Fluids doi: 10.3390/fluids3020044

Authors: Vishwa T. Kasoju Christopher L. Terrill Mitchell P. Ford Arvind Santhanakrishnan

In contrast to larger flight-capable insects such as hawk moths and fruit flies, miniature flying insects such as thrips show the obligatory use of wing&ndash;wing interaction via &ldquo;clap and fling&rdquo; during the end of upstroke and start of downstroke. Although fling can augment lift generated during flapping flight at chord-based Reynolds number (Re) of 10 or lower, large drag forces are necessary to clap and fling the wings. In this context, bristles observed in the wings of most tiny insects have been shown to lower drag force generated in clap and fling. However, the fluid dynamic mechanism underlying drag reduction by bristled wings and the impact of bristles on lift generated via clap and fling remain unclear. We used a dynamically scaled robotic model to examine the forces and flow structures generated during clap and fling of: three bristled wing pairs with varying inter-bristle spacing, and a geometrically equivalent solid wing pair. In contrast to the solid wing pair, reverse flow through the gaps between the bristles was observed throughout clap and fling, resulting in: (a) drag reduction; and (b) weaker and diffuse leading edge vortices that lowered lift. Shear layers were formed around the bristles when interacting bristled wing pairs underwent clap and fling motion. These shear layers lowered leakiness of flow through the bristles and minimized loss of lift in bristled wings. Compared to the solid wing, peak drag coefficients were reduced by 50&ndash;90% in bristled wings. In contrast, peak lift coefficients of bristled wings were only reduced by 35&ndash;60% from those of the solid wing. Our results suggest that the bristled wings can provide unique aerodynamic benefits via increasing lift to drag ratio during clap and fling for Re between 5 and 15.

]]>Fluids doi: 10.3390/fluids3020043

Authors: Laurence Noirez Philipp Kahl

There is little literature on the flow properties of the isotropic phase of liquid crystalline fluids. However, this phase is an ideal tool to bridge the physics of liquid crystals with those of (ordinary) fluids. Optical and mechanical studies are presented, demonstrating that away from any phase transition, the isotropic phase of liquid crystalline molecules (LCs) and liquid crystalline polymers (LCPs) can work as an optical oscillator in response to low-frequency mechanical excitation, establishing the elastic origin of the flow birefringence and “visualizing” the very existence of the elastic nature of the liquid state. Additionally, mimicking the excellent anchoring ability of liquid crystals, an alternative rheological protocol optimizing the fluid/substrate interfaces is presented to access the low-frequency shear elasticity in various one-component liquids and salt-free aqueous solutions.

]]>Fluids doi: 10.3390/fluids3020042

Authors: Yebegaeshet T. Zerihun

The classical Dupuit&ndash;Forchheimer approach, commonly used in analysing unconfined groundwater-flow systems, relies on the assumption of a negligible vertical component of the flow. This approximation is valid only when the convergence of streamlines is very limited and the drawdown of the phreatic surface is small, or the thickness of the horizontal layer of the heterogeneous aquifers is sufficiently small. In this study, a higher-order one-dimensional model is proposed for groundwater-flow problems with significant inclination and curvature of the phreatic surface. The model incorporates non-hydrostatic terms that take into account the effects of the vertical velocity of the flow, and was solved with an implicit finite-difference scheme. The accuracy of the proposed model was demonstrated by simulating various unconfined seepage- and groundwater-flow problems with moderate curvilinear effects. The computational results for steady-state flows were compared with the results of the full two-dimensional potential-flow methods and experimental data, resulting in a reasonably good agreement. In general, the comparison results exhibited the efficiency and validity of the model in simulating complex unconfined flows over curved bedrock and curvilinear flows over planar bedrock with a steep slope.

]]>Fluids doi: 10.3390/fluids3020041

Authors: Maria Cristina Morani Armando Carravetta Giuseppe Del Giudice Aonghus McNabola Oreste Fecarotta

Water systems are usually considered low efficiency systems, due to the large amount of energy that is lost by water leakage and dissipated by pressure reducing valves to control the leakage itself. In water distribution networks, water is often pumped from the source to an elevated tank or reservoir and then supplied to the users. A large energy recovery can be realized by the installation of energy production devices (EPDs) to exploit the excess of pressure that would be dissipated by regulation valves. The feasibility of such a sustainable strategy depends on the potential of energy savings and the amount of energy embedded in water streams, assessed by means of efficiency measures. Alternatively, energy savings can be pursued if the water is directly pumped to the network, bypassing the elevated reservoir. This study focuses on the comparison of two solutions to supply a real network, assessed as a case study. The first solution consists of water pumping to a reservoir, located upstream of the network; the excess of energy is saved by the employment of a pump as turbine (PAT). The second scenario is characterized by a smaller pressure head since a direct variable speed pumping is performed, bypassing the reservoir. The comparison has been carried out in terms of required energy, assessed by means of a new energy index and two literature efficiency indices. Furthermore, differing design conditions have been analyzed by varying the pumping head of both the scenarios, corresponding to different distances and elevation of the water source.

]]>Fluids doi: 10.3390/fluids3020040

Authors: Nityanand Sinha Roozbeh Golshan

The interaction of a developed train of gravity deep water waves with suddenly applied winds is investigated in this manuscript. The direction of the wind is the same as that of the wave train (i.e., following) and its imposed surface shear stress is constant and steady. The focus of this study is on a micro-scale water wave field where the time scale is on the order of ten wave periods and the length scale is on the order of ten wave lengths. Accurate 2D Reynolds-averaged Navier&ndash;Stokes (RANS) multi-phase simulations of Navier&ndash;Stokes equations are performed in a Eulerian framework to capture the flow features, induced by the wave field and the surface wind. The sufficiently large spatial domain in the horizontal direction, combined with the sufficiently long simulation time, permits the development of surface currents and the consequent formation of a near-surface shear layer. The interaction of surface currents with the wave orbital velocity field results in the generation of spilling breaking waves. Downstream of the domain, vertical turbulent structures are observed as the result of such breaking waves. Lagrangian particle tracking is performed, using the RANS simulation velocity and eddy diffusivity data. A second order random acceleration particle tracking method is applied with the vitally important spatial gradients of the eddy diffusivity (Journal of Marine Science and Engineering, 2018, 6, 10.3390/jmse6010007.) also included in calculations. The spatial gradients of the eddy diffusivity were proved to be a key factor in material transport simulations. Our particle tracking results exhibit strong vertical mixing downstream of the domain and by means of visualizing the spiral trajectory of neutrally buoyant particles. Such enhanced vertical mixing (caused by horizontal winds) is the result of the strong near-surface advection (induced by currents) and the turbulence (induced by breaking waves). The objectives of this paper are twofold. Firstly, a numerical approach to simulate wind breaking waves is proposed based on: using K &minus; ϵ RANS model to capture turbulence features, employing the Volume of Fluid Method (VOF) to model the free surface flow, and applying a constant shear stress body force at the interfacial cells to simulate the wind force. Such treatment of the winds eliminates the need for fully resolving the air phase. The computed eddy viscosity profiles are in good agreement with the experimental profiles reported in the literature ( &nu; t = &minus; &kappa; u * z , Journal of Physical Oceanography, 1977, 7, pp. 248&ndash;255; Journal of Physical Oceanography, 1984, 14, pp. 855&ndash;863). Secondly, effects of the horizontally applied wind on the vertical mixing and eddy viscosity profiles on the water column are studied. It is observed that, away from the surface and outside the shear layer, the negative horizontal gradient of eddy diffusivity (induced by the dampening effect of breaking surface waves), combined with the downwards advection velocities (induced by breaking waves), results in an enhanced vertical mixing and reduced horizontal drift of transported material.

]]>Fluids doi: 10.3390/fluids3020039

Authors: Sourav Mondal Ian M. Griffiths Florian Charlet Apala Majumdar

We numerically and analytically study the flow and nematic order parameter profiles in a microfluidic channel, within the Beris&ndash;Edwards theory for nematodynamics, with two different types of boundary conditions&mdash;strong anchoring/Dirichlet conditions and mixed boundary conditions for the nematic order parameter. We primarily study the effects of the pressure gradient, the effects of the material constants and viscosities modelled by a parameter L 2 and the nematic elastic constant L &lowast; , along with the effects of the choice of the boundary condition. We study continuous and discontinuous solution profiles for the nematic director and these discontinuous solutions have a domain wall structure, with a layered structure that offers new possibilities. Our main results concern the onset of flow reversal as a function of L &lowast; and L 2 , including the identification of certain parameter regimes with zero net flow rate. These results are of value in tuning microfluidic geometries, boundary conditions and choosing liquid crystalline materials for desired flow properties.

]]>Fluids doi: 10.3390/fluids3020038

Authors: Yixiang Liao Dirk Lucas

The complexity of flashing flows is increased vastly by the interphase heat transfer as well as its coupling with mass and momentum transfers. A reliable heat transfer coefficient is the key in the modelling of such kinds of flows with the two-fluid model. An extensive literature survey on computational modelling of flashing flows has been given in previous work. The present work is aimed at giving a brief review on available theories and correlations for the estimation of interphase heat transfer coefficient, and evaluating them quantitatively based on computational fluid dynamics simulations of bubble growth in superheated liquid. The comparison of predictions for bubble growth rate obtained by using different correlations with the experimental as well as direct numerical simulation data reveals that the performance of the correlations is dependent on the Jakob number and Reynolds number. No generally applicable correlations are available. Both conduction and convection are important in cases of bubble rising and translating in stagnant liquid at high Jakob numbers. The correlations combining the analytical solution for heat diffusion and the theoretical relation for potential flow give the best agreement.

]]>Fluids doi: 10.3390/fluids3020037

Authors: Alexis Omilion Jodi Turk Wei Zhang

Multi-scale fractal grids can be considered to mimic the fractal characteristic of objects of complex appearance in nature, such as branching pulmonary network and corals in biology, river network, trees, and cumulus clouds in geophysics, and the large-scale structure of the universe in astronomy. Understanding the role that multiple length scales have in momentum and energy transport is essential for effective utilization of fractal grids in a wide variety of engineering applications. Fractal square grids, consisted of the basic square pattern, have been used for enhancing fluid mixing as a passive flow control strategy. While previous studies have solidified the dominant effect of the largest scale, effects of the smaller scales and the interaction of the range of scales on the generated turbulent flow remain unclear. This research is to determine the relationship between the fractal scales (varying with the fractal iteration N), the turbulence statistics of the flow and the pressure drop across the fractal square grids using well-controlled water-tunnel experiments. Instantaneous and ensemble-averaged velocity fields are obtained by a planar Particle Image Velocimetry (PIV) method for a set of fractal square grids (N = 1, 2 and 4) at Reynolds number of 3400. The static pressure drop across the fractal square grid is measured by a differential pressure transducer. Flow fields indicate that the multiple jets, wakes and the shear layers produced by the multiple scales of bars are the fundamental flow physics that promote momentum transport in the fractal grid generated turbulence. The wake interaction length scale model is modified to incorporate the effects of smaller scales and thereof interaction, by the effective mesh size M e f f and an empirical coefficient &beta; . Effectiveness of a fractal square grid is assessed using the gained turbulence intensity and Reynolds shear stress level at the cost of pressure loss, which varies with the distance downstream. In light of the promising capability of the fractal grids to enhance momentum and energy transport, this work can potentially benefit a wide variety of applications where energy efficient mixing or convective heat transfer is a key process.

]]>Fluids doi: 10.3390/fluids3020036

Authors: Stella Tsermentseli Konstantinos Kontogiannopoulos Vassilios Papageorgiou Andreana Assimopoulou

Liposomes are considered to be one of the most successful drug delivery systems. They apply nanotechnology to potentiate the therapeutic efficacy and reduce the toxicity of conventional medicines. Shikonin and alkannin, a pair of chiral natural naphthoquinone compounds, derived from Alkanna and Lithospermum species, are widely used due to their various pharmacological activities, mainly wound healing, antioxidant, anti-inflammatory and their recently established antitumor activity. The purpose of this study was to prepare conventional and PEGylated shikonin-loaded liposomal formulations and measure the effects of different lipids and polyethylene glycol (PEG) on parameters related to particle size distribution, the polydispersity index, the zeta potential, drug-loading efficiency and the stability of the prepared formulations. Three types of lipids were assessed (1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC), 1,2-Distearoyl-sn-glycero-3-phosphocholine (DSPC) and 1,2-distearoyl-sn-glycero-3-phospho-rac-(1-glycerol) (DSPG)), separately and in mixtures, forming anionic liposomes with good physicochemical characteristics, high entrapment efficiencies (varying from 56.5 to 89.4%), satisfactory in vitro release profiles and good physical stability. The addition of the negatively charged DSPG lipids to DOPC, led to an increment in the drug’s incorporation efficiency and reduced the particle size distribution. Furthermore, the shikonin–loaded PEGylated sample with DOPC/DSPG, demonstrated the most satisfactory characteristics. These findings are considered promising and could be used for further design and improvement of such formulations.

]]>Fluids doi: 10.3390/fluids3020035

Authors: Edtson Emilio Herrera Valencia Alejandro D. Rey

Liquid crystal flexoelectric actuation uses an imposed electric field to create membrane bending, this phenomenon is found in outer hair cells (OHC) located in the inner ear, whose role is to amplify sound through the generation of mechanical power. Oscillations in the OHC membranes create periodic viscoelastic flows in the contacting fluid media. A key objective of this work on flexoelectric actuation relevant to OHC is to find the relations and impact of the electro-mechanical properties of the membrane, the rheological properties of the viscoelastic media, and the frequency response of the generated mechanical power output. The model developed and used in this work is based on the integration of: (i) the flexoelectric membrane shape equation applied to a circular membrane attached to the inner surface of a circular capillary, and (ii) the coupled capillary flow of contacting viscoelastic phases, which are characterized by the Jeffreys constitutive equation with different material conditions. The membrane flexoelectric oscillations drive periodic viscoelastic capillary flows, as in OHCs. By applying the Fourier transform formalism to the governing equations and assuming small Mach numbers, analytical equations for the transfer function, associated to the average curvature, and for the volumetric rate flow as a function of the electrical field were found, and these equations can be expressed as a third-order differential equation which depends on the material properties of the system. When the inertial mechanisms are considered, the power spectrum shows several resonance peaks in the average membrane curvature and volumetric flow rate. When the inertia is neglected, the system follows a non-monotonic behavior in the power spectrum. This behavior is associated with the solvent contributions related to the retardation-Jeffreys mechanisms. The specific membrane-viscoelastic fluid properties that control the power response spectrum are identified. The present theory, model, and computations contribute to the evolving fundamental understanding of biological shape actuation through electromechanical couplings.

