Viscous Flow Model Research Articles

Nature of instability in flow-driven porous anodic oxide.

Self-organized porous anodic oxide films are formed by the electrochemical oxidation of reactive metal aluminum in acidic solutions in which the oxide is soluble. Recently, viscous flow models have shown using linear stability analysis that the instability results from a trade-off between the destabilizing effect of viscous flow of oxide and the stabilizing effect of oxide formation, which provides the wavelength selection mechanism for pattern formation. Anion adsorption on surface growth sites causes nonuniform compressive stress at the oxide-solution interface, which drives the flow. This anodic instability is analogous to the classical Marangoni instability induced by surface tension gradients. In this work, nature of the instability beyond the stability threshold is determined using a weakly nonlinear analysis. For the growth of well-developed pores beyond the threshold, a subcritical nature of the instability is essential. However, our weakly nonlinear analysis shows that the solutions emerging from neutral stability are supercritical in nature at all wavenumbers for the practical range of anodizing control parameters investigated. We also determine the region where the model is Hadamard stable, a necessary condition for well-posedness.

Pulsing-induced healing of a surface crack of a nickel-based alloy

In this work, we demonstrate the feasibility of applying electric pulses to heal surface cracks on nickel-based alloy GH4169 under compressive load. There exists an incubation time for the onset of the healing of a crack, which is associated with local temperature at the crack tip. The crack size decreases with increasing the pulsing time at a constant healing rate prior to complete healing of the crack. Increasing compressive load accelerates the healing process. The electric pulsing leads to the formation of an influential zone surrounding the crack with the finest grain sizes in the healed crack and the coarsest grain sizes away from the influential zone. The indentation hardness increases with the increase the distance to the crack tip of the healed crack. A model of viscous flow in the crack channel is proposed for the crack healing. The resultant force on the crack faces due to the crack healing increases with the increase of the healing time and the decrease of the crack width.

Evidence of Kelvin-Helmholtz and tearing mode instabilities at the magnetopause during space weather events

Introduction: Kelvin-Helmholtz (KH) and tearing mode (TM) instabilities are one of the most important mechanisms of solar wind energy, momentum and plasma transport within the magnetosphere.Methods: To investigate the conditions under which KHTM instabilities occur in the Earth environment it is fundamental to combine simultaneous multipoint in situ measurements and MHD simulations. We analyzed data from the THEMIS and Cluster spacecraft considering two Space Weather (SWE) events starting with an M2.0 flare event (hereafter Case-1) that occurred on 21 June 2015 and the most-intensive flare (X9.3) of solar cycle 24 that occurred on 6 September 2017 (hereafter Case-2).Results: Our analysis utilized a 2D MHD model for incompressible and viscous flow. The results from Case-1 indicate the presence of KH and TM instabilities, suggesting existence of observed low-amplitude oscillations at the nose of the magnetopause. However, the MHD simulations for Case-2 did not show any evidence of KH vortices, but did reveal the presence of “magnetic island” structures during a low-shear condition. The reconnection rate derived from the observations is compared with the computed one in the presence of developed instabilities inside the Earth’s magnetopause.

Numerical study of steady pipe flows and head loss coefficients

The study concerns steady pipe flows within 90o-bend and T-junctions, the head loss coefficients and the physical mechanisms responsible for the energy loss. Numerical viscous flow modelling based on SimpleFOAM solver were implemented in the study. Although secondary flow acts as the mechanism of energy loss in both the bend and in the branch flow of T-junction, the head loss coefficient in the former more critically depends on Reynolds (Re) number. This is supported by the comparison of the streamline fields and the radially varying profiles of the pressures from both cases. The location of flow separation prior to the secondary flow in the bend changes with Re number unlike the fixed location at the junction in the branch flow. The study confirms a practical implication related to the dependence of the head loss coefficients for pipe with 90o-bend and T-junction on flow velocity in an analysis of pipe network.

