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Fluids, Volume 2, Issue 4 (December 2017)

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Open AccessArticle On the Applicability of Linear, Axisymmetric Dynamics in Intensifying and Mature Tropical Cyclones
Received: 31 May 2017 / Revised: 20 November 2017 / Accepted: 30 November 2017 / Published: 13 December 2017
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Abstract
The applicability of linearized axisymmetric dynamics to the intensification and structure change of tropical cyclones is investigated. The study is motivated by recent work that presented axisymmetric solutions to the linearized, non-hydrostatic, vortex-anelastic equations of motion (the so-called 3DVPAS model). The work called
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The applicability of linearized axisymmetric dynamics to the intensification and structure change of tropical cyclones is investigated. The study is motivated by recent work that presented axisymmetric solutions to the linearized, non-hydrostatic, vortex-anelastic equations of motion (the so-called 3DVPAS model). The work called into question the importance of a recently proposed nonlinear, system-scale boundary-layer spinup mechanism both in intensifying storms and in mature storms undergoing secondary eyewall formation. The issue is examined using a three-dimensional mesoscale simulation of an intensifying tropical cyclone, alongside the linear 3DVPAS model. Solutions to the linear model, for imposed eddy forcing terms derived from the mesoscale simulation, are shown to be valid only for short times ( t < 1 h) in the inner-core region of the vortex. At later times, the neglected nonlinear terms become significant and the linear results invalid. It follows that the linear results cannot be used to describe all aspects of the tropical cyclone dynamics at later times. In particular, they cannot be used (a) to dismiss the importance of the nonlinear boundary-layer spinup mechanism, nor (b) to isolate the separate effects of diabatic heating from those of friction, within the nonlinear boundary layer at least. Such separation depends on the linear superposition principle, which fails whenever nonlinearity is important. Similar caveats apply to the use of another linear model, the traditional Sawyer–Eliassen balance model. Its applicability is limited not only by linearity, but also by its assumption of strictly balanced motion. Both are incompatible with nonlinear spinup. Full article
(This article belongs to the collection Geophysical Fluid Dynamics)
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Open AccessArticle Axisymmetric Tornado Simulations with a Semi-Slip Boundary
Received: 2 November 2017 / Revised: 28 November 2017 / Accepted: 8 December 2017 / Published: 11 December 2017
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Abstract
The structure of natural tornadoes and simulated analogs are sensitive to the lower boundary condition for friction. Three-dimensional numerical simulations of storms require a choice for turbulence parameterizations and resolution of wind near the lower boundary. This article explores some of the consequences
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The structure of natural tornadoes and simulated analogs are sensitive to the lower boundary condition for friction. Three-dimensional numerical simulations of storms require a choice for turbulence parameterizations and resolution of wind near the lower boundary. This article explores some of the consequences of choices of a surface drag coefficient on the structure of a mature simulated tornado, using a conventional axisymmetric model. The surface drag parameterization is explored over the range of the semi-slip condition, including the extremes of no-slip and free-slip. A moderate semi-slip condition allows for an extreme pressure deficit, but without the unrealistic vortex breakdown of the no-slip condition. Full article
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Open AccessArticle Flow Anisotropy due to Thread-Like Nanoparticle Agglomerations in Dilute Ferrofluids
Received: 16 October 2017 / Revised: 17 November 2017 / Accepted: 1 December 2017 / Published: 7 December 2017
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Abstract
Improved knowledge of the magnetic field dependent flow properties of nanoparticle-based magnetic fluids is critical to the design of biomedical applications, including drug delivery and cell sorting. To probe the rheology of ferrofluid on a sub-millimeter scale, we examine the paths of 550
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Improved knowledge of the magnetic field dependent flow properties of nanoparticle-based magnetic fluids is critical to the design of biomedical applications, including drug delivery and cell sorting. To probe the rheology of ferrofluid on a sub-millimeter scale, we examine the paths of 550 μm diameter glass spheres falling due to gravity in dilute ferrofluid, imposing a uniform magnetic field at an angle with respect to the vertical. Visualization of the spheres’ trajectories is achieved using high resolution X-ray phase-contrast imaging, allowing measurement of a terminal velocity while simultaneously revealing the formation of an array of long thread-like accumulations of magnetic nanoparticles. Drag on the sphere is largest when the applied field is normal to the path of the falling sphere, and smallest when the field and trajectory are aligned. A Stokes drag-based analysis is performed to extract an empirical tensorial viscosity from the data. We propose an approximate physical model for the observed anisotropic drag, based on the resistive force theory drag acting on a fixed non-interacting array of slender threads, aligned parallel to the magnetic field. Full article
(This article belongs to the Special Issue Mechanics of Fluid-Particles Systems and Fluid-Solid Interactions)
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Open AccessArticle Relative Effects of Asymmetry and Wall Slip on the Stability of Plane Channel Flow
Received: 6 October 2017 / Revised: 10 November 2017 / Accepted: 27 November 2017 / Published: 1 December 2017
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Abstract
The effect of wall velocity slip on the stability of a pressure-driven two-dimensional asymmetric channel flow is examined by considering Navier slip condition on the channel walls. The two-parameter families of mean velocity profiles are considered to approximate the underlying asymmetric basic flow.