]]>Fluids doi: 10.3390/fluids3020034

Authors: Shuji Fujii Yuji Sasaki Hiroshi Orihara

Nonlinear rheological properties of chiral crystal cholesteryl oleyl carbonate (COC) in blue phase III (BPIII) were investigated under different shear deformations: large amplitude oscillatory shear, step shear deformation, and continuous shear flow. Rheology of the liquid crystal is significantly affected by structural rearrangement of defects under shear flow. One of the examples on the defect-mediated rheology is the blue phase rheology. Blue phase is characterized by three dimensional network structure of the disclination lines. It has been numerically studied that the rheological behavior of the blue phase is dominated by destruction and creation of the disclination networks. In this study, we find that the nonlinear viscoelasticity of BPIII is characterized by the fracture of the disclination networks. Depending on the degree of the fracture, the nonlinear viscoelasticity is divided into two regimes; the weak nonlinear regime where the disclination network locally fractures but still shows elastic response, and the strong nonlinear regime where the shear deformation breaks up the networks, which results in a loss of the elasticity. Continuous shear deformation reveals that a series of the fracture process delays with shear rate. The shear rate dependence suggests that force balance between the elastic force acting on the disclination lines and the viscous force determines the fracture behavior.

]]>Fluids doi: 10.3390/fluids3020033

Authors: Frank E. Fish Terrie M. Williams Erica Sherman Yae Eun Moon Vicki Wu Timothy Wei

Estimation of force generated by dolphins has long been debated. The problem was that indirect estimates of force production for dolphins resulted in low values that could not be validated. Bubble digital particle image velocimetry (DPIV) measured hydrodynamic force production for swimming dolphins and demonstrated high force production. To validate the bubble DPIV and reconcile force production measurements, two bottlenose dolphins (Tursiops truncatus) performing tail stands were measured with bubble DPIV. Microbubbles were generated from a finely porous hose and compressed air source. Displacement of the bubbles by the propulsive motions of the dolphin was tracked with a high-speed video camera. Oscillations of the dolphin flukes generated strong vortices and a downward directed jet flow into the wake. Application of the Kutta&ndash;Joukowski theorem measuring vortex circulations yielded forces up to 997.3 N. Another video camera recorded body height above the water surface to determine the mass-force of the dolphin above the water surface. For the dolphin to hold its position above the water surface, the mass-force approximately balanced the vertical hydrodynamic force from the flukes. The results demonstrated the fluke motions generate high sustained forces roughly equal to the dolphin&rsquo;s weight out of the water. Bubble DPIV validated high forces measured previously for thrust generated in swimming by animals and demonstrated a more accurate technique compared to standard aerodynamic analysis.

]]>Fluids doi: 10.3390/fluids3020032

Authors: Ayah Lazar Qiong Zhang Andrew F. Thompson

Regions of the ocean near continental slopes are linked to significant vertical velocities caused by advection over a sloping bottom, frictional processes and diffusion. Oceanic motions at submesoscales are also characterized by enhanced vertical velocities, as compared to mesoscale motions, due to greater contributions from ageostrophic flows. These enhanced vertical velocities can make an important contribution to turbulent fluxes. Sloping topography may also induce large-scale potential vorticity gradients by modifying the slope of interior isopycnal surfaces. Potential vorticity gradients, in turn, may feed back on mesoscale stirring and the generation of submesoscale features. In this study, we explore the impact of sloping topography on the characteristics of submesoscale motions. We conduct high-resolution (1 km &times; 1 km) simulations of a wind-driven frontal current over an idealized continental shelf and slope. We explore changes in the magnitude, skewness and spectra of surface vorticity and vertical velocity across different configurations of the topographic slope and wind-forcing orientations. All of these properties are strongly modulated by the background topography. Furthermore, submesoscale characteristics exhibit spatial variability across the continental shelf and slope. We find that changes in the statistical properties of submesoscale motions are linked to mesoscale stirring responding to differences in the interior potential vorticity distributions, which are set by frictional processes at the ocean surface and over the sloping bottom. Improved parameterizations of submesoscale motions over topography may be needed to simulate the spatial variability of these features in coarser-resolution models, and are likely to be important to represent vertical nutrient fluxes in coastal waters.

]]>Fluids doi: 10.3390/fluids3020031

Authors: Sarvenaz Sobhansarbandi Lizon Maharjan Babak Fahimi Fatemeh Hassanipour

One of the most important methods of methane utilization is the conversion to synthesis gas (syngas). However, conventional ways of reforming methane usually require very high temperature, therefore non-thermal (non-equilibrium) plasma methane reforming is an attractive alternative. In this study, a novel plasma based reformer named 3D Gliding Arc Vortex Reformer (3D-GAVR) was investigated for partial oxidation of methane to produce syngas. The tangential input creates a vortex in the plasma zone and an expanded plasma presides within the entire area between the two electrodes. Using this method, the experimental results show that hydrogen can be produced for as low as $ 4.45 per kg with flow rates of around 1 L per minute. The maximum methane conversion percentage which is achieved by this technology is up to 62.38%. In addition, a computational fluid dynamics (CFD) modeling is conducted for a cold plasma reformer chamber named reverse vortex flow gliding arc reactor (RVF-GA) to investigate the effects of geometry and configuration on the reformer performance. In this modified reformer, an axial air input port is added to the top of the reaction vessel while the premixed reactants can enter the cylindrical reaction zone through tangential jets. The CFD results show that a reverse vortex flow (RVF) scheme can be created which has an outer swirling rotation along with a low pressure area at its center with some component of axial flow. The reversed vortex flow utilizes the uniform temperature and heat flux distribution inside the cylinder, and enhances the gas mixtures leading to expedition of the chemical reaction and the rate of hydrogen production.

]]>Fluids doi: 10.3390/fluids3020030

Authors: Mohamed Elshalakani Christoph H. Brücker

This article investigates the formation of spontaneous coordination in a row of flexible 2D flaps (artificial cilia) in a chamber filled with a high viscous liquid (Re = 0.12). Each flap is driven individually to oscillate by a rotary motor with the root of the flap attached to its spindle axle. A computer-vision control loop tracks the flap tips online and toggles the axle rotation direction when the tips reach a pre-defined maximum excursion. This is a vision-controlled implementation of the so-called &ldquo;geometric clutch&rdquo; hypothesis. When running the control loop with the flaps in an inviscid reference situation (air), they remain in their individual phases for a long term. Then, the flaps are studied in the chamber filled with a highly viscous liquid, and the same control loop is started. The flexible flaps now undergo bending due to hydrodynamic coupling and come, after a maximum of 15 beats, into a synchronous metachronal coordination. The study proves in a macroscopic lab experiment that viscous coupling is sufficient to achieve spontaneous synchronization, even for a symmetric cilia shape and beat pattern.

]]>Fluids doi: 10.3390/fluids3020029

Authors: Longfei Zhao Sergey Shkarayev Erlong Su

In the present study, an oscillating membrane flapper was pivotally attached to the tip of a conventional rigid wing. Stroke-averaged aerodynamic forces were measured for the range of the flapping frequency, showing significant increases in the lift coefficient and lift-to-drag ratio for the wing with a flapper. Major vortex patterns were deduced from observations of smoke-wire visualization and 2D phase-locked particle image velocimetry (PIV). The centerline of the primary vortex wanders in the counterclockwise direction. On the contrary, its core rotates in the same sense of rotation as a wingtip vortex in a conventional wing. The secondary weaker vortex of opposite rotation lasts for a half stroke. The vortex ring sheds from the flapper during the second half of the upstroke and pronation. The outer parts of the vortex system are much stronger than the inner ones. The circulation and size of vortices decrease significantly at the most distant station from the wing. Strong vertical jets were found in smoke-wire visualization and confirmed with velocity and vorticity fields obtained by PIV. These jets are formed between undulating vortices and inside of the vortex ring. The jet airflow moves away from the flapper and downward or upward depending on the flapping direction.

]]>Fluids doi: 10.3390/fluids3020028

Authors: Huicong Jiang Hua Tan

In recent years, physics-based computer models have been increasingly applied to design the drop-on-demand (DOD) inkjet devices. The initial design stage for these devices often requires a fast turnaround time of computer models, because it usually involves a massive screening of a large number of design parameters. Thus, in the present study, a 1D model is developed to achieve the fast prediction of droplet ejection process from DOD devices, including the droplet breakup and coalescence. A popular 1D slender-jet method (Egger, 1994) is adopted in this study. The fluid dynamics in the nozzle region is described by a 2D axisymmetric unsteady Poiseuille flow model. Droplet formation and nozzle fluid dynamics are coupled, and hence solved together, to simulate the inkjet droplet ejection. The arbitrary Lagrangian&ndash;Eulerian method is employed to solve the governing equations. Numerical methods have been proposed to handle the breakup and coalescence of droplets. The proposed methods are implemented in an in-house developed MATLAB code. A series of validation examples have been carried out to evaluate the accuracy and the robustness of the proposed 1D model. Finally, a case study of the inkjet droplet ejection with different Ohnesorge number (Oh) is presented to demonstrate the capability of the proposed 1D model for DOD inkjet process. Our study has shown that 1D model can significantly reduce the computational time (usually less than one minute) yet with acceptable accuracy, which makes it very useful to explore the large parameter space of inkjet devices in a short amount of time.

]]>Fluids doi: 10.3390/fluids3020027

Authors: Alvaro Gonzalez-Alvarez Oscar E. Coronado-Hernández Vicente S. Fuertes-Miquel Helena M. Ramos

The 24-h maximum rainfall (P24h-max) observations recorded at the synoptic weather station of Rafael N&uacute;&ntilde;ez airport (Cartagena de Indias, Colombia) were analyzed, and a linear increasing trend over time was identified. It was also noticed that the occurrence of the rainfall value (over the years of record) for a return period of 10 years under stationary conditions (148.1 mm) increased, which evidences a change in rainfall patterns. In these cases, the typical stationary frequency analysis is unable to capture such a change. So, in order to further evaluate rainfall observations, frequency analyses of P24h-max for stationary and non-stationary conditions were carried out (by using the generalized extreme value distribution). The goodness-of-fit test of Akaike Information Criterion (AIC), with values of 753.3721 and 747.5103 for stationary and non-stationary conditions respectively, showed that the latter best depicts the increasing rainfall pattern. Values of rainfall were later estimated for different return periods (2, 5, 10, 25, 50, and 100 years) to quantify the increase (non-stationary versus stationary condition), which ranged 6% to 12% for return periods from 5 years to 100 years, and 44% for a 2-year return period. The effect of these findings were tested in the Gordo creek watershed by first calculating the resulting direct surface runoff (DSR) for various return periods, and then modeling the hydraulic behavior of the downstream area (composed of a 178.5-m creek&rsquo;s reach and an existing box-culvert located at the watershed outlet) that undergoes flooding events every year. The resulting DSR increase oscillated between 8% and 19% for return periods from 5 to 100 years, and 77% for a 2-year return period when the non-stationary and stationary scenarios were compared. The results of this study shed light upon to the precautions that designers should take when selecting a design, based upon rainfall observed, as it may result in an underestimation of both the direct surface runoff and the size of the hydraulic structures for runoff and flood management throughout the city.

]]>Fluids doi: 10.3390/fluids3020026

Authors: Rasmita Sahoo Surajit Dhara

Topological defects are important in determining the properties of physical systems and are known varyingly depending on the broken symmetry. In superfluid helium, they are called vortices; in periodic crystals, one refers to dislocations; and in liquid crystals, they are disclinations. The defects and the inter-defect interaction in some highly chiral liquid crystals stabilize some intermediate complex phases such as Blue Phases (BPs) and Twist Grain Boundary-A (TGBA) phases. The defect dynamics of these phases contributes to the rheological properties. The temperature range of these intermediate phases usually are very small in pure liquid crystals; consequently, a detailed experiment has been difficult to achieve. However, the temperature range could be enhanced significantly in multicomponent systems. In this review article, we discuss some recent experimental progress made in understanding the rheological properties of the wide-temperature-range TGBA and BP liquid crystals.

]]>Fluids doi: 10.3390/fluids3020025

Authors: Cortes Williams Olufemi Kadri Roman Voronov Vassilios Sikavitsas

Flow perfusion bioreactors have been extensively investigated as a promising culture method for bone tissue engineering, due to improved nutrient delivery and shear force-mediated osteoblastic differentiation. However, a major drawback impeding the transition to clinically-relevant tissue regeneration is the inability to non-destructively monitor constructs during culture. To alleviate this shortcoming, we investigated the distribution of fluid shear forces in scaffolds cultured in flow perfusion bioreactors using computational fluid dynamic techniques, analyzed the effects of scaffold architecture on the shear forces and monitored tissue mineralization throughout the culture period using microcomputed tomography. For this study, we dynamically seeded one million adult rat mesenchymal stem cells (MSCs) on 85% porous poly(l-lactic acid) (PLLA) polymeric spunbonded scaffolds. After taking intermittent samples over 16 days, the constructs were imaged and reconstructed using microcomputed tomography. Fluid dynamic simulations were performed using a custom in-house lattice Boltzmann program. By taking samples at different time points during culture, we are able to monitor the mineralization and resulting changes in flow-induced shear distributions in the porous scaffolds as the constructs mature into bone tissue engineered constructs, which has not been investigated previously in the literature. From the work conducted in this study, we proved that the average shear stress per construct consistently increases as a function of culture time, resulting in an increase at Day 16 of 113%.

