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## Über dieses Buch

This book contains invited lectures and selected contributions presented at the Enzo Levi and XIX Annual Meeting of the Fluid Dynamic Division of the Mexican Physical Society in 2013. It is aimed at fourth year undergraduate and graduate students, and scientists in the fields of physics, engineering and chemistry who are interested in fluid dynamics from an experimental and theoretical point of view. The invited lectures are introductory and avoid the use of complicated mathematics. The fluid dynamics applications include multiphase flow, convection, diffusion, heat transfer, rheology, granular material, viscous flow, porous media flow, geophysics and astrophysics. The material contained in the book includes recent advances in experimental and theoretical fluid dynamics and is suitable for both teaching and research.

## Inhaltsverzeichnis

### Compositional Flow in Fractured Porous Media: Mathematical Background and Basic Physics

This chapter presents an overview of the equations describing the flow of multiphase and multicomponent fluids through fractured and unfractured porous media using the framework of continuum mixture theory. The model equations and constraint relationships are described by steps of increasing level of complexity. We first describe the governing equations for multiphase flow in both undeformable and deformable porous media. This model is extended to include the transport of chemical species by first describing the flow of a multicomponent, single-phase fluid and then of a compositional (multiphase and multicomponent) fluid in a porous medium. Finally, the equations governing the flow of compositional fluids in fractured porous media are described. The proposed methodology is suitable for modelling any type of fractured media, including dual-, triple-, and multiple-continuum conceptual models.

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

### Turbulent Thermal Convection

Turbulent thermal convection is a phenomenon of crucial importance in understanding the heat transport and dynamics of several natural and engineering flows. Real world systems such as the Earth’s atmosphere—its oceans as well as the interior—and the interior of stars such as the Sun, are all affected to various degrees by thermal convection. The simplified physical model used to understand this ubiquitous heat transport mechanism is the Rayleigh-Bénard convection, which is a fluid flow driven by a temperature difference between the top and bottom plates of an experimental cell with adiabatic sidewalls. Despite the long history of the subject and the recent progress in theoretical, numerical and experimental domains, many questions remain unresolved. We report some recent results and discuss a few open issues.

Enrico Fonda, Katepalli R. Sreenivasan

### Dissipative Particle Dynamics: A Method to Simulate Soft Matter Systems in Equilibrium and Under Flow

We provide examples and a concise review of the method of Dissipative Particle Dynamics (DPD), as a simulation tool to study soft matter systems and simple liquids in equilibrium and under flow. DPD was initially thought as a simulation method, which in combination with soft potentials, could simulate “fluid particles” with suitable hydrodynamic correlations. Then DPD evolved to a generic “thermostat” to simulate systems in equilibrium and under flow, with arbitrary interaction potential among particles. We describe the application of the method with soft potentials and other coarse-grain models usually used in polymeric and other soft matter systems. We explain the advantages, common problems and limitations of DPD, in comparison with other thermostats widely used in simulations. The implementation of the DPD forces in a working Molecular Dynamics (MD) code is explained, which is a very convenient property of DPD. We present various examples of use, according to our research interests and experiences, and tricks of trade in different situations. The use of DPD in equilibrium simulations in the canonical ensemble, the grand canonical ensemble at constant chemical potential, and stationary Couette and Poiseuille flows is explained. It is also described in detail the use of different interaction models for molecules: soft and hard potentials, electrostatic interactions and bonding interactions to represent polymers. We end this contribution with our personal views and concluding remarks.

C. Pastorino, A. Gama Goicochea

### Flow Coherence: Distinguishing Cause from Effect

The geodesic transport theory unveils the especial fluid trajectory sets, referred to as Lagrangian Coherent Structures (LCS), that cause a flow to organize into ordered patterns. This is illustrated through the analysis of an oceanic flow dataset and contrasted with the tendency of a widely used flow diagnostic to carry coherence imprints as an effect of the influence of LCS on neighboring fluid trajectories.

F. J. Beron Vera

### Parametrisation in Dissipative Particle Dynamics: Applications in Complex Fluids

A brief overview of mesoscopic modelling for neutral and electrostatically charged complex fluids via Dissipative Particle Dynamics (DPD) is presented, with emphasis on the appropriate parametrisation and how to calculate the relevant parameters for given realistic systems. DPD is a technique that consists of carrying out a coarse-graining of the microscopic degrees of freedom and it is highly dependent on parameters describing the different kinds of force fields and the parametrisation. For this reason, we present here a revision of DPD parametrisation together with applications and comparisons with experimental results. The dependence on concentration and temperature of the interaction parameters for electrostatic and non-electrostatic systems is also considered, as well as some applications in complex fluids.

A solver for free-surface flows (DualSPHysics) based on the Smoothed Particle Hydrodynamics (SPH) model is presented. The classical SPH formulation is described along with the governing equations, filters and corrections, boundary conditions and time stepping schemes. The reliability of the DualSPHysics model is discussed by comparing the numerical results with the experimental data for a benchmark test case. The applicability of the code is shown with some examples where wave propagation and wave-structure interaction are simulated.

