Newtonian Viscous Flow Research Articles

Quantum spin representation for the Navier-Stokes equation

We develop a quantum representation for Newtonian viscous fluid flows by establishing a mapping between the Navier-Stokes equation (NSE) and the Schrödinger-Pauli equation (SPE). The proposed nonlinear SPE incorporates the two-component wave function and the imaginary diffusion. Consequently, classical fluid flow can be interpreted as a non-Hermitian quantum spin system. Using the SPE-based numerical simulation of viscous flows, we demonstrate the quantum/wavelike behavior in flow dynamics. Furthermore, the SPE equivalent to the NSE can facilitate the quantum simulation of fluid dynamics. Published by the American Physical Society 2024

Impact of peristaltic inclined Tube of the Newtonian viscous fluid flow with different wavelengths described by linear Navier-Stokes equations

Impact of peristaltic inclined Tube of the Newtonian viscous fluid flow with different wavelengths described by linear Navier-Stokes equations

Construction and investigation of differential hierarchical models for the Newtonian fluids

AbstractWe construct mathematical hierarchical models in Eulerian coordinates for an ideal and a Newtonian viscous fluid flow in the prismatic shell‐like domains. The peculiarities of well‐posedness of boundary conditions for angular domains are discussed.

Finger flow modeling in snow porous media based on lagrangian mechanics

Practical formulation for finger flow is lacking even though such a non-Darcy flow is commonly observed in homogeneous snow porous media. This study generalized physics for porous media flow based on the Lagrangian Mechanics; for instance, Darcy formula was theoretically derived minimizing the energy loss by solving the Euler-Lagrange Equation with Rayleigh dissipation function. This least energy loss (LEL) principle was then used to elucidate the finger flow formation in homogenous media. It was found that the inactive saturation (non-contributing void fraction) plays an important role in finger flow formation. This new theory also linked Darcy-Richards capillary flow and Newtonian viscous flow theories. Predicted flow area fractions by the LEL model were verified by the cold room laboratory experiment using well-controlled, homogeneous snow sample, as performed and documented by Katsushima et al. (2013).

Fluid dynamics, structural, micro-structural, and kinematic analyses on the Kuh-e-Namak (Dashti) salt diapiric rectangular cuboid channel flow, Iran

A study was conducted to investigate the Kuh-e-Namak (Dashti) salt diapir using fluid dynamics, structural, and microstructural, analyses. The study focused on transient flow caused by salt diapirism within the restraining bend of the Kazerun fault system. The salt diapir is located in Bushehr Province, Iran, and it was found that it represents Newtonian viscous flow within a rectangular cuboid channel, rather than a circular channel as previously thought. The study discovered that the salt diapir underwent laminar irrotational flow (Re = 1147.31) upward, with the symmetric parabola velocity profile dominated by Poiseuille flow. When loaded by sedimentary overburden, the salt tended to migrate. The upper part of the salt dome and diapiric flow transferred from irrotational laminar Poiseuille flow to transient Poiseuille-Couette and turbulent Poiseuille-Couette flows with a non-uniform asymmetric parabola profile. The drag sheath folds from diapiric flow showed monoclinic symmetry patterns, which led to a relative increase in the ellipticity of individual sheath fold rings to define the analogous eye-folds and cat ‘s-eye-folds. The presence of porphyroclasts or vortexes of σ, δ, and φ types in sheath folds indicates that the upper sections of the salt dome and diapir went through a Poiseuille-Couette flow or transient and turbulent flow during a later stage. The salt transient and turbulent flow can gradually lead to increased shear stress and high strain rates that are superposed by sub-simple shear, resulting in activation of the faults and consequently, the earthquake as we have seen in the destructive Kaki-Shonbe earthquake (Mw = 6.3).

