spectrometers are particularly relevant. The arguments of this work bring together fluid mechanics, systems biology, and feasible cutting-edge technology.

Julián Chela-Flores

### The Impact of Computational Fluid Mechanics on Cancer Research

This chapter presents an overview of recent contributions that show how fluid mechanics is drastically changing cancer research. The review will mainly focus on the computational modelling of fluid-mediated processes related to cancer dynamics, spanning different representation scales from cells to organs. Fluid mechanics seems to act as a fundamental organizing principle in many aspects of cancer, including its growth, progression, metastasis, and therapy. On the other hand, it is clear that fluid-dynamics modelling can make a huge contribution to many areas of experimental cancer investigation since there is now a wealth of data that requires systematic analysis. The relevance of microfluidics in the isolation, detection, molecular characterization, and migration of tumour cells is also discussed. In the last part of the chapter, future challenges and perspectives are briefly outlined.

Dimas C. Belisario, Leonardo Di. G. Sigalotti

### Growth of Bubbles in Reservoirs and its Consequences on the Foam Formation

The effect of partial confinement on the shape and volume of bubbles generated by injection of gas at a constant flow rate, into a highly viscous liquid is studied numerically and experimentally. By using the Boundary Element Method, numerical solutions of the Stokes equations for the viscous liquid yield the evolution of the surface of a bubble. These solutions and experiments show that cylindrical, conical, and pipe walls with periodic corrugations, concentric with the gas injection orifice in the horizontal bottom of the liquid, may strongly affect the shape and volume of the bubbles. Thus, the presence of walls could be used to control the size of the generated bubbles without changing the gas flow rate. A well-known scaling law for the volume of the bubbles generated by injection of gas at a high flow rate in a highly viscous, unconfined liquid is extended to take into account the presence of cylindrical or conical walls around the injection orifice. In addition, we study numerically the thickness film that is formed between the free surface of a bubble and the cylindrical walls in both cases.

Abel López-Villa, Abraham Medina

### Theoretical Physics of Granular Fluids and Solids

Here we present a brief introduction to some theoretical ideas for granular matter. We start by reviewing the physical properties and constraints of granular materials. We then outline some approaches towards a thermodynamics for granular materials. We analyze the grain flow as a fluid mechanical phenomenon, with a brief introduction to the kinetic theory of inelastically colliding hard particles. We present a nonlinear theory of elasticity for granular solids. Finally, we briefly discuss the problem of formulating continuous field equations in discrete particulate systems and non–local constitutive relations.

Leonardo Trujillo, Leonardo Di. G. Sigalotti

### Shock Structure and Acoustic Waves in a Supersonic Jet

Even though supersonic flows have been studied for a long time, many questions remain unanswered about their behavior. The understanding of jet noise goes in parallel with the understanding of jet turbulence. It has been speculated that different kinds of vortex interactions in the near field, can produce sound. Also, that the interaction between the flow and the shock structure produces noise. It is now known that noise, in supersonic and subsonic jets, is made up of two basic components; one from the large turbulence structures and instability waves, and the other from the fine-scale turbulence. Measurements inside a supersonic jet are difficult. Hot wires are easily broken and homogeneous seeding for Laser Doppler and Particle Image Velocimetries is complicated. We have developed a non-intrusive technique that uses the heterodyne detection of Rayleigh scattering. The laser light scattered elastically by the molecules of the flow at a particular angle, has information about density fluctuations of a particular size. It can be shown that the signal that comes out of a quadratic photo detector is proportional to the spatial Fourier transform as a function of time, of the density fluctuations for a wave vector given by the scattering angle. The spectral analysis of the data has allowed us to identify fluctuations of different origins; entropic and acoustic. We have taken data at many points inside and outside the flow. The technique is sensitive to the wave vector so we can study fluctuations that propagate in different directions. Fluctuations in the direction of the flow are shifted in frequency with respect to fluctuations perpendicular to the flow at the same location. The frequency shift allows us to measure the local speed of the flow. Outside the flow, only acoustic fluctuations are detected. We have been able to determine the far field acoustic radiation pattern for a given wave vector. Inside the jet, the analysis is much more complicated because the acoustic and the entropic peaks overlap when we use simple Fourier transforms. However, with the use of parametric periodgrams we have been able to identify each type of fluctuation. Moreover, we found a third peak at a much lower frequency that appears and disappears as we move along the centerline of the jet. This peak appears also in other positions outside the centerline. We have used Rayleigh scattering and Schlieren to visualize the shock structure. We can then associate each spectrum with a position in the jet relative to the shock structure. The slow peak appears always at a shock, probably due to the interaction between the flow and the shock structure. We are now working on the visualization of the flow, and hope that the combination of all the techniques will give us further insight into the global behavior of the flow, especially in the interfaces between the flow and the shocks and between the mixing layer and the stationary fluid.