A. Barreiro, J. M. Domínguez, A. J. C. Crespo, O. García-Feal, M. Gómez Gesteira

### Numerical Modelling of the Extratropical Storm Delta Over Canary Islands: Importance of High Resolution

The tropical storm “Delta” was formed on November 23, 2005 in a sea zone of the subtropical Atlantic south of the Azores. After days with an erratic movement, the day 27 the storm reinforced their intensity and accelerated its movement towards the Northeast in the direction of the Canary Islands. On 28 and 29, it made a transition to extratropical storm, affecting the Canary Islands with very strong sustained winds with maximum streak of 152 km/h at the airport of La Palma and close to 250 km/h in the Izaña observatory (2,360 m altitude), which caused significant property damage. The aim of this numerical modelling is to reproduce the local effects of Delta storm with high spatial resolution. The WRF-ARW model is applied from 9 to 3 km of horizontal resolution using ECMWF forecasts as IBC. The simulation reproduces the main features that contributed to the high wind speeds observed. Variations in the vertical static stability, vertical wind shear and intense synoptic winds from the southwest part of Delta with a warm core at 850 hPa were the main features that have contributed to the development and amplification of intense gravitational waves, while the large-scale flow interacted with the complex topography of the islands. Nonhydrostatic and hydrostatic experiments were designed taking into account the settings and domain factors. The results associated with changes relative to a controlled simulation showed that the boundary layer, the horizontal resolution, and the nonhydrostatic option have the greatest impact.

O. Jorba, C. Marrero, E. Cuevas, J. M. Baldasano

### Four-Winged Flapping Flyer in Forward Flight

We study experimentally a four-winged flapping flyer with chord-wise flexible wings in a self-propelled setup. For a given physical configuration of the flyer (i.e. fixed distance between the forewing and hindwing pairs and fixed wing flexibility), we explore the kinematic parameter space constituted by the flapping frequency and the forewing-hindwing phase lag. Cruising speed and consumed electric power measurements are performed for each point in the

$$(f,\varphi )$$

(

f

,

φ

)

parameter space and allow us to discuss the problem of performance and efficiency in four-winged flapping flight. We show that different phase-lags are needed for the system to be optimised for fastest flight or lowest energy consumption. A conjecture of the underlying mechanism is proposed in terms of the coupled dynamics of the forewing-hindwing phase lag and the deformation kinematics of the flexible wings.

R. Godoy-Diana, P. Jain, M. Centeno, A. Weinreb, B. Thiria

### Flows from Bins: New Results

Gravity granular flows of cohesionless materials emerging from bottom exits and from lateral exit holes, both in vertical bins, and from face walls in tilted bins were modeled and measured. The models are based on continuum mechanics, whereas friction and gravity are the main involved forces. Measurements of the granular mass flow rates were obtained from temporal measurements of weights by using force sensors. In vertical and tilted bins the face wall thicknesses were considered in the governing correlations. Measurements are in good agreement with the theoretical predictions.

D. A. Serrano, A. Medina, G. Ruíz Chavarría, F. Sanchez Silva

### Some Aspects of Turbulence Role in Oceanic Currents

This manuscript is intended to review some of the methods used to estimate one of the most useful parameters in Ocean Modeling: the diapycnal diffusivity. Specifically it focus on simultaneous measurements carried out at two different locations in the deep ocean. The techniques reviewed here to estimate diapycnal mixing in the ocean interior are: tracer-release experiments, microstructure direct measurements and fine-structure estimates based on LADCP

$$/$$

/

CTD data. There are only few data sets in the world that have simultaneous measurements of the three techniques mentioned above. The importance of the lack of spatial and temporal estimates of the turbulent mixing parameters and the implication of those parameters on modeling the Global Circulation are also reviewed.

A. Ruiz Angulo

### Alya Red CCM: HPC-Based Cardiac Computational Modelling

This paper describes Alya Red CCM, a cardiac computational modelling tool for supercomputers. It is based on Alya, a parallel simulation code for multiphysics and multiscale problems, which can deal with all the complexity of biological systems simulations. The final goal is to simulate the pumping action of the heart: the model includes the electrical propagation, the mechanical contraction and relaxation and the blood flow in the heart cavities and main vessels. All sub-problems are treated as fully transient and solved in a staggered fashion. Electrophysiology and mechanical deformation are solved on the same mesh, with no interpolation. Fluid flow is simulated on a moving mesh using an Arbitrary Lagrangian-Eulerian (ALE) strategy, being the mesh deformation computed through an anisotropic Laplacian equation. The parallel strategy is based on an automatic mesh partition using Metis and MPI tasks. When required and in order to take profit of multicore clusters, an additional OpenMP parallelization layer is added. The paper describes the tool and its different parts. Alya’s flexibility allows to easily program a large variety of physiological models for each of the sub-problems, including the mutual coupling. This flexibility, added to the parallel efficiency to solve multiphysics problems in complex geometries render Alya Red CCM a well suited tool for cardiac biomedical research at either industrial or academic environments.