Three‐dimensional polymer composite flow simulation and associated fiber orientation prediction for large area extrusion deposition additive manufacturing

AbstractMaterial flow and associated fiber orientation are among the most important features in Large Area extrusion deposition Additive Manufacturing (LAAM) of short fiber‐filled composites. Endeavors have been done in 2D flow models, where significant knowledge is achieved in explaining the material anisotropy of the deposited composite parts. Nevertheless, 2D flow models are limited by a couple of assumptions that lose significant characters of the deposition flow. This study is one of the first few that employ a 3D flow model which focuses on the quasi‐steady state of the polymer composite melt flow within the nozzle and the subsequent 90‐degree turning deposition onto the material substrate. The material flow is assumed as a highly viscous Newtonian flow. The fiber orientation is evaluated using the advanced pARD‐RSC fiber orientation tensor evaluation model, via the one‐way weakly‐coupled flow/orientation analysis formulation. Computed results show the fiber orientation state on the entire cross‐section of a deposited bead, which yields a clear view of how the material anisotropy is affected by the locally varied fiber orientation. The 3D‐flow prediction proves that the transverse directional fiber alignments are in high degree of similarity as compared to the over‐predicted results from the simplified 2D planar flows. In addition, the 3D‐model results exhibit a more favorable agreement with the reported experimental data than that yielded by the conventional 2D models.

Construction of a peridynamic model for viscous flow

We derive the Eulerian formulation for a peridynamic (PD) model of Newtonian viscous flow starting from fundamental principles: conservation of mass and momentum. This formulation is nonlocal, different from viscous flow models that utilize numerical methods like, e.g., the so-called “peridynamic differential operator” to approximate solutions of the classical Navier-Stokes equations. We show that the classical continuity equation is a limiting case of the PD one, assuming certain smoothness conditions. The PD model for viscous flow is calibrated by enforcing linear consistency for the viscous stress term with the classical Navier-Stokes equations. Couette and Poiseuille flows, and incompressible fluid flow past a regular lattice of cylinders are used to verify the new formulation, at low Reynolds numbers. The constructive approach in deriving the model allows for a seamless coupling with peridynamic models for corrosion or fracture for simulating complex fluid-structure interaction problems in which solid degradation takes place, such as in erosion-corrosion, hydraulic fracture, etc. Moreover, the new formulation sheds light on the relationships between local and nonlocal models.

Rheological characterization of β-lactoglobulin/lactoferrin complex coacervates

Heteroprotein complex coacervation between lactoferrin (LF) and β-lactoglobulin (β-LG), two oppositely charged proteins from whey, occurred under specific conditions of pH, ionic strength and protein molar ratio. The present work aims at characterizing the rheological properties of the concentrated phase called coacervate obtained after phase separation. Unlike some polysaccharide/protein coacervates, β-LG/LF heteroprotein coacervates exhibit a liquid-like behavior; the loss modulus G” being 100 times higher than the storage modulus G’ at low frequencies. This behavior was confirmed under creep-recovery tests. The heteroprotein coacervates exhibited a Newtonian viscous flow under low shear rate and a shear thinning behavior above 10 s−1. The coacervates are exceptionally viscous, reaching a viscosity value of 55 ± 10 Pa.s which is ∼2500 times higher than that measured on individual protein solutions of equivalent total concentration. Also, a structural change occurred in the coacervates, probably due to the weaknesses of electrostatic interactions inside the protein network at high shear rates. The observed time-dependent structural rearrangement was proved to be reversible. These findings open new ways for the use of coacervates as texturizing agents in food matrices.

Shape evolution of long flexible fibers in viscous flows

The present work studies numerically the dynamics and shape evolution of long flexible fibers suspended in a Newtonian viscous cellular flow using a particle-level fiber simulation technique. The fiber is modeled as a chain of massless rigid cylindrical segments connected by ball and socket joints; one-way coupling between the fibers and the flow is considered while Brownian motion is neglected. The effect of stiffness, equilibrium shape, and aspect ratio of the fibers on the shape evolution of the fibers are analyzed. Moreover, the influence of fiber stiffness and their initial positions and orientations on fiber transport is investigated. For the conditions considered, the results show that the fiber curvature field resembles that of the flow streamline. It is found that the stiffer fibers experience not only a quicker relaxation phase, in which they transient from their initial shape to their “steady-state shape,” but they also regain their equilibrium shape to a larger extent. The findings also demonstrate that even a small deviation of fiber shape from perfectly straight impacts significantly the early-stage evolution of the fiber shape and their bending behavior. Increasing the fiber aspect ratio, when other parameters are kept fixed, leads the fiber to behave more flexible, and it consequently deforms to a larger extent to adjust to the shape of the flow streamlines. In agreement with the available experimental results, the fiber transport studies show that either the fiber becomes trapped within the vortices of the cellular array or it moves across the vortical arrays while exhibiting various complex shapes.