Catalina Stern Forgach, José Manuel Alvarado Reyes

### Complex Fluids, Soft Matter and the Jamming Transition Problem

We present an introductory view of the jamming transition problem, starting from Soft Matter, passing through Granular Matter and ending up with Jamming. Various properties of Soft Matter are discussed, because almost all the systems included in this category can be jammed. Then, we discuss fundamental and intrinsic aspects of Soft Matter systems. Although they look like a hodgepodge of things, they share some common features. Here, we propose that Granular Matter could provide a framework to understand essential aspects of Soft Matter. Granular materials can mimic glassy, liquid, solid, and gas-like behaviours and one can use them to understand the other members of Soft Matter. Finally, we present an overview of the jamming transition problem and outline a program towards a unified theory of Soft Matter.

Alberto A. Díaz, Leonardo Trujillo

### A Multiphase Approach to Model Blood Flow in Micro-tubes

The development of micro-fluidic devices to support the systemic circulation of blood has been used either as a temporary bridge or as a recovery method to treat different heart diseases. Blood flow through these artificial micro-channels is a major challenge because blood at scales from tens to hundreds of microns behaves as a multiphase suspension of deformable particles. A homogeneous model of blood is not adequate if the effect of cell segregation through these devices is of interest to evaluate blood cell damage (e.g., hemolysis or thrombosis). To determine the flow field and model the occurrence of segregation, an Eulerian frame of reference is employed. The simulations are performed in a tube of internal diameter of 217

$$\upmu$$

μ

m. We find that the results contribute to improve the understanding of the fluid dynamics of blood as a multi-component medium. Our simulations are based on an alternative methodology for blood modelling at a lower computational cost compared to DNS.

T. M. Mubita, L. R. Rojas-Solórzano, J. B. Moreno

### Perspective: The Breakup of Liquid Jets and the Formation of Droplets

The breakup of liquid surfaces is a topic of great relevance to industry that often presents complications for both experimental and theoretical physicists. Although they have been widely studied since the end of the eighteenth century, many of the phenomena involved in the processes of the breakup of liquids and the formation of new surfaces and droplets are still not fully understood. In this chapter we discuss some of the current issues faced by researchers working in the field of droplet dynamics.

José R. Castrejón-Pita, Ian M. Hutchings

### Experimental Investigation of Thermal Diffusion in Binary Fluid Mixtures

The mass transport of chemical species in response to a temperature gradient, referred to as the Soret effect or thermal diffusion, leads under certain conditions to a separation of the chemical constituents. The Soret coefficient is the ratio of the thermodiffusion coefficient to the molecular diffusion coefficient. This effect along with molecular diffusion occurs in many natural phenomena and engineering systems. One early application of this effect was the separation of isotopes. Understanding the Soret effect is also important for exploring the mechanics of crude oil extraction and its reservoir characterization, as well as in the research of the global circulation of see water. It has also been used for polymer characterization by thermal field flow fractionation. Moreover, recent studies on the Soret effect of bio-systems, like protein and DNA solutions, indicate that it might help revealing the mechanisms behind the mysterious phenomenon of life. Many experimental techniques have been developed for investigation of the Soret effect: thermogravitational columns, thermal lens, diffusion cells, thermal diffusion forced Rayleigh scattering, thermal field flow fractionation, and microfluidic fluorescence. In this chapter, we focus on the investigation of thermal diffusion behaviour in simple liquid mixtures by a thermal lens method. The big advantage of the thermal lens method is that it is fast, simple, and the experimental set-up is much cheaper compared to other methods. In particular, a calibrated two-beam mode-mismatched thermal lens experiment is used for determining the Soret coefficient for isopropanol/water and ethanol/water mixtures.The fitting curves show a very good agreement between the theoretical model and the experimental data. The experimental results have also shown good agreement with available thermodiffusion coefficient data.

Humberto Cabrera

### Stellar Mass Accretion Rates from Fragmentation of a Rotating Core

We investigate the details of protostellar mass accretion,

$$\dot{M}$$

M

˙

, during the collapse of isolated, initially uniformly rotating, low-mass cores, using hydrodynamic models of star formation. The assumption of rigid rotation is supported by recent observations that there is no apparent correlation between the level of turbulence and fragmentation in dense cores, suggesting that turbulence works mainly before gravitationally bound pre-stellar cores form and that their inner parts are likely to be velocity coherent. We perform high-resolution calculations using the Smoothed Particle Hydrodynamics (SPH) code GADGET-2, modified by the inclusion of sink particles. We compare our results with theoretical models of star formation based on gravoturbulent fragmentation and with observational data. We find that on the small scales of low-mass, dense cores the details of mass accretion and the statistical properties of the resulting stellar ensembles bear little dependence on whether the contracting gas is turbulent or rotating as a whole.