Effects of heat transfer on MHD suction–injection model of viscous fluid flow through Differential transformation and Hermite wavelet techniques

Effects of heat transfer on MHD suction–injection model of viscous fluid flow through Differential transformation and Hermite wavelet techniques

Hopf bifurcation control of a modified continuum traffic flow model

The stability of the transportation system refers to the structural stability of the system. When the system structure is unstable, local or global bifurcation phenomena will occur, which is one of the main reasons for nonlinear traffic phenomena such as congestion. To truly understand the internal mechanism of the formation of these phenomena, it is necessary to analyze the bifurcation of traffic flow. In this paper, the Hopf bifurcation control of a modified viscous macroscopic traffic flow model is studied by using the linear state feedback method, which changes the characteristics of the bifurcation phenomenon of the dynamic system and obtains the required dynamic behavior of the system. First, we can convert the original traffic model into the nonlinear ordinary differential form suitable for bifurcation analysis, solve the equilibrium point of the system, and carry out phase plane analysis. Then, the linear state feedback term is added and the corresponding controlled system is generated, the existence and type of Hopf bifurcation and the existence of saddle node bifurcation are proved. Numerical simulation results show that the analysis and control of Hopf bifurcation in the traffic model are well realized in this paper.

A Hermite-type collocation mesh-free approach for simulating incompressible viscous fluid flows

In this work, a novel Hermite-type mesh-free model for incompressible viscous fluid flows is proposed, as a way, to overcome the numerical difficulties experienced by solving under weak or strong formulation the pure stream-function Navier–Stokes equation. In this model a dimensionless virtual domain is utilized, in order to make an accurate dimensionless shape-functions of the recently developed Hermite-type collocation Weighted Least Square approximation, by using dimensionless scale parameters. Then, a Jacobian transformation matrix is built to express the shape-functions spatial derivatives from the virtual to the considered domain. The resolution of the obtained nonlinear algebraic system is performed by the High Order Continuation Method. Numerical tests were investigated on incompressible viscous isothermal fluid flows in lid-driven cavity, backward-facing step, sudden expansions and around various obstacle shapes. They show the advantages of the proposed model compared to the reference Hermite-type collocation models used for pure stream-function equation and the weak Galerkin procedures as Finite Element Method and Element Free Galerkin method, in term of computation accuracy, number of degree of freedom, implementation simplicity and computation time. The numerical and experimental results of literature confirm the validity and capability of the proposed dimensionless model to simulate fluid flows in a expended-lengths inflow–outflow geometry and around obstacles of circular, inclined elliptical and Joukowski airfoil shapes.

Weakly Nonlinear Analysis of Flow-Driven Porous Anodic Oxide

Porous anodic oxide (PAO) films are formed by the electrochemical oxidation of metals such as titanium, aluminum, and other metals in acidic solutions. The optimal selection of parameters leads to the formation of submicron-sized pores arranged in a parallel hexagonal array within these films. Porous anodic oxide has enormous industrial applications in the development of functional nanodevices. The present study builds upon the flow-driven porous anodic oxide model proposed by Mishra and Hebert. They have shown through a linear stability analysis of the model that the inter-pore distance in PAO is successfully determined by the competition between stabilizing oxide formation and destabilizing viscous flow. In this work, we investigate the weakly nonlinear analysis of the model to determine the nature of instability arising in flow-driven porous anodic films beyond the stability threshold. For formation of well- developed pores, the nature of instability must be subcritical. However, the results of weakly nonlinear analysis show that the solutions resulting from neutral stability exhibit a supercritical nature for the practical range of anodizing control parameters as shown in Figure 1. Thus, in order to make accurate nonlinear predictions about the formation of pores, it is imperative to incorporate additional physics into the viscous flow model. We also determine the Hadamard stability criteria by tracking the neutral wavenumber to ascertain the regions of well- posedness of the viscous flow model. Figure 1

Generalisation of the Penalised Wall Function Method for the Simulation of Turbulent flows With Unfavourable Pressure Gradients

The penalized wall function method for simulation of compressible near-wall turbulent flow regions in the numerical modeling of viscous compressible flows is developed. The method is formulated as a differential condition to match the outer and the wall function solutions and is based on a generalized characteristic-based volume penalization method to transfer shear stress from the outer region of the boundary layer to the wall. The method is modified to extend its applicability to turbulent flows with adverse pressure gradient, when separation and reattachment zones are formed, as well as to use computational meshes with coarser near-wall resolution. These advantages are demonstrated for two test problems, namely, the flow over a flat plate with zero and adverse pressure gradients.