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The effect of wall velocity slip on the stability of a pressure-driven two-dimensional asymmetric channel flow is examined by considering Navier slip condition on the channel walls. The two-parameter families of mean velocity profiles are considered to approximate the underlying asymmetric basic flow. Competing effects of skewness and maximum velocity on the stability of the flow are explored for a range of model parameters. The Orr–Sommerfeld system of the asymmetric flow is solved using a Chebyshev spectral collocation method for both symmetric and non-symmetric type slip boundary conditions. Numerical results indicate that moderate asymmetry in the basic flow has a significant role on the stability of the Poiseuille-kind parallel/nearly parallel flows. Wall slip shows a passive control on the instability of the asymmetric flow by increasing or decreasing the critical Reynolds number and the set of unstable wave numbers. The stabilizing/destabilizing effect of slip velocity on the flow instability is weak or strong depending on the presence of velocity slip at the upper or lower wall. Velocity slip has a profound grip on the flow behaviour by changing the shear rate inside the perturbed flow. Full article
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Open AccessArticle Hasegawa–Wakatani and Modified Hasegawa–Wakatani Turbulence Induced by Ion-Temperature-Gradient Instabilities
Received: 9 October 2017 / Revised: 4 November 2017 / Accepted: 13 November 2017 / Published: 23 November 2017
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Abstract
We review some recent results that have been obtained in the investigation of zonal flow emergence, by means of a gyrokinetic trapped ion model, in the regime of ion temperature gradient instabilities for tokamak plasmas. We show that an analogous formulation of the
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We review some recent results that have been obtained in the investigation of zonal flow emergence, by means of a gyrokinetic trapped ion model, in the regime of ion temperature gradient instabilities for tokamak plasmas. We show that an analogous formulation of the zonal flow dynamics in terms of the Reynolds tensor applies in the fluid and kinetic regimes, where polarization effects play a major role. The kinetic regime leads to the emergence of a resonant mode at a frequency close to the drift frequency. With the objective of modeling both separate fluid and kinetic regimes of zonal flows, we used in this paper a methodology for deriving both Charney–Hasegawa–Mima (CHM) and Hasegawa–Wakatani models. This methodology is based on the trapped ion model and is analogous to the hierarchy leading from the Vlasov equation to the macroscopic fluid equations. The nature of zonal flows in the hierarchy of the Mima, Hasegawa and Wakatani models is investigated and discussed through comparisons with global kinetic simulations. Applications to the CHM equation are discussed, which applies to a broad variety of hydrodynamical systems, ranging from large-scale processes met in magnetically confined plasma to the so-called zonostrophy turbulence emerging in the case of small-scale forced, two-dimensional barotropic turbulence (Sukoriansky et al. Phys. Rev. Letters, 101, 178501, 2008). Full article
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Open AccessCommunication Thermal Jacket Design Using Cellulose Aerogels for Heat Insulation Application of Water Bottles
Received: 2 November 2017 / Revised: 15 November 2017 / Accepted: 17 November 2017 / Published: 23 November 2017
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Abstract
Thermal jacket design using eco-friendly cellulose fibers from recycled paper waste is developed in this report. Neoprene as an outmost layer, cellulose aerogels in the middle and Nylon as an innermost layer can form the best sandwiched laminate using the zigzag stitching method
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Thermal jacket design using eco-friendly cellulose fibers from recycled paper waste is developed in this report. Neoprene as an outmost layer, cellulose aerogels in the middle and Nylon as an innermost layer can form the best sandwiched laminate using the zigzag stitching method for thermal jacket development. The temperature of the ice slurry inside the water bottle covered with the designed thermal jackets remains at 0.1 °C even after 4 h, which is the average duration of an outfield exercise. Interestingly, the insulation performance of the designed thermal jackets is much better than the commercial insulated water bottles like FLOE bottles and is very competition to that of vacuum flasks for a same period of 4 h and ambient conditions. Full article
(This article belongs to the Special Issue Flow and Heat or Mass Transfer in the Chemical Process Industry)
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Open AccessArticle Numerical Simulation of Non-Equilibrium Two-Phase Wet Steam Flow through an Asymmetric Nozzle
