Insertion of twisted tape in a pipe provides heat transfer augmentation due to swirl formation inside the pipe. Understanding of the transitions of such a swirling flow is an important fluid flow problem. This problem has been studied numerically for H/D = 8.0 and 700 ≤ Re ≤ 1400, where H is the pitch of the twisted tape, D is the diameter of the pipe, and Re is the Reynolds number based on the pipe diameter. The results obtained with large eddy simulations (LES) of such a flow are used in the present work to explore the transitions in the flow through a pipe with twisted tape insert. It is observed that the flow is steady laminar for Re ≤ 700 and changes to periodic laminar flow for 700 ≤ Re ≤ 1126. During this flow regime, the flow occurs with sinusoidal variation of streamwise velocity which exhibit single frequency in the flow. For 1126 ≤ Re ≤ 1263, the flow behavior is quasi-periodic in nature and the time series of streamwise velocity shows two incommensurate frequencies namely primary and secondary frequencies with harmonics in the form of linear combination of primary and secondary frequencies. Further, for 1263 ≤ Re ≤ 1400, the flow transits to chaotic behavior. These transitions have been obtained through a bifurcation analysis of instantaneous streamwise velocity signals captured at a point where maximum fluctuations are likely to occur. It is noticed that the Hopf bifurcation occurs three times as flow changes from steady laminar to chaotic flow. It is further observed through the vorticity contours that, at low Reynolds number, the rate of vorticity generation is low and this vorticity is transported by mere diffusion. Beyond critical Reynolds number, the vorticity pumped from boundary layer into the shear layer is high and diffusion is not sufficient to transport the vorticity and hence the convection of vorticity sets in. This causes the vorticity shedding in the flow, and hence, the fluctuations in the velocity. These results should help to improve the understanding of transitions in the flow through a pipe with twisted tape insert.

The local hemodynamic factor plays a vital role in the formation and progression of atherosclerosis. In this study, we simulated pulsatile flow patterns in the three-dimensional stenosed and normal carotid artery bifurcations throughout a cardiac cycle using the multiple-relaxation-time lattice Boltzmann (MRT-LB) method. Additionally, we investigated the time-varied flow rate and its division ratios between the parent and daughter branches, the multidirectionality of the stress field, and the averaged local energy dissipation rate. The results can be used in computational modeling of carotid artery hemodynamics and further investigation of the relationship between hemodynamics and cardiovascular diseases.

Recent rapid development of industrial usage of carbon nanotubes (CNTs) has raised health concerns as these engineered elongated particles resemble the appearance of asbestos, which is a well-known inhalation hazard. While CNTs have elongated rod shaped structure similar to asbestos, they are nanosized, and therefore, their motions are strongly affected by Brownian diffusion. The available studies in this area are rather limited and details of the nanofiber dynamics along the transport route are largely unknown. In this study, the CNTs were modeled as elongated ellipsoids and their full motions including the coupled translational and rotational movement in the human tracheobronchial first airway bifurcation were analyzed. Particular attention was given to the effects of the slip-correction and Brownian motion, which are critical to the accuracy of the modeling of motions of nanoscale CNTs in free molecular and transition regimes.

The performance of a porous disk with hierarchical bifurcating flow passages has been examined. The hierarchical bifurcating flow passages in the heat exchanger mimic those seen in the vascular systems of plants and animals. The effect of bifurcation angle, porosity, and pore size on the pressure drop across a porous disk was examined computationally. The pressure drop across the porous disk was found to increase as the pore size decreased. As the bifurcation angle increased the pressure drop also increased. At high porosities the bifurcation angles did not have an impact on the pressure drop across the porous disk due to flow behavior. Similarly, the effect of bifurcation angle on pressure drop decreased as the pore size increased.

In this study we implemented the network simulation techniques using macromodels (lumped models) for capillary driven flows in microfluidic networks. The flow characteristics in a flow junction, such as meniscus stretching and bifurcation, were studied and their effects on filling time as well as pressure drop were explored for various network configurations. The results from the network simulator are validated numerically using computational fluid dynamics (CFD) simulations by employing the volume-of-fluids (VOF) method. The predictions by the network simulator for free-surface flows in different microfluidic networks were found to be in good agreement with the results obtained from the VOF simulations for filling time and meniscus position.

