Effect of ultrasonic vibrations on the flow of a viscoelastic liquid

The rheological characteristics of a viscoelastic liquid flow, on which finite-amplitude ultrasonic shear vibrations have been superimposed, are investigated. It is shown that at periodic deformation amplitudes of 5 µ or more there is a thixotropic reduction of the viscosity and elasticity of the system owing to the destruction of certain types of structural bonds. The experimental apparatus is described.Moscow Institute of Chemical Machine Building. Translated from Mekhanika Polimerov, No. 6, pp. 1097–1099, November–December, 1971.     

Numerical investigation of blood flow. Part I: In microvessel bifurcations

In some diseases there is a focal pattern of velocity in regions of bifurcation, and thus the dynamics of bifurcation has been investigated in this work. A computational model of blood flow through branching geometries has been used to investigate the influence of bifurcation on blood flow distribution. The flow analysis applies the time-dependent, three-dimensional, incompressible Navier–Stokes equations for Newtonian fluids. The governing equations of mass and momentum conservation were solved to calculate the pressure and velocity fields. Movement of blood flow from an arteriole to a venule via a capillary has been simulated using the volume of fluid (VOF) method. The proposed simulation method would be a useful tool in understanding the hydrodynamics of blood flow where the interaction between the RBC deformation and blood flow movement is important. Discrete particle simulation has been used to simulate the blood flow in a bifurcation with solid and fluid particles. The fluid particle method allows for modeling the plasma as a particle ensemble, where each particle represents a collective unit of fluid, which is defined by its mass, moment of inertia, and translational and angular momenta. These kinds of simulations open a new way for modeling the dynamics of complex, viscoelastic fluids at the micro-scale, where both liquid and solid phases are treated with discrete particles.     

Allocation of long-term financial transmission rights for transmission expansion

Long-term financial transmission rights (FTRs) could be used to create incentives for small-scale transmission investments. However, these new investments may cause negative externalities on existing FTRs. Therefore the system operator needs a protocol for awarding incremental FTRs for new transmission capacity that maximize investors’ preferences while simultaneously accounting for under-allocation of the existing network capacity by existing FTRs. To preserve revenue adequacy, the system operator calculates a minimum amount of currently unallocated FTRs (or proxy FTRs) that satisfies the power flow constraints in the existing network. The challenge is to define the proxy awards. Hogan proposes to define them as the best use of the current network along the same direction as the incremental FTR awards. This includes allowing positive or negative incremental FTR awards. In this paper we present an implementation through bi-level programming of Hogan’s proposal for allocation of long-term FTRs and apply it to a radial line and one of Hogan’s examples. Our results show that the simultaneous feasibility of the transmission investment depends on factors such as investor and preset proxy preferences, existing FTRs, and transmission capacity in both the existing network and all proposed expansions of it.     

An optimal capacity assignment for the robust design problem in capacitated flow networks

This paper proposes an exact algorithm to solve the robust design problem in a capacitated flow network in which each edge has several possible capacities. A capacitated flow network is popular in our daily life. For example, the computer network, the power transmission network, or even the supply chain network are capacitated flow networks. In practice, such network may suffer failure, partial failure or maintenance. Therefore, each edge in the network should be assigned sufficient capacity to keep the network functioning normally. The robust design problem (RDP) in a capacitated flow network is to search for the minimum capacity assignment of each edge such that the network still survived even under the edge’s failure. However, how to optimally assign the capacity to each edge is not an easy task. Although this kind of problem was known of NP-hard, this paper proposes an efficient exact algorithm to search for the optimal solutions for such a network and illustrates the efficiency of the proposed algorithm by numerical examples.     

Temporal variation of velocity components in a turbulent open channel flow: Identification of fractal dimensions

Fractals are objects which have similar appearances when viewed at different scales. Such objects have details at arbitrarily small scales, making them too complex to be represented by Euclidian space; hence, they are assigned a non-integer dimension. Some natural phenomena have been modeled as fractals with success; examples include geologic deposits, topographic surfaces and seismic activities. In particular, time series have been represented as a curve with fractal dimensions between one and two. There are different ways to define fractal dimension, most being equivalent in the continuous domain. However, when applied in practice to discrete data sets, different ways lead to different results. In this study, three methods for estimating fractal dimension are described and two standard algorithms, Hurst’s rescaled range analysis and box-counting method (BC), are compared with the recently introduced variation method (VM). It was confirmed that the last method offers a superior efficiency and accuracy, and hence may be recommended for fractal dimension calculations for time series data. All methods were applied to the measured temporal variation of velocity components in turbulent flows in an open channel in Shiraz University laboratory. The analyses were applied to 2500 measurements at different Reynold’s numbers and it was concluded that a certain degree of randomness may be associated with the velocity in all directions which is a unique character of the flow independent of the Reynold’s number. Results also suggest that the rigid lateral confinement of flow to the fixed channel width allows for designation of a more-or-less constant fractal dimension for the spanwise velocity component. On the contrary, in vertical and streamwise directions more freedom of movements for fluid particles sets more room for variation in fractal dimension at different Reynold’s numbers.     

