Numerical simulation of hemodynamic interactions of red blood cells in micro-capillary flow

The hemodynamic interactions of red blood cells （RBCs） in a microcapillary flow are investigated in this paper. This kind of interaction is considered as the non-contact mutual interaction of cells, which is important in the suspension flow of blood, but not sufficiently understood. The distributed Lagrange multiplier/fictitious domain method in the lattice Boltzmann framework is used to solve the suspension of the RBCs. The modification of the flow due to the cells, the dependence of the cell deformation on the flow and the cell-cell interaction via the fluid are discussed. It is revealed that the long-range hydrodynamic interaction with a long interacting distance, more than about 5 times of the RBC equivalent radius, mainly has effect on the rheology properties of the suspension, such as the mean velocity, and the short-range interaction is sensitive to the shape of the cell in the microcapillary flow. The flow velocity around the cell plays a key role in the cell deformation. In the current configuration of the flow and cells, the cells repel each other along the capillary.     

Couple stress fluid flow in a rotating channel with peristalsis

This article describes a new model for obtaining closed-form semi-analytical solutions of peristaltic flow induced by sinusoidal wave trains propagating with constant speed on the walls of a two-dimensional rotating infinite channel. The channel rotates with a constant angular speed about the z-axis and is filled with couple stress fluid. The governing equations of the channel deformation and the flow rate inside the channel are derived using the lubrication theory approach. The resulting equations are solved, using the homotopy perturbation method(HPM), for exact solutions to the longitudinal velocity distribution, pressure gradient, flow rate due to secondary velocity, and pressure rise per wavelength. The effect of various values of physical parameters, such as, Taylor's number and couple stress parameter, together with some interesting features of peristaltic flow are discussed through graphs. The trapping phenomenon is investigated for different values of parameters under consideration. It is shown that Taylor's number and the couple stress parameter have an increasing effect on the longitudinal velocity distribution till half of the channel, on the flow rate due to secondary velocity, and on the number of closed streamlines circulating the bolus.     

HEMODYNAMICS FOR ASYMMETRIC INLET AXIAL VELOCITY PROFILE IN CAROTID BIFURCATION MODEL

The asymmetric inlet velocity profile has been observed in phantom model using LDA and in health subjects using Magnet Resonance （MR）. The effects of asymmetric inlet axial velocity profile on the flow field and the Wall Shear Stress （WSS） of carotid bifurcation were numerically studied herein with the TF-AHCB model, The results show that the Wall Shear Stress Gradient （WSSG） in the front part of the sinus for inward-tilting inlet axial velocity profile is nearly 2 times of that for the symmetric one in the beginning of systole, the end of systole, and diastole, respectively. The area of WSS below 5× 10^-3 Pa at the outer wall of the sinus for outward-tilting inlet axial velocity profile is 1.5 times of that for the inward-tilting one during diastole of the cardiac cycle. The asymmetric inlet velocity profiles can reduce the flow velocity near the inner wall of the sinus, which has been normally considered a high velocity region. It is concluded that besides bifurcation geometry and flow waveform, the asymmetry of inlet velocity profile is probably a factor influencing atherosclerosis.     

An experimental study of impact loading on deck of shore-connecting jetties exposed to oblique waves and current

The impact pressure from waves is an important issue to be considered in the design of coastal structures. In this paper, the waves acting on the deck of a shore-connecting jetty on a slope exposed to oblique waves and in the presence of current are examined based on laboratory experiments. The impact pressures are measured on a 1：50 scale model of a jetty head with down-standing beams and berthing members. The relations of the impact pressure with the incident wave angle and the current velocity are examined. It is shown that the impact pressure is sensitive to the wave angle and the current velocity. A computational model for the impact load on the deck of shore-connecting jetties exposed to oblique waves and current is developed.     