M. Vázquez, R. Arís, J. Aguado-Sierra, G. Houzeaux, A. Santiago, M. López, P. Córdoba, M. Rivero, J. C. Cajas

### Singularities in Surface Waves

In this paper we investigate the evolution of surface waves produced by a parabolic wave maker. This system exhibits, among other, spatial focusing, wave breaking, the presence of caustics and points of full destructive interference (dislocations). The first approximation to describe this system is the ray theory (also known as geometrical optics). According to it, the wave amplitude becomes infinite along a caustic. However this does not happen because geometrical optics is only an approximation which does not take into account the wave behavior of the system. Otherwise, in ray theory the wave breaking does not hold and interference occurs only in regions delimited by caustics. A second step is the use of a diffraction integral. For linear waves this task has been made by Pearcey (

1946

) (Pearcey, Philos Mag 37 (1946) 311–317) for electromagnetic waves. However the system under study is non linear and some features have not counterpart in the linear theory. In the paper our attention is focused on three types of singularities: caustics, wave breaking and dislocations. The study we made is both experimental and numerical. The experiments were conducted with two different methods, namely, Schlieren synthetic for small amplitudes and Fourier Transform Profilometry. With respect the numerical simulations, the Navier-Stokes and continuity equations were solved in polar coordinates in the shallow water approximation.

G. Ruíz Chavarría, T. Rodriguez Luna

### Isotherms of Natural and Forced Convection Around a Heated Horizontal Cylinder Embedded in a Porous Medium

This work presents an experimental analysis of free and forced convection due to a heated cylinder in a fluid-saturated porous medium. The resulting features of the temperature distribution under the action of a continuous and uniform air stream were investigated through the use of four different configurations: first, by inducing an air stream from below the heated cylinder; second, by placing an air stream on the left-hand side of the heat source; third by an air stream acting from the top of the heat source, and fourth by varying the injection angle. The consequences on the free and forced convection when all phenomena reach the steady state were analyzed by using an infrared camera. Close agreement is found through the conformed plumes with the theoretical solutions proposed by Kurdyumov and Liñán (

2001

).

M. Sánchez, A. Torres, F. Aragón, I. Carvajal, A. Medina

### Parameter Estimation in a Model for Tracer Transport in One-Dimensional Fractals

The problem of parameter estimation in a model for one-dimensional fractals is analysed and solved. The model describes advection and dispersion of a tracer pulse in a one-dimensional fractal continuum with uniform flow. It involves three parameters: fractal dimension of length, connectivity index associated to dispersion and dispersion coefficient. By using synthetic tracer breakthrough data the effect of data noise level, amount of data points and number of fitting parameters on the results have been analysed. It has been found that the developed estimation methodology is in general robust to the standard data noise level, and to the amount of data points between the typical cases of around 10 and 40. It has been also found that the curve fitting procedure is consistently more sensitive to the fractal dimension of length than to the other two parameters: the connectivity and the dispersion coefficient.

### Mixed Convection in a Rectangular Enclosure with Temperature-Dependent Viscosity and Viscous Dissipation

The problem of laminar opposing mixed convection inside a two-dimensional rectangular enclosure with asymmetrical heating is studied numerically using the vorticity-stream function formulation of the Navier-Stokes and energy equations. The model considers viscous dissipation and viscosity is assumed to vary with temperature according to an exponential relation, while other fluid properties are considered constant. Numerical experiments have been performed for fixed values of the geometrical parameters, Reynolds number of

$$Re = 20$$

R

e

=

20

, Prandtl number of

$$Pr = 3{,}060$$

P

r

=

3

,

060

, a range of Richardson numbers from 0 to 10, and Brinkman numbers ranging between 0 to 40. Streamlines, temperature contours, maximum fluid temperature and average Nusselt number at both walls are obtained. The results show that combined viscous dissipation and variable fluid viscosity can be important in the overall flow and heat transfer characteristics.

A. Gómez López, B. Estela García Rojas, R. O. Vargas Aguilar, L. A. Martínez-Suástegui

### Characterization of a Bubble Curtain for PIV Measurements

In this contribution we present the characterization of a bubble curtain produced with compressed air. The final goal is to implement a PIV system, with bubbles as tracers, that will help to understand drag and propulsion of a swimmer during a dolphin kick. The system will be used directly in a swimming pool. The first trials were made in a controlled water channel.