负压抽液分装的数学模型

本文介绍了负压抽液分装的数学模型 .由于考虑到所讨论液态物质的渗透性及污染性大等特点 ,采用负压抽液的原理 ,根据能量守恒理论确定抽液所需的负压 (真空度 ) ;根据克拉珀龙方程、分子流运动论的 Knudsen公式等理论 ,确定达到额定压力 (真空度 )所需的时间 (即装置的起动时间 ) .据此设计了一套含有不完全真空保护系统的分装装置 ,用这套装置进行的实验和实际操作 ,其真空度、时间数据与确定值 (计算值 )基本相符 .表明所建立的数学模型正确 ,据此设计的这套装置已成功用于液态物质的分装 .     

Electromagnetic flow control in liquid metals using Lorentz force techniques

Flow measurement and flow control in opaque and aggressive liquids such as metal melts are challenging tasks in industrial fluid mechanics. Optical measurement techniques as well as submerging probes or control units cannot be applied in case of highly severe environment; hence, contactless electromagnetic methods are of interest for practical flow control because of relatively high electrical conductivity of investigated materials. In this paper we present working principle and experimental results of two such contactless techniques. First, time-of-flight Lorentz force velocimetry (LFV), which allows to determine the flow rate of liquid metal without information about any fluid properties or magnetic field magnitude by cross-correlation of two Lorentz force signals. Secondly, Lorentz torque velocimetry (LTV) - a technique, which uses an electromagnetic pump with a torque sensor connected to the pump's shaft. In the methods so-called Lorentz force [1] is measured, which has electromagnetic nature and is proportional to velocity and flow rate of conductive liquid. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Predicting the flow of two-phase food mixtures

The flows of single-phase liquids and two-phase food mixtureshave been predicted using a model that considers the mixtureas two interpenetrating phases—one liquid and the otherflowing solids. Mass and momentum balances for each phase aresolved using a finite-difference scheme. Predictions of the velocity profile of a single-phase non-Newtonianliquid down a pipe showed agreement with an analytical solutionto the problem. Predictions of the flow of the same liquid arounda 90° bend, with a dead leg, agreed with predictions froma commercial software package. The shear and normal stresses in a food mixture were measuredusing a large-scale annular shear cell. These data were incorporatedinto equations of the Herschel-Bulkley form of rheological modeland implemented in the finite-difference model. Predictionsindicated that mixtures consisting of liquid and solids of nearequal density will exhibit little difference in the velocitiesof the liquid and solids components when the mixture flows downa pipe. Flow profiles around the 90° bend and dead leg showedthe expected pattern of flow around the bend with very low liquidand solids velocities within the dead leg and no recirculationbehind the bend. Further work is needed to verify experimentallythese predictions and to apply the model to other process geometries.     

Two-phase flow simulation for distinguishing deformable particles with a LiMCA system

In the metallurgical industry, Liquid Metal Cleanliness Analyser (LiMCA) commercial equipment cannot distinguish between hard particles (e.g., oxides, borides) and deformable particles (e.g., bubbles, molten salts). Therefore, hard particle concentrations can sometimes be grossly overestimated, which reduces the measurement accuracy. However, the method could potentially discriminate between deformable particles and hard particles by evaluating the particle's ability to deform. In this work, the coupled multiphysics problem of a particle deforming within current-carrying aluminium metal passing through the electric sensing zone (ESZ) is simulated using the conservative level-set (CLS) method. An emphasis is placed on understanding the transient deformation history, and the effect of the capillary number, Reynolds number, and confinement ratio on deformation are studied. Furthermore, a computational basis is given to estimate the influence of particle deformation on electrical resistance pulses (ERP). It is found that ERP features of deformation particles, including the peak magnitude and the pulse width, are different from those of hard particles. Based on the results, the effect of a particle's deformation and the feasibility to discriminate it from non-deformable particles in the LiMCA system is evaluated.     

Locating specialized service capacity in a multi-hospital network

Multi-hospital systems have become very common in today’s healthcare environment. However, there has been limited published research examining the opportunities and challenges of pooling specialized services to a subset of hospitals in the network. Therefore, this paper considers how hospital networks with multiple locations can leverage pooling benefits when deciding where to position specialized services, such as magnetic resonance imaging (MRI), transplants, or neonatal intensive care. Specifically, we develop an optimization model to determine how many and which of a hospital network’s hospitals should be set up to deliver a specialized service. Importantly, this model takes into account both financial considerations and patient service levels. Computational results illustrate the value of optimally pooling resources across a subset of hospitals in the network versus two alternate approaches: (1) delivering the service at all locations and requiring each site to handle its own demand, or (2) locating the service at one hospital that handles all network demand.     

