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Fluids, Volume 5, Issue 2 (June 2020) – 59 articles

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30 pages, 12645 KiB  
Article
Hydrodynamic Analysis of Surge-Type Wave Energy Devices in Variable Bathymetry by Means of BEM
by Alexandros Magkouris, Markos Bonovas and Kostas Belibassakis
Fluids 2020, 5(2), 99; https://doi.org/10.3390/fluids5020099 - 23 Jun 2020
Cited by 7 | Viewed by 2445
Abstract
A variety of devices and concepts have been proposed and thoroughly investigated for the exploitation of renewable wave energy. Many of the devices operate in nearshore and coastal regions, and thus, variable bathymetry could have significant effects on their performance. In particular, Oscillating [...] Read more.
A variety of devices and concepts have been proposed and thoroughly investigated for the exploitation of renewable wave energy. Many of the devices operate in nearshore and coastal regions, and thus, variable bathymetry could have significant effects on their performance. In particular, Oscillating Wave Surge Converters (OWSCs) exploit the horizontal motion of water waves interacting with the flap of the device. In this work, a Boundary Element Method (BEM) is developed, and applied to the investigation of variable bathymetry effects on the performance of a simplified 2D model of a surge-type wave energy converter excited by harmonic incident waves. Numerical results, illustrating the effects of depth variation in conjunction with other parameters, like inertia and power-take-off, on the performance of the device, are presented. Finally, a comparative evaluation of the present simplified surge-type WEC model and point absorbers is presented for a case study in a selected coastal site on the Greek nearshore area, characterized by relatively increased wave energy potential. Full article
(This article belongs to the Special Issue Wind and Wave Renewable Energy Systems)
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15 pages, 5957 KiB  
Article
Experimental Study of Sidewall Pressure Induced by Ferroparticles in Fluid under a Pulsating Magnetic Field
by Or Werner, Asaf Azulay, Boris Mikhailovich and Avi Levy
Fluids 2020, 5(2), 98; https://doi.org/10.3390/fluids5020098 - 22 Jun 2020
Viewed by 1946
Abstract
For several decades, magnetic nano- and microparticles have been used in various applications, as they can be attracted and controlled using external magnetic fields. Recently, carbonyl iron microparticles were used in a feasibility study of a new cardiac pacing application. The particles were [...] Read more.
For several decades, magnetic nano- and microparticles have been used in various applications, as they can be attracted and controlled using external magnetic fields. Recently, carbonyl iron microparticles were used in a feasibility study of a new cardiac pacing application. The particles were inserted into a heart, attracted to its sidewall using a pulsating magnetic field, and applied pulsating pressure on its sidewall. The magnitude of the sidewall pressure is a critical parameter for the success and safety of the application, and it was evaluated analytically using a simplified model. In the present study, the behaviour of carbonyl iron microparticles in a water chamber was studied experimentally. Several masses of these particles were attracted to the sidewall of the chamber using an external pulsating magnetic field; the behaviours of the masses of particles, the particle–particle interaction, and the influence of fluid dynamics on them were examined during different periods of pulses. The sidewall pressure during their attraction was measured using an in-house piezoelectric polyvinylidene fluoride sensor. The relations between the measured sidewall pressure and the mass of the particles, their sizes, and the magnetic field exposure time were investigated. The obtained results suggest an asymptotic sidewall pressure value for the specified magnetic field. The measurements of the sidewall pressure are compared with evaluated results from the analytical model, showing that the model over-predicts the sidewall pressure. Full article
(This article belongs to the Special Issue Classical and Modern Topics in Fluid Dynamics and Transport Phenomena)
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14 pages, 3881 KiB  
Communication
Development of a Passive Spore Sampler for Capture Enhancement of Airborne Crop Pathogens
by James L. Blackall, Jie Wang, Mostafa R. A. Nabawy, Mark K. Quinn and Bruce D. Grieve
Fluids 2020, 5(2), 97; https://doi.org/10.3390/fluids5020097 - 18 Jun 2020
Viewed by 4194
Abstract
Yellow rust spores currently blight commercial and domestic wheat production in areas of East Africa such as Ethiopia. Yellow rust is a hazard to crops which appears asymptomatic for a time, but inevitably causes significant losses in yield once symptoms of infection manifest [...] Read more.
Yellow rust spores currently blight commercial and domestic wheat production in areas of East Africa such as Ethiopia. Yellow rust is a hazard to crops which appears asymptomatic for a time, but inevitably causes significant losses in yield once symptoms of infection manifest themselves to the point where they can be readily observed by the naked eye. Regionally recurrent losses of up to 5% are common and reach as high as 25% in rare cases. Historically, spore sampling has been undertaken by large, cumbersome devices that require heavy power supplies and significant expertise to reliably operate. Moreover, tools for the design and development of such devices are currently limited. This paper, therefore, proposes design and testing processes to develop a spore sampling device that is compact, passive (requires no power to operate), and can better direct spores onto a biomimetic sensor platform enhancing the capture and detection of pathogens. This represents a novel design context for fluidic devices. Performance of the device has been simulated using Lagrangian particle tracking embedded into computational fluid dynamics (CFD) simulations, demonstrating significant improvements across a range of spore Stokes numbers. Experimental validation of numerical simulations was performed using wind tunnel testing and practical performance such as weathervaning was demonstrated. Results show that that the developed sampler is capable of enhancing the probability of yellow rust spores interacting with an internal sensor by a factor of between 20 and 25; demonstrating the effectiveness of the developed design. Full article
(This article belongs to the Special Issue Recent Numerical Advances in Fluid Mechanics, Volume II)
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17 pages, 8458 KiB  
Article
Numerical Simulation of Breathing Mode Oscillation on Bubble Detachment
by Takao Oku, Hiroyuki Hirahara, Tomohiro Akimoto and Daiki Tsuchida
Fluids 2020, 5(2), 96; https://doi.org/10.3390/fluids5020096 - 16 Jun 2020
Cited by 2 | Viewed by 3023
Abstract
When a bubble detaches from a nozzle immersed in water, a sound is emitted owing to the detachment. The bubble deformation and sound emission generated after detachment has been investigated in many studies, in which the breathing mode with a natural frequency was [...] Read more.
