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2013 | Book

Fluid Dynamics in Physics, Engineering and Environmental Applications

Editors: Jaime Klapp, Abraham Medina, Anne Cros, Carlos A. Vargas

Publisher: Springer Berlin Heidelberg

Book Series : Environmental Science and Engineering

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About this book

The book contains invited lectures and selected contributions presented at the Enzo Levi and XVII Annual Meeting of the Fluid Dynamic Division of the Mexican Physical Society in 2011. It is aimed to fourth year undergraduate and graduate students, and scientists in the field of physics, engineering and chemistry that have interest in Fluid Dynamics from the experimental and theoretical point of view. The invited lectures are introductory and avoid the use of complicate mathematics. The other selected contributions are also adequate to fourth year undergraduate and graduate students. 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 adequate for both teaching and research.

Table of Contents

Frontmatter

Invited Lectures

Frontmatter
Applied Fluid Mechanics in the Environment, Technology and Health

The objective of this chapter is to review the importance of fluid dynamics research and its impact on science and technology. Here we consider four particular areas of study, namely environmental fluid mechanics, turbulence, nano- and microfluids, and biofluid dynamics, with deeper emphasis on environmental flows. Each of these topics is illustrative of how improved scientific knowledge of fluid dynamics can have a major impact on important national needs and worldwide economies, as well as help developed nations to maintain their leadership in the production of novel technologies.

J. Klapp, L. Di G. Sigalotti, L. Trujillo, C. Stern
Waves and Instabilities in Rotating and Stratified Flows

This review intended primarily for Master degree students, presents the different types of classical waves that can occur in astro and geophysical flows. Inertial waves, caused by the rotation of the fluid, will first be introduced as well as their 2D version called Rossby waves. Then it will be shown how a density stratification of the fluid can make internal gravity waves appear. In each case and in the case where both rotation and stratification are present, the dispersion relations of the waves are derived. A differential rotation will then be added on the flow. The classical Rayleigh criterium for the centrifugal instability is recovered in the case of an homogeneous fluid but it will be shown that a new instability, called the strato-rotational instability (SRI), can occur when the fluid is stratified. Some experiments will be described. Finally, we will show how the application of a magnetic field can create Alfven waves in a rotating electrically conducting fluid and in which conditions the magneto-rotational instability (MRI) can grow.

Patrice Le Gal
The Sloshing-Induced Motion of Free Containers

Experiments for the time-periodic liquid sloshing-induced sideways motion of free containers are compared with theory using standard normal mode representations for rectangular boxes, upright cylinders, wedges and cones of

$$90^{\circ }$$

apex angles, and cylindrical annuli. While the wedge and cone exhibit only one mode of oscillation, the boxes, cylinders and annuli have an infinite number of modes. In some cases we have been able to excite the second mode of oscillation. Frequencies

$$\omega $$

were acquired as the average of three experimental determinations for every filling of mass

$$m$$

in the dry containers of mass

$$m_0$$

. Measurements of the dimensionless frequencies

$$\omega /\omega _R$$

over a range of dimensionless liquid masses

$$M = m/m_0$$

are found to be in essential agreement with theoretical predictions. The frequencies

$$\omega _R$$

used for normalization arise naturally in the mathematical analysis, different for each geometry considered.

Patrick D. Weidman, Andrzej Herczynski
Experimental Investigation of the North Brazil Current Rings During Their Interaction with the Lesser Antilles

Interaction of the North Brazil Current Rings (NBCR) with the Lesser Antilles Arc and their penetration into the Caribbean Sea was investigated by laboratory experiments. Self-propagating cyclonic vortices were made with barotropic fluid by one of two methods: suction and electromagnetic. The parameters causing the reflection, destruction and penetration of the rings into the Caribbean Sea were as follows: The Rossby number associated with the vortex, the width of the strait between islands, the incidence angle with the barrier, and the velocity of translation and intensity of interaction with the barrier. The principal observations were made by lagrangian measurements, using particle image velocimetry. It is concluded that the formation of bigs rings within the Caribbean Sea can be attributed to the interaction of vestiges of the NBCR with the chain of islands at the Antilles.

Raúl C. Cruz Gómez
Physical Processes of Interstellar Turbulence

This review discusses the role of radiative heating and cooling, as well as self-gravity, in shaping the nature of the turbulence in the interstellar medium (ISM) of our galaxy. The ability of the gas to radiatively cool, while simultaneously being immersed in a radiative heat bath, causes it to be much more compressible than if it were adiabatic, and, in some regimes of density and temperature, to become thermally unstable, and thus tend to spontaneously segregate into separate phases, one warm and diffuse, the other dense and cold. On the other hand, turbulence is an inherently mixing process, thus tending to replenish the density and temperature ranges that would be forbidden under thermal processes alone. The turbulence in the ionized ISM appears to be transonic (i.e, with Mach numbers

$$M_{\text{s}}\,{\sim }\,1$$

), and thus to behave essentially incompressibly. However, in the neutral medium, thermal instability causes the sound speed of the gas to fluctuate by up to factors of

$${\sim}30$$

, and thus the flow can be highly supersonic with respect to the dense, cold gas. However, numerical simulations suggest that the supersonic velocity dispersion corresponds more to the ensemble of cold clumps than to the clumps’ internal velocity dispersion. Finally, coherent large-scale compressions in the warm neutral medium (induced by, say, the passage of spiral arms or by supernova shock waves) can produce large, dense, and turbulent clouds that are affected by their own self-gravity, and begin to contract gravitationally. Because they are populated by the nonlinear turbulent density fluctuations, whose local free-fall times can be significantly smaller than that of the whole cloud, the fluctuations terminate their collapse earlier, giving rise to a regime of hierarchical gravitational fragmentation, with small-scale collapses occurring within larger-scale ones. Thus, the “turbulence” in the cold, dense clouds may actually consist primarily of gravitationally contracting motions at all scales within them.

