Viscous Flow Model Research Articles

A multi-branch finite deformation constitutive model for a shape memory polymer based syntactic foam

A multi-branch thermoviscoelastic-themoviscoplastic finite deformation constitutive model incorporated with structural and stress relaxation is developed for a thermally activated shape memory polymer (SMP) based syntactic foam. In this paper, the total mechanical deformation of the foam is divided into the components of the SMP and the elastic glass microballoons by using the mixture rule. The nonlinear Adam-Gibbs model is used to describe the structural relaxation of the SMP as the temperature crosses the glass transition temperature (Tg). Further, a multi-branch model combined with the modified Eying model of viscous flow is used to capture the multitude of relaxation processes of the SMP. The deformation of the glass microballoons could be split into elastic and inelastic components. In addition, the phenomenological evolution rule is implemented in order to further characterize the macroscopic post-yield strain softening behaviors of the syntactic foam. A comparison between the numerical simulation and the thermomechanical experiment shows an acceptable agreement. Moreover, a parametric study is conducted to examine the predictability of the model and to provide guidance for reasonable design of the syntactic foam.

A hyperbolic model for viscous Newtonian flows

We discuss a pure hyperbolic alternative to the Navier–Stokes equations, which are of parabolic type. As a result of the substitution of the concept of the viscosity coefficient by a microphysics-based temporal characteristic, particle settled life (PSL) time, it becomes possible to formulate a model for viscous fluids in a form of first-order hyperbolic partial differential equations. Moreover, the concept of PSL time allows the use of the same model for flows of viscous fluids (Newtonian or non-Newtonian) as well as irreversible deformation of solids. In the theory presented, a continuum is interpreted as a system of material particles connected by bonds; the internal resistance to flow is interpreted as elastic stretching of the particle bonds; and a flow is a result of bond destructions and rearrangements of particles. Finally, we examine the model for simple shear flows, arbitrary incompressible and compressible flows of Newtonian fluids and demonstrate that Newton’s viscous law can be obtained in the framework of the developed hyperbolic theory as a steady-state limit. A basic relation between the viscosity coefficient, PSL time, and the shear sound velocity is also obtained.

Derivation of a simplified relation for assessing aortic root pressure drop incorporating wall compliance.

Aging and some pathologies such as arterial hypertension, diabetes, hyperglycemia, and hyperinsulinemia cause some geometrical and mechanical changes in the aortic valve microstructure which contribute to the development of aortic stenosis (AS). Because of the high rate of mortality and morbidity, assessing the impact and progression of this disease is essential. Systolic transvalvular pressure gradient (TPG) and the effective orifice area are commonly used to grade the severity of valvular dysfunction. In this study, a theoretical model of the transient viscous blood flow across the AS is derived by taking into account the aorta compliance. The derived relation of the new TPG is expressed in terms of clinically available surrogate variables (anatomical and hemodynamic data). The proposed relation includes empirical constants which need to be empirically determined. We used a numerical model including an anatomically 3D geometrical model of the aortic root including the sinuses of Valsalva for their identification. The relation was evaluated using clinical values of pressure drops for cases for which the modified Gorlin equation is problematic (low flow, low gradient AS).

Solitary Wave Breaking on Irregular 3D Bathymetry Using a Coupled Potential + Viscous Flow Model

A three-dimensional (3D) coupled potential + viscous flow model based on a domain decomposition method is developed and applied to study shoaling and breaking of a solitary wave on a nonuniform bathymetry. The flow domain is decomposed into two subdomains separated by an interface: a wave generation and propagation subdomain modeled by a potential-flow (PF) solver and a shoaling and surf zone subdomain modeled by a Navier-Stokes equation (NSE) solver. The PF solver, based on a boundary-element method, is capable of modeling the motion of a piston wavemaker and the propagation of the resulting wave downstream. After the wave passes through the interface, it continues to propagate in the viscous-flow (NSE) subdomain, which is solved by a FEM. A free-surface capturing feature of the NSE solver allows simulation of wave breaking and the postbreaking behavior. Numerical results show good agreement with those of a large-scale wave-basin experiment of a solitary wave run-up on a 3D wedge. The simulation shows that breaking criteria and categorization for plane slopes do not apply to this particular bathymetry. The velocity and vorticity patterns during wave breaking are also examined to demonstrate the capabilities of the viscous-flow solver.

Global classical solution for a three-dimensional viscous liquid-gas two-fluid flow model with vacuum

This is a continuation of the paper (J. Math. Phys., 52(2011), 093102). We consider the Cauchy problem to the three-dimensional viscous liquid-gas two-fluid flow model. The global existence of classical solution is proved, where the initial vacuum is allowed.