Jaime Klapp, Leonardo Di G. Sigalotti, Miguel Zavala

### Biocompatible Treatment of Extra Heavy Oil Produced in Venezuela

In this chapter, we investigate the behaviour of biocompatible mixtures in the treatment of Venezuelan extra heavy oil, using the non-ionic surfactant Polysorbate 80 (Tween 80) and low molecular weight linear n-alcohols with even and odd numbers of carbon atoms. Venezuelan extra heavy oil was recovered from mixtures that contained water, NaCl, polysorbate 80, and n-alcohols ranging from 1 to 8 carbon atoms. Water retained (in enhanced oil), density, conductivity, viscosity, drop weight, and retained oil (in the borosilicate glass tube) were measured and compared for the different n-alcohols in the mixture. We find that the mean (10.99 mS) of the conductivities of the aqueous phase from mixtures with C-2 – C-5 alcohols is statistically different and higher than the mean (4.91 mS) of the conductivities of the aqueous phase from mixtures with C-6 – C-8 alcohols. Among the properties of the recovered oil we find that there is a direct and oscillating correlation of viscosity and water retained in the crude oil fraction, and an inverse correlation of both with drop weight, indicating that the viscoelastic properties of recovered crude oil after treatment are a function of the n-alcohol in the mixture. Oil retained in the borosilicate glass tube as a function of the carbon number of the n-alcohol is directly proportional to toxicity of the alcohol (expressed as A) and ovality of the alcohol (expressed as molecular volume,

$$\uptheta$$

θ

3D), and inversely proportional to acentric factor of the alcohol (expressed as

$$\upomega$$

ω

). Moreover, the polarity, shape, and size associated with the number of carbons in the n-alcohol may be responsible for the high conductivity (10.99 mS) in the aqueous phase released after treatment with the C-2 – C-5 alcohols and the low conductivity (4.91 mS) in the aqueous phase released after treatment with the C-6–C-8 alcohols.

Ledys Y. Sánchez, Efrén D. J. Andrades, Erick A. Pacheco, Hilda C. Grassi, Carlos R. Vera-Lagos, Victor J. Andrades-Grassi

### Dynamical Behaviour of As(V) and Se(IV) Adsorption in Biofilters: Analysis of Dimensions, Flux and Removal Percentage

In this work, we study the dynamical behaviour of As(V) and Se(IV) absorption in a biofilter through a mathematical simulation, comparing dimensions, flux, and removal percentage in packed columns. From the numerical simulation we obtained breakthrough curves. When comparing the experimental and numerical breakthrough curves, the best correlation gives

$$R^{2}=0.9825$$

R

2

=

0.9825

. A set of columns with different dimensions and feed streams were simulated. “The higher and lower” calculated values in the adsorption of selenium (IV) were 3 and 17 %, respectively, whereas the corresponding values for arsenic (V) adsorption were 6 and 17 %, respectively.

Jaime Klapp, Carlos E. Alvarado-Rodríguez, Elizabeth Teresita Romero-Guzmán

### The Geometry of Drop-Formed Vortex Rings

Vortex rings are among the most important objects of fluid mechanics for their numerous technological applications. They are common in inviscid and low viscosity fluids and represent the simplest examples of organized structure formation. The coalescence of a drop with a liquid surface is one process that can result in a vortex ring. Although the phenomenon was observed more than a century ago, the appearance of vorticity and its organization into a toroidal vortex have not yet been completely understood. Here we use fast digital video imaging to study the geometry of drop-formed vortices and the dependence of the early drop inflow on the underlying dynamics above the liquid surface.

Franklin Peña-Polo, Armando Blanco, Leonardo Di G. Sigalotti

### Hydrodynamics of Multiple Coalescence Collisions of Liquid Drops: From the Modelling of the Coalescence Phenomenon to Flocculation of Drops in 3D Using the SPH Formalism

In this chapter, we present three-dimensional numerical calculations of the collision and coalescence of multiple water drops of equal size in a vacuum environment, using a Lagrangian mesh-free scheme based on the Smoothed Particle Hydrodynamics (SPH) formalism. The water drops are modelled using a general Mie-Grüneisen equation of state. Attention is focused for collision velocities from low to moderate so that shattering separation is excluded. Depending on the collision velocity three different possible outcomes are predicted by the calculations: permanent coalescence, coalescence accompanied by fragmentation into a few satellite droplets, and flocculation of the drops with no coalescence.