Enrique Vázquez-Semadeni
Assessing Significant Phenomena in 1D Linear Perturbation Multiphase Flows

A procedure based on small perturbations linearization is developed for the assessment of relevant physical effects in fast fluidized beds. The fluid compressibility and wall interaction effects onto a main incompressible behavior are appreciated. A model by contributions is developed and the coefficients of all terms are evaluated in order to assess their significance. The process to get a lumped model is performed and the equivalence of lumped terms and variables under asymptotic conditions is developed. It is shown how wall effects are able to change a parabolic to a hyperbolic structure and how a third order waving structure collapses to a first order one onto a diffusive operator, under the limit of the incompressibility assumption.

Alberto Soria, Elizabeth Salinas-Rodríguez
Critical and Granular Casimir Forces: A Methodological Convergence from Nano to Macroscopic Scales

Recent advances in colloidal science that have lead to directly measuring depletion and critical Casimir interaction potentials are reviewed. Methodological convergence of these studies is exploited and extended to granular systems in order to measure effective interactions among their constituent particles. Experimental evidence of depletion interactions as well as a novel “granular Casimir effect” is presented and subtle differences are discussed.

Y. Nahmad-Molinari, G. M. Rodríguez-Liñán, J. F. Reyes-Tendilla, G. Pérez-Ángel
High Speed Shadowgraphy for the Study of Liquid Drops

The principles of shadowgraph photography are described in this work together with a few examples of its utilisation in the study of free liquid surfaces. Shadowgraph photography is utilized in combination with high speed imaging and image analysis to study the behaviour of sub-millimetre and millimetre-sized droplets and jets. The temporal and physical scales of these examples cover operational ranges of industrial, commercial, and academic interest. The aim of this work is to summarize the necessary optical and illumination properties to design an appropriate shadowgraph imaging system.

José Rafael Castrejón-Pita, Rafael Castrejón-García, Ian Michael Hutchings
Formation of Coherent Structures in a Class of Realistic 3D Unsteady Flows

The formation of coherent structures in three-dimensional (3D) unsteady laminar flows in a cylindrical cavity is reviewed. The discussion concentrates on two main topics: the role of symmetries and fluid inertia in the formation of coherent structures and the ramifications for the Lagrangian transport properties of passive tracers. We consider a number of time-periodic flows that each capture a basic dynamic state of 3D flows: 1D motion on closed trajectories, (quasi-)2D motion within (approximately) 2D subregions of the flow domain and truly 3D chaotic advection. It is shown that these states and their corresponding coherent structures are inextricably linked to symmetries (or absence thereof) in the flow. Symmetry breaking by fluid inertia and the resulting formation of intricate coherent structures and (local) onset of 3D chaos is demonstrated. Finally, first experimental analyses on coherent structures and the underlying role of symmetries are discussed.

Michel F. M. Speetjens, Herman J. H. Clercx
Jets in Symbiotic Stars: The R Aqr Case

In this paper we analyse the jet like features observed in some symbiotic systems, we present the objects in which such features were detected. One of this objects is R Aqr. In this object high collimated outflows emerging from the central region has been observed since the 1970s. We present the possible explanation for this outflows and analyse some new kinematic data of this object comparing them with previous observations.

Silvana G. Navarro, Luis J. Corral
Granular Hydrodynamics

Sand flowing through the constriction of an hourglass or jumping on a vibrating plate is fluidized in the sense that it moves analogously to a fluid. Dense flows of grains driven by gravity down inclines occur in nature and in industrial processes. Natural examples include rock avalanches and landslides. Applications are found in the chemical, pharmaceutical and petroleum industry. Grain flow can be modeled as a fluid-mechanical phenomenon. However, granular fluids teach us about an astounding complexity that emerges from simple, macroscopic particles. For example, starting from an homogenous fluidized system, structures evolve and a dilute granular fluid co-exists with much denser solid-like clusters. Another example is the so-called Brazil nut effect, whereby larger and heavier particles placed into an agitated granular bed rise to the top. We present an outlook of the hydrodynamic description of granular materials. Our purpose is to outline a theory of grain flow which is based upon the description of continuous matter fields derived from the kinetic theory for dense gases, as is usually encountered in fluid dynamics.

