Search

A few basic, intuitive, properties of the Navier–Stokes system of equations for incompressible fluid flows are discussed in this paper. We present a rephrased interpretation of the Navier–Stokes equation in a space having an arbitrary number of dimensions. We then derive spatially periodic solutions for the velocity and pressure fields that span an unbounded domain in three and four dimensions, given a smooth solenoidal initial velocity vector field. In these solutions all velocity components depend non-trivially on all coordinate directions. [ABSTRACT FROM AUTHOR]

This work presents a reduced order modeling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order models thanks to their capabilities to seamlessly handle large deformations of parametrized domains and in general to handle topological changes. The combination of embedded methods and reduced order models allows us to obtain fast evaluation of parametrized problems, avoiding remeshing as well as the reference domain formulation, often used in the reduced order modeling for boundary fitted finite element formulations. The resulting novel methodology is presented on linear elliptic and Stokes problems, together with several test cases to assess its capability. The role of a proper extension and transport of embedded solutions to a common background is analyzed in detail. [ABSTRACT FROM AUTHOR]

• A bubble transported by a highly viscous liquid takes a wide variety of shapes. • The bubble elongates in the direction of the flow upstream of the orifice. • Downstream of the orifice, the bubble contracts in the direction of the flow. • Bubbles contracted in the flow direction take 'crescent-moon' shapes. • Shape well-predicted by theory that assumes deformation follows the bulk flow field. Experiments and theory concern the behaviour of a small bubble carried through an orifice by a very viscous liquid. The liquid was polybutene oil, of viscosity about 70 Pa s, i.e. 70,000 times that of water. The Reynolds number of the flow is substantially less than one, hence the flow pattern is approximately radial flowing into, and away from, the orifice. These flow patterns have profound effects on the shape of an entrained bubble. On the upstream side, the acceleration of the liquid, as it approaches the orifice, causes elongation of the bubble since the front of the bubble moves faster than the back. On the downstream side, the reverse occurs: the back of the bubble moves fast than the front. Thus the height of the bubble diminishes as it moves away from the orifice, leading to the formation of a 'crescent-moon' shape. The shape of these bubbles can be predicted by considering the motion of a droplet of the same liquid replacing the bubble: the resulting geometric theory gives good predictions of bubble deformation approaching the orifice and of 'crescent-moon' formation downstream of the orifice. [ABSTRACT FROM AUTHOR]

Resonant three-dimensional nonlinear sloshing in a square-base basin is analysed numerically to investigate swirling instability. The aim of this research is based on understanding how viscosity influences this instability. Four different fluids at increasing Reynolds number were considered in a tank forced to oscillate in a horizontal motion. The present study investigates the tight relation between the energy dissipation and this instability, showing that water tends to dissipate more energy during its rotating motion than the other three liquids characterised by higher viscosity. This aspect is strictly linked to the occurrence of free-surface fragmentation and liquid impacts. The numerical solutions are provided using an enhanced version of the Smoothed Particle Hydrodynamics (SPH) model called δ -LES-SPH model which proved to be suitable for the simulation of violent free-surface flows. [ABSTRACT FROM AUTHOR]

A two-stage approach to the selection of the parameters of hydraulic channels of the spray nozzles is proposed. On the first stage, the preliminary assessment of their quality is made according to the nature of the flow of the atomized medium using the inviscid incompressible fluid model. On the second stage, the detailed calculation of the Navier-Stokes equations, the thermal conductivity, and the vorticity of the nonisothermal viscous flow are performed, taking into account the phenomena of phase transitions of the real medium for the nozzle designs and their parameters selected at the first stage. The technique of high-quality, simplified, cost-effective computing costs by assessing the impact of the geometric parameters of the sprayer channels to form fuel jets. The calculation of the velocity field and flow lines and flow field transformation to parametric rectangle with an orthogonal grid calculated by numerical conformal mapping are demonstrated. The influence of the channel configuration on the formation of the jet is analyzed. The distribution of velocities in different zones of the channel is estimated from the point of view of the possibility of controlling the spraying characteristics of the injector. [ABSTRACT FROM AUTHOR]