]]>Fluids doi: 10.3390/fluids3020024

Authors: Amir-Hasan Kakaee Parvaneh Jafari Amin Paykani

In the current study, a comparative study is performed using Large Eddy Simulation (LES) and Reynolds-averaged Navier–Stokes (RANS) turbulence models on a natural gas/diesel Reactivity Controlled Compression Ignition (RCCI) engine. The numerical results are validated against the available research work in the literature. The RNG (Re-Normalization Group) k − ε and dynamic structure models are employed to model turbulent flow for RANS and LES simulations, respectively. Parameters like the premixed natural gas mass fraction, the second start of injection timing (SOI2) of diesel and the engine speed are studied to compare performance of RANS and LES models on combustion and pollutant emissions prediction. The results obtained showed that the LES and RANS model give almost similar predictions of cylinder pressure and heat release rate at lower natural gas mass fractions and late SOI2 timings. However, the LES showed improved capability to predict the natural gas auto-ignition and pollutant emissions prediction compared to RANS model especially at higher natural gas mass fractions.

]]>Fluids doi: 10.3390/fluids3010023

Authors: Ebraheam Al-Zaidi Xianfeng Fan Katriona Edlmann

CO2 sequestration in saline aquifers and hydrocarbon reservoirs is a promising strategy to reduce CO2 concentration in the atmosphere and/or enhance hydrocarbon production. Change in subsurface conditions of pressure and temperature and CO2 state is likely to have a significant impact on capillary and viscous forces, which, in turn, will have a considerable influence on the injection, migration, displacement, and storage capacity and integrity of CO2 processes. In this study, an experimental investigation has been performed to explore the impact of fluid pressure, temperature, and injection rate, as a function of CO2 phase, on the dynamic pressure evolution and the oil recovery performance of CO2 during oil displacement in a Berea sandstone core sample. The results reveal a considerable impact of the fluid pressure, temperature, and injection rate on the differential pressure profile, cumulative produced volumes, endpoint CO2 relative permeability, and oil recovery; the trend and the size of the changes depend on the CO2 phase as well as the pressure range for gaseous CO2–oil displacement. The residual oil saturation was in the range of around 0.44–0.7; liquid CO2 gave the lowest, and low-fluid-pressure gaseous CO2 gave the highest. The endpoint CO2 relative permeability was in the range of about 0.015–0.657; supercritical CO2 gave the highest, and low-pressure gaseous CO2 gave the lowest. As for increasing fluid pressure, the results indicate that viscous forces were dominant in subcritical CO2 displacements, while capillary forces were dominant in supercritical CO2 displacements. As temperature and CO2 injection rates increase, the viscous forces become more dominant than capillary forces.

]]>Fluids doi: 10.3390/fluids3010022

Authors: Kevin Anderson Jun Lin Alexander Wong

Windage (drag) losses have been found to be a key design factor for high power density and high-speed electric motor development. Inducing axial flow between rotor and stator is a common method in cooling the rotor. Hence, it is necessary to understand the effect on windage while forced axial airflow is in present in the air gap. The current paper presents results from experimental testing and modeling of a high-speed motor designed to operate at 30,000 revolutions per minute (RPM) and utilize axial air cooling of 200 Liters per minute (LPM) to cool the motor. Details of the experimental apparatus and computational fluid dynamics (CFD) modeling of the small gap narrow region of the stator/rotor are outlined in the paper. The experimental results are used to calibrate the CFD model. Results for windage losses, flow rate of cooling air, power and torque of the motor versus mass flow rate are given in the paper. Trade studies of CFD on the effect of inlet cooling flow rate, and parasitic heat transfer losses on the Taylor–Couette flow coherent flow structure breakdown are presented. Windage losses on the order of 20 W are found to be present in the configuration tested and simulated.

]]>Fluids doi: 10.3390/fluids3010021

Authors: Dmitri Kondrashov Mickaël Chekroun Pavel Berloff

The multiscale variability of the ocean circulation due to its nonlinear dynamics remains a big challenge for theoretical understanding and practical ocean modeling. This paper demonstrates how the data-adaptive harmonic (DAH) decomposition and inverse stochastic modeling techniques introduced in (Chekroun and Kondrashov, (2017), Chaos, 27), allow for reproducing with high fidelity the main statistical properties of multiscale variability in a coarse-grained eddy-resolving ocean flow. This fully-data-driven approach relies on extraction of frequency-ranked time-dependent coefficients describing the evolution of spatio-temporal DAH modes (DAHMs) in the oceanic flow data. In turn, the time series of these coefficients are efficiently modeled by a family of low-order stochastic differential equations (SDEs) stacked per frequency, involving a fixed set of predictor functions and a small number of model coefficients. These SDEs take the form of stochastic oscillators, identified as multilayer Stuart–Landau models (MSLMs), and their use is justified by relying on the theory of Ruelle–Pollicott resonances. The good modeling skills shown by the resulting DAH-MSLM emulators demonstrates the feasibility of using a network of stochastic oscillators for the modeling of geophysical turbulence. In a certain sense, the original quasiperiodic Landau view of turbulence, with the amendment of the inclusion of stochasticity, may be well suited to describe turbulence.

]]>Fluids doi: 10.3390/fluids3010020

Authors: Steven Herring Pablo Huq

Many models exist for predicting the atmospheric transport and dispersion of material following its release into the atmosphere. The purpose of these models may be to support air quality assessments and/or to predict the hazard resulting from releases of harmful materials to inform emergency response actions. In either case it is essential that the user understands the level of predictive accuracy that might be expected. However, contrary to expectation, this is not easily determined from published comparisons of model predictions against data from dispersion experiments. The paper presents and reviews the methods adopted and issues involved in comparing the predictive performance of atmospheric transport and dispersion models to experimental data, by reference to a number of experimental data sets and comparison results. It then presents an approach which is designed to make the performance of atmospheric dispersion models more transparent, through clearly defining the basis on which the comparison is made, and comparing the performance of the chosen model to that of a reference model. Such an approach establishes a clear baseline against which the accuracy of models can be evaluated and the performance benefits of more sophisticated approaches quantified. The use of a simple analytic reference model applicable to continuous ground level releases in open terrain and urban areas is shown as a proof-of-principle.

]]>Fluids doi: 10.3390/fluids3010019

Authors: Rajinder Pal

The theoretical background for entropy generation and exergy destruction in the flow of fluids is reviewed briefly. New experimental results are presented on the quantification of exergy destruction rates in flows of emulsions (oil droplets dispersed in a polymeric liquid), suspensions (solid particles dispersed in a polymeric liquid), and blends of emulsions and suspensions (dispersions of oil droplets and solid particles in a polymeric liquid). A new model is proposed to estimate the exergy destruction rate, and hence power loss, in the flow of multi-phase dispersions of oil droplets, solid particles, and polymeric matrix.

]]>Fluids doi: 10.3390/fluids3010018

Authors: German E. Cortes Garcia Kevin M. P. van Eeten Michiel M. de Beer Jaap C. Schouten John van der Schaaf

The Danckwerts’ plot method is a commonly used graphical technique to independently determine the interfacial area and mass-transfer coefficient in gas–liquid contactors. The method was derived in 1963 when computational capabilities were limited and intensified process equipment did not exist. A numerical analysis of the underlying assumptions of the method in this paper has shown a bias in the technique, especially for situations where mass-transfer rates are intensified, or where there is limited liquid holdup in the bulk compared to the film layers. In fact, systematic errors of up to 50% in the interfacial area, and as high as 90% in the mass-transfer coefficients, can be expected for modern, intensified gas–liquid contactors, even within the commonly accepted validity limits of a pseudo-first-order reaction and Hatta numbers in the range of 0.3 &lt; Ha &lt; 3. Given the current computational capabilities and the intensified mass-transfer rates in modern gas–liquid contactors, it is therefore imperative that the equations for reaction and diffusion in the liquid films are numerically solved and subsequently used to fit the interfacial area and mass-transfer coefficient to experimental data, which would traditionally be used in the graphical Danckwerts’ method.

]]>Fluids doi: 10.3390/fluids3010017

Authors: William Layton

The problem of accurate and reliable prediction of turbulent flows is a central and intractable challenge that crosses disciplinary boundaries. [...]

]]>Fluids doi: 10.3390/fluids3010016

Authors: Jonathan Lilly

A four-parameter kinematic model for the position of a fluid parcel in a time-varying ellipse is introduced. For any ellipse advected by an arbitrary linear two-dimensional flow, the rates of change of the ellipse parameters are uniquely determined by the four parameters of the velocity gradient matrix, and vice versa. This result, termed ellipse/flow equivalence, provides a stronger version of the well-known result that a linear velocity field maps an ellipse into another ellipse. Moreover, ellipse/flow equivalence is shown to be a manifestation of Stokes’ theorem. This is done by deriving a matrix-valued extension of the classical Stokes’ theorem that involves a spatial integral over the velocity gradient tensor, thus accounting for the two strain terms in addition to the divergence and vorticity. General expressions for various physical properties of an elliptical ring of fluid are also derived. The ellipse kinetic energy is found to be composed of three portions, associated respectively with the circulation, the rate of change of the moment of inertia, and the variance of parcel angular velocity around the ellipse. A particular innovation is the use of four matrices, termed the I J K L basis, that greatly facilitate the required calculations.

]]>Fluids doi: 10.3390/fluids3010015

Authors: Žiga Kos Miha Ravnik

Analytic formulations of elementary flow field profiles in weakly anisotropic nematic fluid are determined, which can be attributed to biological or artificial micro-swimmers, including Stokeslet, stresslet, rotlet and source flows. Stokes equation for a nematic stress tensor is written with the Green function and solved in the k-space for anisotropic Leslie viscosity coefficients under the limit of leading isotropic viscosity coefficient. Analytical expressions for the Green function are obtained that are used to compute the flow of monopole or dipole swimmers at various alignments of the swimmers with respect to the homogeneous director field. Flow profile is also solved for the flow sources/sinks and source dipoles showing clear emergence of anisotropy in the magnitude of flow profile as the result of fluid anisotropic viscosity. The range of validity of the presented analytical solutions is explored, as compared to exact numerical solutions of the Stokes equation. This work is a contribution towards understanding elementary flow motifs and profiles in fluid environments that are distinctly affected by anisotropic viscosity, offering analytic insight, which could be of relevance to a range of systems from microswimmers, active matter to microfluidics.

]]>Fluids doi: 10.3390/fluids3010014

Authors: Suranga Dharmarathne Venkatesh Pulletikurthi Luciano Castillo

Direct numerical simulations of a turbulent channel flow with a passive scalar at R e τ = 394 with blowing perturbations is carried out. The blowing is imposed through five spanwise jets located near the upstream end of the channel. Behind the blowing jets (about 1 D , where D is the jet diameter), we observe regions of reversed flow responsible for the high temperature region at the wall: hot spots that contribute to further heating of the wall. In between the jets, low pressure regions accelerate the flow, creating long, thin, streaky structures. These structures contribute to the high temperature region near the wall. At the far downstream of the jet (about 3 D ), flow instabilities (high shear) created by the blowing generate coherent vortical structures. These structures move hot fluid near the wall to the outer region of the channel; thereby, these are responsible for cooling of the wall. Thus, for engineering applications where cooling of the wall is necessary, it is critical to promote the generation of coherent structures near the wall.

]]>Fluids doi: 10.3390/fluids3010013

Authors: Shahrouz Mohagheghian Brian Elbing

The current study experimentally examines bubble size distribution (BSD) within a bubble column and the associated characteristic length scales. Air was injected into a column of water via a single injection tube. The column diameter (63–102 mm), injection tube diameter (0.8–1.6 mm) and superficial gas velocity (1.4–55 mm/s) were varied. Large samples (up to 54,000 bubbles) of bubble sizes measured via 2D imaging were used to produce probability density functions (PDFs). The PDFs were used to identify an alternative length scale termed the most frequent bubble size (dmf) and defined as the peak in the PDF. This length scale as well as the traditional Sauter mean diameter were used to assess the sensitivity of the BSD to gas injection rate, injector tube diameter, injection tube angle and column diameter. The dmf was relatively insensitive to most variation, which indicates these bubbles are produced by the turbulent wakes. In addition, the current work examines higher order statistics (standard deviation, skewness and kurtosis) and notes that there is evidence in support of using these statistics to quantify the influence of specific parameters on the flow-field as well as a potential indicator of regime transitions.

]]>Fluids doi: 10.3390/fluids3010012

Authors: Chrysafenia Koutsou Anastasios Karabelas Margaritis Kostoglou

The time-varying flow field in spacer-filled channels of spiral-wound membrane (SWM) modules is mainly due to the development of fouling layers on the membranes that modify the channel geometry. The present study is part of an approach to tackling this extremely difficult dynamic problem at a small spatial scale, by uncoupling the fluid dynamics and mass transfer from the fouling-layer growth process. Therefore, fluid dynamics and mass transfer are studied for a spacer-filled channel whose geometry is altered by a uniform deposit thickness h. For this purpose, 3D direct numerical simulations are performed employing the “unit cell” approach with periodic boundary conditions. Specific thickness values are considered in the range 2.5–10% of the spacer-filament diameter D as well as other conditions of practical significance. The qualitative characteristics of the altered flow field are found to be very similar to those of the reference geometry with no gap reduction. For a given flow rate, the pressure drop, time-average wall-shear stresses and mass-transfer coefficients significantly increase with increasing thickness h due to reduced channel-gap, as expected. Correlations are obtained, applicable at the “unit cell” scale, of the friction factor f and Sherwood number Sh, which exhibit similar functional dependence of f and Sh on the Reynolds and Schmidt numbers as in the reference no-fouling case. In these correlations the effect of channel-gap reduction is incorporated, permitting predictions in the studied range of fouling-layer thickness (h/D) = 0–0.10. The usefulness of the new results and correlations is discussed in the context of ongoing research toward improved modeling and dynamic simulation of SWM-module operation.