When a bubble detaches from a nozzle immersed in water, a sound is emitted owing to the detachment. The bubble deformation and sound emission generated after detachment has been investigated in many studies, in which the breathing mode with a natural frequency was discussed based on the dynamics of the interface between the air and water. In this study, the deformation of a bubble was observed, and the sound emitted upon detachment was measured experimentally. To analyze the bubble deformation process, a computational fluid dynamics (CFD) simulation was conducted using the volume of fluid (VOF) method to predict the sound emission. In the analysis, the deformation behavior, the oscillation frequencies, sound pressure, and radius variation were discussed by comparing the numerical and experimental data. Furthermore, the natural frequency and low frequency vibrations were discussed based on the interference between the detached bubbles and the air column vibrations. Full article
(This article belongs to the Special Issue Advances in Numerical Methods for Multiphase Flows)
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15 pages, 1821 KiB  
Article
Continuous Project-Based Learning in Fluid Mechanics and Hydraulic Engineering Subjects for Different Degrees
by Modesto Pérez-Sánchez and P. Amparo López-Jiménez
Fluids 2020, 5(2), 95; https://doi.org/10.3390/fluids5020095 - 15 Jun 2020
Cited by 5 | Viewed by 4013
Abstract
Subjects related to fluid mechanics for hydraulic engineers ought to be delivered in interesting and active modes. New methods should be introduced to improve the learning students’ abilities in the different courses of the Bachelor’s and Master’s degree. Related to active learning methods, [...] Read more.
Subjects related to fluid mechanics for hydraulic engineers ought to be delivered in interesting and active modes. New methods should be introduced to improve the learning students’ abilities in the different courses of the Bachelor’s and Master’s degree. Related to active learning methods, a continuous project-based learning experience is described in this research. This manuscript shows the developed learning methodology, which was included on different levels at Universitat Politècnica de València. The main research goal is to show the active learning methods used to evaluate both skills competences (e.g., “Design and Project”) and specific competences of the students. The research shows a particular developed innovation teaching project, which was developed by lecturers and professors of the Hydraulic Engineering Department, since 2016. This project proposed coordination in different subjects that were taught in different courses of the Bachelor’s and Master’s degrees, in which 2200 students participated. This coordination improved the acquisition of the learning results, as well as the new teaching methods increased the student’s satisfaction index. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics, Volume II)
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23 pages, 587 KiB  
Article
On the Data-Driven Modeling of Reactive Extrusion
by Ruben Ibañez, Fanny Casteran, Clara Argerich, Chady Ghnatios, Nicolas Hascoet, Amine Ammar, Philippe Cassagnau and Francisco Chinesta
Fluids 2020, 5(2), 94; https://doi.org/10.3390/fluids5020094 - 15 Jun 2020
Cited by 15 | Viewed by 3361
Abstract
This paper analyzes the ability of different machine learning techniques, able to operate in the low-data limit, for constructing the model linking material and process parameters with the properties and performances of parts obtained by reactive polymer extrusion. The use of data-driven approaches [...] Read more.
This paper analyzes the ability of different machine learning techniques, able to operate in the low-data limit, for constructing the model linking material and process parameters with the properties and performances of parts obtained by reactive polymer extrusion. The use of data-driven approaches is justified by the absence of reliable modeling and simulation approaches able to predict induced properties in those complex processes. The experimental part of this work is based on the in situ synthesis of a thermoset (TS) phase during the mixing step with a thermoplastic polypropylene (PP) phase in a twin-screw extruder. Three reactive epoxy/amine systems have been considered and anhydride maleic grafted polypropylene (PP-g-MA) has been used as compatibilizer. The final objective is to define the appropriate processing conditions in terms of improving the mechanical properties of these new PP materials by reactive extrusion. Full article
(This article belongs to the Special Issue Advances in Experimental and Computational Rheology, Volume II)
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16 pages, 5341 KiB  
Article
On the Formation and Accumulation of Solid Carbon Particles in High-Enthalpy Flows Mimicking Re-Entry in the Titan Atmosphere
by Antonio Esposito, Marcello Lappa, Gennaro Zuppardi, Christophe Allouis, Barbara Apicella, Mario Commodo, Patrizia Minutolo and Carmela Russo
Fluids 2020, 5(2), 93; https://doi.org/10.3390/fluids5020093 - 12 Jun 2020
Cited by 5 | Viewed by 2160
Abstract
The problem relating to the formation of solid particles enabled by hypersonic re-entry in methane-containing atmospheres (such as that of Titan) has been tackled in the framework of a combined experimental–numerical approach implemented via a three-level analysis hierarchy. First experimental tests have been [...] Read more.
The problem relating to the formation of solid particles enabled by hypersonic re-entry in methane-containing atmospheres (such as that of Titan) has been tackled in the framework of a combined experimental–numerical approach implemented via a three-level analysis hierarchy. First experimental tests have been conducted using a wind tunnel driven by an industrial arc-heated facility operating with nitrogen as working gas (the SPES, i.e., the Small Planetary Entry Simulator). The formation of solid phases as a result of the complex chemical reactions established in such conditions has been detected and quantitatively measured with high accuracy. In a second stage of the study, insights into the related formation process have been obtained by using multispecies models relying on the NASA CEA code and the Direct Simulation Monte Carlo (DSMC) method. Through this approach the range of flow enthalpies in which carbonaceous deposits can be formed has been identified, obtaining good agreement with the experimental findings. Finally, the deposited substance has been analyzed by means of a set of complementary diagnostic techniques, i.e., SEM, spectroscopy (Raman, FTIR, UV–visible absorption and fluorescence), GC–MS and TGA. It has been found that carbon produced by the interaction of the simulated Titan atmosphere with a solid probe at very high temperatures can be separated into two chemically different fractions, which also include “tholins”. Full article
(This article belongs to the Special Issue Classical and Modern Topics in Fluid Dynamics and Transport Phenomena)
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23 pages, 2099 KiB  
Article
Consistent Velocity–Pressure Coupling for Second-Order L2-Penalty and Direct-Forcing Methods
by Arthur Sarthou, Stéphane Vincent and Jean-Paul Caltagirone
Fluids 2020, 5(2), 92; https://doi.org/10.3390/fluids5020092 - 10 Jun 2020
Cited by 1 | Viewed by 1765
Abstract
The present work studies the interactions between fictitious-domain methods on structured grids and velocity–pressure coupling for the resolution of the Navier–Stokes equations. The pressure-correction approaches are widely used in this context but the corrector step is generally not modified consistently to take into [...] Read more.