A numerical methodology is developed to combine the advantages of adaptive mesh refinement (AMR) and interface sharpening technique. A five-equation compressible multiphase model with capillary and viscous effects is considered. The solver employs a wave propagation method along with the Tangent of Hyperbola for INterface Capturing (THINC) scheme. To calculate interface normal and curvature, an implicit filtering method is introduced which transforms the sharpened volume fraction variable to a variant with smoothed distribution. The accuracy and performance of our method is assessed through its application to multiple compressible interface problems ranging from high-Mach number shock–interface interaction to gravity driven flows with viscosity and surface tension effects. The results obtained for one-dimensional shock-tube and tin–air interaction problems are shown to compare well with analytical data. The flow patterns predicted for shock–bubble interaction and under-water explosion match those from the landmark experimental and numerical studies. Furthermore, the trends and values predicted for spike position in the Rayleigh–Taylor instability and bubble’s center location in bubble rising are consistent with those found in literature. Particularly, it is shown that the coupled AMR-THINC method remarkably prevents excessive interface smearing and captures delicate interfacial features such as shear-induced instabilities encountered in shock–bubble interaction. [ABSTRACT FROM AUTHOR]

The method of numerical flow simulation in diesel engine spray devices channels is reviewed in the article. The efficiency of conformal mappings use for converting the flow domain to a parametric rectangle with orthogonal grid is declared and illustrated. In this method, the reduced boundary value problem for Navier-Stokes equations for velocity and pressure fields is solved in this rectangle. The numerical conformal mapping, based on Finite Element Method (FEM) is described. Boundary value problems of Laplace equations for real and imaginary component of mapping function are solved by FEM algorithm. The proposed simulation and qualitative estimation method for various configurations of the flow channel of the spray head is analyzed in the article. The influence of the angle of deflection from the axis channel sprayer nozzle on the flow velocity in the channel is described. The capacities of a software package for numerical conformal mapping are presented. [ABSTRACT FROM AUTHOR]

We present a numerical investigation of the simultaneous loading of a cocktail of propanediol and dimethyl sulfoxide into human sperm cells inside of a microchannel. The microchannel simulated has one central upstream inlet for cells, two upstream sheath inlets with one of the cryoprotective agents, and two downstream sheath inlets with the other cryoprotective agent. Of primary interest is how the complicated viscosity and velocity profiles caused by the viscous and miscible fluids affects the cells, both in terms of strain rate and cryoprotective agent mass transport. Despite the characteristic time scale of the trans-membrane mass transport being small, at certain flow rates, the high Peclet number flow inside of the microchannel limits the extracellular cryoprotectant concentration available to the cells. At low flow rates, the intracellular concentrations of both components will reach those of the perfectly mixed values. Increasing to moderate flow rates (near 1 μ L/min), the intracellular concentration of the upstream cryoprotective agent will exceed the perfectly mixed value, “super-loading”, while there is still appreciable loading of the downstream cryoprotectant. Increasing the flow rate towards 10 μ L/min, a large distribution of the upstream cryoprotectant is seen across the cells while minimal downstream cryoprotectant enters the cells. The utility of such a model to aid in the optimization of cryopreservation protocols for a range of cells and cryoprotective cocktails is discussed. [ABSTRACT FROM AUTHOR]

