Fluids
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Latest open access articles published in Fluids at http://www.mdpi.com/journal/fluids<![CDATA[Fluids, Vol. 2, Pages 11: The Elder Problem]]>
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This paper presents an autobiographical and biographical historical account of the genesis, evolution and resolution of the Elder Problem. It begins with John W. Elder and his autobiographical story leading to his groundbreaking work on natural convection at Cambridge in the 1960’s. His seminal work published in the Journal of Fluid Mechanics in 1967 became the basis for the modern benchmark of variable density flow simulators that we know today as “The Elder Problem”. There have been well known and major challenges with the Elder Problem model benchmark—notably the multiple solutions that were ultimately uncovered using different numerical models. Most recently, it has been shown that the multiple solutions are indeed physically realistic bifurcation solutions to the Elder Problem and not numerically spurious artefacts. The quandary of the Elder Problem has now been solved—a major scientific breakthrough for fluid mechanics and for numerical modelling. This paper—records, reflections, reminiscences, stories and anecdotes—is an historical autobiographical and biographical memoir. It is the personal story of the Elder Problem told by some of the key scientists who established and solved the Elder Problem. 2017 marks the 50 year anniversary of the classical work by John W. Elder published in Journal of Fluid Mechanics in 1967. This set the stage for this scientific story over some five decades. This paper is a celebration and commemoration of the life and times of John W. Elder, the problem named in his honour, and some of the key scientists who worked on, and ultimately solved, it.Fluids2017-03-2121Review10.3390/fluids2010011112311-55212017-03-21doi: 10.3390/fluids2010011John ElderCraig SimmonsHans-Jörg DierschPeter FrolkovičEkkehard HolzbecherKlaus Johannsen<![CDATA[Fluids, Vol. 2, Pages 12: Uncertainty Quantification at the Molecular–Continuum Model Interface †]]>
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Non-equilibrium molecular dynamics simulations are widely employed to study transport fluid properties. Observables measured at the atomistic level can serve as inputs for continuum calculations, allowing for improved analysis of phenomena involving multiple scales. In hybrid modelling, uncertainties present in the information transferred across scales can have a significant impact on the final predictions. This work shows the influence of force-field variability on molecular measurements of the shear viscosity of water. In addition, the uncertainty propagation is demonstrated by quantifying the sensitivity of continuum velocity distribution to the particle-based calculations. The uncertainty is modelled with polynomial chaos expansion using a non-intrusive spectral projection strategy. The analysis confirms that low-order polynomial basis are sufficient to calculate the dispersion of observables.Fluids2017-03-2121Article10.3390/fluids2010012122311-55212017-03-21doi: 10.3390/fluids2010012Małgorzata ZimońRobert SawkoDavid EmersonChristopher Thompson<![CDATA[Fluids, Vol. 2, Pages 10: A Quasi-Mechanistic Mathematical Representation for Blood Viscosity]]>
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Blood viscosity is a crucial element for any computation of flow fields in the vasculature or blood-wetted devices. Although blood is comprised of multiple elements, and its viscosity can vary widely depending on several factors, in practical applications, it is commonly assumed to be a homogeneous, Newtonian fluid with a nominal viscosity typically of 3.5 cP. Two quasi-mechanistic models for viscosity are presented here, built on the foundation of the Krieger model of suspensions, in which dependencies on shear rate, hematocrit, and plasma protein concentrations are explicitly represented. A 3-parameter Asymptotic Krieger model (AKM) exhibited excellent agreement with published Couette experiments over four decades of shear rate (0–1000 s-1, root mean square (RMS) error = 0.21 cP). A 5-parameter Modified Krieger Model (MKM5) also demonstrated a very good fit to the data (RMS error = 1.74 cP). These models avoid discontinuities exhibited by previous models with respect to hematocrit and shear rate. In summary, the quasi-mechanistic, Modified-Krieger Model presented here offers a reasonable compromise in complexity to provide flexibility to account for several factors that affect viscosity in practical applications, while assuring accuracy and stability.Fluids2017-03-0121Review10.3390/fluids2010010102311-55212017-03-01doi: 10.3390/fluids2010010Samuel HundMarina KamenevaJames Antaki<![CDATA[Fluids, Vol. 2, Pages 9: Emulsion Flow Analysis of a Sensor Probe for Sustainable Machine Operation]]>
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Working fluids possess several applications in manufacturing processes, for instance lubricants in metals machining. Typical metal working fluids are formulated as oil-in-water emulsions. The maintenance of the physical stability of the working fluid during operation is a key factor for the sustainability of the relevant process. Therefore, continuous control of the working fluids stability and performance during machine operation is an essential tool for maintenance of the process performance. Turbidity measurement (TM) is a process technique for emulsion stability and quality assessment, where light transmission and absorption of an emulsion system is analyzed. However, for in-process measurement and fluid quality detection during the machine operation by TM, it is necessary to implement a transmission inline sensor into the working fluid flow line. The continuous flow measurement may cause problems for long-term sensor operation regarding, e.g., biofouling of the sensor optical glasses or erroneous measurements due to emulsion droplets segregation effects. In the present investigation, computational fluid dynamic (CFD) simulations have been adapted to obtain the emulsion flow conditions within a typical TM sensor probe, thereby allowing an assessment of the adhesion probability of microorganisms as well as droplet segregation effects. The simulation results indicate some temporal changes of the dispersed phase concentration in the detected emulsion flow. Due to droplet segregation in the emulsion, the flow velocity needs to exceed a certain value for reliable operation. It is shown here that in this flow regime microbiological attachments on the probe surfaces may be sufficiently avoided. A minimum critical flow velocity is derived to avoid biomolecule adhesion and thus durable operation of the sensor.Fluids2017-02-2321Article10.3390/fluids201000992311-55212017-02-23doi: 10.3390/fluids2010009Sören SanderBenjamin GlasseLucas GroscheJose de PaivaRoberto GuardaniUdo Fritsching<![CDATA[Fluids, Vol. 2, Pages 8: On the CFD Analysis of a Stratified Taylor-Couette System Dedicated to the Fabrication of Nanosensors]]>
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Since the pioneering work of Taylor, the analysis of flow regimes of incompressible, viscous fluids contained in circular Couette systems with independently rotating cylinders have charmed many researchers. The characteristics of such kind of flows have been considered for some industrial applications. Recently, Taylor-Couette flows found an innovative application in the production of optical fiber nanotips, to be used in molecular biology and medical diagnostic fields. Starting from the activity of Barucci et al., the present work concerns the numerical analysis of a Taylor-Couette system composed by two coaxial counter-rotating cylinders with low aspect ratio and radius ratio, filled with three stratified fluids. An accurate analysis of the flow regimes is performed, considering both the variation of inner and outer rotational speed and the reduction of fiber radius due to etching process. The large variety of individuated flow configurations provides useful information about the possible use of the Taylor-Couette system in a wide range of engineering applications. For the present case, the final objective is to provide accurate information to manufacturers of fiber nanotips about the expected flow regimes, thus helping them in the setup of the control process that will be used to generate high-quality products.Fluids2017-02-1821Article10.3390/fluids201000882311-55212017-02-18doi: 10.3390/fluids2010008Duccio GriffiniMassimiliano InsinnaSimone SalvadoriAndrea BarucciFranco CosiStefano PelliGiancarlo Righini<![CDATA[Fluids, Vol. 2, Pages 7: Surface Quasi-Geostrophy]]>
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Oceanic and atmospheric dynamics are often interpreted through potential vorticity, as this quantity is conserved along the geostrophic flow. However, in addition to potential vorticity, surface buoyancy is a conserved quantity, and this also affects the dynamics. Buoyancy at the ocean surface or at the atmospheric tropopause plays the same role of an active tracer as potential vorticity does since the velocity field can be deduced from these quantities. The surface quasi-geostrophic model has been proposed to explain the dynamics associated with surface buoyancy conservation and seems appealing for both the ocean and the atmosphere. In this review, we present its main characteristics in terms of coherent structures, instabilities and turbulent cascades. Furthermore, this model is mathematically studied for the possible formation of singularities, as it presents some analogies with three-dimensional Euler equations. Finally, we discuss its relevance for the ocean and the atmosphere.Fluids2017-02-1621Review10.3390/fluids201000772311-55212017-02-16doi: 10.3390/fluids2010007Guillaume Lapeyre<![CDATA[Fluids, Vol. 2, Pages 6: A Reduced Model for Salt-Finger Convection in the Small Diffusivity Ratio Limit]]>