The present work studies the interactions between fictitious-domain methods on structured grids and velocity–pressure coupling for the resolution of the Navier–Stokes equations. The pressure-correction approaches are widely used in this context but the corrector step is generally not modified consistently to take into account the fictitious domain. A consistent modification of the pressure-projection for a high-order penalty (or penalization) method close to the Ikeno–Kajishima modification for the Immersed Boundary Method is presented here. Compared to the first-order correction required for the L 2 -penalty methods, the small values of the penalty parameters do not lead to numerical instabilities in solving the Poisson equation. A comparison of the corrected rotational pressure-correction method with the augmented Lagrangian approach which does not require a correction is carried out. Full article
(This article belongs to the Special Issue Advances in Numerical Methods for Multiphase Flows)
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19 pages, 2035 KiB  
Review
Nebulization Criteria and Quantification
by Nardos Hailu, Michiel Postema, Ondrej Krejcar and Dawit Assefa
Fluids 2020, 5(2), 91; https://doi.org/10.3390/fluids5020091 - 06 Jun 2020
Cited by 2 | Viewed by 6510
Abstract
The application of atomization technology is common in fields such as agriculture, cosmetics, environmental sciences, and medicine. Aerosolized drugs are administered using nebulizers to treat both pulmonary and nonpulmonary diseases. The characterization and measurement of nebulizers are of great significance in analyzing the [...] Read more.
The application of atomization technology is common in fields such as agriculture, cosmetics, environmental sciences, and medicine. Aerosolized drugs are administered using nebulizers to treat both pulmonary and nonpulmonary diseases. The characterization and measurement of nebulizers are of great significance in analyzing the performance and accuracy of the nebulizing system and the advancement of the technology. Nevertheless, the characterization of aerosols has been a long-standing challenge in scientific disciplines ranging from atmospheric physics to health sciences. The study of factors that influence nebulization has not been undertaken systematically using experimental techniques. Numerical modeling (NM) and computational fluid dynamics (CFD) can address such issues. This article provides a concise overview of the literature on the application of computational fluid dynamics to medical nebulizers and aerosol measurements. Full article
(This article belongs to the Special Issue Fluid Mechanics of Medical Ventilation)
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26 pages, 40295 KiB  
Article
Experiments on Flexible Filaments in Air Flow for Aeroelasticity and Fluid-Structure Interaction Models Validation
by Jorge Silva-Leon and Andrea Cioncolini
Fluids 2020, 5(2), 90; https://doi.org/10.3390/fluids5020090 - 05 Jun 2020
Cited by 6 | Viewed by 2704
Abstract
Several problems in science and engineering are characterized by the interaction between fluid flows and deformable structures. Due to their complex and multidisciplinary nature, these problems cannot normally be solved analytically and experiments are frequently of limited scope, so that numerical simulations represent [...] Read more.
Several problems in science and engineering are characterized by the interaction between fluid flows and deformable structures. Due to their complex and multidisciplinary nature, these problems cannot normally be solved analytically and experiments are frequently of limited scope, so that numerical simulations represent the main analysis tool. Key to the advancement of numerical methods is the availability of experimental test cases for validation. This paper presents results of an experiment specifically designed for the validation of numerical methods for aeroelasticity and fluid-structure interaction problems. Flexible filaments of rectangular cross-section and various lengths were exposed to air flow of moderate Reynolds number, corresponding to laminar and mildly turbulent flow conditions. Experiments were conducted in a wind tunnel, and the flexible filaments dynamics was recorded via fast video imaging. The structural response of the filaments included static reconfiguration, small-amplitude vibration, large-amplitude limit-cycle periodic oscillation, and large-amplitude non-periodic motion. The present experimental setup was designed to incorporate a rich fluid-structure interaction physics within a relatively simple configuration without mimicking any specific structure, so that the results presented herein can be valuable for models validation in aeroelasticity and also fluid-structure interaction applications. Full article
(This article belongs to the Special Issue Recent Advances in Fluid Mechanics: Feature Papers)
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12 pages, 2302 KiB  
Article
Scaling of Second-Order Structure Functions in Turbulent Premixed Flames in the Flamelet Combustion Regime
by Peter Brearley, Umair Ahmed, Nilanjan Chakraborty and Markus Klein
Fluids 2020, 5(2), 89; https://doi.org/10.3390/fluids5020089 - 02 Jun 2020
Cited by 6 | Viewed by 2387
Abstract
The second-order velocity structure function statistics have been analysed using a DNS database of statistically planar turbulent premixed flames subjected to unburned gas forcing. The flames considered here represent combustion for moderate values of Karlovitz number from the wrinkled flamelets to the thin [...] Read more.
The second-order velocity structure function statistics have been analysed using a DNS database of statistically planar turbulent premixed flames subjected to unburned gas forcing. The flames considered here represent combustion for moderate values of Karlovitz number from the wrinkled flamelets to the thin reaction zones regimes of turbulent premixed combustion. It has been found that the second-order structure functions exhibit the theoretical asymptotic scalings in the dissipative and (relatively short) inertial ranges. However, the constant of proportionality for the theoretical asymptotic variation for the inertial range changes from one case to another, and this value also changes with structure function orientation. The variation of the structure functions for small length scale separation remains proportional to the square of the separation distance. However, the constant of proportionality for the limiting behaviour according to the separation distance square remains significantly different from the theoretical value obtained in isotropic turbulence. The disagreement increases with increasing turbulence intensity. It has been found that turbulent velocity fluctuations within the flame brush remain anisotropic for all cases considered here and this tendency strengthens towards the trailing edge of the flame brush. It indicates that the turbulence models derived based on the assumptions of homogeneous isotropic turbulence may not be fully valid for turbulent premixed flames. Full article
(This article belongs to the Special Issue Recent Advances in Fluid Mechanics: Feature Papers)
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17 pages, 3360 KiB  
Article
Numerical Study of the Magnetic Damping Effect on the Sloshing of Liquid Oxygen in a Propellant Tank
by Yutaro Furuichi and Toshio Tagawa
Fluids 2020, 5(2), 88; https://doi.org/10.3390/fluids5020088 - 01 Jun 2020
Cited by 7 | Viewed by 3286
Abstract
Nowadays, the use of baffle plates is anticipated to be one of potential devices used to dampen the sloshing of propellant in rocket tanks. However, some of previous studies reported that the use of a baffle plate may cause larger pressure fluctuations in [...] Read more.