The laminar flow in microfluidic devices has shown promise as an effective delivery mechanism for cryoprotective agents to biological cells. For this method to gain more prevalence, its potential for use with more realistic and more complicated mixtures of cryoprotectants requires further exploration. In this work, we investigate the transport phenomena associated with a cryoprotectant cocktail consisting of 1.5 M 1,2-propanediol, 1.5 M dimethyl sulfoxide, and pure water. The viscous and miscible liquids are driven through a 25-cm long microchannel by a pressure gradient with inlet flow rate as the operating parameter. Our model resolves the spatially varying viscosity field, velocity field, and the concentrations of the three chemical species. With equal flow rates at each inlet, viscous sheets are formed and span the vertical direction of the channel. Depending on which cryoprotectant is introduced at the upstream inlets, the viscous sheets can move towards the center of the channel and be surrounding by less the less viscous mixture. This causes a unique velocity profile with three maxima in the transverse direction. As the inlet flow rates are decreased, the miscible liquids are afforded more time for molecular diffusion. Further decreasing the flow rate leads to a well-mixed viscous mixture of the three chemical species. The features of this cryoprotectant loading configuration are unique and, with additional optimization, could lead to improved cell survival rates during cryopreservation. [ABSTRACT FROM AUTHOR]

Within the framework of natural configurations developed by Rajagopal and Srinivasa, evolution within continuum thermodynamics is formulated as evolution of a natural configuration linked with the current configuration. On the other hand, withing the General Equation for Non-Equilibrium Reversible–Irreversible Coupling (GENERIC) framework, the evolution is split into Hamiltonian mechanics and (generalized) gradient dynamics. These seemingly radically different approaches have actually a lot in common and we show their compatibility on a wide range of models. Both frameworks are illustrated on isotropic and anisotropic rate-type fluid models. We propose an interpretation of the natural configurations within GENERIC and vice versa (when possible). • Equilibrium thermodynamics is considered to be a closed theory • Non-equilibrium thermodynamics, on the contrary, is not • In many frameworks an intensive research has been conducted separately • However, less attention is paid to their relation and general understanding • We compare the Natural Configuration framework and GENERIC on particular models [ABSTRACT FROM AUTHOR]

Abstract: We shake harmonically a thin horizontal viscous fluid layer (frequency forcing , only one harmonic), to reproduce the Faraday experiment and using the system derived in Rojas et al. (2010) invariant under horizontal rotations. When the physical parameters are suitably chosen, there is a critical value of the amplitude of the forcing such that instability occurs with at the same time the mode oscillating at frequency , and the mode with frequency . Moreover, at criticality the corresponding wave lengths and are such that if we define the family of equally spaced (horizontal) wave vectors on the circle of radius , then . It results under the above conditions that 0 is an eigenvalue of the linearized operator in a space of time-periodic functions (frequency ) having a spatially quasiperiodic pattern if . Restricting our study to solutions invariant under rotations of angle , gives a kernel of dimension 4. In the spirit of Rucklidge and Silber (2009) we derive formally amplitude equations for perturbations possessing this symmetry. Then we give simple necessary conditions on coefficients, for obtaining the bifurcation of (formally) stable time-periodic (frequency ) quasipatterns. In particular, we obtain a solution such that a time shift by half the period, is equivalent to a rotation of angle of the pattern. [Copyright &y& Elsevier]

Abstract: Gullies are widespread on slopes on the surface of Mars and have been investigated by numerous authors, yet their formation processes remain elusive. In an attempt to understand the possibility of a water-based origin for these forms, we undertook a series of flume experiments at Earth surface temperatures and pressures. Our objectives were to produce forms that resemble those most commonly observed on Mars, documenting their morphometric characteristics and identifying any statistically significant relationships between form and controlling factors of slope and flow rate. Experiments were conducted in a 1×1.5m2 flume filled with medium grain size sand. The experiments were run over a slope angle range of 10–30°, corresponding to the range for gullies on Mars. Water from a constant-head tank fed through 5mm silicone hose to a rotameter and then released just below the surface at the top of the slope. Gullies were produced at slope angle values of 10°, 20°, and 30° and flow rate values of 445, 705, 965, and 1260mLmin−1 at each angle. Eighteen parameters were identified and subsequently measured on each gully produced in the flume. Gully forms were successfully reproduced and displayed development of the fundamental morphological components observed on Mars: alcove, channel, and apron. Slope–gully form relationships for each component revealed the following results: higher slope angles formed shorter gullies with thicker apron deposits. Moreover, longer gullies were seen at higher flow rates. We concluded that forms visually similar to those observed on Mars can be created by water in the laboratory flume under terrestrial conditions. Morphometric parameters can be measured and permit identification of controlling factors. Experimental simulation of gullies appears possible with proper scaling of experimental parameters. Although not directly scalable to Mars, flume gully parameters may be used to develop numerical models in the future. [Copyright &y& Elsevier]