Augmentation of heat transfer via nanofluids in duct flows using Fourier-type conditions: Theoretical and numerical study

Motivated by developments in thermal duct processing, an investigation is presented to study the behavior of viscous nanoparticle suspensions flowing in a vertical duct subject to Fourier-type conditions. The left wall temperature is kept lower than that of the right wall. Brownian motion and thermophoresis which are invoked via the presence of nanoparticles are incorporated in the study. Numerical solutions with an efficient Runge–Kutta shooting method are also presented at all values of the control parameters. The impact of thermal Grashof number [Formula: see text], Eckert number [Formula: see text], thermophoresis [Formula: see text], and Brownian motion parameters [Formula: see text] on the velocity, temperature, and nanoparticle concentration distributions for identical [Formula: see text] and differing Biot numbers [Formula: see text] (at the duct walls) are computed and visualized graphically. With vanishing thermophoresis and Brownian motion parameters, the solutions match exactly with the earlier Newtonian viscous flow computations. Symmetric and asymmetric wall heat conditions are also acknowledged. Intensifying the thermal Grashof number, Eckert number, thermophoresis parameter, and Brownian parameter serve to amplify magnitudes of the velocity and temperature, whereas the nanoparticle concentration field is suppressed. The skin friction and Sherwood number are also computed with various combinations of the flow control parameters. Nusselt number values at the hot duct wall are enhanced with an increase in thermal buoyancy parameter, Eckert number, Brownian motion parameter, and thermophoresis parameter for equal Biot numbers. The opposite trend is computed for different Biot numbers. For any given values of Biot numbers, the mean velocity and bulk temperature are boosted with increase in thermal buoyancy parameter, Eckert number, Brownian motion parameter, and thermophoresis parameter. Hence, it may be inferred that the transport characteristics computed using Fourier-type boundary conditions are substantially different from those based on isothermal boundary conditions in nanofluid duct flows.

A criterion of ideal thermoplastic forming ability for metallic glasses

A simplified approach to evaluate the thermoplastic forming ability (TPFA) of metallic glasses is proposed by comprehensive consideration of flow instability and phase stability. We found that primary factors influencing the maximum stress achievable under a Newtonian viscous flow (NVF) condition are the fragility and processing temperature, which identifies the effect of viscosity on the TPFA under mixed NVF and non-NVF conditions. Further, the degree of undercooling from the liquidus melting temperature, which reflects the supercooled liquid stability against thermal and mechanical fluctuations, is suggested as a practical indicator of ideal TPFA under isothermal and NVF conditions in metallic glasses.

Computation of Metallic Nanofluid Natural Convection in a Two-Dimensional Solar Enclosure with Radiative Heat Transfer, Aspect Ratio and Volume Fraction Effects

As a model of nanofluid direct absorber solar collectors (nano-DASCs), the present article describes recent numerical simulations of steady-state nanofluid natural convection in a two-dimensional enclosure. Incompressible laminar Newtonian viscous flow is considered with radiative heat transfer. The ANSYS FLUENT finite volume code (version 19.1) is employed. The enclosure has two adiabatic walls, one hot (solar receiving) and one colder wall. The Tiwari–Das volume fraction nanofluid model is used and three different nanoparticles are studied (Copper (Cu), Silver (Ag) and Titanium Oxide (TiO2)) with water as the base fluid. The solar radiative heat transfer is simulated with the P1 flux and Rosseland diffusion models. The influence of geometrical aspect ratio and solid volume fraction for nanofluids is also studied and a wider range is considered than in other studies. Mesh independence tests are conducted. Validation with published studies from the literature is included for the copper–water nanofluid case. The P1 model is shown to more accurately predict the actual influence of solar radiative flux on thermal fluid behaviour compared with Rosseland radiative model. With increasing Rayleigh number (natural convection, i.e. buoyancy effect), significant modification in the thermal flow characteristics is induced with emergence of a dual structure to the circulation. With increasing aspect ratio (wider base relative to height of the solar collector geometry), there is a greater thermal convection pattern around the whole geometry, higher temperatures and the elimination of the cold upper zone associated with lower aspect ratio. Titanium Oxide nanoparticles achieve slightly higher Nusselt number at the hot wall compared with Silver nanoparticles. Thermal performance can be optimized with careful selection of aspect ratio and nanoparticles and this is very beneficial to solar collector designers.