R. G. Ramírez de la Torre, D. C. Vargas-Ortega, M. S. Centeno-Sierra, R. Méndez-Fragoso, C. Stern Forgach

### Numerical Simulation of a Gas-Stirred Ladle

In this paper we present three-dimensional, numerical simulations of the turbulent recirculatory flow in a gas-stirred vessel. The physical model consists of air injected in a water cylindrical vessel, corresponding to a one-seventh scale model of an industrial 35 tons steel-making ladle. Plume development and recirculation is investigated for air blowing through an eccentric porous plug placed at the bottom of the vessel. The experimentally observed plume behaviour and the mixing process due to recirculatory water motion within the ladle is qualitatively well reproduced by the numerical simulations. When the airflow rate is increased, the intensity of agitation and turbulence increases, thereby enhancing the mixing in the ladle.

H. Zambrano, A. Bencomo, L. Trujillo, L. Di G. Sigalotti

### Folding of the Apolipoprotein A1 Driven by the Salt Concentration as a Possible Mechanism to Improve Cholesterol Trapping

The folding of the cholesterol—trapping apolipoprotein A1 in aqueous solution at increasing ionic strength—is studied using atomically detailed molecular dynamics simulations. We calculate various structural properties to characterize the conformation of the protein, such as the radius of gyration, the radial distribution function and the end-to-end distance. Additionally we report information using tools specifically tailored for the characterization of proteins, such as the mean smallest distance matrix and the Ramachandran plot. We find that two qualitatively different configurations of this protein are preferred: one where the protein is extended, and one where it forms loops or closed structures. It is argued that the latter promote the association of the protein with cholesterol and other fatty acids.

M. A. Balderas Altamirano, A. Gama Goicochea, E. Pérez

### Graphical Analysis of Fluid Flow Through Polymeric Complex Structures Using Multi-scale Simulations

Efficient and detailed visualization of fluid flow simulations through complex meso-porous structures are fundamental for many applications in different areas such as medicine, biotechnology, oil recovery procedures, industry applications, environmental science and design of new intelligent and efficient meso-porous materials. Here we present the visual results of polymeric fluid flow through different complex porous media using multi-scale simulations performed over graphical processors (GPU’s). A Lagrangian numerical model known as Smoothed Particle Hydrodynamics (SPH) was used in order to simulate the flow through complex structures taken from real images or from other simulations which represents different porous media. Performance of the model and its visualization were analyzed for a regular and also for an irregular three-dimensional array of solid spheres that represents a porous media with different polymeric fluids. The comprehensive examination of different sections in the system help us to analyze in an improved way the dynamical behavior of fluids through sophisticated structures. Micro-channels built via mesoscopic Dissipative Particle Dynamics (DPD) simulations were also introduced with great detail and the flow through these micro-porous structures was analyzed in order to understand microvascular turbulent fluid flow. Detailed visualization in real time could be used not only to help in the study of different systems but also to obtain amazing images that would be impossible to achieve by other techniques, here we present some of this beautiful pictures.

Estela Mayoral-Villa, Mario A. Rodríguez-Meza, Jaime Klapp, Eduardo de la Cruz-Sánchez, César Ruiz-Ferrel, Aaron Gómez-Villanueva

### Mass Flow Rate of Granular Material from an L-Valve Without Aeration

In this work we introduce a correlation to estimate the mass flow rate from an L-valve, without aeration, but under gravity flow, of a non-cohesive granular material. This criterion is based on the mass flow rate formula for vertical pipes and the comparison among, the here termed L-valve angle, and the angle of repose of the material. Experiments support this criterion.

D. A. Serrano, G. Ruíz Chavarría, S. Álvarez, A. Medina

### Heat Transfer in Biological Tissues

The heat transfer process in biological tissues is studied through the Pennes bioheat equation, in dimensionless form, taking into account the temperature gradient delay by the Maxwell-Cattaneo model. Stochastic perturbations from the environment applied on the surface of the tissue and different external energy sources are considered. Comparison of temperature distributions with constant biological parameters are presented, from the skin surface and through the tissue transfer processes and to contribute to a better understanding on how nature works, it is essential to include biological, physical and biochemical.

M. E. Bravo, P. De Jesús Sánchez, R. O. Vargas Aguilar, A. E. Chávez

### Simulation of In-situ Combustion in a Matrix-Fracture System at Laboratory Scale

In this work, a mathematical model for in-situ combustion (ISC) was numerically solved for one heterogeneous system composed by a porous-matrix adjacent to a fracture. The main aim was to investigate the effect of fractures on the ISC behaviour. Three mobile-phases were considered: non-volatile single-component oil, incondensable gas, and water. The combustion process was modeled with a kinetic model and two chemical reactions: cracking reaction (coke production), and combustion reaction (coke consumption). A benchmark case was established by comparison of suited numerical results against experimental data from a homogeneous combustion tube experiment reported from the literature. It was found an acceptable agreement between theoretical and experimental data for the temperature field and other variables of interest. The validated mathematical model was extended for one system including adjacent fractures, and their effects over the ISC were investigated. It was observed gas breakthrough because it moves preferably through fractures. It was found that around the combustion front, significant amount of oxygen penetrates from the fracture to the porous matrix, as here the coke combustion takes relevance. In addition, an important amount of oil is expelled from the matrix to the fracture.