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A simple model of nonlinear salt-ﬁnger convection in two dimensions is derived and studied. The model is valid in the limit of a small solute to heat diffusivity ratio and a large density ratio, which is relevant to both oceanographic and astrophysical applications. Two limits distinguished by the magnitude of the Schmidt number are found. For order one Schmidt numbers, appropriate for astrophysical applications, a modiﬁed Rayleigh–Bénard system with large-scale damping due to a stabilizing temperature is obtained. For large Schmidt numbers, appropriate for the oceanic setting, the model combines a prognostic equation for the solute ﬁeld and a diagnostic equation for inertia-free momentum dynamics. Two distinct saturation regimes are identiﬁed for the second model: the weakly driven regime is characterized by a large-scale ﬂow associated with a balance between advection and linear instability, while the strongly-driven regime produces multiscale structures, resulting in a balance between energy input through linear instability and energy transfer between scales. For both regimes, we analytically predict and numerically conﬁrm the dependence of the kinetic energy and salinity ﬂuxes on the ratio between solutal and thermal Rayleigh numbers. The spectra and probability density functions are also computed.Fluids2017-01-3021Article10.3390/fluids201000662311-55212017-01-30doi: 10.3390/fluids2010006Jin-Han XieBenjamin MiquelKeith JulienEdgar Knobloch<![CDATA[Fluids, Vol. 2, Pages 5: A Note on the Drag Coefficient of Steady Flow of Non-Newtonian, Power-Law Fluids across Unbounded Two-Dimensional Bodies at Low Reynolds Numbers]]>
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The flow of a non-Newtonian, power-law fluid, directed normally to long, two-dimensional horizontal bodies, is considered in the present note. It is found that for low Reynolds numbers ( Re ≤ 0.1 ) and a low power-law index (shear-thinning fluids) the drag coefficient always obeys the relationship c D = A / Re , whereas at a high power-law index (shear-thickening fluids) the drag coefficient tends to become identical for all bodies irrespective of their cross-section form.Fluids2017-01-2721Short Note10.3390/fluids201000552311-55212017-01-27doi: 10.3390/fluids2010005Asterios Pantokratoras<![CDATA[Fluids, Vol. 2, Pages 4: On the Three Dimensional Interaction between Flexible Fibers and Fluid Flow]]>
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In this paper we discuss the deformation of a flexible fiber clamped to a spherical body and immersed in a flow of fluid moving with a speed ranging between 0 and 50 cm/s by means of three dimensional numerical simulation developed in COMSOL . The effects of flow speed and initial configuration angle of the fiber relative to the flow are analyzed. A rigorous analysis of the numerical procedure is performed and our code is benchmarked against well established cases. The flow velocity and pressure are used to compute drag forces upon the fiber. Of particular interest is the behavior of these forces as a function of the flow speed and fiber orientation. The Vogel exponents, which characterize the rate of bending of a fiber in a flow, are found for the various configurations examined here and seem to display interesting variations. These exponents are then compared with our previously studied two-dimensional models.Fluids2017-01-2221Article10.3390/fluids201000442311-55212017-01-22doi: 10.3390/fluids2010004Bogdan NitaRyan Allaire<![CDATA[Fluids, Vol. 2, Pages 3: Acknowledgement to Reviewers of Fluids in 2016]]>
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The editors of Fluids would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2016.[...]Fluids2017-01-1121Editorial10.3390/fluids201000332311-55212017-01-11doi: 10.3390/fluids2010003Fluids Editorial Office<![CDATA[Fluids, Vol. 2, Pages 2: RANS Simulations of Aerodynamic Performance of NACA 0015 Flapped Airfoil]]>
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An analysis of 2D subsonic flow over an NACA 0015 airfoil with a 30% trailing edge flap at a constant Reynolds number of 106 for various incidence angles and a range of flap deflections is presented. The steady-state governing equations of continuity and momentum conservation are solved combined with the realizable k-ε turbulence model using the ANSYS-Fluent code (Version 13.7, ANSYS, Inc., Canonsburg, PA, USA). The primary objective of the study is to provide a comprehensive understanding of flow characteristics around the NACA 0015 airfoil as a function of the angle of attack and flap deflection at Re = 106 using the realizable k-ε turbulence model. The results are validated through comparison of the predictions with the free field experimental measurements. Consistent with the experimental observations, the numerical results show that increased flap deflections increase the maximum lift coefficient, move the zero-lift angle of attack (AoA) to a more negative value, decrease the stall AoA, while the slope of the lift curve remains unchanged and the curve just shifts upwards. In addition, the numerical simulations provide limits for lift increment Δ C l and Cl, max values to be 1.1 and 2.2, respectively, obtained at a flap deflection of 50°. This investigation demonstrates that the realizable k-ε turbulence model is capable of predicting flow features over an airfoil with and without flap deflections with reasonable accuracy.Fluids2017-01-0521Article10.3390/fluids201000222311-55212017-01-05doi: 10.3390/fluids2010002Sohaib ObeidRatneshwar JhaGoodarz Ahmadi<![CDATA[Fluids, Vol. 2, Pages 1: Large Eddy Simulation of Pulsatile Flow through a Channel with Double Constriction]]>
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Pulsatile flow in a 3D model of arterial double stenoses is investigated using a large eddy simulation (LES) technique. The computational domain that has been chosen is a simple channel with a biological-type stenosis formed eccentrically on the top wall. The pulsation was generated at the inlet using the first four harmonics of the Fourier series of the pressure pulse. The flow Reynolds numbers, which are typically suitable for a large human artery, are chosen in the present work. In LES, a top-hat spatial grid-filter is applied to the Navier–Stokes equations of motion to separate the large-scale flows from the sub-grid scale (SGS). The large-scale flows are then resolved fully while the unresolved SGS motions are modelled using a localized dynamic model. It is found that the narrowing of the channel causes the pulsatile flow to undergo a transition to a turbulent condition in the downstream region; as a consequence, a severe level of turbulent fluctuations is achieved in these zones. Transitions to turbulent of the pulsatile flow in the post stenosis are examined through the various numerical results, such as velocity, streamlines, wall pressure, shear stresses and root mean square turbulent fluctuations.Fluids2016-12-2821Article10.3390/fluids201000112311-55212016-12-28doi: 10.3390/fluids2010001Md. MollaManosh Paul<![CDATA[Fluids, Vol. 1, Pages 42: Reynolds Stresses and Hemolysis in Turbulent Flow Examined by Threshold Analysis]]>
http://www.mdpi.com/2311-5521/1/4/42
Use of laminar flow-derived power law models to predict hemolysis with turbulence remains problematical. Flows in a Couette viscometer and a capillary tube have been simulated to investigate various combinations of Reynolds and/or viscous stresses power law models for hemolysis prediction. A finite volume-based computational method provided Reynolds and viscous stresses so that the effects of area-averaged and time-averaged Reynolds stresses, as well as total, viscous, and wall shear on hemolysis prediction could be assessed. The flow computations were conducted by using Reynolds-Averaged Navier-Stokes models of turbulence (k-ε and k-ω SST) to simulate four different experimental conditions in a capillary tube and seven experimental conditions in a Couette viscometer taken from the literature. Power law models were compared by calculating standard errors between measured hemolysis values and those derived from power law models with data from the simulations. In addition, suitability of Reynolds and viscous stresses was studied by threshold analysis. Results showed there was no evidence of a threshold value for hemolysis in terms of Reynolds and viscous stresses. Therefore, Reynolds and viscous stresses are not good predictors of hemolysis. Of power law models, the Zhang power law model (Artificial Organs, 2011, 35, 1180–1186) gives the lowest error overall for the hemolysis index and Reynolds stress (0.05570), while Giersiepen’s model (The International journal of Artificial Organs, 1990, 13, 300–306) yields the highest (6.6658), and intermediate errors are found through use of Heuser’s (Biorheology, 1980, 17, 17–24) model (0.3861) and Fraser’s (Journal of Biomechanical Engineering, 2012, 134, 081002) model (0.3947).Fluids2016-12-2114Article10.3390/fluids1040042422311-55212016-12-21doi: 10.3390/fluids1040042Mesude OzturkEdgar O’RearDimitrios Papavassiliou<![CDATA[Fluids, Vol. 1, Pages 41: The Onset of Convection in an Unsteady Thermal Boundary Layer in a Porous Medium]]>
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In this study, the linear stability of an unsteady thermal boundary layer in a semi-infinite porous medium is considered. This boundary layer is induced by varying the temperature of the horizontal boundary sinusoidally in time about the ambient temperature of the porous medium; this mimics diurnal heating and cooling from above in subsurface groundwater. Thus if instability occurs, this will happen in those regions where cold fluid lies above hot fluid, and this is not necessarily a region that includes the bounding surface. A linear stability analysis is performed using small-amplitude disturbances of the form of monochromatic cells with wavenumber, k. This yields a parabolic system describing the time-evolution of small-amplitude disturbances which are solved using the Keller box method. The critical Darcy-Rayleigh number as a function of the wavenumber is found by iterating on the Darcy-Rayleigh number so that no mean growth occurs over one forcing period. It is found that the most dangerous disturbance has a period which is twice that of the underlying basic state. Cells that rotate clockwise at first tend to rise upwards from the surface and weaken, but they induce an anticlockwise cell near the surface at the end of one forcing period, which is otherwise identical to the clockwise cell found at the start of that forcing period.Fluids2016-12-0814Article10.3390/fluids1040041412311-55212016-12-08doi: 10.3390/fluids1040041Biliana BidinD. Rees<![CDATA[Fluids, Vol. 1, Pages 40: Fundamental Rheology of Disperse Systems Based on Single-Particle Mechanics]]>