Alejandro Acevedo-Malavé

### A Three-Dimensional SPH Approach for Modelling the Collision Process Between Liquid Drops: The Formation of Clusters of Unequal-Sized Drops

In this chapter, we present three-dimensional simulations of the coalescence collision and clustering of unequal-sized water drops in vacuum, using the method of Smoothed Particle Hydrodynamics (SPH). The thermodynamics of the problem is represented by a Mie-Grüneisen equation of state. Depending on the magnitude of the collision velocity three different outcomes are observed: permanent coalescence, permanent coalescence accompanied by fragmentation into satellite droplets, and drop clustering with no coalescence (flocculation). When the inertial forces prevail and the surface tension forces are too low permanent coalescence with or without fragmentation into satellite droplets is observed, but for low collision velocities of 0.5 mm/ms, or less, the simulations predict drop flocculation. In this latter case, the drops remain attached to one another, forming a drop clustering.

Alejandro Acevedo-Malavé

### Numerical Simulations of Freely Oscillating Drops

The non-linear oscillations of a viscous drop is a fundamental problem in diverse areas of science and technology. In this paper, we analyze the large-amplitude oscillations of an initially elongated liquid drop in two-dimensions by solving the free boundary problem comprised of the Navier-Stokes equations, using two different numerical codes. The drop models all start from the same deformation in vacuum with zero gravity and varied Reynolds numbers (Re). We find that non-isothermal drops undergo stronger damping than isothermal ones due to the additional dissipative effects of heat conduction. Regardless of the drop parameters and physical mechanisms of dissipation, the transition from periodic to aperiodic decay is seen to occur for

$$\mathrm{Re} \le 1.5$$

Re

1.5

in good agreement with linear theory and previous numerical simulations.

Jorge Troconis, Armando Blanco, Dominique Legendre, Leonardo Trujillo, Leonardo Di G. Sigalotti

### Brownian Dynamics Simulation by Reticular Mapping Matrix Method

In this chapter, we present a method for the two-dimensional simulation of Brownian particles in a fluid with restrictions. The method combines characteristics of the cellular automata and Monte Carlo approaches, and is based on simple numerical rules that use two matrices for controlling the movement of the particles. One matrix serves to identify all particles on which statistical rules are adopted for their motion. This information is then mapped onto another matrix representing the positions of particles. The motion of the particles is governed by a statistical assignation mechanism, which allows to define either a random or non-random movement direction. The same probability of movement in each direction is assumed at each time step and for each particle to simulate the physical behaviour of Brownian movement in a two-dimensional network. For model validation, the predicted root-mean-square displacement of all particles along with their translational velocities are compared to theoretical values of the diffusion coefficient. The dependence of the computational time on the number of particles and concentration is calculated for the models.

Eric Plaza

### Faraday Wave Patterns on a Triangular Cell Network

We present experimental observations of the Faraday instability when an air/water interface is split over a network of small triangular cells for exciting frequencies in the range

$$10\le f\le 30$$

10

f

30

Hz. Just above the threshold for instability, waves appear on the water surfaces within all individual cells. After a transient state, adjacent cells progressively synchronize and self-organize to produce a regular pattern covering the whole grid. Collective cell behaviour is seen to lead to four different patterns depending on the forcing frequency range. Beyond

$${\approx }{28}$$

28

Hz, adjacent cells no longer interact as the vibration wavelength becomes smaller than half the altitudes of the triangular cells and so the waves remain constrained within individual cells in the form of localized harmonic oscillons.

Franklin Peña-Polo, Iván Sánchez, Leonardo Di G. Sigalotti

### Gas-Liquid-Solid Volumetric Phase Distribution Estimation in a Cold Slurry Bubble Column System for Hydro-Conversion Processes

Hydro-cracking slurry bubble column design, scale-up, and operation are strongly influenced by a fluid-dynamic parameter known as volumetric phase distribution. This parameter depends on the operating conditions (gas flow, liquid flow, pressure, and temperature) as well as on the gas, liquid, and solid physical properties. Experiments were carried out at ambient temperature and atmosphere pressure (cold conditions) in a 120 mm inner diameter plexiglas column (without any gas sparger) with air and

$$\mathrm{{CO}}_{2}$$

, mineral oil, and coke with average particle sizes of 630 microns. The column was operated to up-flow continuous recirculation with superficial gas velocities ranging from 3 to 10 cm/s and a constant liquid-solid flow about 29 l/h. Experimental measurements were done by two methods: direct phase trapping and pressure drop. Measurement results indicate that the volumetric gas phase is highly affected by the superficial gas velocity. However, the superficial gas velocity effect on solid concentration is negligible. The experimental results were also compared with experimental data from other authors, obtaining a good agreement. A gas volumetric phase correlation was proposed.

