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1
Zaks, Michael A., and Alexander Nepomnyashchy. "Subdiffusive and superdiffusive transport in plane steady viscous flows." Proceedings of the National Academy of Sciences 116, no. 37 (March 19, 2018): 18245–50. http://dx.doi.org/10.1073/pnas.1717225115.
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Deterministic transport of passive tracers in steady laminar plane flows of incompressible viscous fluids through lattices of solid bodies or arrays of steady vortices can be anomalous. Motion along regular patterns of streamlines is often aperiodic: Repeated slow passages near stagnation points and/or solid surfaces serve for eventual decorrelation. Singularities of passage times near the obstacles, dictated by the boundary conditions, affect the character of transport anomalies: Flows past arrays of vortices are subdiffusive whereas tracers advected through lattices of solid obstacles can feature superdiffusion. We calculate the transport characteristics with the help of the simple and computationally efficient model: the special flow.
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Liu, Chun-Ho. "Turbulent Plane Couette Flow and Scalar Transport at Low Reynolds Number." Journal of Heat Transfer 125, no. 6 (November 19, 2003): 988–98. http://dx.doi.org/10.1115/1.1571084.
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The turbulence structure and passive scalar (heat) transport in plane Couette flow at Reynolds number equal to 3000 (based on the relative speed and distance between the walls) are studied using direct numerical simulation (DNS). The numerical model is a three-dimensional trilinear Galerkin finite element code. It is found that the structures of the mean velocity and temperature in plane Couette flow are similar to those in forced channel flow, but the empirical coefficients are different. The total (turbulent and viscous) shear stress and total (turbulent and conductive) heat flux are constant throughout the channel. The locations of maximum root-mean-square streamwise velocity and temperature fluctuations are close to the walls, while the location of maximum root-mean-square spanwise and vertical velocity fluctuations are at the channel center. The correlation coefficients between velocities and temperature are fairly constant in the center core of the channel. In particular, the streamwise velocity is highly correlated with temperature (correlation coefficient ≈−0.9). At the channel center, the turbulence production is unable to counterbalance the dissipation, in which the diffusion terms (both turbulent and viscous) bring turbulent kinetic energy from the near-wall regions toward the channel center. The snapshots of the DNS database help explain the nature of the correlation coefficients. The elongated wall streaks for both streamwise velocity and temperature in the viscous sublayer are well simulated. Moreover, the current DNS shows organized large-scale eddies (secondary rotations) perpendicular to the direction of mean flow at the channel center.
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Karniadakis, George E., Bora B. Mikic, and Anthony T. Patera. "Minimum-dissipation transport enhancement by flow destabilization: Reynolds’ analogy revisited." Journal of Fluid Mechanics 192 (July 1988): 365–91. http://dx.doi.org/10.1017/s0022112088001909.
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A classical transport enhancement problem is concerned with increasing the heat transfer in a system while minimizing penalties associated with shear stress, pressure drop, and viscous dissipation. It is shown by Reynolds' analogy that viscous dissipation in a wide class of flows scales linearly with the Nusselt number and quadratically with the Reynolds number. It thus follows that transport enhancement optimization is equivalent to a problem in hydrodynamic stability theory; a more unstable flow will achieve the same Nusselt number at a lower Reynolds number, and therefore at a fraction of the dissipative cost. This transport-stability theory is illustrated in a numerical study of supercritical (unsteady) two-dimensional flow in an eddy-promoter channel comprising a plane channel with an infinite periodic array of cylindrical obstructions.It is shown that the addition of small cylinders to a plane channel results in stability modes that are little changed in form or frequency from plane-channel Tollmien-Schlichting waves. However, eddy-promoter flows are dramatically less stable than their plane-channel counterparts owing to cylinder-induced shear-layer instability (with critical Reynolds numbers on the order of hundreds rather than thousands), and thus these flows yield heat transfer rates commensurate with those of a plane-channel turbulent flow but at much lower Reynolds number. Small-cylinder supercritical eddy-promoter flows are shown to roughly preserve the convective-diffusive Reynolds analogy, and it thus follows from the transport-stability theory that eddy-promoter flows achieve the same heat transfer rates as plane-channel turbulent flows while incurring significantly less dissipation.
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Tutar, Mustafa, and Ali Karakus. "A numerical study of solidification and viscous dissipation effects on polymer melt flow in plane channels." Journal of Polymer Engineering 33, no. 2 (April 1, 2013): 95–110. http://dx.doi.org/10.1515/polyeng-2012-0060.
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Abstract The combined effects of solidification and viscous dissipation on the hydrodynamic and thermal behavior of polymer melt flow during the injection process in a straight plane channel of constant cross section are numerically studied by considering the shear-rate and temperature-dependent viscosity and transient-phase change behavior. A numerical finite volume method, in conjunction with a modified form of the Cross constitutive equation to account for shear rate, temperature-dependent viscosity changes and a slightly modified form of the method proposed by Voller and Prakash to account for solidification of the liquid phase, is used and a validation with an analytical solution is presented for viscous heating effects. The hydrodynamic and solidified layers growth under the influence of a transient phase-change process and viscous dissipation, are analyzed for a commercial polymer melt flow, polypropylene (PP) for different parametric conditions namely, inflow velocity, polymer injection (inflow) temperature, the channel wall temperature, and the channel height. The results demonstrate that the proposed numerical formulations, including conjugate effects of viscous heating and transient-solidification on the present thermal transport process, can provide an accurate and realistic representation of polymer melt flow behavior during the injection molding process in plane channels with less simplifying assumptions.
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Béthune, William, and Henrik Latter. "Electric heating and angular momentum transport in laminar models of protoplanetary discs." Monthly Notices of the Royal Astronomical Society 494, no. 4 (May 5, 2020): 6103–19. http://dx.doi.org/10.1093/mnras/staa908.
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ABSTRACT The vertical temperature structure of a protoplanetary disc bears on several processes relevant to planet formation, such as gas and dust grain chemistry, ice lines, and convection. The temperature profile is controlled by irradiation from the central star and by any internal source of heat such as might arise from gas accretion. We investigate the heat and angular momentum transport generated by the resistive dissipation of magnetic fields in laminar discs. We use local 1D simulations to obtain vertical temperature profiles for typical conditions in the inner disc (0.5–4 au). Using simple assumptions for the gas ionization and opacity, the heating and cooling rates are computed self-consistently in the framework of radiative non-ideal magnetohydrodynamics. We characterize steady solutions that are symmetric about the mid-plane and which may be associated with saturated Hall-shear unstable modes. We also examine the dissipation of electric currents driven by global accretion-ejection structures. In both cases we obtain significant heating for a sufficiently high opacity. Strong magnetic fields can induce an order-unity temperature increase in the disc mid-plane, a convectively unstable entropy profile, and a surface emissivity equivalent to a viscous heating of α ∼ 10−2. These results show how magnetic fields may drive efficient accretion and heating in weakly ionized discs where turbulence might be inefficient, at least for a range of radii and ages of the disc.
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Mortikov, Evgeny V., Andrey V. Glazunov, and Vasily N. Lykosov. "Numerical study of plane Couette flow: turbulence statistics and the structure of pressure–strain correlations." Russian Journal of Numerical Analysis and Mathematical Modelling 34, no. 2 (April 24, 2019): 119–32. http://dx.doi.org/10.1515/rnam-2019-0010.
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AbstractThe paper presents the results of direct numerical simulation of turbulent plane Couette flow. The calculations were performed for Reynolds numbers Re =U0H/ν(His the height of the channel, ±U0/2 is the motion velocities of the lower and upper walls, respectively,νis the kinematic viscosity) from 5200 (where viscous effects significantly affect the flow structure) to 80000 (where a logarithmic layer is clearly observed). Estimates of terms of the equation for the balance of turbulent Reynolds stresses are obtained, which indicate the importance of the kinetic energy transport by velocity fluctuations. The vertical transport of the turbulent momentum flux is less important and partly compensated by the transport of pressure fluctuations. It is shown that in the logarithmic layer the normal components of the ‘pressure–strain rate’ correlation tensor are described in the framework of the ‘isotropization of production’ model, and in the central part of the channel they are described by the linear Rotta model [29]. The additive model considering both the interaction of the velocity field fluctuation and the influence of the mean velocity gradient is a good approximation only for the off-diagonal component of the tensor entering the balance equation for the turbulent momentum flux.
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Eu, Byung Chan, Roger E. Khayat, Gert D. Billing, and Carl Nyeland. "Nonlinear transport coefficients and plane Couette flow of a viscous, heat-conducting gas between two plates at different temperatures." Canadian Journal of Physics 65, no. 9 (September 1, 1987): 1090–103. http://dx.doi.org/10.1139/p87-180.
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By using the example of plane Couette flow between two plates maintained at different temperatures, we present a method of calculating flow profiles for rarefied gases. In the method, generalized hydrodynamic equations are derived from the Boltzmann equation. They are then solved with boundary conditions calculated by taking into consideration the interfacial interaction between the surface and the gas molecule. The nonlinear transport coefficients employed in the generalized hydrodynamic equations are obtained from the Boltzmann equation by means of the modified-moment method. The profiles calculated are in agreement with the Liu–Lees theory as long as the boundary values are in agreement. It is found that the viscous-heating effect has a significant influence on the temperature and velocity profiles. The nonlinearity of transport coefficients also has significant effects on the profiles as the Knudsen and Mach numbers increase.