In this study, we investigate the phenomena of flow streaming in micro-/minichannel networks of symmetrical bifurcations using computer simulations with analytical validation. The phenomena of the flow streaming can be found in zero-mean velocity oscillating flows in a wide range of channel geometries. Although there is no net mass flow (zero-mean velocity) passing through the channels, the discrepancy in velocity profiles between the forward flow and backward flow causes fluid particles near the walls to drift toward one end while particles near the centerline to drift toward the opposite end. The unique characteristics of flow streaming could be used for various applications. The advantages include enhanced mixing, pumpless fluid propulsion, multichannel fluid distribution, easy system integration, and cost-effective operation. The results of computer simulations showed that oscillation amplitude is the dominant effect on streaming velocity in channel networks. Streaming velocity was directly proportional to the oscillation frequency and can be used as a cost-effective and reliable convective transport means when the particle diffusivity is less than the fluid kinematic viscosity. A considerable amount of work is needed to further study and understand the flow streaming phenomenon.

Hopf bifurcation of steady base flow and onset of vortex shedding over a transverse periodic array of circular cylinders is considered. The influence of transverse spacing on critical Reynolds number is investigated by systematically varying the gap between the cylinders from a small value to large separations. The critical Reynolds number behavior for the periodic array of circular cylinders is compared with the corresponding result for a periodic array of long rectangular cylinders considered in [ Balanchandar, S., and Parker, S. J., 2002, “Onset of Vortex Shedding in an Inline and Staggered Array of Rectangular Cylinders,” Phys. Fluids, 14, pp. 3714–3732 ]. The differences between the two cases are interpreted in terms of differences between their wake profiles.

The effect of three dimensionality on low Reynolds number flows past a symmetric sudden expansion in a channel was investigated. The geometric expansion ratio in the current study was 2:1 and the aspect ratio was 6:1. Both experimental velocity measurements and two- and three-dimensional simulations for the flow along the centerplane of the rectangular duct are presented for Reynolds numbers in the range of 150 to 600. Comparison of the two-dimensional simulations with the experiments revealed that the simulations failed to capture completely the total expansion effect on the flow, which is influenced by both geometric and hydrodynamic effects. To properly do so requires the definition of an effective expansion ratio, which is the ratio of the downstream and upstream hydraulic diameters and is therefore a function of both the expansion and aspect ratios. When two-dimensional simulations were performed using the effective expansion ratio, the new results agreed well with the three-dimensional simulations and the experiments. Furthermore, in the range of Reynolds numbers investigated, the laminar flow through the expansion underwent a symmetry-breaking bifurcation. The critical Reynolds number evaluated from the experiments and the simulations were compared to other values reported in the literature. Overall, side-wall proximity was found to enhance flow stability, thus sustaining laminar flow symmetry to higher Reynolds numbers. Last, and most important, when the logarithm of the critical Reynolds number was plotted against the reciprocal of the effective expansion ratio, a linear trend emerged that uniquely captured the bifurcation dynamics of all symmetric double-sided planar expansions.

This investigation analyzes the calibration nonlinearity of the ball-in-vortex flow-meter, designed to work on the principle of a rotating sphere in and due to a vortex flow. The comparison of this flow-meter reading with the standard flow-meter indicates the existence of different calibration regimes, bifurcated by a sharp change in slope of the calibration curve. Based on the governing mechanics of this flow-meter, this paper explains this nonlinearity, and proposes its mathematical form. In particular, the bifurcation in calibration characteristics is attributed to the change in the surface contact frictional force, due to translation of the ball. The mathematical model captures the various calibration regimes associated with this translation, from one plane of rotation in the flow-meter to another, or from one periphery to another. Thus, calibration nonlinearity of this flow-meter can be fully comprehended through its governing mechanics, and harnessed for flow measurement.

This paper describes optimality principles for the design of an engineering bifurcating-tube tree consisting of the convection and diffusion zones to attain the most effective gas transport. An optimality principle is formulated for the diffusion zone to maximize the total diffusion mass-transfer rate of gas across tube walls under a constant total-volume constraint. This optimality principle produces a new diameter distribution for the diffusion zone in contrast to the classical distribution for the convection zone. In addition. this paper gives a length distribution for an engineering tree based on an optimality principle for minimizing the total weight of the tree under constraints of a finite surface and elastic criteria for structural stability. Furthermore, the optimum branching angles are evaluated based on local optimality principles for a single bifurcating-tube branch.