### Numerical Simulation of In-situ Combustion in a Fracture-Porous Medium System

In this work, the numerical simulation of in-situ combustion in a fracture-porous medium system at laboratory scale, was done. The simulations were developed in a commercial reservoir simulator designed to evaluate oil recovery by thermal methods. The simulator involves the mass, momentum (Darcy law) and energy balance equations for multiphase and multicomponent flows. The main aim of this work was to study the effect of the airflow rate and oil saturation on the in-situ combustion behaviour. In the first stage of this study, the in-situ combustion was simulated in a homogeneous porous medium and the simulation was validated using experimental data. In a second stage, such simulation was modified in order to incorporate fractures in the porous medium. It was found that the oxygen diffusion from fractures to porous medium controls the in-situ combustion in fractured systems. Moreover, it is necessary to restrict the injected air flow rate due to the breakthrough phenomenon and because the oil recovery is not substantially increased for larger flow rates.

O. Cazarez-Candia, P. V. Verazaluce-Barragán, J. R. Hernández-Pérez

### Mathematical Modeling of Steam Injection in Vertical Wells

In this work, a steady-state hydrodynamic model for steam injection vertical wells and a transient thermal model (2D energy diffusion equation) for the heat losses from a well towards the porous medium are presented. The hydrodynamic model is formed by mass, momentum and energy conservation equations (drift-flux model) for a steam-water two-phase flow. The steady-state drift-flux model was resolved using the finite differences method and the explicit Godunov scheme, while the thermal model solution was found with an implicit Godunov scheme. Models allow predicting the next parameters: pressure, temperature, steam quality, heat losses and flow patterns along the well. The parameter predictions presented good agreement against field data and simulations reported in literature. For the conditions simulated, it was found that: (1) the thermal model reaches its steady state at 500 h, (2) due to few steam condensation, pressure drop due to gravity is smaller than the friction and acceleration contributions, and (3) temperature gradients are large at the beginning of steam injection, but they diminish along time.

F. Aguilar-Gastelum, O. Cazarez-Candia

### Oxygen Transport Under Combustion Conditions in a Fracture-Porous Medium System

In this work the oxygen transport was modeled numerically, at pore scale, in a matrix-fracture system saturated by nitrogen. This system appears when the in-situ combustion (ISC) method is applied for oil recovery in fractured reservoirs. The main aim was to study the effect of oxygen flow rate and the fracture width on the oxygen transport from the fracture to the porous matrix due to this controls the combustion front propagation. The porous matrix microstructure was modeled as a medium composed by circular particles in a periodic arrangement. In order to simulate the combustion reaction that occurs in an in-situ combustion process, the coke-oxygen reaction was taken into account on the particles surface. The gas, coke and oxygen mass balances as well as the gas momentum balance were resolved using a software that involves the finite element technique. The oxygen distribution was studied in the matrix-fracture system as a function of: (1) the oxygen flow rate, and (2) the fracture width. It was found that increasing such parameters stimulate the coke consumption. Moreover, they increase the oxygen transport from the fracture to the matrix.

O. Cazarez-Candia, G. Rojas Altamirano, C. G. Aguilar-Madera

### Numerical Simulation of the Flow in an Open Cavity with Heat and Mass Transfer

In the present work, we analyze the laminar steady-state fluid dynamics, heat and mass transfer in a two-dimensional open cavity for the decomposition of a substance. The numerical study is carried out for Reynolds numbers of 10, 25 and 50 with a Schmidt number of 425. A hot plate is provided at the bottom of the cavity which generates the thermal decomposition of the substance. In order to investigate the effect of the length of the plate two different plate sizes are considered. The governing equations of continuity, momentum, mass transport and energy for incompressible flow are solved by the finite element method combined with an operator-splitting scheme. We calculate the temperature field, the streamlines, the velocity and the concentration field and analyze the velocity, concentration and temperature profiles as a function of the transversal position. We find that the Reynolds number plays a major role in the mass transport and the thermal behavior of the flow inside the cavity.

G. E. Ovando Chacon, S. L. Ovando Chacon, J. C. Prince Avelino, A. Servin Martínez, J. A. Hernández Zarate

### 3D Numerical Simulation of Rayleigh-Bénard Convection in a Cylindrical Container

The heat transport by natural convection is a central mechanism in the explanation of many natural phenomena. Despite many existing work on the Rayleigh-Bénard convection, often the phenomenon is studied by making a two-dimensional approach or using a rectangular container. In this work, we solve numerically the Navier-Stokes, continuity and energy equations in cylindrical coordinates. To this end a finite difference scheme is used for the time and spatial coordinates

$$r$$

r

and

$$z$$

z

, whereas a Fourier spectral method is used for the angular coordinate. The advantage of this procedure is that it can be easily parallelized. The numerical results include the formation of concentric rolls and other patterns, which are compared with experimental results reported in the literature.