Miguel V. Paiva-Rojas, Virginia Contreras-Andrade, Solange C. Araujo

### Feasibility of Slug Flow Simulation Using the Commercial Code CFX

We evaluate the feasibility of simulating multiphase slug flow regimes in a horizontal pipe using Computational Fluid Dynamics (CFD) with a transient analysis and a Shear Stress Transport (SST) turbulence model available in the commercial code Ansys CFX, which is used as an improvement of the

$$k-\omega$$

k

-

ω

or

$$k-\varepsilon$$

k

-

ε

models. An Eulerian method is employed for solving the hydrodynamics of each fluid phase. To generate the flow regime, a sinusoidal geometric distribution of the phases is established in the computational domain, and a sinusoidal inlet time-dependent condition is used as a disturbance. Seventeen cases were simulated at different flow regimes. The results show that the slug pattern varies when the gas superficial velocity changes. The use of velocities corresponding to patterns such as the annular regime generated a phase distribution different from the slug flow even when using the same inlet function, tending to the expected morphology indicated by the Mandhane diagram in several cases. The effects of varying the amplitude of the sinusoidal-wave inlet function on the model were also analyzed. We find that a minimum of amplitude is required at the inlet to generate the slug flow pattern. An application of the model to the approximate calculation of safety factors for a pipe section subject to slug flow is given. In general, we find that it is feasible to simulate slug flow patterns with the proposed methodology using a commercial code such as Ansys CFX.

Mauricio A. Labarca, Juan J. González, Carlos Araujo

### Heavy Oil Transportation as a Solid-Liquid Dispersion

Traditionally, heavy oil pipelines are designed to handle liquids with effective viscosity below 0.5 Pa s at the pump outlet, in order to minimize the frictional pressure gradient and obtain a pipeline size and economically optimum pumping requirements. Asphaltenes and resins are the components of crude oil which have the highest molecular weights and are, also, the more polar ones. It has been determined that the characteristics of the asphaltenes play an important role in the high viscosity of heavy oils of the Orinoco Oil Belt. This chapter presents an experimental investigation of the behaviour of a potential transport method for heavy oils based on precipitation and conditioning of asphaltenes, followed by an ulterior reincorporation into the de-asphalted oil to obtain a solid-liquid dispersion (slurry) with a lower effective viscosity than the one of the original crude oil. The study comprises two steps: an analysis under static conditions to identify the rheological behaviour of the slurry for different solid contents, from 0 to 12 % (weight basis), and a fluid dynamic study to characterize the effectiveness of the solid–liquid dispersion method in a laminar flow regimen in a 1 inch horizontal pipeline, for mixture velocities between 0.2 and 2.3 m/s, corresponding to Reynolds Number values

$$<$$

<

1,400. A maximum effective viscosity of 0.15 Pa s @ 20

$$^{\circ }$$

C was measured 24 h after conducting the dynamic test, which implies a significant reduction compared to a typical viscosity range of 100–1,000 Pa s @20

$$^{\circ }$$

C for an original crude oil of similar API density and SARA composition. As expected, dispersion viscosity increases with time as asphaltenes are progressively reabsorbed into the de-asphalted oil as a colloidal suspension. The investigated transport method can be implemented together with a low pressure–low temperature de-asphalting process to improve transport properties of the heavy oils of Orinoco Oil Belt.

Adriana Brito, H. Salazar, Ramón Cabello, Jorge Trujillo, L. Mendoza, L. Alvarez

### Comprehensive Evaluation of Gas-Liquid Cyclonic Separation Technologies

PDVSA-Intevep has developed a portfolio of technologies for gas–liquid phase separation based on centrifugal forces effects on fluids of different densities. Research has been focused on both separation technologies cylindrical–conical cyclonic (CYCINT

$$^{{\circledR }}$$

®

) and multiple cylindrical cyclones (

$$\mathrm{{CIMCI}}^{{\circledR }}$$

CIMCI

®

), contemplating numerical modeling, construction, and extensive experimental tests conducted for a wide range of inflow rates and multiphase mixture properties (Brito et al.

2001

,

2003

,

2009

; González et al.

2002

; Martínez

2002

; Carrasco

2008

; Matson and Brito

2008

; Cáliz et al.

2009

; Valdez et al.

2009

; Martínez

2010

). Cyclonic separators are centrifugal technologies whose geometry construction promotes rotational flow within them. Centrifugal forces generated inside the separators conduct the fluid to follow a spiral trajectory with the heavier phase forced to flow nearby the separator walls, whilst the lighter phase is directed to the centre of the equipment ascending to the top of the device. This paper presents a comprehensive quantitative evaluation methodology based on a thorough parametric matrix developed to screen the most promising technologies based on experimental essays results. As a consequence, an optimal allocation of resources will allow further development of the top ranked technologies to conduct further field tests. The processing of experimental data from laboratory tests conducted on cyclonic technologies comprises parameters of great interest for the purpose of this evaluation. Gas carry under, liquid carry over, pressure loss, and generated G forces, in hand with liquid level control strategies, operational envelope width, operability, and compact design are some of the parameters used for the evaluation of technologies considered in this study. The evaluation of parameters was conducted through group categorization followed by variables grading on a 0–8 scale by means of a binary comparison methodology. The evaluation of technologies was conducted based on the results obtained during experimental tests and further analysis. As a result, an unbiased technology ranking was obtained, in which the multi-cylindrical technology (

