Recent Advances in Fluid Dynamics with Environmental Applications

In the present work, the laminar steady state fluid dynamics and heat transfer, in a two-dimensional open cavity with a cross flow due to a secondary jet injected at the top wall, are analyzed. The numerical study is carried out for a Reynolds number of 500 with different Richardson and Prandtl numbers. A hot plate is provided on the bottom of the cavity which generates the heating of the fluid. In order to investigate the effect of the length of the plate two different plate sizes are considered. The governing equations of continuity, momentum and energy for incompressible flow are solved by the finite element method combined with the splitting operator scheme. It is studied the streamlines and isotherms inside the cavity and it is analyzed the average Nusselt number, the average temperature and the outlet temperature as a function of the Richardson and Prandtl numbers. It is observed that the Prandtl and Richardson numbers play a major role in the thermal and fluid behavior of the flow inside the cavity with a cross flow. Moreover the results indicate that a secondary jet injected at the top wall enhances the average Nusselt number.

This experimental study deals with the oscillation of a flexible plate inside the von Kármán street. The flow velocities are much lower than the threshold above which the fluttering instability would develop. The flexible plate is fixed at its leading edge whereas its leading edge is free. The vortices are detected by tin oxide and the whole system is recorded by a videocamera. We find that the trailing edge of the plate oscillates with a small amplitude and with the same frequency as the incoming vortices. Moreover, the plate wavelength is more than twice the plate length. These results are different from the previous experiments of Allen and Smits (2001) performed with larger plates and at much higher Reynolds numbers. Alben (2010) theoretical study permits to explain these differences.

At the outlet of estuary-like systems, three vortices are formed: a dipole and a spanwise vortex. The spanwise vortex is formed due to the separation of the bottom boundary layer, just in front of the dipole. If a step occurs at the bottom in the channel output, a single vortex will be formed, the dipole becomes a part of a structure having a horseshoe shape. In a periodic driving flow, after a while this structure results in a dipole and a spanwise vortex. To study in laboratory this kind of vortices we made experiments in a system consisting of two domains connected by a channel in which the flow is induced by a periodic forcing. The channel layer depth is different with respect the depth in the two others domains. In order to investigate this system some measurements of velocity field using PIV were carried out in the vertical plane passing along the channel centerline. On the other hand, the detection of vortices composing the dipole was made with the synthetic Schlieren method. Vortices are low pressure regions, then they produce a deformation of the free surface which can be detected with this method. We observed that at the channel output a horseshoe vortex is formed by the flushing into the open domain. This structure remains for some time, after it decomposes in a dipole and a spanwise vortex. Finally all three vortices are destroyed.

In this work fluid forces acting on a flexible circular cylinder in Vortex-Induced Vibrations (VIV) were studied. An experimental campaing was conducted at low mass-damping ratio ($$\mathrm {m_{cil}^{*}\zeta }$$mcil∗ζ = 0.126) covering the entire lock-in region. The dynamic response of the cylinder was computed using the Particle Tracking Velocimetry technique on the cylinder free end tip. Drag and lift coefficients ($$C_{D}$$CD and $$C_{L}$$CL) were determined using the experimental data from the cylinder response in a spring-mass-damping model. Results show that $$C_{L}$$CL is one order of magnitude greater than $$C_{D}$$CD. Strong cylinder oscillations are associated with a flow pattern showing two vortex center lines corresponding mainly at the upper end of the initial region.

Different vortical patterns are observed behind flapping foils in a uniform water flow. Previous studies have described these structures and delimited the parameter intervals for which each pattern develops. Generally, the two pertinent nondimensional numbers are the Strouhal number St _D , proportional to the foil oscillation frequency, and A _D , related to the foil oscillation amplitude. In this experimental study, we show that the value of the foil aspect ratio radically changes the transition diagram. More particularly, for the St _D and A _D values for which the reversed von Kármán street develops when the foil is “long”, another pattern is generated when the foil is shorter.