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da SILVA, C. B., and O. MÉTAIS. "On the influence of coherent structures upon interscale interactions in turbulent plane jets." Journal of Fluid Mechanics 473 (December 10, 2002): 103–45. http://dx.doi.org/10.1017/s0022112002002458.
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The influence of the coherent structures on grid/subgrid-scale (GS/SGS) interactions in free shear layers is analysed through the application of a top-hat filter to several plane jet direct numerical simulations (DNS). The Reynolds number based on the plane jet inlet slot width is Reh = 3000. The study deals with energy containing (Kelvin–Helmholtz) and inertial range (streamwise) vortices, from the far field of the turbulent plane jet. The most intense kinetic energy exchanges between GS and SGS occur near these structures and not randomly in the space. The GS kinetic energy is dominated by GS advection and GS pressure/velocity interactions which appear located next to the Kelvin–Helmholtz rollers. Surprisingly, GS/SGS transfer is not very well correlated with the coherent vortices and GS/SGS diffusion plays an important role in the local dynamics of both GS and SGS kinetic energy. The so-called ‘local equilibrium assumption’ holds globally but not locally as most viscous dissipation of SGS kinetic energy takes place within the vortex cores whereas forward and backward GS/SGS transfer occurs at quite different locations. Finally, it was shown that SGS kinetic energy advection may be locally large as compared to the other terms of the SGS kinetic energy transport equation.
9
Somigliana, Alice, Claudia Toci, Giuseppe Lodato, Giovanni Rosotti, and Carlo F. Manara. "Effects of photoevaporation on protoplanetary disc ‘isochrones’." Monthly Notices of the Royal Astronomical Society 492, no. 1 (December 11, 2019): 1120–26. http://dx.doi.org/10.1093/mnras/stz3481.
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ABSTRACT Protoplanetary discs are the site of star and planet formation, and their evolution and consequent dispersal deeply affect the formation of planetary systems. In the standard scenario they evolve on time-scales ∼Myr due to the viscous transport of angular momentum. The analytical self-similar solution for their evolution predicts specific disc isochrones in the accretion rate–disc mass plane. However, photoevaporation by radiation emitted by the central star is likely to dominate the gas disc dispersal of the innermost region, introducing another (shorter) time-scale for this process. In this paper, we include the effect of internal (X and EUV) photoevaporation on the disc evolution, finding numerical solutions for a population of protoplanetary discs. Our models naturally reproduce the expected quick dispersal of the inner region of discs when their accretion rates match the rate of photoevaporative mass loss, in line with previous studies. We find that photoevaporation preferentially removes the lightest discs in the sample. The net result is that, counter-intuitively, photoevaporation increases the average disc mass in the sample, by dispersing the lightest discs. At the same time, photoevaporation also reduces the mass accretion rate by cutting the supply of material from the outer to the inner disc. In a purely viscous framework, this would be interpreted as the result of a longer viscous evolution, leading to an overestimate of the disc age. Our results thus show that photoevaporation is a necessary ingredient to include when interpreting observations of large disc samples with measured mass accretion rates and disc masses. Photoevaporation leaves a characteristic imprint on the shape of the isochrone. Accurate data of the accretion rate–disc mass plane in the low disc mass region therefore give clues on the typical photoevaporation rate.
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Chiodi, Filippo, Philippe Claudin, and Bruno Andreotti. "A two-phase flow model of sediment transport: transition from bedload to suspended load." Journal of Fluid Mechanics 755 (August 22, 2014): 561–81. http://dx.doi.org/10.1017/jfm.2014.422.
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AbstractThe transport of dense particles by a turbulent flow depends on two dimensionless numbers. Depending on the ratio of the shear velocity of the flow to the settling velocity of the particles (or the Rouse number), sediment transport takes place in a thin layer localized at the surface of the sediment bed (bedload) or over the whole water depth (suspended load). Moreover, depending on the sedimentation Reynolds number, the bedload layer is embedded in the viscous sublayer or is larger. We propose here a two-phase flow model able to describe both viscous and turbulent shear flows. Particle migration is described as resulting from normal stresses, but is limited by turbulent mixing and shear-induced diffusion of particles. Using this framework, we theoretically investigate the transition between bedload and suspended load.
11
Kretke, Katherine A., D. N. C. Lin, and Neal J. Turner. "Planet formation around intermediate mass stars." Proceedings of the International Astronomical Union 3, S249 (October 2007): 293–300. http://dx.doi.org/10.1017/s1743921308016724.
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AbstractWe present a mechanism by which gas giants form efficiently around intermediate mass stars. MRI-driven turbulence effectively drives angular momentum transport in regions of the disk with sufficiently high ionization fraction. In the inner regions of the disk, where the midplane temperature is above ∼1000K, thermal ionization effectively couples the disk to the magnetic field, providing a relatively large viscosity. A pressure maximum will develop outside of this region as the gaseous disk approaches a steady-state surface density profile, trapping migrating solid material. This rocky material will coagulate into planetesimals which grow rapidly until they reach isolation mass. Around intermediate mass stars, viscous heating will push the critical radius for thermal ionization of the midplane out to around 1 AU. This will increase the isolation mass for solid cores. Planets formed here may migrate inwards due to type II migration, but they will induce the formation of subsequent giant planets at the outer edge of the gap they have opened. In this manner, gas giants can form around intermediate mass stars at a few AU.
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Hastings, R. C. "A theoretical description of viscous flow along a flat plate." Aeronautical Journal 109, no. 1101 (November 2005): 585–89. http://dx.doi.org/10.1017/s0001924000000920.
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Theoretical quantification of viscous effects in fluid flows is difficult, even if turbulence is absent, except when it is legitimate to simplify the Navier-Stokes equations in some way; for example by invoking the boundary-layer approximation in appropriate cases of interacting viscous and inviscid flow. The technical importance of viscous effects was thought sufficient incentive to re-examine a very simple flow configuration — namely plane, uniform and steady flow of an incompressible, viscous fluid toward a vanishingly-thin flat plate aligned with the undisturbed stream — in search of fresh insights into the general theory for viscous-inviscid interactions. The strategy was to exploit the analogy between vorticity transport in a viscous fluid and heat conduction in a moving solid. The key to doing so was the realization that, if the perturbation of the undisturbed flow by the plate might be represented as the sum of a series of successive approximations, then the stream function of the viscous part of the flow field — not merely the vorticity which resulted from its existence — might be expressible at every stage as the solution of an analogous heat conduction problem.
13
Proudman, Ian, and Mir Asadullah. "Steady viscous flow near a stationary contact line." Journal of Fluid Mechanics 187 (February 1988): 35–43. http://dx.doi.org/10.1017/s0022112088000321.
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The paper presents the asymptotic solution, near a stationary contact line at a plane boundary, for steady viscous incompressible flow of two immiscible liquids. The eigenvalues which determine this Stokes flow are determined by the contact angle α of the more viscous liquid and the ratio μ of the two viscosities. The dominant eigenvalues are found for all values of α and μ. As μ → 0 the results agree with those of Moffatt's (1964) one-phase theory for the case μ = 0 only when α > 81°. For α < 81° the two sets of results are qualitatively different. In particular, the eddy structure corresponding to complex eigenvalues occurs only in the α-range (34°, 81°). As μ increases from 0 to 1, this range steadily decreases to zero, which is located at 60°. The transport of energy across the liquid interface is almost always from the obtuse-angled sector to the acute-angled sector, irrespective of α, μ, and the location of the global power supply.
14
GWINN, ALLAN W., and S. J. JACOBS. "Mass transport in viscous flow under a progressive water wave." Journal of Fluid Mechanics 340 (June 10, 1997): 61–82. http://dx.doi.org/10.1017/s002211209700520x.
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We consider two-dimensional free surface flow caused by a pressure wavemaker in a viscous incompressible fluid of finite depth and infinite horizontal extent. The governing equations are expressed in dimensionless form, and attention is restricted to the case δ[Lt ]ε[Lt ]1, where δ is the characteristic dimensionless thickness of a Stokes boundary layer and ε is the Strouhal number. Our aim is to provide a global picture of the flow, with emphasis on the steady streaming velocity.The asymptotic flow structure near the wavenumber is found to consist of five distinct vertical regions: bottom and surface Stokes layers of dimensionless thickness O(δ), bottom and surface Stuart layers of dimensionless thickness O(δ/ε) lying outside the Stokes layers, and an irrotational outer region of dimensionless thickness O(1). Equations describing the flow in all regions are derived, and the lowest-order steady streaming velocity in the near-field outer region is computed analytically.It is shown that the flow far from the wavemaker is affected by thickening of the Stuart layers on the horizontal length scale O[(ε/δ)2], by viscous wave decay on the scale O(1/δ), and by nonlinear interactions on the scale O(1/ε2). The analysis of the flow in this region is simplified by imposing the restriction δ=O(ε2), so that all three processes take place on the same scale. The far-field flow structure is found to consist of a viscous outer core bounded by Stokes layers at the bottom boundary and water surface. An evolution equation governing the wave amplitude is derived and solved analytically. This solution and near-field matching conditions are employed to calculate the steady flow in the core numerically, and the results are compared with other theories and with observations.
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Hussong, Jeanette, Wim-Paul Breugem, and Jerry Westerweel. "A continuum model for flow induced by metachronal coordination between beating cilia." Journal of Fluid Mechanics 684 (August 30, 2011): 137–62. http://dx.doi.org/10.1017/jfm.2011.282.
