Hemodynamics and Wall Shear Stress of Blood Vessels in Aortic Coarctation with Computational Fluid Dynamics Simulation

The purpose of this study was to identify the characteristics of blood flow in aortic coarctation based on stenotic shape structure, stenosis rate, and the distribution of the wall load delivered into the blood vessels and to predict the impact on aneurysm formation and rupture of blood vessels by using a computational fluid dynamics modeling method. It was applied on the blood flow in abdominal aortic blood vessels in which stenosis occurred by using the commercial finite element software ADINA on fluid-solid interactions. The results of modeling, with an increasing stenosis rate and Reynolds number, showed the pressure drop was increased and the velocity was greatly changed. When the stenosis rate was the same, the pressure drop and the velocity change were larger in the stenosis with a symmetric structure than in the stenosis with an asymmetric one. Maximal changes in wall shear stress were observed in the area before stenosis and minimal changes were shown in stenosis areas. The minimal shear stress occurred at different locations depending on the stenosis shape models. With an increasing stenosis rate and Reynolds number, the maximal wall shear stress was increased and the minimal wall shear stress was decreased. Through such studies, it is thought that the characteristics of blood flow in the abdominal aorta where a stenosis is formed will be helpful in understanding the mechanism of growth of atherosclerosis and the occurrence and rupture of the abdominal aortic flow.     

Transport phenomena in an agitated vessel with an eccentrically located impeller

The paper presents results of an experimental analysis of the transport phenomena at the vicinity of the wall of an unbaffled agitated vessel with an eccentrically located impeller. Distributions of the transport coefficients were experimentally studied using an electrochemical method within the turbulent regime of the Newtonian liquid flow. Measurements were carried out in an agitated vessel with the inner diameter T = 0.3 m. Liquid height in the vessel was equal to the inner diameter, H = T. The agitated vessel was equipped with a Rushton or a Smith turbine or an A 315 impeller. Eccentricity of the impeller shaft was varied from 0 to 0.53. Local values of the dimensionless shear rate, shear stress, dynamic velocity and friction coefficient were integrated numerically for the whole surface area of the cylindrical wall of the vessel. Averaged values of these quantities were correlated with the impeller eccentricity and modified Reynolds number. The proposed Eqs. (5)–(8), with the coefficients given in Table 2, have no equivalent in open literature concerning this subject. Distributions of the shear rate, γ/n, and friction coefficient, f, at the vicinity of the cylindrical wall of the unbaffled vessel equipped with eccentric Rushton or Smith turbine or A 315 impeller are very uneven and they depend significantly on the impeller eccentricity, e/R. Maximum local values of these variables are located on the wall section closest to the impeller blades. From among the tested impellers, the greatest effects of the impeller eccentricity, e/R, and the liquid turbulence (described by the modified Reynolds number Re _P,M) on the averaged dimensionless shear rate (γ/n)_m and friction coefficient, f _m, are found for the radial-flow Rushton turbine located eccentrically in an unbaffled agitated vessel.     

Numerical investigation of the magnetic field effect on the heat transfer and fluid flow of ferrofluid inside helical tube

The effect of a magnetic field on heat and fluid flow of ferrofluid in a helical tube is studied numerically. The helical tube is under constant wall temperature boundary condition. Parametric studies are done to investigate the effects of different factors such as the magnetic field gradient value and Reynolds number on heat transfer rate and pressure drop. Results indicate that the magnetic field increases the Nusselt number by about 40%. At high magnetic gradient value, Nusselt number and friction factor rise slightly, while at low magnetic gradient value, the increment of Nusselt number is considerable. Furthermore, the growth of wall shear stress on tube wall results in lower thermal–hydraulic performance at the high magnetic gradient value. There is an optimum case for thermal–hydraulic performance which results in most top performance of helical tube in the presence of the magnetic field.

