Parametric resonance of a composite cylindrical shell containing pulsatile flow of hot fluid

Vast literature is available for modeling the coupled fluid structure interaction involving the flow of a pulsatile fluid through pipes/shells under ambient temperature. In contrast it is found that there is no literature on such problems under the influence of temperature. This paper considers the evaluation of dynamic instability regions due to a flow of pulsating hot fluid through an insulated composite cylindrical shell. A coupled fluid structure interaction model in conjunction with uncoupled thermomechanical model is used for analysis. The system's equations of motion containing periodic coefficients are expressed in modal domain considering linear transformation. Fourth order Runge–Kutta method using Gill's coefficient is adopted to compute the state transition matrix which provides the stability information of the periodic system following the Floquet–Liapunov theory. Pulsatile flow of water at various magnitude of steady state temperature is considered and hence the effect of water temperature on the instability regions is analyzed. The influence of lamina fibre angle on the instability regions is also examined.     

Computational model on pulsatile flow of blood through a tapered arterial stenosis with radially variable viscosity and magnetic field

An unsteady two-fluid model of blood flow through a tapered arterial stenosis with variable viscosity in the presence of variable magnetic field has been analysed in the present paper. In this article, blood in the core region is assumed to obey the law of Jeffrey fluid and plasma in the peripheral layer is assumed to be Newtonian. The values for velocity, wall shear stress, flow rate and flow resistance are numerically computed by employing finite-difference method in solving the governing equations. A comparison study between the velocity profiles obtained by the present study and the experimental data represented graphically shows that that the rheology of blood obeys the law of Jeffrey fluid rather than that of Newtonian fluid. The effects of parameters such as taper angle, radially variable viscosity, hematocrit, Jeffrey parameter, magnetic field and plasma layer thickness on physiologically important parameters such as wall shear stress distribution and flow resistance have been investigated. The results in the case of radially variable magnetic field and constant magnetic field are compared to observe the effect of magnetic field in driving the blood flow. It is observed that increase in hematocrit increases the wall shear stress. The values of wall shear stress and flow resistance are obtained at various time instances and compared. It is pertinent to note that the magnitudes of flow resistance are higher in the case of converging tapered than non-tapered and diverging tapered artery.     

Effect of reverse flow on the pattern of wall shear stress near arterial branches

Atherosclerotic lesions have a patchy distribution within arteries that suggests a controlling influence of haemodynamic stresses on their development. The distribution near aortic branches varies with age and species, perhaps reflecting differences in these stresses. Our previous work, which assumed steady flow, revealed a dependence of wall shear stress (WSS) patterns on Reynolds number and side-branch flow rate. Here, we examine effects of pulsatile flow. Flow and WSS patterns were computed by applying high-order unstructured spectral/hp element methods to the Newtonian incompressible Navier–Stokes equations in a geometrically simplified model of an aorto-intercostal junction. The effect of pulsatile but non-reversing side-branch flow was small; the aortic WSS pattern resembled that obtained under steady flow conditions, with high WSS upstream and downstream of the branch. When flow in the side branch or in the aortic near-wall region reversed during part of the cycle, significantly different instantaneous patterns were generated, with low WSS appearing upstream and downstream. Time-averaged WSS was similar to the steady flow case, reflecting the short duration of these events, but patterns of the oscillatory shear index for reversing aortic near-wall flow were profoundly altered. Effects of reverse flow may help explain the different distributions of lesions.     

Uniform pulsatile flow of an incompressible liquid in a tube of parallelogram cross-section

Laminar steady and pulsatile flow in a tube of parallogram cross-section has been derived analytically for incompressible viscous liquid. Velocity profiles have been determined and the influence of various parameters, such as skew angle, side ratio and forced frequency parameter Ωa²/v have been determined. In addition the flow resistance is presented for various side ratios as a function of the skew angle.     

Coning during withdrawal from two fluids of different density in a porous medium

The steady response of the interface between two fluids with different density in a porous medium is considered during extraction through a line sink. Supercritical withdrawal, or coning as it is often called, in which both fluids are being withdrawn, is investigated using a coupled integral equation formulation. It is shown that for each entry angle of the interface into the sink there is a range of supercritical solutions that depend on the flow rate, and that as the flow rate decreases the cone narrows. As the magnitude of the entry angle increases this range of flow-rate values decreases to a narrow range as the entry becomes vertical. Only one branch of solutions (that with horizontal entry) has the property that the interface levels off at a finite height, and this is investigated as a separate branch of solution.     