Flow through fractal-like branching networks is investigated using a three-dimensional computational fluid dynamics approach. Results are used to assess the validity of, and provide insight for improving, assumptions imposed in a previously developed one-dimensional model. Assumptions in the one-dimensional model include (1) reinitiating boundary layers following each bifurcation, (2) constant thermophysical fluid properties, and (3) negligible minor losses at the bifurcations. No changes to the redevelopment of hydrodynamic boundary layers following a bifurcation are recommended. It is concluded that temperature varying fluid properties should be incorporated in the one-dimensional model to improve its predictive capabilities, especially at higher imposed heat fluxes. Finally, a local pressure recovery at each bifurcation results from an increase in flow area. Ultimately, this results in a lower total pressure drop and should be incorporated in the one-dimensional model.

An analysis is made of the flow of an electrically conducting fluid in a channel with constrictions in the presence of a uniform transverse magnetic field. A solution technique for governing magnetohydrodynamic (MHD) equations in primitive variable formulation is developed. A coordinate stretching is used to map the long irregular geometry into a finite computational domain. The governing equations are discretized using finite difference approximations and the well-known staggered grid of Harlow and Welch is used. Pressure Poisson equation and pressure-velocity correction formulas are derived and solved numerically. It is found that the flow separates downstream of the constriction. With increase in the magnetic field, the flow separation zone diminishes in size and for large magnetic field, the separation zone disappears completely. Wall shear stress increases with increase in the magnetic field strength. It is also found that for symmetrically situated constrictions on the channel walls, the critical Reynolds number for the flow bifurcation (i.e., flow asymmetry) increases with increase in the magnetic field.

Both axial and secondary flow were experimentally studied in a 90-degree bifurcation of square tubes, under pulsating conditions and equal branch flow rates. The examined peak Reynolds number (Re) was in the range 330–830, and the Womersley parameter (α) between 5 and 15. In the extension of the mother tube during deceleration, axial flow separated from the wall opposite of the 90-degree branch. The formed shear layer rolled up, for higher values of Re and low α, generating discrete vortices. However, for the highest value of α, the shear layer was limited close to the wall, without rolling up, for all the examined Re. During acceleration, all recirculation zones were washed out and the flow became attached before flow peak. In the 90-degree branch during acceleration, a vortex was formed at the bifurcation apex and moved streamwise towards the center of the cross-section where it degenerated. The secondary flow of this branch had the following characteristics: during deceleration two Dean vortices were located close to the outer bend side of the cross-section, and their strength was progressively reduced. A little before flow peak any Dean vortices of the previous phase were destroyed and two new ones were born. Maximum secondary velocities were on the order of 20% higher than the bulk velocity of the branch.

Computational investigations have been performed into the behavior of an incompressible fluid flow in the vicinity of a plane symmetric channel contraction. Our aim is to determine the critical Reynolds number, above which the flow becomes asymmetric with respect to the channel geometry using the bifurcation diagram. Three channels, which are characterized by the contraction ratio, are studied and the critical Reynolds numbers are determined as 3075, 1355, and 1100 for channels with contraction ratios of 2, 4, and 8, respectively. The cause and mechanism explaining the transition from symmetric to asymmetric states in the symmetric contraction channel are also provided.

The bifurcation structure of viscous flow in curved square ducts is studied numerically and the stability of solutions on various solution branches is examined extensively. The solution structure of the flow is determined using the Euler-Newton continuation, the arc-length continuation, and the local parameterization continuation scheme. Test function and branch switch technique are used to monitor the bifurcation points in each continuation step and to switch branches. Up to 6 solution branches are found for the case of a flow in the curved square channel within the parameter range under consideration. Among them, three are new. The flow patterns on various bifurcation branches are also examined. A direct transient calculation is made to determine the stability of various solution branches. The results indicate that, within the scope of the present work, at given set of parameter values, the arbitrary initial disturbances lead all solutions to the same state. In addition to stable steady two-vortex solutions and temporally periodic solutions, intermittent and chaotic oscillations are discovered within a certain region of the parameter space. Temporal intermittency that is periodic for certain time intervals manifests itself by bursts of aperiodic oscillations of finite duration. After the burst, a new periodic phase starts, and so on. The intermittency serves as one of the routes for the onset of chaos. The results show that the chaotic flow in the curved channel develops through the intermittency. The chaotic oscillations appear when the number of bursts becomes large. The calculations also show that transient solutions on various bifurcation branches oscillate chaotically about the common equilibrium states at a high value of the dynamic parameter.