]]>Fluids doi: 10.3390/fluids3010011

Authors: Antonio Carozza

An unsteady numerical investigation on mixed convection in a two dimensional open ended cavity with different aspect ratios is carried out. In this investigation, uniform temperature is set to the left and the right sides of the cavity while the other surfaces are adiabatic. The simulation is performed for a wide range of Reynolds numbers (Re = 100–1000) and Richardson numbers (Ri = 0.132–6.5 × 102), and various cavity aspect ratios (L/D = 0.5–4.0) and H/D = 0.1. Governing equations are solved using a cell centered finite volume code, a SIMPLE numerical projection scheme and a 2nd order accuracy. Results are presented in the form of streamlines, isothermal lines, and velocity profiles in the channel. The conclusion is that the enhancement of heat transfer rate is generated principally by the increasing Re and the assisting configuration is thermally more efficient when compared to the opposing one.

]]>Fluids doi: 10.3390/fluids3010010

Authors: Athanasios Kanaris Aikaterini Mouza

In this work, the efficiency of a new μ-mixer design is investigated. As in this type of devices the Reynolds number is low, mixing is diffusion dominated and it can be enhanced by creating secondary flows. In this study, we propose the introduction of helical inserts into a straight tube to create swirling flow. The influence of the insert’s geometrical parameters (pitch and length of the propeller blades) and of the Reynolds number on the mixing efficiency and on the pressure drop are numerically investigated. The mixing efficiency of the device is assessed by calculating a number—i.e., the index of mixing efficiency—that quantifies the uniformity of concentration at the outlet of the device. The influence of the design parameters on the mixing efficiency is assessed by performing a series of ‘computational’ experiments, in which the values of the parameter are selected using design of experiments (DOE) methodology. Finally using the numerical data, appropriate design equations are formulated, which, for given values of the design parameters, can estimate with reasonable accuracy both the mixing efficiency and the pressure drop of the proposed mixing device.

]]>Fluids doi: 10.3390/fluids3010009

Authors: Francesco Farsaci Ester Tellone Antonio Galtieri Silvana Ficarra

In this paper, we present the theoretical approach developed by us in the network of dielectric fractional theories. In particular, we mention the general aspects of the non-equilibrium thermodynamics, and after an introduction to the interaction between biological tissues and electrical fields, we highlight the role of phenomenological and state equations; therefore, we recall a general formulation on linear response theory. In Section 6, we introduce the classical fractional model. All of this is essential to show the role and the importance of fractional models in the context of thermodynamic dielectric investigations (of living or inert matter), giving a complete vision of the fractional approach. In Section 7 and Section 8, we introduce our new fractional model derived from non-equilibrium thermodynamic considerations.

]]>Fluids doi: 10.3390/fluids3010008

Authors: Sophie Rüttinger Marko Hoffmann Michael Schlüter

Bubble column reactors are ubiquitous in engineering processes. They are used in waste water treatment, as well as in the chemical, pharmaceutical, biological and food industry. Mass transfer and mixing, as well as biochemical or chemical reactions in such reactors are determined by the hydrodynamics of the bubbly flow. The hydrodynamics of bubbly flows is dominated by bubble wake interactions. Despite the fact that bubble wakes have been investigated intensively in the past, there is still a lack of knowledge about how mass transfer from bubbles is influenced by bubble wake interactions in detail. The scientific scope of this work is to answer the question how bubble wakes are influenced by external flow structures like a vortex street behind a cylinder. For this purpose, the flow field in the vicinity of a single bubble is investigated systematically with high spatial and temporal resolution. High-speed Particle Image Velocimetry (PIV) measurements are conducted monitoring the flow structure in the equatorial plane of the single bubble. It is shown that the root mean square (RMS) velocity profiles downstream the bubble are influenced significantly by the interaction of vortices. In the presence of a vortex street, the deceleration of the fluid behind the bubble is compensated earlier than in the absence of a vortex street. This happens due to momentum transfer by cross-mixing. Both effects indicate that the interaction of vortices enhances the cross-mixing close to the bubble. Time series of instantaneous velocity fields show the formation of an inner shear layer and coupled vortices. In conclusion, this study shows in detail how the bubble wake is influenced by a vortex street and gives deep insights into possible effects on mixing and mass transfer in bubbly flows.

]]>Fluids doi: 10.3390/fluids3010007

Authors: Fluids Editorial Office

Peer review is an essential part in the publication process, ensuring that Fluids maintains high quality standards for its published papers.[...]

]]>Fluids doi: 10.3390/fluids3010006

Authors: Aftab Ahmed Javed Siddique Muhammad Sagheer

The aim of the present study is to investigate the combined effects of the thermal radiation, viscous dissipation, suction/injection and internal heat generation/absorption on the boundary layer flow of a non-Newtonian power law fluid over a semi infinite permeable flat plate moving in parallel or reversely to a free stream. The resulting system of partial differential equations (PDEs) is first transformed into a system of coupled nonlinear ordinary differential equations (ODEs) which are then solved numerically by using the shooting technique. It is found that the dual solutions exist when the flat plate and the free stream move in the opposite directions. Dimensionless boundary layer velocity and temperature distributions are plotted and discussed for various values of the emerging physical parameters. Finally, the tables of the relevant boundary derivatives are presented for some values of the governing physical parameters.

]]>Fluids doi: 10.3390/fluids3010005

Authors: Florian Ries Yongxiang Li Martin Rißmann Dario Klingenberg Kaushal Nishad Benjamin Böhm Andreas Dreizler Johannes Janicka Amsini Sadiki

In the present paper, direct numerical simulation (DNS) and particle image velocimetry (PIV) have been applied complementarily in order to generate a database of near-wall turbulence properties of a highly turbulent jet impinging on a solid surface under different inclination angles. Thereby, the main focus is placed on an impingement angle of 45 ∘ , since it represents a good generic benchmark test case for a wide range of technical fluid flow applications. This specific configuration features very complex flow properties including the presence of a stagnation point, development of the shear boundary layer and strong streamline curvature. In particular, this database includes near-wall turbulence statistics along with mean and rms velocities, budget terms in the turbulent kinetic energy equation, anisotropy invariant maps, turbulent length/time scales and near-wall shear stresses. These properties are useful for the validation of near-wall modeling approaches in the context of Reynolds-averaged Navier–Stokes (RANS) and large-eddy simulations (LES). From this study, in which further impingement angles ( 0 ∘ , 90 ∘ ) have been considered in the experiments only, it turns out that (1) the production of turbulent kinetic energy appears negative at the stagnation point for an impingement angle other than 0 ∘ and is balanced predominantly by pressure-related diffusion, (2) quasi-coherent thin streaks with large characteristic time scales appear at the stagnation region, while the organization of the flow is predominantly toroidal further downstream, and (3) near-wall shear stresses are low at the stagnation region and intense in regions where the direction of the flow changes suddenly.

]]>Fluids doi: 10.3390/fluids3010003

Authors: Mariana Simão Modesto Pérez-Sánchez Armando Carravetta Petra López-Jiménez Helena Ramos

Velocity profiles originated by a pump as turbine (PAT) were measured using an ultrasonic doppler velocimetry (UDV). PAT behavior is influenced by the velocity data. The effect of the rotational speed and the associated flow velocity variations were investigated. This research focuses, particularly, on the velocity profiles achieved for different rotational speeds and discharge values along the impeller since that is where the available hydraulic power is transformed into the mechanical power. Comparisons were made between experimental test results and computational fluid dynamics (CFD) simulations. The used CFD model was calibrated and validated using the same conditions as the experimental facility. The numerical simulations showed good approximation with the velocity measurements for different cross-sections along the PAT system. The application of this CFD numerical model and experimental tests contributed to better understanding the system behavior and to reach the best efficiency operating conditions. Improvements in the knowledge about the hydrodynamic flow behavior associated with the velocity triangles contribute to improvements in the PAT concept and operation.

]]>Fluids doi: 10.3390/fluids3010004

Authors: Agathoklis Passos Dimitris Tziafas Aikaterini Mouza Spiros Paras

This work deals with the numerical investigation of the delivery of potential therapeutic agents through dentinal discs (i.e., a cylindrical segment of the dentinal tissue) towards the dentin–pulp junction. The aim is to assess the main key features (i.e., molecular size, initial concentration, consumption rate, disc porosity and thickness) that affect the delivery of therapeutic substances to the dental pulp and consequently to define the necessary quantitative and qualitative issues related to a specific agent before its potential application in clinical practice. The computational fluid dynamics (CFD) code used for the numerical study is validated with relevant experimental data obtained using micro Laser Induced Fluorescence (μ-LIF) a non-intrusive optical measuring technique. As the phenomenon is diffusion dominated and strongly dependent on the molecular size, the time needed for the concentration of released molecules to attain a required value can be controlled by their initial concentration. Finally, a model is proposed which, given the maximum acceptable time for the drug concentration to attain a required value at the pulpal side of the tissue along with the aforementioned key design parameters, is able to estimate the initial concentration to be imposed and vice versa.

]]>Fluids doi: 10.3390/fluids3010002

Authors: Rajinder Pal

A new model is proposed for the viscosity of Pickering emulsions at low shear rates. The model takes into consideration the increase in the effective volume fraction of droplets, due to the presence of an interfacial layer of solid nanoparticles at the oil-water interface. The model also considers aggregation of droplets and eventual jamming of Pickering emulsion at high volume fraction of dispersed phase. According to the proposed model, the relative viscosity of a Pickering emulsion at low shear rates is dependent on three factors: contact angle, ratio of bare droplet radius to solid nanoparticle radius, and the volume fraction of bare droplets. For a given radius of nanoparticles, the relative viscosity of a Pickering emulsion increases with the decrease in bare droplet radius. For O/W Pickering emulsions, the relative viscosity decreases with the increase in contact angle. The W/O Pickering emulsion exhibits an opposite behavior in that the relative viscosity increases with the increase in contact angle. The proposed model describes the experimental viscosity data for Pickering emulsions reasonably well.

]]>Fluids doi: 10.3390/fluids3010001

Authors: Parama Ghoshal Min Kim Silvana Cardoso

Reactive convection in a porous medium has received recent interest in the context of the geological storage of carbon dioxide in saline formations. We study theoretically and numerically the gravitational instability of a diffusive boundary layer in the presence of a first-order precipitation reaction. We compare the predictions from normal mode, linear stability analysis, and nonlinear numerical simulations, and discuss the relative deviations. The application of our findings to the storage of carbon dioxide in a siliciclastic aquifer shows that while the reactive-diffusive layer can become unstable within a timescale of 1 to 1.5 months after the injection of carbon dioxide, it can take almost 10 months for sufficiently vigorous convection to produce a considerable increase in the dissolution flux of carbon dioxide.

]]>Fluids doi: 10.3390/fluids2040069

Authors: Michael Montgomery Roger Smith

The applicability of linearized axisymmetric dynamics to the intensification and structure change of tropical cyclones is investigated. The study is motivated by recent work that presented axisymmetric solutions to the linearized, non-hydrostatic, vortex-anelastic equations of motion (the so-called 3DVPAS model). The work called into question the importance of a recently proposed nonlinear, system-scale boundary-layer spinup mechanism both in intensifying storms and in mature storms undergoing secondary eyewall formation. The issue is examined using a three-dimensional mesoscale simulation of an intensifying tropical cyclone, alongside the linear 3DVPAS model. Solutions to the linear model, for imposed eddy forcing terms derived from the mesoscale simulation, are shown to be valid only for short times ( t &lt; 1 h) in the inner-core region of the vortex. At later times, the neglected nonlinear terms become significant and the linear results invalid. It follows that the linear results cannot be used to describe all aspects of the tropical cyclone dynamics at later times. In particular, they cannot be used (a) to dismiss the importance of the nonlinear boundary-layer spinup mechanism, nor (b) to isolate the separate effects of diabatic heating from those of friction, within the nonlinear boundary layer at least. Such separation depends on the linear superposition principle, which fails whenever nonlinearity is important. Similar caveats apply to the use of another linear model, the traditional Sawyer–Eliassen balance model. Its applicability is limited not only by linearity, but also by its assumption of strictly balanced motion. Both are incompatible with nonlinear spinup.

]]>Fluids doi: 10.3390/fluids2040068

Authors: Brian Fiedler

The structure of natural tornadoes and simulated analogs are sensitive to the lower boundary condition for friction. Three-dimensional numerical simulations of storms require a choice for turbulence parameterizations and resolution of wind near the lower boundary. This article explores some of the consequences of choices of a surface drag coefficient on the structure of a mature simulated tornado, using a conventional axisymmetric model. The surface drag parameterization is explored over the range of the semi-slip condition, including the extremes of no-slip and free-slip. A moderate semi-slip condition allows for an extreme pressure deficit, but without the unrealistic vortex breakdown of the no-slip condition.

]]>Fluids doi: 10.3390/fluids2040067

Authors: Alexander Cali Wah-Keat Lee A. Trubatch Philip Yecko

Improved knowledge of the magnetic field dependent flow properties of nanoparticle-based magnetic fluids is critical to the design of biomedical applications, including drug delivery and cell sorting. To probe the rheology of ferrofluid on a sub-millimeter scale, we examine the paths of 550 μm diameter glass spheres falling due to gravity in dilute ferrofluid, imposing a uniform magnetic field at an angle with respect to the vertical. Visualization of the spheres’ trajectories is achieved using high resolution X-ray phase-contrast imaging, allowing measurement of a terminal velocity while simultaneously revealing the formation of an array of long thread-like accumulations of magnetic nanoparticles. Drag on the sphere is largest when the applied field is normal to the path of the falling sphere, and smallest when the field and trajectory are aligned. A Stokes drag-based analysis is performed to extract an empirical tensorial viscosity from the data. We propose an approximate physical model for the observed anisotropic drag, based on the resistive force theory drag acting on a fixed non-interacting array of slender threads, aligned parallel to the magnetic field.