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A comprehensive review of the fundamental rheology of dilute disperse systems is presented. The exact rheological constitutive equations based on rigorous single-particle mechanics are discussed for a variety of disperse systems. The different types of inclusions (disperse phase) considered are: rigid-solid spherical particles with and without electric charge, rigid-porous spherical particles, non-rigid (soft) solid particles, liquid droplets with and without surfactant, bubbles with and without surfactant, capsules, core-shell particles, non-spherical solid particles, and ferromagnetic spherical and non-spherical particles. In general, the state of the art is good in terms of the theoretical development. However, more experimental work is needed to verify the theoretical models and to determine their range of validity. This is especially true for dispersions of porous particles, capsules, core-shell particles, and magnetic particles. The main limitation of the existing theoretical developments on the rheology of disperse systems is that the matrix fluid is generally assumed to be Newtonian in nature. Rigorous theoretical models for the rheology of disperse systems consisting of non-Newtonian fluid as the matrix phase are generally lacking, especially at arbitrary flow strengths.Fluids2016-12-0714Review10.3390/fluids1040040402311-55212016-12-07doi: 10.3390/fluids1040040Rajinder Pal<![CDATA[Fluids, Vol. 1, Pages 39: The Formation of Counter-Rotating Vortex Pair and the Nature of Liftoff-Reattachment in Film-Cooling Flow]]>
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Traditionally, the formation of the Counter-Rotating Vortex Pair (CRVP) has been attributed to three main sources: the jet-mainstream shear layer where the jet meets with the mainstream flow right outside the pipe, the in-tube boundary layer developing along the pipe wall, and the in-tube vortices associated with the tube inlet vorticity; whereas the liftoff-reattachment phenomenon occurring in the main flow along the plate right downstream of the jet has been associated with the jet flow trajectory. The jet-mainstream shear layer has also been demonstrated to be the dominant source of CRVP formation, whereby the shear layer disintegrates into vortex rings that deform as the jet convects downstream, becoming a pair of CRVPs flowing within the jet and eventually turning into the main flow direction. These traditional findings are assessed qualitatively and quantitatively for film-cooling flow in gas turbines by simulating numerically the flow and evaluating the extent to which the traditional flow phenomena are taking place particularly for CRVP and for flow liftoff-reattachment. To this end, three flow simulation cases are used; they are referred to as 1—the baseline case; 2—the free-slip in-tube wall case (FSIT); and 3—the unsteady flow case. The baseline case is a typical film-cooling case. The FSIT case is used to assess the in-tube boundary layer. Cases 1 and 2 are simulated using the Reynolds-averaged Navier-Stokes equations (RANS), whereas Case 3 solves a Detached Eddy Simulation (DES) model. It is concluded that decreasing the strength of the CRVP, which is the case for e.g., shaped holes, provides high cooling performance, and the liftoff-reattachment phenomenon was thus found to be strongly influenced by the entrainment caused by the CRVP, rather than the jet flow trajectory. These interpretations of the flow physics that are more relevant to gas turbine cooling flow are new and provide a physics-based guideline for designing new film-cooling schemes.Fluids2016-12-0214Article10.3390/fluids1040039392311-55212016-12-02doi: 10.3390/fluids1040039Hao LiWahid GhalyIbrahim Hassan<![CDATA[Fluids, Vol. 1, Pages 38: Modeling the Link between Left Ventricular Flow and Thromboembolic Risk Using Lagrangian Coherent Structures]]>
http://www.mdpi.com/2311-5521/1/4/38
A thrombus is a blood clot that forms on a surface, and can grow and detach, presenting a high risk for stroke and pulmonary embolism. This risk increases with blood-contacting medical devices, due to the immunological response to foreign surfaces and altered flow patterns that activate the blood and promote thromboembolism (TE). Abnormal blood transport, including vortex behavior and regional stasis, can be assessed from Lagrangian Coherent Structures (LCS). LCS are flow structures that bound transport within a flow field and divide the flow into regions with maximally attracting/repelling surfaces that maximize local shear. LCS can be identified from finite time Lyapunov exponent (FTLE) fields, which are computed from velocity field data. In this study, the goal was to use FTLE analysis to evaluate LCS in the left ventricle (LV) using velocity data obtained from flow visualization of a mock circulatory loop. A model of dilated cardiomyopathy (DCM) was used to investigate the effect of left ventricular assist device (LVAD) support on diastolic filling and transport in the LV. A small thrombus in the left ventricular outflow tract was also considered using data from a corresponding LV model. The DCM LV exhibited a direct flow of 0.8 L/cardiac cycle, which was tripled during LVAD support Delayed ejection flow was doubled, further illustrating the impact of LVAD support on blood transport. An examination of the attracting LCS ridges during diastolic filling showed that the increase is due primarily to augmentation of A wave inflow, which is associated with increased vortex circulation, kinetic energy and Forward FTLE. The introduction of a small thrombus in the left ventricular outflow tract (LVOT) of the LV had a minimal effect on diastolic inflow, but obstructed systolic outflow leading to decreased transport compared with the unobstructed LVOT geometry. Localized FTLE in the LVOT increased dramatically with the small thrombus model, which reflects greater recirculation distal to the thrombus location. The combination of the thrombus and the LVAD increased stasis distal to the thrombus, increasing the likelihood of recurring coagulation during Series flow conditions. The extension of the results of the previous studies with this analysis provides a more sensitive indicator of TE risk than the Eulerian velocity values do, and may provide an important tool for evaluating medical device design, surgical implantation, and treatment options.Fluids2016-11-2214Article10.3390/fluids1040038382311-55212016-11-22doi: 10.3390/fluids1040038Karen May-NewmanVi VuBrian Herold<![CDATA[Fluids, Vol. 1, Pages 37: Unconfined Unsteady Laminar Flow of a Power-Law Fluid across a Square Cylinder]]>
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The flow of a non-Newtonian, power-law fluid, directed normally to a horizontal cylinder with square cross-section (two-dimensional flow) is considered in the present paper. The problem is investigated numerically with a very large calculation domain in order that the flow could be considered unconfined. The investigation covers the power-law index from 0.1 up to 2 and the Reynolds number ranges from 60 to 160. Over this range of Reynolds numbers the flow is unsteady. It is found that the drag coefficient and the Strouhal number are higher in a confined flow compared to those of an unconfined flow. In addition some flow characteristics are lost in a confined flow. Complete results for the drag coefficient and Strouhal number in the entire shear-thinning and shear-thickening region have been produced. In shear-thinning fluids chaotic structures exist which diminish at higher values of power-law index. This study represents the first investigation of unsteady, non-Newtonian power-law flow past a square cylinder in an unconfined field.Fluids2016-11-1814Article10.3390/fluids1040037372311-55212016-11-18doi: 10.3390/fluids1040037Asterios Pantokratoras<![CDATA[Fluids, Vol. 1, Pages 36: Hydrodynamics of Highly Viscous Flow past a Compound Particle: Analytical Solution]]>
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To investigate the translation of a compound particle in a highly viscous, incompressible fluid, we carry out an analytic study on flow past a fixed spherical compound particle. The spherical object is considered to have a rigid kernel covered with a fluid coating. The fluid within the coating has a different viscosity from that of the surrounding fluid and is immiscible with the surrounding fluid. The inertia effect is negligible for flows both inside the coating and outside the object. Thus, flows are in the Stokes regime. Taking advantage of the symmetry properties, we reduce the problem in two dimensions and derive the explicit formulae of the stream function in the polar coordinates. The no-slip boundary condition for the rigid kernel and the no interfacial mass transfer and force equilibrium conditions at fluid interfaces are considered. Two extreme cases: the uniform flow past a sphere and the uniform flow past a fluid drop, are reviewed. Then, for the fluid coating the spherical object, we derive the stream functions and investigate the flow field by the contour plots of stream functions. Contours of stream functions show circulation within the fluid coating. Additionally, we compare the drag and the terminal velocity of the object with a rigid sphere or a fluid droplet. Moreover, the extended results regarding the analytical solution for a compound particle with a rigid kernel and multiple layers of fluid coating are reported.Fluids2016-11-1214Article10.3390/fluids1040036362311-55212016-11-12doi: 10.3390/fluids1040036Longhua Zhao<![CDATA[Fluids, Vol. 1, Pages 35: Laser-Induced Motion of a Nanofluid in a Micro-Channel]]>
http://www.mdpi.com/2311-5521/1/4/35