On the internal velocity structure of sub-aqueous, gravity-driven granular flow: Measurements using MHz frequency sound

The vertical structure of downslope velocity within sub-aqueous gravity-driven flows of (smoother) glass beads and (rougher) natural sand is investigated for both fixed roughness and erodible beds using high-resolution, MHz-frequency acoustics. The observed velocity profiles within the O(1) cm thick, O(10) cm/s flows exhibit a negative shear layer extending downward from the sediment–water interface to a velocity maximum at ∼ 9 grain diameters depth within the layer, below which the velocities decrease to near-zero values at the pre-flow bed location for fixed roughness beds and to non-zero values for mobile beds. The attenuation of sound transmitted through the moving layer is used to constrain the depth-averaged solids concentration to a value of ∼ 0.52. The observed negative shear at the interface indicates that, unlike the sub-aerial case, interfacial friction is dynamically important in gravity-driven sub-aqueous granular flows. It is shown that the observed vertical structure of velocity within the layer can be well represented by continuum viscous flow models. Solids concentration and effective viscosity are estimated from the best-fit model parameters using the Zarraga–Hill–Leighton (2000) empirical relation for suspensions of negatively buoyant particles, yielding vertically averaged values ∼ 0.57. While the sub-millimeter vertical resolution of the measurements is too coarse to provide precise estimates of the friction velocity at the interface, the model-data comparisons nevertheless indicate that the vertical structure of the downslope flow consists of a weakly stratified dense layer and a thin, dilute transition layer between the dense flow and the overlying water.

Particle detachment in reservoir flows by breakage due to induced stresses and drag

Suspension-colloidal-nano transport in porous media encompasses the detachment of detrital fines against electrostatic attraction and authigenic fines by breakage, from the rock surface. While much is currently known about the underlying mechanisms governing detachment of detrital particles, including detachment criteria at the pore scale and its upscaling for the core scale, a critical gap exists due to absence of this knowledge for authigenic fines. For the first time, we integrate the 3D version of Timoshenko's beam theory of elastic cylinder deformation with a CFD-based model for viscous flow around the attached particle and with strength failure criteria for particle-rock bond. This results in a novel explicit criterium for fines detachment by breakage at the pore scale. The criterium includes analytical expressions for tensile and shear stress maxima along with two geometric diagrams which allow determining the breaking stress. This leads to an explicit formula for the flow velocity that provides the particle-rock bond breakage. Its upscaling yields a novel mathematical model for fines detachment by breakage, expressed in the form of the maximum retained concentration of attached fines versus flow velocity – maximum retention function (MRF) for breakage. We performed corefloods with piecewise constant increasing flow rates, measuring breakthrough concentration and pressure drop across the core. It was found out that the behaviour of the measured data is consistent with two-population colloidal transport, attributed to detrital and authigenic fines migration. Indeed, the laboratory data show high match with the analytical model for two-population colloidal transport, which validates the proposed mathematical model for fines detachment by breakage.

A new thin layer model for viscous flow between two nearby non‐static surfaces

AbstractWe propose a two‐dimensional flow model of a viscous fluid between two close moving surfaces. We show, using a formal asymptotic expansion of the solution, that its asymptotic behavior, when the distance between the two surfaces tends to zero, is the same as that of the the Navier‐Stokes equations.The leading term of the formal asymptotic expansions of the solutions to the new model and Navier‐Stokes equations are solution of the same limit problem, and the type of the limit problem depends on the boundary conditions. If slip velocity boundary conditions are imposed on the upper and lower bound surfaces, the limit is a solution of a lubrication model, but if the tractions and friction forces are known on both bound surfaces, the limit is a solution of a thin fluid layer model.The model proposed has been obtained to be a valuable tool for computing viscous fluid flow between two nearby moving surfaces, without the need to decide a priori whether the flow is typical of a lubrication or a thin fluid layer problem, and without the enormous computational effort that would be required to solve the Navier‐Stokes equations in such a thin domain.

Control of nonlinear bulk deformation and large shear strain on first-order phase transformation kinetics