A numerical study of pulsatile blood flow in an eccentric catheterized artery using a fast algorithm

The pulsatile blood flow in an eccentric catheterized artery is studied numerically by making use of an extended version of the fast algorithm of Borges and Daripa [J. Comp. Phys., 2001]. The mathematical model involves the usual assumptions that the arterial segment is straight, the arterial wall is rigid and impermeable, blood is an incompressible Newtonian fluid, and the flow is fully developed. The flow rate (flux) is considered as a periodic function of time (prescribed). The axial pressure gradient and velocity distribution in the eccentric catheterized artery are obtained as solutions of the problem. Through the computed results on axial pressure gradient, the increases in mean pressure gradient and frictional resistance in the artery due to catheterization are estimated. These estimates can be used to correct the error involved in the measured pressure gradients using catheters.     

Effect of Reynolds number and flow division on patterns of haemodynamic wall shear stress near branch points in the descending thoracic aorta

Atherosclerotic lesions are non-uniformly distributed at arterial bends and branch sites, suggesting an important role for haemodynamic factors, particularly wall shear stress (WSS), in their development. The pattern of lesions at aortic branch sites depends on age and species. Using computational flow simulations in an idealized model of an intercostal artery emerging perpendicularly from the thoracic aorta, we studied the effects of Reynolds number and flow division under steady conditions. Patterns of flow and WSS were strikingly dependent on these haemodynamic parameters. With increasing Reynolds number, WSS, normalized by the fully developed aortic value, was lowered at the sides of the ostium and increased upstream and downstream of it. Increasing flow into the side branch exacerbated these patterns and gave rise to a reversing flow region downstream of the ostium. Incorporation of more realistic geometric features had only minor effects and patterns of mean WSS under pulsatile conditions were similar to the steady flow results. Aspects of the observed WSS patterns correlate with, and may explain, some but not all of the lesion patterns in human, rabbit and mouse aortas.     

An in vitro study of the effects of Doppler angle, fibrinogen, and hematocrit on ultrasonic Doppler power

For a better understanding of the relationship between the Doppler power and erythrocyte aggregation of whole blood under steady flow in a conduit, the effects of Doppler angle, fibrinogen concentration, and hematocrit were investigated in a mock flow loop. The results show that, at a mean shear rate of 102 s(-1), there was minimal angular dependence; but at a mean shear rate of 52 s(-1), there was a weak angular dependence as the Doppler angle was varied from 40 degrees to 70 degrees . These results suggest that there was, perhaps, no or little alignment of the red cell aggregates at high shear rates. The Doppler power was found to increase nonlinearly as the fibrinogen concentration was increased; and the effect of other plasma proteins on red cell aggregation may not be negligible, although fibrinogen is the dominant factor. The results show that the variation of the Doppler power over the lumen is hematocrit dependent for hematocrits below 26%     

Two-Dimensional Numerical Simulation for Flow Pattern Transition of Thermal-Solutal Capillary Convection in an Annular Pool

In order to understand the transition characteristics of the thermal-solutal capillary convection in an annular pool, a series of two-dimensional numerical simulations were conducted. The bottom of the pool is adiabatic rigid wall and the top is adiabatic and non-deformable free surface. The inner and outer cylindrical walls maintain at constant temperature and solute concentration, respectively. The thermo-capillary force is supposed to equal to the solute-capillary force, but their directions are contrary. Results show that the thermal-solutal capillary convection is steady at a small Reylonds number. When the capillary Reynolds number exceeds a critical value, the steady flow transits into unstable thermal-solutal capillary convection. The transition from the steady to oscillatory flow undergoes a Hopf bifurcation. Furthermore, the effects of the liquid layer aspect ratio, the radius ratio, the Prandtl number and the Lewis number on the onset of flow pattern transition are discussed. The physical mechanism of the unstable thermal-solutal capillary convection is also analyzed.     