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AbstractIn this numerical study we investigate the flow induced by metachronal coordination between beating cilia arranged in a densely packed layer by means of a continuum model. The continuum approach allows us to treat the problem as two-dimensional as well as stationary, in a reference frame moving with the speed of the metachronal wave. The model is used as a computationally efficient design tool to investigate cilia-induced transport of a Newtonian fluid in a plane channel. Contrary to prior continuum models, the present approach accounts for spatial variations in the porosity along the metachronal wave and thus ensures conservation of mass within the cilia layer. Using porous-media theory the governing volume-averaged Navier–Stokes (VANS) equations are derived and closure formulations are given explicitly for the model. This makes it possible to investigate cilia-induced flow with a continuum model in both the viscous regime and the inertial regime. The results show that metachronal coordination can act as a transport mechanism in both regimes. Porosity variations appear to be the key mechanism for correct prediction of the fluid transport in the viscous flow regime. The reason is that spatial variations in the porosity break the symmetry of the drag distribution along the metachronal wave. A new insight that has been gained is that the fluid transport reverses, thus switches from plectic to antiplectic metachronism, for the same cilia beat cycle when the wavespeed is increased such that inertial effects occur. Based on a parameter study, the net transport in the channel is described by a power-law relation of the amplitude, length and speed of the metachronal wave. It is found that the wavelength has the strongest effect on the viscosity-dominated fluid transport.
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Mekheimer, Kh S., and T. H. Al-Arabi. "Nonlinear peristaltic transport of MHD flow through a porous medium." International Journal of Mathematics and Mathematical Sciences 2003, no. 26 (2003): 1663–82. http://dx.doi.org/10.1155/s0161171203008056.
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In order to determine the characteristics of peristaltic transport of magnetohydrodynamic flow through a porous medium, the motion of a hydromagnetic (electrically conducting), viscous, and incompressible fluid in planer channel filled with a homogeneous porous medium and having electrically insulated walls that are transversely displaced by an infinite, harmonic travelling wave of large wavelength was analyzed using a perturbation expansion in terms of a variant wave number. We obtain an explicit form for the velocity field, a relation between the pressure rise and flow rate, in terms of Reynolds number, wave number, Hartmann number, permeability parameter, and the occlusion. The effects of all parameters of the problem are numerically discussed and graphically explained.
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Yang, Di, and Lian Shen. "Direct numerical simulation of scalar transport in turbulent flows over progressive surface waves." Journal of Fluid Mechanics 819 (April 18, 2017): 58–103. http://dx.doi.org/10.1017/jfm.2017.164.
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The transport of passive scalars in turbulent flows over progressive water waves is studied using direct numerical simulation. A combined pseudo-spectral and finite-difference scheme on a wave-surface-fitted grid is used to simulate the flow and scalar fields above the wave surface. Three representative wave ages (i.e. wave-to-wind speed ratios) are considered, corresponding to slow, intermediate and fast wind-waves, respectively. For each wave condition, four Schmidt numbers are considered for the scalar transport. The presence of progressive surface waves is found to induce significant wave-phase-correlated variation to the scalar field, with the phase dependence varying with the wave age. The time- and plane-averaged profiles of the scalar over waves of various ages exhibit similar vertical structures as those found in turbulence over a flat wall, but with the von Kármán constant and effective wave surface roughness for the mean scalar profile exhibiting considerable variation with the wave age. The profiles of the root-mean-square scalar fluctuations and the horizontal scalar flux exhibit good scaling in the viscous sublayer that agrees with the scaling laws previously reported for flat-wall turbulence, but with noticeable wave-induced variation in the viscous wall region. The profiles of the vertical scalar flux in the viscous sublayer exhibit apparent discrepancies from the reported scaling law for flat-wall turbulence, due to a negative vertical flux region above the windward face of the wave crest. Direct observation and quadrant-based conditional averages indicate that the wave-dependent distributions of the scalar fluctuations and fluxes are highly correlated with the coherent vortical structures in the turbulence, which exhibit clear wave-dependent characteristics in terms of both shape and preferential location.
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Bunnell, R. A., and S. D. Heister. "Three-Dimensional Unsteady Simulation of Cavitating Flows in Injector Passages." Journal of Fluids Engineering 122, no. 4 (July 11, 1999): 791–97. http://dx.doi.org/10.1115/1.1315590.
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Fully 3-D, unsteady, viscous simulations are performed on a plain-orifice pressure atomizer being fed by a manifold with a crossflow. This geometry replicates features present in both liquid rocket and diesel engine injectors. Both noncavitating and cavitating conditions are considered to determine the role of cavitation on the orifice discharge characteristics. The presence of cavitation is shown to affect both the mean and unsteady components of the orifice discharge coefficient. The presence of a significant cavitation zone can inhibit vorticity transport causing nearly all the fluid to be ejected through a crescent-shaped sector of the orifice exit plane. [S0098-2202(00)01604-7]
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Iyer, Kartik P., Janet D. Scheel, Jörg Schumacher, and Katepalli R. Sreenivasan. "Classical 1/3 scaling of convection holds up to Ra = 1015." Proceedings of the National Academy of Sciences 117, no. 14 (March 25, 2020): 7594–98. http://dx.doi.org/10.1073/pnas.1922794117.
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The global transport of heat and momentum in turbulent convection is constrained by thin thermal and viscous boundary layers at the heated and cooled boundaries of the system. This bottleneck is thought to be lifted once the boundary layers themselves become fully turbulent at very high values of the Rayleigh numberRa—the dimensionless parameter that describes the vigor of convective turbulence. Laboratory experiments in cylindrical cells forRa≳1012have reported different outcomes on the putative heat transport law. Here we show, by direct numerical simulations of three-dimensional turbulent Rayleigh–Bénard convection flows in a slender cylindrical cell of aspect ratio1/10, that the Nusselt number—the dimensionless measure of heat transport—follows the classical power law ofNu=(0.0525±0.006)×Ra0.331±0.002up toRa=1015. Intermittent fluctuations in the wall stress, a blueprint of turbulence in the vicinity of the boundaries, manifest at allRaconsidered here, increasing with increasingRa, and suggest that an abrupt transition of the boundary layer to turbulence does not take place.
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Gizon, L., D. Fournier, and M. Albekioni. "Effect of latitudinal differential rotation on solar Rossby waves: Critical layers, eigenfunctions, and momentum fluxes in the equatorial β plane." Astronomy & Astrophysics 642 (October 2020): A178. http://dx.doi.org/10.1051/0004-6361/202038525.
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Context. Retrograde-propagating waves of vertical vorticity with longitudinal wavenumbers between 3 and 15 have been observed on the Sun with a dispersion relation close to that of classical sectoral Rossby waves. The observed vorticity eigenfunctions are symmetric in latitude, peak at the equator, switch sign near 20°–30°, and decrease at higher latitudes. Aims. We search for an explanation that takes solar latitudinal differential rotation into account. Methods. In the equatorial β plane, we studied the propagation of linear Rossby waves (phase speed c < 0) in a parabolic zonal shear flow, U = − U̅ ξ2 < 0, where U̅ = 244 m s−1, and ξ is the sine of latitude. Results. In the inviscid case, the eigenvalue spectrum is real and continuous, and the velocity stream functions are singular at the critical latitudes where U = c. We add eddy viscosity to the problem to account for wave attenuation. In the viscous case, the stream functions solve a fourth-order modified Orr-Sommerfeld equation. Eigenvalues are complex and discrete. For reasonable values of the eddy viscosity corresponding to supergranular scales and above (Reynolds number 100 ≤ Re ≤ 700), all modes are stable. At fixed longitudinal wavenumber, the least damped mode is a symmetric mode whose real frequency is close to that of the classical Rossby mode, which we call the R mode. For Re ≈ 300, the attenuation and the real part of the eigenfunction is in qualitative agreement with the observations (unlike the imaginary part of the eigenfunction, which has a larger amplitude in the model). Conclusions. Each longitudinal wavenumber is associated with a latitudinally symmetric R mode trapped at low latitudes by solar differential rotation. In the viscous model, R modes transport significant angular momentum from the dissipation layers toward the equator.
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van Reeuwijk, Maarten, and Markus Holzner. "The turbulence boundary of a temporal jet." Journal of Fluid Mechanics 739 (December 18, 2013): 254–75. http://dx.doi.org/10.1017/jfm.2013.613.
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AbstractWe examine the structure of the turbulence boundary of a temporal plane jet at$\mathit{Re}= 5000$using statistics conditioned on the enstrophy. The data is obtained by direct numerical simulation and threshold values span 24 orders of magnitude, ranging from essentially irrotational fluid outside the jet to fully turbulent fluid in the jet core. We use two independent estimators for the local entrainment velocity${v}_{n} $based on the enstrophy budget. The data show clear evidence for the existence of a viscous superlayer (VSL) that envelopes the turbulence. The VSL is a nearly one-dimensional layer with low surface curvature. We find that both its area and viscous transport velocity adjust to the imposed rate of entrainment so that the integral entrainment flux is independent of threshold, although low-Reynolds-number effects play a role for the case under consideration. This threshold independence is consistent with the inviscid nature of the integral rate of entrainment. A theoretical model of the VSL is developed that is in reasonably good agreement with the data and predicts that the contribution of viscous transport and dissipation to interface propagation have magnitude$2{v}_{n} $and$- {v}_{n} $, respectively. We further identify a turbulent core region (TC) and a buffer region (BR) connecting the VSL and the TC. The BR grows in time and inviscid enstrophy production is important in this region. The BR shows many similarities with the turbulent–non-turbulent interface (TNTI), although the TNTI seems to extend into the TC. The average distance between the TC and the VSL, i.e. the BR thickness is about 10 Kolmogorov length scales or half a Taylor length scale, indicating that intense turbulent flow regions and viscosity-dominated regions are in close proximity.