Circulation Control is an aerodynamic method in which the Coanda effect is induced in specific sections of the airfoil, typically near the trailing edge on the suction side in such a way that, the aerodynamic properties of an airfoil are improved. Although the Coanda effect was discovered in the 1930s, research on Circulation Control can be tracked to the 1960s. The bases for Circulation Control technology are mainly empirical given by: the experiments performed in those days, the use of aerodynamic tools and the use of numerical methods. Since its discovery, this technology has not been used widely but nowadays it is thought that it is mature enough to be applied to the next generation aircrafts. As an example, the goal of some NASA Subsonic Fixed Wing projects such as the Cruise Efficient Short Take Off and Landing program (Couluris et al. 2010), is to apply this technology to design aircrafts that can take-off in much smaller distances than the typical airport runway. The key for the development of this technology is the understanding, simulation and control of the flowfield around the airfoil; for this purpose physical experiments are required for validation of numerical methods and such methods will be used then for design purposes. On the other hand, various numerical methods lead to different ranges of uncertainty in the flowfield simulation. This article presents a review of the state of the art on circulation control research, a comparative study of articles from the 1960s to 2014 of different physical experiments, numerical methods, simulations of the Coanda effect and Circulation Control and its results. Finally, the conclusion of the work is a complete vision of the usage of the analyzed techniques in future applications.

In the present work, the Circulation Control technology applied to an airfoil with a discontinuous not-rounded surface is explored. First a numerical model is constructed and compared against a physically-tested and well known Circulation Control airfoil. Then the model is modified to analyze the airfoil with discontinuous not-rounded surfaces. This last numerical model suggests that, if enough jet momentum is applied, the Coanda effect can be induced in the airfoil with discontinuous not-rounded surfaces. The model also suggests that when the Coanda effect is induced, a small vortex is generated at the geometric discontinuities and the flow acts as if the geometry was in fact rounded.

A Background Oriented Schlieren (BOS) experiment was designed to measure density gradients in a transparent medium. The BOS technique presented here consists on a comparison between a reference image of a dot matrix and another image of the same matrix behind the flow of a transparent gas. The presence of the flow induces changes in the refractive index, so the dots in the matrix appear displaced in the second image. The displacement of each dot is determined through a cross-correlation algorithm between both images. From the displacement, the changes in the refractive index can be determined, which in turn are related to the density by the Gladstone-Dale equation. In the experiment described in this paper, two different gases with known properties were used for the calibration.

Shock waves are usually modeled as sharp discontinuities in pressure, density and temperature. A Background Oriented Schlieren (BOS) system was set-up to determine the actual widths of the density gradients in these regions of a supersonic jet. The technique consists on a comparison between a reference image of a dot matrix and another image of the same matrix deformed by the flow of a transparent gas. The apparent displacement of the dots in the second image, due to changes in the index of refraction, can be related to changes in the density. The flow is generated when compressed air passes through a straight nozzle with a diameter of 4 mm. Density measurements along the centerline are presented for three Mach numbers: 2.79, 1.89 and 1.79.

Solar cooling is an interesting application regarding the use of renewable energy to activate climatization systems. Thermally driven chillers (absorption or desorption systems) use the solar energy to provide heat to the generator of an absorption chiller. In this work, an experimental facility, designed for testing innovative components of a simple effect absorption cooling system, is presented. The study is focused on performance analysis of evaporators and its influence on the overall performance of the machine. Experimental results indicate the detection of some operational difficulties. Due to the particular design of the machine, which contains two evaporators, the distribution of refrigerant mass flow rate is not symmetrical in some cases. Therefore, one of the evaporators could be not operating. This situation explains the decrease of cooling power when it is supposed to have an increasing tendency, according to the thermal power supplied to the generator of the machine.