Separation of plasma from whole human blood in a continuous cross-flow in a molded microfluidic device

We designed, fabricated, and tested a microfluidic device for separation of plasma from whole human blood by size exclusion in a cross-flow. The device is made of a single mold of a silicone elastomer poly(dimethylsiloxane) (PDMS) sealed with a cover glass and is essentially disposable. When loaded with blood diluted to 20% hematocrit and driven with pulsatile pressure to prevent clogging of the channels with blood cells, the device can operate for at least 1 h, extracting approximately 8% of blood volume as plasma at an average rate of 0.65 microL/min. The flow in the device causes very little hemolysis; the extracted plasma meets the standards for common assays and is delivered to the device outlet approximately 30 s after injection of blood to the inlet. Integration of the cross-flow microchannel array with on-chip assay elements would create a microanalysis system for point-of-care diagnostics, reducing costs, turn-around times, and volumes of blood sample and reagents required for the assays.     

Oscillatory magnetogasdynamic slip flow in a microchannel

The problem of pressure-driven magnetogasdynamic (MGD) slip flow with small rarefaction through a long microchannel is considered. The flow is driven by a steady or oscillatory pressure gradient. The study of MGD flows in microchannels is of interest since they occur in many electromagnetic microscale devices. In obtaining the microfluidic solutions in the presence of a magnetic field, some additional physical, mathematical, and numerical issues need to be considered. These issues deal with the scaling laws for microscale MGD flows and the relevant parameters such as Mach number, Reynolds number, Hartmann number, magnetic Reynolds number, and Knudsen number. For planar constant area microchannels, it is possible to obtain the analytical solutions for both steady and oscillatory pressure-driven flows at low magnetic Reynolds numbers. The flow field is assumed to be quasi-isothermal, which is a good assumption in the absence of a strong electric field. As physically expected, at higher values of the magnetic field (that is at a higher Hartmann number) the velocity profile in the channel flattens, and the pressure varies nonlinearly along the channel.     

Experimental evaluation of intrinsic and nonstationary ultrasonic Doppler spectral broadening in steady and pulsatile flow loop models

Intrinsic and nonstationary Doppler spectral broadening, and the skewness of the spectral representation, were evaluated experimentally using porcine red cell suspensions as ultrasonic scatterers. Theoretically, the relative Doppler bandwidth, defined as the intrinsic bandwidth divided by the mean Doppler frequency shift, should be velocity independent. The relative Doppler bandwidth invariance theorem was experimentally verified with an in vitro steady laminar blood flow model. It is shown that the relative bandwidth is both independent of the flow velocity and blood hematocrit. Using a pulsatile laminar flow model, the authors demonstrated that the relative Doppler bandwidth invariance theorem did not hold during flow acceleration and deceleration. In addition, a positive skewness of the Doppler spectra was observed during acceleration while a negative skewness was measured during the deceleration of blood. The effect of the window duration used in the Fourier spectral computation, on nonstationary broadening, is characterized.     

Effect of dialyzer reprocessing on glucose homeostasis

While dialyzer manufacturers only provide information about their products as a black box, this study aimed at optimizing dialyzer geometry by looking in detail at transport processes and fluid properties inside the dialyzer using numerical modeling. A three‐dimensional computer model of a single hollow fiber with its surrounding membrane and dialysate compartment was developed. Different equations govern blood and dialysate flow (Navier‐Stokes), radial filtration flow (Darcy), and solute transport (convection‐diffusion). Blood was modeled as a non‐ Newtonian fluid with a viscosity varying in radial and axial direction because of the influence of local hematocrit, diameter of the capillaries, and local shear rate. Dialysate flow was assumed as an incompressible, laminar Newtonian flow with a constant viscosity. The permeability characteristics of the asymmetrical polysulphone membrane were calculated from laboratory tests for forward and backfiltration. The influence of the oncotic pressure induced by the plasma proteins was implemented as well as the reduction of the overall permeability caused by the adhesion of a protein layer on the membrane. Urea (MW60) was used as a marker to simulate small molecule removal, while middle molecule transport was modeled using vitamin B12 (MW1355) and inulin (MW5200). The corresponding diffusion coefficients were determined by counting for the fluid and membrane characteristics. Fiber diameter and length were changed in a wide range for evaluation of solute removal efficiency. The presented model allowed us to investigate the impact of flow, hematocrit, and capillary dimensions on the presence and localization of backfiltration. Furthermore, mass transfer was found enhanced for increased fiber lengths and/or smaller diameters, most pronounced for the middle molecules compared to urea.     