Received: 30 September 2017 / Revised: 10 November 2017 / Accepted: 13 November 2017 / Published: 15 November 2017
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Abstract
The present study reported of the numerical investigation of a high-speed wet steam flow through an asymmetric nozzle. The spontaneous non-equilibrium homogeneous condensation of wet steam was numerically modeled based on the classical nucleation theory and droplet growth rate equation combined with the
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The present study reported of the numerical investigation of a high-speed wet steam flow through an asymmetric nozzle. The spontaneous non-equilibrium homogeneous condensation of wet steam was numerically modeled based on the classical nucleation theory and droplet growth rate equation combined with the field conservations within the computational fluid dynamics (CFD) code of ANSYS Fluent 13.0. The equations describing droplet formations and interphase change were solved sequentially after solving the main flow conservation equations. The calculations were carried out assuming the flow two-dimensional, compressible, turbulent, and viscous. The SST k-ω model was used for modeling the turbulence within an unstructured mesh solver. The validation of numerical model was accomplished, and the results showed a good agreement between the numerical simulation and experimental data. The effect of spontaneous non-equilibrium condensation on the jet and shock structures was revealed, and the condensation shown a great influence on the jet structure. Full article
(This article belongs to the Special Issue Non-Equilibrium Thermodynamics in Multiphase Flows)
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Open AccessArticle Three-Dimensional Low Reynolds Number Flows near Biological Filtering and Protective Layers
Received: 5 September 2017 / Revised: 30 October 2017 / Accepted: 6 November 2017 / Published: 13 November 2017
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Abstract
Mesoscale filtering and protective layers are replete throughout the natural world. Within the body, arrays of extracellular proteins, microvilli, and cilia can act as both protective layers and mechanosensors. For example, blood flow profiles through the endothelial surface layer determine the amount of
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Mesoscale filtering and protective layers are replete throughout the natural world. Within the body, arrays of extracellular proteins, microvilli, and cilia can act as both protective layers and mechanosensors. For example, blood flow profiles through the endothelial surface layer determine the amount of shear stress felt by the endothelial cells and may alter the rates at which molecules enter and exit the cells. Characterizing the flow profiles through such layers is therefore critical towards understanding the function of such arrays in cell signaling and molecular filtering. External filtering layers are also important to many animals and plants. Trichomes (the hairs or fine outgrowths on plants) can drastically alter both the average wind speed and profile near the leaf’s surface, affecting the rates of nutrient and heat exchange. In this paper, dynamically scaled physical models are used to study the flow profiles outside of arrays of cylinders that represent such filtering and protective layers. In addition, numerical simulations using the Immersed Boundary Method are used to resolve the three-dimensional flows within the layers. The experimental and computational results are compared to analytical results obtained by modeling the layer as a homogeneous porous medium with free flow above the layer. The experimental results show that the bulk flow is well described by simple analytical models. The numerical results show that the spatially averaged flow within the layer is well described by the Brinkman model. The numerical results also demonstrate, however, that the flow can be highly three-dimensional with fluid moving into and out of the layer. These effects are not described by the Brinkman model and may be significant for biologically relevant volume fractions. The results of this paper can be used to understand how variations in density and height of such structures can alter shear stresses and bulk flows. Full article
(This article belongs to the Special Issue Mechanics of Fluid-Particles Systems and Fluid-Solid Interactions)
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Open AccessArticle Urban Floods Adaptation and Sustainable Drainage Measures
Received: 8 October 2017 / Revised: 25 October 2017 / Accepted: 1 November 2017 / Published: 7 November 2017
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Abstract
Sustainability is crucial to the urban zones, especially related to the water management, which is vulnerable to flood occurrence. This research applies the procedure contemplated by the Soil Conservation Service (SCS) to determine the generated volumes when the impervious areas can exceed the