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JAKIRLIĆ, S., and K. HANJALIĆ. "A new approach to modelling near-wall turbulence energy and stress dissipation." Journal of Fluid Mechanics 459 (May 25, 2002): 139–66. http://dx.doi.org/10.1017/s0022112002007905.
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A new model for the transport equation for the turbulence energy dissipation rate ε and for the anisotropy of the dissipation rate tensor εij, consistent with the near-wall limits, is derived following the term-by-term approach and using results of direct numerical simulations (DNS) for several generic wall-bounded flows. Based on the two-point velocity covariance analysis of Jovanović, Ye & Durst (1995) and reinterpretation of the viscous term, the transport equation is derived in terms of the ‘homogeneous’ part εh of the energy dissipation rate. The algebraic expression for the components of εij was then reformulated in terms of εh, which makes it possible to satisfy the exact wall limits without using any wall-configuration parameters. Each term in the new equation is modelled separately using DNS information. The rational vorticity transport theory of Bernard (1990) was used to close the mean curvature term appearing in the dissipation equation. A priori evaluation of εij, as well as solving the new dissipation equation as a whole using DNS data for quantities other than εij, for flows in a pipe, plane channel, constant-pressure boundary layer, behind a backward-facing step and in an axially rotating pipe, all show good near-wall behaviour of all terms. Computations of the same flows with the full model in conjunction with the low-Reynolds number transport equation for (uiui) All Overbar, using εh instead of ε, agree well with the direct numerical simulations.
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Zanke, Ulrich, and Aron Roland. "Sediment Bed-Load Transport: A Standardized Notation." Geosciences 10, no. 9 (September 16, 2020): 368. http://dx.doi.org/10.3390/geosciences10090368.
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Morphodynamic processes on Earth are a result of sediment displacements by the flow of water or the action of wind. An essential part of sediment transport takes place with permanent or intermittent contact with the bed. In the past, numerous approaches for bed-load transport rates have been developed, based on various fundamental ideas. For the user, the question arises which transport function to choose and why just that one. Different transport approaches can be compared based on measured transport rates. However, this method has the disadvantage that any measured data contains inaccuracies that correlate in different ways with the transport functions under comparison. Unequal conditions also exist if the factors of transport functions under test are fitted to parts of the test data set during the development of the function, but others are not. Therefore, a structural formula comparison is made by transferring altogether 13 transport functions into a standardized notation. Although these formulas were developed from different perspectives and with different approaches, it is shown that these approaches lead to essentially the same basic formula for the main variables. These are shear stress and critical shear stress. However, despite the basic structure of these 13 formulas being the same, their coefficients vary significantly. The reason for that variation and the possible effect on the bandwidth of results is identified and discussed. A further result is the finding that not only shear stress affects bed-load transport rates as is expressed by many transport formulas. Transport rates are also significantly affected by the internal friction of the moving sediment as well as by the friction fluid-bed. In the case of not fully rough flow conditions, also viscous effects and thus the Reynolds number becomes of importance.
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Scepi, N., G. Lesur, G. Dubus, and M. Flock. "Impact of convection and resistivity on angular momentum transport in dwarf novae." Astronomy & Astrophysics 609 (January 2018): A77. http://dx.doi.org/10.1051/0004-6361/201731900.
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The eruptive cycles of dwarf novae are thought to be due to a thermal-viscous instability in the accretion disk surrounding the white dwarf. This model has long been known to imply enhanced angular momentum transport in the accretion disk during outburst. This is measured by the stress to pressure ratio α, with α ≈ 0.1 required in outburst compared to α ≈ 0.01 in quiescence. Such an enhancement in α has recently been observed in simulations of turbulent transport driven by the magneto-rotational instability (MRI) when convection is present, without requiring a net magnetic flux. We independently recover this result by carrying out PLUTO magnetohydrodynamic (MHD) simulations of vertically stratified, radiative, shearing boxes with the thermodynamics and opacities appropriate to dwarf novae. The results are robust against the choice of vertical boundary conditions. The thermal equilibrium solutions found by the simulations trace the well-known S-curve in the density-temperature plane that constitutes the core of the disk thermal-viscous instability model. We confirm that the high values of α ≈ 0.1 occur near the tip of the hot branch of the S-curve, where convection is active. However, we also present thermally stable simulations at lower temperatures that have standard values of α ≈ 0.03 despite the presence of vigorous convection. We find no simple relationship between α and the strength of the convection, as measured by the ratio of convective to radiative flux. The cold branch is only very weakly ionized so, in the second part of this work, we studied the impact of non-ideal MHD effects on transport. Ohmic dissipation is the dominant effect in the conditions of quiescent dwarf novae. We include resistivity in the simulations and find that the MRI-driven transport is quenched (α ≈ 0) below the critical density at which the magnetic Reynolds number Rm ≤ 104. This is problematic because the X-ray emission observed in quiescent systems requires ongoing accretion onto the white dwarf. We verify that these X-rays cannot self-sustain MRI-driven turbulence by photo-ionizing the disk and discuss possible solutions to the issue of accretion in quiescence.
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Kurotani, Yuji, and Hajime Tanaka. "A novel physical mechanism of liquid flow slippage on a solid surface." Science Advances 6, no. 13 (March 2020): eaaz0504. http://dx.doi.org/10.1126/sciadv.aaz0504.
Full textAbstract:
Viscous liquids often exhibit flow slippage on solid walls. The occurrence of flow slippage has a large impact on the liquid transport and the resulting energy dissipation, which are crucial for many applications. It is natural to expect that slippage takes place to reduce the dissipation. However, (i) how the density fluctuation is affected by the presence of the wall and (ii) how slippage takes place through forming a gas layer remained elusive. Here, we report possible answers to these fundamental questions: (i) Density fluctuation is intrinsically enhanced near the wall even in a quiescent state irrespective of the property of wall, and (ii) it is the density dependence of the viscosity that destabilizes the system toward gas-layer formation under shear flow. Our scenario of shear-induced gas-phase formation provides a natural physical explanation for wall slippage of liquid flow, covering the slip length ranging from a microscopic (nanometers) to macroscopic (micrometers) scale.
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Bosman, Arthur D., Alexander G. G. M. Tielens, and Ewine F. van Dishoeck. "Efficiency of radial transport of ices in protoplanetary disks probed with infrared observations: the case of CO2." Astronomy & Astrophysics 611 (March 2018): A80. http://dx.doi.org/10.1051/0004-6361/201732056.
Full textAbstract:
Context. Radial transport of icy solid material from the cold outer disk to the warm inner disk is thought to be important for planet formation. However, the efficiency at which this happens is currently unconstrained. Efficient radial transport of icy dust grains could significantly alter the composition of the gas in the inner disk, enhancing the gas-phase abundances of the major ice constituents such as H2O and CO2.Aim. Our aim is to model the gaseous CO2 abundance in the inner disk and use this to probe the efficiency of icy dust transport in a viscous disk. From the model predictions, infrared CO2 spectra are simulated and features that could be tracers of icy CO2, and thus dust, radial transport efficiency are investigated.Methods. We have developed a 1D viscous disk model that includes gas accretion and gas diffusion as well as a description for grain growth and grain transport. Sublimation and freeze-out of CO2 and H2O has been included as well as a parametrisation of the CO2 chemistry. The thermo-chemical code DALI was used to model the mid-infrared spectrum of CO2, as can be observed with JWST-MIRI.Results. CO2 ice sublimating at the iceline increases the gaseous CO2 abundance to levels equal to the CO2 ice abundance of ~10−5, which is three orders of magnitude more than the gaseous CO2 abundances of ~10−8 observed by Spitzer. Grain growth and radial drift increase the rate at which CO2 is transported over the iceline and thus the gaseous CO2 abundance, further exacerbating the problem. In the case without radial drift, a CO2 destruction rate of at least 10−11 s−1 or a destruction timescale of at most 1000 yr is needed to reconcile model prediction with observations. This rate is at least two orders of magnitude higher than the fastest destruction rate included in chemical databases. A range of potential physical mechanisms to explain the low observed CO2 abundances are discussed.Conclusions. We conclude that transport processes in disks can have profound effects on the abundances of species in the inner disk such as CO2. The discrepancy between our model and observations either suggests frequent shocks in the inner 10 AU that destroy CO2, or that the abundant midplane CO2 is hidden from our view by an optically thick column of low abundance CO2 due to strong UV and/or X-rays in the surface layers. Modelling and observations of other molecules, such as CH4 or NH3, can give further handles on the rate of mass transport.
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Fomin, Oleksij, Alyona Lovska, Oleksandr Gorobchenko, Serhii Turpak, Iryna Kyrychenko, and Oleksii Burlutski. "ANALYSIS OF DYNAMIC LOADING OF IMPROVED CONSTRUCTION OF A TANK CONTAINER UNDER OPERATIONAL LOAD MODES." EUREKA: Physics and Engineering 2 (March 31, 2019): 61–70. http://dx.doi.org/10.21303/2461-4262.2019.00876.
