Numerical prediction of flow in a model of a (potential) soft acting peristaltic blood pump

This paper presents a numerical study of the flow field in a novel ‘soft’ acting peristaltic pump. The pump has potential applications wherever pumping of biological or sensitive fluids with reduced damage is required. The application of the device presented is as a blood pump. The model of the pump comprises a cylindrical tube that forms three chambers. The walls of these chambers move radially as a function of time. The pumping action is initiated by applying phased movement between the chambers. The flow is treated as laminar, unsteady, incompressible, Newtonian, and with a moving boundary. The governing equations are solved using a finite element method (FEM). An operating speed of 60 cycle min⁻¹ has been chosen. The results show that a periodic solution can be achieved after four cycles. The velocity field, streamline and shear stress are presented and discussed. The flow has generally a two‐way pulsatile nature, moving forwards and backwards. However, at the outlet, there is a net outflow over one cycle against a zero pressure head. Net flow linearly decreases to zero with increasing pressure head. Copyright © 2000 John Wiley & Sons, Ltd.     

Pressure-driven flow of wormlike micellar solutions in rectilinear microchannels

In this paper the inhomogeneous response of the (two species) VCM model (Vasquez et al., A network scission model for wormlike micellar solutions. I. Model formulation and homogeneous flow predictions, J. Non-Newtonian Fluid Mech. 144 (2007) 122–139) is examined in steady rectilinear pressure-driven flow through a planar channel. This microstructural network model incorporates elastically active network connections that break and reform mimicking the behavior of concentrated wormlike micellar solutions. The constitutive model, which includes non-local effects arising from Brownian motion and from the coupling between the stress and the microstructure (finite length worms), consists of a set of coupled nonlinear partial differential equations describing the two micellar species (a long species ‘A’ and a shorter species ‘B’) which relax due to reptative and Rouse-like mechanisms as well as rupture of the long micellar chains. In pressure-driven flow, the velocity profile predicted by the VCM model deviates from the regular parabolic profile expected for a Newtonian fluid and exhibits a complex spatial structure. An apparent slip layer develops near the wall as a consequence of the microstructural boundary conditions and the shear-induced diffusion and rupture of the micellar species. Above a critical pressure drop, the flow exhibits shear banding with a high shear rate band located near the channel walls. This pressure-driven shear banding transition or ‘spurt’ has been observed experimentally in macroscopic and microscopic channel flow experiments. The detailed structure of the shear banding profiles and the resulting flow curves predicted by the model depend on the magnitude of the dimensionless diffusion parameter. For small channel dimensions, the solutions exhibit ‘non-local’ effects that are consistent with very recent experiments in microfluidic geometries (Masselon et al., Influence of boundary conditions and confinement on non local effects in flows of wormlike micellar systems, Phys. Rev. E 81 (2010) 021502).     

The cumulative stress hazard density as an alternative to the Weibull model

A simple, easily reproduced experiment based on artificial flaws has been proposed which demonstrates that the distribution of the minimum failure load does not necessarily follow a Weibull distribution. The experimental result presented in the paper clearly indicates that the Weibull distribution with its strictly increasing function, is incapable of approximating a constant probability of failure over a loading region.New fundamental concepts have been introduced referred to as ‘hazard stress density’ and ‘cumulative hazard stress density’. These concepts helped derive an equation giving the probability of failure without making use of the notions ‘flaws’ and ‘locally initiated failure by flaws’. As a result, the derived equation is more general than earlier models. The cumulative hazard stress density is an important fingerprint of materials and can be used for determining the reliability of loaded components. It leaves materials to ‘speak for themselves’ by not imposing a power law dependence on the variation of the critical flaws which is always the case if the Weibull model is used.An important link with earlier models has also been established. We show that the cumulative hazard stress density is numerically equal to the product of the number density of the flaws with a potential to cause failure and the probability that a flaw will be critical at the specified loading stress.We show that, predictions of the probability of failure from tests related to a small gauge length to a large gauge length are associated with large errors which increase in proportion with the ratio of the gauge lengths. Large gauge length ratios amplify the inevitable errors in the probability of failure associated with the small gauge length to a level which renders the predicted probability for failure of the large gauge length meaningless.Finally, a general integral has been derived, giving the reliability associated with time interval and random loading of a material with flaws. The integral has been validated by a Monte Carlo simulation.     