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Sustainability is crucial to the urban zones, especially related to the water management, which is vulnerable to flood occurrence. This research applies the procedure contemplated by the Soil Conservation Service (SCS) to determine the generated volumes when the impervious areas can exceed the drainage capacity of existing pluvial water networks. Several computational simulations were developed for the current scenario of an existing basin in Lisbon. Using CivilStorm software from Bentley Systems (Bentley EMEA, Bentley Systems International Limited, Dublin, Ireland), it enabled the evaluation of the volumes of flood peaks and the hydraulic behavior of a small hydrographic basin in the continuation of an urbanization process, considering the modification of its superficial impervious parts and the growth of the urbanized area. Several measures are suggested to solve the limited capacity of the existing drainage system. This study analyzes the efficiency of the application of constructive measures, pondering the viability of their effectiveness, individually and combined. The option that best minimizes the effects of the urbanization is the combination of different structural measures, in particular retention ponds, storage blocks, ditches and specific drainage interventions in some parts of the network. Full article
(This article belongs to the Special Issue Advances in Hydrodynamics)
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Open AccessArticle Horizontal Cellular Oscillations Caused by Time-Periodic Resonant Thermal Forcing in Weakly Nonlinear Darcy-Bénard Convection
Received: 14 September 2017 / Revised: 25 October 2017 / Accepted: 27 October 2017 / Published: 4 November 2017
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Abstract
The onset of Rayleigh-Bénard convection in a horizontally unbounded saturated porous medium is considered. Particular attention is given to the stability of weakly nonlinear convection between two plane horizontal surfaces heated from below. The primary aim is to study the effects on postcritical
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The onset of Rayleigh-Bénard convection in a horizontally unbounded saturated porous medium is considered. Particular attention is given to the stability of weakly nonlinear convection between two plane horizontal surfaces heated from below. The primary aim is to study the effects on postcritical convection of having small amplitude time-periodic resonant thermal forcing. Amplitude equations are derived using a weakly nonlinear theory and they are solved in order to understand how the flow evolves with changes in the Darcy-Rayleigh number and the forcing frequency. When convection is stationary in space, it is found to consist of one of two different types depending on its location in parameter space: either a convection pattern where each cell rotates in the same way for all time with a periodic variation in amplitude (Type I) or a pattern where each cell changes direction twice within each forcing period (Type II). Asymptotic analyses are also performed (i) to understand the transition between convection of types I and II; (ii) for large oscillation frequencies and (iii) for small oscillation frequencies. In a large part of parameter space the preferred pattern of convection when the layer is unbounded horizontally is then shown to be one where the cells oscillate horizontally—this is a novel form of pattern selection for Darcy-Bénard convection. Full article
(This article belongs to the Special Issue Convective Instability in Porous Media)
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Open AccessArticle A New Non-Equilibrium Thermodynamic Fractional Visco-Inelastic Model to Predict Experimentally Inaccessible Processes and Investigate Pathophysiological Cellular Structures
Received: 25 September 2017 / Revised: 23 October 2017 / Accepted: 24 October 2017 / Published: 1 November 2017
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Abstract
After remarking on non-equilibrium thermodynamics with internal variables, this paper highlights the importance of these variables to the study of biological systems. Internal variables can provide a more detailed description of biological processes that occur inside cells, tissues and organs. In order to
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After remarking on non-equilibrium thermodynamics with internal variables, this paper highlights the importance of these variables to the study of biological systems. Internal variables can provide a more detailed description of biological processes that occur inside cells, tissues and organs. In order to introduce a fractional model on a visco-inelastic medium based on Kluitenberg’s non-equilibrium thermodynamics, the origin of the complex dynamic modulus is shown by means of linear response theory. This research recalls our previous work to develop an ultrasound wave technique that allows us to investigate biological systems, and introduces the fractional visco-inelastic model and relative generalized relaxation time, to show that it is possible to obtain the Cole–Cole model in a particular case. Full article