     

Non-newtonian behavior of an insoluble monolayer: effects of inertia

Interfacial velocity measurements were performed in an optical annular channel, consisting of stationary inner and outer cylinders, a floor rotating at a constant rate, and a flat free surface on which an insoluble monolayer was initially spread. Measurements for essentially inviscid monolayers and some viscous monolayers on water show good agreement with numerical predictions for a Newtonian interface (Boussinesq-Scriven surface model) coupled to a bulk flow described by the Navier-Stokes equations. Here, we consider in detail a viscous monolayer, namely hemicyanine, and find that above a certain concentration, the monolayer does not behave Newtonian at a Reynolds number of about 250. We show that the discrepancies between the measurements and predicted Newtonian behavior are not due to compositional effects (i.e., nonuniform monolayer distribution), Reynolds number (i.e., inertia and/or secondary flows), or surface dilatational viscosity (which does not play any role in the parameter regime investigated). We show prima facie evidence that the observed shear thinning nature of the velocity profile is associated with a phase transition at C approximately 0.9 mg/m(2) at low Reynolds numbers. At large Reynolds numbers (Re=8500), hemicyanine is found to flow like a viscous Newtonian monolayer on the air/water interface, with viscosity dependent only on the local concentration.     

Numerical Analysis of 3‐D Flow Past a Stationary Sphere with Slip Condition at Low and Moderate Reynolds Numbers

Computations are performed to determine the steady 3‐D viscous fluid flow forces acting on the stationary spherical suspended particle at low and moderate Reynolds numbers in the range of 0.1≤Re≤200. A slip is supposed on the boundary so that the slip velocity becomes proportional to the shear stress. This model possesses a single parameter to account for the slip coefficient λ (Pa.s/m), which is made dimensionless and is called Trostel number (Tr=λ a/μ). Decreasing slip, increases drag in all Reynolds limits, but slip has smaller effects on drag coefficient at lower Reynolds number regimes. Increasing slip at known Reynolds number causes to delay of flow separation and inflect point creation in velocity profiles. At full slip conditions, shear drag coefficient will be zero and radial drag coefficient reaches to its maximum values. Flow around of sphere at full‐slip condition is not equal to potential flow around a sphere. Present numerical results corresponding to full slip (Tr→0) are in complete accord with certain results of flow around of inviscid bubbles, and the results corresponding to no‐slip (Tr→∞) have excellent agreement with the results predicted by the no‐slip boundary condition.     

Effect of the reaction temperature on the morphology of nanosized HAp

The main purpose of this study is numerically investigating the flow and heat transfer of nanofluid flow inside a microchannel with L-shaped porous ribs as well as studying the effect of porous media properties on the performance evaluation criterion (PEC) of the fluid. In the present paper, in addition to the pure water fluid, the effect of using water/CuO nanofluid on the PEC of microchannel was investigated. The flow was simulated in four Reynolds numbers and two different volume fractions of nanoparticles in laminar flow regime. The investigated parameters are the thermal conductivity and the porosity rate of porous medium. The results indicate that with the existence of porous ribs, the nanofluid does not have a significant effect on heat transfer increase. By using porous ribs in flow with Reynolds number of 1200, the heat transfer rate increases up to 42% and in flow with Reynolds number of 100, this rate increases by 25%.

     

Rheological behavior of fiber suspensions in a turbulent channel flow

Rheological behavior of fiber suspensions in a turbulent channel flow was investigated theoretically and numerically. A model of turbulent fiber suspensions was proposed to predict the orientation distribution of fibers. The fluctuating equation for the orientation distribution function (ODF) of fibers was theoretically solved using the method of characteristics. The self-governed mean equation for orientation distribution function (ODF) was derived by relating the fluctuating ODF and angular velocities-correlated terms to the gradient of mean ODF. Then the ODF of fibers was predicted by numerically solving the mean equation for ODF. Finally the shear stress and first normal stress difference of suspensions were obtained. The results, some of which agree with the available relevant experimental data, show that the orientation distribution of fibers in the vicinity of the center of the flow is relatively broad in turbulent regime, and becomes broader with the increase of Reynolds number. The shear stress of fiber suspensions increases, while the first normal stress difference decreases, from the wall to the center of the flow for varying Reynolds number.     