Numerical study of hysteresis in annular swirling jets with a stepped‐conical nozzle

This study investigates the experimentally observed hysteresis in the mean flow field of an annular swirling jet with a stepped‐conical nozzle. The flow is simulated using the Reynolds‐averaged Navier–Stokes (RANS) approach for incompressible flow with a k–ε and a Reynolds stress transport (RSTM) turbulence model. Four different flow structures are observed depending on the swirl number: ‘closed jet flow’, ‘open jet flow low swirl’, ‘open jet flow high swirl’ and ‘coanda jet flow’. These flow patterns change with varying swirl number and hysteresis at low and intermediate swirl numbers is revealed when increasing and subsequently decreasing the swirl. The influence of the inlet velocity profile on the transitional swirl numbers is investigated. When comparing computational fluid dynamics with experiments, the results show that both turbulence models predict the four different flow structures and the associated hysteresis and multiple solutions at low and intermediate swirl numbers. Therefore, a good agreement exists between experiments and numerics. Copyright © 2006 John Wiley & Sons, Ltd.     

Symmetric and anti-symmetric Rayleigh–Lamb modes in sinusoidally corrugated waveguides: An analytical approach

The wave propagation analysis in corrugated waveguides is considered in this paper. Elastic wave propagation in a two-dimensional periodically corrugated plate is studied here analytically. The dispersion equation is obtained by applying the traction free boundary conditions. Solution of the dispersion equation gives both symmetric and anti-symmetric modes. In a periodically corrugated waveguide all possible spectral order of wave numbers are considered for the analytical solution. It has been observed that the truncation of the spectral order influences the results. Truncation number depends on the degree of corrugation and the frequency of the wave. Usually increasing frequency requires increasing number of terms in the series solution, or in other words, a higher truncation number. For different degrees of corrugation the Rayleigh–Lamb symmetric and anti-symmetric modes are investigated for their non-propagating ‘stop bands’ and propagating ‘pass bands’. To generate the dispersion equation for corrugated plates with a wide range of the degree of corrugation, appropriate truncation of the spectral orders has to be considered. Analytical results are given for three different degrees of corrugation in three plates. Resonance of symmetric and anti-symmetric modes in these plates, their ‘cut-off’, ‘cut-on’, ‘branch-point’, ‘change-place’, ‘mode conversion’ and ‘pinch points’ at various frequencies are also studied.     

Influence of bubble expansion and relative velocity on the performance and stability of an airlift pump

An airlift pump which raises liquid by means of compressed air introduced near the lower end of the eduction pipe is an example of a self-control system. It has been shown by Hjalmars (1973) that an occasionally observed breakdown in the self-control mechanism, which leads to instability, is due to the fact that the control mechanism is delayed, with the effect that a small, time-dependent perturbation of the stationary flow satisfies a differential equation with delayed argument. This investigation was carried out with the assumption of a single-phase flow of an ideal incompressible liquid. The aim of the present study is to consider the stability conditions of an airlift pump within the frame of a more general flow model, namely a separate two-phase flow of compressible gas and incompressible liquid, which takes into account the effects of the expasion of gas bubbles during their lift and of the relative velocity, i.e. the difference in the velocity of gas bubbles and the liquid.     

Flow Separation and Turbulence in Jet Pumps for Thermoacoustic Applications

The effect of flow separation and turbulence on the performance of a jet pump in oscillatory flows is investigated. A jet pump is a static device whose shape induces asymmetric hydrodynamic end effects when placed in an oscillatory flow. This will result in a time-averaged pressure drop which can be used to suppress acoustic streaming in closed-loop thermoacoustic devices. An experimental setup is used to measure the time-averaged pressure drop as well as the acoustic power dissipation across two different jet pump geometries in a pure oscillatory flow. The results are compared against published numerical results where flow separation was found to have a negative effect on the jet pump performance in a laminar flow. Using hot-wire anemometry the onset of flow separation is determined experimentally and the applicability of a critical Reynolds number for oscillatory pipe flows is confirmed for jet pump applications. It is found that turbulence can lead to a reduction of flow separation and hence, to an improvement in jet pump performance compared to laminar oscillatory flows.     

