A time-dependent numerical analysis of flow in a mechanical heart valve: Comparison with experimental results

There is a great need to fabricate heart valves that have similar haemodynamic properties with the natural ones. Towards this goal, we examine the dynamics of fluid flow in a mechanical heart valve with one leaflet. The fluid is incompressible and Newtonian and the leaflet is a neo-Hookean material. The Arbitrary Lagrangian Eulerian method is used to model the fluid-leaflet interaction, and the system of equations is solved using the Finite Element method. The pseudo solid approach along with a set of algebraic equations are used to deform the mesh, while care is taken to avoid remeshing of the domain, at the moment of valve closure. The computational results are compared against the experimental results, and we find an excellent agreement for the time period of valve closure, the time the valve is fully opened, and the value of the maximum valve opening angle. This study indicates that the present model is capable of describing the valve dynamics in physiological geometries.     

Visualization of the flow structure in a vortex tube

The temperature separation in a vortex tube has been investigated for the purpose of exploring the phenomenon and improving the tube performance. Different explanations for the temperature separation have been proposed. However, there has not been a consensus in the hypothesis.This paper reports on a study in progress exploring the flow structure in a vortex tube. Flow visualization, using water as a working fluid, is used to reveal the existence of multiple circulation regions within the vortex tube and a new hypothesis describes the temperature separation mechanism. This research contributes to the understanding of the flow behavior in a vortex tube and supports the previous works that show the generation of the cold component of the flow is the result of the expansion near the cold nozzle and the hot component is produced due to the friction between the layers of flow.     

Visualization of three-dimensional flow in a four-roll mill

Flow visualization has been used to study the motion of a Newtonian fluid in a four-roll mill. Observations of the effect of increasing Reynolds number on the evolution of steady three-dimensional flow between the rollers are reported. The flow visualization experiments have been conducted for two values of the aspect ratio (defined as the ratio of roller length to gap width between rollers). The rollers have been constrained to rotate in a manner which generates an approximately two-dimensional pure extensional flow near the center of the apparatus at low speeds. Steady, symmetrically positioned vortices grow near the top and bottom walls of the container as the Reynolds number is increased up to a critcal value. An increase in Reynolds number beyond this critical value results in a loss of symmetry in the flow pattern. The nature of this transition is strongly dependent upon the aspect ratio.     

Active flow control on a 1:4 car model

Lift and drag of a passenger car are strongly influenced by the flow field around its rear end. The bluff body geometry produces a detached, transient flow which induces fluctuating forces on the body, affecting the rear axle, which may distress dynamic stability and comfort significantly. The investigations presented here deal with a 1:4 scale model of a simplified test car geometry that produces fluctuating lift and drag due to its strongly rounded rear geometry. To examine the influence of active flow control on this behavior, steady air jets were realized to exhaust from thin slots across the rear in three different configurations. Investigations were performed at $Re = 2.1 \times 10^{6}$ and included the capturing of effective integral lift and drag, velocity measurements in the surrounding flow field with Laser Doppler Anemometry, surface pressure measurements and surface oil flow visualization on the rear. The flow field was found to be dominated by two longitudinal vortices, developing from the detachment of the flow at the upper C-pillar positions, and a recirculating, transverse vortex above the rear window. With an air jet emerging from a slot across the surface right below the rear window section, tangentially directed upstream toward the roof section, total lift could be reduced by more than 7 %, with rear axle lift reduction of about 5 % and negligible drag affection ( $<$ 1 %).     

Visualization study of the flow in and around a Savonius rotor

Flow in and around a Savonius rotor has been studied by flow visualization experiments, and the rotation effect is discussed in comparison with the measured pressure distributions on the blade surfaces. It is observed that the flow separating regions on the blade surfaces are fairly reduced by the rotation effect and the flow through the overlap is weakened by the appearance of resisting flow. The former contributes to the torque production of the rotating rotor while the latter acts as a resistance. These phenomena together with the stagnation effect on the front side of the rotor contribute to the power producing mechanism of the Savonius rotor.     

Reynolds-number-effects in flow around a rectangular cylinder with aspect ratio 1:5