SYNERGY OF WALL SHEAR STRESS AND CIRCUMFERENTIAL STRESS IN STRAIGHT ARTERIES

The Wall Shear Stress （WSS） generated by blood flow and Circumferential Stress （CS） driven by blood pressure have been thought to play an important role in blood flow-dependent phenomena such as angiogenesis, vascular remodeling, and atherosgenesis. The WSS and CS in straight arteries were calculated by measuring the blood pressure, center-line velocity, wall thickness, and radius of vessels. The WSS and CS in the time domain were then decomposed into the amplitude and phase in the frequency domain. The CS amplitude to the WSS amplitude ratio （referred as stress ampli tude ratio, Zs ） and the phase difference between the CS and the WSS （referred as stress phase difference, SPA） in the fre quency domain were calculated to characterize the synergy of the CS and WSS. Numerical results demonstrated that the CS is not in phase with the WSS, a time delay in the time domain or a stress phase difference in the frequency domain between the WSS and the CS exists. Theoretical analysis demonstrated that the Zs and SPA are primarily determined by the local fac tors （blood viscosity, local inertial effects, local geometry, loeal elasticity） and the input impedance of whole downstream arterial beds. Because the arterial input impedance has been shown to reflect the physiological and pathological states of whole downstream arterial beds, the stress amplitude ratio Zs and stress phase difference SPA would be thought to be the appropriate indices to reflect the effects of states of whole downstream arterial beds on the local blood flow dependent phenomena such as angiogenesis, vascular remodeling, and atherosgenesis.     

The simulation of multiphase flow field in implantable blood pump and analysis of hemolytic capability

The numerical simulation of the axial flow impeller blood pump NIVADIII is carried out by using a CFD multiphase flow model. The hydrodynamic performance of the pump and the flow field in the pump are analyzed, and the shear stress distribution is obtained. A hemolytic prediction model based on the shear stress is built based on the calculation results, and it can be used for quantitative predictions of the hemolytic behavior of a blood pump. Hemolysis tests in vitro were performed 6 times with fresh bovine blood. At each time, the flow of the pump NIVADIII is 5 L/min and the outflow tract pressure is 100 mmHg. According to the tests, the plasma free hemoglobin (FHB) content and the hematocrit (HCT) are measured after 0 s, 0.5 s, 1 s, 1.5 s, …4 s. At the end of each experiment Normal Index of Hemolysis (NIH) of NIVADIII is calculated. The average of NIH is 0.0055 g/100L, almost identical with that obtained from the hemolytic prediction model. This method can be applied in the selection stage of a blood pump.     

A NEW METHOD FOR PREDICTION OF PRODUCTIVITY OF FRACTURED HORIZONTAL WELLS BASED ON NON-STEADY FLOW

Hydraulic fracturing technologies of horizontal well are important ways to develop oil-gas field with low permeability. Productivity forecast of fractured horizontal wells is a difficult problem of hydraulic fracturing technologies. Basing on non-steady flow of fractures fluid during production, applying potential function principles, superposition principle and mathematical method for solving, coupling of seepage flow in the formation and pipe flow in the well bore, a new model on multi-fracture interference productivity forecast of fractured horizontal well is established in this article. The results indicate the coincidence rate between this model and practice is high. The pressure loss in the horizontal well bore has definite influence on the production status of fractured horizontal wells. The productions of different fractures in horizontal well bore are unequal, the productions of outer fractures are higher than middle fractures; the pressure in the well bore shows an uneven distribution, the pressure declines gradually from finger tip to heel end. Asymmetry of fractures may make productivity of fractured horizontal wells decline. The conclusions are instructive in designing fractured horizontal well for low permeability reservoir.     

INFLUENCE OF SURFACTANT ON TWO-PHASE FLOW REGIME AND PRESSURE DROP IN UPWARD INCLINED PIPES

The influence of a surfactant on the two-phase flow regime and the pressure drop in upward inclined pipes is investigated for various gas/liquid flow rates.The air/water and air/100 ppm sodium dodecyl sulphate aqueous solution are used as the working fluids.The influence of the surfactant on the two-phase flow regime in upward inclined pipes is investigated using the electrical tomographic technique.For 0o,2.5o and 5o pipe inclinations,the surfactant has obvious effect on the transition from the stratified wavy flow to the annular flow,and the range of the stratified smooth flow regime is also extended to higher gas velocities.For 10o pipe inclination,no stratified flow regime is observed in the air/water flow.In the air/surfactant solution system,however,the stratified flow regime can be found in the range of and.For all inclination angles,the changes of the pressure gradient characteristics are accompanied with the flow pattern transitions.Adding surfactant in a two-phase flow would reduce the pressure gradient significantly in the slug flow and annular flow regimes.In the annular flow regime,the pressure gradient gradually becomes free of the influence of the upward inclined angle,and is only dependent on the property of the two-phase flow.     