Flow and evaporation in single micrometer and nanometer scale pipes

We report measurements of pressure driven flow of fluids entering vacuum through a single pipe of micrometer or nanometer scale diameter. Nanopores were fabricated by etching a single ion track in polymer or mica foils. A calibrated mass spectrometer was used to measure the flow rates of nitrogen and helium through pipes with diameter ranging from 10 μm to 31 nm. The flow of gaseous and liquid nitrogen was studied near 77 K, while the flow of helium was studied from the lambda point (2.18 K) to above the critical point (5.2 K). Flow rates were controlled by changing the pressure drop across the pipe in the range 0–31 atm. When the pressure in the pipe reached the saturated vapor pressure, an abrupt flow transition was observed. A simple viscous flow model is used to determine the position of the liquid/vapor interface in the pipe. The observed mass flow rates are consistent with no slip boundary conditions.

SPECTRAL NUMERICAL SIMULATION OF MAGNETO-PHYSIOLOGICAL LAMINAR DEAN FLOW

A computational simulation of magnetohydrodynamic laminar blood flow under pressure gradient through a curved bio-vessel, with circular cross-section is presented. Electrical conductivity and other properties of the biofluid (blood) are assumed to be invariant. A Newtonian viscous flow (Navier–Stokes magnetohydrodynamic) model is employed which is appropriate for large diameter blood vessels, as confirmed in a number of experimental studies. Rheological effects are therefore neglected as these are generally only significant in smaller diameter vessels. Employing a toroidal coordinate system, the steady-state, three-dimensional mass and momentum conservation equations are developed. With appropriate transformations, the transport model is non-dimensionalized and further simplified to a pair of axial and secondary flow momenta equations with the aid of a stream function. The resulting non-linear boundary value problem is solved with an efficient, spectral collocation algorithm, subject to physically appropriate boundary conditions. The influence of magnetic body force parameter, Dean number and vessel curvature on the flow characteristics is examined in detail. For high magnetic parameter and Dean number and low curvature, the axial flow is observed to be displaced toward the center of the vessel with corresponding low fluid particle vorticity strengths. Visualization is achieved with the MAPLE software. The simulations are relevant to cardiovascular biomagnetic flow control.

Rarefied gas flow in pressure and vacuum measurements

Flows of a gas through the piston-cylinder gap of a gas-operated pressure balance and in a general vacuum system have one aspect in common, namely that the gas is rarefied due, respectively, to the small dimensions and the low pressure. The flows in both systems could be characterised as being in either slip-flow or transition regimes. Therefore, fundamental research of flow in these regimes is useful for both pressure and vacuum metrology, especially for the gas-operated pressure balance where a continuum viscous flow model is widely used for determining the effective area of the pressure balance. The consideration of gas flow using the most suitable assumption would improve the accuracy of such a calculation. Moreover, knowledge about rarefied gas flow will enable gas behaviour in vacuum and low-flow leak detection systems to be predicted. This paper provides useful information about rarefied gas flow in both slip-flow and transition regimes.

The strength of gravitational core-mantle coupling

Gravitational coupling between Earth's core and mantle has been proposed as an explanation for a 6 year variation in the length-of-day (ΔLOD) signal and plays a key role in the possible superrotation of the inner core. Explaining the observations requires that the strength of the coupling, Γ, falls within fairly restrictive bounds; however, the value of Γ is highly uncertain because it depends on the distribution of mass anomalies in the mantle. We estimate Γ from a broad range of viscous mantle flow models with density anomalies inferred from seismic tomography. Requiring models to give a correlation larger than 70% to the surface geoid and match the dynamic core-mantle boundary ellipticity inferred from Earth's nutations, we find that 3 × 10 19 < Γ < 2 × 10 20 N m, too small to explain the 6 year ΔLOD signal. This new constraint on Γ has important implications for core-mantle angular momentum transfer and on the preferred mode of inner core convection.

Scale effects on tip loaded propeller performance using a RANSE solver

Traditionally, the quality of alternative propeller designs at full scale has been assessed by means of model scale tests. Due the large differences in Reynolds numbers between model and full scales, model-scale-based performance predictions may be questionable in cases where viscous effects are dominant. This paper presents a numerical study about scale effects on performance coefficients for a CLT propeller with different endplate geometries. Twelve endplate shape variations were analyzed in model and full scale using RANS code FINFLO. The SST k-ω turbulence model is used as a basic model for the study. Additional computations are made with other turbulence models. A special procedure for the generation of the computational grids is implemented to minimize computational errors in the comparison of the alternative geometries. The study provides also a RANS-based scale effect on the shape of radial circulation distribution predicted for different geometry variations. The research work gives an insight into which type of modifications at full scale could be analyzed by model scale viscous flow theory or model tests in ranking alternative designs. Differences found between model and full scale numerical results make model scale analysis questionable for some specific type of modifications when full-scale performance is sought.