Finding the operating point of Eulerian flow machines

Examples of Eulerian flow machines (EFM) are turbomachines, jet pumps and vortex amplifiers working with incompressible non-cavitating flow. They are ‘Eulerian’ in the sense used by Paynter² in his work on turbomachines subject primarily to dynamic flow forces. Efficient methods are specified in this paper for finding the operating point of an EFM from its characteristics and any two state-defining variables. A trivial example is to find the torque and pressure of a pump when the speed and flow are given. This is simple because the usual constant-speed characterisation favours the solution, but if other pairs of variables are given, the problem is less simple. For jet pumps or the many ‘power fluidic’ devices the variety of problems is much greater because of combinatorial aspects, although the fluid mechanics is analogous to that of the turbomachine. Solution procedures are specified first for turbomachines; there are six ‘algorithms’. For general ‘3-terminal’ EFM (jet-pumps etc) it is shown that there are 108 characterisation formats and that the 30 listed algorithms enable any of them to be solved given any possible variable-pair. Graphical and computational implementations are described     

Opposing mixed convection and its interaction with radiation inside eccentric horizontal cylindrical annulus

In the present investigation, the coupled phenomenon of opposing mixed convection and radiation within differentially heated eccentric horizontal cylindrical annulus has been numerically simulated. The radiation transfer contributed from the participating medium is obtained by solving the nonlinear integro‐differential radiative transfer equation using discrete ordinate method. The participating gray medium is considered to be emitting, absorbing and isotropically scattering. The walls of the annulus are considered to be opaque, diffuse and gray. In the study it has been observed that the Richardson number ‘Ri’ has a small effect on the total Nusselt number ‘Nu’ in mixed convection heat transfer with or without radiation. From the present investigation it is found that substantial changes occur in isotherms as well as in flow patterns, when the Richardson number is allowed to vary in the range of 0.01–1. The influence of radiative parameters on the interaction phenomenon has been delineated through isotherm and streamline pattern. Copyright © 2008 John Wiley & Sons, Ltd.     

Stabilization of a cantilever pipe conveying fluid using electromagnetic actuators of the transformer type

The article presents an investigation of the stabilization of a cantilever pipe discharging fluid using electromagnetic actuators of the transformer type. With the flow velocity reaching a critical value, the straight equilibrium position of the pipe becomes unstable, and self-excited lateral vibrations arise. Supplying voltage to the actuators yields two opposite effects. First, each of the actuators attracts the pipe, thus introduces the effect of negative stiffness which destabilizes the middle equilibrium. Second, lateral vibrations change the gap in magnetic circuits of the actuators, which leads to oscillations of magnetic field in the cores and the electromagnetic phenomena of induction and hysteresis that impede the motion of the pipe. The combination of these two non-linear effects is ambiguous, so the problem is explored both theoretically and experimentally. First, a mathematical model of the system in form of a partial differential equation governing the dynamics of the pipe coupled with two ordinary differential equations of electro-magnetodynamics of the actuators is presented. Then, the equation of the pipe’s dynamics is discretized using the Galerkin procedure, and the resultant set of ordinary equations is solved numerically. It has been shown that the overall effect of actuators action is positive: the critical flow velocity has been increased and the amplitude of post-critical vibrations reduced. These results have been validated experimentally on a test stand.

     

电动潜油离心泵流道堵塞振动模型研究

电动潜油泵以其独具的特点和优势在油田生产过程中得到了日益广泛的应用,但过高的故障率给油田开发带来效率和经济上的损失。其核心部件离心泵也是故障易发部件,经常出现流道堵塞,严重影响机组的正常运转。本文结合电潜泵机组的工作特性和力学性能,建立了一套潜油离心泵流道堵塞的振动识别模型,并推导了振动模型的运动方程。利用自建的大型实验装置,模拟了该类故障井的实际生产并测得了井口三维振动信号,绘制了信号的时域图和频域图。此外,本文引入小波分析方法对信号进行了细致化分析,研究了此类故障的振动特性并验证了所建模型的可靠性。     