DEPENDENCE OF DYNAMIC VISCOSITY OF NAPHTHENIC HYDROCARBONS IN CYCLOPENTANE SERIES ON QUANTUM AND STRUCTURAL PARAMETERS

Interrelation of parameters for Newtonian fluid viscous flow of monocyclic hydrocarbons with quantum and structural (topological) characteristics of molecules are considered. Ionization potentials and topological indices, respectively, were considered as quantum and topological characteristics. The vertical ionization potentials were calculated by the Koopmans ' theorem of quantum chemical methods with full molecular geometry optimization. We have studied topological indices that take into account the size and shape of the molecular graph. As a topological descriptors the Wiener index, the Balaban centric index, the Randic index (the index of molecular connectivity), Gutman (Szeged) index, Platt index and the Harary index were considered. For hydrocarbons in cyclopentane series with side chains, the kinetic compensation effect of dynamic viscosity has been established, which connects the activation energy and Arrhenius factor in the framework of the Frenkel-Eyring model. It is established that for compounds of a number of five-membered naphthenes, the apparent activation energy for viscous flow and the associated pre-exponential factor, depends on quantum parameters (ionization potentials) and the topology of the molecules. In this paper, a regression quantitative structure−property relationship (QSPR) is proposed using as descriptors the ionization potentials and topological indices for the prediction of dynamic viscosity. Prognostics capabilities of the proposed model and the adequacy of the forecast were verified by calculating the values of the dynamic viscosity of hydrocarbons that are not included in the base series. Experimental and theoretical substantiation of the proposed regularity was given within the framework of the representation of the viscous flow activation energy as a measure of intermolecular interaction and the predominance of dispersion interaction in hydrocarbon molecules for cyclopentane series. The equation obtained during the study can be used to predict the viscosity characteristics of synthesized and natural five-membered naphthenes.

Vortex-induced vibration prediction via an impedance criterion

The vortex-induced vibration of a spring-mounted, damped, rigid circular cylinder, immersed in a Newtonian viscous flow and capable of moving in the direction orthogonal to the unperturbed flow is investigated for Reynolds numbers in the vicinity of the onset of unsteadiness (15<Re<60) using the incompressible linearised Navier–Stokes equations. In a first step, we solve the linear problem considering an imposed harmonic motion of the cylinder. Results are interpreted in terms of the mechanical impedance, i.e. the ratio between the vertical force coefficient and the cylinder velocity, which is represented as function of the Reynolds number and the driving frequency. Considering the energy transfer between the cylinder and the fluid, we show that impedance results provide a simple criterion allowing the prediction of the onset of instability of the coupled fluid-elastic structure case. A global stability analysis of the fully coupled fluid/cylinder system is then performed. The instability thresholds obtained by this second approach are found to be in perfect agreement with the predictions of the impedance-based criterion. A theoretical argument, based on asymptotic developments, is then provided to give a prediction of eigenvalues of the coupled problem, as well as to characterise the region of instability beyond the threshold as function of the reduced velocity U^*, the dimensionless mass m^* and the Reynolds number. The influence of the damping parameter ???? on the instability region is also explored.

Correlation between High Temperature Deformation and β Relaxation in LaCeBased Metallic Glass.

High-temperature deformation around the glass transition temperature Tg and the dynamic mechanical behavior of La30Ce30Al15Co25 metallic glass were investigated. According to dynamic mechanical analysis (DMA) results, La30Ce30Al15Co25 metallic glass exhibits a pronounced slow β relaxation process. In parallel, strain-rate jump experiments around the glass transition temperature were performed in a wide range of strain rate ranges. The apparent viscosity shows a strong dependence on temperature and strain rate, which reflects the transition from non-Newtonian to Newtonian flow. At low strain or high temperature, a transition was observed from a non-Newtonian viscous flow to Newtonian viscous flow. It was found that the activation volume during plastic deformation of La30Ce30Al15Co25 metallic glass is higher than that of other metallic glasses. Higher values of activation volume in La30Ce30Al15Co25 metallic glass may be attributed to existence of a pronounced slow β relaxation. It is reasonable to conclude that slow β relaxation in La30Ce30Al15Co25 metallic glass corresponds to the “soft” regions (structural heterogeneities) in metallic glass.