L. Trujillo, L. Di G. Sigalotti, J. Klapp
Efficient Neighborhood Search in SPH

One of the main problems found during the implementation of an N-body algorithm, is its inefficiency when the number of points to evaluate is increased. This is a consequence of the order

$$O(N^2)$$

of these methods. With this in mind, when we use the method of Smoothed Particle Hydrodynamics (SPH), it is necessary to find an algorithm that allows us to make the computation in an efficient way. The method presented in this article is of order

$$O(N)$$

, being more efficient as well as easy to implement, reducing the computing time.

Juan Pablo Cruz Pérez, José Antonio González Cervera

Multiphase and Granular Flow

Frontmatter
On the Film Thickness Between a Bubble and the Wall in Liquids in Vertical Tubes

We study numerically the film thickness that is formed between the free surface of a bubble and the inner wall in a vertical tube. The bubble is formed by gas injection in a tube filled with a viscous fluid. The computations were performed through the use of the Boundary element method (BEM) to solve the Stokes equations and a fourth order Runge–Kutta scheme to build the bubble shape. After the computation of the bubble shape, the thickness of the annular film was calculated for low Bond numbers,

Bo

, and a wide range of Capillary numbers,

Ca

. For the case

Ca

1 (inviscid approximation) it is found that the film actually touches the wall, meanwhile for the viscous case we found that the film thickness, scaled by radius of the tube, is a function of

Ca

and

Bo

. We also discuss experiments that validate the numerical results.

Abel López-Villa, Abraham Medina Ovando
Mathematical Model for “Bubble Gas-Stratified Oil” Flow in Horizontal Pipes

A one-dimensional, isothermal, transient model for bubble gas-stratified oil flow is presented. Bubble gas- stratified oil flow pattern of heavy oil, water and gas, in horizontal pipelines, consists of two regions: (1) a stratified region with a gross water layer in the bottom, an oil layer in the middle and a thin water layer in the top, (2) a region with a water layer in the bottom, an oil layer in the middle and a gas bubble in the top. The two-fluid mathematical model consists of mass, momentum and energy conservation equations for every phase, considering the hydrostatic gradient. The model takes into account: (1) wall shear stress, (2) interfacial shear stress, and (3) the non-Newtonian oil behavior. The model is able to predict pressure, volumetric fraction, temperature, and velocity profiles for every phase. The numerical solution is based on the finite difference technique in an implicit scheme. The model was validated using experimental data reported in literature, for a heavy crude oil (14 °API), and it was observed that the pressure drop calculated by the model was reasonably close to the experimental data.

C. Centeno-Reyes, O. Cazarez-Candia
Pseudoturbulence in Bubbly and Transition Flow Regimes

Computational fluid-dynamics codes use the two-fluid model to simulate transport phenomena in liquid–gas flows. Numerical instabilities arise when flow regime transition occurs, i.e. bubbly flow to slug flow. One mechanism that produces the transition between regimes is the fluctuation induced over the liquid phase velocity due the relative movement of ascending bubbles. Using multi-tip impedance probe and Laser Doppler Anemometry (LDA), the main local flow parameters of the two-phase flow were obtained. The flow conditions selected were single phase flow up to liquid–gas flow at 30 % gas concentration. The power spectral energy distributions obtained show that turbulence intensity and the energy exponent decay have a nearly constant value when wall peak is observed (wall peak distribution occurs when the radial void fraction distribution shows a peak concentration near to the channel wall). Under the flow conditions tested, pseudo-turbulence effects can be observed at low gas concentrations in bubbly flow regime and the decay energy has a nearly constant slope; whereas at transition and slug regimes the exponent decay in PSD’s shows a non-constant value, and the lift force would be less important.

Santos Mendez-Diaz, Roberto Zenit, Sergio Chiva Vicent, José Luis Muñoz-Cobo, Arturo Morales-Fuentes
Single- and Two-Phase Flow Models for Concentric Casing Underbalanced Drilling

Underbalanced Drilling process (UBD) is applied to oil fields where the original pressure has been depleted as a consequence of an intensive exploitation. In such technique, due to the incorporation of nitrogen into the Drilling Fluid (DF), the downhole pressure is close to the reservoir pressure. This work presents a single-phase, one-dimensional and transient mathematical model for the flow of: (1) nitrogen in an annulus, and (2) DF in a drill pipe. It is also presented a one-dimensional, transient, mathematical drift-flux model for the DF-gas two-phase flow in an annulus. The mathematical models are based on the mass, momentum and energy conservation equations, which are solved numerically using the finite difference technique in an implicit scheme. The models allow predicting pressure, velocity and temperature profiles. The predictions are in agreement with experimental and field data reported in the literature.

J. Omar Flores-León, Octavio Cazarez-Candia, Rubén Nicolás-López
Study of Structural Properties in Complex Fluids by Addition of Surfactants Using DPD Simulation

In this work we study the tertiary structure of ionic and surfactant when the pH in the system is modified using electrostatic dissipative particle dynamics simulations (DPD). The dependence with pH and kind of surfactant is presented. Our simulations reproduce the experimental behavior reported in the literature. The scaling for the radius of gyration with the size of the molecule as a function of pH is also obtained.