Considering steady laminar incompressible flow in a triple bifurcation, which represents generations three to six of the human respiratory system, air flow fields and micron-particle transport have been simulated for several combinations of relatively high and low inlet Reynolds and Stokes numbers. While the upstream bifurcations are hardly affected by the third bifurcation, complex air and particle flow fields occur in the daughter tubes leading to the third dividers. Variations in Reynolds number, 500 ⩽ Re ⩽ 2000 , and Stokes number, 0.04 ⩽ St ⩽ 0.12 , cause locally changing vortical air flows as well as irregular particle motions. Preferential concentration of particles can be induced by the secondary vortical flow in the tubes when the inlet Reynolds number is high enough. The air and particle velocity profiles in the third daughter tubes are still quite different from those in the upstream tubes, which indicates that additional downstream effects are possible. This work may contribute to respiratory dose estimation in health risk assessment studies, as well as the analyses of drug aerosol delivery.

Steady divergent flow (inspiration directed) is measured using Laser Doppler Velocimetry in a large-scale model carefully mimicing the morphometry of small human airways. The anatomical features, which induced vorticity in the flow from vorticity free entrance flow, are evaluated under conditions of convective similitude. The flow pattern in the daughter tubes is typical of laminar flow within the entrance to sharp bends (Dean number >500) with rapid development of strong secondary flows (maximum secondary velocity is 45 percent of mean axial velocity). The secondary flow consists of two main vortices, with two smaller and weaker secondary vortex activities toward the inner wall of curvature. There appears to be time dependent interaction with these vortices causing warbling at specific flow conditions. The calculated vorticity transport along the flow axis showed interaction between the viscous force at the new boundary layer development along the carinal wall and centrifugal force of curvature, with a significant influence by the upstream flow prior to entering the actual flow division. This interplay results in an overshoot of the calculated vorticity transport comparable to flow entering curved bends and suppression for the tendency to separate at the inner wall of these tight bends. The maximum primary flow velocities are skewed toward the carinal side (outer wall of curvature) and development of a second peak occurred with convection of the high velocity elements toward the inner wall of curvature by the strong secondary flow. [S0098-2202(00)01903-9]

The pulsating flow field in a 90 deg bifurcation was examined by performing LDV measurements in a model with square cross-sections and equal branch flow rates. The three-dimensional separation zones of both branches were studied revealing details of their temporal evolution. During acceleration the flow was attached, but close to the peak flow condition, separation initiated at both branches. The basic feature of the reverse flow zones at a given time instant was that these shrank streamwise in a direction perpendicular to the bifurcation plane and grew at the symmetry plane. Flow instabilities were strong in the horizontal branch during acceleration, in contrast to the vertical branch in which these appeared during deceleration. Comparison of this flow field for a particular time instant with the flow field under steady inlet conditions and similar Re, revealed that for the steady case the flow separated in the horizontal branch upstream of the unsteady case. [S0098-2202(00)03002-9]

A nonbarotropic continuum bubbly mixture model is used to study the one-dimensional cavitating flow through a converging-diverging nozzle. The nonlinear dynamics of the cavitation bubbles are modeled by the Rayleigh-Plesset equation. Analytical results show that the bubble/bubble interaction through the hydrodynamics of the surrounding liquid has important effects on this confined flow field. One clear interaction effect is the Bernoulli effect caused by the growing and collapsing bubbles in the nozzle. It is found that the characteristics of the flow change dramatically even when the upstream void fraction is very small. Two different flow regimes are found from the steady state solutions and are termed: quasi-steady and quasi-unsteady. The former is characterized by large spatial fluctuations downstream of the throat which are induced by the pulsations of the cavitation bubbles. The quasi-unsteady solutions correspond to flashing flow. Bifurcation occurs as the flow transitions from one regime to the other. An analytical expression for the critical bubble size at the bifurcation is obtained. Physical reasons for this quasi-static instability are also discussed.

Numerical investigation of the oscillatory instability of convective flows in laterally heated rectangular cavities is presented. Cavities with no-slip isothermal vertical boundaries, no-slip adiabatic lower boundary, and stress-free adiabatic upper boundary are considered. Dependence of the critical Grashof number and the critical frequency of oscillations on the aspect ratio (A = length/height) of the cavity are investigated. The stability diagrams were obtained for the whole interval of the aspect ratio 1 ≤ A ≤ 10. The study was carried out for two values of the Prandtl number, Pr = 0 and 0.015. It was shown that the oscillatory instability sets in as a result of the Hopf bifurcation. It was found that at two different values of the Prandtl number considered the instability is caused by different infinitely small dominant perturbations, which means that the convective heat transfer strongly affects stability of the flow even for cases having small Prandtl number. No asymptotic behavior for large aspect ratios was found up to A = 10. Slightly supercritical oscillatory flows were approximated asymptotically by means of the weakly nonlinear analysis of the calculated bifurcation.