]]>Fluids doi: 10.3390/fluids2040066

Authors: Sukhendu Ghosh

The effect of wall velocity slip on the stability of a pressure-driven two-dimensional asymmetric channel flow is examined by considering Navier slip condition on the channel walls. The two-parameter families of mean velocity profiles are considered to approximate the underlying asymmetric basic flow. Competing effects of skewness and maximum velocity on the stability of the flow are explored for a range of model parameters. The Orr–Sommerfeld system of the asymmetric flow is solved using a Chebyshev spectral collocation method for both symmetric and non-symmetric type slip boundary conditions. Numerical results indicate that moderate asymmetry in the basic flow has a significant role on the stability of the Poiseuille-kind parallel/nearly parallel flows. Wall slip shows a passive control on the instability of the asymmetric flow by increasing or decreasing the critical Reynolds number and the set of unstable wave numbers. The stabilizing/destabilizing effect of slip velocity on the flow instability is weak or strong depending on the presence of velocity slip at the upper or lower wall. Velocity slip has a profound grip on the flow behaviour by changing the shear rate inside the perturbed flow.

]]>Fluids doi: 10.3390/fluids2040064

Authors: Hai Duong Ziyang Xie Koh Wei Ng Nian Kenneth Tan Hong Lim An Li Ka-Shing Chung Wen Lim

Thermal jacket design using eco-friendly cellulose fibers from recycled paper waste is developed in this report. Neoprene as an outmost layer, cellulose aerogels in the middle and Nylon as an innermost layer can form the best sandwiched laminate using the zigzag stitching method for thermal jacket development. The temperature of the ice slurry inside the water bottle covered with the designed thermal jackets remains at 0.1 °C even after 4 h, which is the average duration of an outfield exercise. Interestingly, the insulation performance of the designed thermal jackets is much better than the commercial insulated water bottles like FLOE bottles and is very competition to that of vacuum flasks for a same period of 4 h and ambient conditions.

]]>Fluids doi: 10.3390/fluids2040065

Authors: Daniele Sarto Alain Ghizzo

We review some recent results that have been obtained in the investigation of zonal flow emergence, by means of a gyrokinetic trapped ion model, in the regime of ion temperature gradient instabilities for tokamak plasmas. We show that an analogous formulation of the zonal flow dynamics in terms of the Reynolds tensor applies in the fluid and kinetic regimes, where polarization effects play a major role. The kinetic regime leads to the emergence of a resonant mode at a frequency close to the drift frequency. With the objective of modeling both separate fluid and kinetic regimes of zonal flows, we used in this paper a methodology for deriving both Charney–Hasegawa–Mima (CHM) and Hasegawa–Wakatani models. This methodology is based on the trapped ion model and is analogous to the hierarchy leading from the Vlasov equation to the macroscopic fluid equations. The nature of zonal flows in the hierarchy of the Mima, Hasegawa and Wakatani models is investigated and discussed through comparisons with global kinetic simulations. Applications to the CHM equation are discussed, which applies to a broad variety of hydrodynamical systems, ranging from large-scale processes met in magnetically confined plasma to the so-called zonostrophy turbulence emerging in the case of small-scale forced, two-dimensional barotropic turbulence (Sukoriansky et al. Phys. Rev. Letters, 101, 178501, 2008).

]]>Fluids doi: 10.3390/fluids2040063

Authors: Miah Alam Manabu Takao Toshiaki Setoguchi

The present study reported of the numerical investigation of a high-speed wet steam flow through an asymmetric nozzle. The spontaneous non-equilibrium homogeneous condensation of wet steam was numerically modeled based on the classical nucleation theory and droplet growth rate equation combined with the field conservations within the computational fluid dynamics (CFD) code of ANSYS Fluent 13.0. The equations describing droplet formations and interphase change were solved sequentially after solving the main flow conservation equations. The calculations were carried out assuming the flow two-dimensional, compressible, turbulent, and viscous. The SST k-ω model was used for modeling the turbulence within an unstructured mesh solver. The validation of numerical model was accomplished, and the results showed a good agreement between the numerical simulation and experimental data. The effect of spontaneous non-equilibrium condensation on the jet and shock structures was revealed, and the condensation shown a great influence on the jet structure.

]]>Fluids doi: 10.3390/fluids2040062

Authors: Christopher Strickland Laura Miller Arvind Santhanakrishnan Christina Hamlet Nicholas Battista Virginia Pasour

Mesoscale filtering and protective layers are replete throughout the natural world. Within the body, arrays of extracellular proteins, microvilli, and cilia can act as both protective layers and mechanosensors. For example, blood flow profiles through the endothelial surface layer determine the amount of shear stress felt by the endothelial cells and may alter the rates at which molecules enter and exit the cells. Characterizing the flow profiles through such layers is therefore critical towards understanding the function of such arrays in cell signaling and molecular filtering. External filtering layers are also important to many animals and plants. Trichomes (the hairs or fine outgrowths on plants) can drastically alter both the average wind speed and profile near the leaf’s surface, affecting the rates of nutrient and heat exchange. In this paper, dynamically scaled physical models are used to study the flow profiles outside of arrays of cylinders that represent such filtering and protective layers. In addition, numerical simulations using the Immersed Boundary Method are used to resolve the three-dimensional flows within the layers. The experimental and computational results are compared to analytical results obtained by modeling the layer as a homogeneous porous medium with free flow above the layer. The experimental results show that the bulk flow is well described by simple analytical models. The numerical results show that the spatially averaged flow within the layer is well described by the Brinkman model. The numerical results also demonstrate, however, that the flow can be highly three-dimensional with fluid moving into and out of the layer. These effects are not described by the Brinkman model and may be significant for biologically relevant volume fractions. The results of this paper can be used to understand how variations in density and height of such structures can alter shear stresses and bulk flows.

]]>Fluids doi: 10.3390/fluids2040061

Authors: Helena Ramos Modesto Pérez-Sánchez A. Franco P. López-Jiménez

Sustainability is crucial to the urban zones, especially related to the water management, which is vulnerable to flood occurrence. This research applies the procedure contemplated by the Soil Conservation Service (SCS) to determine the generated volumes when the impervious areas can exceed the drainage capacity of existing pluvial water networks. Several computational simulations were developed for the current scenario of an existing basin in Lisbon. Using CivilStorm software from Bentley Systems (Bentley EMEA, Bentley Systems International Limited, Dublin, Ireland), it enabled the evaluation of the volumes of flood peaks and the hydraulic behavior of a small hydrographic basin in the continuation of an urbanization process, considering the modification of its superficial impervious parts and the growth of the urbanized area. Several measures are suggested to solve the limited capacity of the existing drainage system. This study analyzes the efficiency of the application of constructive measures, pondering the viability of their effectiveness, individually and combined. The option that best minimizes the effects of the urbanization is the combination of different structural measures, in particular retention ponds, storage blocks, ditches and specific drainage interventions in some parts of the network.

]]>Fluids doi: 10.3390/fluids2040060

Authors: Ibrahim M. Jais D. Andrew S. Rees

The onset of Rayleigh-Bénard convection in a horizontally unbounded saturated porous medium is considered. Particular attention is given to the stability of weakly nonlinear convection between two plane horizontal surfaces heated from below. The primary aim is to study the effects on postcritical convection of having small amplitude time-periodic resonant thermal forcing. Amplitude equations are derived using a weakly nonlinear theory and they are solved in order to understand how the flow evolves with changes in the Darcy-Rayleigh number and the forcing frequency. When convection is stationary in space, it is found to consist of one of two different types depending on its location in parameter space: either a convection pattern where each cell rotates in the same way for all time with a periodic variation in amplitude (Type I) or a pattern where each cell changes direction twice within each forcing period (Type II). Asymptotic analyses are also performed (i) to understand the transition between convection of types I and II; (ii) for large oscillation frequencies and (iii) for small oscillation frequencies. In a large part of parameter space the preferred pattern of convection when the layer is unbounded horizontally is then shown to be one where the cells oscillate horizontally—this is a novel form of pattern selection for Darcy-Bénard convection.

]]>Fluids doi: 10.3390/fluids2040059

Authors: Francesco Farsaci Silvana Ficarra Antonio Galtieri Ester Tellone

After remarking on non-equilibrium thermodynamics with internal variables, this paper highlights the importance of these variables to the study of biological systems. Internal variables can provide a more detailed description of biological processes that occur inside cells, tissues and organs. In order to introduce a fractional model on a visco-inelastic medium based on Kluitenberg’s non-equilibrium thermodynamics, the origin of the complex dynamic modulus is shown by means of linear response theory. This research recalls our previous work to develop an ultrasound wave technique that allows us to investigate biological systems, and introduces the fractional visco-inelastic model and relative generalized relaxation time, to show that it is possible to obtain the Cole–Cole model in a particular case.

]]>Fluids doi: 10.3390/fluids2040058

Authors: Argus Dunca

In this report, we present several results in the theory of α -models of turbulence with improved accuracy that have been developed in recent years. The α -models considered herein are the Leray- α model, the zeroth Approximate Deconvolution Model (ADM) turbulence model, the modified Leray- α and the Navier–Stokes- α model. For all of the models from above, the accuracy is limited to α 2 in smooth flow regions. Better accuracy requires decreasing the filter radius α , which, in turn, requires a smaller mesh width that will lead in the end to a higher computational cost. Instead, one can use approximate deconvolution (without decreasing the mesh size) to attain better accuracy. Such deconvolution methods have been considered recently in many studies that show the efficiency of this approach. For smooth flows, periodic boundary conditions and van Cittert deconvolution operator of order N, the expected accuracy is α 2 N + 2 . In a bounded domain, such results are valid only in case special conditions are satisfied. In more general conditions, the author has recently proved that, in the case of the ADM, the expected accuracy of the finite element method with Taylor–Hood elements and Crank–Nicolson time stepping method is Δ t 2 + h 2 + K N α 2 , where the constant K &lt; 1 depends on the ratio α / h , which is assumed constant. In this study, we present the extension of the result to the rest of the models.

]]>Fluids doi: 10.3390/fluids2040057

Authors: Charly de Marez Xavier Carton Mathieu Morvan Jean Reinaud

We study the influence of bottom topography on the interaction of two identical vortices in a two-layer, quasi-geostrophic model. The two vortices have piecewise-uniform potential vorticity and are lying in the upper layer of the model. The topography is a smooth bottom slope. For two cyclones, topography modifies the merger critical distance and the merger efficiency: the topographic wave and vortices can advect the two cyclones along the shelf when they are initially far from it or towards the shelf when they are initially closer to it. They can also advect the two cyclones towards each other and thus favour merger. The cyclones deform, and the potential vorticity field undergoes filamentation. Regimes of partial vortex merger or of vortex splitting are then observed. The interaction of the vorticity poles in the two layers are analysed to explain the evolution of the two upper layer cyclones. For taller topography, two new regimes appear: vortex drift and splitting; and filamentation and asymmetric merger. They are due to the hetonic coupling of lower layer vorticity with the upper layer vortices (a heton is a baroclinic vortex dipole, carrying heat and momentum and propagating horizontally in the fluid), or to the strong shear that the former exerts on the latter. The interaction of two anticyclones shows regimes of co-rotation or merger, but specifically, it leads to the drift of the two vortices away from the slope, via a hetonic coupling with oppositely-signed vorticity in the lower layer. This vorticity originates in the breaking of the topographic wave. The analysis of passive tracer evolution confirms the inshore or offshore drift of the fluid, the formation of tracer fronts along filaments and its stirring in regions of vortex merger. The trajectories of particles indicate how the fluid initially in the vortices is finally partitioned.

]]>Fluids doi: 10.3390/fluids2040056

Authors: Anthony G. Dixon Nicholas J. Medeiros

The effective medium approach to radial fixed bed dispersion models, in which radial dispersion of mass is superimposed on axial plug flow, is based on a constant effective dispersion coefficient, DT. For packed beds of a small tube-to-particle diameter ratio (N), the experimentally-observed decrease in this parameter near the tube wall is accounted for by a lumped resistance located at the tube wall, the wall mass transfer coefficient km. This work presents validated computational fluid dynamics (CFD) simulations to obtain detailed radial velocity and concentration profiles for eight different computer-generated packed tubes of spheres in the range 5.04 ≤ N ≤ 9.3 and over a range of flow rates 87 ≤ Re ≤ 870 where Re is based on superficial velocity and the particle diameter dp. Initial runs with pure air gave axial velocity profiles vz(r) averaged over the length of the packing. Then, simulations with the tube wall coated with methane yielded radial concentration profiles. A model with only DT could not describe the radial concentration profiles. The two-parameter model with DT and km agreed better with the bed-center concentration profiles, but not with the sharp decreases in concentration close to the tube wall. A three-parameter model based on classical two-layer mixing length theory, with a wall-function for the decrease in transverse radial convective transport in the near-wall region, showed greatly improved ability to reproduce the near-wall concentration profiles.

]]>Fluids doi: 10.3390/fluids2040055

Authors: Young Yi Sonya Legg Robert Nazarian

Breaking internal waves are an important contributor to mixing in the stratified ocean interior. We use two-dimensional, nonhydrostatic numerical simulations to examine the breaking of internal waves generated by tidal flow over sinusoidal bottom topography. We explore the sensitivity of the internal wave breaking to the topographic steepness and Coriolis frequency, focusing on the vertical structure of kinetic energy dissipation and the ratio of local dissipation to the barotropic-to-baroclinic energy conversion. When the tidal frequency is twice the local Coriolis frequency, wave breaking above the topography is driven by wave–wave interactions which transfer wave energy from the tidal forcing frequency to the inertial frequency. The greater shear associated with the inertial frequency waves leads to enhanced dissipation in a thick layer above the topography. The topographic steepness strongly modulates this dependence of dissipation on Coriolis frequency; for some steep sinusoidal topographies, most wave energy propagates downward into the topographic troughs, eliminating the possibility for significant breaking above the topographic peaks. Current parameterizations of tidal dissipation in use in global ocean models need to be adapted to include the dependence of the local dissipation on both the Coriolis frequency and the topographic steepness.