Estela Mayoral, Eduardo Nahmad-Achar, José Manuel Martínez-Magadán, Alejandro Ortega, Ismael Soto
Study of Slug Flow in Horizontal, Inclined, and Vertical Pipes

In the literature several mathematical models have been reported for the slug flow, which uses the concept of the unit slug in common. This concept requires the longitudes of the liquid slug and the Taylor bubble to be known, for the correct evaluation of the terms: phase-wall and interfacial shear stresses, and virtual mass forces. In this work are presented the results of an experimental study of the upward slug flow (in an acrylic pipe with 6 m of length and 0.01905 m of internal diameter). The working fluids are water and air. They were carried out experiments for several angles of tube inclination from horizontal to vertical. The length of liquid slug and Taylor bubble were measured. Also, using voltage signals of two infrared sensors, was determined: (1) The Taylor bubble velocity by means of the cross correlation and (2) The slug frequency when applying the Fourier transform to these obtained data; this information allows to determine the length of liquid slug. It was observed that the Taylor bubble length decreases when increasing the flow of the liquid so much as the angle of inclination, while the Slug length varies with a similar tendency.

Omar C. Benítez-Centeno, Octavio Cazarez Candia
Modeling of Water-Steam Slug Flow in Inclined Pipes Undergoing a Heating Process

This work presents a one-dimensional transient mathematical model for the steam-water slug flow. The model is based on the two-fluid modeling technique. This consists in mass and momentum equations for each phase. Total thermal equilibrium was assumed, nucleation is neglected and the difference between steam and water pressures is taken into account. The model was solved using the finite difference technique. The model allows estimating: pressure, steam volume fraction, velocity, mixture temperature, and internal-wall pipe temperature. Different slug frequency correlations were evaluated. It was found that the best prediction of pressure drop was obtained with the Greskovic and Shrier (

1971

) correlation. The pressure predictions are in agreement with simulations obtained from a commercial simulator.

P. Mendoza-Maya, O. Cazarez-Candia, S. L. Moya-Acosta
Crystal-Liquid Transition in Binary Mixtures of Charged Colloidal Particles

In this work we present experimental results on the melting of binary colloidal crystals composed by two different sized charged colloidal particles. As the number fraction of the smallest particles is increased, we observe a crystal-liquid transition. The melting line is characterized by studying the structural and dynamic properties of the colloidal suspensions by means of cross-correlation dynamic light scattering. The initial crystal structure consists of a body centered cubic lattice and after reaching a certain concentration of small particles, the system melts. At the melting point the resulting structure measured by static light scattering represents that of a strongly correlated fluid.

Catalina Haro-Pérez, Gualberto Ojeda-Mendoza, Carlos A. Vargas, Eduardo Basurto-Uribe, Luis F. Rojas-Ochoa
On the Mass Flow Rate of Granular Material in Silos with Lateral Exit Holes

The mass flow rate,

$$ \dot{m} $$

, associated with the outflow of dry, cohesionless granular material through orifices located in vertical walls of silos was analyzed experimentally in order to reveal the dependence of this quantity on

D

and

w

,

i.e.,

the diameter of the orifice and the wall’s thickness, respectively. A series of experiments enable us to give a general correlation, which has the form

$$ \dot{m} = \dot{m}_{0} - wA, $$

where

A

is a constant and

$$ \dot{m}_{0} $$

is the mass flow rate to the minimum allowable wall thickness.

Abraham Medina, G. Juliana Gutiérrez-Paredes, Satyan Chowdary, Anoop Kumar, K. Kesava Rao
Traction Force Due to Aqueous Foam Flow Rising in a Vertical Pipe

This paper discusses in an experimental way the traction force exerted by a flow of aqueous foam through the annular space between a central rod and the inner walls of the pipe. These studies were made to prove if foam behaves as a granular material or as a power-law fluid. Experiments allow concluding that the flow of dry foam is a type of slipping flow where the traction does not depend on the radius of the pipe or on the radius of the rod.

A. Pérez Terrazo, V. S. Álvarez Salazar, I. Carvajal Mariscal, F. Sánchez Silva, A. Medina
A Discrete Model for Simulating Gas Displacement in Fractured Porous Media

A physically based approach to numerical miscible displacement model in a matrix-fracture system was developed. Matrix-fracture configuration was divided in two different domains: fractured media was considered as a free flow channel. Then Navier–Stokes, continuity and convection–diffusion equations were also employed. The matrix is solved with Darcy mass conservation and Diffusion for porous media. The system equation is solved about the scheme of finite differential method and finite volume.

S. Pérez-Morales, A. Méndez-Ancona, M. Ortega-Rocha, R. Islas-Juárez, R. Herrera-Solís, G. Domínguez-Zacarías
Profile Deformation of a Non Cohesive Granular Material in an Accelerated Box

When a dry non cohesive granular material confined in a box in such a way that the initial profile of the free surface is a horizontal plane and it is accelerated uniformly, the final equilibrium profile changes to a tilted straight plane whose slope is a function of the magnitude of the acceleration, the magnitude of the gravity acceleration and the friction coefficient of the granular material. Here are presented a simple model, based on the Coulomb’s law, that describes correctly such a deformation and some experiments that back the theoretical predictions.