Flow of a micropolar fluid in a micro-channel under the action of an alternating electric field: Estimates of flow in bio-fluidic devices

The paper is devoted to a study of the electro-osmotic flow of a micropolar bio-fluid, when the flow takes place between two plates that are in a state of periodic vibrations. Considering blood as a micropolar fluid, it is found that the amplitude of oscillation of the microparticles of blood increases when the micropolar effect is pronounced more and more and that a rise in DebyeHückel parameter enhances both the velocity and microrotation gradient. The results provide guidelines for the improvement of design of bio-sensing and micro-fluidic devices. The study leads to the conclusion that electrical double layers formed in the vicinity of the wall can significantly alter the flow dynamics of physiological fluids in micro-bio-fluidic devices.     

EFFECTS OF PARENT ARTERY SEGMENTATION AND ANEURISMALWALL ELASTICITY ON PATIENT-SPECIFIC HEMODYNAMIC SIMULATIONS

It is well known that hemodynamics and wall tension play an important role in the formation,growth and rupture of aneurysms.In the present study,the authors investigated the influence of parent artery segmentation and aneurismal-wall elasticity on patient-specific hemodynamic simulations with two patient-specific cases of cerebral aneurysms.Realistic models of the aneurysms were constructed from 3-D angiography images and blood flow dynamics was studied under physiologically representative waveform of inflow.For each aneurysm three computational models were constructed:Model 1 with more extensive upstream parent artery with the rigid arterial and aneurismal wall,Model 2 with the partial upstream parent artery with the elastic arterial and aneurismal wall,Model 3 with more extensive upstream parent artery with the rigid wall for arterial wall far from the aneurysm and the elastic wall for arterial wall near the aneurysm.The results show that Model 1 could predict complex intra-aneurismal flow patterns and wall shear stress distribution in the aneurysm,but is unable to give aneurismal wall deformation and tension,Model 2 demonstrates aneurismal wall deformation and tension,but fails to properly model inflow pattern contributed by the upstream parent artery,resulting in local misunderstanding Wall Shear Stress (WSS) distribution,Model 3 can overcome limitations of the former two models,and give an overall and accurate analysis on intra-aneurismal flow patterns,wall shear stress distribution,aneurismal-wall deformation and tension.Therefore we suggest that the proper length of extensive upstream parent artery and aneurismal-wall elasticity should be considered carefully in establishing computational model to predict the intra-aneurismal hemodynamic and wall tension.     

THE CALCULATION OF THE PROFILE-LINEAR AVERAGE VELOCITY IN THE TRANSITION REGION FOR ULTRASONIC HEAT METER BASED ON THE METHOD OF LES

The measurement accuracy of an ultrasonic heat meter depends on the relationship of the profile-linear average velocity.There are various methods for the calculation of the laminar and turbulence flow regions,but few methods for the transition region.At present,the traditional method to deal with the transition region is to adopt the relationship for the turbulent flow region.In this article,a simplified model of the pipe is used to study the characteristics of the transition flow with specific Reynolds number.The k-εmodel and the Large Eddy Simulation(LES)model are,respectively,used to calculate the flow field of the transition region,and a comparison with the experiment results shows that the LES model is more effective than the k-εmodel,it is also shown that there will be a large error if the relationship based on the turbulence flow is used to calculate the profile-linear average velocity relationship of the transition flow.The profile-linear average velocity for the Reynolds number ranging from 5 300 to 10 000 are calculated,and the relationship curve is obtained.The results of this article can be used to improve the measurement accuracy of ultrasonic heat meter and provide a theoretical basis for the research of the whole transition flow.     

Influence of artificial ecological floating beds on river hydraulic characteristics

The artificial ecological floating bed is widely used in rivers and lakes to repair and purify polluted water. However, the water flow pattern and the water level distribution are significantly changed by the floating beds, and the influence on the water flow is different from that of aquatic plants. In this paper, based on the continuous porous media model, a moveable two-layer combination model is built to describe the floating bed. The influences of the floating beds on the water flow characteristics are studied by numerical simulations and experiments using an experimental water channel. The variations of the water level distribution are discussed under conditions of different flow velocities（ v= 0.1 m/s, 0.2 m/s, 0.30 m/s, 0.4 m/s）, floating bed coverage rates（20%, 40%, 60%） and arrangement positions away from the channel wall（ D= 0 m, 0.1 m, 0.2 m）. The results indicate that the flow velocity increases under the floating beds, and the water level rises significantly under high flow velocity conditions in the upstream region and the floating bed region. In addition, the average rising water level value（ARWLV） increases significantly with the increase of the floating bed coverage rate, and the arrangement position of floating beds in the river can also greatly influence the water level distribution under a high-flow velocity condition（v ？0.2 m /s）.     