]]>Fluids doi: 10.3390/fluids2040054

Authors: Hailu Kong Malte Jansen

Geostrophic turbulent eddies play a crucial role in the oceans, mixing properties such as heat, salt, and geochemical tracers. A useful reduced model for geostrophic turbulence is barotropic (2D) turbulence. The focus of this study is on 2D β -plane turbulence with quadratic drag, which, although arguably the most realistic barotropic model of ocean turbulence, has remained unexplored thus far. We first review and test classical scaling arguments for the eddy diffusivity in three regimes: the strong friction limit, the weak friction/strong β limit, and a transition regime. We then develop a generalized theory by parameterizing the nonlinear eddy–eddy interactions as a stochastic process, which leads to an analytical solution for the eddy diffusivity spectrum, whose integral yields a “bulk” diffusivity. The theory successfully predicts the smooth transition of diffusivity across the three regimes, and echoes with the recent argument that eddy phase propagation relative to the mean flow suppresses the eddy diffusivity. Moreover, the generalized theory reduces to the classical scaling arguments in both the strong friction and strong β limits, which has not been clear from the previous work on diffusivity suppression by flow-relative phase propagation.

]]>Fluids doi: 10.3390/fluids2040053

Authors: C. S. Jog Nilesh Potghan

In this work, we develop a numerical strategy for analyzing the flows of an incompressible fluid in the gap between an arbitrarily shaped inner boundary that rotates inside a circular outer boundary. Such flows occur very commonly in turbomachinery applications. The numerical strategy is based on a noninertial frame of reference that is fixed to the rotating inner boundary so that Coriolis and angular acceleration effects have to be accounted for in its development. Since this strategy is based on a fixed mesh, it is much more economical and accurate than a general arbitrary Eulerian–Lagrangian strategy, which would typically require remeshing. In addition, we also conduct a numerical study for circular Couette flow with varying angular speed of the inner cylinder in an inertial frame of reference; such a study may prove useful in validating a theoretical stability analysis which currently seems to have been carried out only for the case of constant angular speed.

]]>Fluids doi: 10.3390/fluids2040052

Authors: Dambaru Bhatta Daniel Riahi

Here, we investigate weakly nonlinear hydrothermal two-dimensional convective flow in a horizontal aquifer layer with horizontal isothermal and rigid boundaries. We treat such a layer as a porous medium, where Darcy’s law holds, subjected to the conditions that the porous layer’s permeability and the thermal conductivity are variable in the vertical direction. This analysis is restricted to the case that the subsequent hydraulic resistivity and diffusivity have a small rate of change with respect to the vertical variable. Applying the weakly nonlinear approach, we derive various order systems and express their solutions. The solutions for convective flow quantities such as vertical velocity and the temperature that arise as the Rayleigh number exceeds its critical value are computed and presented in graphical form.

]]>Fluids doi: 10.3390/fluids2040051

Authors: Modesto Pérez-Sánchez Mariana Simão P. López-Jiménez Helena Ramos

Analysis of a PAT modeling is presented for application in water pipe systems as an interesting and promising energy converter to improve the system energy efficiency. The study is focused on the use of a Computational Fluid Dynamics (CFD) model in conjunction with laboratory data for representing PAT performance. The first stage of the procedure concerns a systematic analysis of the role played by the characteristic PAT parameters in the computational mesh definitions of the CFD model, with the aim of defining the most efficient set of capturing the main features of the PAT behaviour under different operating conditions. In the second stage, comparisons of CFD results and experiments were carried out to examine some system components for better understanding the PAT response. Specifically, the behavior of the pressure distribution along the PAT installation when implemented in a water pipe system are analyzed, and the links between pressure variation and the head drop in different system components responsible for the head losses and net head definition are also examined.

]]>Fluids doi: 10.3390/fluids2040050

Authors: Giovanni Conti Gualtiero Badin

A new method to describe hyperbolic patterns in two-dimensional flows is proposed. The method is based on the Covariant Lyapunov Vectors (CLVs), which have the properties of being covariant with the dynamics, and thus, being mapped by the tangent linear operator into another CLVs basis, they are norm independent, invariant under time reversal and cannot be orthonormal. CLVs can thus give more detailed information about the expansion and contraction directions of the flow than the Lyapunov vector bases, which are instead always orthogonal. We suggest a definition of Hyperbolic Covariant Coherent Structures (HCCSs), which can be defined on the scalar field representing the angle between the CLVs. HCCSs can be defined for every time instant and could be useful to understand the long-term behavior of particle tracers. We consider three examples: a simple autonomous Hamiltonian system, as well as the non-autonomous “double gyre” and Bickley jet, to see how well the angle is able to describe particular patterns and barriers. We compare the results from the HCCSs with other coherent patterns defined on finite time by the Finite Time Lyapunov Exponents (FTLEs), to see how the behaviors of these structures change asymptotically.

]]>Fluids doi: 10.3390/fluids2040049

Authors: Yebegaeshet Zerihun

This study describes the results of a numerical investigation aimed at developing and validating a non-hydrostatic depth-averaged model for flow problems where the horizontal length scales close to flow depth. For such types of problems, the steep-slope shallow-water equations are inadequate to describe the two-dimensional structure of the curvilinear flow field. In the derivation of these equations, the restrictive assumptions of negligible bed-normal acceleration and bed curvature were employed, thus limiting their applicability to shallow flow situations. Herein, a Boussinesq-type model is deduced from the depth-averaged energy equation by relaxing the weakly-curved flow approximation to deal with the non-hydrostatic steep flow problems. The proposed model is solved with an implicit finite difference scheme and then applied to simulate steady free-surface flow problems with strong curvilinear effects. The numerical results are compared to experimental data, resulting in a reasonable overall agreement. Further, it is shown that the discharge characteristics of free flow over a round-crested weir are accurately described by using a Boussinesq-type approximation, and the drawbacks arising from a standard hydrostatic approach are overcome. The suggested numerical method to determine the discharge coefficient can be extended and adopted for other types of short-crested weirs.

]]>Fluids doi: 10.3390/fluids2030048

Authors: Franca Franchi Roberta Nibbi Brian Straughan

In this work, we present a system of equations which describes non-isothermal flow in a bidispersive porous medium under conditions of local thermal non-equilibrium. The porous medium consists of macro pores, and in the solid skeleton are cracks or fissures which give rise to micro pores. The temperatures in the solid skeleton and in the fluids in the macro and micro pores are all allowed to be independent. After presenting the general model, we derive a result of universal stability, which guarantees exponential decay of the solution for all initial data. We further present a concrete example by specializing the model to the problem of thermal convection in a layer heated from below.

]]>Fluids doi: 10.3390/fluids2030047

Authors: Michaela Kubacki Hoang Tran

We present an overview of a modern, efficient approach for uncoupling groundwater–surface water flows governed by the fully evolutionary Stokes–Darcy equations. Referred to as non-iterative partitioned methods, these algorithms treat the coupling terms explicitly and at each time level require only one Stokes and one Darcy sub-physics solve, thus taking advantage of existing solvers optimized for each sub-flow. This strategy often results in a time-step condition for stability. Furthermore, small problem parameters, specifically those related to the physical characteristics of the porous media domain, can render certain time-step conditions impractical. Despite these obstacles, researchers have made significant progress towards efficient, stable, and accurate partitioned methods. Herein, we provide a comprehensive survey and comparison of recent developments utilizing these non-iterative numerical schemes.

]]>Fluids doi: 10.3390/fluids2030046

Authors: Quoc Nguyen Samuel Feher Dimitrios Papavassiliou

The paper is focused on the simulation and modeling of the dispersion from an instantaneous source of heat or mass located at the center of a turbulent flow channel. The flow is modeled with a direct numerical simulation, and the dispersion is modeled with Lagrangian methods based on Lagrangian scalar tracking (LST). The LST technique allows the simulation of scalar sources that span a range of Prandtl or Schmidt numbers that cover orders of magnitude. The trajectories of individual heat or mass markers are tracked, generating a probability distribution function that describes the behavior of instantaneous point sources of a scalar in the turbulent field. The effect of the Prandtl or Schmidt number on turbulent dispersion is examined, with emphasis on the dispersion pattern. Results for Prandtl or Schmidt numbers between 0.1 and 15,000 are presented. For an instantaneous source at the channel center, it is found that there are two zones of cloud development: one where molecular diffusion plays a role at very small times (early stage of the dispersion), and one where turbulent convection dominates. The asphericity of the scalar marker cloud is found to increase monotonically, in contrast to published results for isotropic, homogenous turbulence, where the asphericity goes through a maximum.

]]>Fluids doi: 10.3390/fluids2030045

Authors: Joakim Kjellsson Laure Zanna

The ocean is a turbulent fluid with processes acting on a variety of spatio-temporal scales. The estimates of energy fluxes between length scales allows us to understand how the mean flow is maintained as well as how mesoscale eddies are formed and dissipated. Here, we quantify the kinetic energy budget in a suite of realistic global ocean models, with varying horizontal resolution and horizontal viscosity. We show that eddy-permitting ocean models have weaker kinetic energy cascades than eddy-resolving models due to discrepancies in the effect of wind forcing, horizontal viscosity, potential to kinetic energy conversion, and nonlinear interactions on the kinetic energy (KE) budget. However, the change in eddy kinetic energy between the eddy-permitting and the eddy-resolving model is not enough to noticeably change the scale where the inverse cascade arrests or the Rhines scale. In addition, we show that the mechanism by which baroclinic flows organise into barotropic flows is weaker at lower resolution, resulting in a more baroclinic flow. Hence, the horizontal resolution impacts the vertical structure of the simulated flow. Our results suggest that the effect of mesoscale eddies can be parameterised by enhancing the potential to kinetic energy conversion, i.e., the horizontal pressure gradients, or enhancing the inverse cascade of kinetic energy.

]]>Fluids doi: 10.3390/fluids2030044

Authors: Shatha Haddad

The stability of the thermal convection in a fluid-saturated rotating anisotropic porous material is investigated. We take into account the rotation of a layer of saturated porous medium about an axis orthogonal to the planes bounding the layer. The permeability is allowed to be an anisotropic tensor. In particular, we restrict our attention to the case where the permeability in the vertical direction is different to that in the horizontal plane. The linear instability and nonlinear stability analysis, in the case where the inertial term vanishes, are performed. It is shown, by using an energy method, that the nonlinear critical Rayleigh numbers coincide with those of the linear analysis. The results reveal that the system becomes more stable when the rotation is present.

]]>Fluids doi: 10.3390/fluids2030043

Authors: Eugene Benilov

This paper presents a model which yields examples of stable vortices in a continuously stratified rotating fluid, thus providing a possible explanation of the observed longevity of oceanic eddies. The model is based on two assumptions. Firstly, the ocean comprises a thin upper (active) layer and a thick lower (passive) one, with large and small vertical gradients of density, respectively. Secondly, the Rossby number is small, justifying the use of the geostrophic and quasi-geostrophic approximations for the active and passive layers (the two are treated differently because the vortex-induced displacement of the isopycnal surfaces is comparable to the depth of the active layer, but is much smaller than that of the passive one). Using the asymptotic equations derived on the basis of the above assumptions, we prove a stability criterion and thus identify a class of stable vortex profiles. This class is much wider than the one following from the standard requirement that the potential vorticity be monotonic in the whole bulk of the fluid.

]]>Fluids doi: 10.3390/fluids2030042

Authors: Abdoulaye Gueye Mohamed Ouarzazi Silvia Hirata Haikel Hamed

We analyze the thermal convection thresholds and linear characteristics of the primary and secondary instabilities for viscoelastic fluids saturating a porous horizontal layer heated from below by a constant flux. The Galerkin method is used to solve the eigenvalue problem by taking into account the elasticity of the fluid, the ratio between the viscosity of the solvent and the total viscosity of the fluid and the lateral confinement of the medium. For the primary instability, we found out that depending on the rheological parameters, two types of convective structures may appear when the basic conductive solution loses its stability: stationary long wavelength instability as for Newtonian fluids and oscillatory convection. The effect of the lateral confinement of the porous medium by adiabatic walls is to stabilize the oblique and longitudinal rolls and therefore selects transverse rolls at the onset of convection. In the range of the rheological parameters where stationary long wave instability develops first, we use a parallel flow approximation to determine analytically the velocity and temperature fields associated with the monocellular convective flow. The linear stability analysis of the monocellular flow is performed, and the critical conditions above which the flow becomes unstable are determined. The combined influence of the viscoelastic parameters and the lateral confinement on the characteristics of the secondary instability is quantified. The major new findings concerning the secondary instabilities may be summarized as follows: (i) For concentrated viscoelastic fluids, computations showed that the most amplified mode of convection corresponds to oscillatory transverse rolls, which appears via a Hopf bifurcation. This pattern selection is independent of both the fluid elasticity and the lateral confinement of the porous medium. (ii) For diluted viscoelastic fluids, the preferred mode of convection is found to be oscillatory transverse rolls for a very laterally-confined medium. Otherwise, stationary or oscillatory longitudinal rolls may develop depending on the fluid elasticity. Results also showed the destabilizing effect of the relaxation fluid elasticity and the stabilizing effect of the viscosity ratio for the onset of both primary and secondary instabilities.