Since a photon carries both energy and momentum, when it interacts with a particle, photon-particle energy and momentum transfer occur, resulting in mechanical forces acting on the particle. In this paper we report our theoretical study on the use of a laser beam to manipulate and control the flow of nanofluids in a micro-channel. We calculate the velocity induced by a laser beam for TiO2, Fe2O3, Al2O3 MgO, and SiO2 nanoparticles with water as the base fluid. The particle diameter is 50 nm and the laser beam is a 4 W continuous beam of 6 mm diameter and 532 nm wavelength. The results indicate that, as the particle moves, a significant volume of the surrounding water (up to about 8 particle diameters away from the particle surface) is disturbed and dragged along with the moving particle. The results also show the effect of the particle refractive index on the particle velocity and the induced volume flow rate. The velocity and the volume flowrate induced by the TiO2 nanoparticle (refractive index n = 2.82) are about 0.552 mm/s and 9.86 fL, respectively, while those induced by SiO2 (n = 1.46) are only about 7.569 μm/s and 0.135, respectively.Fluids2016-10-2614Article10.3390/fluids1040035352311-55212016-10-26doi: 10.3390/fluids1040035Tran PhuocMehrdad MassoudiPing Wang<![CDATA[Fluids, Vol. 1, Pages 34: The Effects of Mesoscale Ocean–Atmosphere Coupling on the Quasigeostrophic Double Gyre]]>
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We investigate the effects of sea surface temperature (SST)-dependent wind stress on the wind-driven quasigeostrophic (QG) double gyre. The main effects are to reduce the strength of the circulation and to shift the inter-gyre jet to the south. The SST front across the inter-gyre jet induces a zonal wind stress anomaly over the jet that accelerates the southern flank of the jet and decelerates the northern flank. This local wind stress anomaly causes the jet to shift southwards. Shifting the jet south, away from the peak wind stress, reduces the net power input to the ocean circulation. Allowing the wind stress to depend on the difference between the atmospheric and oceanic velocity also reduces the net wind power input, and has a larger impact than SST dependence. When wind stress depends only on SST, the impact on the circulation is stronger than when wind stress depends on both SST and ocean surface velocity. Ocean surface velocity dependence leads to direct extraction of mesoscale energy by the winds. In contrast, SST dependence leads to injection (extraction) of mesoscale energy in the subtropical (subpolar) gyres, with almost complete cancellation because of the symmetric wind field.Fluids2016-10-2114Article10.3390/fluids1040034342311-55212016-10-21doi: 10.3390/fluids1040034Ian GroomsLouis-Philippe Nadeau<![CDATA[Fluids, Vol. 1, Pages 33: Estimating Eulerian Energy Spectra from Drifters]]>
http://www.mdpi.com/2311-5521/1/4/33
The relations between the kinetic energy spectrum and the second-order longitudinal structure function for 2D non-divergent flow are derived, and several examples are considered. The transform from spectrum to structure function is illustrated using idealized power-law spectra of turbulent inertial ranges. The results illustrate how the structure function integrates contributions across wavenumber, which can obscure the dependencies when the inertial ranges are of finite extent. The transform is also applied to the kinetic energy spectrum of Nastrom and Gage (1985), derived from aircraft data in the upper troposphere; the resulting structure function agrees well with that of Lindborg (1999), calculated with the same data. The transform from structure function to spectrum is then tested with data from 2D turbulence simulations. When applied to the (Eulerian) structure function obtained from the transform of the spectrum, the result closely resembles the original spectrum, except at the largest wavenumbers. The deviation at large wavenumbers occurs because the transform involves a filter function which magnifies contributions from large separations. The results are noticeably worse when applied to the structure function obtained from pairs of particles in the flow, as this is usually noisy at large separations. Fitting the structure function to a polynomial improves the resulting spectrum, but not sufficiently to distinguish the correct inertial range dependencies. Furthermore, the transform of steep (non-local) spectra is largely unsuccessful. Thus, it appears that with Lagrangian data, it is probably preferable to focus on structure functions, despite their shortcomings.Fluids2016-10-1514Article10.3390/fluids1040033332311-55212016-10-15doi: 10.3390/fluids1040033J. LaCasce<![CDATA[Fluids, Vol. 1, Pages 32: Neutrality Versus Materiality: A Thermodynamic Theory of Neutral Surfaces]]>
http://www.mdpi.com/2311-5521/1/4/32
In this paper, a theory for constructing quasi-neutral density variables γ directly in thermodynamic space is formulated, which is based on minimising the absolute value of a purely thermodynamic quantity J n . Physically, J n has a dual dynamic/thermodynamic interpretation as the quantity controlling the energy cost of adiabatic and isohaline parcel exchanges on material surfaces, as well as the dependence of in-situ density on spiciness, in a description of water masses based on γ, spiciness and pressure. Mathematically, minimising | J n | in thermodynamic space is showed to be equivalent to maximising neutrality in physical space. The physics of epineutral dispersion is also reviewed and discussed. It is argued, in particular, that epineutral dispersion is best understood as the aggregate effect of many individual non-neutral stirring events (being understood here as adiabatic and isohaline events with non-zero buoyancy), so that it is only the net displacement aggregated over many events that is approximately neutral. This new view resolves an apparent paradox between the focus in neutral density theory on zero-buoyancy motions and the overwhelming evidence that lateral dispersion in the ocean is primarily caused by non-zero buoyancy processes such as tides, residual currents and sheared internal waves. The efficiency by which a physical process contributes to lateral dispersion can be characterised by its energy signature, with those processes releasing available potential energy (negative energy cost) being more efficient than purely neutral processes with zero energy cost. The latter mechanism occurs in the wedge of instability, and its source of energy is the coupling between baroclinicity, thermobaricity, and density compensated temperature/salinity anomalies. Such a mechanism, which can only exist in a salty ocean, is speculated to be important for dissipating spiciness anomalies and neutral helicity. The paper also discusses potential conceptual difficulties with the use of neutral rotated diffusion tensors in numerical ocean models, as well as with the construction of neutral density variables in physical space. It also emphasises the irreducible character of thermobaric forces in the ocean. These are argued to be the cause for adiabatic thermobaric dianeutral dispersion, and to forbid the existence of density surfaces along which fluid parcels can be exchanged without experiencing buoyancy forces, in contrast to what is assumed in the theory of neutral surfaces.Fluids2016-09-2814Article10.3390/fluids1040032322311-55212016-09-28doi: 10.3390/fluids1040032Rémi Tailleux<![CDATA[Fluids, Vol. 1, Pages 31: Boundary Layer Flow and Heat Transfer of FMWCNT/Water Nanofluids over a Flat Plate]]>
http://www.mdpi.com/2311-5521/1/4/31
In the present study, the heat transfer and flow of water/FMWCNT (functionalized multi-walled carbon nanotube) nanofluids over a flat plate was investigated using a finite volume method. Simulations were performed for velocity ranging from 0.17 mm/s to 1.7 mm/s under laminar regime and nanotube concentrations up to 0.2%. The 2-D governing equations were solved using an in-house FORTRAN code. For a specific free stream velocity, the presented results showed that increasing the weight percentage of nanotubes increased the Nusselt number. However, an increase in the solid weight percentage had a negligible effect on the wall shear stress. The results also indicated that increasing the free stream velocity for all cases leads to thinner boundary layer thickness, while increasing the FMWCNT concentration causes an increase in the boundary layer thickness.Fluids2016-09-2614Article10.3390/fluids1040031312311-55212016-09-26doi: 10.3390/fluids1040031Mohammad SafaeiGoodarz AhmadiMohammad GoodarziAmin KamyarS. Kazi<![CDATA[Fluids, Vol. 1, Pages 30: Meridional and Zonal Wavenumber Dependence in Tracer Flux in Rossby Waves]]>
http://www.mdpi.com/2311-5521/1/3/30
Eddy-driven jets are of importance in the ocean and atmosphere, and to a first approximation are governed by Rossby wave dynamics. This study addresses the time-dependent flux of fluid and a passive tracer between such a jet and an adjacent eddy, with specific regard to determining zonal and meridional wavenumber dependence. The flux amplitude in wavenumber space is obtained, which is easily computable for a given jet geometry, speed and latitude, and which provides instant information on the wavenumbers of the Rossby waves which maximize the flux. This new tool enables the quick determination of which modes are most influential in imparting fluid exchange, which in the long term will homogenize the tracer concentration between the eddy and the jet. The results are validated by computing backward- and forward-time finite-time Lyapunov exponent fields, and also stable and unstable manifolds; the intermingling of these entities defines the region of chaotic transport between the eddy and the jet. The relationship of all of these to the time-varying transport flux between the eddy and the jet is carefully elucidated. The flux quantification presented here works for general time-dependence, whether or not lobes (intersection regions between stable and unstable manifolds) are present in the mixing region, and is therefore also easily computable for wave packets consisting of infinitely many wavenumbers.Fluids2016-09-0613Article10.3390/fluids1030030302311-55212016-09-06doi: 10.3390/fluids1030030Sanjeeva Balasuriya<![CDATA[Fluids, Vol. 1, Pages 28: Eddy Backscatter and Counter-Rotating Gyre Anomalies of Midlatitude Ocean Dynamics]]>