V. S. Álvarez Salazar, A. Pérez Terrazo, A. Medina, C. A. Vargas

Convection, Diffusion and Vortex Dynamics

Frontmatter
Experimental and Computational Modeling of Venlo Type Greenhouse

Currently, experimental data gathered with high frequency and good quality allows us to feed more complex mathematical models by using high speed and large memory computational devices with numerical technique like finite element method. Simple models had been enriched including details of internal flow patterns and temperature profiles. Recent progress in flow modeling by means of computational fluid dynamics (CFD) software facilitates the fast analysis of such scalar and vector fields, solving numerically the transport equations like mass, momentum and heat transfer equations. As a result, this work shows us the mechanical air behavior in terms of velocity and temperature patterns near to the plant benches in a Venlo type greenhouse by using Boussinesq assumptions.

Abraham Rojano, Raquel Salazar, Jorge Flores, Irineo López, Uwe Schmidt, Abraham Medina.
Numerical Simulation of an Open Cavity with Heating in the Bottom Wall

This work presents the numerical simulation of heat transfer and fluid dynamic in steady state of a two-dimensional Cartesian flow inside a cavity with one inflow and one outflow for Re = 100 and 1,000. The domain of the simulation consists in a rectangular section with two different aspect ratios. Three different lengths of the heater at the bottom wall were analyzed. The governing equations of continuity, momentum and energy for incompressible flow were solved by the finite element method. The velocity fields, isotherms, streamlines and vortex formation were studied. The simulation indicates that is possible to control the dynamic and vortex formation inside the cavity due to the variation of the length of the heater.

Guillermo E. Ovando-Chacon, Sandy L. Ovando-Chacon, Juan C. Prince-Avelino, Eslí Vázquez-Nava, José A. Ortiz-Martínez
Natural Convection and Entropy Generation in a Large Aspect Ratio Cavity with Walls of Finite Thickness

In this work we study the heat transfer and fluid flow process in a vertical cavity of large aspect ratio,

$$AR=12$$

, with walls of finite thickness, heated from two portions localized in the side walls of the cavity near the bottom. The equations of motion are written in non-dimensional form, depending of four non dimensional parameters (the Rayleigh number, the Prandtl number, the ratio of thermal diffusivities of the fluid and the material of the cavity and the non-dimensional width of the walls) and are solved numerically by the use of the SIMPLE algorithm. Calculations are performed for three different values of the Rayleigh number.

D. Pastrana, J. C. Cajas, C. Treviño
Spectral Analysis of Chaos Transition in a Dynamic System: Application to Backward Facing Step Flow in Mixed Convection

This work focuses on the study of the transition from steady to chaotic behavior in mixed convection flow over a backward-facing step. Direct numerical simulations are performed in a two-dimensional horizontal channel of expansion ratio

ER

= 2 at step level. The effects of the temperature difference between the heated bottom wall and the inflow temperature are investigated by keeping constant the Richardson number at 1. The covered range of Grashof and Reynolds numbers is respectively 3.31 × 10

4

≤ Gr ≤ 2.72 × 10

5

and 182.03 ≤ Re ≤ 521.34. The thermodynamic instabilities which cause the onset of unsteady flow are described in detail. A spectral and phase portrait analysis of the temperature time series allows us to observe that the transition from steady to chaotic flow occurs by period-doubling bifurcations.

Héctor Barrios-Piña, Stéphane Viazzo, Claude Rey, Hermilo Ramírez-León
Turbulence Model Validation in Vegetated Flows

This work presents the validation of a two-layer mixing-length model for turbulence applied to shallow water flows in presence of vegetation. In order to determine the vertical velocity variations when submerged vegetation exists, a multilayer numerical model-based approach is used. A second-order finite difference method is used for spatial discretization and a semi-implicit lagrangian–eulerian method is used for time discretization. The comparisons to experimental data for validating the turbulence model show good agreement for two cases, a channel with submerged vegetation and other one with both submerged and emergent vegetation.

R. González-López, H. Ramírez-León, H. Barrios-Piña, C. Rodríguez-Cuevas
CFD on Graphic Cards

In the last decade, the entertainment and graphic design industries demand for higher resolution and more realistic graphics has motivated graphic card manufacturers to develop high performance graphic processing units (GPUs) at low cost. Nowadays GPUs are highly efficient parallel processing units that can be used for general purposes. Such developments open a new alternative within scientific computation, promising high performance parallel computation at everyones reach. Graphic cards seem to be an attractive option, specially for research groups and institutions with limited computational resources and for teaching purposes. Here, an overview of parallel computation on GPUs is presented, as well as the efforts to manipulate and promote this technology within the UNAM, particularly in Fluid Mechanics applications.

C. Málaga, J. Becerra, C. Echeverría, F. Mandujano
Vortex in the Wakes of Airplanes

This paper describes the disturbances caused by wing trailing vortices and their effect on aircraft flying into them. We briefly discuss the physical characteristics of the wing trailing vortices together with their control and alleviation and emphasis is done about the importance that it has in order to diminish the problems generated by the increase in air traffic and in the fly safety.