]]>Fluids doi: 10.3390/fluids2030041

Authors: Susie Wright Sylvie Su Hélène Scolan Roland Young Peter Read

We present a numerical study of axisymmetric flow in a rotating annulus in which local thermal forcing, via a heated annular ring on the outside of the base and a cooled circular disk in the centre of the top surface, drives convection. This new configuration is a variant of the classical thermally-driven annulus, where uniform heating and cooling are applied through the outer and inner sidewalls respectively. The annulus provides an analogue to a planetary circulation and the new configuration, with its more relaxed vertical thermal boundary conditions, is expected to better emulate vigorous convection in the tropics and polar regions as well as baroclinic instability in the mid-latitude baroclinic zone. Using the Met Office/Oxford Rotating Annulus Laboratory (MORALS) code, we have investigated a series of equilibrated, two dimensional axisymmetric flows across a large region of parameter space. These are characterized in terms of their velocity and temperature fields. When rotation is applied several distinct flow regimes may be identified for different rotation rates and strengths of differential heating. These regimes are defined as a function of the ratio of the horizontal Ekman layer thickness to the non-rotating thermal boundary layer thickness and are found to be similar to those identified in previous annulus experiments. Convection without rotation is also considered and the scaling of the heat transport with Rayleigh number is calculated. This is then compared with existing work on the classical annulus as well as horizontal and Rayleigh-Bénard convection. As with previous studies on both rotating and non-rotating convection the system’s behaviour is found to be aspect ratio dependent. This dependence is seen in the scaling of the non-rotating Nusselt number and in transitions between regimes in the rotating case although further investigation is required to fully explain these observations.

]]>Fluids doi: 10.3390/fluids2030040

Authors: Sean Breckling Monika Neda Tahj Hill

The time relaxation model has proven to be effective in regularization of Navier–Stokes Equations. This article reviews several published works discussing the development and implementations of time relaxation and time relaxation models (TRMs), and how such techniques are used to improve the accuracy and stability of fluid flow problems with higher Reynolds numbers. Several analyses and computational settings of TRMs are surveyed, along with parameter sensitivity studies and hybrid implementations of time relaxation operators with different regularization techniques.

]]>Fluids doi: 10.3390/fluids2030039

Authors: Tatyana Lyubimova Igor Muratov

The onset of convection in a three-layer system consisting of two fluid-saturated porous layers separated by a homogeneous fluid layer is studied. It is shown that both a longwave convective regime developing in the whole system and a finite-wavelength regime of convection concentrated in the homogeneous fluid layer are possible. Due to the hydraulic resistance of the porous matrix, the flow intensity in the longwave convective regime is much lower than that in the finite-wavelength regime. Moreover, it grows at a much slower pace with the increase of the Grashof number. Because of that, the long-wave convective regime becomes unstable at small supercriticalities and is replaced by a finite-wavelength regime.

]]>Fluids doi: 10.3390/fluids2030038

Authors: Abigail L. Bowers Leo G. Rebholz

This paper gives a review of recent results for the reduced Navier–Stokes-α (rNS-α) model of incompressible flow. The model was recently developed as a numerical approximation to the well known Navier–Stokes-α model, for the purpose of more efficiently computations in the C0 finite element setting. Its performance in initial numerical tests was remarkable, which led to analytical studies and further numerical tests, all of which provided excellent results. This paper reviews the main results established thus far for rNS-α, and presents some open problems for future work.

]]>Fluids doi: 10.3390/fluids2030037

Authors: Jean N. Reinaud Xavier Carton David G. Dritschel

We investigate the interaction between a heton and a current generated by a filament of buoyancy anomaly at the surface. Hetons are baroclinic dipoles consisting of a pair of vortices of opposite signs lying at different depths. Such structures have self-induced motion whenever the pair of vortices are offset horizontally. A surface buoyancy filament generates a shear flow since the density perturbation locally modifies the pressure field. The vertical shear induced by the filament offsets the vortices of the heton if vertically aligned initially. Moreover, if the vortex nearer the surface is in adverse horizontal shear with the buoyancy filament, the heton tends to move towards the filament. Conversely, if the upper vortex is in cooperative horizontal shear with the buoyancy filament, the heton moves away from it. The filament is also naturally unstable and eventually breaks into a series of billows as it is perturbed by the heton. Moderate to large intensity surface buoyancy distributions separate the vortices of the heton, limiting its advection as a baroclinic dipole. Instead, the vortices of the heton start to interact strongly with surface billows. Additionally, the vortices of the heton can be partially destroyed by the filament if the shear it induces is sufficiently large.

]]>Fluids doi: 10.3390/fluids2030036

Authors: Kurt Polzin Yuri Lvov

There is no theoretical underpinning that successfully explains how turbulent mixing is fed by wave breaking associated with nonlinear wave-wave interactions in the background oceanic internal wavefield. We address this conundrum using one-dimensional ray tracing simulations to investigate interactions between high frequency internal waves and inertial oscillations in the extreme scale separated limit known as “Induced Diffusion”. Here, estimates of phase locking are used to define a resonant process (a resonant well) and a non-resonant process that results in stochastic jumps. The small amplitude limit consists of jumps that are small compared to the scale of the resonant well. The ray tracing simulations are used to estimate the first and second moments of a wave packet’s vertical wavenumber as it evolves from an initial condition. These moments are compared with predictions obtained from the diffusive approximation to a self-consistent kinetic equation derived in the ‘Direct Interaction Approximation’. Results indicate that the first and second moments of the two systems evolve in a nearly identical manner when the inertial field has amplitudes an order of magnitude smaller than oceanic values. At realistic (oceanic) amplitudes, though, the second moment estimated from the ray tracing simulations is inhibited. The transition is explained by the stochastic jumps obtaining the characteristic size of the resonant well. We interpret this transition as an adiabatic ‘saturation’ process which changes the nominal background wavefield from supporting no mixing to the point where that background wavefield defines the normalization for oceanic mixing models.

]]>Fluids doi: 10.3390/fluids2030035

Authors: Mohan Anand Kumbakonam Rajagopal

Several advances have taken place since the early 2000s in the field of blood flow modelling. These advances have been driven by the development of assist devices such as Left Ventricular Assist Devices (LVADs), etc., and by the acceptance of in silico tests for the generation of hypotheses concerning clot formation and lysis. We give an overview of the developments in modelling of blood rheology and clot formation/lysis in the last 10 to 15 years. In blood rheology, advances are increasingly supplemented by flow simulation studies. In clot formation (or coagulation), advances have taken place in both single-scale modeling under quiescent conditions as well as in multi-scale modeling in the presence of flow. The future will possibly see more blood flow simulations in complex geometries and, simultaneously, development and simulation of multi-scale models for clot formation and lysis.

]]>Fluids doi: 10.3390/fluids2020034

Authors: Chen-Yu Chiang Olivier Pironneau Tony Sheu Marc Thiriet

An algorithm is derived for a hyperelastic incompressible solid coupled with a Newtonian fluid. It is based on a Eulerian formulation of the full system in which the main variables are the velocities. After a fully implicit discretization in time it is possible to eliminate the displacements and solve a variational equation for the velocities and pressures only. The stability of the method depends heavily on the use of characteristic-Galerkin discretization of the total derivatives. For comparison with previous works, the method is tested on a three-dimensional (3D) clamped beam in a pipe filled with a fluid. Convergence is studied numerically on an axisymmetric case.

]]>Fluids doi: 10.3390/fluids2020033

Authors: Antonio Barletta Michele Celli

A linear stability analysis of the parallel uniform flow in a horizontal channel with open upper boundary is carried out. The lower boundary is considered as an impermeable isothermal wall, while the open upper boundary is subject to a uniform heat flux and it is exposed to an external horizontal fluid stream driving the flow. An eigenvalue problem is obtained for the two-dimensional transverse modes of perturbation. The study of the analytical dispersion relation leads to the conditions for the onset of convective instability as well as to the determination of the parametric threshold for the transition to absolute instability. The results are generalised to the case of three-dimensional perturbations.

]]>Fluids doi: 10.3390/fluids2020032

Authors: Vandita Sharma Satyajit Pramanik Manoranjan Mishra

Viscous fingering is ubiquitous in miscible displacements in porous media, in particular, oil recovery, contaminant transport in aquifers, chromatography separation, and geological CO2 sequestration. The viscosity contrasts between heavy oil and water is several orders of magnitude larger than typical viscosity contrasts considered in the majority of the literature. We use the finite element method (FEM)-based COMSOL Multiphysics simulator to simulate miscible displacements in homogeneous porous media with very large viscosity contrasts. Our numerical model is suitable for a wide range of viscosity contrasts covering chromatographic separation as well as heavy oil recovery. We have successfully captured some interesting and previously unexplored dynamics of miscible blobs with very large viscosity contrasts in homogeneous porous media. We study the effect of viscosity contrast on the spreading and the degree of mixing of the blob. Spreading (variance of transversely averaged concentration) follows the power law t 3 . 34 for the blobs with viscosity ∼ O ( 10 2 ) and higher, while degree of mixing is found to vary non-monotonically with log-mobility ratio. Moreover, in the limit of very large viscosity contrast, the circular blob behaves like an erodible solid body and the degree of mixing approaches the viscosity-matched case.

]]>Fluids doi: 10.3390/fluids2020031

Authors: Mariana Simão Jorge Ferreira António C. Tomás José Fragata Helena Ramos

Computational fluid dynamics (CFD) can be seen as complementary tool alongside the visualization capabilities of cardiovascular magnetic resonance (CMR) and computed tomography (CT) imaging for decision-making. In this research CT images of three cases (i.e., a healthy heart pilot project and two patients with complex aortic disease) are used to validate and analyse the corresponding computational results. Three 3D domains of the thoracic aorta were tested under hemodynamic conditions. Under normal conditions, the flow inside the thoracic aorta is more streamlined. In the presence of ascending aortic aneurysm, large areas of blue separation zones (i.e., low velocities) are identified, as well as an internal geometry deformation of the aortic wall, respectively. This flow separation is characterized by the reversal of flow and sudden drop of the wall shear stress (WSS) in the aorta. Moreover, the aortic aneurysm simulations adversely affect the flow by increasing the pressure drop and flow inefficiency, due to the anatomical configuration of the ascending aorta. Altered hemodynamics led to a vortex formation and locally reversed the flow that eventually induced a low flow velocity and oscillating WSS in the thoracic aorta. Significant changes in the hemodynamic characteristics affect the normal blood circulation with strong turbulence occurrence, damaging the aortic wall, leading ultimately to the need of surgical intervention to avoid fatal events.

]]>Fluids doi: 10.3390/fluids2020030

Authors: Nils T. Basse

Turbulence intensity profiles are compared for smooth- and rough-wall pipe flow measurements made in the Princeton Superpipe. The profile development in the transition from hydraulically smooth to fully rough flow displays a propagating sequence from the pipe wall towards the pipe axis. The scaling of turbulence intensity with Reynolds number shows that the smooth- and rough-wall level deviates with increasing Reynolds number. We quantify the correspondence between turbulence intensity and the friction factor.

]]>Fluids doi: 10.3390/fluids2020029

Authors: Iris Rukshin Josef Mohrenweiser Pengtao Yue Shahriar Afkhami

Magnetic drug targeting is a technique that involves the binding of medicine to magnetizable particles to allow for more specific transport to the target location. This has recently come to light as a method of drug delivery that reduces the disadvantages of conventional, systemic treatments. This study developed a mathematical model for tracking individual superparamagnetic nanoparticles in blood flow in the presence of an externally applied magnetic field. The model considers the magnetic attraction between the particles and the external magnet, influence of power law flow, diffusive interaction between the particles and blood, and random collisions with red blood cells. A stochastic system of differential equations is presented and solved numerically to simulate the paths taken by particles in a blood vessel. This study specifically focused on localized cancer treatment, in which a surface tumor is accessed through smaller blood vessels, which are more conducive to this delivery method due to slower flow velocities and smaller diameters. The probability of the particles reaching the tumor location is found to be directly dependent on ambient factors; thus, diffusion through Brownian motion and red blood cell collisions, different magnetic field and force models, blood viscosities, and release points are considered.

]]>Fluids doi: 10.3390/fluids2020028

Authors: Amrik Sen

Kinetic equations for rapidly rotating flows are developed in this paper using multiple scales perturbation theory. The governing equations are an asymptotically reduced set of equations that are derived from the incompressible Navier-Stokes equations. These equations are applicable for rapidly rotating flow regimes and are best suited to describe anisotropic dynamics of rotating flows. The independent variables of these equations inherently reside in a helical wave basis that is the most suitable basis for inertial waves. A coupled system of equations for the two global invariants: energy and helicity, is derived by extending a simpler symmetrical system to the more general non-symmetrical helical case. This approach of deriving the kinetic equations for helicity follows naturally by exploiting the symmetries in the system and is different from the derivations presented in an earlier weak wave turbulence approach that uses multiple correlation functions to account for the asymmetry due to helicity. Stationary solutions, including Kolmogorov solutions, for the flow invariants are obtained as a scaling law of the anisotropic wave numbers. The scaling law solutions compare affirmatively with results from recent experimental and simulation data. Thus, anisotropic wave turbulence of the reduced hydrodynamic system is a weak turbulence model for strong anisotropy with a dominant k ⊥ cascade where the waves aid the turbulent cascade along the perpendicular modes. The waves also enable an appropriate closure of the kinetic equation through averaging of their phases.

]]>Fluids doi: 10.3390/fluids2020027

Authors: D. Rees Eugen Magyari

Recent interest in the effects of viscous dissipation on convective flows in porous media has centred almost exclusively on forced convection flows. In this paper, we investigate the manner in which it affects the onset and early stages of convection in Darcy–Bénard convection. A weakly nonlinear theory is described briefly, and it is shown that hexagonal cells are preferred over rolls when the Rayleigh number is sufficiently close to 4 π 2 . At higher Rayleigh numbers, two-dimensional rolls are preferred. When weak form drag is included, then subcritical convection eventually disappears as the Forchheimer parameter increases, yielding a highly novel situation wherein hexagonal convection arises supercritically. The range of stability of hexagons is found to increase.