http://www.mdpi.com/2311-5521/1/3/28
This work concerns how two competing mechanisms—eddy backscatter and counter-rotating gyre anomalies—influence the midlatitude ocean dynamics, as described by the eddy-resolving quasi-geostrophic (QG) model of wind-driven gyres. We analyzed dynamical balances and effects of different eddy forcing components, as well as their dependencies on increasing vertical resolution and decreasing eddy viscosity and found that the eastward jet and its adjacent recirculation zones are maintained mostly by the eddy forcing via the eddy backscatter mechanism, whereas the time-mean eddy-forcing component plays not only direct jet-supporting but also indirect jet-inhibiting role. The latter is achieved by inducing zonally elongated anticyclonic/cyclonic Counter-rotating Gyre Anomaly (CGA) in the subpolar/subtropical gyre. The indirect effect of CGAs on the eastward jet is found to be moderate relative to the dominant eddy backscatter mechanism. We also found that the higher the vertical baroclinic mode, the weaker its backscatter role and the stronger its CGA-driving role. Although the barotropic and first baroclinic modes are the most efficient ones in maintaining the backscatter, the higher, up to the fifth baroclinic modes also have significant but reverse impact that reduces the backscatter.Fluids2016-09-0213Article10.3390/fluids1030028282311-55212016-09-02doi: 10.3390/fluids1030028Igor ShevchenkoPavel Berloff<![CDATA[Fluids, Vol. 1, Pages 29: Baseline Model for Bubbly Flows: Simulation of Monodisperse Flow in Pipes of Different Diameters]]>
http://www.mdpi.com/2311-5521/1/3/29
CFD simulations of the multiphase flow in technical equipment are feasible within the framework of interpenetrating continua, the so-called two-fluid modelling. Predictions with multiphase CFD are only possible if a fixed set of closures for the interfacial exchange terms is available that has been validated for a wide range of flow conditions and can therefore reliably be used also for unknown flow problems. To this end, a baseline model, which is applicable for adiabatic bubbly flow, has been specified recently and has been implemented in OpenFOAM. In this work, we compare simulation results obtained using the baseline model with three different sets of experimental data for dispersed gas-liquid pipe flow. Air and water under similar flow conditions have been used in the different experiments, so that the main difference between the experiments is the variation of the pipe diameter from 25 mm to 200 mm. Gas fraction and liquid velocity are reasonably well reproduced, in particular in the bulk of the flow. Discrepancies can be seen in the turbulent kinetic energy, the gas velocity and in the wall peaks of the gas fraction. These can partly be explained by the simplified modelling, but to some extent must be attributed to uncertainty in the experimental data. The need for improved near-wall modelling, turbulence modelling and modelling of the bubble size distribution is highlighted.Fluids2016-09-0113Article10.3390/fluids1030029292311-55212016-09-01doi: 10.3390/fluids1030029Sebastian KriebitzschRoland Rzehak<![CDATA[Fluids, Vol. 1, Pages 27: Scalar Flux Kinematics]]>
http://www.mdpi.com/2311-5521/1/3/27
The first portion of this paper contains an overview of recent progress in the development of dynamical-systems-based methods for the computation of Lagrangian transport processes in physical oceanography. We review the considerable progress made in the computation and interpretation of key material features such as eddy boundaries, and stable and unstable manifolds (or their finite-time approximations). Modern challenges to the Lagrangian approach include the need to deal with the complexity of the ocean submesoscale and the difficulty in computing fluxes of properties other than volume. We suggest a new approach that reduces complexity through time filtering and that directly addresses non-material, residual scalar fluxes. The approach is “semi-Lagrangian” insofar as it contemplates trajectories of a velocity field related to a residual scalar flux, usually not the fluid velocity. Two examples are explored, the first coming from a canonical example of viscous adjustment along a flat plate and the second from a numerical simulation of a turbulent Antarctic Circumpolar Current in an idealized geometry. Each example concentrates on the transport of dynamically relevant scalars, and the second illustrates how substantial material exchange across a baroclinically unstable jet coexists with zero residual buoyancy flux.Fluids2016-08-2513Article10.3390/fluids1030027272311-55212016-08-25doi: 10.3390/fluids1030027Larry PrattRoy BarkanIrina Rypina<![CDATA[Fluids, Vol. 1, Pages 25: Diapycnal Velocity in the Double-Diffusive Thermocline]]>
http://www.mdpi.com/2311-5521/1/3/25
A series of large-scale numerical simulations is presented, which incorporate parameterizations of vertical mixing of temperature and salinity by double-diffusion and by small-scale turbulence. These simulations reveal the tendency of double-diffusion to constrain diapycnal volume transport, both upward and downward. For comparable values of mixing coefficients, the average diapycnal velocity in the double-diffusive thermocline is much less than in the corresponding turbulent regime. The insulating effect of double-diffusion is rationalized using two theoretical models. The first argument is based on the assumed vertical advective-diffusive balance. The second theory uses the Rhines and Young technique to evaluate the net diapycnal transport across regions bounded by closed streamlines at a given density surface. The numerical simulations and associated analytical arguments in this study underscore fundamental differences between double-diffusive mixing and mechanically generated small-scale turbulence. When both double-diffusion and turbulence are taken into account, we find that the constraints on diapycnal velocity loosen (tighten) with the increase (decrease) of the fraction of the overall mixing attributed to turbulence. The range of diapycnal velocities that could be realized in doubly-diffusive fluids is determined by the variation in the heat/salt flux ratio. We hypothesize that the unique ability of double-diffusive mixing to actively control diapycnal volume transport may have significant ramifications for the structure and dynamics of thermohaline circulation in the ocean.Fluids2016-08-2513Article10.3390/fluids1030025252311-55212016-08-25doi: 10.3390/fluids1030025Timour RadkoErick Edwards<![CDATA[Fluids, Vol. 1, Pages 26: Stabilization of Isolated Vortices in a Rotating Stratified Fluid]]>
http://www.mdpi.com/2311-5521/1/3/26
The key element of Geophysical Fluid Dynamics—reorganization of potential vorticity (PV) by nonlinear processes—is studied numerically for isolated vortices in a uniform environment. Many theoretical studies and laboratory experiments suggest that axisymmetric vortices with a Gaussian shape are not able to remain circular owing to the growth of small perturbations in the typical parameter range of abundant long-lived vortices. An example of vortex destabilization and the eventual formation of more intense self-propagating structures is presented using a 3D rotating stratified Boussinesq numerical model. The peak vorticity growth found during the stages of strong elongation and fragmentation is related to the transfer of available potential energy into kinetic energy of vortices. In order to develop a theoretical model of a stable circular vortex with a small Burger number compatible with observations, we suggest a simple stabilizing procedure involving the modification of peripheral PV gradients. The results have important implications for better understanding of real-ocean eddies.Fluids2016-08-2413Article10.3390/fluids1030026262311-55212016-08-24doi: 10.3390/fluids1030026Georgi SutyrinTimour Radko<![CDATA[Fluids, Vol. 1, Pages 24: Nonlinear Convection in a Partitioned Porous Layer]]>
http://www.mdpi.com/2311-5521/1/3/24
Convection in a partitioned porous layer is considered where the thin partition causes a mechanical isolation of the two identical sublayers from one another, but heat may neveretheless conduct freely. An unsteady solver that employs the multigrid method is employed to determine steady-state strongly nonlinear for values of the Darcy–Rayleigh number up to eight times its critical value. The predictions of linear stability theory are confirmed and the accuracy of the computations are carefully monitored and controlled. It is found that the wavenumber for which the maximum rate of heat transfer is attained at any chosen value of the Darcy–Rayleigh number, Ra increases quite strongly from roughly 2.33 at onset to 6.25 when Ra = 200 . It is also found that convection generally cannot take place with wavenumbers which are close to the left-hand branch of the neutral stability curve because nonlinear interactions favour modes selected from higher harmonics.Fluids2016-08-2313Article10.3390/fluids1030024242311-55212016-08-23doi: 10.3390/fluids1030024D. Rees<![CDATA[Fluids, Vol. 1, Pages 23: The Hydrodynamic Nonlinear Schrödinger Equation: Space and Time]]>
http://www.mdpi.com/2311-5521/1/3/23
The nonlinear Schrödinger equation (NLS) is a canonical evolution equation, which describes the dynamics of weakly nonlinear wave packets in time and space in a wide range of physical media, such as nonlinear optics, cold gases, plasmas and hydrodynamics. Due to its integrability, the NLS provides families of exact solutions describing the dynamics of localised structures which can be observed experimentally in applicable nonlinear and dispersive media of interest. Depending on the co-ordinate of wave propagation, it is known that the NLS can be either expressed as a space- or time-evolution equation. Here, we discuss and examine in detail the limitation of the first-order asymptotic equivalence between these forms of the water wave NLS. In particular, we show that the the equivalence fails for specific periodic solutions. We will also emphasise the impact of the studies on application in geophysics and ocean engineering. We expect the results to stimulate similar studies for higher-order weakly nonlinear evolution equations and motivate numerical as well as experimental studies in nonlinear dispersive media.Fluids2016-07-1913Article10.3390/fluids1030023232311-55212016-07-19doi: 10.3390/fluids1030023Amin ChabchoubRoger Grimshaw<![CDATA[Fluids, Vol. 1, Pages 22: Dynamically Consistent Parameterization of Mesoscale Eddies—Part II: Eddy Fluxes and Diffusivity from Transient Impulses]]>