$$\mathrm{{CIMCI}}^{{\circledR }}$$

CIMCI

®

) provides an overall best performance with emphasis in a superior gas separation efficiency and easier constructability, whilst the cylindrical-conic cyclonic technology (CYCINT

$$^{{\circledR }}$$

®

), on the other hand, presented the upmost liquid separation efficiency and wider operational envelope. Further efforts will focus on continuous development of these two technologies to provide more compact, efficient, and economical gas–liquid separation solutions.

Yessica Arellano, Adriana Brito, Jorge Trujillo, Ramón Cabello

### Geometric Design Optimization of a Prototype Axial Gas-Liquid Cyclonic Separator

Oil and gas industry faces new challenges these days: new off-shore fields are located in harsher environments, at longer distances from shore, in deeper waters, demanding more compact and efficient process facilities, to optimize investment costs and then, to guarantee the economic feasibility of these new projects. On the other hand, brown fields with decaying production experience significant changing process conditions which usually impose constrains in existing facilities. The bottlenecking of these facilities requires process improvements to increase their capacity and efficiency, minimizing at the same time any production deferment which could translates into unwanted higher operational costs. Usually, in both cases there are severe space limitations to deploy solutions, demanding these solutions to become more and more compact. PDVSA-Intevep has identified the need for a compact, high efficiency, and high capacity separation technology to address potential gas scrubbing problems in both green and brown fields, and started the development of an axial gas liquid cyclone as an answer to these needs. The separator consists of a flow conditioning section, a swirl generator section, and a segregating section with a discharge for gas and liquid phases in the outlet. An extensive planning, design, construction, and further experimental validation process of a prototype was conducted in the multiphase flow loop facilities of PDVSA-Intevep to demonstrate the axial cyclone concept. As a result of the experimental validation, several aspects of geometrical design were identified to be susceptible to improvements in order to achieve target separation efficiency. The geometric variables identified and addressed in order to improve the performance of this equipment are: incorporating a pre-separation chamber to remove segregated flow incoming to the device, a static mixer to homogenize the gas liquid mixture incoming to the swirl generator, of swirl generator configuration for constructability purposes, improvement of the liquid annular outlet, gas recycle, and outlet gas flow conditioner configurations. The new design is the result of a comprehensive process of revisiting and evaluating the state-of-the-art of axial separation technologies, incorporating lessons learned during the concept demonstration tests and mechanistic modelling of the prototype. Design was conducted considering the operating envelope of the multiphase flow loop of PDVSA-Intevep, to carry out an experimental performance assessment of the incorporated improvements.

Luis D. Peréz Guerra, Jorge Trujillo , William Blanco

### Effect of Hydrotreating Reaction Conditions on Viscosity, API Gravity and Specific Gravity of Maya Crude Oil

The hydrotreatment of Maya crude oil was carried out in a Parr batch reactor, using alumina-supported catalysts based on NiMo and CoMo sulfides, carbides, and nitrides, which were sulfided ex situ with a mixture of H

$$_{2}$$

2

/CS

$$_{2}$$

2

, prior to reaction. Hydrotreating reactions were carried out under the following conditions: temperature: 320

$$^{\circ }$$

C, pressure: 70–80 kg/cm

$$^{2}$$

2

, time: 4 h, stirring: 500 rpm, and catalyst mass: 2 g. The products of reaction were analyzed by simulated distillation, and the physical properties of the hydrotreated crude were obtained, such as the specific weight and viscosity, at different temperatures, and these values were used to determine specific gravity (SG) and API. In this contribution, we illustrate changes in the physical properties of Maya crude oil before and after hydrotreatment reaction with variations on residue conversion when different hydrotreatment catalysts were used.

Yanet Villasana, Sergio Ramírez, Jorge Ancheyta, Joaquín L. Brito

### Mechanistic Model for Eccentric Annular Gas-Liquid Flow in Horizontal Pipelines

A mechanistic model for the prediction of pressure drop in horizontal pipelines is presented for annular flow. A new empirical correlation for the liquid/wall interfacial friction is proposed, where the effects of the annular flow eccentricity, due to the difference between the fluid density and viscosity, are accounted for. The model is compared to three different correlation models and five mechanistic models in current use. Its accuracy has been validated against experimental data for annular gas-liquid flow in horizontal pipelines, taken from different sources. A number of 240 experiments were carried out with superficial liquid velocities between 0.003 and 5.96 m/s, superficial gas velocities between 9 and 69.6 m/s, liquid viscosities between 1 and 1200 cP, and pipeline diameters between 0.0261 and 0.0953 m. We find that the mechanistic model proposed here reduces the absolute error of the pressure drop prediction by approximately 20 % compared to other mechanistic models.