]]>Fluids doi: 10.3390/fluids2020026

Authors: Peter Vadasz

A review of the research on the instability of steady porous media convection leading to chaos, and the possibility of controlling the transition from steady convection to chaos is presented. The governing equations consisting of the continuity, the extended Darcy, and the energy equations subject to the assumption of local thermal equilibrium and the Boussinesq approximation are converted into a set of three nonlinear ordinary differential equations by assuming two-dimensional convection and expansion of the dependent variables into a truncated spectrum of modes. Analytical (weak nonlinear), computational (Adomian decomposition) as well as numerical (Runge-Kutta-Verner) solutions to the resulting set of equations are presented and compared to each other. The analytical solution for the transition point to chaos is identical to the computational and numerical solutions in the neighborhood of a convective fixed point and deviates from the accurate computational and numerical solutions as the initial conditions deviate from the neighborhood of a convective fixed point. The control of this transition is also discussed.

]]>Fluids doi: 10.3390/fluids2020025

Authors: Carles Torras Esther Lorente Simelys Hernández Nunzio Russo Joan Salvadó

Miniaturized cells can be used in photo-electrochemistry to perform water splitting. The geometry, process variables and removal of oxygen bubbles in these cells need to be optimized. Bubbles tend to remain attached to the catalytic surface, thus blocking the reaction, and they therefore need to be dragged out of the cell. Computational Fluid Dynamics simulations have been carried out to assess the design of miniaturized cells and their results have been compared with experimental results. It has been found that low liquid inlet velocities (~0.1 m/s) favor the homogeneous distribution of the flow. Moderate velocities (0.5–1 m/s) favor preferred paths. High velocities (~2 m/s) lead to turbulent behavior of the flow, but avoid bubble coalescence and help to drag the bubbles. Gravity has a limited effect at this velocity. Finally, channeled cells have also been analyzed and they allow a good flow distribution, but part of the catalytic area could be lost. The here presented results can be used as guidelines for the optimum design of photocatalytic cells for the water splitting reaction for the production of solar fuels, such as H2 or other CO2 reduction products (i.e., CO, CH4, among others).

]]>Fluids doi: 10.3390/fluids2020024

Authors: Richard Blender Gualtiero Badin

A systematic method to derive the Hamiltonian and Nambu form for the shallow water equations using the conservation for energy and potential enstrophy is presented. Different mechanisms, such as vortical flows and emission of gravity waves, emerge from different conservation laws for total energy and potential enstrophy. The equations are constructed using exterior differential forms and self-adjoint operators, and result in the sum of two Nambu brackets—one for the vortical flow and one for the wave-mean flow interaction—and a Poisson bracket representing the interaction between divergence and geostrophic imbalance. The advantage of this approach is that the Hamiltonian and Nambu forms can here be written in a coordinate-independent form.

]]>Fluids doi: 10.3390/fluids2020023

Authors: Yi-Huan Kao Zhou-Wei Jiang Sheng-Cyuan Fang

In this work, the fluid mechanics performance of four different contraction wall shapes has been studied and compared side-by-side by computational simulation, and the effect of contraction cross-sectional shape on the flow uniformity at the contraction exit has been included as well. A different contraction wall shape could result in up to an extra 4% pressure drop of a closed-loop wind tunnel, and the contraction wall shape has a stronger influence on the pressure loss than the contraction cross-sectional shape. The first and the second derivatives from different wall shape equations could provide a hint for qualitatively comparing the flow uniformity at the contraction exits. A wind tunnel contraction with an octagonal shape provides not only better fluid mechanics performance than that with a circular or a square cross-sectional shape, but also lower manufacturing costs. Moreover, a smaller blockage ratio within the test section can be achieved by employing an octagonal cross-sectional shape instead of a circular cross-sectional shape under the same hydraulic diameter circumstance. A wind tunnel contraction with an octagonal cross-sectional shape is recommended to be a design candidate.

]]>Fluids doi: 10.3390/fluids2020022

Authors: Amit Mahajan Sunil Mahesh Sharma

Penetrative convection due to purely internal heating in a horizontal ferrofluid-saturated porous layer is examined by performing linear stability analysis. Four different types of heat supply functions are considered. The Darcy model is used to incorporate the effect of the porous medium. Numerical solutions are obtained by using the Chebyshev pseudospectral method, and the results are discussed for all three boundary conditions: when both boundaries are impermeable and conducting; when both boundaries are conducting with lower boundary impermeable and free upper boundary; and when both boundaries are impermeable with lower boundary conducting and upper with constant heat flux. The effect of the Langevin parameter, width of ferrofluid layer, permeability parameter, and nonlinearity of the fluid magnetization has been observed at the onset of penetrative convection for water- and ester-based ferrofluids. It is seen that the Langevin parameter, width of ferrofluid layer, and permeability parameter have stabilizing effects on the onset of convection, while the nonlinearity of the fluid magnetization advances the onset of convection.

]]>Fluids doi: 10.3390/fluids2020021

Authors: Weijia Chen Edmond Lo

This paper presents a numerical study of high wavenumber coherent structure evolution in boundary layer transition flow using recently-developed high order Combined compact difference schemes with non-uniform grids in the wall-normal direction for efficient simulation of such flows. The study focuses on a simulation of an Adverse-Pressure-Gradient (APG) boundary layer transition induced by broadband disturbance corresponding to the experiment of Borodulin et al. (Journal of Turbulence, 2006, 7, pp. 1–30). The results support the experimental observation that although the coherent structures seen during transition to turbulence have asymmetric shapes and occur in a random pattern, their local evolutional behaviors are quite similar. Further calculated local wavelet spectra of these coherent structures are also very similar. The wavelet spectrum of the streamwise disturbance velocity demonstrates high wavenumber clusters at the tip and the rear parts of the Λ-vortex. Both parts are imbedded at the primary Λ-vortex stage and spatially coincide with the spike region and high shear layer. The tip part is associated with the later first ring-like vortex, while the rear part with the remainder of the Λ-vortex. These observations help to shed light on the generation of turbulence, which is dominated by high wavenumber coherent structures.

]]>Fluids doi: 10.3390/fluids2020020

Authors: Rémi Tailleux

McDougall, Groeskamp and Griffies (MGG) strongly criticise all aspects of Tailleux (2016) that challenge the current conventional wisdom about the use of neutral density concepts for studying and parameterising lateral ocean stirring and mixing. However, their claim that most of Tailleux (2016)’s results or conclusions are incorrect is easily shown to originate: (1) from mistakingly confusing Tailleux’s Eulerian arguments for Lagrangian ones; (2) from their irrational belief that only one particular kind of quasi-material surface is somehow endorsed by Nature and hence relevant to the description of stirring and mixing—namely the locally-defined neutral tangent planes—stating at one point: “why should the ocean care about human constructed density variables”? MGG appear to overlook the simple fact that solutions of the Navier–Stokes equations—which synthesise our ideas about how Nature works—never require the introduction of any form of quasi-material or quasi-neutral density variable. This implies that the empirical isopycnal/isentropic stirring property is necessarily an emergent property of the Navier–Stokes equations, and hence that all forms of isopycnal surfaces—both neutral and not—are necessarily all human constructs. To establish the relevance of any particular construct to the actual ocean, an explicit model of stirring is needed to elucidate the nature of the dynamical/energetics constraints on lateral stirring. Even in the simplest model of stirring, neutral stirring represents only one possible mode out of a continuum of stirring modes responsible for lateral stirring in the ocean, without any evidence that it should dominate over the other ones. To help clarify the issues involved, it is proposed to regard the rigorous study of ocean stirring and mixing as relying on at least five distinct stages, from defining a model of stirring to constructing physically-based mixing parameterisations in numerical ocean models.

]]>Fluids doi: 10.3390/fluids2020019

Authors: Trevor McDougall Sjoerd Groeskamp Stephen Griffies

Tailleux has written about the concept of epineutral mixing and has attempted to justify it from an energetic viewpoint. However, Tailleux’s approach is incorrect because it ignores the unsteady nature of the density field during baroclinic motions, which in turn leads to incorrect conclusions. Tailleux also asserts that “adiabatic and isohaline parcel exchanges can only be meaningfully defined on material surfaces” that are functions of only Absolute Salinity and Conservative Temperature and are not separately a function of pressure. We disagree with this assertion because there is no physical reason why the ocean should care about a globally-defined function of Absolute Salinity and Conservative Temperature that we construct. Rather, in order to understand and justify the concept of epineutral mixing, we consider the known physical processes that occur at the in situ pressure of the mixing. The Tailleux paper begins with two incorrect equations that ignore the transience of the ocean. These errors echo throughout Tailleux, leading to sixteen conclusions, most of which we show are incorrect. (Comment on Tailleux, R. Neutrality Versus Materiality: A Thermodynamic Theory of Neutral Surfaces. Fluids 2016, 1, 32, doi:10.3390/fluids1040032.)

]]>Fluids doi: 10.3390/fluids2020018

Authors: Giorgia Sinibaldi Giovanni Romano

In the present work, the flow field in a splitting-junction micro channel with a Y shape, which is the simplest geometry to be employed for heat and mass transfer in micro-devices such as micro-heat-exchangers and micro-mixers, is investigated experimentally using micro Particle Image Velocimetry (μPIV). The angular divergence in the Y splitting is changed, as well as the Reynolds number, in order to investigate the instantaneous and mean flow fields to determine which configurations are more suitable for practical applications. The results show that the flow configuration is strongly dependent on the Y shape angle, especially in the junction part, and that there is also a significant dependence on the Reynolds number.

]]>Fluids doi: 10.3390/fluids2020017

Authors: Carlo Gualtieri Athanasios Angeloudis Fabian Bombardelli Sanjeev Jha Thorsten Stoesser

Computational Fluid Dynamics (CFD) has consolidated as a tool to provide understanding and quantitative information regarding many complex environmental flows. The accuracy and reliability of CFD modelling results oftentimes come under scrutiny because of issues in the implementation of and input data for those simulations. Regarding the input data, if an approach based on the Reynolds-Averaged Navier-Stokes (RANS) equations is applied, the turbulent scalar fluxes are generally estimated by assuming the standard gradient diffusion hypothesis (SGDH), which requires the definition of the turbulent Schmidt number, Sct (the ratio of momentum diffusivity to mass diffusivity in the turbulent flow). However, no universally-accepted values of this parameter have been established or, more importantly, methodologies for its computation have been provided. This paper firstly presents a review of previous studies about Sct in environmental flows, involving both water and air systems. Secondly, three case studies are presented where the key role of a correct parameterization of the turbulent Schmidt number is pointed out. These include: (1) transverse mixing in a shallow water flow; (2) tracer transport in a contact tank; and (3) sediment transport in suspension. An overall picture on the use of the Schmidt number in CFD emerges from the paper.

]]>Fluids doi: 10.3390/fluids2020016

Authors: Laxman Kallekar Chinthapenta Viswanath Mohan Anand

The effect of varying wall flexibility on the deformation of an artery during steady and pulsatile flow of blood is investigated. The artery geometry is recreated from patient-derived data for a stenosed left coronary artery. Blood flow in the artery is modeled using power-law fluid. The fluid-structure interaction of blood flow on artery wall is simulated using ANSYS 16.2, and the resulting wall deformation is documented. A comparison of wall deformation using flexibility models like Rigid, Linear Elastic, Neo-hookean, Mooney-Rivlin and Holzapfel are obtained for teady flow in the artery. The maximum wall deformation in coronary flow onditions predicted by the Holzapfel model is only around 50% that predicted by the Neo-Hookean model. The flow-induced deformations reported here for patient-derived stenosed coronary artery with physiologically accurate model are the first of its kind. These results help immensely in the planning of angioplasty.

]]>Fluids doi: 10.3390/fluids2020015

Authors: Dejan Brkić Žarko Ćojbašić

This paper presents evolutionary optimization of explicit approximations of the empirical Colebrook’s equation that is used for the calculation of the turbulent friction factor (λ), i.e., for the calculation of turbulent hydraulic resistance in hydraulically smooth and rough pipes including the transient zone between them. The empirical Colebrook’s equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of the inner pipe surface (ε/D). It is implicit in the unknown friction factor (λ). The implicit Colebrook’s equation cannot be rearranged to derive the friction factor (λ) directly, and therefore, it can be solved only iteratively [λ = f(λ, R, ε/D)] or using its explicit approximations [λ ≈ f(R, ε/D)], which introduce certain error compared with the iterative solution. The optimization of explicit approximations of Colebrook’s equation is performed with the aim to improve their accuracy, and the proposed optimization strategy is demonstrated on a large number of explicit approximations published up to date where numerical values of the parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After that improvement, the computational burden stays unchanged while the accuracy of approximations increases in some of the cases very significantly.

]]>Fluids doi: 10.3390/fluids2020014

Authors: Romit Maulik Omer San

Solving two-dimensional compressible turbulence problems up to a resolution of 16, 3842, this paper investigates the characteristics of two promising computational approaches: (i) an implicit or numerical large eddy simulation (ILES) framework using an upwind-biased fifth-order weighted essentially non-oscillatory (WENO) reconstruction algorithm equipped with several Riemann solvers, and (ii) a central sixth-order reconstruction framework combined with various linear and nonlinear explicit low-pass spatial filtering processes. Our primary aim is to quantify the dissipative behavior, resolution characteristics, shock capturing ability and computational expenditure for each approach utilizing a systematic analysis with respect to its modeling parameters or parameterizations. The relative advantages and disadvantages of both approaches are addressed for solving a stratified Kelvin-Helmholtz instability shear layer problem as well as a canonical Riemann problem with the interaction of four shocks. The comparisons are both qualitative and quantitative, using visualizations of the spatial structure of the flow and energy spectra, respectively. We observe that the central scheme, with relaxation filtering, offers a competitive approach to ILES and is much more computationally efficient than WENO-based schemes.

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