Deformation–activation model of viscous flow of glass-forming liquids

We suggest a model, according to which the local low activation stretching of a valence bond network is a necessary condition for the realization of an elementary act of viscous flow of inorganic glasses and their melt-activated transition of the kinetic unit (bridge atom) into a deformed microregion. Exactly this kind of local configurational change of structure of a kinetic unit responsible for yield plays an important role in the temperature dependence of the viscosity of these systems, especially in the vicinity of vitrification of liquids. In the framework of this model the temperature dependence of free activation energy of viscous flow of glass melts in the wide temperature range is described and explained.

A nonlinear effective slip interface law for transport phenomena between a fracture flow and a porous medium

We present modeling of an incompressible viscous flow through a fracture adjacent to a porous medium. We consider a fast stationary flow, predominantly tangential to the porous medium. Slow flow in such setting can be described by the Beavers-Joseph-Saffman slip. For fast flows, a nonlinear filtration law in the porous medium and a non- linear interface law are expected. In this paper we rigorously derive a quadratic effective slip interface law which holds for a range of Reynolds numbers and fracture widths. The porous medium flow is described by the Darcys law. The result shows that the interface slip law can be nonlinear, independently of the regime for the bulk flow. Since most of the interface and boundary slip laws are obtained via upscaling of complex systems, the result indicates that studying the inviscid limits for the Navier-Stokes equations with linear slip law at the boundary should be rethought.

Rheological behavior of coir‐fiber‐filled polypropylene composites at constant shear stress

The rheological behavior of coir‐fiber‐filled polypropylene (PP) composite has been studied at constant shear stress. The shear stress versus shear rate relationship for the composite follows power law model of viscous flow. Unlike similar studies in the literature, the viscosity is treated as a stress‐independent parameter, which increases with the increase of fiber loading; but decreases with the rise of temperature. The SEM reveals that the fibers are loosely bound to the polymer matrix and the outer surface of the composite is rough and irregular, making it susceptible to high friction with the wall of the flow channel. With analogy to nth order chemical reaction, new formula has been derived for the activation energy of viscous flow, which is found to increase with the increase in the fiber content. The die‐swell ratio decreases with the increase of fiber loading, but increases with the rise of temperature. The elastics parameters of the composite such as the recoverable shear strain, the first normal stress difference, and the elastic strain induced by the stored energy in the capillary reservoir have been estimated based on the die‐swell data. POLYM. COMPOS., 36:51–61, 2015. © 2014 Society of Plastics Engineers

CFD Simulation for Separation of Carbon Dioxide-Methane Mixture by Pressure Swing Adsorption

A developing technology for gas separations is pressure swing adsorption, which has been proven to be more economical and energy efficient compared to other separation methods like cryogenic distillation and membrane separation. A pressure swing adsorption (PSA) column, with carbon dioxide-methane as feed mixture and 6-FDA based polyimides as the adsorbent, was modeled and simulated in this work. Ansys Fluent 12.1, along with supplementary user defined functions, was used to develop a 2D transient Eulerian laminar viscous flow model for the PSA column. The model was validated by comparing the simulated results with established analytical models for PSA. The developed numerical model was used to determine the carbon dioxide concentration in the column as a function of time based on different operating conditions. Effect of various operating parameters like pressure, temperature, and flow rate on the separation efficiency has been studied and reported. Optimization studies were carried out to obtain suitable operating conditions for the feed gases separation. Simulation studies were carried out to determine the separation length required for complete separation of the feed mixture corresponding to different inlet feed concentrations which were entering the column at a given flow rate.

Numerical study of free convective MHD flow past a vertical cone in non-Darcian porous media

A numerical study of buoyancy-driven unsteady natural convection boundary layer flow past a vertical cone embedded in a non-Darcian isotropic porous regime with transverse magnetic field applied normal to the surface is considered. The heat and mass flux at the surface of the cone is modeled as a power-law according to qw(x) = xm and q*w (x) = xn respectively, where x denotes the coordinate along the slant face of the cone. Both Darcian drag and Forchheimer quadratic porous impedance are incorporated into the two-dimensional viscous flow model. The transient boundary layer equations are then non-dimensionalized and solved by the Crank-Nicolson implicit difference method. The velocity, temperature and concentration fields have been studied for the effect of Grashof number, Darcy number, Forchheimer number, Prandtl number, surface heat flux power-law exponent (m), surface mass flux power-law exponent (n), Schmidt number, buoyancy ratio parameter and semi-vertical angle of the cone. Present results for selected variables for the purely fluid regime are compared with the non-porous study by Hossain and Paul [9] and are found to be in excellent agreement. The local skin friction, Nusselt number and Sherwood number are also analyzed graphically. The study finds important applications in geophysical heat transfer, industrial manufacturing processes and hybrid solar energy systems.