The paper reports on experiments carried out over a wide range of Reynolds numbers in a high pressure wind tunnel. The model was a sharp-edged rectangular cylinder with aspect ratio height/width 1:5 (width/span ratio 1:10.8), which was investigated in both basic orientations, lengthwise (4×10³<Re<4×10⁵) and perpendicular to the flow (2.7×10⁴<Re<6.4×10⁵). The Reynolds number is based on the height of the model normal to the flow. Steady and unsteady forces were measured with a piezoelectric balance. Thus along with steady (i.e. time averaged values) including the base pressure coefficient, also power spectra and probability density functions were measured yielding for example Strouhal numbers, higher statistical moments, etc. A response diagram for the vortex resonance phenomenon was taken for the natural bending motion of the slender model. If lift coefficient for constant angle of attack is plotted against Reynolds number, a significant Reynolds number effect is seen. For α=4°, the curve shows an inflection point and the lift varies between 0.3 and 0.6. For α=6° and 2° there are similar variations shifted to lower and higher values of Re, respectively. Probably the shapes of separation bubbles that depend on the Reynolds number are responsible for these effects. No Reynolds number effects were observed when the long side was normal to the flow, an orientation where reattachment at the side walls is not possible. Comparing both basic cases (α=0° and 90°), the interpretation of the probability distributions of lift force leads to the conclusion that the possibility of reattachment (α=0°) seems to enhance the degree of order in the vortex shedding process.     

Core-annular oil/water flow: the turbulent-lubricating-film model and measurements in a 5 cm pipe loop

Core-flow tests with a 3000 mPas fuel oil in a 5 cm test facility have revealed important information on the amplitudes and lengths of waves at the oil/water interface. The wavelengths vary considerably with water fraction and oil velocity. Moreover, the flow in the water annulus is turbulent. A previously developed theoretical model for steady core-annular flow in pipes has been extended by incorporating the effect of turbulence in the water film surrounding the oil core. The adapted model predicts the pressure-gradient increase with oil velocity correctly, provided that actual wave amplitudes and wavelengths observed during these tests are used as input data. The possible contribution of inertial effects is discussed.     

Scale-up of an unsteady flow field for enhanced spatial and temporal resolution of PIV measurements: application to leaflet wake flow in a mechanical heart valve

A scale-up approach is developed to enhance effective spatial and temporal resolution of PIV measurements. An analysis shows that complete similarity can be maintained for certain unsteady flows and that all types of error in PIV are either reduced or unaffected by scale-up. Implementation and results are described for flow through a mechanical heart valve (MHV), in which high resolution is necessary to advance understanding of the effects of small-scale flow structure on blood cells. With a large-scale model geometry and a low-viscosity model fluid, spatial and temporal resolutions are increased by factors of 5.8 and 118, respectively, yielding the finest resolution to date for MHV flow. Measurements near the downstream tip of a valve leaflet detect eddies as small as 400 μm shed in the leaflet wake. Impulsively started flow exhibits vortex shedding frequencies broadly consistent with the literature on flat-plate and aerofoil wakes, while the physiological unsteady flow waveform promotes 40% higher frequency at peak flow.     

Influence of the initial conditions on axisymmetric jets in a parallel flow

An experimental investigation was made of the initial-section flow of axisymmetric helium, air, and freon-12 jets in a parallel air flow for two different velocity profiles at the nozzle exit near the boundary of the jet. In one case, the velocity profile was determined by boundary layers on the nozzle walls; in the other case, it was produced artificially by means of a honeycomb of tubes of variable length. Measurements were made of the profiles of the mean and the pulsation velocity and the temperature. The flow was also photographed. The investigations showed that, depending on the initial conditions, the intensity of mixing of the jets in the initial section at Reynolds numbers Re 10⁴ (calculated using the jet diameter) can change from the level determined by molecular diffusion to the level characteristic of developed turbulent flow. The flow structure in the annular mixing layer also depends strongly on the initial conditions. The observed ordered structures in the mixing layer are related to a section of development of perturbations near the nozzle. The ordered structures are strongly influenced by the effect on the jet of acoustic vibrations from an external source. When the initial velocity profile is produced by the honeycomb, the transition to developed turbulence may be due to the development of long-wavelength perturbations or to the development of small-scale turbulence generated by the flow over the end of the honeycomb.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 18–24, July–August, 1980.We thank V. M. levlev and K. I. Artamonov for assistance and for discussing the work.     

Visualization of flow boiling of liquid nitrogen in a vertical mini-tube

The flow boiling patterns of liquid nitrogen in a vertical mini-tube with an inner diameter of 1.931 mm are visualized with a high-speed digital camera. The superficial gas and liquid velocities are in the ranges of 0.01–26.5 m/s and 0.01–1.2 m/s, respectively. Four typical flow patterns, namely, bubbly, slug, churn and annular flow are observed. Some interesting scenes about the entrainment and liquid droplet deposition in the churn and annular flow, and the flow reversal with the indication of negative pressure drop, are also presented. Based on the visualization, the two-phase flow regime maps are obtained. Compared with the flow regime maps for gas–water flow in tubes with similar hydraulic diameters, the region of slug flow in the present study reduces significantly. Correspondingly, the transition boundary from the bubbly flow to slug flow shifts to higher superficial gas velocity, and that of churn to annular flow moves to lower superficial gas velocity. Moreover, time-averaged void fraction is calculated by quantitative image-digitizing technique and compared with various prediction models. Finally, three kinds of oscillations with long-period and large-amplitude are found, possible explanation for the oscillations is given by comparing the instantaneous flow images with the data of pressure, mass flux and temperature recorded synchronously.     