Full textAbstract:
An increase in the volume of bulk cargo transportation through international transport corridors necessitates the commissioning of tank containers. Intermodalization of a tank container predetermines its load in various operating conditions depending on the type of vehicle on which it is carried: aviation, sea, air or rail. The analysis of the operating conditions of tank containers, as well as the regulatory documents governing their workload, led to the conclusion that the most dynamic loads acting on the supporting structures during transportation by rail. Namely, during the maneuvering collision of a wagon-platform, on which there are tank containers. In this case, it is stipulated that for a loaded tank container, the dynamic load is assumed to be 4g, and for an empty (for the purpose of checking the reinforcement) – 5g. It is important to note that when the tank container is underfilled with bulk cargo and taking into account movements of fittings relative to fittings, the maximum value of dynamic load can reach significantly larger values. Therefore, in order to ensure the strength of tank containers, an improvement of their structures has been proposed by introducing elastic-viscous bonds into the fittings. To determine the dynamic loading of the tank container, taking into account the improvement measures, mathematical models have been compiled, taking into account the presence of elastic, viscous and elastic-viscous bonds between the fittings, stops and fittings. It is established that the elastic bond does not fully compensate for the dynamic loads acting on the tank container. The results of mathematical modeling of dynamic loading, taking into account the presence of viscous and elastic-viscous coupling in the fittings, made it possible to conclude that the maximum accelerations per tank container do not exceed the normalized values. The determination of the dynamic loading of the tank container is also carried out by computer simulation using the finite element method. The calculation takes place in the software package CosmosWorks. The maximum values of accelerations are obtained, as well as their distribution fields relative to the supporting structure of the tank container. The developed models are verified by the Fisher criterion. The research will contribute to the creation of tank containers with improved technical, operational, as well as environmental characteristics and an increase in the efficiency of the liquid cargo transportation process through international transport corridors.
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Choi, Y. D., H. Iacovides, and B. E. Launder. "Numerical Computation of Turbulent Flow in a Square-Sectioned 180 Deg Bend." Journal of Fluids Engineering 111, no. 1 (March 1, 1989): 59–68. http://dx.doi.org/10.1115/1.3243600.
Full textAbstract:
Fine-grid computations are reported of turbulent flow through a square sectioned U-bend corresponding to that for which Chang et al. (1983a) have provided detailed experimental data. A sequence of modeling refinements is introduced: the replacement of wall functions by a fine mesh across the sublayer; the abandonment of the PSL approximation (in which pressure variations across the near-wall sublayer are neglected); and the introduction of an algebraic second-moment (ASM) closure in place of the usual k–ε eddy-viscosity model. Each refinement is shown to lead to an appreciable improvement in the agreement between measurement and computation. Direct comparisons with the measured rms turbulent velocity give further support to the view that the ASM scheme achieves a generally satisfactory description of the Reynolds stress field. Even with the most refined model some discrepancies between the experiment and computed development are apparent. It is suggested that their removal may require the use of a turbulent transport model in the semi-viscous sublayer in place of the van Driest (1956) mixing-length treatment used at present.
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Vorobyov, Eduard I., Aleksandr M. Skliarevskii, Vardan G. Elbakyan, Yaroslav Pavlyuchenkov, Vitaly Akimkin, and Manuel Guedel. "Gravitoviscous protoplanetary disks with a dust component." Astronomy & Astrophysics 627 (July 2019): A154. http://dx.doi.org/10.1051/0004-6361/201935438.
Full textAbstract:
Aims. The central region of a circumstellar disk is difficult to resolve in global numerical simulations of collapsing cloud cores, but its effect on the evolution of the entire disk can be significant. Methods. We used numerical hydrodynamics simulations to model the long-term evolution of self-gravitating and viscous circumstellar disks in the thin-disk limit. Simulations start from the gravitational collapse of pre-stellar cores of 0.5–1.0 M⊙ and both gaseous and dusty subsystems were considered, including a model for dust growth. The inner unresolved 1.0 au of the disk is replaced with a central smart cell (CSC), a simplified model that simulates physical processes that may occur in this region. Results. We found that the mass transport rate through the CSC has an appreciable effect on the evolution of the entire disk. Models with slow mass transport form more massive and warmer disks, and are more susceptible to gravitational instability and fragmentation, including a newly identified episodic mode of disk fragmentation in the T Tauri phase of disk evolution. Models with slow mass transport through the CSC feature episodic accretion and luminosity bursts in the early evolution, while models with fast transport are characterized by a steadily declining accretion rate with low-amplitude flickering. Dust grows to a larger, decimeter size in the slow transport models and efficiently drifts in the CSC, where it accumulates and reaches the limit where a streaming instability becomes operational. We argue that gravitational instability, together with a streaming instability likely operating in the inner disk regions, constitute two concurrent planet-forming mechanisms, which may explain the observed diversity of exoplanetary orbits. Conclusions. We conclude that sophisticated models of the inner unresolved disk regions should be used when modeling the formation and evolution of gaseous and dusty protoplanetary disks.
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Weeks, S. W., G. C. Sander, and J. Y. Parlange. "n-Dimensional first integral and similarity solutions for two-phase flow." ANZIAM Journal 44, no. 3 (January 2003): 365–80. http://dx.doi.org/10.1017/s1446181100008087.
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AbstractThis paper considers similarity solutions of the multi-dimensional transport equation for the unsteady flow of two viscous incompressible fluids. We show that in plane, cylindrical and spherical geometries, the flow equation can be reduced to a weakly-coupled system of two first-order nonlinear ordinary differential equations. This occurs when the two phase diffusivity D(θ) satisfies (D/D′)′ = 1/α and the fractional flow function f (θ) satisfies df/dθ = kDn/2, where n is a geometry index (1, 2 or 3), α and k are constants and primes denote differentiation with respect to the water content θ. Solutions are obtained for time dependent flux boundary conditions. Unlike single-phase flow, for two-phase flow with n = 2 or 3, a saturated zone around the injection point will only occur provided the two conditions and f′(1) ≠ 0 are satisfied. The latter condition is important due to the prevalence of functional forms of f (θ) in oil/water flow literature having the property f′(1) = 0.
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Jia, Pan, Bruno Andreotti, and Philippe Claudin. "Giant ripples on comet 67P/Churyumov–Gerasimenko sculpted by sunset thermal wind." Proceedings of the National Academy of Sciences 114, no. 10 (February 21, 2017): 2509–14. http://dx.doi.org/10.1073/pnas.1612176114.
Full textAbstract:
Explaining the unexpected presence of dune-like patterns at the surface of the comet 67P/Churyumov–Gerasimenko requires conceptual and quantitative advances in the understanding of surface and outgassing processes. We show here that vapor flow emitted by the comet around its perihelion spreads laterally in a surface layer, due to the strong pressure difference between zones illuminated by sunlight and those in shadow. For such thermal winds to be dense enough to transport grains—10 times greater than previous estimates—outgassing must take place through a surface porous granular layer, and that layer must be composed of grains whose roughness lowers cohesion consistently with contact mechanics. The linear stability analysis of the problem, entirely tested against laboratory experiments, quantitatively predicts the emergence of bedforms in the observed wavelength range and their propagation at the scale of a comet revolution. Although generated by a rarefied atmosphere, they are paradoxically analogous to ripples emerging on granular beds submitted to viscous shear flows. This quantitative agreement shows that our understanding of the coupling between hydrodynamics and sediment transport is able to account for bedform emergence in extreme conditions and provides a reliable tool to predict the erosion and accretion processes controlling the evolution of small solar system bodies.
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McCorquodale, Mark W., and R. J. Munro. "Experimental study of oscillating-grid turbulence interacting with a solid boundary." Journal of Fluid Mechanics 813 (January 26, 2017): 768–98. http://dx.doi.org/10.1017/jfm.2016.843.
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The interaction between oscillating-grid turbulence and a solid, impermeable boundary (positioned below, and aligned parallel to, the grid) is studied experimentally. Instantaneous velocity measurements, obtained using two-dimensional particle imaging velocimetry in the vertical plane through the centre of the (horizontal) grid, are used to study the effect of the boundary on the root-mean-square velocity components, the vertical flux of turbulent kinetic energy (TKE) and the terms in the Reynolds stress transport equation. Identified as a critical aspect of the interaction is the blocking of a vertical flux of TKE across the boundary-affected region. Terms of the Reynolds stress transport equations show that the blocking of this energy flux acts to increase the boundary-tangential turbulent velocity component, relative to the far-field trend, but not the boundary-normal velocity component. The results are compared with previous studies of the interaction between zero-mean-shear turbulence and a solid boundary. In particular, the data reported here are in support of viscous and ‘return-to-isotropy’ mechanisms governing the intercomponent energy transfer previously proposed, respectively, by Perot & Moin (J. Fluid Mech., vol. 295, 1995, pp. 199–227) and Walkeret al.(J. Fluid Mech., vol. 320, 1996, pp. 19–51), although we note that these mechanisms are not independent of the blocking of energy flux and draw parallels to the related model proposed by Magnaudet (J. Fluid Mech., vol. 484, 2003, pp. 167–196).
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Dudarev, I., V. Chucui, S. Dmitrieva, and M. Korol'kova. "OPTIMAL TECHNOLOGICAL MODES OF SCREW CONVEYORS." Аграрний вісник Причорномор'я, no. 94 (December 25, 2019): 130–39. http://dx.doi.org/10.37000/abbsl.2019.94.19.