Parabolic evolution equations in interpolation spaces: boundedness, stability, and applications

We develop a general approach for the study of the boundedness and stability of solution to general parabolic semi-linear evolution equations in real-interpolation spaces. Our approach yields a unified method to handle problems in Newtonian viscous incompressible fluid flows. Moreover, our method will be applied to derive new results for the existence and polynomial stability of bounded solutions to the Ornstein–Uhlenbeck semi-linear equations and various diffusion equations with rough coefficients. The method is based on a combination of interpolation functors, duality estimates, smoothing properties of the linearized equation, and fixed point arguments.

COMPUTATION OF GOLD-WATER NANOFLUID NATURAL CONVECTION IN A THREE-DIMENSIONAL TILTED PRISMATIC SOLAR ENCLOSURE WITH ASPECT RATIO AND VOLUME FRACTION EFFECTS

Nanofluids are increasingly being deployed in numerous energy applications owing to their impressive thermal enhancement properties. Motivated by these developments in the current study we present finite volume numerical simulations of natural convection in an inclined 3-dimensional prismatic direct absorber solar collector (DASC)containing gold-water nanofluid. Steady-state, incompressible laminar Newtonian viscous flow is assumed. The enclosure has two adiabatic walls, one hot (solar receiving) and one colder wall. ANSYS FLUENT software(version 19.1) is employed. The Tiwari-Das volume fraction nanofluid model is utilized to simulate nanoscale effects and allows a systematic exploration of volume fraction effects. The effects of thermal buoyancy (Rayleighnumber), geometrical aspect ratio and enclosure tilt angle on isotherm and temperature contour distributions are presented with extensive visualizationin three dimensions. Grid-independence tests are included. Validation with published studies from the literature is also conducted. A significant modification in vortex structure and temperature distribution is computed with volume fraction, Rayleigh number, aspect ratio and tilt angle. Heat flux and average Nusselt number results are also included. Gold nano-particles even at relatively low volume fractions are observed to achieve substantial improvement in heat transfer characteristics.

High-temperature creep behavior of a SiOC glass ceramic free of segregated carbon

In this study we present the high-temperature creep behavior of a dense SiOC glass ceramic free of segregated carbon. Solid-state NMR spectroscopy, XRD and TEM investigations indicate that the sample consists of β-SiC nanoparticles homogeneously dispersed in an amorphous silica matrix. Compression creep experiments were performed at 1100–1300°C and stresses of 50–100MPa. The calculated creep viscosity of SiOC is two orders of magnitude higher than that of pure silica. Whereas the activation energy for creep (696kJ/mol) is close to that determined in pure silica glass. However, a stress exponent of 1.7 was calculated, suggesting that other mechanisms might contribute to the creep in addition to the Newtonian viscous flow. The strong difference in the creep rates and creep mechanism of the SiOC glass ceramic and amorphous silica is discussed in terms of possible contributions of the interface between the silica matrix and the β-SiC nanoparticles.

The 27 April 1975 Kitimat, British Columbia, submarine landslide tsunami: a comparison of modeling approaches

We present numerical simulations of the April 27, 1975, landslide event in the northern extreme of Kitimat Arm, British Columbia. The event caused a tsunami with an estimated wave height of 8.2 m at Kitimat First Nations Settlement and 6.1 m at Clio Bay, at the northern and southern ends of Kitimat Arm, respectively. We use the nonhydrostatic model NHWAVE to perform a series of numerical experiments with different slide configurations and with two approaches to modeling the slide motion: a solid slide with motion controlled by a basal Coulomb friction and a depth-integrated numerical slide based on Newtonian viscous flow. Numerical tests show that both models are capable of reproducing observations of the event if an adequate representation of slide geometry is used. We further show that comparable results are obtained using estimates of either Coulomb friction angle or slide viscosity that are within reasonable ranges of values found in previous literature.

On Varifold Solutions of Two-Phase Incompressible Viscous Flow with Surface Tension

In this paper using diffuse approximations the existence of a varifold solution to the two-phase Newtonian incompressible viscous flow problem is derived. On the free surface between the two phases we consider surface tension force. Also we prove that for axisymmetric, possibly with swirl, initial velocities and cylindrically symmetric initial volumes occupied by each fluid there exists a global in time axisymmetric, with swirl, solution.