(This article belongs to the Special Issue Non-Equilibrium Thermodynamics in Multiphase Flows)
Open AccessArticle Improving Accuracy in α-Models of Turbulence through Approximate Deconvolution
Received: 29 June 2017 / Revised: 24 September 2017 / Accepted: 11 October 2017 / Published: 27 October 2017
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Abstract
In this report, we present several results in the theory of α-models of turbulence with improved accuracy that have been developed in recent years. The α-models considered herein are the Leray-α model, the zeroth Approximate Deconvolution Model (ADM) turbulence model,
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In this report, we present several results in the theory of α -models of turbulence with improved accuracy that have been developed in recent years. The α -models considered herein are the Leray- α model, the zeroth Approximate Deconvolution Model (ADM) turbulence model, the modified Leray- α and the Navier–Stokes- α model. For all of the models from above, the accuracy is limited to α 2 in smooth flow regions. Better accuracy requires decreasing the filter radius α , which, in turn, requires a smaller mesh width that will lead in the end to a higher computational cost. Instead, one can use approximate deconvolution (without decreasing the mesh size) to attain better accuracy. Such deconvolution methods have been considered recently in many studies that show the efficiency of this approach. For smooth flows, periodic boundary conditions and van Cittert deconvolution operator of order N, the expected accuracy is α 2 N + 2 . In a bounded domain, such results are valid only in case special conditions are satisfied. In more general conditions, the author has recently proved that, in the case of the ADM, the expected accuracy of the finite element method with Taylor–Hood elements and Crank–Nicolson time stepping method is Δ t 2 + h 2 + K N α 2 , where the constant K < 1 depends on the ratio α / h , which is assumed constant. In this study, we present the extension of the result to the rest of the models. Full article
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Open AccessArticle The Interaction of Two Surface Vortices Near a Topographic Slope in a Stratified Ocean
Received: 21 July 2017 / Revised: 10 October 2017 / Accepted: 17 October 2017 / Published: 25 October 2017
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Abstract
We study the influence of bottom topography on the interaction of two identical vortices in a two-layer, quasi-geostrophic model. The two vortices have piecewise-uniform potential vorticity and are lying in the upper layer of the model. The topography is a smooth bottom slope.
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We study the influence of bottom topography on the interaction of two identical vortices in a two-layer, quasi-geostrophic model. The two vortices have piecewise-uniform potential vorticity and are lying in the upper layer of the model. The topography is a smooth bottom slope. For two cyclones, topography modifies the merger critical distance and the merger efficiency: the topographic wave and vortices can advect the two cyclones along the shelf when they are initially far from it or towards the shelf when they are initially closer to it. They can also advect the two cyclones towards each other and thus favour merger. The cyclones deform, and the potential vorticity field undergoes filamentation. Regimes of partial vortex merger or of vortex splitting are then observed. The interaction of the vorticity poles in the two layers are analysed to explain the evolution of the two upper layer cyclones. For taller topography, two new regimes appear: vortex drift and splitting; and filamentation and asymmetric merger. They are due to the hetonic coupling of lower layer vorticity with the upper layer vortices (a heton is a baroclinic vortex dipole, carrying heat and momentum and propagating horizontally in the fluid), or to the strong shear that the former exerts on the latter. The interaction of two anticyclones shows regimes of co-rotation or merger, but specifically, it leads to the drift of the two vortices away from the slope, via a hetonic coupling with oppositely-signed vorticity in the lower layer. This vorticity originates in the breaking of the topographic wave. The analysis of passive tracer evolution confirms the inshore or offshore drift of the fluid, the formation of tracer fronts along filaments and its stirring in regions of vortex merger. The trajectories of particles indicate how the fluid initially in the vortices is finally partitioned. Full article
(This article belongs to the collection Geophysical Fluid Dynamics)
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Open AccessArticle Computational Fluid Dynamics Simulations of Gas-Phase Radial Dispersion in Fixed Beds with Wall Effects
Received: 8 September 2017 / Revised: 7 October 2017 / Accepted: 18 October 2017 / Published: 21 October 2017
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Abstract