BASIC EQUATIONS AND WAVE THEORY OF GAS-LIQUID TWO-PHASE TRANSIENT FLOW

This paper is aimed at a systematic discussion on the basic equations for two-phasetransient flow and the theory of pressure waves and interfacial waves.The characters of the ba-sic equations have been analyzed.The formulas for wave speed of pressure and interfacial waveshave been derived.It has been proved that various mathematical models can be unified by theproposed integrating model and various wave speed formulas can be unified by the derived uni-versal formula.The basic equations for the separated flow model are ill-conditioned because ofthe unreasonable neglect of the pressure differences between the phases and the interfaces.Driftflux model can improve the accuracy if some additional equations are provided.However theymust be carefully chosen.The basic equations for homogeneous flow model are well-conditionedand they can be used in two-phase transient flow,especially in the cases of no velocity slips be-tween the phases.     

SPH numerical investigation of the characteristics of an oscillating hydraulic jump at an abrupt drop

This paper shows the results of the smooth particle hydrodynamics(SPH) modelling of the hydraulic jump at an abrupt drop,where the transition from supercritical to subcritical flow is characterised by several flow patterns depending upon the inflow and tailwater conditions. SPH simulations are obtained by a pseudo-compressible XSPH scheme with pressure smoothing; turbulent stresses are represented either by an algebraic mixing-length model, or by a two-equation k-ε model. The numerical model is applied to analyse the occurrence of oscillatory flow conditions between two different jump types characterised by quasi-periodic oscillation,and the results are compared with experiments performed at the hydraulics laboratory of Bari Technical University. The purpose of this paper is to obtain a deeper understanding of the physical features of a flow which is in general difficult to be reproduced numerically,owing to its unstable character: in particular, vorticity and turbulent kinetic energy fields, velocity, water depth and pressure spectra downstream of the jump, and velocity and pressure cross-correlations can be computed and analysed.     

Kelvin-Helmholtz instability.with mass transfer through porous media： Effect of irrotational viscous pressure

This paper studies the effect of the irrotational viscous pressure on Kelvin-Helmholtz instability of the plane interface of two viscous and incompressible fluids in a fully saturated porous media with mass and heat transfers across the interface. In the earlier work, the instability of the plane interface of two viscous and streaming miscible fluids through porous media was studied by assuming that the motion and the pressure are irrotational and the viscosity enters the normal stress balance. This theory is called the viscous potential flow theory. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by considering viscous contributions of the irrotational pressure. The Darcy-Brinkman model is used in the investigation and the stability criterion is formulated in terms of a critical value of the relative velocity. It is observed that the heat and mass transfer has a destabilizing effect on the stability of the system while the irrotational shearing stresses stabilize the system.     

High-speed water impacts of flat plates in different ditching configuration through a Riemann--ALE SPH model

The violent water entry of flat plates is investigated using a Riemann-arbitrary Eulerian-Lagrangian(ALE) smoothed particle hydrodynamics(SPH) model. The test conditions are of interest for problems related to aircraft and helicopter emergency landing in water. Three main parameters are considered: the horizontal velocity, the approach angle(i.e., vertical to horizontal velocity ratio) and the pitch angle, a. Regarding the latter, small angles are considered in this study. As described in the theoretical work by Zhao and Faltinsen(1993), for small a a very thin, high-speed jet of water is formed, and the time-spatial gradients of the pressure field are extremely high. These test conditions are very challenging for numerical solvers. In the present study an enhanced SPH model is firstly tested on a purely vertical impact with deadrise angle α=4°. An in-depth validation against analytical solutions and experimental results is carried out, highlighting the several critical aspects of the numerical modelling of this kind of flow, especially when pressure peaks are to be captured. A discussion on the main difficulties when comparing to model scale experiments is also provided. Then, the more realistic case of a plate with both horizontal and vertical velocity components is discussed and compared to ditching experiments recently carried out at CNR-INSEAN. In the latter case both 2-D and 3-D simulations are considered and the importance of 3-D effects on the pressure peak is discussed for α=4° and α=10°.     