Nowadays, the use of baffle plates is anticipated to be one of potential devices used to dampen the sloshing of propellant in rocket tanks. However, some of previous studies reported that the use of a baffle plate may cause larger pressure fluctuations in the tank. In this study, aiming at damping the sloshing without a baffle plate, we paid attention to the characteristic that liquid oxygen is paramagnetic and numerically investigated damping effect of a magnetic field when liquid oxygen sloshing occurs. An incompressible gas–liquid two-phase flow of gaseous oxygen and liquid oxygen was assumed in a spherical spacecraft tank with a diameter of 1 m in a non-gravitational field, and a triangular impact force was assumed to be imposed as the excitation force. In addition, an electric circular coil was placed outside the spherical tank to generate a static magnetic field. For the sake of simplicity, the effect of heat was not taken into consideration. As a result of computation, the sloshing was damped to a certain extent when the magnetic flux density at the coil center was 1.0 T, and a sufficient damping effect was obtained by setting it to 3.0 T. In fact, it is anticipated that less than 3.0 T is sufficient if the coil is placed on the tank surface. This may contribute to damping of the movement of the center of gravity of a spacecraft and prevention of mixing of ullage gas into the piping. Full article
(This article belongs to the Special Issue Recent Advances in Fluid Mechanics: Feature Papers)
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29 pages, 1004 KiB  
Article
The Effects of Surface Wind Stress and Buoyancy Flux on the Evolution of a Front in a Turbulent Thermal Wind Balance
by Matthew N. Crowe and John R. Taylor
Fluids 2020, 5(2), 87; https://doi.org/10.3390/fluids5020087 - 01 Jun 2020
Cited by 5 | Viewed by 2840
Abstract
Here we consider the effects of surface buoyancy flux and wind stress on a front in turbulent thermal wind (TTW) balance using the framework of Crowe and Taylor (2018). The changes in the velocity and density profiles induced by the wind stress and [...] Read more.
Here we consider the effects of surface buoyancy flux and wind stress on a front in turbulent thermal wind (TTW) balance using the framework of Crowe and Taylor (2018). The changes in the velocity and density profiles induced by the wind stress and buoyancy flux interact with the TTW and can qualitatively change the evolution of the front. In the absence of surface-forcing, Crowe and Taylor (2018) found that shear dispersion associated with the TTW circulation causes the frontal width to increase. In many cases, the flow induced by the surface-forcing enhances the spreading rate. However, if the wind stress drives a cross-front flow which opposes the frontal buoyancy gradient or the buoyancy flux drives an unstable stratification, it is possible to obtain an up-gradient cross-front buoyancy flux, which can act to sharpen the front. In certain conditions, an equilibrium state develops where the tendency for the TTW circulation to spread the front is balanced by the frontogenetic tendency of the surface forces. We use numerical solutions to a nonlinear diffusion equation in order to test these predictions. Finally, we describe the connection between surface-forcing and vertical mixing and discuss typical parameters for mid-ocean fronts. Full article
(This article belongs to the Special Issue Submesoscale Processes in the Ocean)
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15 pages, 4717 KiB  
Article
A Numerical Study of Metachronal Propulsion at Low to Intermediate Reynolds Numbers
by Shawtaroh Granzier-Nakajima, Robert D. Guy and Calvin Zhang-Molina
Fluids 2020, 5(2), 86; https://doi.org/10.3390/fluids5020086 - 31 May 2020
Cited by 17 | Viewed by 2930
Abstract
Inspired by the forward swimming of long-tailed crustaceans, we study an underwater propulsion mechanism for a swimming body with multiple rigid paddles attached underneath undergoing cycles of power and return strokes with a constant phase-difference between neighboring paddles, a phenomenon known as metachronal [...] Read more.
Inspired by the forward swimming of long-tailed crustaceans, we study an underwater propulsion mechanism for a swimming body with multiple rigid paddles attached underneath undergoing cycles of power and return strokes with a constant phase-difference between neighboring paddles, a phenomenon known as metachronal propulsion. To study how inter-paddle phase-difference affects flux production, we develop a computational fluid dynamics model and a numerical algorithm based on the immersed boundary method, which allows us to simulate metachronal propulsion at Reynolds numbers (RE) ranging from close to 0 to about 100. Our main finding is that the highest average flux is generated when nearest-neighbor paddles maintain an approximate 20%–25% phase-difference with the more posterior paddle leading the cycle; this result is independent of stroke frequency across the full range of RE considered here. We also find that the optimal paddle spacing and the number of paddles depend on RE; we see a qualitative transition in the dynamics of flow generated by metachronal propulsion as RE rises above 80. Roughly speaking, in terms of average flux generation, a tight paddle spacing is preferred when RE is less than 10, but a wider spacing becomes clearly favored when RE is close to or above 100. In terms of efficiency of flux generation, at RE 0.1 the maximum efficiency occurs at two paddles, and the efficiency decreases as the number of paddles increases. At RE 100 the efficiency increases as the number of paddles increases, and it appears to saturate by eight paddles, whereas using four paddles is a good tradeoff for both low and intermediate RE. Full article
(This article belongs to the Special Issue Advances in Biological Flows and Biomimetics)
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23 pages, 6965 KiB  
Article
Computational Predictions for Boger Fluids and Circular Contraction Flow under Various Aspect Ratios
by J. Esteban López-Aguilar and Hamid R. Tamaddon-Jahromi
Fluids 2020, 5(2), 85; https://doi.org/10.3390/fluids5020085 - 31 May 2020
Cited by 8 | Viewed by 2325
Abstract
This work puts forward a modeling study contrasted against experimental, with focus on abrupt circular contraction flow of two highly-elastic constant shear-viscosity Boger fluids, i.e., a polyacrylamide dissolved in corn-syrup PAA/CS (Fluid-1) and a polyisobutylene dissolved in polybutene PIB/PB (Fluid-2), in various contraction-ratio [...] Read more.