http://www.mdpi.com/2311-5521/1/3/22
This work continues development of the framework for dynamically consistent parameterization of mesoscale eddy effects in non-eddy-resolving ocean circulation models. Here, we refine and extend the previous results obtained for the double gyres and aim to account for the eddy backscatter mechanism that maintains eastward jet extension of the western boundary currents. We start by overcoming the local homogeneity assumption and by taking into account full large-scale circulation. We achieve this by considering linearized-dynamic responses to finite-time transient impulses. Feedback from these impulses on the large-scale circulation are referred to as footprints. We find that the local homogeneity assumption yields only quantitative errors in most of the gyres but breaks down in the eastward jet region, which is characterized by the most significant eddy effects. The approach taken provides new insights into the eddy/mean interactions and framework for parameterization of unresolved eddy effects. Footprints provide us with maps of potential vorticity anomalies expected to be induced by transient eddy forcing. This information is used to calculate the equivalent eddy potential vorticity fluxes and their divergences that partition the double-gyre circulation into distinct geographical regions with specific eddy effects. In particular, this allows approximation of the real eddy effects that maintain the eastward jet extension of the western boundary currents and its adjacent recirculation zones. Next, from footprints and their equivalent eddy fluxes and from underlying large-scale flow gradients, we calculate spatially inhomogeneous and anisotropic eddy diffusivity tensor. Its properties suggest that imposing parameterized source terms, that is, equivalent eddy flux divergences, is a better parameterization strategy than implementation of the eddy diffusion.Fluids2016-06-3013Article10.3390/fluids1030022222311-55212016-06-30doi: 10.3390/fluids1030022Pavel Berloff<![CDATA[Fluids, Vol. 1, Pages 20: Heat Transfer and Pressure Drop in Fully Developed Turbulent Flows of Graphene Nanoplatelets–Silver/Water Nanofluids]]>
http://www.mdpi.com/2311-5521/1/3/20
This study examined the heat transfer coefficient, friction loss, pressure drop and pumping power needed for the use of nanofluid coolants made of a mixture of suspension of graphene nanoplatelets–silver in water in a rectangular duct. A series of calculations were performed for the coolant volume flow rate in the range of 5000 ≤ Re ≤ 15,000 under a fully developed turbulent flow regime and different nanosheet concentrations up to 0.1 weight percent. The thermo-physical properties of the nanofluids were extracted from the recent experimental work of Yarmand et al. (Graphene nanoplatelets-silver hybrid nanofluids for enhanced heat transfer. Energy Convers. Manag. 2015, 100, 419–428). The presented results indicated that the heat transfer characteristics of the nanofluid coolants improved with the increase in nanosheet concentration as well as the increase in the coolant Reynolds number. However, there was a penalty in the duct pressure drop and an increase in the required pumping power. In summary, the closed conduit heat transfer performance can be improved with the use of appropriate nanofluids based on graphene nanoplatelets–silver/water as a working fluid.Fluids2016-06-2913Article10.3390/fluids1030020202311-55212016-06-29doi: 10.3390/fluids1030020Mohammad SafaeiGoodarz AhmadiMohammad GoodarziMostafa Safdari ShadlooHamid GoshayeshiMahidzal Dahari<![CDATA[Fluids, Vol. 1, Pages 21: A Numerical Study on Curvilinear Free Surface Flows in Venturi Flumes]]>
http://www.mdpi.com/2311-5521/1/3/21
Venturi flumes are one of the most important flow-measuring structures commonly investigated by physical model tests in the past. The solutions to the Venturi flume flow problems were generally found on the basis of empirical equations arising from such tests. Nonetheless, the overall accuracy and range of applicability of these equations rely on the scope of the tests. Additionally, the hydraulic characteristics of free flows in short-throated flumes cannot be modelled by the conventional hydrostatic pressure approaches. In this study, a one-dimensional model, which incorporates a higher-order dynamic pressure correction for the effects of the sidewalls and streamline vertical curvatures, is applied to simulate such flows and elucidate relevant flow features. The model equations are discretised and solved using the finite difference scheme. The computed results for free surface profiles, pressure distributions at different sections and discharge characteristics are compared to measured data. The computational results exhibit good agreement with measured data. Overall, it is shown that the developed model is capable of accurately simulating the curvilinear flows in short-throated flumes with rounded transition and bottom humps. The results also highlight the detailed dependence of the discharge characteristics of the critical-flow flumes under free flow conditions on the curvature of the streamlines.Fluids2016-06-2913Article10.3390/fluids1030021212311-55212016-06-29doi: 10.3390/fluids1030021Yebegaeshet Zerihun<![CDATA[Fluids, Vol. 1, Pages 19: On Thermomechanics of a Nonlinear Heat Conducting Suspension]]>
http://www.mdpi.com/2311-5521/1/2/19
In this short paper, we discuss and provide constitutive relations for the stress tensor and the heat flux vector for a nonlinear density-gradient dependent (Korteweg-type) fluid. Specifically, we attempt to present a unified thermo-mechanical approach to the two models given in papers of Massoudi (International Journal of Non-Linear Mechanics, 2001, 36(1), pp. 25–37.) and Massoudi (Mathematical Methods in the Applied Sciences, 2006, 29(13), pp. 1599–1613.) where the entropy law is used and restrictions are also obtained on the constitutive parameters. In most thermomechanical studies of nonlinear fluids using the entropy law, the stress tensor is assumed to be nonlinear and the heat flux vector still has the form of the Fourier type, i.e., it is proportional to the temperature gradient. In this paper, we use a generalized (nonlinear) form for the heat flux vector. When our model is linearized we obtain constraints, due to the entropy inequality, which are in agreement with the earlier results.Fluids2016-06-1812Article10.3390/fluids1020019192311-55212016-06-18doi: 10.3390/fluids1020019Mehrdad MassoudiA. Kirwan<![CDATA[Fluids, Vol. 1, Pages 18: Rendering the Navier–Stokes Equations for a Compressible Fluid into the Schrödinger Equation for Quantum Mechanics]]>
http://www.mdpi.com/2311-5521/1/2/18
The mass and momentum transfer phenomena in a compressible fluid represented by the Navier–Stokes equations are shown to convert into the Schrödinger equation for quantum mechanics. The complete Navier–Stokes equations render into an extended generalized version of Schrödinger equation. These results complement the Madelung’s (Zeitschrift für Physik 40 (3–4), pp. 322–326, 1926–1927) derivations that show how Schrödinger’s equation in quantum mechanics can be converted into the Euler equations for irrotational compressible flow. The theoretical results presented here join the classical Madelung paper to suggest the possibility that quantum effects at sub-atomic levels deal with a compressible fluid susceptible to wave propagation, rather than a particle. The link between such a fluid and the “quantum particle” is under current investigation.Fluids2016-06-1312Article10.3390/fluids1020018182311-55212016-06-13doi: 10.3390/fluids1020018Peter Vadasz<![CDATA[Fluids, Vol. 1, Pages 16: Mathematical Modeling and Computer Simulations of Nanofluid Flow with Applications to Cooling and Lubrication]]>
http://www.mdpi.com/2311-5521/1/2/16
There is a growing range of applications of nanoparticle-suspension flows with or without heat transfer. Examples include enhanced cooling of microsystems with low volume-fractions of nanoparticles in liquids, improved tribological performance with lubricants seeded with nanoparticles, optimal nanodrug delivery in the pulmonary as well as the vascular systems to combat cancer, and spray-coating using plasma-jets with seeded nanoparticles. In order to implement theories that explain experimental evidence of nanoparticle-fluid dynamics and predict numerically optimum system performance, a description of the basic math modeling and computer simulation aspects is necessary. Thus, in this review article, the focus is on the fundamental understanding of the physics of nanofluid flow and heat transfer with summaries of microchannel-flow applications related to cooling and lubrication.Fluids2016-05-2712Review10.3390/fluids1020016162311-55212016-05-27doi: 10.3390/fluids1020016Clement KleinstreuerZelin Xu<![CDATA[Fluids, Vol. 1, Pages 17: A Theoretical Model of Long Rossby Waves in the Southern Ocean and Their Interaction with Bottom Topography]]>
http://www.mdpi.com/2311-5521/1/2/17