David Flores-García, Tiburcio Fernández-Roque, Jorge Hernández-Tamayo
The Activity of La Bufadora, A Natural Marine Spout in Northwestern Mexico

La Bufadora

is a natural marine spout characterized by frequent eruptions of sea water. It is located about 20 km to the southwest of Ensenada, on a cliff of basaltic andesite where the essential elements for the occurrence of this type of spouts are present; namely: a littoral cave with a thin opening, a sea level which is always close to the opening’s tip point and surface waves that vary from mild to strong all year round. We analyzed the activity of La Bufadora, under various conditions of surface waves and ocean tide, by monitoring the recurrence time of the eruptions (

T

). It was found that

T

typically lies in the range 13–17 s, which is also the dominant period of the surface waves, and that more and longer periods of inactivity appear as the tide ebbs.

Oscar Velasco Fuentes
A CNC Machine for Stationary Drop Deposition and Coalescence in Liquid–Liquid Systems

The controlled deposition of a dispensed liquid drop onto the surface layer of another liquid is a process that is widely applied in the industry. In most applications, the deposition of stationary drops requires a micrometric translational approach to the surface. Here we describe a computer controlled apparatus that has been constructed to perform precision translation of pendant drops and deposition at liquid and solid surfaces. Different settings of the experimental setup can be easily implemented in the laboratory for use in a variety of other applications, including surface tension measurements and wire bonding in microelectronics. Some experimental tests of partial drop coalescence with a miscible liquid are presented which validate the reliability of the apparatus.

F. Peña-Polo, L. Trujillo, J. Klapp, L. Di G. Sigalotti

Meteorology and Pollution

Frontmatter
Numerical Study of Wind Field Adjustment with Radial Basis Functions

A collocation method based on radial basis functions (RBF) is introduced for wind field adjustment in meteorology. The numerical solutions are shown to be more accurate than those obtained with the finite element method (FEM), and they also require much less computational effort. A detailed analysis shows how inconsistent boundary conditions may affect numerical solutions.

Rafael Reséndiz, L. Héctor Juárez, Pedro González-Casanova, Daniel A. Cervantes, Christian Gout
Dispersion of Air Pollutants in the Guadalajara Metropolitan Zone

The objective of this work is to identify the main factors influencing the dispersion of air pollution in the Guadalajara Metropolitan Zone (ZMG). To this end, we analyzed the behavior of atmospheric pollutants, the speed of the winds and the presence of thermal inversions (IT) over the past 10 years. The results showed that during the early hours of the day, the dominant factors are the influence of IT and the frequency of calmer winds (winds between 0 and 5 km/h), which do not allow the dispersal of pollutants in the area. Past the noon (12:00 h) the solar radiation increases the temperature of the bottom layer of the IT, reaching the equilibrium temperature that breaking the IT, thus starting the dispersion of pollutants. This process occurs in addition to the increase of the wind speed in the afternoon, generating horizontal dispersion to the outside of the ZMG, possibly affecting the Toluquilla Valley. In conclusion, the dominant factors in the dispersion of air pollutants in the ZMG are thermal inversions and the wind speed.

Hermes Ulises Ramírez-Sánchez, Mario Enrique García-Guadalupe
Modeling of Funnel and Gate Systems for Remediation of Contaminated Sediment

Capping is typically used to control contaminant release from the underlying sediments. While conventional capping doesn’t necessarily provide the removal of contaminants, incorporating a “funnel and gate” reactive barrier with capping has the potential to treat contaminants or limit contaminant migration. The purpose of this study was to develop a model of funnel and gate systems for remediation of contaminated sediment. Numerical modeling of vertical two dimensional water flow and solute transport was built in COMSOL MULTIPHYSICS 3.4. The model was employed to evaluate the performance of the funnel and gate system, i.e. residence time, removal efficiency, and breakthrough curve. Two types of gate, reactive and adsorptive gates, were evaluated for the remediation of phenanthrene contaminated sediment. The simulated results showed that the performance of the reactive gates depended on Damkohler number at the gate, and adsorptive gate could effectively slow contaminate migration into water body, and decrease the maximum concentration at the gate. This model could potentially serve as a design tool of funnel and gate systems for a range of typical sediment capping conditions.

Fei Yan, Danny D. Reible
Analysis of Transport Parameters for a Cr(VI) Contaminated Aquifer in México

In the Buenavista area of Leon City, Mexico, Cr(VI) groundwater contamination was detected, originating from an industrial landfill with chromium compounds. A 2D vertical simulation model was established for the Buenavista study area. Laboratory and field data were incorporated into a finite element groundwater flow model and a solute transport model to analyze the transport parameters in the Buenavista shallow aquifer. A sensitivity analysis was performed to obtain values representative of the transport parameters (hydraulic conductivity [K], longitudinal, horizontal and vertical transverse dispersivities [α

L

, α

TV

], distribution coefficient [

K

d

], the initial concentration [C

o

] and pumping rates [Q]). This analysis allowed a good calibration of the model. The incorporation of the resulting set of parameters in the finite element model enabled the reproduction the observed contaminant plume in Buenavista close to 95 % match. The values obtained were α

L

= 50.0 m, α

TV

= 2.5 m,

K

d

= 0.007 mL/g, C

o

= 160 mg/L and Q = 100 m

3

/d. The sensitivity analysis indicated that the dispersion of the Cr(VI) plume is most sensitive to variations in hydraulic conductivity, the distribution coefficient, longitudinal and transverse dispersivity and pumping rates. In addition to the sensitivity analysis, it was observed that Q strongly affects the plume geometry.