Phase transformations play a key role in numerous coupled natural processes, and they are important for many industrial applications. However, the kinetics of phase transformations in coupled chemo-mechanical systems undergoing large mechanical deformations still needs to be better quantified. Here, we study the phase transformation kinetics of a two-phase binary mixture using the diffuse interface approach. We couple a Cahn–Hilliard type model with a mechanical model for a compressible viscous flow. The bulk compressibility is a nonlinear function of the pressure, and the shear viscosity is a nonlinear function of the concentration. The mechanical coupling is achieved by employing a pressure-dependent mechanical mixing term in the equation for the Gibbs energy. We derive a dimensionless system of equations which we solve numerically with a pseudo-transient method using conservative finite differences for discretization. We perform numerical simulations in 1D and 2D model setups considering far-field simple shear and pure shear. For a chemo-mechanically coupled system, we show that the velocity of the phase boundary is a linear function of the degree of metastability and, hence, confirm the hypothesis of “normal growth.” A stronger mechanical coupling and a larger volumetric effect of the chemical reaction result in lower phase boundary velocities. The 2D results show a significant impact of the mechanical coupling and the far-field deformation on the orientation and kinetics of the phase transformations. Under far-field simple shear and pure shear in 2D, the phase transformations generate string-like patterns. The orientation of these patterns is controlled by the applied far-field deformation and orientations differ by 45 degrees between simple shear and pure shear.

Astrocyte endfeet may theoretically act as valves to convert pressure oscillations to glymphatic flow.

The glymphatic system of cerebrospinal fluid transport through the perivascular spaces of the brain has been implicated in metabolic waste clearance, neurodegenerative diseases and in acute neurological disorders such as stroke and cardiac arrest. In other biological low-pressure fluid pathways such as in veins and the peripheral lymphatic system, valves play an important role in ensuring the flow direction. Though fluid pressure is low in the glymphatic system and directed bulk flow has been measured in pial and penetrating perivascular spaces, no valves have yet been identified. Valves, which asymmetrically favour forward flow to backward flow, would imply that the considerable oscillations in blood and ventricle volumes seen in magnetic resonance imaging could cause directed bulk flow. Here, we propose that astrocyte endfeet may act as such valves using a simple elastic mechanism. We combine a recent fluid mechanical model of viscous flow between elastic plates with recent measurements of in vivo elasticity of the brain to predict order of magnitude flow-characteristics of the valve. The modelled endfeet are effective at allowing forward while preventing backward flow.

Effects of heat transfer on MHD suction–injection model of viscous fluid flow through differential transformation and Bernoulli wavelet techniques

AbstractIn this study, a numerical solution of the velocity and heat transfer on the magnetohydrodynamic suction–injection model of viscous fluid flow has been studied. We use the differential transformation method and Bernoulli wavelet method to solve the highly nonlinear governing equations; applying appropriate similarity transformations and reducing governing equations to highly nonlinear coupled ordinary differential equations. The objective of this analysis is to determine how the suction parameter, Hartmann number, squeeze number, thermophoresis parameter, and Prandtl number affect the velocity and temperature profiles. When the current findings are compared with those that have already been published in the literature, confident suppositions are made, and it is discovered that there is considerable agreement. Graphs have been used to discuss the influence of nondimensional characteristics on velocity and temperature.

Nonlinear stability of planar stationary solutions to the viscous two-phase flow model in [formula omitted

In this paper, we consider the outflow problem of the viscous two-phase flow model in R+3. We show the global existence of the strong solution to the outflow problem and its convergences to the corresponding the planar stationary solution as time grows up with respect to the supersonic, subsonic, or sonic state respectively at the far field.

Influence of printing conditions on the extrudate shape and fiber orientation in extrusion deposition additive manufacturing

A numerical framework was developed in this study to investigate the influence of relevant Extrusion Deposition Additive Manufacturing (EDAM) processing conditions on the final fiber orientation, inter-bead void and cross-sectional geometry of the bead laid down as the extrudate. Specifically, four key processes of the EDAM process are studied, namely: (i) flow of 90° angle turn as the extrudate exits the nozzle and is laid down on the previous layer or the substrate, (ii) flow of the bead during compaction, (iii) flow of an extrudate deposited adjacent to the previously compacted bead, and (iv) flow of the adjacent bead during compaction. The simulations utilize an anisotropic viscous flow model implemented using the smoothed particle hydrodynamics method in Abaqus and fiber orientation vectors are evolved under the assumption of affine motion. The simulation results are compared with experiments for printed bead geometries produced and this comparison was shown to validate the modeling approach as useful for predicting fiber orientation, bead geometry, and bead-to-bead contact interface geometry. The processing parameters considered are nozzle height from the substrate, the ratio of the print speed to the extrusion speed (Vb/Ve), and the bead-to-bead lateral overlap distance. A series of virtual experiments were conducted, and the following observations were noted: (i) the bead printed with a high nozzle height has significantly more fiber alignment in the printing direction than the lower nozzle height, (ii) the ratio of the print speed and extrudate speed, Vb/Ve, of greater than unity results in greater fiber alignment than for Vb/Ve <1. The developed model illuminates the roles of process parameters in determining the microstructure of the printed bead and bead geometry.