This work puts forward a modeling study contrasted against experimental, with focus on abrupt circular contraction flow of two highly-elastic constant shear-viscosity Boger fluids, i.e., a polyacrylamide dissolved in corn-syrup PAA/CS (Fluid-1) and a polyisobutylene dissolved in polybutene PIB/PB (Fluid-2), in various contraction-ratio geometries. Moreover, this work goes hand-in-hand with the counterpart matching of experimental pressure-drops observed in such 4:1 and 8:1 aspect-ratio contraction flows, as described experimentally in the literature. In this study, the experimental findings, for Boger fluids with severe strain-hardening features, reveal significant vortex-evolution characteristics, correlated with enhanced pressure-drop phasing and normal-stress response in the corner region. It is shown how such behavior may be replicated through simulation and the rheological dependencies that are necessary to bring this about. Predictive solutions with an advanced hybrid finite-element/volume (fe/fv) algorithm are able to elucidate the rheological properties (extensional viscosity and normal-stress response) that rule such vortex-enhancement evolution. This is accomplished by employing the novel swanINNFM(q) family of fluids, through the swIM model-variant, with its strong and efficient control on elongational properties. Full article
(This article belongs to the Special Issue Advances in Experimental and Computational Rheology, Volume II)
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24 pages, 9530 KiB  
Article
Verification and Validation of openInjMoldSim, an Open-Source Solver to Model the Filling Stage of Thermoplastic Injection Molding
by João Pedro, Bruno Ramôa, João Miguel Nóbrega and Célio Fernandes
Fluids 2020, 5(2), 84; https://doi.org/10.3390/fluids5020084 - 29 May 2020
Cited by 12 | Viewed by 3766
Abstract
In the present study, the simulation of the three-dimensional (3D) non-isothermal, non-Newtonian fluid flow of polymer melts is investigated. In particular, the filling stage of thermoplastic injection molding is numerically studied with a solver implemented in the open-source computational library [...] Read more.
In the present study, the simulation of the three-dimensional (3D) non-isothermal, non-Newtonian fluid flow of polymer melts is investigated. In particular, the filling stage of thermoplastic injection molding is numerically studied with a solver implemented in the open-source computational library O p e n F O A M ® . The numerical method is based on a compressible two-phase flow model, developed following a cell-centered unstructured finite volume discretization scheme, combined with a volume-of-fluid (VOF) technique for the interface capturing. Additionally, the Cross-WLF (Williams–Landel–Ferry) model is used to characterize the rheological behavior of the polymer melts, and the modified Tait equation is used as the equation of state. To verify the numerical implementation, the code predictions are first compared with analytical solutions, for a Newtonian fluid flowing through a cylindrical channel. Subsequently, the melt filling process of a non-Newtonian fluid (Cross-WLF) in a rectangular cavity with a cylindrical insert and in a tensile test specimen are studied. The predicted melt flow front interface and fields (pressure, velocity, and temperature) contours are found to be in good agreement with the reference solutions, obtained with the proprietary software M o l d e x 3 D ® . Additionally, the computational effort, measured by the elapsed wall-time of the simulations, is analyzed for both the open-source and proprietary software, and both are found to be similar for the same level of accuracy, when the parallelization capabilities of O p e n F O A M ® are employed. Full article
(This article belongs to the Special Issue Advances in Experimental and Computational Rheology, Volume II)
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20 pages, 1673 KiB  
Article
Three-Dimensional Convective Planforms for Inclined Darcy-Bénard Convection
by D. Andrew S. Rees and Antonio Barletta
Fluids 2020, 5(2), 83; https://doi.org/10.3390/fluids5020083 - 27 May 2020
Cited by 2 | Viewed by 1887
Abstract
We investigate the onset of convection in an inclined Darcy-Bénard layer. When such a layer is unbounded in the spanwise direction it is generally known that longitudinal rolls comprise the most unstable planform. On the other hand, when a layer has a sufficiently [...] Read more.
We investigate the onset of convection in an inclined Darcy-Bénard layer. When such a layer is unbounded in the spanwise direction it is generally known that longitudinal rolls comprise the most unstable planform. On the other hand, when a layer has a sufficiently small spanwise width, then transverse rolls form the most unstable planform. However, the layer remains stable to transverse roll disturbances when the inclination is above roughly 31 degrees from the horizontal. This paper considers the transition between these two extreme cases where the spanwise width takes moderate values and where rectangular cells are considered. It is found that the most unstable planform is quite strongly sensitive to the magnitude of the spanwise width and that there are large regions of parameter space within which three-dimensional convection patterns have the smallest critical Darcy-Rayleigh number. Full article
(This article belongs to the Special Issue Classical and Modern Topics in Fluid Dynamics and Transport Phenomena)
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18 pages, 2600 KiB  
Article
Interpreting the Spatial-Temporal Structure of Turbulent Chemical Plumes Utilized in Odor Tracking by Lobsters
by Kyle W. Leathers, Brenden T. Michaelis and Matthew A. Reidenbach
Fluids 2020, 5(2), 82; https://doi.org/10.3390/fluids5020082 - 24 May 2020
Cited by 10 | Viewed by 3504
Abstract
Olfactory systems in animals play a major role in finding food and mates, avoiding predators, and communication. Chemical tracking in odorant plumes has typically been considered a spatial information problem where individuals navigate towards higher concentration. Recent research involving chemosensory neurons in the [...] Read more.
Olfactory systems in animals play a major role in finding food and mates, avoiding predators, and communication. Chemical tracking in odorant plumes has typically been considered a spatial information problem where individuals navigate towards higher concentration. Recent research involving chemosensory neurons in the spiny lobster, Panulirus argus, show they possess rhythmically active or ‘bursting’ olfactory receptor neurons that respond to the intermittency in the odor signal. This suggests a possible, previously unexplored olfactory search strategy that enables lobsters to utilize the temporal variability within a turbulent plume to track the source. This study utilized computational fluid dynamics to simulate the turbulent dispersal of odorants and assess a number of search strategies thought to aid lobsters. These strategies include quantification of concentration magnitude using chemosensory antennules and leg chemosensors, simultaneous sampling of water velocities using antennule mechanosensors, and utilization of antennules to quantify intermittency of the odorant plume. Results show that lobsters can utilize intermittency in the odorant signal to track an odorant plume faster and with greater success in finding the source than utilizing concentration alone. However, the additional use of lobster leg chemosensors reduced search time compared to both antennule intermittency and concentration strategies alone by providing spatially separated odorant sensors along the body. Full article
(This article belongs to the Special Issue Advances in Biological Flows and Biomimetics)
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28 pages, 18030 KiB  
Article
Droplet Impact on Suspended Metallic Meshes: Effects of Wettability, Reynolds and Weber Numbers
by Konstantinos Vontas, Cristina Boscariol, Manolia Andredaki, Anastasios Georgoulas, Cyril Crua, Jens Honoré Walther and Marco Marengo
Fluids 2020, 5(2), 81; https://doi.org/10.3390/fluids5020081 - 22 May 2020
Cited by 25 | Viewed by 4782
Abstract
Liquid penetration analysis in porous media is of great importance in a wide range of applications such as ink jet printing technology, painting and textile design. This article presents an investigation of droplet impingement onto metallic meshes, aiming to provide insights by identifying [...] Read more.