Generalizing the Boussinesq approximation to stratified compressible flow

The simplifications required to apply the Boussinesq approximation to compressible flow are compared with those in an incompressible fluid. The larger degree of approximation required to describe mass conservation in a stratified compressible fluid using the Boussinesq continuity equation has led to the development of several different sets of ‘anelastic’ equations that may be regarded as generalizations of the original Boussinesq approximation. These anelastic systems filter sound waves while allowing a more accurate representation of non-acoustic perturbations in compressible flows than can be obtained using the Boussinesq system. The energy conservation properties of several anelastic systems are compared under the assumption that the perturbations of the thermodynamic variables about a hydrostatically balanced reference state are small. The ‘pseudo-incompressible’ system is shown to conserve total kinetic and anelastic dry static energy without requiring modification to any governing equation except the mass continuity equation. In contrast, other energy conservative anelastic systems also require additional approximations in other governing equations. The pseudo-incompressible system includes the effects of temperature changes on the density in the mass conservation equation, whereas this effect is neglected in other anelastic systems. A generalization of the pseudo-incompressible equation is presented and compared with the diagnostic continuity equation for quasi-hydrostatic flow in a transformed coordinate system in which the vertical coordinate is solely a function of pressure. To cite this article: D.R. Durran, A. Arakawa, C. R. Mecanique 335 (2007).     

An Alternative Description of Viscous Coupling in Two-Phase Flow through Porous Media

A new formalism is developed to describe the viscous coupling phenomena between two immiscible, flowing fluids in porous media. The formulation is based on the notation of ‘two-phase mixture’ in which the relative motion between an individual phase and the mixture in porous media can be described by a diffusion equation. The present formulation is derived from Darcy's law with cross-terms without making further approximations. However, the new formulation requires fewer effective parameters to be determined experimentally, thus offering a more viable tool for the study of two-phase flow dynamics with viscous coupling in porous media. Moreover, it is found that no new term appears in the present model in cases with and without viscous coupling; instead, the incorporation of viscous coupling only modifies the effective parameters. It can thus be concluded that viscous coupling does not represent a fundamentally new phenomenon within the framework of the present formulation.     

On the Construction of an Experimentally Based Set of Equations to Describe Cocurrent and Countercurrent, Two-Phase Flow of Immiscible Fluids Through Porous Media

Generalized flow equations developed for two-phase flow through porous media contain a second term that enables proper account to be taken of capillary coupling between the two flowing phases. In this study, a partition concept, together with a novel capillary pressure equation for countercurrent flow, have been introduced into Kalaydjian’s generalized flow equations to construct modified flow equations which enable a better understanding of the role of capillary coupling in horizontal, two-phase flow. With the help of these equations it is demonstrated that the reduced flux observed in countercurrent flow, as compared to cocurrent flow, can be explained by the reduction in the driving force per unit volume which comes about because of capillary coupling. Also, it is shown experimentally that, because fluids flow through a void space reduced in magnitude due to the presence of immobile irreducible and residual saturations, the capillary coupling parameter should be defined in terms of a reduced porosity, rather than in terms of porosity. Moreover, it is shown statistically that the countercurrent relative permeability curve is proportional to the cocurrent relative permeability curve, the constant of proportionality being the capillary coupling parameter. Finally it is suggested that one can eliminate the need to determine experimentally countercurrent relative permeability curves by making use of an equation constructed for predicting the magnitude of the capillary coupling parameter.     

Near‐wall profiles of mean flow and turbulence quantities predicted by eddy‐viscosity turbulence models

This paper presents for the simple flow over a flat plate the near‐wall profiles of mean flow and turbulence quantities determined with seven eddy‐viscosity turbulence models: the one‐equation turbulence models of Menter and Spalart & Allmaras; the k‐ω two‐equation model proposed by Wilcox and its TNT, BSL and SST variants and the $k-\sqrt{k}L$ two‐equation model. The results are obtained at several Reynolds numbers ranging from 10⁷ to 2.5 × 10⁹. Sets of nine geometrically similar Cartesian grids are adopted to demonstrate that the numerical uncertainty of the finest grid predictions is negligible. The profiles obtained numerically have relevance for the application of so‐called ‘wall function’ boundary conditions. Such wall functions refer to assumptions about the flow in the viscous sublayer and the ‘log law’ region. It turns out that these assumptions are not always satisfied by our results, which are obtained by computing the flow with full near‐wall resolution. In particular, the solution in the ‘log‐law’ region is dependent on the turbulence model and on the Reynolds number, which is a disconcerting result for those who apply wall functions. Copyright © 2009 John Wiley & Sons, Ltd.     