An analytical model of long Rossby waves is developed for a continuously-stratified, planetary geostrophic ocean in the presence of arbitrary bottom topography under the assumption that the potential vorticity is a linear function of buoyancy. The remaining dynamics are controlled by equations for material conservation of buoyancy along the sea surface and the sea floor. The mean, steady-state surface circulation follows characteristics that are intermediate to f and f / H contours, where f is the Coriolis parameter and H is the ocean depth; for realistic stratification and weak bottom currents, these characteristics are mostly zonal with weak deflections over the major topographic features. Equations are derived for linear long Rossby waves about this mean state. These are qualitatively similar to the long Rossby wave equations for a two-layer ocean, linearised about a state of rest, except that the surface characteristics in the wave equation, which dominate the propagation, follow precisely the same path as the mean surface flow. In addition to this topographic steering, it is shown that a weighted integral of the Rossby propagation term vanishes over any area enclosed by an f / H contour, which has been shown in the two-layer model to lead to Rossby waves “jumping” across the f / H contour. Finally, a nonlinear Rossby wave equation is derived as a specialisation of the result previously obtained by Rick Salmon. This consists of intrinsic westward propagation at the classical long Rossby speed, modified to account for the finite ocean depth, and a Doppler shift by the depth-mean flow. The latter dominates within the Antarctic Circumpolar Current, consistent with observed eastward propagation of sea surface height anomalies.Fluids2016-05-2712Article10.3390/fluids1020017172311-55212016-05-27doi: 10.3390/fluids1020017David Marshall<![CDATA[Fluids, Vol. 1, Pages 15: Modeling the Viscoelastic Behavior of Amorphous Shape Memory Polymers at an Elevated Temperature]]>
http://www.mdpi.com/2311-5521/1/2/15
Shape memory polymers (SMPs) are soft active materials, their special property is the ability to hold a temporary shape and when exposed to a suitable trigger, they come back to their original shape. These external stimuli can be temperature, light or electro-magnetic fields. Amorphous SMPs are a class of thermally-activated SMPs that rely on glass transition to retain their temporary shape. Above the glass transition temperature (T &gt; Tg), (amorphous SMPs exhibit finite deformation and viscoelastic behavior. In this work we develop a model to capture the viscoelastic behavior of the amorphous SMPs at elevated temperatures. The model uses an approach that was initially developed to study non-Newtonian viscoelastic fluids. We accomplish this by developing a multi-branch model based on the theory of multiple natural configurations using the maximization of the rate dissipation to determine the evolution of the natural configurations. We apply our model to study several different deformations at an elevated temperature T = 130 °C and show that this approach is able to capture the viscoelastic behavior of these polymers. The predictions of the theory are then compared with experimental results.Fluids2016-05-1312Article10.3390/fluids1020015152311-55212016-05-13doi: 10.3390/fluids1020015Fangda CuiSwapnil MoonI. Rao<![CDATA[Fluids, Vol. 1, Pages 6: Natural Drag-Reducing Polymers: Discovery, Characterization and Potential Clinical Applications]]>
http://www.mdpi.com/2311-5521/1/2/6
About seven decades ago, it was discovered that special long-chain soluble polymers added to fluid at nanomolar concentrations significantly reduce resistance to turbulent flow (Toms effect). These so-called drag-reducing polymers (DRPs) do not affect resistance to laminar flow. While the flow parameters associated with the Toms effect do not occur in the cardiovascular system, many later studies demonstrated that intravenous injections of DRPs given to experimental animals produced significant hemodynamic effects, such as increasing tissue perfusion, suggesting potential clinical use of these polymers. Moreover, it was found that the specific viscoelastic properties of these polymers make them capable of modifying traffic of blood cells in microvessels and beneficially redistributing them in the blood capillary system—a phenomenon related to rheological properties of DRPs and not related to their specific chemistry. The domain of drag reducing polymers includes many organic and water-soluble, synthetic and natural long-chain molecules. The study presented here employed chemical and rheological methods, as well as macro and microfluidic tests, to characterize the DRP that we discovered in the Aloe vera plant, which was found to be a more powerful drag reducer and less fragile than many synthetic DRPs. The drag-reducing component of aloe gel was purified and chemically identified, which helped to standardize preparation and made this polymer a strong candidate for clinical use. Examples of successful testing of the aloe-derived DRP in animal models are described.Fluids2016-05-0612Article10.3390/fluids102000662311-55212016-05-06doi: 10.3390/fluids1020006Joie MarhefkaMarina Kameneva<![CDATA[Fluids, Vol. 1, Pages 14: Review of CFD Guidelines for Dispersion Modeling]]>
http://www.mdpi.com/2311-5521/1/2/14
This is the review of CFD (Computational Fluid Dynamics) guidelines for dispersion modeling in the USA, Japan and Germany. Most parts of this review are based on the short report of the special meeting on CFD Guidelines held at the International Symposium on Computational Wind Engineering (CWE2014), University of Hamburg, June 2014. The objective of this meeting was to introduce and discuss the action program to make worldwide guidelines of CFD gas-dispersion modeling. The following six gas-dispersion guidelines including Verification and Validation (V&amp;V) schemes are introduced by each author; (1) US CFD guidelines; (2) COST/ES1006; (3) German VDI (Verein Deutscher Ingenieure) guidelines; (4) Atomic Energy Society of Japan; (5) Japan Society of Atmospheric Environment; (6) Architectural Institute of Japan. All guidelines were summarized in the same format table shown in the main chapters in order to compare them with each other. In addition to the summary of guidelines, the overview of V&amp;V schemes and many guidelines of CFD modeling in the USA are explained.Fluids2016-05-0512Review10.3390/fluids1020014142311-55212016-05-05doi: 10.3390/fluids1020014Robert MeroneyRyohji OhbaBernd LeitlHiroaki KondoDavid GraweYoshihide Tominaga<![CDATA[Fluids, Vol. 1, Pages 13: Fofonoff Negative Modes]]>
http://www.mdpi.com/2311-5521/1/2/13
The classic solution of Fofonoff to the problem of free inertial flow in a closed basin is extended to the case where the potential vorticity, q, is linearly proportional to the streamfunction, with a negative definite constant, − K 2 . Such a relation arises naturally in the presence of an eastward flow, instead of Fofonoff’s westward zonal flow on the β plane. The resulting solutions can be wavelike if K 2 = β L 2 / U π 2 exceeds the critical value of 1 where U is the magnitude of the eastward flow and L is the characteristic meridional scale of the motion. Solutions are presented with various boundary conditions on the basin boundaries, and conditions for which the solutions suffer a resonance are also obtained. It is suggested that oceanic circulations with eastward flows naturally excite these Fofonoff negative modes. The possibility of resonance and instability adds additional physical complexity to the modes.Fluids2016-04-1512Article10.3390/fluids1020013132311-55212016-04-15doi: 10.3390/fluids1020013Joseph Pedlosky<![CDATA[Fluids, Vol. 1, Pages 12: Splash Dynamics of Paint on Dry, Wet, and Cooled Surfaces]]>
http://www.mdpi.com/2311-5521/1/2/12
In his classic study in 1908, A.M. Worthington gave a thorough account of splashes and their formation through visualization experiments. In more recent times, there has been renewed interest in this subject, and much of the underlying physics behind Worthington’s experiments has now been clarified. One specific set of such recent studies, which motivates this paper, concerns the fluid dynamics behind Jackson Pollock’s drip paintings. The physical processes and the mathematical structures hidden in his works have received serious attention and made the scientific pursuit of art a compelling area of exploration. Our current work explores the interaction of watercolors with watercolor paper. Specifically, we conduct experiments to analyze the settling patterns of droplets of watercolor paint on wet and frozen paper. Variations in paint viscosity, paper roughness, paper temperature, and the height of a released droplet are examined from time of impact, through its transient stages, until its final, dry state. Observable phenomena such as paint splashing, spreading, fingering, branching, rheological deposition, and fractal patterns are studied in detail and classified in terms of the control parameters.Fluids2016-04-1412Article10.3390/fluids1020012122311-55212016-04-14doi: 10.3390/fluids1020012David BaronHaiyan SuAshwin Vaidya<![CDATA[Fluids, Vol. 1, Pages 11: Modeling the Viscosity of Concentrated Nanoemulsions and Nanosuspensions]]>
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The modeling of the viscous behavior of nanoemulsions and nanosuspensions is discussed. The influences of the viscosity ratio, solvation and aggregation of nanodroplets and nanoparticles on the relative viscosity of nanofluids are considered. The relative viscosity of a nanofluid is strongly affected by solvation of nanoparticles. The scaling of the relative viscosity of nanoemulsions is successfully carried out using the volume fraction of the solvated nanodroplets. Four sets of experimental relative viscosity data of nanoemulsions consisting of different diameter nanodroplets (27.5 nm–205 nm) all collapse on a single unique curve when the data are scaled on the basis of the volume fraction of the solvated nanodroplets. A similar scaling is achieved using six sets of experimental relative viscosity data on nanosuspensions consisting of different diameter nanoparticles (29 nm–146 nm). A new modified version of the Oldroyd model is proposed to describe and predict the viscosity of nanofluids. The model takes into consideration the influences of the viscosity ratio, solvation and aggregation of nanoparticles/nanodroplets. The same model is applicable to both nanoemulsions and nanosuspensions as it includes the effect of the viscosity ratio (ratio of droplet viscosity to matrix viscosity) on the relative viscosity of nanofluids. More experimental work is needed on nanoemulsions to explore the effect of the viscosity ratio, especially at low values of the viscosity ratio.Fluids2016-04-1212Article10.3390/fluids1020011112311-55212016-04-12doi: 10.3390/fluids1020011Rajinder Pal<![CDATA[Fluids, Vol. 1, Pages 9: Semicompressible Ocean Thermodynamics and Boussinesq Energy Conservation]]>