Full textAbstract:
Lifting and transport engineering traditionally occupies an important place in the structure of the industrial complex of Ukraine, where specialized enterprises are built for the manufacture of cranes, conveyors, loaders and other equipment for food processing enterprises, and the agro-industrial complex. One of the ways to improve the efficiency of labor in the agricultural sector of the economy and in processing enterprises is the mechanization of heavy and labor-intensive work. When a high degree of mechanization of labor is achieved, conditions are created for the introduction of progressive production methods for processing raw materials and manufacturing finished products, with an increase in its volumes, quality improvement, is the basis for the development of a profitable enterprise. The most labor-intensive and heavy are loading and unloading operations, which occupy a significant amount in the production activities of enterprises. The movement of materials and loading and unloading operations are carried out at many stages of the main production processes, therefore lifting and transport equipment is used to mechanize such operations. Screw conveyors are widely used in various sectors of the national economy to move piece, bulk, viscous-plastic and liquid goods. Most widely screw conveyors are used as one of the links of a complex transport or technological systems. In the sphere of mechanization of loading and unloading operations, during transportation of agricultural goods, screw conveyors are used in the form of a mobile inclined structure, as well as in the form of a mobile vertical conveyor. In agriculture, screw conveyors are most often used. The main advantages of the use of auger norias: practically absent or represents any maintenance; quite convenient implementation of intermediate unloading; tightness that allows to transport any materials.
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Wilson, Duncan W. "Motor Skills: Recruitment of Kinesins, Myosins and Dynein during Assembly and Egress of Alphaherpesviruses." Viruses 13, no. 8 (August 17, 2021): 1622. http://dx.doi.org/10.3390/v13081622.
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The alphaherpesviruses are pathogens of the mammalian nervous system. Initial infection is commonly at mucosal epithelia, followed by spread to, and establishment of latency in, the peripheral nervous system. During productive infection, viral gene expression, replication of the dsDNA genome, capsid assembly and genome packaging take place in the infected cell nucleus, after which mature nucleocapsids emerge into the cytoplasm. Capsids must then travel to their site of envelopment at cytoplasmic organelles, and enveloped virions need to reach the cell surface for release and spread. Transport at each of these steps requires movement of alphaherpesvirus particles through a crowded and viscous cytoplasm, and for distances ranging from several microns in epithelial cells, to millimeters or even meters during egress from neurons. To solve this challenging problem alphaherpesviruses, and their assembly intermediates, exploit microtubule- and actin-dependent cellular motors. This review focuses upon the mechanisms used by alphaherpesviruses to recruit kinesin, myosin and dynein motors during assembly and egress.
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Khantuleva, Tatiana A., and Dmitry S. Shalymov. "Modelling non-equilibrium thermodynamic systems from the speed-gradient principle." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, no. 2088 (March 6, 2017): 20160220. http://dx.doi.org/10.1098/rsta.2016.0220.
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The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed. This article is part of the themed issue ‘Horizons of cybernetical physics’.
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HUA, BACH LIEN, JAMES C. McWILLIAMS, and PATRICE KLEIN. "Lagrangian accelerations in geostrophic turbulence." Journal of Fluid Mechanics 366 (July 10, 1998): 87–108. http://dx.doi.org/10.1017/s0022112098001001.
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A distinctive property of Lagrangian accelerations in geostrophic turbulence is that they are governed by the large and intermediate scales of the flow, both in time and space, so that the inertial part of the dynamics plays a much larger role than in three-dimensional turbulence where viscous effects are stronger. For the case of geostrophic turbulence on a β-plane, three terms contribute to the Lagrangian accelerations: the ageostrophic pressure gradient which often is the largest term, a meridional acceleration due to the β-effect, and an acceleration due to horizontally divergent ageostrophic motions. Both their spectral characteristics and patterns in physical space are studied in this paper. In particular the total accelerations field has an inertial spectrum slope which is identical to the geostrophic velocity field inertial slope.The accelerations gradient tensor is shown to govern the topology of quasi-geostrophic stirring and transport properties. Its positive eigenvalues locate accurately the position of extrema of potential vorticity gradients. The three-dimensional distribution of tracer gradients is such that the vertical distribution is entirely constrained by the horizontal one, while the reverse is not true. We make explicit analytically their dependence on the three-dimensional accelerations gradient.
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Coenen, Wilfried, and Alejandro Sevilla. "The structure of the absolutely unstable regions in the near field of low-density jets." Journal of Fluid Mechanics 713 (October 17, 2012): 123–49. http://dx.doi.org/10.1017/jfm.2012.441.
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AbstractThe viscous spatiotemporal stability properties of low-density laminar round jets emerging from circular nozzles or tubes are investigated numerically providing, for the first time, a separate treatment of the two particular cases typically studied in experiments: a hot gas jet discharging into a quiescent cold ambient of the same species, and an isothermal jet consisting of a mixture of two gases with different molecular weight, discharging into a stagnant ambient of the heavier species. To that end, use is made of a realistic representation for the base velocity and density profiles based on boundary-layer theory, with account taken of the effect of variable transport properties. Our results show significant quantitative differences with respect to previous parametric studies, and reveal that hot jets are generically more unstable than light jets, in the sense that they have larger associated critical density ratios for values of the Reynolds number and momentum thickness typically used in experiments. In addition, for several values of the jet-to-ambient density ratio, $S$, the downstream evolution of the local stability properties of the jet is computed as a function of the two main control parameters governing the jet, namely the Reynolds number, $\mathit{Re}$, and the momentum thickness of the initial velocity profile, ${\theta }_{0} / D$. It is shown that, for a given value of $S$, the $(\mathit{Re}, {\theta }_{0} / D)$ parameter plane can be divided in three regions. In the first region, defined by low values of $\mathit{Re}$ or very thick shear layers, the flow is locally convectively unstable everywhere. In the second region, with moderately large values of $\mathit{Re}$ and thin shear layers, the jet exhibits a localized pocket of absolute instability, away from boundaries. Finally, in the third region, that prevails in most of the $(\mathit{Re}, {\theta }_{0} / D)$ parameter plane, the absolutely unstable domain is bounded by the jet outlet. All the experiments available in the literature are shown to lie in the latter region, and the global transition observed in experiments is demonstrated to take place when the absolutely unstable domain becomes sufficiently large. The marginal frequency of the resulting global self-excited oscillations is shown to be fairly well described by the absolute frequency evaluated at the jet outlet, in agreement with the numerical results obtained by Lesshafft et al. (J. Fluid Mech., vol. 554, 2006, pp. 393–409) for synthetic jets.
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Fabian, A. C. "Active galaxies and cluster gas." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 363, no. 1828 (January 12, 2005): 725–38. http://dx.doi.org/10.1098/rsta.2004.1514.
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Two lines of evidence indicate that active galaxies, principally radio galaxies, have heated the diffuse hot gas in clusters. The first is the general need for additional heating to explain the steepness of the X–ray luminosity–temperature relation in clusters, the second is to solve the cooling–flow problem in cluster cores. The inner core of many clusters is radiating energy as X–rays on a time–scale much shorter than its likely age. Although the temperature in this region drops by a factor of about three from that of the surrounding gas, little evidence is found for gas much cooler than that. Some form of heating appears to be taking place, probably by energy transported outward from the central accreting black hole or radio source. How that energy heats the gas depends on poorly understood transport properties (conductivity and viscosity) of the intracluster medium. Viscous heating is discussed as a possibility. Such heating processes have consequences for the truncation of the luminosity function of massive galaxies.
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Buttinoni, Ivo, Jinwoong Cha, Wei-Hsun Lin, Stéphane Job, Chiara Daraio, and Lucio Isa. "Direct observation of impact propagation and absorption in dense colloidal monolayers." Proceedings of the National Academy of Sciences 114, no. 46 (October 30, 2017): 12150–55. http://dx.doi.org/10.1073/pnas.1712266114.
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Dense colloidal suspensions can propagate and absorb large mechanical stresses, including impacts and shocks. The wave transport stems from the delicate interplay between the spatial arrangement of the structural units and solvent-mediated effects. For dynamic microscopic systems, elastic deformations of the colloids are usually disregarded due to the damping imposed by the surrounding fluid. Here, we study the propagation of localized mechanical pulses in aqueous monolayers of micron-sized particles of controlled microstructure. We generate extreme localized deformation rates by exciting a target particle via pulsed-laser ablation. In crystalline monolayers, stress propagation fronts take place, where fast-moving particles (Vapproximately a few meters per second) are aligned along the symmetry axes of the lattice. Conversely, more viscous solvents and disordered structures lead to faster and isotropic energy absorption. Our results demonstrate the accessibility of a regime where elastic collisions also become relevant for suspensions of microscopic particles, behaving as “billiard balls” in a liquid, in analogy with regular packings of macroscopic spheres. We furthermore quantify the scattering of an impact as a function of the local structural disorder.
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Zouache, M. A., I. Eames, C. A. Klettner, and P. J. Luthert. "Flow and passive transport in planar multipolar flows." Journal of Fluid Mechanics 858 (November 2, 2018): 184–227. http://dx.doi.org/10.1017/jfm.2018.771.