The effective medium approach to radial fixed bed dispersion models, in which radial dispersion of mass is superimposed on axial plug flow, is based on a constant effective dispersion coefficient, DT. For packed beds of a small tube-to-particle diameter ratio (N),
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The effective medium approach to radial fixed bed dispersion models, in which radial dispersion of mass is superimposed on axial plug flow, is based on a constant effective dispersion coefficient, DT. For packed beds of a small tube-to-particle diameter ratio (N), the experimentally-observed decrease in this parameter near the tube wall is accounted for by a lumped resistance located at the tube wall, the wall mass transfer coefficient km. This work presents validated computational fluid dynamics (CFD) simulations to obtain detailed radial velocity and concentration profiles for eight different computer-generated packed tubes of spheres in the range 5.04 ≤ N ≤ 9.3 and over a range of flow rates 87 ≤ Re ≤ 870 where Re is based on superficial velocity and the particle diameter dp. Initial runs with pure air gave axial velocity profiles vz(r) averaged over the length of the packing. Then, simulations with the tube wall coated with methane yielded radial concentration profiles. A model with only DT could not describe the radial concentration profiles. The two-parameter model with DT and km agreed better with the bed-center concentration profiles, but not with the sharp decreases in concentration close to the tube wall. A three-parameter model based on classical two-layer mixing length theory, with a wall-function for the decrease in transverse radial convective transport in the near-wall region, showed greatly improved ability to reproduce the near-wall concentration profiles. Full article
(This article belongs to the Special Issue Flow and Heat or Mass Transfer in the Chemical Process Industry)
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Open AccessArticle The Impact of Topographic Steepness on Tidal Dissipation at Bumpy Topography
Received: 31 July 2017 / Revised: 29 September 2017 / Accepted: 11 October 2017 / Published: 14 October 2017
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Abstract
Breaking internal waves are an important contributor to mixing in the stratified ocean interior. We use two-dimensional, nonhydrostatic numerical simulations to examine the breaking of internal waves generated by tidal flow over sinusoidal bottom topography. We explore the sensitivity of the internal wave
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Breaking internal waves are an important contributor to mixing in the stratified ocean interior. We use two-dimensional, nonhydrostatic numerical simulations to examine the breaking of internal waves generated by tidal flow over sinusoidal bottom topography. We explore the sensitivity of the internal wave breaking to the topographic steepness and Coriolis frequency, focusing on the vertical structure of kinetic energy dissipation and the ratio of local dissipation to the barotropic-to-baroclinic energy conversion. When the tidal frequency is twice the local Coriolis frequency, wave breaking above the topography is driven by wave–wave interactions which transfer wave energy from the tidal forcing frequency to the inertial frequency. The greater shear associated with the inertial frequency waves leads to enhanced dissipation in a thick layer above the topography. The topographic steepness strongly modulates this dependence of dissipation on Coriolis frequency; for some steep sinusoidal topographies, most wave energy propagates downward into the topographic troughs, eliminating the possibility for significant breaking above the topographic peaks. Current parameterizations of tidal dissipation in use in global ocean models need to be adapted to include the dependence of the local dissipation on both the Coriolis frequency and the topographic steepness. Full article
(This article belongs to the collection Geophysical Fluid Dynamics)
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Open AccessArticle The Eddy Diffusivity in Barotropic β-Plane Turbulence
Received: 1 September 2017 / Revised: 4 October 2017 / Accepted: 6 October 2017 / Published: 12 October 2017
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Abstract
Geostrophic turbulent eddies play a crucial role in the oceans, mixing properties such as heat, salt, and geochemical tracers. A useful reduced model for geostrophic turbulence is barotropic (2D) turbulence. The focus of this study is on 2D β-plane turbulence with quadratic