A fractal analysis of rainfall events registered in Baja California was carried out. Rainfall data from 92 climatological stations distributed along the studied region with at least 30 years of records were used. By studying rainfall series patterns, Hurst exponent values were obtained. The rescalated range method (R/S), box-counting method and the Multifractal Detrended Fluctuation Analysis (MF-DFA) were used, having as a result the Hurst exponent values for different time scales (entire record, 25, 10, and 5 years scales). Data showed that the daily rainfall series tended to present a persistent pattern. The analysis from the Hurst exponent on the previously mentioned time scales showed that, at a lesser time scale, their values increase; thus, the series tended to present a stronger persistent behavior.

The Guájaro reservoir is the most important water body located at the north of Colombia. It is supplied by an artificial channel (Canal del Dique) through a two floodgates system. As a result of excess nutrients and other pollution loads from the drainage basin in recent decades, the Guájaro reservoir suffers eutrophication and other pollution problems; however it still continues being exploited. For this reason, it is necessary to regulate the hydraulic structures that supply this water body, as they play an important role in managing levels, and these in turn for water supply and environmental purposes. The present work is carried out as a sustainability management alternative of the reservoir. The implementation of a two-dimensional hydrodynamic model and its calibration is achieved using time series of the free surface levels, and comparing the measured velocities and those estimated by the model for two different climatic periods, to assist the operation of the Canal del Dique-Guájaro hydrosystem. The corresponding comparisons showed a good behavior between measured and simulated data. Based on the quantitative results of the Nash-Sutcliffe reliability method, the results are considered quite satisfactory for estimating and predicting the amount of water flowing in and out of the reservoir through the channel reservoir hydrosystem.

In this paper a study of the hydrodynamics of the Agua Brava lagoon system is performed by numerical modeling. The importance of studying this lagoon system lies with aquaculture activities carried out by shrimp farms. The $$ \pi $$-HYDRO model is used for the numerical simulations of hydrodynamics and temperature and salinity dispersion. The boundary conditions regarding ocean properties were generated with the HYCOM ocean model, whereas tides were calculated from the tidal predictions of the MAR V1.0. A hydrological study was also performed to calculate the freshwater contributions and take them into account in the numerical simulations. The scenarios analyzed are the dry and wet seasons particularly for 2013. For the case of the dry season, a slight influence of hydrological contributions to the dynamics of the lagoon is observed, where the effects of the tidal flow are predominant. For the wet scenario, the effects of both tidal and hydrological flow drive the motion within the lagoon, especially being predominant the hydrological flow due to the river discharges in the near region to the shrimp farms.

This work focuses on the integral design of an offshore outfall as an alternative to the proper disposal of produced water generated by the oil industry in the Campeche Sound Marine Region. In recent years, the volume of extracted oil has increased and therefore produced water has grown in the same way. This effluent consists of high levels of salinity, temperature and some pollutants related to hydrocarbons. For this reason it cannot be exploited by the oil industry and the only way for managing it is to dispose of it to the sea. Through the implementation of hydrodynamic and water quality numerical models, it was possible to simulate the trajectory and pollutant levels of the effluent when it is transported by the currents outside the outfall. The results showed consistency according to values stipulated by regulations about water disposal.

Air pollution has effects on ecosystems, infrastructure and human health, and therefore it is important to develop pollution exposure reduction. Large cities, like Mexico Megacity, have high pollution concentration episodes, even though an air quality monitoring network can measure and issue alarms when high level of air pollutants concentrations are reached, the population is exposed to harmful air pollutants before being aware of it. Air quality forecast information can reduce exposure to air pollution high concentrations for sensitive and general public. This work describes an operative air quality forecast modeling (AQFM) system. The modeling domain covers Mexico country, it uses a meteorology-chemistry coupled model in a high performance computing hardware, the AQFM forecasts primary (carbon monoxide CO, sulfur dioxide SO$$_2$$) and secondary (ozone O$$_3$$) air pollutants, and the time span is for up to 42 h starting at 12Z. Model results are given in terms of pollutant concentration distribution images, which are displayed in a web site. System like this can be applied for regional or urban areas in order to advice and to reduce pollution exposure.

