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, 384^2, 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.

]]>Fluids doi: 10.3390/fluids2020013

Authors: Amber McClung Gyaneshwar Tandon Jeffery Baur

The majority of aerospace structural composites use thermoset resins for their processing flexibility, temperature capability, and environmental durability. In this study, the recovery behavior of Veriflex-E, an epoxy-based, thermosetting, thermally-triggered shape memory polymer (SMP) resin, is investigated in glassy (25 °C) and rubbery (130 °C) states, as a function of shape memory cycles, and as a means to evaluate its potential as a resin for a shape memory composite. At 25 °C, Veriflex-E exhibits a promising high elastic modulus and a positive, nonlinear strain rate sensitivity in monotonic loading. At 130 °C, the strain rate sensitivity in monotonic loading decreases. Stress relaxation after storage in the deformed temporary state and subsequent shape recovery is of particular interest, a challenge to measure, and has not been widely reported for SMPs. The current experimental program measures the influence of strain rate changes in the 10−4–10−2 s−1 range on the stress relaxation response of the material, as well as on the strain recovery behavior at both 25 °C and 130 °C. As expected, the post-relaxation strain is larger with faster loading. Unexpectedly, the total strain recovered after shape memory cycling is more similar to the low temperature deformation. Overall, the results suggest that, while being influenced by both the loading rate and the test temperature, Veriflex-E is a promising candidate for a shape memory composite which could enable adaptive structures.

]]>Fluids doi: 10.3390/fluids2010011

Authors: John Elder Craig Simmons Hans-Jörg Diersch Peter Frolkovič Ekkehard Holzbecher Klaus Johannsen

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.

]]>Fluids doi: 10.3390/fluids2010012

Authors: Małgorzata Zimoń Robert Sawko David Emerson Christopher Thompson

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.

]]>Fluids doi: 10.3390/fluids2010010

Authors: Samuel Hund Marina Kameneva James Antaki

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.

]]>Fluids doi: 10.3390/fluids2010009

Authors: Sören Sander Benjamin Glasse Lucas Grosche Jose de Paiva Roberto Guardani Udo Fritsching

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.

]]>Fluids doi: 10.3390/fluids2010008

Authors: Duccio Griffini Massimiliano Insinna Simone Salvadori Andrea Barucci Franco Cosi Stefano Pelli Giancarlo Righini

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.

]]>Fluids doi: 10.3390/fluids2010007

Authors: Guillaume Lapeyre

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.

]]>Fluids doi: 10.3390/fluids2010006

Authors: Jin-Han Xie Benjamin Miquel Keith Julien Edgar Knobloch

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.

]]>Fluids doi: 10.3390/fluids2010005

Authors: Asterios Pantokratoras

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.

]]>Fluids doi: 10.3390/fluids2010004

Authors: Bogdan Nita Ryan Allaire

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.

]]>Fluids doi: 10.3390/fluids2010003

Authors: Fluids Editorial Office

The editors of Fluids would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2016.[...]

]]>Fluids doi: 10.3390/fluids2010002

Authors: Sohaib Obeid Ratneshwar Jha Goodarz Ahmadi

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.

]]>Fluids doi: 10.3390/fluids2010001

Authors: Md. Molla Manosh Paul

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.

]]>Fluids doi: 10.3390/fluids1040042

Authors: Mesude Ozturk Edgar O’Rear Dimitrios Papavassiliou

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).

]]>Fluids doi: 10.3390/fluids1040041

Authors: Biliana Bidin D. Rees

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.

]]>Fluids doi: 10.3390/fluids1040040

Authors: Rajinder Pal

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.

]]>Fluids doi: 10.3390/fluids1040039

Authors: Hao Li Wahid Ghaly Ibrahim Hassan

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.

]]>Fluids doi: 10.3390/fluids1040038

Authors: Karen May-Newman Vi Vu Brian Herold

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.

]]>Fluids doi: 10.3390/fluids1040037

Authors: Asterios Pantokratoras

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.

]]>Fluids doi: 10.3390/fluids1040036

Authors: Longhua Zhao

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.

]]>Fluids doi: 10.3390/fluids1040035

Authors: Tran Phuoc Mehrdad Massoudi Ping Wang

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.