绝热毛细管流量数值计算

根据两相流动的均相流假设 ,建立了绝热毛细管分布参数的稳态数学模型 ,结合制冷工质HFC 134a基于MH状态方程的热力学性质计算模型 ,采用新的基团贡献法计算粘度 ,用熵增判据考虑壅塞流动的影响 ,对绝热毛细管流量进行数值模拟计算。对理论计算结果与相关文献的实验数据进行了比较。针对以HFC 134a为工质的制冷系统 ,编制了一套较为实用的绝热毛细管流量计算软件     

Problem of Drying of a Layer of Combustible Forest Materials

Physical and mathematical modeling of drying of a layer of combustible forest materials (CFMs) is considered in a conjugate formulation within the framework of which the equations of a binary boundary layer and the equations of heat and mass transfer in a layer of combustible forest materials are solved. Boundary conditions for the laws of conservation of mass and energy are written on the interface of media. It is found experimentally and theoretically that the velocities of the flow and radiation strongly affect the time of drying of a layer of combustible forest materials, whereas the effect of the angle of inclination (slope) between the underlying surface and the horizontal plane is insignificant.     

Unsteady free-surface flow induced by a line sink

The unsteady flow of fluid from a deep reservoir through a line sink beneath a free surface with surface tension is considered. Two different initial conditions are discussed; the first effectively represents impulsive withdrawal from rest, and the second can be regarded as a disturbance to an existing steady flow. Small-time expansions and numerical methods are used to investigate both the movement to steady states and the critical drawdown of the free surface in the two situations. It is shown that there are several different critical values of flow parameters at which the flow changes its nature. In the zero-surface-tension case, the situation is not fully resolved, but the addition of surface tension clarifies the flow behaviour greatly, and drawdown or movement to a steady state becomes evident. For the second class of initial conditions, it appears that either movement to a steady state or drawdown are the only subcritical possibilities.     

The dynamic stability of a pipe conveying a pulsatile flow

This investigation concern the small displacements of a pipe conveying a pressurized flow whose velocity possesses a harmonic fluctuation about a mean value. A new derivation of the fluid forces is used to obtain the partial differential equation of motion. General equations applicable to any set of boundary conditions are specialized for the case of a simply supported pipe and the Galerkin method is utilized to find solutions. An analysis of the case of steady flow shows that the pipe exhibits the divergence type of instability which is predictable by static structural theory. In the presence of pulsatile flow the pipe has regions of dynamic instability whose extent increases with increased amounts of fluctuation. The results have great similarity to those for beams carrying pulsating end forces.     

Prediction of incidence effects on oscillating airfoil aerodynamics by a locally analytical method

A complete mathematical model is formulated to analyse the effects of mean flow incidence angle on the unsteady aerodynamics of an oscillating airfoil in an incompressible flow field. A velocity potential formulation is utilized. The steady flow is independent of the unsteady flow field. However, the unsteady flow is coupled to the steady flow field through the boundary conditions on the oscillating airfoil. The numerical solution technique for both the steady and unsteady flow fields is based on a locally analytical method. In this method, analytical solutions are incorporated into the numerical technique, with the discrete algebraic equations which represent the differential flow field equations obtained from analytic solutions in individual local computational grid elements. This flow model and locally analytic numerical solution method are then verified through the excellent correlation obtained with the Theodorsen oscillating flat plate and Sears transverse gust classical solutions. The effects of mean flow incidence on the steady and oscillating airfoil aerodynamics are then investigated.     

Hall effects on the unsteady hydromagnetic flows of an Oldroyd-B fluid

The influence of Hall currents and rotation on the oscillatory flows of an infinite plate is investigated. Exact solutions for the two problems are obtained.The fluid considered is a homogeneous Oldroyd-B. During the mathematical analysis it is found that governing differential equation for steady flow in an Oldroyd-B fluid is identical to that of viscous fluid. Further, it is observed that in absence of the strength of transverse magnetic field (B₀) the solution in resonance case does not satisfy the boundary condition at infinity. Physical significance of mathematical results is also discussed.     

The interaction between capillary waves near a charged liquid-liquid interface with a tangential discontinuity of the velocity field

The evolution of capillary waves in a system of two liquid layers with a charged interface and the upper layer with a free surface and finite thickness translating at a constant velocity parallel to the semi-infinite lower layer is studied numerically within the framework of a linear mathematical model of capillary wave motion. The interacting waves generated at the free surface of the upper layer and at the interface give rise to an oscillatory instability of the interface, in addition to the Kelvin-Helmholtz instability. The new instability arises if the upper layer velocity is sufficiently small. The increment of oscillations depends on the density ratio of the liquids, velocity magnitude, and the charge at the interface.