Flow analysis for a double suction centrifugal machine in the pump and turbine operation modes

A double suction centrifugal machine has been studied, both experimentally and numerically, operating as a pump and as a turbine. Experimentally, the static performance of the machine working as a pump was obtained. These measurements were compared with equivalent numerical results from a URANS calculation. As a second step, the numerical results have been exploited to get detailed information about the flow in both operating modes (pump and turbine). The main goals of the study are, first, the validation of the numerical procedure proposed and second, the possible turbine operation of the impeller, which could point out a wider working range for the machine. The first aspect is handled by detailed analysis in the pump mode, according to previous experience of the research group. The second objective is obtained by using the numerical model to explore the flow fields obtained, when working in an inverse mode. Therefore, the presented results join the use of a numerical methodology and the turbine mode of operation for a centrifugal impeller, providing insight into the flow characteristics. When working as a pump, the flow at the suction side is characterized by the existence of an inlet tongue, which tends to enforce a uniform flow for the nominal conditions. For the turbine mode, flow patterns in the impeller, volute and suction regions are carefully investigated. The influence of the specific geometrical arrangement is also considered for this operation mode. Copyright © 2008 John Wiley & Sons, Ltd.     

Investigation on periodically developed heat transfer in a specially enhanced channel

The heat transfer and the flow resistance in the channel with periodic flow-inclining fins attached on the wall have been studied numerically and experimentally on the characteristics in the periodically fully developed flow region. The effect of the fin angle from 0° to 23.2° has been verified on the thermal performance and the flow resistance. The results reveal that the heat transfer is obviously enhanced for both the laminar and the turbulent flow. Analyses also show that the enhancement is accordant to the improvement of the field synergy between the flow velocity and the temperature gradient. Assessments under the identical pump power consumption show that the fin of β = 16.0° is the best in most cases. The most enhancement ratio fall in between 2 and 7.5. The conductivity of the fin material has also been demonstrated to be an important factor to the thermal performance.     

Advantageous swirling flow in 45° end-to-side anastomosis

The effects of swirling flow on the flow field in 45° end-to-side anastomosis are experimentally investigated using a particle image velocimetry technique to reveal fluid dynamic advantages of swirling flow in the vascular graft. Non-swirling Poiseuille inlet flow unnecessarily induces pathological hemodynamic features, such as high wall shear stress (WSS) at the ‘bed’ side and large flow separation at the ‘toe’ side. The introduction of swirling flow is found to equalize the asymmetric WSS distribution and reduces the peak magnitude of WSS. In particular, the intermediate swirling intensity of S = 0.45 induces the most uniform axial velocity and WSS distributions compared with weaker or stronger swirling flows, which addresses the importance of proper selection of swirling intensity in the vascular graft to obtain optimum flow fields at the host vessel. In addition, swirling flow reduces the size of flow separation because it disturbs the formation of Dean-type vortices in secondary flow and inhibits secondary flow collision. The beneficial fluid dynamic features of swirling flow obtained in this study are helpful for designing better vascular graft suppressing pathological hemodynamic features in the recipient host vessel.     

激波与堆积粉尘相互作用的数值模拟

基于双流体模型和测定的堆积粉尘的本构方程 ,利用AUSM+ 格式 ,对激波与堆积粉尘的相互作用进行了数值模拟。计算所反映的流场结构与实验图像一致。此外还对激波强度 ,颗粒材料密度等对流场的影响进行了讨论。     

An investigation of the effects of solution heat treatment on mechanical properties for AA 6xxx alloys: experimentation and modelling

A series of thermal-mechanical tests have been designed and carried out on the aluminium alloy AA 6082 to investigate the effects of solution heat treatment (SHT) time on the mechanical properties for a range of deformation rates at the SHT temperature of 525 °C. Particularly the effects of SHT time on the flow stress, ductility and anisotropy of the material are investigated experimentally. Based on Pearl’s growth rate equation and diffusion theory, a SHT completeness variable is introduced to model the microstructural evolution of the material during the SHT period. This SHT evolution variable is incorporated into a viscoplastic material model to simulate the material flow at different levels of SHT completeness. A new set of unified SHT viscoplastic constitutive equations is formulated and the constants within the equation set are determined from the experimental data of AA 6082, using an Evolutionary Programming (EP) based optimisation software package. Further experimental work has been carried out for different deformation and SHT conditions to validate the model predictions.