Geodynamics of the Caucasus – Anatolian-Arabian region and Turkey-Syria Earthquakes 2023

The activation of natural disasters in the world requires the development of new approaches to the study of geological processes, in particular, at the boundaries of lithospheric plates, characterized by earthquakes, increased seismicity, volcanism, landslide processes, tsunamis and other dangerous natural processes and hazards. Earthquake of M 7.8 struck south -eastern Turkey and north - western Syria on 6 February 2023. The M 7.8 earthquake is the largest in Turkey since the 1939 Erzincan earthquake, and the second-strongest recorded in the country, after the 1668 North Anatolia earthquake. More than 52,800 deaths were confirmed: more than 46,100 in Turkey, and more than 6,700 in Syria. It is the deadliest natural disaster in Turkey's modern history. The earthquakes caused over US$100 billion in damages. The geodynamic models construction for the deep structure of natural hazards regions is an important contribution to the study of active continental margins, which is necessary for the earthquake forecast, prediction and prognosis, assessing geoecological risks and preparing population actions in the event of natural disasters and catastrophes. The Caucasus - Arabian region is a complex highly-stressed geodynamic structure, characterized by increased heat flow, high seismicity, magmatism and volcanism. The geodynamics of the Caucasus - Arabian region is determined by the collision of the Eurasian and Arabian lithosphere plates, as well as the complex history of the development of the Alpine-Himalayan belt and surrounding territories. The problem solution of geological structures formation and evolution in various complex geodynamic settings and natural hazards forecast and prognosis requires an analysis of all available geological - geophysical data, as well as the formulation and solution of problems of mechanical and mathematical modeling. Slow lithospheric deformations are simulated by models of viscous flow in multi-layered, incompressible, high-viscosity Newtonian fluid, using Navier-Stocks equation and discontinuity equation. The solution of the inverse problem of geodynamics by the direct method is developed. The first inverse problem of geodynamics was solved - the restoration of the velocity fields, pressures and stresses at the depth of the lithosphere according to the available data on the velocities on the surface. The second inverse problem of geodynamics has been posed and solved - the determination of the movement of boundaries at the depth of the lithosphere based on the given movements of the surface. The solutions obtained can be used to analyze deep geodynamic problems, and together with geothermal modeling, geological and geophysical methods and seismic tomography can serve as a reliable apparatus for studying deep geodynamics due to the formation and evolution of geological structures and the lithosphere stress-strain state researches. The solution of the problem is analyzed on the example of the Caucasus - Arabian region geodynamics. The Geodynamic concept of geoenvironment has been developed. Geodynamic models of the regions of hazardous natural processes in order to predict and prevent natural disasters and catastrophes are constructed. An algorithm for creating monitoring systems is suggested.

Global classical solutions to the viscous two-phase flow model with slip boundary conditions in 3D exterior domains

We consider the two-phase flow model in 3D exterior domains with slip boundary conditions. We establish the global existence of classical solutions of this system, provided that the initial energy is suitably small. Furthermore, we prove that the pressure has large oscillations and contains vacuum states when the initial pressure allows large oscillations and a vacuum. Finally, we also obtain the large-time behavior of the classical solutions.

Liquid sloshing in a baffled rectangular tank under irregular excitations

Sloshing responses in vertical and horizontal baffled tanks under irregular external excitations are investigated by employing a viscous fluid flow model with the Navier–Stokes solver. After the extensive validation of the present numerical model, the numerical experiment reveals many new understandings of the problem. A three-phase variation is suggested to describe the sloshing response under irregular excitations, that is, the first-order natural period controlling stage, the second-order natural period controlling stage, and the transitional stage between them. The sloshing periods are always around the corresponding natural periods with small standard deviations at the first- and second-order natural period controlling stages; while the decreased sloshing periods with large standard deviations can be observed at the transitional stage between them. The sloshing energy concentrated at a single natural frequency or multiple natural frequencies is the major reason for the phenomena. Compared to the results under regular excitations, smaller and larger sloshing amplitudes can be observed in the results of irregular excitations around the resonant and non-resonant frequency ranges, respectively. The normalized sloshing amplitudes calculated from the samplings of the large free surface amplitudes are always smaller than the samplings of the small free surface amplitudes.