This study presents the observation of large amplitude internal wave activity, of the order of 50 m, near the head of the Petacalco submarine canyon located in the Mexican Pacific. The waves propagate with periods similar to the $$M_2$$ tide component and the observations show that the rates of change of temperature reached up to 10 $$^{\circ }$$C/hr. The presence of submarine canyons enhances turbulent mixing locally. The slopes of the canyon’s wall trap the waves as they propagate up-canyon. Based on linear wave theory, along the axis slope of the Petacalco canyon there are regions where the critical refraction is reached, suggesting that there are regions favorable for wave breakage. This process enhances mixing of cold water masses with shelf hot water. Through this mechanism, the mixed waters remain near the surface for longer periods of time, resulting in an alternative process to upwelling. Additionally, it is suggested that this process may be very important in the region since the winds there are very weak and do not support wind driven upwelling transport for most of the year.

This paper presents a stochastic simulation technique to the classic problem of the flow between parallel plates (Couette) for Newtonian and viscoelastic fluids. From the Cauchy equation, the total stress tensor splits up into two contributions, the viscous and polymeric (elastic) terms. An implicit finite difference scheme is used to solve the momentum equation (macro) and an explicit second order scheme is employed for the polymer (stochastic) contribution. The influence of important parameters such as the number of Hookean dumbbells, the Weissenberg number and the solvent/polymer viscosity ratio in both the velocity and shear stress tensor fields are analyzed.

In this work we present the two-dimensional motion of a viscoelastic membrane immersed in incompressible inviscid and viscous fluids. The motion of the fluid is modelled by two-dimensional Navier-Stokes equations, and a constitutive equation is considered for the membrane which captures along with the fluid equations the essential features of the vibrations of the fluid. By using the Fourier transform, the linearized equations are reduced to a functional equation for membrane displacement which is solved analytically and the inverse transform is evaluated asymptotically. Results obtained show some of the basic known characteristics of cochlear mechanics.

The rotational flow continuously driven by electromagnetic forcing of an electrolytic fluid in the gap of a concentric spheres set-up is studied experimentally and theoretically. The driving Lorentz force is generated by the interaction of a dc electric current radially injected and the dipolar magnetic field produced by a permanent magnet (0.38 T). Laminar velocity profiles in the equatorial plane were obtained with particle image velocimetry. Steady-state and time-dependent flows were explored for injected currents ranging from 1 to 500 mA. A full three-dimensional numerical model that introduces the dipolar magnetic field and the radial dependency of the applied current was developed. A simple analytical solution for the azimuthal velocity was obtained. The theoretical models reproduce the main characteristic behaviour of the electromagnetically forced flow.

The behavior of a water drop on a hydrophobic substrate subject to vertical vibrations is described. The dynamics of the surface passes through different phases: harmonic, geometric and chaotic (Flores Galicia et al.). To characterize the motion in terms of quantifiable variables, the height at different points on the surface was measured as a function of time. A Fourier analysis of the signal was made to determine the frequency response to changes in the forcing.

An annular magnetohydrodynamic (MHD) device that may be used for the stirring of electrically conducting fluids in microfluidic applications is analyzed theoretically. A thin fluid layer is contained in the gap between two coaxial conducting cylinders connected to a potential difference under a uniform axial magnetic field. The imposed radial electric current that circulates in the fluid layer interacts with the magnetic field to produce an azimuthal Lorentz force that drives the fluid. A quasi-two-dimensional model that considers a linear friction due to the boundary layer attached to the insulating bottom wall is implemented and analytical solutions for the azimuthal flow are obtained for two different cases. The first case corresponds to a high conductivity fluid (a liquid metal) where the electric potential is coupled to the fluid velocity. The second case considers a low conductivity fluid (an electrolyte) where the electric potential is uncoupled from the fluid motion. The effect of slip boundary conditions at the walls of inner and outer cylinders, as well as the space between them, is explored.

In this paper we introduce a correlation for the trajectories of sand jets, of a non-cohesive granular material, emerging from vertical sidewall orifices of diameter D and wall thickness w. A contrast with water jet in similar configurations has been performed. We found that the theoretical trajectories agree well with the experimental ones.