EXPERIMENTAL STUDIES AND NUMERICAL CALCULATION ON TURBULENT BOUNDARY LAYER OF WATER FLOW ALONG CURVED SURFACE

This paper will introduce experimental studies and numerical calculation onturbulent boundary layer of water flow along curved surface in our country in recent years.Onthe basis of the experimental studies,the effects of curvature and roughness on velocitydistribution and pressure distribution and the change of turbulent flow boundary layer onoverflow bucket concave surface is discussed.We proposed the empirical formula of velocity,pressure and the change of turbulent flow boundary layer on outlet bucket concave.According tothe momentum principle,we have deduced the momentum integral equation full water depthboundary layer and using the element as control unit inside the boundary layer on concavesurface of bucket.Combining with continuity equation,we have computed the boundary layerdevelopment on the bucket of a spillway.Compared with the field experimental data,thecalculation results are available.Under polar coordinates,a mathematical model for simulatingtime-averaged flow characteristics in concave surface of bucket is established.The turbulent flowfield on concave surface of bucket is calculated by SIMPLE method and this mathematicalmodel.The flow velocity field,pressure field,distribution of turbulent kinetic energy,distribution of turbulent energy dissipating rate and distribution of shear stress are available.Thecalculation value is consistent with measured test data.     

A NUMERICAL ANALYSIS OF THE BLOOD FLOW AROUND THE BILEAFLET MECHANICAL HEART VALVES WITH DIFFERENT ROTATIONAL IMPLANTATION ANGLES

The effects of implantation angles of Bileaflet Mechanical Heart Valves (BMHVs) on the blood flow and the leaflet motion are investigated in this paper.The physiological blood flow interacting with the moving leaflets of a BMHV is simulated with a strongly coupled implicit Fluid-Structure Interaction (FSI) method based on the Arbitrary-Lagrangian-Eulerian (ALE) approach and the dynamic mesh method (remeshing) in Fluent.BMHVs are widely used to be implanted to replace the diseased heart valves,but the patients would suffer from some complications such as hemolysis,platelet activation,tissue overgrowth and device failure.These complications are closely related to both the flow characteristics near the valves and the leaflet dynamics.The current numerical model is validated against a previous experimental study.The numerical results show that as the rotation angle of BMHV is increased the degree of asymmetry of the blood flow and the leaflet motion is increased,which may lead to an unbalanced force acting on the BMHVs.This study shows the applicability of the FSI model for the interaction between the blood flow and the leaflet motion in BMHVs.     

Analytical approach to entropy generation and heat transfer in CNT-nanofluid dynamics through a ciliated porous medium

The transportation of biological and industrial nanofluids by natural propulsion like cilia movement and self-generated contraction-relaxation of flexible walls has significant applications in numerous emerging technologies. Inspired by multi-disciplinary progress and innovation in this direction, a thermo-fluid mechanical model is proposed to study the entropy generation and convective heat transfer of nanofluids fabricated by the dispersion of single-wall carbon nanotubes(SWCNT) nanoparticles in water as the base fluid. The regime studied comprises heat transfer and steady, viscous, incompressible flow, induced by metachronal wave propulsion due to beating cilia, through a cylindrical tube containing a sparse(i.e., high permeability) homogenous porous medium. The flow is of the creeping type and is restricted under the low Reynolds number and long wavelength approximations. Slip effects at the wall are incorporated and the generalized Darcy drag-force model is utilized to mimic porous media effects. Cilia boundary conditions for velocity components are employed to determine analytical solutions to the resulting non-dimensionalized boundary value problem. The influence of pertinent physical parameters on temperature, axial velocity, pressure rise and pressure gradient, entropy generation function, Bejan number and stream-line distributions are computed numerically. A comparative study between SWCNT-nanofluids and pure water is also computed. The computations demonstrate that axial flow is accelerated with increasing slip parameter and Darcy number and is greater for SWCNT-nanofluids than for pure water. Furthermore the size of the bolus for SWCNT-nanofluids is larger than that of the pure water. The study is applicable in designing and fabricating nanoscale and microfluidics devices, artificial cilia and biomimetic micro-pumps.