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We study the flow and transport of heat or mass, modelled as passive scalars, within a basic geometrical unit of a three-dimensional multipolar flow – a triangular prism – characterised by a side length $L$, a normalised thickness $0.01\leqslant \unicode[STIX]{x1D700}\leqslant 0.1$ and an apex angle $0<\unicode[STIX]{x1D6FC}<\unicode[STIX]{x03C0}$, and connected to inlet and outlet pipes of equal normalised radius $0.01\leqslant \unicode[STIX]{x1D6FF}\leqslant 0.1$ perpendicularly to the plane of the flow. The flow and scalar fields are investigated over the range $0.1\leqslant Re_{p}\leqslant 10$ and $0.1\leqslant Pe_{p}\leqslant 1000$, where $Re_{p}$ and $Pe_{p}$ are respectively the Reynolds and Péclet numbers imposed at the inlet pipe when either a Dirichlet ($\text{D}$) or a Neumann ($\text{N}$) scalar boundary condition is imposed at the wall unattached to the inlets and outlets. A scalar no-flux boundary condition is imposed at all the other walls. An axisymmetric model is applied to understand the flow and scalar transport in the inlet and outlet regions, which consist of a turning region close to the pipe centreline and a channel region away from it. A separate two-dimensional model is then developed for the channel region by solving the integral form of the momentum and scalar advection–diffusion equations. Analytical relations between geometrical, flow and scalar transport parameters based on similarity and integral methods are generated and agree closely with numerical solutions. Finally, three-dimensional numerical calculations are undertaken to test the validity of the axisymmetric and depth-averaged analyses. Dominant flow and scalar transport features vary dramatically across the flow domain. In the turning region, the flow is a largely irrotational straining flow when $\unicode[STIX]{x1D700}\geqslant \unicode[STIX]{x1D6FF}$ and a dominantly viscous straining flow when $\unicode[STIX]{x1D700}\ll \unicode[STIX]{x1D6FF}$. The thickness of the scalar boundary layer scales to the local Péclet number to the power $1/3$. The diffusive flux $j_{d}$ and the scalar $C_{s}$ at the wall where ($\text{D}$) or ($\text{N}$) is imposed, respectively, are constant. In the channel region, the flow is parabolic and dominated by a source flow near the inlet and an irrotational straining flow away from it. When $(\text{D})$ is imposed the scalar decreases exponentially with distance from the inlet and the normalised scalar transfer coefficient converges to $\unicode[STIX]{x1D6EC}_{\infty }=2.5694$. When $(\text{N})$ is imposed, $C_{s}$ varies proportionally to surface area. Transport in the straining region downstream of the inlet is diffusion-limited, and $j_{d}$ and $C_{s}$ are functions of the geometrical parameters $L$, $\unicode[STIX]{x1D700}$, $\unicode[STIX]{x1D6FC}$ and $\unicode[STIX]{x1D6FF}$. In addition to describing the fundamental properties of the flow and passive transport in multipolar configurations, the present work demonstrates how geometrical and flow parameters should be set to control transfers in the different regions of the flow domain.
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van Ertbruggen, Caroline, Charles Hirsch, and Manuel Paiva. "Anatomically based three-dimensional model of airways to simulate flow and particle transport using computational fluid dynamics." Journal of Applied Physiology 98, no. 3 (March 2005): 970–80. http://dx.doi.org/10.1152/japplphysiol.00795.2004.
Full textAbstract:
We have studied gas flow and particle deposition in a realistic three-dimensional (3D) model of the bronchial tree, extending from the trachea to the segmental bronchi (7th airway generation for the most distal ones) using computational fluid dynamics. The model is based on the morphometrical data of Horsfield et al. (Horsfield K, Dart G, Olson DE, Filley GF, and Cumming G. J Appl Physiol 31: 207–217, 1971) and on bronchoscopic and computerized tomography images, which give the spatial 3D orientation of the curved ducts. It incorporates realistic angles of successive branching planes. Steady inspiratory flow varying between 50 and 500 cm3/s was simulated, as well as deposition of spherical aerosol particles (1–7 μm diameter, 1 g/cm3 density). Flow simulations indicated nonfully developed flows in the branches due to their relative short lengths. Velocity flow profiles in the segmental bronchi, taken one diameter downstream of the bifurcation, were distorted compared with the flow in a simple curved tube, and wide patterns of secondary flow fields were observed. Both were due to the asymmetrical 3D configuration of the bifurcating network. Viscous pressure drop in the model was compared with results obtained by Pedley et al. (Pedley TJ, Schroter RC, and Sudlow MF. Respir Physiol 9: 387–405, 1970), which are shown to be a good first approximation. Particle deposition increased with particle size and was minimal for ∼200 cm3/s inspiratory flow, but it was highly heterogeneous for branches of the same generation.
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Heidari, Parvaneh, and Hassan Hassanzadeh. "Modeling of Carbon Dioxide Leakage from Storage Aquifers." Fluids 3, no. 4 (October 23, 2018): 80. http://dx.doi.org/10.3390/fluids3040080.
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Long-term geological storage of CO2 in deep saline aquifers offers the possibility of sustaining access to fossil fuels while reducing emissions. However, prior to implementation, associated risks of CO2 leakage need to be carefully addressed to ensure safety of storage. CO2 storage takes place by several trapping mechanisms that are active on different time scales. The injected CO2 may be trapped under an impermeable rock due to structural trapping. Over time, the contribution of capillary, solubility, and mineral trapping mechanisms come into play. Leaky faults and fractures provide pathways for CO2 to migrate upward toward shallower depths and reduce the effectiveness of storage. Therefore, understanding the transport processes and the impact of various forces such as viscous, capillary and gravity is necessary. In this study, a mechanistic model is developed to investigate the influence of the driving forces on CO2 migration through a water saturated leakage pathway. The developed numerical model is used to determine leakage characteristics for different rock formations from a potential CO2 storage site in central Alberta, Canada. The model allows for preliminary analysis of CO2 leakage and finds applications in screening and site selection for geological storage of CO2 in deep saline aquifers.
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Bég, O. Anwar, R. Bhargava, S. Rawat, H. S. Takhar, and Tasweer A. Bég. "A Study of Steady Buoyancy-Driven Dissipative Micropolar Free Convection Heat and Mass Transfer in a Darcian Porous Regime with Chemical Reaction." Nonlinear Analysis: Modelling and Control 12, no. 2 (April 25, 2007): 157–80. http://dx.doi.org/10.15388/na.2007.12.2.14707.
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In the present paper we examine the steady double-diffusive free convective heat and mass transfer of a chemically-reacting micropolar fluid flowing through a Darcian porous regime adjacent to a vertical stretching plane. Viscous dissipation effects are included in the energy equation. Assuming incompressible, micro-isotropic fluid behaviour the transport equations are formulated in a two-dimensional coordinate system (x, y) using boundary-layer theory. The influence of the bulk porous medium retardation is modeled as a drag force term in the translational momentum equation. Transformations render the conservation equations into dimensionless form in terms of a single independent variable, η, transverse to the stretching surface. A simplified first order homogenous reaction model is also used to simulate chemical reaction in the flow. Using the finite element method solutions are generated for the angular velocity field, translational velocity field, temperature and species transfer fields. The effects of buoyancy, porous drag and chemical reaction rate are studied. Chemical reaction is shown to decelerate the flow and also micro-rotation values, in particular near the wall. Mass transfer is also decreased with increasing chemical reaction rate. Increasing Darcy number is shown to accelerate the flow. Applications of the study include cooling of electronic circuits, packed-bed chemical reactors and also the near field flows in radioactive waste geo-repositories.
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Chen, Hung-Cheng, Jai-Houng Leu, Yong Liu, He-Sheng Xie, and Qiang Chen. "A Validated Study of a Modified Shallow Water Model for Strong Cyclonic Motions and Their Structures in a Rotating Tank." Mathematical Problems in Engineering 2021 (April 30, 2021): 1–15. http://dx.doi.org/10.1155/2021/5529601.
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A joint theoretical and numerical study was carried out to investigate the fluid dynamical aspect of the motion of a vortex generated in a rotating tank with a sloping bottom. This study aims at understanding the evolution of strong cyclonic motions on a β-plane in the Northern Hemisphere. The strong cyclonic vortices were characterized by four nondimensional parameters which were derived through a scale analysis of the depth variations of fluid. By simplifying the model flow field and the prototype flow field, respectively, through the conservation of potential vorticity, two sets of dynamic similarity conditions are derived. This study proposed a sophisticated modified shallow water model (MSWM) to investigate the flow features of such strong vortices. A detailed numerical calculation adopted by multidimensional positive definite advection transport algorithm (MPDATA) was carried out to validate those effects considered in the MSWM model, including sloping bottom, parabolic free surface deformation, and viscous dissipation. Close agreements were found between the experimental and numerical results, including the streamlines patterns and the vortex trajectory. Comprehensive simulations for strong cyclonic vortices over different sloping bottoms were investigated to understand the impact of planetary β effect on vortex. The results calculated by MSWM demonstrate a variety of flow features of interactions between the primary vortex and induced secondary Rossby wave wakes that were essential and prominent in environmental geophysical flows.
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Béthune, William, Henrik Latter, and Wilhelm Kley. "Spiral structures in gravito-turbulent gaseous disks." Astronomy & Astrophysics 650 (June 2021): A49. http://dx.doi.org/10.1051/0004-6361/202040094.
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Context. Gravitational instabilities can drive small-scale turbulence and large-scale spiral arms in massive gaseous disks under conditions of slow radiative cooling. These motions affect the observed disk morphology, its mass accretion rate and variability, and could control the process of planet formation via dust grain concentration, processing, and collisional fragmentation. Aims. We study gravito-turbulence and its associated spiral structure in thin gaseous disks subject to a prescribed cooling law. We characterize the morphology, coherence, and propagation of the spirals and examine when the flow deviates from viscous disk models. Methods. We used the finite-volume code PLUTO to integrate the equations of self-gravitating hydrodynamics in three-dimensional spherical geometry. The gas was cooled over longer-than-orbital timescales to trigger the gravitational instability and sustain turbulence. We ran models for various disk masses and cooling rates. Results. In all cases considered, the turbulent gravitational stress transports angular momentum outward at a rate compatible with viscous disk theory. The dissipation of orbital energy happens via shocks in spiral density wakes, heating the disk back to a marginally stable thermal equilibrium. These wakes drive vertical motions and contribute to mix material from the disk with its corona. They are formed and destroyed intermittently, and they nearly corotate with the gas at every radius. As a consequence, large-scale spiral arms exhibit no long-term global coherence, and energy thermalization is an essentially local process. Conclusions. In the absence of radial substructures or tidal forcing, and provided a local cooling law, gravito-turbulence reduces to a local phenomenon in thin gaseous disks.