Bubble shapes and orientations in low Re simple shear flow

We present measurements of shape and orientation of air bubbles in a viscous Newtonian fluid deformed by simple shear. The apparatus is a variation of the "parallel band" device developed by G. I. Taylor. Previous experimental studies on low viscosity ratio, low Reynolds number (Re < 1) bubble deformation have focussed on either small or large deformations (mostly small deformation) and have only qualitatively examined the orientation of bubbles except for small deformations. Our data set spans both the theoretical small deformation and high deformation limits. With these data we confirm theoretical relationships and assess the range of capillary numbers (Ca) over which theoretical relationships for shape and orientation of bubbles are appropriate. We also examine the geometry of deformed bubbles as they relax to a spherical shape once shear stresses are removed. Our data indicate that for extremely small Reynolds numbers and viscosity ratios, the small deformation theoretical relationship first developed by Taylor, is a good approximation for Ca<0.5. The large deformation results for both shape and bubble orientation derived by Hinch and Acrivos agree with our data for Ca>1 and Ca>0.5, respectively.     

CFD simulation of shear-induced aggregation and breakage in turbulent Taylor-Couette flow

An experimental and computational investigation of the effects of local fluid shear rate on the aggregation and breakage of approximately 10 microm latex spheres suspended in an aqueous solution undergoing turbulent Taylor-Couette flow was carried out. First, computational fluid dynamics (CFD) simulations were performed and the flow field predictions were validated with data from particle image velocimetry experiments. Subsequently, the quadrature method of moments (QMOM) was implemented into the CFD code to obtain predictions for mean particle size that account for the effects of local shear rate on the aggregation and breakage. These predictions were then compared with experimental data for latex sphere aggregates (using an in situ optical imaging method). Excellent agreement between the CFD-QMOM and experimental results was observed for two Reynolds numbers in the turbulent-flow regime.     

Flow of a liquid-crystalline polymer solution around an obstacle

The behaviour of an anisotropic solution of hydroxypropylcellulose around an obstacle is investigated in shear and during relaxation. Experiments were carried out with an optical rheometer equipped with transparent cone-and-plate. The obstacle is a 200 micron glass sphere stuck on the plate. A typical Reynolds number past the obstacle is about 10^-5. The flow of the anisotropic solution perturbed by the obstacle shows specific phenomena: distorted downstream streamlines, a very long wake behind the obstacle during shear which persists a long time after the ceasing shear, a change in the behaviour at very high shear rates and in particular, the appearance of a wake in front of the obstacle. To date there has not been any theoretical bases with which to explain these new findings. An interesting point is that the wake behind the obstacle is a good illustration of the problem of weldlines in injection moulding.     

Mixing characterization in batch reactors using the radiotracer technique

The infusion rate of a slug of tracer into an anchor agitated 100-liter batch mixer was characterized by a decay rate constant. This constant was then used to define a dimensionless mixing-rate number which was related to the stirrer Reynolds number. This correlationship allows the calculation of time or rotational speed needed to achieve any desired degree of uniformity of the mixture.^99mTc was used as radiotracer and the mixing process was followed by a scintillation Nal(Tl) counter situated on the reactor wall near the injection point.     

Calculation of Capillary Disintegration of Fluid Jet into Drops in Terms of Linear Theory

A formula is derived for calculating the wave number at which the highest rate of perturbationbuild-up is observed in relation to the Reynolds number. The diameter of drops appearing in spontaneousdisintegration of a fluid jet into drops, the time elapsed from the appearance of a perturbation till the fluidjet disintegration into drops are plotted as functions of the Reynolds number.     

Microalgae separation by inertia-enhanced pinched flow fractionation

To improve the accuracy and efficiency of ships’ ballast water detection, the separation of microalgae according to size is significant. In this article, a method to separate microalgae based on inertia-enhanced pinched flow fractionation (iPFF) was reported. The method utilized the inertial lift force induced by flow to separate microalgae according to size continuously. The experimental results show that, as the Reynolds number increases, the separation effect becomes better at first, but then stays unchanged. The best separation effect can be obtained when the Reynolds number is 12.3. In addition, with the increase of the flow rate ratio between sheath fluid and microalgae mixture, the separation effect becomes better and the best separation effect can be obtained when the flow rate ratio reaches 10. In this case, the recovery rate of Tetraselmis sp. is about 90%, and the purity is about 86%; the recovery rate of Chlorella sp. is as high as 99%, and the purity is about 99%. After that, the separation effect keeps getting better but very slowly. In general, this study provides a simple method for the separation of microalgae with different sizes, and lays a foundation for the accurate detection of microalgae in the ballast water.     