泄爆外流场的可视化

通过实验和数值方法,对泄爆外流场进行了可视化研究。实验中采用YA-16高速阴影系统,拍摄了泄爆外流场的时序阴影照片。基于K-湍流模型和漩涡破碎（eddy dissipation）燃烧模型,利用同位网格SIMPLE算法,对泄爆过程进行了数值模拟。根据计算结果,由计算光学获得泄爆外流场的时序计算阴影图。实验阴影图与计算阴影图较一致,都形象地揭示了泄爆后湍流火焰的发展及二次爆炸的产生和变化过程。     

Two-phase flow distribution of air–water annular flow in a parallel flow heat exchanger

The air and water flow distribution are experimentally studied for a round header – flat tube geometry simulating a parallel flow heat exchanger. The number of branch flat tube is 30. The effects of tube outlet direction, tube protrusion depth as well as mass flux, and quality are investigated. The flow at the header inlet is identified as annular. For the downward flow configuration, the water flow distribution is significantly affected by the tube protrusion depth. For flush-mounted configuration, most of the water flows through frontal part of the header. As the protrusion depth increases, more water is forced to the rear part of the header. The effect of mass flux or quality is qualitatively the same as that of the protrusion depth. Increase of the mass flux or quality forces the water to rear part of the header. For the upward flow configuration, however, most of the water flows through rear part of the header. The protrusion depth, mass flux, or quality does not significantly alter the flow pattern. Possible explanations are provided based on the flow visualization results. Negligible difference on the water flow distribution was observed between the parallel and the reverse flow configuration.     

Two-phase flow in heterogeneous porous media III: Laboratory experiments for flow parallel to a stratified system

Two-phase flow in stratified porous media is a problem of central importance in the study of oil recovery processes. In general, these flows are parallel to the stratifications, and it is this type of flow that we have investigated experimentally and theoretically in this study. The experiments were performed with a two-layer model of a stratified porous medium. The individual strata were composed of Aerolith-10, an artificial: sintered porous medium, and Berea sandstone, a natural porous medium reputed to be relatively homogeneous. Waterflooding experiments were performed in which the saturation field was measured by gamma-ray absorption. Data were obtained at 150 points distributed evenly over a flow domain of 0.1 × 0.6 m. The slabs of Aerolith-10 and Berea sandstone were of equal thickness, i.e. 5 centimeters thick. An intensive experimental study was carried out in order to accurately characterize the individual strata; however, this effort was hampered by both local heterogeneities and large-scale heterogeneities.The theoretical analysis of the waterflooding experiments was based on the method of large-scale averaging and the large-scale closure problem. The latter provides a precise method of discussing the crossflow phenomena, and it illustrates exactly how the crossflow influences the theoretical prediction of the large-scale permeability tensor. The theoretical analysis was restricted to the quasi-static theory of Quintard and Whitaker (1988), however, the dynamic effects described in Part I (Quintard and Whitaker 1990a) are discussed in terms of their influence on the crossflow.Roman Letters A interfacial area between the -region and the -region contained within V, m² - a vector that maps onto , m - b vector that maps onto , m - b vector that maps onto , m - B second order tensor that maps onto , m² - C second order tensor that maps onto , m² - E energy of the gamma emitter, keV - f fractional flow of the -phase - g gravitational vector, m/s² - h characteristic length of the large-scale averaging volume, m - H height of the stratified porous medium , m - i unit base vector in the x-direction - K local volume-averaged single-phase permeability, m² - K - {K}, large-scale spatial deviation permeability - { K} large-scale volume-averaged single-phase permeability, m² - K ^* large-scale single-phase permeability, m² - K ^** equivalent large-scale single-phase permeability, m² - K local volume-averaged -phase permeability in the -region, m² - K local volume-averaged -phase permeability in the -region, m² - K - {K } , large-scale spatial deviation for the -phase permeability, m² - K ^* large-scale permeability for the -phase, m² - l thickness of the porous medium, m - l characteristic length for the -region, m - l characteristic length for the -region, m - L length of the experimental porous medium, m - characteristic length for large-scale averaged quantities, m - n outward unit normal vector for the -region - n outward unit normal vector for the -region - n unit normal vector pointing from the -region toward the -region (n = - n ) - N number of photons - p pressure in the -phase, N/m² - p ₀ reference pressure in the -phase, N/m² - local volume-averaged intrinsic phase average pressure in the -phase, N/m² - large-scale volume-averaged pressure of the -phase, N/m² - large-scale intrinsic phase average pressure in the capillary region of the -phase, N/m² - - , large-scale spatial deviation for the -phase pressure, N/m² - p_c , capillary pressure, N/m² - p _c capillary pressure in the -region, N/m² - p capillary pressure in the -region, N/m² - {p _c } ^c large-scale capillary pressure, N/m² - q -phase velocity at the entrance of the porous medium, m/s - q -phase velocity at the entrance of the porous medium, m/s - S_wi irreducible water saturation - S /, local volume-averaged saturation for the -phase - S _i initial saturation for the -phase - S _r residual saturation for the -phase - S ^* { }^*/}^*, large-scale average saturation for the -phase - S saturation for the -phase in the -region - S saturation for the -phase in the -region - t time, s - v -phase velocity vector, m/s - v local volume-averaged phase average velocity for the -phase, m/s - {v } large-scale averaged velocity for the -phase, m/s - v local volume-averaged phase average velocity for the -phase in the -region, m/s - v local volume-averaged phase average velocity for the -phase in the -region, m/s - v -{v } , large-scale spatial deviation for the -phase velocity, m/s - v -{v } , large-scale spatial deviation for the -phase velocity in the -region, m/s - v -{v } , large-scale spatial deviation for the -phase velocity in the -region, m/s - V large-scale averaging volume, m³ - y position vector relative to the centroid of the large-scale averaging volume, m - {y}^c large-scale average of y over the capillary region, m Greek Letters local porosity - local porosity in the -region - local porosity in the -region - local volume fraction for the -phase - local volume fraction for the -phase in the -region - local volume fraction for the -phase in the -region - {}^* { }^*+{ }^*, large-scale spatial average volume fraction - { }^* large-scale spatial average volume fraction for the -phase - mass density of the -phase, kg/m³ - mass density of the -phase, kg/m³ - viscosity of the -phase, N s/m² - viscosity of the -phase, Ns/m² - V /V , volume fraction of the -region ( + =1) - V /V , volume fraction of the -region ( + =1) - attenuation coefficient to gamma-rays, m^-1 - -      