]]>Fluids doi: 10.3390/fluids1040034

Authors: Ian Grooms Louis-Philippe Nadeau

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.

]]>Fluids doi: 10.3390/fluids1040033

Authors: J. LaCasce

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.

]]>Fluids doi: 10.3390/fluids1040032

Authors: Rémi Tailleux

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.

]]>Fluids doi: 10.3390/fluids1040031

Authors: Mohammad Safaei Goodarz Ahmadi Mohammad Goodarzi Amin Kamyar S. Kazi

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.

]]>Fluids doi: 10.3390/fluids1030030

Authors: Sanjeeva Balasuriya

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.

]]>Fluids doi: 10.3390/fluids1030028

Authors: Igor Shevchenko Pavel Berloff

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.

]]>Fluids doi: 10.3390/fluids1030029

Authors: Sebastian Kriebitzsch Roland Rzehak

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.

]]>Fluids doi: 10.3390/fluids1030027

Authors: Larry Pratt Roy Barkan Irina Rypina

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.

]]>Fluids doi: 10.3390/fluids1030025

Authors: Timour Radko Erick Edwards

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.

]]>Fluids doi: 10.3390/fluids1030026

Authors: Georgi Sutyrin Timour Radko

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.

]]>Fluids doi: 10.3390/fluids1030024

Authors: D. Rees

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.

]]>Fluids doi: 10.3390/fluids1030023

Authors: Amin Chabchoub Roger Grimshaw

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.

]]>Fluids doi: 10.3390/fluids1030022

Authors: Pavel Berloff

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.

]]>Fluids doi: 10.3390/fluids1030020

Authors: Mohammad Safaei Goodarz Ahmadi Mohammad Goodarzi Mostafa Safdari Shadloo Hamid Goshayeshi Mahidzal Dahari

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.

]]>Fluids doi: 10.3390/fluids1030021

Authors: Yebegaeshet Zerihun

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.

]]>Fluids doi: 10.3390/fluids1020019

Authors: Mehrdad Massoudi A. Kirwan

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.

]]>Fluids doi: 10.3390/fluids1020018

Authors: Peter Vadasz

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.

]]>Fluids doi: 10.3390/fluids1020016

Authors: Clement Kleinstreuer Zelin Xu

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.

]]>Fluids doi: 10.3390/fluids1020017

Authors: David Marshall

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.

]]>Fluids doi: 10.3390/fluids1020015

Authors: Fangda Cui Swapnil Moon I. Rao

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.

]]>Fluids doi: 10.3390/fluids1020006

Authors: Joie Marhefka Marina Kameneva

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.

]]>Fluids doi: 10.3390/fluids1020014

Authors: Robert Meroney Ryohji Ohba Bernd Leitl Hiroaki Kondo David Grawe Yoshihide Tominaga

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.

]]>Fluids doi: 10.3390/fluids1020013

Authors: Joseph Pedlosky

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.

]]>Fluids doi: 10.3390/fluids1020012

Authors: David Baron Haiyan Su Ashwin Vaidya

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.

]]>Fluids doi: 10.3390/fluids1020011

Authors: Rajinder Pal

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.

]]>Fluids doi: 10.3390/fluids1020009

Authors: William Dewar Joseph Schoonover Trevor McDougall Rupert Klein

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.

]]>Fluids doi: 10.3390/fluids1020010

Authors: Arafat Bhuiyan Md. Karim James Hart Peter Witt Jamal Naser

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.

]]>Fluids doi: 10.3390/fluids1020005

Authors: Kumbakonam Rajagopal

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.

]]>Fluids doi: 10.3390/fluids1010004

Authors: Wei-Tao Wu Mehrdad Massoudi

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.

]]>Fluids doi: 10.3390/fluids1010008

Authors: Wenhao Zhang Wenhao Li Chen Yang Akira Nakayama

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.

]]>Fluids doi: 10.3390/fluids1010003

Authors: A. Kirwan

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.

]]>Fluids doi: 10.3390/fluids1010007

Authors: Sergey Litvinov Qingguang Xie Xiangyu Hu Nikolaus Adams Marco Ellero

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.

]]>Fluids doi: 10.3390/fluids1010001

Authors: Bekir Yilbas

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. [...]

]]>Fluids doi: 10.3390/fluids1010002

Authors: Rafail Abramov

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.

]]>