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Malhotra, Sahil, Eric R. Lehman, and Mukul M. Sharma. "Proppant Placement Using Alternate-Slug Fracturing." SPE Journal 19, no. 05 (March 10, 2014): 974–85. http://dx.doi.org/10.2118/163851-pa.
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Summary New fracturing techniques, such as hybrid fracturing (Sharma et al. 2004), reverse-hybrid fracturing (Liu et al. 2007), and channel (HiWAY) fracturing (Gillard et al. 2010), have been deployed over the past few years to effectively place proppant in fractures. The goal of these methods is to increase the conductivity in the proppant pack, providing highly conductive paths for hydrocarbons to flow from the reservoir to the wellbore. This paper presents an experimental study on proppant placement by use of a new method of fracturing, referred to as alternate-slug fracturing. The method involves an alternate injection of low-viscosity and high-viscosity fluids, with proppant carried by the low-viscosity fluid. Alternate-slug fracturing ensures a deeper placement of proppant through two primary mechanisms: (i) proppant transport in viscous fingers, formed by the low-viscosity fluid, and (ii) an increase in drag force in the polymer slug, leading to better entrainment and displacement of any proppant banks that may have formed. Both these effects lead to longer propped-fracture length and better vertical placement of proppant in the fracture. In addition, the method offers lower polymer costs, lower pumping horsepower, smaller fracture widths, better control of fluid leakoff, less risk of tip screenouts, and less gel damage compared with conventional gel fracture treatments. Experiments are conducted in simulated fractures (slot cells) with fluids of different viscosity, with proppant being carried by the low-viscosity fluid. It is shown that viscous fingers of low-viscosity fluid and viscous sweeps by the high-viscosity fluid lead to a deeper placement of proppant. Experiments are also conducted to demonstrate slickwater fracturing, hybrid fracturing, and reverse-hybrid fracturing. Comparison shows that alternate-slug fracturing leads to the deepest and most-uniform placement of proppant inside the fracture. Experiments are also conducted to study the mixing of fluids over a wide range of viscosity ratios. Data are presented to show that the finger velocities and mixing-zone velocities increase with viscosity ratio up to viscosity ratios of approximately 350. However, at higher viscosity ratios, the velocities plateau, signifying no further effect of viscosity contrast on the growth of fingers and mixing zone. The data are an integral part of design calculations for alternate-slug-fracturing treatments.
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Rushmer, Tracy. "Melt segregation in the lower crust: how have experiments helped us?" Earth and Environmental Science Transactions of the Royal Society of Edinburgh 87, no. 1-2 (1996): 73–83. http://dx.doi.org/10.1017/s0263593300006490.
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ABSTRACT:The rheological and chemical behaviour of the lower crust during anatexis has been a major focus of geological investigations for many years. Modern studies of crustal evolution require significant knowledge, not only of the potential source regions for granites, but also of the transport paths and emplacement mechanisms operating during granite genesis. We have gained significant insights into the segregation and transport of granitoid melts from the results of experimental studies on rock behaviour during partial melting. Experiments performed on crustal rock cores under both hydrostatic conditions and during deformation have led, in part, to two conclusions. (1) The interfacial energy controlling melt distribution is anisotropic and, as a result, the textures deviate significantly from those predicted for ideal systems—planar solid-melt interfaces are developed in addition to triple junction melt pockets. The ideal dihedral angle model for melt distribution cannot be used as a constraint to predict melt migration in the lower crust. (2) The ‘critical melt fraction’ model, which requires viscous, granitic melt to remain in the source until melt fractions reach >25 vol%, is not a reliable model for melt segregation. The most recent experimental results on crustal rock cores which have helped advance our understanding of melt segregation processes have shown that melt segregation is controlled by several variables, including the depth of melting, the type of reaction and the volume change associated with that reaction. Larger scale processes such as tectonic environment determine the rate at which the lower crust heats and deforms, thus the tectonic setting controls the melt fraction at which segregation takes place, in addition to the pressure and temperature of the potential melting reactions. Melt migration therefore can occur at a variety of different melt fractions depending on the tectonic environment; these results have significant implications for the predicted geochemistry of the magmas themselves.
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Joel, Anna-Christin, and Margret Weissbach. "Same Principles but Different Purposes: Passive Fluid Handling throughout the Animal Kingdom." Integrative and Comparative Biology 59, no. 6 (March 28, 2019): 1673–80. http://dx.doi.org/10.1093/icb/icz018.
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Abstract Everything on earth is subject to physical laws, thus they influence all facets of living creatures. Although these laws restrain animals in many ways, some animals have developed a way to use physical phenomena in their favor to conserve energy. Many animals, which have to handle fluids, for example, have evolved passive mechanisms by adapting their wettability or using capillary forces for rapid fluid spreading. In distinct animals, a similar selection pressure always favors a convergent development. However, when assessing the biological tasks of passive fluid handling mechanisms, their diversity is rather surprising. Besides the well-described handling of water to facilitate drinking in arid regions, observed in, e.g., several lizards, other animals like a special flat bug have developed a similar mechanism for a completely different task and fluid: Instead of water, these bugs passively transport an oily defense secretion to a region close to their head where it finally evaporates. And again some spiders use capillary forces to capture prey, by sucking in the viscous waxy cuticle of their prey with their nanofibrous threads. This review highlights the similarities and differences in the deployed mechanisms of passive fluid handling across the animal kingdom. Besides including well-studied animals to point out different mechanisms in general, we stretch over to not as extensively studied species for which similar mechanisms are described for different tasks. Thus, we provide an extensive overview of animals for which passive fluid handling is described so far as well as for future inspiration.
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Bush, J. W. M., H. A. Stone, and J. Bloxham. "Axial drop motion in rotating fluids." Journal of Fluid Mechanics 282 (January 10, 1995): 247–78. http://dx.doi.org/10.1017/s0022112095000139.
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A theoretical and experimental investigation of drop motion in rotating fluids is presented. The theory describing the vertical on-axis translation of an axisymmetric rigid body through a rapidly rotating low-viscosity fluid is extended to the case of a buoyant deformable fluid drop of arbitrary viscosity. In the case that inertial and viscous effects are negligible within the bulk external flow, motions are constrained to be two-dimensional in compliance with the Taylor–Proudman theorem, and the rising drop is circumscribed by a Taylor column. Calculations for the drop shape and rise speed decouple, so that theoretical predictions for both are obtained analytically. Drop shapes are set by a balance between centrifugal and interfacial tension forces, and correspond to the family of prolate ellipsoids which would arise in the absence of drop translation. In the case of a drop rising through an unbounded fluid, the Taylor column is dissipated at a distance determined by the outer fluid viscosity, and the rise speed corresponds to that of an identically shaped rigid body. In the case of a drop rising through a sufficiently shallow plane layer of fluid, the Taylor column extends to the boundaries. In such bounded systems, the rise speed depends further on the fluid and drop viscosities, which together prescribe the efficiency of the Ekman transport over the drop and container surfaces.A set of complementary experiments is also presented, which illustrate the effects of drop viscosity on steady drop motion in bounded rotating systems. The experimental results provide qualitative agreement with the theoretical predictions; in particular, the poloidal circulation observed inside low-viscosity drops is consistent with the presence of a double Ekman layer at the interface, and is opposite to that expected to arise in non-rotating systems. The steady rise speeds observed are larger than those predicted theoretically owing to the persistence of finite inertial effects.
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Baker, J. L., C. G. Johnson, and J. M. N. T. Gray. "Segregation-induced finger formation in granular free-surface flows." Journal of Fluid Mechanics 809 (November 9, 2016): 168–212. http://dx.doi.org/10.1017/jfm.2016.673.
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Geophysical granular flows, such as landslides, pyroclastic flows and snow avalanches, consist of particles with varying surface roughnesses or shapes that have a tendency to segregate during flow due to size differences. Such segregation leads to the formation of regions with different frictional properties, which in turn can feed back on the bulk flow. This paper introduces a well-posed depth-averaged model for these segregation-mobility feedback effects. The full segregation equation for dense granular flows is integrated through the avalanche thickness by assuming inversely graded layers with large particles above fines, and a Bagnold shear profile. The resulting large particle transport equation is then coupled to depth-averaged equations for conservation of mass and momentum, with the feedback arising through a basal friction law that is composition dependent, implying greater friction where there are more large particles. The new system of equations includes viscous terms in the momentum balance, which are derived from the $\unicode[STIX]{x1D707}(I)$-rheology for dense granular flows and represent a singular perturbation to previous models. Linear stability calculations of the steady uniform base state demonstrate the significance of these higher-order terms, which ensure that, unlike the inviscid equations, the growth rates remain bounded everywhere. The new system is therefore mathematically well posed. Two-dimensional simulations of bidisperse material propagating down an inclined plane show the development of an unstable large-rich flow front, which subsequently breaks into a series of finger-like structures, each bounded by coarse-grained lateral levees. The key properties of the fingers are independent of the grid resolution and are controlled by the physical viscosity. This process of segregation-induced finger formation is observed in laboratory experiments, and numerical computations are in qualitative agreement.