Liquid penetration analysis in porous media is of great importance in a wide range of applications such as ink jet printing technology, painting and textile design. This article presents an investigation of droplet impingement onto metallic meshes, aiming to provide insights by identifying and quantifying impact characteristics that are difficult to measure experimentally. For this purpose, an enhanced Volume-Of-Fluid (VOF) numerical simulation framework is utilised, previously developed in the general context of the OpenFOAM CFD Toolbox. Droplet impacts on metallic meshes are performed both experimentally and numerically with satisfactory degree of agreement. From the experimental investigation three main outcomes are observed—deposition, partial imbibition, and penetration. The penetration into suspended meshes leads to spectacular multiple jetting below the mesh. A higher amount of liquid penetration is linked to higher impact velocity, lower viscosity and larger pore size dimension. An estimation of the liquid penetration is given in order to evaluate the impregnation properties of the meshes. From the parametric analysis it is shown that liquid viscosity affects the adhesion characteristics of the drops significantly, whereas droplet break-up after the impact is mostly controlled by surface tension. Additionally, wettability characteristics are found to play an important role in both liquid penetration and droplet break-up below the mesh. Full article
(This article belongs to the Special Issue Classical and Modern Topics in Fluid Dynamics and Transport Phenomena)
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18 pages, 3432 KiB  
Article
Nutrient Patchiness, Phytoplankton Surge-Uptake, and Turbulent History: A Theoretical Approach and Its Experimental Validation
by Mathilde Schapira and Laurent Seuront
Fluids 2020, 5(2), 80; https://doi.org/10.3390/fluids5020080 - 22 May 2020
Cited by 1 | Viewed by 2166
Abstract
Despite ample evidence of micro- and small-scale (i.e., millimeter- to meter-scale) phytoplankton and zooplankton patchiness in the ocean, direct observations of nutrient distributions and the ecological importance of this phenomenon are still relatively scarce. In this context, we first describe a simple procedure [...] Read more.
Despite ample evidence of micro- and small-scale (i.e., millimeter- to meter-scale) phytoplankton and zooplankton patchiness in the ocean, direct observations of nutrient distributions and the ecological importance of this phenomenon are still relatively scarce. In this context, we first describe a simple procedure to continuously sample nutrients in surface waters, and subsequently provide evidence of the existence of microscale distribution of ammonium in the ocean. We further show that ammonium is never homogeneously distributed, even under very high conditions of turbulence. Instead, turbulence intensity appears to control nutrient patchiness, with a more homogeneous or a more heterogeneous distribution observed under high and low turbulence intensities, respectively, under the same concentration in nutrient. Based on a modelling procedure taking into account the stochastic properties of intermittent nutrient distributions and observations carried out on natural phytoplankton communities, we introduce and verify the hypothesis that under nutrient limitation, the “turbulent history” of phytoplankton cells, i.e., the turbulent conditions they experienced in their natural environments, conditions their efficiency to uptake ephemeral inorganic nitrogen patches of different concentrations. Specifically, phytoplankton cells exposed to high turbulence intensities (i.e., more homogeneous nutrient distribution) were more efficient to uptake high concentration nitrogen pulses (2 µM). In contrast, under low turbulence conditions (i.e., more heterogeneous nutrient distribution), uptake rates were higher for low concentration nitrogen pulses (0.5 µM). These results suggest that under nutrient limitation, natural phytoplankton populations respond to high turbulence intensities through a decrease in affinity for nutrients and an increase in their transport rate, and vice versa. Full article
(This article belongs to the Special Issue Fluid Mechanics of Plankton)
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21 pages, 4624 KiB  
Article
Hydrodynamic Dispersion in Porous Media and the Significance of Lagrangian Time and Space Scales
by Vi Nguyen and Dimitrios V. Papavassiliou
Fluids 2020, 5(2), 79; https://doi.org/10.3390/fluids5020079 - 21 May 2020
Cited by 17 | Viewed by 6058
Abstract
Transport in porous media is critical for many applications in the environment and in the chemical process industry. A key parameter for modeling this transport is the hydrodynamic dispersion coefficient for particles and scalars in a porous medium, which has been found to [...] Read more.
Transport in porous media is critical for many applications in the environment and in the chemical process industry. A key parameter for modeling this transport is the hydrodynamic dispersion coefficient for particles and scalars in a porous medium, which has been found to depend on properties of the medium structure, on the dispersing compound, and on the flow field characteristics. Previous studies have resulted in suggestions of different equation forms, showing the relationship between the hydrodynamic dispersion coefficient for various types of porous media in various flow regimes and the Peclet number. The Peclet number is calculated based on a Eulerian length scale, such as the diameter of the spheres in packed beds, or the pore diameter. However, the nature of hydrodynamic dispersion is Lagrangian, and it should take the molecular diffusion effects, as well as the convection effects, into account. This work shifts attention to the Lagrangian time and length scales for the definition of the Peclet number. It is focused on the dependence of the longitudinal hydrodynamic dispersion coefficient on the effective Lagrangian Peclet number by using a Lagrangian length scale and the effective molecular diffusivity. The lattice Boltzmann method (LBM) was employed to simulate flow in porous media that were constituted by packed spheres, and Lagrangian particle tracking (LPT) was used to track the movement of individual dispersing particles. It was found that the hydrodynamic dispersion coefficient linearly depends on the effective Lagrangian Peclet number for packed beds with different types of packing. This linear equation describing the dependence of the dispersion coefficient on the effective Lagrangian Peclet number is both simpler and more accurate than the one formed using the effective Eulerian Peclet number. In addition, the slope of the line is a characteristic coefficient for a given medium. Full article
(This article belongs to the Special Issue Recent Advances in Fluid Mechanics: Feature Papers)
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12 pages, 7396 KiB  
Article
Rotational Maneuvers of Copepod Nauplii at Low Reynolds Number
by Kacie T. M. Niimoto, Kyleigh J. Kuball, Lauren N. Block, Petra H. Lenz and Daisuke Takagi
Fluids 2020, 5(2), 78; https://doi.org/10.3390/fluids5020078 - 21 May 2020
Cited by 7 | Viewed by 3112
Abstract
Copepods are agile microcrustaceans that are capable of maneuvering freely in water. However, the physical mechanisms driving their rotational motion are not entirely clear in small larvae (nauplii). Here we report high-speed video observations of copepod nauplii performing acrobatic feats with three pairs [...] Read more.