N. Y. Sánchez Torres, E. J. López Sánchez, S. Hernández Zapata, G. Ruiz Chavarría

### Solidification in the Presence of Natural Convection in a Hele-Shaw Cell

The solidification of water with particles in a suspension that fills the gap in a Hele-Shaw cell has been experimentally studied by visualization and using particle image velocimetry (PIV). The upper wall of the cell is kept at a temperature lower than 0

$$^{\circ }$$

C, while the lower wall is exposed to ambient temperature. Water starts solidifying near the upper wall of the cell, and a solidification front moves in the downward direction. Since the temperature gradient established is unstable in the gravity acceleration field, the liquid acquires a natural convective motion, and the solidification and convection interact with each other. The growth of the solidification region in the Hele-Shaw cell modifies the volume available to the liquid and in this way determines the convection pattern. In turn, the convective flow of the liquid is an efficient heat pump at the liquid-solid boundary, and determines the velocity and geometry of the solidification front. We present quantitative data of the velocity and shape of the solidification front and the velocity field in the liquid region as functions of time. We have found that the convective motion stops when the aspect ratio (height/width) of the liquid region is approximately 0.45 and from this time on, the motion of the solidification front follows Stefan’s law.

G. Ramírez, J. E. Cisneros, G. Hernández Cruz, E. Ramos

### Confinement and Interaction Effects on the Diffusion of Passive Particles

We use Molecular Dynamics simulations to study the effect of interactions and confinement (walls) on particle diffusion. We extend previous studies by analyzing the mean squared displacement (MSD) of an interacting fluid constrained to a circular, square and triangular cavity of nanometric size. The interactions among particles and walls are modeled by means of three classic potentials namely, Lenard-Jones (CLJ), soft Lenard-Jones (SLJ) and hard Lenard-Jones (HLJ) potentials. For hard spheres, for all cavities, and for very diluted densities, diffusion is shown to be less favorable in comparison with particles interacting with a CLJ. It is also observed that HLJ particles do not show difference in their MSD with SLJ particles at these densities. Confinement effects also appear at these densities and it is shown that diffusion decreases in the following cavity shape order: triangular, square and circular. For moderated densities, the combination of confinement and interactions shows a non-trivial effect. It is observed that particles inside a triangular cavity interacting by means of HLJ, reduce their MSD in comparison with CLJ or SLJ particles, since for this cavity shape, hard collisions reduce the particles’ speed. For higher densities, another non-trivial effect appears. Once again, the combination of interactions and confinement gives rise to order in the system that clearly reduces the system MSD. It is also shown that order appears for SLJ particles but it is absent for CLJ or HLJ particles.

A. Gonzalez, E. Diaz Herrera, M. Sandoval, M. A. Chavez Rojo, J. A. Moreno Razo

### Thermal Convection in a Cylindrical Enclosure with Wavy Sidewall

An axisymmetric convection flow within a vertical cylindrical enclosure with adiabatic wavy sidewall was studied. Two important cases of thermal convection were considered, heating from below and heating from the top, while the wavy sidewall is adiabatic. An analytical coordinate transformation was used to obtain a coordinate frame for computation in which the irregular domain fits into a square. Non-dimensional parameters which include the cavity aspect ratio, dimensionless wavelength, dimensionless amplitude, constant Prandtl number equal to

$$7$$

7

, and Rayleigh numbers between

$$10^{3}$$

10

3

and

$$10^{6}$$

10

6

, were used to characterize the convection heat transfer through the cavity. Computational solutions showed that the wavy wall promotes thermal stratification and low velocity multiple cells patterns. The effect of the wavy wall was found to restrict the convection fluid flow which yields low heat transfer through the cavity.

F. A. Sánchez Cruz, S. Martínez Martínez, H. G. Ramírez Hernández, S. Méndez Díaz

### Numerical Simulation of the Flow Past a Pair of Magnetic Obstacles

We present a quasi-two-dimensional numerical simulation of the flow of a thin layer of electrolyte past a pair of localized Lorentz forces, named

magnetic obstacles

, placed side by side. Opposing Lorentz forces are produced by the interaction of the magnetic field created by a pair of small permanent magnets and a D.C. current applied tranversally to the main flow. By varying the separation between the magnets and the intensity of the applied current, different flow regimes are analyzed. The attention is focused on the interference of the wakes created by the magnetic obstacles.

J. Román, A. Beltrán, S. Cuevas

In this paper, we present a numerical and experimental study of the laminar flow that results from the interaction of vortices driven electromagnetically in a thin layer of an electrolyte. The fluid motion is generated by a Lorentz force due to a uniform D.C. current and a non-uniform magnetic field produced by different symmetric arrays of small permanent magnets placed on the perimeter of a circle. Depending on the number of magnets and the intensity of the electric current, we find that steady or unsteady vortex flow patterns may arise. We developed a quasi-two-dimensional numerical model that accounts for the effect of the boundary layer adhered to the bottom wall. Once the velocity field is obtained, we perform a Lagrangian tracking that shows a good qualitative comparison with the experimental flow visualization. From numerical and experimental results, a map of stability that defines regions of steady and unsteady flow, according to the electric current intensity and magnet arrays, is built. We find that the larger the number of magnets, the less intense the applied current required to transit from steady to unsteady flow patterns.