In this paper we study the evolution of charged droplets for ionic solutions using a model described by Poisson-Boltzmann equation coupled with Stokes system. One of our main motivations is to describe the so-called Rayleigh jets studied in the laboratory and present in the functioning of technological devices as Electrospray, Mass Spectrometer, inkjet printers, etc. We show how the finite electrical conductivity and the presence of Debye layers in the electrolytic solutions induce the formation of these Rayleigh jets. We further estimate the main characteristics of the jet, such as speed and size.

Brake system has an impact on the dynamic behavior of the vehicle, during brake episodes, the disc rotor can reach 900 °C, this rise of temperature could cause loss of brake response or failure of the braking system; to reduce overheating problems on disc rotors it is important to increase the air flux through the ventilation posts or vanes, which are between the braking surfaces of the disc brake rotors. Within this research, it is designed, produced and validated an internally ventilated disc brake rotor with a geometric configuration of 22 circular arrays of 9 ventilation pillars with drop tear shape of pillar posts, which increase air speed; to validate the model, it was produced by additive manufacturing, a prototype, to which, were carried out Particle Image Velocimetry tests on a wind tunnel to determine the distribution of air speed at the inlet and outlet of the disc, under three different rotation conditions: 187.2, 561.6 and 748.8 rpm. The results show that the geometric array has higher air speed in comparison with models, which have similar configurations.

Bouncing droplets on a fluid surface have recently been shown to provide a surprising analogy to quantum behaviour. Here we discuss the limitation of this analogy in the context of the double-slit experiment, which our colleagues and we have analysed in a recent paper [Phys. Rev. E 92, 013006 (2015)]. The present paper is based on the talk given by Tomas Bohr at the XX Congreso de la División de Dinámica de Fluidos, Sociedad Mexicana de Física, Centro Mesoamericana de Física Teórica, Tuxtla Gutiérrez, November 2014.

This work describes the dynamics of a drop of benzyl alcohol, (partially miscible in water), as it traverses a stratified fluid formed by two layers, water on the top and salted water with a 1.68 molar concentration on the bottom. The width and stability of the interface depends on the temperature and on the way the upper layer mixes as it is introduced into the container. In this case, the procedure was controlled to produce a stable interface for several minutes, and to have a repeatable experiment. The width and position of the interface was measured each time through shadowgraphs. The processes that occur during the fall of the drop depend on various parameters like its geometry, the width of the upper layer and the density of the lower layer. First the drop seems to have a free fall. After it enters in contact with the interface, the behavior is similar to a damped harmonic oscillator. The drag force was calculated using models for a rigid sphere and for an ellipsoid with varying dimensions. A comparison between the measured and the calculated values is presented in a graph.

Eight X-ray observations of V4743 Sgr (2002), observed with Chandra and XMM-Newton, are presented, covering three phases: Early optically thin hard emission (day 50.2), photospheric emission from the ejecta (days 180.4, 196.1, 301.9, 371, 526), and faint post-outburst emission (days 742 and 1286). The flux level at Earth during the first and last phase is of order $$10^{-12}$$ erg cm$$^{-2}$$ s$$^{-1}$$ over the energy range 0.3–2.5 keV. These values are higher than an upper limit obtained in September 1990 with ROSAT. The nova thus continued fading in the soft band (0.1–2.4 keV). The nova turned off some time between days 301.9 and 371, and the X-ray flux subsequently decreased from day 301.9–526, following an exponential decline time scale of $$(96 \pm 3)$$ days. We use the absorption lines present in the SSS spectrum for diagnostic purposes, and characterize the physics and the dynamics of the expanding atmosphere during the explosion of the nova. The information extracted from this first stage is then used as input for computing full photoionization models of the ejecta in V4743 Sgr. The SSS spectrum is modeled with a simple black-body and multiplicative Gaussian lines, which provides us of a general kinematical picture of the system, before it decays to its faint phase (Ness et al. 2003). In the grating spectra taken between days 180.4 and 370, we can resolve the line profiles of absorption lines arising from H-like and He-like C, N, and O, including transitions involving higher principal quantum numbers. Except for a few interstellar lines, all lines are significantly blue-shifted, yielding velocities between 1000 and 6000 km $$\mathrm{s}^{-1}$$ which implies an ongoing mass loss. It is shown that significant expansion and mass loss occur during this phase of the explosion, at a rate $$\dot{M} \approx (3-5) \times 10^{-4} ~ (L/L_{38}) ~ M_{\odot }/yr$$. Our measurements show that the efficiency of the amount of energy used for the motion of the ejecta, defined as the ratio between the kinetic luminosity $$L_\mathrm{kin}$$ and the radiated luminosity $$L_\mathrm{rad}$$, is of the order of one.