Development of instability in the wake of a plate positioned parallel to the flow

The data of systematic calculations of the development of instability in a wake under the influence of given external disturbances are presented. The evolution (linear and nonlinear) of a disturbance of given frequencyf of each mode and, moreover, the intermodal interaction are studied. Considerable attention is given to the investigation of the instability of the wake under the influence of a pair of disturbances: fundamental and subharmonic. In the calculations the amplitudes and phases of the disturbances were varied over a broad range.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 26–32, January–February, 1992.     

Visualization of flow structures in a turbulent boundary layer using a new technique

In this paper, an experimental investigation on the flow structures in a turbulent boundary layer employing a special laser light sheet-Hydrogen bubble flow visualization technique is described. It is observed that the high/low speed streaks are directly related to the hairpin or horseshoe-like vortices. This observation can give a better understanding of the physical mechanism in the turbulent boundary layer. Fluid Mechanic Institute, BUAA     

On the stable posture of a pair of parallel cylinders in a uniform flow *

The stable posture of a pair of parallel circular cylinders in a uniform flow was experimentally studied when it was free to rotate about an axis at the middle of the two cylinders. The cylinder pair comes to rest facing the oncoming flow side by side, the line connecting the centers of the two cylinders being perpendicular to the flow, when s/d = 0.5, where s is the distance between the center of rotation and the central axis of each cylinder and d is the diameter of the cylinder. When s/d = 1.0 or 1.5, the cylinder pair is stable both in tandem, with one cylinder behind the other, and in side-by-side arrangements to the oncoming flow. When s/d 2.0, the cylinder pair is stable only in tandem arrangements.     

Two-phase fluid flow in a porous tube: a model for blood flow in capillaries

A theoretical study of blood flow, under the influence of a body force, in a capillary is presented. Blood is modeled as a two-phase fluid consisting of a core region of suspension of all erythrocytes, represented by a micropolar fluid and a plasma layer free from cells modeled as a Newtonian fluid. The capillary is modeled as a porous tube consisting of a thin transition Brinkman layer overlying a porous Darcy region. Analytical expressions for the pressure, microrotation, and velocities for the different regions are given. Plots of pressure, microrotation, and velocities for varying micropolar parameters, hydraulic resistivity, and Newtonian fluid layer thickness are presented. The overall system was found to be sensitive to variations in micropolar coupling number. It was also discovered that high values of hydraulic resistivity result in an overall slower velocity of the micropolar and Newtonian fluid.     

Propagation of an underexpanded turbulent jet in a parallel supersonic flow

The characteristics of supersonic off-design turbulent jets discharging into parallel supersonic flows are investigated numerically using approximate equations for the effective turbulent viscosity which are derived by analysis of the experimental data.