C. G. Lara, A. Figueroa, S. Cuevas

### Numerical Simulation of a Spanwise Vortex in a Periodic Forced Flow

In geophysical flows, vortices are present at very different scales. Examples of them are the meddies, formed at the outlet of the Mediterranean Sea or the vorticity dipoles, occurring when water flushes from a channel into the open sea. In this paper we investigate the formation and the evolution of a spanwise vortex in the latter system, when a periodic forcing is imposed. To this end the Navier-Stokes and continuity equations are solved with a finite volume code (OpenFOAM 2008). The numerical solution has been obtained for a Reynolds number

$$Re = 1{,}000$$

R

e

=

1

,

000

and a Strouhal number

$$S = 0.02$$

S

=

0.02

. For comparison, we carried a simulation in a flow produced by a single pulse. We have found that the spanwise vortex appears in front of the dipole. It detaches from the bottom and moves away. When flow is produced by a pulse, this vortex has a horseshoe shape, while for a periodic forcing flow, the shape of the spanwise vortex evolves in time.

E. J. López-Sánchez, G. Ruíz Chavarría

### Erosion and Deposition of Particles in a Periodic Forced Flow

In this paper we present an experimental study of the erosion and accumulation of particles produced by a periodic forced flow in two domains connected by a channel. For this purpose a thin layer of sand is deposited on the bottom of the channel and one of these domains. Then, a periodic flow rate is produced with the aid of a block partially submerged in the fluid and subject to a sinusoidal vertical motion. The evolution of the system was observed for thousands of periods. The aim of this study is to model the particle transport in a tidal induced flow between an estuary and the open sea. The erosion and accumulation zones observed in our study are compared with results obtained in numerical simulations and observational works.

P. Villamil Sapien, I. Sánchez Calvo González, E. J. López-Sánchez, G. Ruíz Chavarría

### Numerical and Simplified Analytical Solutions for Typical Spillways

The present work compares the numerical solution and the simplified analytical solution to describe behavior of spillways. Specifically, the study focuses on the identification of the water fall profile formed at crossing a spillway. Both, the numerical and simplified analytical solutions are derived from the Navier-Stokes equations. The numerical solution can take into account information regarding the velocities, pressure and sources distributed in space within the regime of turbulence. However, numerical solutions provide detailed information that usually demand a significant amount of time and computational resources. Alternatively, the simplified analytical solution can be reduced to the most important variables such as the head of water arrival and the slope of the facing. Such simplification can incorporate additional information obtained from numerical solutions to improve the accuracy of the predictions. The objective of this study is to show how the simplified analytical solutions can better describe the water fall profiles due to a modification that takes into account a limited number of numerical solutions. This modified analytical solution uses the Reynolds number (Re) and the coefficient (a) associated to the turbulent regime.

F. Rojano, A. Rojano, W. Ojeda, R. Mercado, M. Iniguez, T. Espinosa

### Modeling and Simulation of a Biopolymer Processing in a Single Screw Extruder

Modeling and numerical simulation of a biopolymer processing in a single screw extruder is developed. Polylactic acid (PLA) is one of the natural polymers proposed as a substitute for synthetic polymers because of the similarity in physical properties as well as processing conditions. The PLA behaves as a shear thinning fluid, in order to involve this feature the Power Law model is used as a constitutive equation and the temperature dependent viscosity is also considered. The model is validated comparing typical flow curves of a Newtonian fluid generated by the model with results previously reported in the literature. Finally, the drag flows and pressure flows are analyzed, the effect of the power index and the flow curves for Newtonian and non-Newtonian fluids are compared.

U. Romero Ortiz, A. López Villa, R. O. Vargas Aguilar

### An Analytical Solution for Friction Stir Welding of an AISI 1018 Steel

Friction stir welding process has been usually studied from the solid mechanics point of view although the use of CFD’s techniques has been increasing for the numerical treatment of the problem. In this work, a simple analytical solution using series expansions for Cauchy momentum and energy equation-set is obtained. The Power Law model takes into account the shear thinning fluid and the Arrhenius-type relationship the temperature dependent viscosity. Friction dissipation as an external heat source is considered.

V. H. Ferrer L., C. A. Hernández C., R. O. Vargas Aguilar

### Numerical Simulation of Water Flow in a Venturi Tube Using the Smoothed Particle Hydrodynamics Method

A numerical simulation of water flow through a Venturi tube was made with the DualSPHysics code, which uses the Smoothed Particle Hydrodynamics (SPH) method. The dimensions of the simulated system are equal to the laboratory experimental setup. The experimental data were measured in the laboratory using a rotameter and a mercury manometer. The experimental and numerical results show a similar behavior. Discharge coefficient values are obtained from the numerical results.