We report on the performance of the statistical X-ray absorption lines identification procedure xline-id. As illustration, it is used to estimate the time averaged gas density $$n_H(r)$$ of a representative AGN’s warm absorber ($$T\approx 10^5$$ K) X-ray simulated spectrum. The method relies on three key ingredients: (1) a well established emission continuum level; (2) a robust grid of photoionization models spanning several orders of magnitude in gas density ($$n_H$$), plasma column density ($$N_H$$), and in ionization states; (3) theoretical curves of growth for a large set of atomic lines. By comparing theoretical and observed equivalent widths of a large set of lines, spanning highly ionized charge states from O, Ne, Mg, Si, S, Ar, and the Fe L-shell and K-shell, we are able to infer the location of the X-ray warm absorber.

The air-flow dynamics in crops (cultures), when a crop is considered as porous media, is determined by factors depending of the phenological stage which define size and shape of the leaves. Leaves topology with respect to the wind direction determines the porosity of the media and in consequence the flow rate. This flow rate is a function of the porosity and permeability, which determines the dragging coefficient. The presence of crops in a greenhouse causes a consumption of momentum due to the resistance that the leaves offer for the friction force (drag forces). In this paper the greenhouse airflow dynamics is analyze for four different crops with different leaf configurations. Computational Fluid Dynamics (CFD) was used to model the airflow dynamic behavior considering a crop as porous media. The pressure reduction due to the effect of inertial force is represented by a Forcchaimer equation, which describe dragging forces (drag effect) depending on the crop density foliar area. The results indicate a reduction of 33 % in the wind speed along the cropped area; this causes a thermal gradient increase of 6 K in a length of 34 m.

The human knee synovial joint is considered one of the three joints having the higher damage or injury incidence, along with the hip and the ankle. Here, a 2D model of a knee synovial junction is presented, where the Condyle is modeled by a mobile circular wall, the condylar concave cavity by a larger circular wall, the Articular Cartilage with a porous medium, and the Synovial Fluid by a high viscosity Newtonian fluid. The model focuses in the study of the angular pressure distribution along the Synovial Fluid/Cartilage interface when the fluid zone undergoes a deformation in the direction of the symmetry axis due to simulated loads. The model equations were solved using FLUENT® as a numerical tool for the study of biological systems, considering small deformations at the fluid zone, low deformation rates, high fluid viscosities, constant porous fractions and different initial thickness. The results show that the pressure decreases gradually from the center of the join to its ends. The maximum values obtained were in the order of 109 for the dimensionless pressure (i.e. the total pressure with respect to dynamic pressure), these values correspond to 103 Pa for the total pressure. The greater the fluid zone to cartilage thickness ratio the lower the maximum pressure. The numerical model was validated with an analytical model previously proposed by Jurczak in (2006).

Double diffusive convection is discussed in context of the simultaneity problem emerged from the thermal energy flux, where the temperature gradient (the cause) and the energy flux (the effect) appear at the same time. We used Cattaneo’s law, as a correction of the conventional Fourier’s law for thermal transport, in order to consider a delay time in the interaction, the so called relaxation time. For the sinking of a convective blob in a Newtonian fluid, Fourier’s equation describes a steady state flow, however the Cattaneo’s law predicts damped oscillations for times of the order of this relaxation time. Physical systems as the salt-finger phenomenon (for the Fourier regime), and the superfluid Helium II and pulsars micro-oscillations (for the Cattaneo regime) are studied through simulations of the temporal evolution of the speed of the convective blobs. Concluding that the dynamic of convective blobs in systems where the relaxation time is important presents quasi-static oscillations, even for degenerate matter. A further study about the complete description of the light curve of pulsars is suggested.