Peculiarities of rheological properties and flow of highly concentrated emulsions: The role of concentration and droplet size

Results of a complete study of the rheological properties of highly concentrated emulsions of the w/o type with the content of the dispersed phase up to 96% are reported. The aqueous phase is a supersaturated solution of nitrates, where the water content does not exceed 20%. Dispersed droplets are characterized by a polyhedral shape and a broad size distribution. Highly concentrated emulsions exhibit the properties of rheopectic media. In steady-state regimes of shearing, these emulsions behave as viscoplastic materials with a clearly expressed yield stress. Highly concentrated emulsions are characterized by elasticity due to the compressed state of droplets. Shear storage modulus is constant in a wide range of frequencies that reflect solid-like behavior of such emulsions at small deformations. The storage (dynamic) modulus coincides with the elastic modulus measured in terms of the reversible deformations after the cessation of creep. Normal stresses appear in the shearing. In the low shear rate domain, normal stresses do not depend on shear rate, so that it can be assumed that they have nothing in common with normal stresses arising owing to the Weissenberg effect. These normal stresses can be attributed to Reynolds’ dilatancy (elastic dilatancy). Normal stresses sharply decrease beyond some threshold value of the shear rate and slightly increase only in a high shear rate domain. Observed anomalous flow curves and unusual changes of normal stresses with shear rate are explained by the two-step model of emulsion flow. Direct optical observations show that emulsions move by the mechanism of the rolling of larger droplets over smaller ones without noticeable changes of their shape at low shear rates, while strong distortions of the droplet shape is evident at high shear rates. The transition from one mechanism to the other is attributed to a certain critical value of the capillary number. The concentration dependence of the elastic modulus (as well as the yield stress) can be described by the Princen-Kiss model, but this model fails to predict the droplet size dependence of the elastic modulus. Numerous experiments demonstrated that the modulus and yield stress are proportional to the squared reciprocal size, while the Princen-Kiss model predicts their linear dependence on the reciprocal size. A new model based on dimensional arguments is proposed. This model correctly describes the influence of the main structural parameters on the rheological properties of highly concentrated emulsions. The boundaries of the domain of highly concentrated emulsions are estimated on the basis of the measurement of their elasticity and yield stress.     

Hollow-fibre membrane module design: comparison of different curved geometries with Dean vortices

The performance of several designs of curved membrane modules with Dean vortices was compared through experiments using a colloidal bentonite suspension and cellulose acetate hollow-fibre ultrafiltration (UF) membranes. The different module geometries were: straight, helically coiled, twisted and sinusoidal, or meander-shaped. The experiments show a remarkable increase in mass transfer in curved modules as compared to conventional straight ones. Comparisons were made for modules equipped with the same hollow fibres and the same Dean number (De) for a given Reynolds number (Re). At the same Dean number, all the curved geometries gave the same limiting permeate flux. A mass transfer correlation relating limiting UF flux with the mean wall shear stress has been obtained.     

Dean vortices: comparison of numerical simulation of shear stress and improvement of mass transfer in membrane processes at low permeation fluxes

In order to rationalize the effect of Dean vortices on mass transfer improvement during membrane filtration, we present preliminary calculations of the wall shear stress in curved tube with non-porous walls. Previous experimental work has already shown strong positive effect of Dean vortices on mass transfer. In this paper, a numerical simulation of shear stress is proposed in order to determine the influence of the geometric parameters in four different tubes: straight, torus, helical and woven tube. The simulation results are tested against the analytical solutions which are available for velocity and pressure distributions in straight tubes. The simulation gives local values from which the location of Dean vortices in cross-section can be deduced and which depends on geometry and Reynolds number. Moreover, published results dealing with oxygenation of water by a membrane process and pervaporation of organic volatile compounds are considered using the present simulation results.     