C. E. Alvarado-Rodríguez, A. Aviles, J. Klapp, F. I. Gomez-Castro

### Dynamic Behavior of a Drop on a Vertically Oscillating Surface

In the present paper the dynamic behavior of a drop of water subject to a vertical oscillating force is studied experimentally. A hydrophobic surface was used to maintain the form of the drop. The deformation of the drop as a response to several frequencies was analyzed by visualizing the oscillating patterns and measuring the maximum height of the drop as a function of time. The dynamic behavior has been classified in three phases: harmonic, geometric and chaotic.

Fátima Flores Galicia, Flor Guadalupe Haro Velázquez, Gerardo Rangel Paredes, David Porta Zepeda, Carlos Echeverría Arjonilla, Catalina Stern Forgach

### Critical Phenomena of a Drop Through a Stratified Fluid

The present paper describes the dynamics of a drop as it falls through a stratified fluid with two layers. As it enters the fluid, the drop forms an annular vortex that suffers different deformation processes depending on the conditions of the experiment. In this work, the only variables that have been modified are the density of the drop and the height of the upper fluid. Images of the phenomena were taken directly with a high speed video camera and through a shadowgraph set-up. To access the videos of the experiment, a http address and a QR image are provided at the end of the paper.

Verónica Álvarez González, Angélica Zarazúa Cruz, Carlos Echeverría Arjonilla, David Porta Zepeda, Catalina Stern Forgach

### Accretion Centers Induced in a Molecular Cloud Core After a Penetrating Collision

The aim of this paper is to present a set of numerical simulations of a penetrating collision, in which a small gas core (the bullet) penetrates a larger gas core (the target). In the target core, the gravitational collapse is supposed to be ongoing before the collision. Each colliding core has a uniform density profile and rigid body rotation; besides the mass and size of the target core have been chosen to represent the observed molecular cloud core L1544. We modified the Lagrangian code

$$\textit{Gagdet}2$$

Gagdet

2

to identify when a gas particle can become an accretion center, and to inherit the mass and momentum of all the very close neighboring particles. Three collision models are here considered for pre-collision velocities

$$v/c_0=$$

v

/

c

0

=

$$2.5$$

2.5

,

$$5.0$$

5.0

, and

$$10$$

10

Mach. The outcome of these collision models are presented only for two different values of the bullet’s radius, that is for

$$R_0/4$$

R

0

/

4

, and

$$R_0/2$$

R

0

/

2

where

$$R_0$$

R

0

is the radius of the target core. Such collision models reveal how accretion centers are formed, with a spatial distribution that strongly depends on the pre-collision velocity. We thus show hereby that penetrating collisions may have a major and favorable influence in the star formation process.

G. Arreaga-García, J. Klapp

### Numerical Simulations of Interacting Galaxies: Bar Morphology

We present several numerical simulations of the collision of two spiral galaxies. A spiral galaxy is modelled with a spherical bulge and halo and a Freeman disc. The bulge is composed of a collisionless collection of stars; the halo is composed of a set of collisionless particles of unknown nature, we only need to know their gravitational influence and that the halo particles do not collide among them; and the disc is composed of stars only, gas or dust are not considered in this work. A bar is usually formed due to tidal effects after the first encounter of the spirals and we have found that this was the case in all the numerical experiments we did. The bar morphology is then studied during the evolution of the collision process. Here the morphology is the bar formation in the spiral discs, its geometry, i.e., minor and major axis length; and also we show how one of the collision galaxy partners change its disc geometry due to impact of the other galaxy. We show finally how the morphology of spiral galaxies changes due to collision geometrical parameters: impact parameter or the angle between symmetry axes of the spiral discs.

J. C. Luna Sánchez, M. A. Rodríguez Meza, A. Arrieta, R. Gabbasov

### A Newtonian Approach to the Cosmological Dark Fluids

We review the hydrodynamics of the dark sector components in Cosmology. For this purpose we use the approach of Newtonian gravitational instability, and thereafter we add corrections to arrive to a full relativistic description. In Cosmology and Astrophysics, it is usual to decompose the dark sector into two species, dark matter and dark energy. We will use instead a unified approach by describing a single unified dark fluid with very simple assumptions, namely that the dark fluid is barotropic and that its sound speed vanishes.

A. Aviles, J. L. Cervantes-Cota, J. Klapp, O. Luongo, H. Quevedo

### Capillary Rise in a Taylor-Hauksbee Cell with a Tilted Edge

In this work we discuss a series of experiments to get the equilibrium profiles when a viscous liquid rises spontaneously in the wedge-shaped gap between two vertical plates intersecting at a tight angle

$$\upalpha \ll 1$$

α

1

. We contrast the differences between the case with vertical edge and those where the aristae is tilted to the vertical. Our theoretical model agrees very well with the experimental data.

A. Jara, S. de Santiago, F. J. Higuera, M. Pliego, A. Medina, C. A. Vargas
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