Lázaro Raymundo Reyes-Gutiérrez, Ramiro Rodríguez-Castillo, Elizabeth Teresita Romero-Guzmán, José Alfredo Ramos-Leal
Numerical Simulation of Dispersion and Sorption of Se(IV) Through Packed Columns with Non-Living Biomass: Experimental and Numerical Results

A continuous fixed bed study was carried out using the non-living biomass

Lemna minor

as a biosorbent for the removal of Se(IV) from an aqueous solution. A 3D numerical model was constructed for solving the

Navier

Stokes

Brinkman

and mass transport equations using the finite element technique with 161,764 tetrahedral elements. Experimental and numerical results were obtained and compared to validate the model, obtaining correlation factors of up to R

2

= 0.95. From the sensibility analysis, the parameters for the Thomas model best match were obtained, with a value of

k

= 2.95 × 10

−3

m/s,

K

f

= 0.1201 L/kg, α

L

= 0.5 m and α

TH

= α

TV

= 0.005 m was possible to predict the breakthrough curves of sorption of Se(IV) in packed column with non-living biomass of

Lemna minor

in aqueous solution. Using the numeric model, seven fixed bed columns with different dimensions were simulated, and from the simulation results the removal of 15 % of Se(IV) was obtained.

Carlos E. Alvarado-Rodríguez, Jaime Klapp-Escribano, Elizabeth T. Romero-Guzmán, Zayre I. González-Acevedo, Ricardo Duarte-Pérez
Tridimensional Analysis of Migration of 226Ra Through a Saturated Porous Media

Transport simulation of radioactive contaminants in fluids through saturated porous media provides a powerful tool to prevent the risk they could represent to the environment. This kind of waste is stored in containers. These containers are collocated in subterranean places for being confined. Proper election of those places requires the appropriate classification according to the properties of the site. This work is presenting the 3D numerical simulation of migration of

226

Ra through a tridimensional saturated porous media. The numerical solution is obtained solving the transport equations using Darcy’s approximation for flux in saturated media by finite element method (FEM). The governing equations for this model are described as well as the numerical tool employed. The results are analyzed at different simulation time showing the behavior of the system.

N. Perez-Quezadas, E. Mayoral, J. Klapp, E. de la Cruz, R. González
Evaluation of a Temporary Repository of Radioactive Waste

The confinement of radioactive waste (radionuclides) in underground installations has to take into account its influence on the environment, the solvent action and the waste groundwater drag. This work evaluates by computer simulations how radionuclides migrate through the subsurface of a typical site in Mexico. The simulations show preferential routes that the contaminant plume follows over time. Results indicate that the radionuclides flow is highly irregular and it is influenced by failures in the area and its interactions in the fluid–solid matrix. The obtained concentration of the radionuclide is as expected.

Roberto González-Galán, Eduardo de la Cruz-Sánchez, Jaime Klapp-Escribano, Estela Mayoral-Villa, Nora Pérez-Quezadas, Salvador Galindo Uribarri

General Fluid Dynamics

Frontmatter
Friction Coefficient in Plastic Pipelines

Currently, plastic pipes are beginning to be more used because of its low cost, easy installation, flexibility, durability, low weight, etc. However, this kind of pipes may have a friction coefficient sensitive to variations of flow and temperature, which can affect in the design of an analytic leak diagnosis system. The variations of friction in a plastic pipeline can be caused by the following: the flow is not in a fully developed regime. In the same way, temperature affects the viscosity of water which affects the value of the Reynolds number and then, the value of the friction coefficient. This work illustrates the sensitivity of the friction coefficient due to changes in flow and temperature with experiments performed in a plastic pipeline prototype located at the Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV-Guadalajara).

E. A. Padilla, O. Begovich, A. Pizano-Moreno
Super Free Fall in Concentric Pipes

In the present work we have analyzed experimentally the characteristics of the free surface of a liquid column starting off of the rest in a vertical container (concentric tubes). We have two tubes of different areas A

1

< A

2

interconnected where a great transition due to this difference of areas is registered. To small times for which the viscous effects are despised, the free surface in the superior tube reaches acceleration greater than gravity (

g

).

C. Treviño, S. Peralta, Carlos A. Vargas, A. Medina
Super Accelerated Flow in Diverging Conical Pipes

The motion of the upper free surface of a liquid column released from the rest in a vertical conical container is analyzed theoretically and experimentally. An inviscid one dimensional model for a weakly increasing cross section in vertical tubes describes how the recently reported super free fall of liquids occurs in liquids of very low viscosity. Experiments show that the inviscid one dimensional model developed here agrees with theoretical results.

A. Torres, F. J. Higuera, A. Medina
Analysis of the Blasius’ Formula and the Navier–Stokes Fractional Equation

The objective of this paper is to find the relationship between the Blasius formula for friction factor and the Navier–Stokes Fractional equation. The renormalization that produces changes of scale of the boundary layer equations contains the essential hypothesis of the thinness of said layer, a characteristic which appears in all important outcomes, such as friction force and drag coefficient and gives rise to a multi-fractal description. A generalization of experimental results for the Blasius friction factor that is interpreted and generalized as a multi-fractal is obtained. Applying Hadamard functionals the friction factor is described as a fractional derivative whose order depends on the

spatial occupancy index

. Results are applied to the interactions between currents and boundaries (in rivers, deserts and hurricanes).