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Equations more accurate than the Boussinesq set that still filter out sound were recently introduced. While these equations were shown to have a consistent potential energy, their thermodynamical behavior and associated implications were not fully analyzed. These shortcomings are remedied in the present note that argues both sets are fully consistent from a thermodynamic perspective. It is further argued that both sets remain computationally competitive with the Boussinesq set.Fluids2016-04-0812Article10.3390/fluids102000992311-55212016-04-08doi: 10.3390/fluids1020009William DewarJoseph SchoonoverTrevor McDougallRupert Klein<![CDATA[Fluids, Vol. 1, Pages 10: Investigation of Slot-Burner Aerodynamics with Recessed-Type Nozzle Geometry]]>
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The aerodynamics of fully turbulent jets supplied from rectangular slot-burners was modelled using the Reynolds Averaged Navier–Stokes (RANS) model. Three different turbulent models were considered, such as standard k-ε, RNG k-ε and Reynolds stress turbulence models. The recessed-type nozzle geometry was investigated to determine the effect of burner geometry on jet development. The slot-burner was based on physical models, which were designed to be representative of typical burner geometries found in tangentially-fired coal boilers. The study was validated against the physical models. The detailed flow field obtained from the simulations was used to explain the aerodynamic development of jets in such burners. It was found that the addition of a recess section to the nozzle geometry introduced significant changes to the flow due to complex pressure and mixing fields being set up inside the recess, which altered the jets once they exited into the open atmosphere.Fluids2016-04-0812Article10.3390/fluids1020010102311-55212016-04-08doi: 10.3390/fluids1020010Arafat BhuiyanMd. KarimJames HartPeter WittJamal Naser<![CDATA[Fluids, Vol. 1, Pages 5: On the Flows of Fluids Defined through Implicit Constitutive Relations between the Stress and the Symmetric Part of the Velocity Gradient]]>
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Though implicit constitutive relations have been in place for a long time, wherein the stress, the strain (or the symmetric part of the velocity gradient), and their time derivatives have been used to describe the response of viscoelastic and inelastic bodies, it is only recently purely algebraic relationships between the stress and the displacement gradient (or the velocity gradient) have been introduced to describe the response of non-linear fluids and solids. Such models can describe phenomena that the classical theory, wherein the stress is expressed explicitly in terms of kinematical variables, is incapable of describing, and they also present a sensible way to approach important practical problems, such as the flows of colloids and suspensions and the turbulent flows of fluids, and that of the fracture of solids. In this paper we review this new class of algebraic implicit constitutive relations that can be used to describe the response of fluids.Fluids2016-03-2412Article10.3390/fluids102000552311-55212016-03-24doi: 10.3390/fluids1020005Kumbakonam Rajagopal<![CDATA[Fluids, Vol. 1, Pages 4: Heat Transfer and Dissipation Effects in the Flow of a Drilling Fluid]]>
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In this paper we study the effects of dissipation in the Couette flow and heat transfer in a drilling fluid, and explore the effects of concentration and the shear-rate and temperature-dependent viscosity, along with a variable thermal conductivity. A brief discussion on the constitutive relations for the stress tensor, the diffusive particle flux vector, and the heat flux vector is presented. The one-dimensional forms of the governing equations are solved numerically and the results are presented through a parametric study by varying the dimensionless numbers.Fluids2016-03-1811Article10.3390/fluids101000442311-55212016-03-18doi: 10.3390/fluids1010004Wei-Tao WuMehrdad Massoudi<![CDATA[Fluids, Vol. 1, Pages 8: A Volume Averaging Theory for Convective Flow in a Nanofluid Saturated Metal Foam]]>
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A rigorous derivation of the macroscopic governing equations for convective flow in a nanofluid saturated metal foam has been conducted using the volume averaging theory originally developed for analyzing heat and fluid flow in porous media. The nanoparticle conservation equation at a pore scale based on the Buongiorno model has been integrated over a local control volume together with the equations of continuity, Navier–Stokes and energy conservation. The unknown terms resulting from the volume averaging procedure were modeled mathematically to obtain a closed set of volume averaged versions of the governing equations. This set of the volume averaged governing equations was analytically solved to find the velocity, temperature and nanoparticle distributions and heat transfer characteristics resulting from both thermal and nanoparticle mechanical dispersions in a nanofluid saturated metal foam. Eventually, the analysis revealed that an unconventionally high level of the heat transfer rate (about 80 times as high as the case of base fluid convection without a metal foam) can be attained by combination of metal foam and nanofluid.Fluids2016-03-0811Article10.3390/fluids101000882311-55212016-03-08doi: 10.3390/fluids1010008Wenhao ZhangWenhao LiChen YangAkira Nakayama<![CDATA[Fluids, Vol. 1, Pages 3: On Objectivity, Irreversibility and Non-Newtonian Fluids]]>
http://www.mdpi.com/2311-5521/1/1/3
Early progress in non-Newtonian fluid mechanics was facilitated by the emergence of two fundamental and complementary principles: objective constitutive characterizations and unambiguous identification of irreversible processes. Motivated by practical and economic concerns in recent years, this line of fluid research has expanded to include debris flows, slurries, biofluids and fluid-solid mixtures; i.e., complex nonlinear fluids with disparate flow properties. Phenomenological descriptions of these fluids now necessarily include strong nonlinear coupling between the fluxes of mass, energy and momentum. Here, I review these principles, illustrate how they constrain the constitutive equations for non-Newtonian fluids and demonstrate how they have impacted other areas of fluid research.Fluids2016-03-0111Article10.3390/fluids101000332311-55212016-03-01doi: 10.3390/fluids1010003A. Kirwan<![CDATA[Fluids, Vol. 1, Pages 7: Simulation of Individual Polymer Chains and Polymer Solutions with Smoothed Dissipative Particle Dynamics]]>
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In an earlier work (Litvinov et al., Phys.Rev.E 77, 066703 (2008)), a model for a polymer molecule in solution based on the smoothed dissipative particle dynamics method (SDPD) has been presented. In the present paper, we show that the model can be extended to three-dimensional situations and simulate effectively diluted and concentrated polymer solutions. For an isolated suspended polymer, calculated static and dynamic properties agree well with previous numerical studies and theoretical predictions based on the Zimm model. This implies that hydrodynamic interactions are fully developed and correctly reproduced under the current simulated conditions. Simulations of polymer solutions and melts are also performed using a reverse Poiseuille flow setup. The resulting steady rheological properties (viscosity, normal stress coefficients) are extracted from the simulations and the results are compared with the previous numerical studies, showing good results.Fluids2016-02-0611Article10.3390/fluids101000772311-55212016-02-06doi: 10.3390/fluids1010007Sergey LitvinovQingguang XieXiangyu HuNikolaus AdamsMarco Ellero<![CDATA[Fluids, Vol. 1, Pages 1: The Journal of Fluids: An International and Interdisciplinary Scientific Open Access Journal]]>
http://www.mdpi.com/2311-5521/1/1/1
The science of fluids started from early civilizations when mankind understood the nature of channel flow. Archimedes discovered the hydrodynamics of floating bodies in early 250 B.C. [...]Fluids2016-01-0411Editorial10.3390/fluids101000112311-55212016-01-04doi: 10.3390/fluids1010001Bekir Yilbas<![CDATA[Fluids, Vol. 1, Pages 2: A Simple Stochastic Parameterization for Reduced Models of Multiscale Dynamics]]>
http://www.mdpi.com/2311-5521/1/1/2
Multiscale dynamics are frequently present in real-world processes, such as the atmosphere-ocean and climate science. Because of time scale separation between a small set of slowly evolving variables and much larger set of rapidly changing variables, direct numerical simulations of such systems are difficult to carry out due to many dynamical variables and the need for an extremely small time discretization step to resolve fast dynamics. One of the common remedies for that is to approximate a multiscale dynamical systems by a closed approximate model for slow variables alone, which reduces the total effective dimension of the phase space of dynamics, as well as allows for a longer time discretization step. Recently, we developed a new method for constructing a deterministic reduced model of multiscale dynamics where coupling terms were parameterized via the Fluctuation-Dissipation theorem. In this work we further improve this previously developed method for deterministic reduced models of multiscale dynamics by introducing a new method for parameterizing slow-fast interactions through additive stochastic noise in a systematic fashion. For the two-scale Lorenz 96 system with linear coupling, we demonstrate that the new method is able to recover additional features of multiscale dynamics in a stochastically forced reduced model, which the previously developed deterministic method could not reproduce.Fluids2015-12-2411Article10.3390/fluids101000222311-55212015-12-24doi: 10.3390/fluids1010002Rafail Abramov