Free Convective MHD Flow Past a Vertical Cone with Variable Heat and Mass Flux

A numerical study of buoyancy-driven unsteady natural convection boundary layer flow past a vertical cone embedded in a non-Darcian isotropic porous regime with transverse magnetic field applied normal to the surface is considered. The heat and mass flux at the surface of the cone is modeled as a power law according to qwx=xm and qw*(x)=xm, respectively, where x denotes the coordinate along the slant face of the cone. Both Darcian drag and Forchheimer quadratic porous impedance are incorporated into the two-dimensional viscous flow model. The transient boundary layer equations are then nondimensionalized and solved by the Crank-Nicolson implicit difference method. The velocity, temperature, and concentration fields have been studied for the effect of Grashof number, Darcy number, Forchheimer number, Prandtl number, surface heat flux power-law exponent (m), surface mass flux power-law exponent (n), Schmidt number, buoyancy ratio parameter, and semivertical angle of the cone. Present results for selected variables for the purely fluid regime are compared with the published results and are found to be in excellent agreement. The local skin friction, Nusselt number, and Sherwood number are also analyzed graphically. The study finds important applications in geophysical heat transfer, industrial manufacturing processes, and hybrid solar energy systems.

Pulse propagation by a capacitive mechanism drives embryonic blood flow

Pulsatile flow is a universal feature of the blood circulatory system in vertebrates and can lead to diseases when abnormal. In the embryo, blood flow forces stimulate vessel remodeling and stem cell proliferation. At these early stages, when vessels lack muscle cells, the heart is valveless and the Reynolds number (Re) is low, few details are available regarding the mechanisms controlling pulses propagation in the developing vascular network. Making use of the recent advances in optical-tweezing flow probing approaches, fast imaging and elastic-network viscous flow modeling, we investigated the blood-flow mechanics in the zebrafish main artery and show how it modifies the heart pumping input to the network. The movement of blood cells in the embryonic artery suggests that elasticity of the network is an essential factor mediating the flow. Based on these observations, we propose a model for embryonic blood flow where arteries act like a capacitor in a way that reduces heart effort. These results demonstrate that biomechanics is key in controlling early flow propagation and argue that intravascular elasticity has a role in determining embryonic vascular function.

Added Mass and Aeroelastic Stability of a Flexible Plate Interacting With Mean Flow in a Confined Channel

This work presents a review and theoretical study of the added-mass and aeroelastic instability exhibited by a linear elastic plate immersed in a mean flow. We first present a combined added-mass result for the model problem with a mean incompressible and compressible flow interacting with an elastic plate. Using the Euler–Bernoulli model for the plate and a 2D viscous potential flow model, a generalized closed-form expression of added-mass force has been derived for a flexible plate oscillating in fluid. A new compressibility correction factor is introduced in the incompressible added-mass force to account for the compressibility effects. We present a formulation for predicting the critical velocity for the onset of flapping instability. Our proposed new formulation considers tension effects explicitly due to viscous shear stress along the fluid-structure interface. In general, the tension effects are stabilizing in nature and become critical in problems involving low mass ratios. We further study the effects of the mass ratio and channel height on the aeroelastic instability using the linear stability analysis. It is observed that the proximity of the wall parallel to the plate affects the growth rate of the instability, however, these effects are less significant in comparison to the mass ratio or the tension effects in defining the instability. Finally, we conclude this paper with the validation of the theoretical results with experimental data presented in the literature.

Self-Ordering Process of Hexagonal Cells in Porous Anodic TiO&lt;sub&gt;2&lt;/sub&gt; Nanotubes

Cylindrical TiO2nanotubes and hexagonal TiO2nanotubes were obtained in the anodizing process of titanium in fluoride-containing electrolyte. Based on the experimental findings and viscous flow model, a mechanism of self-ordering process of hexagonal cells arrangement for porous anodic TiO2nanotubes (PATNT) is proposed in this paper. The analysis results show that oxygen evolution in the pore bottoms plays an important role in the self-ordering process. Oxide grows around the oxygen bubbles in the pore bottoms, which results in the formation of cylindrical TiO2nanotubes. Volume expansion of TiO2takes place during the anodizing process. Plastic deformation and repulsive force caused by volume expansion are responsible for self-ordering process of PATNT hexagonal cells.

Model of viscous flow of glass-forming liquids and glasses

Model of viscous flow of glass-forming liquids and glasses