Copepods are agile microcrustaceans that are capable of maneuvering freely in water. However, the physical mechanisms driving their rotational motion are not entirely clear in small larvae (nauplii). Here we report high-speed video observations of copepod nauplii performing acrobatic feats with three pairs of appendages. Our results show rotations about three principal axes of the body: yaw, roll, and pitch. The yaw rotation turns the body to one side and results in a circular swimming path. The roll rotation consists of the body spiraling around a nearly linear path, similar to an aileron roll of an airplane. We interpret the yaw and roll rotations to be facilitated by appendage pronation or supination. The pitch rotation consists of flipping on the spot in a maneuver that resembles a backflip somersault. The pitch rotation involved tail bending and was not observed in the earliest stages of nauplii. The maneuvering strategies adopted by plankton may inspire the design of microscopic robots, equipped with suitable controls for reorienting autonomously in three dimensions. Full article
(This article belongs to the Special Issue Fluid Mechanics of Plankton)
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15 pages, 337 KiB  
Article
The Heat Flux Vector(s) in a Two Component Fluid Mixture
by A. D. Kirwan, Jr. and Mehrdad Massoudi
Fluids 2020, 5(2), 77; https://doi.org/10.3390/fluids5020077 - 20 May 2020
Cited by 2 | Viewed by 2092
Abstract
Bulk kinematic properties of mixtures such as velocity are known to be the density weighed averages of the constituent velocities. No such paradigm exists for the heat flux of mixtures when the constituents have different temperatures. Using standard principles such as frame indifference, [...] Read more.
Bulk kinematic properties of mixtures such as velocity are known to be the density weighed averages of the constituent velocities. No such paradigm exists for the heat flux of mixtures when the constituents have different temperatures. Using standard principles such as frame indifference, we address this topic by developing linear constitutive equations for the constituent heat fluxes, the interaction force between constituents, and the stresses for a mixture of two fluids. Although these equations contain 18 phenomenological coefficients, we are able to use the Clausius-Duhem inequality to obtain inequalities involving the principal and cross flux coefficients. The theory is applied to some special cases and shown to reduce to standard results when the constituents have the same temperature. Full article
(This article belongs to the Special Issue Recent Advances in Fluid Mechanics: Feature Papers)
9 pages, 1631 KiB  
Article
Antibiotic Activity Screened by the Rheology of S. aureus Cultures
by Raquel Portela, Filipe Valcovo, Pedro L. Almeida, Rita G. Sobral and Catarina R. Leal
Fluids 2020, 5(2), 76; https://doi.org/10.3390/fluids5020076 - 18 May 2020
Cited by 1 | Viewed by 2845
Abstract
Multidrug resistant bacteria are one of the most serious public health threats nowadays. How bacteria, as a population, react to the presence of antibiotics is of major importance to the outcome of the chosen treatment. In this study we addressed the impact of [...] Read more.
Multidrug resistant bacteria are one of the most serious public health threats nowadays. How bacteria, as a population, react to the presence of antibiotics is of major importance to the outcome of the chosen treatment. In this study we addressed the impact of oxacillin, a β-lactam, the most clinically relevant class of antibiotics, in the viscosity profile of the methicillin resistant Staphylococcus aureus (MRSA) strain COL. In the first approach, the antibiotic was added, at concentrations under the minimum inhibitory concentration (sub-MIC), to the culture of S. aureus and steady-state shear flow curves were obtained for discrete time points during the bacterial growth, with and without the presence of the antibiotic, showing distinct viscosity progress over time. The different behaviors obtained led us to test the impact of the sub-inhibitory concentration and a concentration that inhibited growth. In the second approach, the viscosity growth curves were measured at a constant shear rate of 10 s−1, over time. The obtained rheological behaviors revealed distinctive characteristics associated to the presence of each concentration of the tested antibiotic. These results bring new insights to the bacteria response to a well-known bacteriolytic antibiotic. Full article
(This article belongs to the Special Issue Advances in Experimental and Computational Rheology, Volume II)
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11 pages, 3468 KiB  
Article
The Method of Image Singularities Employed for Oscillating Oblate Spheroids under a Free Surface
by Eirini I. Anastasiou, Eva Loukogeorgaki and Ioannis K. Chatjigeorgiou
Fluids 2020, 5(2), 75; https://doi.org/10.3390/fluids5020075 - 17 May 2020
Cited by 2 | Viewed by 2313
Abstract
The main objective of this study is to develop a semi-analytical formulation for the radiation problem of a fully immersed spheroid in a liquid field of infinite depth. The term “spheroid” refers herein to the oblate geometry of arbitrary eccentricity and to the [...] Read more.
The main objective of this study is to develop a semi-analytical formulation for the radiation problem of a fully immersed spheroid in a liquid field of infinite depth. The term “spheroid” refers herein to the oblate geometry of arbitrary eccentricity and to the axisymmetric case, where the axis of symmetry is normal to the free surface. The proposed numerical approach is based on the method of image singularities, and it enables the accurate and fast calculation of the hydrodynamic coefficients for the translational degrees of freedom of the oblate spheroid. The excellent agreement of the results, with those of other investigators for the limiting case of the sphere and with those obtained using a respected boundary integral equation code, demonstrates the accuracy of the proposed methodology. Finally, extensive calculations are presented, illustrating the direct impact of the immersion depth and the slenderness of the spheroid on the hydrodynamic coefficients. Full article
(This article belongs to the Special Issue Wind and Wave Renewable Energy Systems)
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15 pages, 2772 KiB  
Article
Electrical Conductivity of Field-Structured Emulsions
by Arthur R. Zakinyan, Ludmila M. Kulgina, Anastasia A. Zakinyan and Sergey D. Turkin
Fluids 2020, 5(2), 74; https://doi.org/10.3390/fluids5020074 - 16 May 2020
Cited by 4 | Viewed by 3125
Abstract
The structure formation influence on various macroscopic properties of fluid–fluid disperse systems is poorly investigated. The present work deals with the experimental study of the charge transfer in emulsions whose dispersed phase droplets are arranged into chainlike structures under the action of an [...] Read more.