Adriana Brito, Nelson MacQuhae, Francisco García, Nelson Fernández, José Colmenares

### Scaling Properties in the Adsorption of Ionic Polymeric Surfactants on Generic Nanoparticles of Metallic Oxides by Mesoscopic Simulation

We study the scaling of adsorption isotherms of polyacrylic dispersants on generic surfaces of metallic oxides

$$XnOm$$

X

n

O

m

as a function of the number of monomeric units, using Electrostatic Dissipative Particle Dynamics simulations. The simulations show how the scaling properties in these systems emerge and how the isotherms re-scale to a universal curve, reproducing reported experimental results. The critical exponent for these systems is also obtained, in perfect agreement with the scaling theory of de Gennes. Some important applications are mentioned.

### Effect of Mixtures of Polysorbate 80 and Low Molecular Weight Alcohols on Density and $$^\circ$$ ∘ API Gravity of Treated Venezuelan Extra Heavy Oil

Formulations of extra heavy oil with biocompatible polyethoxilated compounds have not received much attention. We investigate the behaviour of biocompatible mixtures in the treatment of Venezuelan extra heavy oil, using the non-ionic surfactant Polysorbate 80 (Tween 80) and low molecular weight linear n-alcohols with even and odd number of carbon atoms, in order to predict the best fit in the ethoxide—alcohol interaction. Venezuelan extra heavy oil was recovered from mixtures that contained water, NaCl, polysorbate 80, and n-alcohols ranging from 1 to 8 carbon atoms. The density,

$$^\circ$$

API gravity (American Petroleum Institute gravity), and other properties were measured and compared for the even and odd numbered n-alcohols. We found a significant difference in density and

$$^\circ$$

API gravity values in the treated and recovered extra heavy oil, for n-alcohols with even and odd number of carbons, in the presence of polysorbate 80. This finding suggests that the ether within the ethoxide-repeating units of polysorbate 80 is the hydrogen bond acceptor of the n-alcohol donor. However, this interaction is favoured for the even number alcohols that interact in an “in-frame” manner with the ethoxide. We propose the formation of a micellar nanoparticle that promotes the improvement of Venezuelan extra heavy oil.

Efrén D. J. Andrades, Ledys Y. Sánchez, Hilda C. Grassi, Erick A. Pacheco, Silvia E. Andrades-Grassi, Gerardo E. Medina-Ramírez

### On the Construction of a Continuous Theory for Granular Flows

We present a brief introduction of the coarse graining technique, which we shall use to construct a continuous matter field for discrete particulate systems. In particular, we address the problem of the micro to macro transition in the theoretical framework of granular hydrodynamics. The equations for momentum conservation, elastic stress tensor, and elastic energy are obtained introducing a harmonic interaction between the particles. These equations are compared with previous work, where the microscopic discrete nature of granular matter has not been considered. The microscopic description of a granular system leads to a matrix for the definition of the elastic moduli, which depends on position and coarse graining resolution. This provides some insight into the mathematical description of the origin of force chains in granular packings.

Juan C. Petit, Juan F. Marín, Leonardo Trujillo

### Integral Representation for Continuous Matter Fields in Granular Dynamics

We introduce a mathematical formalism towards the construction of a continuum-field theory for particulate fluids and solids. We briefly outline a research program aimed at unifying the fundamentals of the coarse-graining theory and the numerical method of Smoothed Particle Hydrodynamics (SPH). We show that the coarse-graining functions must satisfy well defined mathematical properties that comply with those of the SPH kernel integral representation of continuous fields. Given the appropriate dynamics for the macroscopic response, the present formalism is able to describe both the solid and fluid-like behaviour of granular materials.

Juan F. Marín, Juan C. Petit, Leonardo Di. G. Sigalotti, Leonardo Trujillo

### Numerical SPH Calculations of Fluid Flow Through Saturated and Non-saturated Porous Media

The fluid flow through saturated and non-saturated homogeneous porous media is studied numerically using a modified version of a Smoothed Particle Hydrodynamics (SPH) code. The modifications implemented in the original SPH code to model the incompressible flow at low Reynolds numbers through a porous medium are described. The performance of the model is demonstrated for three-dimensional flow through idealized porous media consisting of regular square and hexagonal arrays of solid spheres. For each of these configurations we consider a set of flow calculations through saturated and non-saturated porous matrices differing in the magnitude of the

$$z$$

z

-component of the hydraulic gradient. For the saturated case, the Darcy’s law is recovered and the hydraulic conductivity is calculated for both geometries. The numerical results are consistent with previous two-dimensional simulations in that the square case has a lower hydraulic conductivity than the hexagonal case. Finally, for the non-saturated case the relaxation time is calculated for different body forces. In this case, the system never reaches steady-state conditions.