Despite the ubiquitousness and technological and scientific importance of granular matter, our understanding is still very poor compared to molecular fluids and solids. Until today, there is no unified description, which indeed seems unreachable. However, it has been proposed that important advances could be attained for noncohesive, hard-sphere like systems, by combining fluid dynamics with phase-field modeling through an appropriate order parameter (Aranson and Tsimring 2006). Here, we present a review of the dynamics of confined granular matter, for which this systematic approach has proven its value. Motivated by the pioneering work of Olafsen and Urbach (1998), many experimental, theoretical and numerical studies of model confined granular systems have been realized, which have unveiled a very large variety of fundamental phenomena. In this review, we focus on few of these fundamental aspects, namely phase coexistence, effective surface tension, and a detailed description of the liquid state.

Equations to estimate the K coefficient have been obtained for devices of change direction of ducts under forced regime. For this approach, a state of art was carried out where it was noticed that the traditionally utilized methods that evaluate the losses of the devices needed tables and/or graphics when estimating the K coefficient, which is singular to each accessory. Each theory was analyzed and classified accordingly to each piece whenever these are present in sudden or gradual conditions. The data was homogenized with the purpose to obtain average curves values of the coefficient. The results were used as data in methods of multiple linear regressions until obtain a representative equation for each case studied. These equations have the advantage of being reliable to determine the loss of K coefficient without having to manipulate tables and graphics; this allows saving time when designing and testing the hydraulic behavior in forced ducts. Finally, these equations can be implemented in advanced computational algorithms which will allow the analysis and modeling of the losses caused by friction in different scenarios.

Smoothed Particle Hydrodynamics (SPH) is a numerical method particularly suitable to describe a variety of complex free-surface flows with large discontinuities. However, SPH simulations are computationally expensive and typical runtimes are too high to study real problems with high resolution. The proposed solution is the parallel computation to accelerate the SPH executions. This work introduces several high performance techniques applied to SPH to allow simulation of real problems at reasonable time. In this way, OpenMP was used to exploit all cores in the classical CPUs. On the other hand, CUDA language was used to take advantage of the high parallel computing power of GPUs (Graphics Processing Units). Finally, Message Passing Interface (MPI) was implemented to combine the power of several machines connected by network. These parallelization techniques are implemented in the code DualSPHysics and results are shown in terms of performance, efficiency and scalability using different CPU and GPU models.

MoWC-NiC-WC was produced by mechanical alloying at the following grinding times: 0, 40, 80, 120, 160, 200 and 240 h. XRD results indicated that by increasing the milling time from 0 to 240 h, the nanostructured carbide phases were synthesized with a crystal size ranging from 125.6 to 10.1 nm. The performance of the nano-catalysts in the heavy oil before and after the reaction was analyzed by Fourier transform infrared spectroscopy (FTIR), Viscosimetry, SARA method analysis by Thin-layer chromatography-flame ionization detection (TLC-FID), elemental (EL) analysis, and gas chromatography/mass spectroscopy (GC/MS). As the milling time increased, the ratio of the viscosity reduction of the heavy oil increased from 80.4 to 97.1 % by using the catalyst milled for 240 h. In addition, the results showed that some reactions were observed during the aquathermolysis: pyrolysis, depolymerization, hydrogenation, isomerization, ring opening, desulphurization, etc. It was also found that the catalysts at short milling times caused more changes in the resin, saturated hydrocarbon, and oxygen-containing groups, whereas the 240 h catalyst led to more changes in the asphaltene, aromatic hydrocarbon, and sulfur-containing groups.