J. R. Mercado, E. P. Guido, A. J. Sánchez-Sesma, M. Íñiguez, A. González
Relativistic Hydrodynamics and Dynamics of Accretion Disks Around Black Holes

We give a brief overview of a formulation of the equations of general relativistic hydrodynamics, and one method for their numerical solution. The system of equations can be cast as first-order, hyperbolic system of conservation laws, following a explicit choice of an Eulerian observer and suitable vector of variables. We also present a brief overview of the numerical techniques used to solve this equation, providing an example of their applicability in one scenario of relativistic astrophysics namely, the quasi periodic oscillations of a thick accretion disk.

Juan Carlos Degollado, Claudia Moreno
Low-Re μUAV Rotor Design

This paper presents a novel approach to the design, optimization and testing of rotors for small helicopters using Bezier curves as airfoils. Blade design with low Reynolds numbers (5,000–60,000) is seriously affected by air viscosity; therefore our approach to this scenario is to analyze the propellers through the use of 3D BEM/VPM (Blade Element Momentum/ Vortex panel method) theory, further refined by estimates of blade tip and blade root losses. In addition, the code used throughout this report creates a CAD file that allows the propeller to be visualized in 3D. This report also contains the rotor build for a micro-helicopter with its results compared to the performance of current propellers; the rotor features a 15 cm blade under a 10,000 Reynolds number at cruising speed.

Oscar Rubio, Fidel Gutiérrez, Juan Carlos Zuñiga, Marcelo Funes-Gallanzi
Oscillation Characteristics of a Vertical Soft Pipe Conveying Air Flow

This study takes place in the “fluid–structure interaction” area. The experiment consists of a large vertical thin fabrics tube whose lower extreme is fixed to an air blower exit. For a sufficient intensity of the air flow, the tube stands up. Whereas these kinds of systems have different characteristics than previous studies (Païdoussis

1998

) we find that at the instability threshold, the tube oscillates with a frequency of the same order of magnitude as in these previous works.

Héctor Manuel De La Rosa Zambrano, Anne Cros
Capillary Rise in a Convergent Hele-Shaw Cell

The capillary rise of a viscous liquid into a convergent Hele-Shaw cell whose plates make a wedge-like channel along the downwards coordinate z has been analyzed theoretically by using the lubrication theory. The solution to this problem allows to determine the existence of a continuous flow which is atypical in problems of capillary rise.

C. A. Vargas, A. Medina, F. Aragón
Manufacturing of Polymeric Micro-Lenses by Drip Injection

In this work we study an alternative and innovative method for the manufacture of polymeric micro-lenses and how the characterization of its physical, mechanical and optical parameters is relevant for their application. We study the equilibrium shapes of drops that emerge slowly from vertical thick-walled tubes, as a result, it is found that the sizes and shapes of drops depend on the Bond number, the injection pressure and the value of the contact angle, so that finally with this technique we are able to make lenses. The manufacture will be made though drip injection since it is easier to control the shape of the lens.

Miguel Ortega, Abel López-Villa, Guadalupe Juliana Gutiérrez, Carlos A. Vargas

Gallery of Fluids

Frontmatter
Visualization of Flow Inside a Ranque-Hilsch Tube

A Ranque-Hilsch tube is a device that separates—in absence of mobile parts—a flow into two fractions; one hot and the other one cold.

David Porta Zepeda, Carlos Echeverría Arjonilla, Catalina Elizabeth Stern Forgach, Marcos Ley Koo
Splashing of Solid Spheres Impinging in Various Fluids

A solid object with spherical symmetry splashes when it impinges on a liquid surface. A cavity is formed and structures with fancy shapes appear surrounding it. As the sphere sinks, it is surrounded by small bubbles, and once it reaches the bottom a jet is ejected as a consequence of the conservation of energy.

Sergio Valente Gutierrez Quijada, Martha Yadira Salazar Romero, Catalina Elizabeth Stern Forgach
Bubbles in Isotropic Homogeneous Turbulence

An experimental study of the bubble deformation in an isotropic homogeneous turbulent flow field was carried out. It is of a fundamental importance to understand the rate of coalescence and breakup in two phase disperse flows.

Ernesto Mancilla, Roberto Zenit, Gabriel Ascanio, Enrique Soto
CDF on Graphic Cards

Examples of 2 and 3D simulations using graphi cards. The equations of motion were solved using a Lattice Boltzmann Method and a semi-lagrangian method.

C. Malaga, J. Becerra, C. Echeverría, F. Mandujano
Metadata
Title
Fluid Dynamics in Physics, Engineering and Environmental Applications
Editors
Jaime Klapp
Abraham Medina
Anne Cros
Carlos A. Vargas
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-27723-8
Print ISBN
978-3-642-27722-1
DOI
https://doi.org/10.1007/978-3-642-27723-8