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Geostrophic turbulent eddies play a crucial role in the oceans, mixing properties such as heat, salt, and geochemical tracers. A useful reduced model for geostrophic turbulence is barotropic (2D) turbulence. The focus of this study is on 2D β -plane turbulence with quadratic drag, which, although arguably the most realistic barotropic model of ocean turbulence, has remained unexplored thus far. We first review and test classical scaling arguments for the eddy diffusivity in three regimes: the strong friction limit, the weak friction/strong β limit, and a transition regime. We then develop a generalized theory by parameterizing the nonlinear eddy–eddy interactions as a stochastic process, which leads to an analytical solution for the eddy diffusivity spectrum, whose integral yields a “bulk” diffusivity. The theory successfully predicts the smooth transition of diffusivity across the three regimes, and echoes with the recent argument that eddy phase propagation relative to the mean flow suppresses the eddy diffusivity. Moreover, the generalized theory reduces to the classical scaling arguments in both the strong friction and strong β limits, which has not been clear from the previous work on diffusivity suppression by flow-relative phase propagation. Full article
(This article belongs to the collection Geophysical Fluid Dynamics)
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Open AccessArticle A Finite Element Method for Incompressible Fluid Flow in a Noninertial Frame of Reference and a Numerical Study of Circular Couette Flow with Varying Angular Speed
Received: 5 September 2017 / Revised: 28 September 2017 / Accepted: 2 October 2017 / Published: 11 October 2017
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Abstract
In this work, we develop a numerical strategy for analyzing the flows of an incompressible fluid in the gap between an arbitrarily shaped inner boundary that rotates inside a circular outer boundary. Such flows occur very commonly in turbomachinery applications. The numerical strategy
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In this work, we develop a numerical strategy for analyzing the flows of an incompressible fluid in the gap between an arbitrarily shaped inner boundary that rotates inside a circular outer boundary. Such flows occur very commonly in turbomachinery applications. The numerical strategy is based on a noninertial frame of reference that is fixed to the rotating inner boundary so that Coriolis and angular acceleration effects have to be accounted for in its development. Since this strategy is based on a fixed mesh, it is much more economical and accurate than a general arbitrary Eulerian–Lagrangian strategy, which would typically require remeshing. In addition, we also conduct a numerical study for circular Couette flow with varying angular speed of the inner cylinder in an inertial frame of reference; such a study may prove useful in validating a theoretical stability analysis which currently seems to have been carried out only for the case of constant angular speed. Full article
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Open AccessArticle Convective Flow in an Aquifer Layer
Received: 28 August 2017 / Revised: 29 September 2017 / Accepted: 29 September 2017 / Published: 8 October 2017
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Abstract
Here, we investigate weakly nonlinear hydrothermal two-dimensional convective flow in a horizontal aquifer layer with horizontal isothermal and rigid boundaries. We treat such a layer as a porous medium, where Darcy’s law holds, subjected to the conditions that the porous layer’s permeability and
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Here, we investigate weakly nonlinear hydrothermal two-dimensional convective flow in a horizontal aquifer layer with horizontal isothermal and rigid boundaries. We treat such a layer as a porous medium, where Darcy’s law holds, subjected to the conditions that the porous layer’s permeability and the thermal conductivity are variable in the vertical direction. This analysis is restricted to the case that the subsequent hydraulic resistivity and diffusivity have a small rate of change with respect to the vertical variable. Applying the weakly nonlinear approach, we derive various order systems and express their solutions. The solutions for convective flow quantities such as vertical velocity and the temperature that arise as the Rayleigh number exceeds its critical value are computed and presented in graphical form. Full article
(This article belongs to the Special Issue Convective Instability in Porous Media)
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Open AccessArticle CFD Analyses and Experiments in a PAT Modeling: Pressure Variation and System Efficiency
Received: 14 August 2017 / Revised: 23 September 2017 / Accepted: 2 October 2017 / Published: 3 October 2017
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Abstract
Analysis of a PAT modeling is presented for application in water pipe systems as an interesting and promising energy converter to improve the system energy efficiency. The study is focused on the use of a Computational Fluid Dynamics (CFD) model in conjunction with