Abstract: We introduce a dynamical description based on a probability density of the vorticity in two-dimensional viscous flows such that the average vorticity evolves according to the Navier–Stokes equations. A time-dependent mixing index is defined and the class of probability densities that maximizes this index is studied. The time dependence of the Lagrange multipliers can be chosen in such a way that the masses associated with each vorticity value are conserved. When the masses are conserved then (1) the mixing index satisfies an H-theorem and (2) the mixing index is the time-dependent analogue of the entropy employed in the statistical mechanical theory of inviscid 2D flows. In the context of our class of probability densities we also discuss the reconstruction of the probability density of the quasi-stationary coherent structures from the experimentally determined vorticity-stream function relations. [Copyright &y& Elsevier]

Abstract: A differential geometrical formulation of the motion of an incompressible viscous fluid is presented. The geodesic equation on a manifold is extended with an additional term consisting of an endomorphism of the tangent space, and a class of curves defined by the resultant equation is introduced. Based on this extension, the motion of an incompressible viscous fluid is formulated as curves of this class in a diffeomorphism group, and the expression for the variational equation of the curves is derived. The expression is then shown to coincide with the governing equations for the Lagrangian displacement, which interprets the physical meaning of variation vector fields of the curves. The variational equation is reduced to a more simplified form which can be used to study evolution of the distances between fluid particles advected by a given basic flow. [Copyright &y& Elsevier]

Abstract: We consider the system of quasilinear equations describing 1D radiative and reactive viscous flows with arbitrarily large data. The large-time behavior of solutions in the case of first-order kinetics has been recently studied. In this paper, we present new results concerning the case of higher-order kinetics for fairly general kinetics law (unbounded with respect to density and temperature, and dealing with the ignition phenomenon), including and -stabilization rate bounds of power type. The power exponents of bounds improve essentially those known for related problems and are partially proved to be sharp. An effect of “faster equaling” of values in space for the concentration of unburned gas is also found. Finally we show how our results are modified in the case of reaction without diffusion. [Copyright &y& Elsevier]

• A model of microregion moving over a heated surface with wettability defects or patterns is developed. Heat transfer enhancement is found when receding micro-region passes through a localized region of increased substrate wettability. • For a patterned surface, even relatively narrow stripes of increased wettability lead to better heat transfer rates. • Marangoni stresses tend to decrease local evaporation rates. Modeling of evaporation in the microregion separating an adsorbed film and a macroscopic meniscus is important for a number of applications such as pool boiling and micro heat pipes. We develop a model of a moving microregion incorporating the effects of evaporation, viscous flow, surface tension, and two-component disjoining pressure and apply it to study motion of microregions over heated surfaces with wettability defects or patterns. Substantial heat transfer enhancement is found when a receding microregion passes over the portion of the substrate with higher wettability than the surrounding areas. The effect is explained in physical terms by widening of the part of the microregion with low thermal resistance. To achieve sustained heat transfer enhancement, we then consider a configuration in which the substrate is patterned by an array of high-wettability stripes and investigate the evaporative flux as a function of the geometry of the pattern. The effects of Marangoni stress at the interface are also studied and found to result in slight reduction of the average evaporative flux, as the tangential stress at the interface reduces the liquid supply into the microregion. [ABSTRACT FROM AUTHOR]