Estela Mayoral, Mario A. Rodríguez-Meza, Eduardo de la Cruz-Sánchez, Jaime Klapp, Francisco Solórzano-Araujo, César Ruiz-Ferrel, Leonardo Di. G. Sigalotti

### Propagation of Longitudinal Waves in Super-Radially Expanding Solar Plumes

Recent observations indicate that coronal plumes are the preferred channels for the propagation of slow magnetosonic waves from the Sun’s poles to the corona. This problem is of relevance in solar physics because polar plumes are well observed exactly at the heights of the solar wind acceleration. In this chapter, we study the effects of the basal geometric spreading of polar plumes on the propagation of slow-mode waves up to

$$r=5R_{\odot }$$

by means of a non-linear analysis of the equations of hydrodynamics. We find that super-radial expansion at the base of the flux tube induces a strong dilution of the wave energy flux close to the solar surface, implying a steep decrease of the wave amplitude from the very beginning. Slow waves with periods of 7–25 min diffuse out at heights between

$${\approx } {1.6}$$

and

$$2.4R_{\odot }$$

owing to dissipation. This result is in good agreement with recent observations.

Leonardo Di. G. Sigalotti, Jordan A. Guerra, Hailleen Varela

### Comparing Accretion Centres Between Rotating and Turbulent Cloud Cores

In this chapter we use the method of Smoothed Particle Hydrodynamics (SPH) to study the number and properties of accretion centres formed when a molecular gas cloud collapses, starting with initial conditions corresponding either to a turbulent or a rigidly rotating sphere. To do so we use a modified version of the SPH code GADGET-2, which is capable to detect when a gas particle becomes an accretion centre, inheriting the mass and momentum of all its closest neighbours. For both types of models (turbulent and uniformly rotating), we also study the effects of considering two different initial mass distributions: a uniform-density and a centrally condensed Plummer profile. We find that the turbulent models are more propense to fragment into a larger number of protostellar objects than the purely rotating clouds. However, in both types of models the average protostellar mass increases with increasing size of the kinetic energy content of the cloud.

Guillermo Arreaga-García, Jaime Klapp

### Statistical Methods for the Detection of Flows in Active Galactic Nuclei Using X-Ray Spectral Lines

Using robust statistical methods, we are able to detect and identify absorption lines in the X-ray spectra of quasars and active galactic nuclei taking as reference the Seyfert 1 galaxy NGC 3783. The high resolution spectrum of this object shows evidence of partially ionized gas outflowing from the centre of the system at velocities of

$$\approx 625$$

625

$$\pm$$

±

35 km

$$\mathrm{s}^{-1}$$

s

-

1

. This velocity differs from a previously reported value by

$$\approx 6$$

6

%. The understanding of these flows is important to draw a general picture of the feedback observed between the analyzed objects and the host galaxy.

Luis F. Pérez, José M. Ramírez

### Reproducing the X-Ray Soft Step @ 0.9 keV Observed in the Spectrum of Ark 564 Using Reflection Models

Using reliable atomic data, we attempt to reproduce the global 100 ks X-ray spectrum of the narrow-line Seyfert 1 Galaxy Ark 564, observed with the Low Energy Transmission Grating Spectrometer (LETGS) on board

Chandra

. In order to do this, we use accretion disk and reflection flow models.

José M. Ramírez, Snell Rojas

### Dynamics of Relativistic, Dissipative and Anisotropic Self-Gravitating Fluids

This chapter deals with the study of dissipative, locally anisotropic, and spherically symmetric self-gravitating fluids. The analysis is based on a full causal approach, where the dynamical equations are coupled to causal transport equations for the heat flux, shear, and bulk viscosity in the context of the Müller-Israel-Stewart theory by including the thermodynamic viscous/heat coupling coefficients.

Orlenys Troconis

### Hydrodynamic Version of the Equation of Motion of a Charged Complex Scalar Field

In this chapter we derive the equation for a charged complex scalar field in its hydrodynamic form. This is done by re-writing the Klein-Gordon (KG) equation for the complex scalar field as a new Gross-Pitaevskii (GP)-like equation. In particular, we use as the potential of the scalar field the Mexican-hat potential, and assume that the field is in a thermal bath with a one loop contribution. We interpret the new GP equation as a finite temperature generalization of the GP equation for a charged field. From its hydrodynamic form, we derive the corresponding thermodynamics and obtain a generalized first law for a charged Bose-Einstein Condensate (BEC).

Mario A. Rodríguez-Meza, Tonatiuh Matos
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