Approximate decomposition methods for the analysis of multicommodity flow routing in generalized queuing networks

In this study we deal with network routing decisions and approximate performance evaluation approaches for generalized open queuing networks (OQN), in which commodities enter the network, receive service at one or more arcs and then leave the network. Exact performance evaluation has been applied for the analysis of Jackson OQN, where the arrival and service processes of the commodities are assumed to be Poisson. However, the Poisson processes’ hypotheses are not a plausible or acceptable assumption for the analysis of generalized OQN, as their arrival and service processes can be much less variable than Poisson processes, resulting in overestimated system performance measures and inappropriate flow routing solutions. In this paper we merge network routing algorithms and network decomposition methods to solve multicommodity flow problems in generalized OQN. Our focus is on steady-state performance measures as average delays and waiting times in queue. The main contributions are twofold: (i) to highlight that solving the corresponding multicommodity flow problem by representing the generalized OQN as a Jackson OQN may be a poor approximation and may lead to inaccurate estimates of the system performance measures, and (ii) to present a multicommodity flow algorithm based on a routing step and on an approximate decomposition step, which leads to much more accurate solutions. Computational results are presented in order to show the effectiveness of the proposed approach.     

Modeling unsteady flow characteristics using smoothed particle hydrodynamics

Smoothed particle hydrodynamics (SPH) method has been extensively used to simulate unsteady free surface flows. The works dedicated to simulation of unsteady internal flows have been generally performed to study the transient start up of steady flows under constant driving forces and for low Reynolds number regimes. However, most of the fluid flow phenomena are unsteady by nature and at moderate to high Reynolds numbers. In this study, first a benchmark case (transient Poiseuille flow) is simulated to evaluate the ability of SPH to simulate internal transient flows at low and moderate Reynolds numbers (Re = 0.05, 500 and 1500). For this benchmark case, the performance of the two most commonly used formulations for viscous term modeling is investigated, as well as the effect of using the XSPH variant. Some points regarding using the symmetric form for pressure gradient modeling are also briefly discussed. Then, the application of SPH is extended to oscillating flows imposed by oscillating body force (Womersley type flow) and oscillating moving boundary (Stokes’ second problem) at different frequencies and amplitudes. There is a very good agreement between SPH results and exact solution even if there is a large phase lag between the oscillating pressure difference and moving boundary and the movement of the SPH particles generated. Finally, a modified formulation for wall shear stress calculations is suggested and verified against exact solutions. In all presented cases, the spatial convergence analysis is performed.     

A Lagrangian-based SPH-DEM model for fluid–solid interaction with free surface flow in two dimensions

A Lagrangian-based SPH-DEM coupling model is proposed to study fluid–solid interaction (FSI) problems with free-surface flow. In this model, SPH uses an incompressible divergence-free scheme for simulating complex flow problems. Based on the Mohr–Coulomb criterion with tension cut, the DEM describes the characteristics of solid deformation and failure by means of contact models between particles. The coupling mechanism between SPH and DEM is realised by the decoupling of the force field during the process of fluid–solid interaction. That is, the motions of fluid and solid particles are reflected by the Navier–Stokes equations and interactions among solid particles are determined by Newton's second law in the DEM. To demonstrate the applicability of the SPH-DEM model, three case studies are used to verify the different fluid interaction situations with rigid bodies, deformable objects, and granular assemblies, respectively. The results of the proposed model shows good agreement with experimental data and indicates that it is capable of capturing the features of solid movement, deformation and failure under complex flow conditions with convincing accuracy and high efficiency.     

stresses and reversible deformations during shear flow of polymer solutions and melts

The influence of the accumulated elastic energy on the relationships between tangential stresses, the first difference between the normal stresses and the reversible deformations during isothermal shearing steady-state flow of polymer solutions and melts, is analyzed. It is shown that the reversible deformation in the non-Newtonian flow region is related to the tangential and normal stresses by Lodge's formula, if the thixotropic disruption of the structural flow units is accompanied by the dissipation of the elastic energy accumulated in them; the conservation of the elastic energy accumulated during the flow causes exceeding of the reversible deformation values as compared with the values calculated by Lodge's formula.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 886–895, September–October, 1972.     

Lattice Boltzmann 3D flow simulations on a metallic foam

In this paper a lattice Boltzmann method (LBM) is used to simulate isothermal incompressible flow in a RCM-NCX-1116 metallic foam. The computational technique is a multiple relaxation time (MRT) lattice Boltzmann equation model. Computer aided X-ray micro-tomography is used to obtain 3D images of the metallic foam, providing the geometry and information required for LB simulations of a single phase flow.Pressure drops are computed and successfully compared to experimental measures and correlated with Ergun’s equation. Invariance of Ergun’s parameters A and B with the sampling rate of the images is observed.     