The structure formation influence on various macroscopic properties of fluid–fluid disperse systems is poorly investigated. The present work deals with the experimental study of the charge transfer in emulsions whose dispersed phase droplets are arranged into chainlike structures under the action of an external force field. The emulsions studied are the fluid system in which water droplets are dispersed in a hydrocarbon-based magnetic fluid. Under the effect of an external uniform magnetic field, anisotropic aggregates form from the emulsion dispersed phase drops. The low-frequency electrical conductivity of emulsions has been measured. It is demonstrated that the emulsions’ conductivity grows several times under the effect of magnetic field parallel to the measuring electrical field. The anisotropic character of the emulsion electrical conductivity in the presence of magnetic field has been demonstrated. It is revealed that the maximal response of conductivity on the magnetic field action takes place at the dispersed phase volume fraction of about 20%. The dynamics of the conductivity variation is analyzed in dependence on the magnetic field strength and the dispersed phase volume fraction. The obtained results may be of interest in the development of potential applications of disperse systems with magnetic-field-controllable properties. Full article
(This article belongs to the Special Issue Classical and Modern Topics in Fluid Dynamics and Transport Phenomena)
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2 pages, 141 KiB  
Editorial
Recent Numerical Advances in Fluid Mechanics
by Omer San
Fluids 2020, 5(2), 73; https://doi.org/10.3390/fluids5020073 - 15 May 2020
Viewed by 1591
Abstract
In recent decades, the field of computational fluid dynamics has made significant advances in enabling advanced computing architectures to understand many phenomena in biological, geophysical, and engineering fluid flows [...] Full article
(This article belongs to the Special Issue Recent Numerical Advances in Fluid Mechanics)
16 pages, 5663 KiB  
Article
Jet Oscillation Frequency Characterization of a Sweeping Jet Actuator
by Furkan Oz and Kursat Kara
Fluids 2020, 5(2), 72; https://doi.org/10.3390/fluids5020072 - 14 May 2020
Cited by 16 | Viewed by 3616
Abstract
The time-resolved flow field of a spatially oscillating jet emitted by a sweeping jet (SWJ) actuator is investigated numerically using three-dimensional Reynolds-averaged Navier–Stokes (3D-URANS) equations. Numerical simulations are performed for a range of mass flow rates providing flow conditions varying from incompressible to [...] Read more.
The time-resolved flow field of a spatially oscillating jet emitted by a sweeping jet (SWJ) actuator is investigated numerically using three-dimensional Reynolds-averaged Navier–Stokes (3D-URANS) equations. Numerical simulations are performed for a range of mass flow rates providing flow conditions varying from incompressible to subsonic compressible flows. After a detailed mesh study, the computational domain is represented using two million hexagonal control volumes. The jet oscillation frequency is predicted by analyzing velocity time histories at the actuator exit, and a linear relationship between the jet oscillation frequency and time-averaged exit nozzle Mach number is found ( f = 511.22   M + 46.618 , R² = 0.97). The results of our numerical model are compared with data from the literature, and a good agreement is found. In addition, we confirmed that the Strouhal number is almost constant with the Mach number for the subsonic oscillating jet and has an average value of St = 0.0131. The 3D-URANS model that we presented here provides a computationally inexpensive yet accurate alternative to the researchers to investigate jet oscillation characteristics. Full article
(This article belongs to the Special Issue Recent Numerical Advances in Fluid Mechanics, Volume II)
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17 pages, 5577 KiB  
Article
Liquid-Cooling System of an Aircraft Compression Ignition Engine: A CFD Analysis
by Alessandro Coclite, Maria Faruoli, Annarita Viggiano, Paolo Caso and Vinicio Magi
Fluids 2020, 5(2), 71; https://doi.org/10.3390/fluids5020071 - 13 May 2020
Cited by 5 | Viewed by 3258
Abstract
The present work deals with an analysis of the cooling system for a two-stroke aircraft engine with compression ignition. This analysis is carried out by means of a 3D finite-volume RANS equations solver with k- ϵ closure. Three different cooling system geometries [...] Read more.
The present work deals with an analysis of the cooling system for a two-stroke aircraft engine with compression ignition. This analysis is carried out by means of a 3D finite-volume RANS equations solver with k- ϵ closure. Three different cooling system geometries are critically compared with a discussion on the capabilities and limitations of each technical solution. A first configuration of such a system is considered and analyzed by evaluating the pressure loss across the system as a function of the inlet mass-flow rate. Moreover, the velocity and vorticity patterns are analyzed to highlight the features of the flow structure. Thermal effects on the engine structure are also taken into account and the cooling system performance is assessed as a function of both the inlet mass-flow rate and the cylinder jackets temperatures. Then, by considering the main thermo-fluid dynamics features obtained in the case of the first configuration, two geometrical modifications are proposed to improve the efficiency of the system. As regards the first modification, the fluid intake is split in two manifolds by keeping the same total mass-flow rate. As regards the second configuration, a new single-inlet geometry is designed by inserting restrictions and enlargements within the cooling system to constrain the coolant flow through the cylinder jackets and by moving downstream the outflow section. It is shown that the second geometry modification achieves the best performances by improving the overall transferred heat of about 20% with respect to the first one, while keeping the three cylinders only slightly unevenly cooled. However, an increase of the flow characteristic loads occurs due to the geometrical restrictions and enlargements of the cooling system. Full article
(This article belongs to the Special Issue Recent Numerical Advances in Fluid Mechanics)
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25 pages, 6446 KiB  
Article
On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization
by Farzad Mohebbi and Ben Evans
Fluids 2020, 5(2), 70; https://doi.org/10.3390/fluids5020070 - 13 May 2020
Cited by 1 | Viewed by 3166
Abstract
This study proposeda novel exact expression for step length (size) in gradient-based aerodynamic shape optimization for an airfoil in steady inviscid transonic flows. The airfoil surfaces were parameterized using Bezier curves. The Bezier curve control points were considered as design variables and the [...] Read more.
This study proposeda novel exact expression for step length (size) in gradient-based aerodynamic shape optimization for an airfoil in steady inviscid transonic flows. The airfoil surfaces were parameterized using Bezier curves. The Bezier curve control points were considered as design variables and the finite-difference method was used to compute the gradient of the objective function (drag-to-lift ratio) with respect to the design variables. An exact explicit expression was derived for the step length in gradient-based shape optimization problems. It was shown that the derived step length was independent of the method used for calculating the gradient (adjoint method, finite-difference method, etc.). The obtained results reveal the accuracy of the derived step length. Full article
(This article belongs to the Special Issue Recent Numerical Advances in Fluid Mechanics, Volume II)
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