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Analysis of a PAT modeling is presented for application in water pipe systems as an interesting and promising energy converter to improve the system energy efficiency. The study is focused on the use of a Computational Fluid Dynamics (CFD) model in conjunction with laboratory data for representing PAT performance. The first stage of the procedure concerns a systematic analysis of the role played by the characteristic PAT parameters in the computational mesh definitions of the CFD model, with the aim of defining the most efficient set of capturing the main features of the PAT behaviour under different operating conditions. In the second stage, comparisons of CFD results and experiments were carried out to examine some system components for better understanding the PAT response. Specifically, the behavior of the pressure distribution along the PAT installation when implemented in a water pipe system are analyzed, and the links between pressure variation and the head drop in different system components responsible for the head losses and net head definition are also examined. Full article
(This article belongs to the Special Issue Advances in Hydrodynamics)
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Open AccessArticle Hyperbolic Covariant Coherent Structures in Two Dimensional Flows
Received: 22 August 2017 / Revised: 20 September 2017 / Accepted: 21 September 2017 / Published: 27 September 2017
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Abstract
A new method to describe hyperbolic patterns in two-dimensional flows is proposed. The method is based on the Covariant Lyapunov Vectors (CLVs), which have the properties of being covariant with the dynamics, and thus, being mapped by the tangent linear operator into another
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A new method to describe hyperbolic patterns in two-dimensional flows is proposed. The method is based on the Covariant Lyapunov Vectors (CLVs), which have the properties of being covariant with the dynamics, and thus, being mapped by the tangent linear operator into another CLVs basis, they are norm independent, invariant under time reversal and cannot be orthonormal. CLVs can thus give more detailed information about the expansion and contraction directions of the flow than the Lyapunov vector bases, which are instead always orthogonal. We suggest a definition of Hyperbolic Covariant Coherent Structures (HCCSs), which can be defined on the scalar field representing the angle between the CLVs. HCCSs can be defined for every time instant and could be useful to understand the long-term behavior of particle tracers. We consider three examples: a simple autonomous Hamiltonian system, as well as the non-autonomous “double gyre” and Bickley jet, to see how well the angle is able to describe particular patterns and barriers. We compare the results from the HCCSs with other coherent patterns defined on finite time by the Finite Time Lyapunov Exponents (FTLEs), to see how the behaviors of these structures change asymptotically. Full article
(This article belongs to the collection Geophysical Fluid Dynamics)
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Open AccessArticle A Non-Hydrostatic Depth-Averaged Model for Hydraulically Steep Free-Surface Flows
Received: 5 August 2017 / Revised: 16 September 2017 / Accepted: 18 September 2017 / Published: 23 September 2017
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Abstract
This study describes the results of a numerical investigation aimed at developing and validating a non-hydrostatic depth-averaged model for flow problems where the horizontal length scales close to flow depth. For such types of problems, the steep-slope shallow-water equations are inadequate to describe
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This study describes the results of a numerical investigation aimed at developing and validating a non-hydrostatic depth-averaged model for flow problems where the horizontal length scales close to flow depth. For such types of problems, the steep-slope shallow-water equations are inadequate to describe the two-dimensional structure of the curvilinear flow field. In the derivation of these equations, the restrictive assumptions of negligible bed-normal acceleration and bed curvature were employed, thus limiting their applicability to shallow flow situations. Herein, a Boussinesq-type model is deduced from the depth-averaged energy equation by relaxing the weakly-curved flow approximation to deal with the non-hydrostatic steep flow problems. The proposed model is solved with an implicit finite difference scheme and then applied to simulate steady free-surface flow problems with strong curvilinear effects. The numerical results are compared to experimental data, resulting in a reasonable overall agreement. Further, it is shown that the discharge characteristics of free flow over a round-crested weir are accurately described by using a Boussinesq-type approximation, and the drawbacks arising from a standard hydrostatic approach are overcome. The suggested numerical method to determine the discharge coefficient can be extended and adopted for other types of short-crested weirs. Full article
(This article belongs to the Special Issue Advances in Hydrodynamics)
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