A cycle augmentation algorithm for minimum cost multicommodity flows on a ring

Minimum cost multicommodity flows are a useful model for bandwidth allocation problems. These problems are arising more frequently as regional service providers wish to carry their traffic over some national core network. We describe a simple and practical combinatorial algorithm to find a minimum cost multicommodity flow in a ring network. Apart from 1 and 2-commodity flow problems, this seems to be the only such “combinatorial augmentation algorithm” for a version of exact mincost multicommodity flow. The solution it produces is always half-integral, and by increasing the capacity of each link by one, we may also find an integral routing of no greater cost. The “pivots” in the algorithm are determined by choosing an >0, increasing and decreasing sets of variables, and adjusting these variables up or down accordingly by . In this sense, it generalizes the cycle cancelling algorithms for (single source) mincost flow. Although the algorithm is easily stated, proof of its correctness and polynomially bounded running time are more complex.     

流形上的微分Harnack 估计

In the thesis, we study the differential Harnack estimate for the heat equation of the Hodge Laplacian deformation of (p, p)-forms on both fixed and evolving (by Kähler-Ricci flow) Kähler manifolds, which generalize the known differential Harnack estimates for (1, 1)-forms. On a Kähler manifold, we define a new curvature cone C_p and prove that the cone is invariant under Kähler-Ricci flow and that the cone ensures the preservation of the nonnegativity of the solutions to Hodge Laplacian heat equation. After identifying the curvature conditions, we prove the sharp differential Harnack estimates for the positive solution to the Hodge Laplacian heat equation. We also prove a nonlinear version coupled with the Kähler-Ricci flow after obtaining some interpolating matrix differential Harnack type estimates for curvature operators between Hamilton’s and Cao’s matrix Harnack estimates. Similarly, we define another new curvature cone, which is invariant under Ricci flow, and prove another interpolating matrix differential Harnack estimates for curvature operators on Riemannian manifolds.     

Study of the cosmic rays transport problems using second order parabolic type partial differential equation

It has been exactly 100 years since Hess’s historical discovery: an extraterrestrial origin of cosmic rays [1]. Galactic cosmic rays (GCR) being charged particles, penetrate the heliosphere and are modulated by the solar magnetic field. The propagation of cosmic rays is described by Parker’s transport equation [2], which is a second order parabolic type partial differential equation. It is time dependent 4-variables (with r, θ, φ, R, meaning: distance from the Sun, heliolatitudes, heliolongitudes and particles’ rigidity, respectively) equation which is a well known tool for studying problems connected with solar modulation of cosmic rays. Transport equation contains all fundamental processes taking place in the heliosphere: convection, diffusion, energy changes of the GCR particles owing to the interaction with solar wind’s inhomogeneities, drift due to the gradient and curvature of the regular interplanetary magnetic field and on the heliospheric current sheet.     

Influence of power-law index on transitional Reynolds numbers for flow over a semi-circular cylinder

In this work, the governing partial differential equations (continuity and Cauchy’s momentum equations) describing the flow of power-law type non-Newtonian fluids across a semi-circular cylinder (oriented with its curved surface in the upstream direction) have been solved numerically. In particular, consideration has been given to the delineation of the critical Reynolds numbers denoting the onset of flow separation from the surface of the cylinder and the onset of the laminar vortex shedding regime. This information is germane to establish the scaling of the macroscopic characteristics like drag coefficient and Strouhal number on the governing parameters, namely, Reynolds number and power-law index. The present results clearly suggest that the transitional Reynolds numbers show a strong dependence on the type (shear-thinning and shear-thickening) of fluid behavior as well as on the severity of the shear-dependence of the viscosity. With reference to the behavior seen in Newtonian fluids, the flow remains not only attached to the surface up to higher Reynolds numbers, but shear-thinning behavior also delays the onset of the laminar vortex shedding regime. As expected, shear-thickening fluids, of course, display the opposite characteristics.     

Asymmetric flow networks

This paper provides a new model of network formation that bridges the gap between the two benchmark game-theoretic models by Bala and Goyal (2000a) – the one-way flow model, and the two-way flow model – and includes both as limiting cases. As in both the said models, a link can be initiated unilaterally by any player with any other in what we call an “asymmetric flow” network, and the flow through a link towards the player who supports it is perfect. Unlike those models, there is friction or decay in the opposite direction. When this decay is complete there is no flow and this corresponds to the one-way flow model. The limit case when the decay in the opposite direction (and asymmetry) disappears corresponds to the two-way flow model. We characterize stable and strictly stable architectures for the whole range of parameters of this “intermediate” and more general model. A study of the efficiency of these architectures shows that in general stability and efficiency do not go together. We also prove the convergence of Bala and Goyal’s dynamic model in this context.