Turbulent heat transfer and fluid flow of alumina nanofluid inside three-lobed twisted tube

Turbulent flow characteristics and heat transfer applications of a twisted heat exchanger with 3-lobed cross section along with Y-tape insert are numerically studied. The working fluids for the simulations are pure water and water–Al₂O₃ nanofluid using two-phase mixture model. The study is carried out for various nanofluid volume fractions of 0.01, 0.02 and 0.03 with Reynolds number in the range of 5000–20,000. The effect of nanoparticles in heat transfer augmentation for smooth and lobed tubes is discussed based on presenting the highest thermal performance, which is a relation between heat transfer rate and pressure loss. Results show that implementing the twisted tube with Y-tape insert enhances the heat transfer more than the twisted tube. Relative Nusselt numbers for twisted tubes decrease with Reynolds number in comparison with the plain tube. Turbulent intensity, swirl number and tangential velocity of twisted tube with insert are higher than empty twisted tube indicating that inserting the Y-tape intensifies the turbulence and disturbs the fluid flow further. On the other hand, although the twisted tube increases the pressure drop more than plain tube, the case with Y-tape drastically increases the friction factor. So, the thermal performance of twisted tube with insert is lower than empty twisted tube. Adding nanoparticles to the base fluid has different influence on the investigated cases. It augments the relative Nusselt number inside plain tube and empty twisted tube with slight increment in friction factor. Increasing the nanoparticles concentration enhances the heat transfer rates for these cases while it does not increase the relative Nusselt number inside twisted tube with Y-tape insert at high Reynolds number and nanoparticle concentration. Moreover, it can be found that twisted tube with or without Y-tape insert is more efficient at low Reynolds number in comparison with the plain tube.

     

Surfactant-Influenced Gas-Liquid Interfaces: Nonlinear Equation of State and Finite Surface Viscosities

A canonical flow geometry was utilized for a fundamental study of the coupling between bulk flow and a Newtonian gas-liquid interface in the presence of an insoluble surfactant. We develop a Navier-Stokes numerical model of the flow in the deep-channel surface viscometer geometry, which consists of stationary inner and outer cylinders, a floor rotating at a constant angular velocity, and an interface covered initially by a uniformly distributed surfactant. Here, the floor of the annular channel is rotated fast enough so the flow is nonlinear and drives the film toward the inner cylinder. The boundary conditions at the interface are functions of the surface tension, surface shear viscosity, and surface dilatational viscosity, as described by the Boussinesq-Scriven surface model. A physical surfactant system, namely hemicyanine, an insoluble monolayer on an air-water interface, with measured values of surface tension and surface shear viscosity versus concentration, was used in this study. We find that a surfactant front can form, depending on the Reynolds number and the initial surfactant concentration. The stress balance in the radial direction was found to be dominated by the Marangoni stress, but the azimuthal stress was only due to the surface shear viscosity. Numerical studies are presented comparing results of surfactant-influenced interface cases implementing the derived viscoelastic interfacial stress balance with those using a number of idealized stress balances, as well as a rigid no-slip surface, providing added insight into the altered dynamics that result from the presence of a surfactant monolayer. Copyright 2000 Academic Press.     

Investigation of turbulent flow field in a Kenics static mixer by Laser Doppler Anemometry

The main purpose of the present paper was to apply the Laser Doppler Anemometry (LDA) technique to measure turbulent liquid flow in a Kenics static mixer. The LDA set-up was a one-channel backscatter system with argon-ion laser. Measurements in the static mixer were carried out for three values of the Reynolds number: 5000, 10000, and 18000. Water was used as the process liquid. Values of the axial and tangential components of the local, mean, and root mean square velocities were measured inside the static mixer. It was observed that the shape of the velocity profile depends strongly on the Reynolds number, Re, as well as on the axial, h, and radial, α, position of the measurement point. Strong dependence of the velocity fluctuations on the Reynolds number was found in the investigated range of Re and the measurement point position. Furthermore, one-dimensional energy spectra of the velocity fluctuations were also obtained by means of the Fast Fourier Transform. Fluctuation spectra of the axial and tangential velocities provided information about the energy density of velocity fluctuations in the observed range of Reynolds numbers. A study of the energy spectra led to the conclusion that the energy density increases with the increasing radial distance from the mixer walls at constant values of h, _Re, and α. Minor variations in the mean value of the energy density, E, were observed together with variations of the measurement point angular position, α. In addition, it was observed that an increase of the Reynolds number causes significant increase of the power spectral density.