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Secondary flow (also termed as stagnation flow, dead space, recirculation zone, and vortex) is rheological phenomenon occurring during flow of polymer melts through abrupt contraction channels as result of flow separation from solid boundary leading to accelerating flow regime with recirculating material in corners. Polymer melt captured in secondary flow slowly rotates in direction opposite to main flow direction and simultaneously moves in third direction through helical motion. This may first reduce flow stability and second increase residence time initiating highly undesirable thermal degradation of polymer melt. Since the first visual experimental observation performed by Tordella and preliminary theoretical prediction made by Langlois and Rivlin at the end of the 1950s, this phenomenon represents one of the most fundamental rheological problems ever with many practical and theoretical impacts discussed here. This comprehensive review written in historical perspective summarizes key factors (Newtonian viscosity, shear thinning, viscoelasticity, flow geometry, and extensional viscosity) influencing secondary entry flows for polymer melts and provides deep and critical discussion of the most important experimental and theoretical works on this topic (such as branched low-density polyethylene, LDPE, linear low-density polyethylene, LLDPE, high-density polyethylene, HDPE, polystyrene, PS, isotactic polypropylene, PP, polymethyl methacrylate, PMMA, polyamide, Nylon PA 66, or polybutadiene, BR). [ABSTRACT FROM AUTHOR]

Highlights • Both numerical and analytical models are compared for ice slurry flow in bends. • The k − ε per-phase model provides accurate predictions in solving turbulence of ice slurry. • The secondary flow is improved with increasing flow velocity and decreasing ice fraction. • The phase slip velocity and pressure drop profiles are affected by the secondary flow. Abstract Ice slurry, which is a solid–liquid phase change fluid, is attracting wide attention when determining the use of secondary refrigerants in practice. To best represent the performance of ice slurry, it is important to accurately characterize ice slurry flow through pipes and fittings. However, the characteristics of ice slurry flow, especially in fittings, are still far from being fully understood. Therefore, this study investigated the behavior of ice slurry flow through horizontal bends to provide a greater understanding of the physics. The concentration, velocity and pressure fields were solved using the Eulerian–Eulerian model based on the kinetic theory of granular flow. Of particular interest was the modeling and prediction of the turbulence that develops in ice slurry that flows through pipes and bends. The predictions using different turbulence models were compared with the analytical models for predicting ice slurry flow through bends. It was found that the ice slurry flow varied through the cross-section of a bend due to the development of secondary flows. Better predictions were achieved using the Eulerian–Eulerian model coupled with the k − ε per-phase turbulence model. Recommendations were made to control ice particle agglomeration and reduce flow resistance in bends. [ABSTRACT FROM AUTHOR]

Mass and momentum transfer characteristics in a 90° elbow with a radius to pipe diameter ratio of 1.5 are studied experimentally with the aid of the plaster dissolution method, planar velocity measurement by particle image velocimetry (PIV), and surface flow visualization in the Reynolds number (Re) range of 5 × 10 4 to 20 × 10 4 . The experimental results indicate that the most significant change in mass transfer distribution occurs on the inner wall of the elbow. The mass transfer coefficient increases along the centerline of the first half of the elbow and decreases in the second half with increasing Reynolds number. The near-wall velocity measurements by PIV show that the flow accelerates on the first half of the inner wall and decelerates on the second half, which contributes to the growth of the turbulent intensities on the second half of the inner wall. The surface flow visualization indicates that the secondary flow is weak on the inner wall of the elbow with higher Reynolds number. These results show that the mass transfer characteristics change on the inner wall of the elbow with increase in the Reynolds number, even when it is larger than Re = 5 × 10 4 . [ABSTRACT FROM AUTHOR]

The thermal and hydraulic performances of an air-cooled, planar, oblique-finned heat sink (OF HS) were investigated for two oblique angles: 30° and 45°. The conjugate heat transfer between the heat sink and the air flow were computed numerically in ANSYS Fluent for a range of air flow rates for the smallest periodically repeating portion of the heat sink. The RNG k-ε turbulence model with enhanced wall treatment was used to solve the fluid flow and heat transfer. Followed by the experimental validation, the numerical results were scrutinized further to understand the effects of the flow field on the measured heat transfer performances. Apart from boundary layer disruption, vortices generated within the secondary channels due to flow separation particularly improved the advection component of the convective heat transfer, resulting in a heat transfer enhancement, exceeding the pressure drop penalty. The strong flow mixing, showing chaotic behavior, enabled a more uniform increase in the air temperature in the streamwise direction, utilizing the cooling potential of the air flow more effectively. 30° oblique-finned heat sink was observed to induce higher rates of secondary flow rates and improve the heat transfer performance more than its 45° counterpart. Due to the migration of the flow in the direction of the secondary channels, the heat transfer enhancement was compromised at high Reynolds numbers, the pressure drop penalty exceeded the heat transfer enhancement, causing a reduction in the thermal-hydraulic performance factor. The effects of flow migration on the flow and temperature fields were investigated with full domain numerical simulations. Experimental investigations showed significant improvements in the junction temperatures. [ABSTRACT FROM AUTHOR]

This paper investigates the existence of secondary flow superimposed on the reactive fluid a channel filled with porous materials. At maximum temperature, it is well-known that the energy equation has two solutions. For this purpose, the exact solution of the velocity profile is obtained and used to compute the multiple solutions arising from the nonlinear internal heat generation within the flow region. The effect of various flow parameters on the multiple solutions are presented graphically and discussed based on the physics of the fluid. [ABSTRACT FROM AUTHOR]

The geometry considered in the present work (serpentine pipe) is a sequence of U-bends of alternate curvature. It is characterized by pipe diameter, d = 2 a and bend diameter, D = 2 c . The repeated curvature inversion forces the secondary flow pattern, typical of all flows in curved ducts, to switch between two mirror-like configurations. This causes (i) pressure drop and heat or mass transfer characteristics much different from those occurring either in a straight pipe or in a constant-curvature pipe, and (ii) an early loss of stability of the base steady-state flow. In the present work, four values of the curvature δ = a / c (0.2, 0.3, 0.4 and 0.5) were considered. For each value of δ , the friction velocity Reynolds number Re τ = u τ a / ν was made to vary in steps between 10 and 50. Fully developed flow was simulated using a three-dimensional, time-dependent finite volume method and computational grids with a number of nodes ranging from ∼1.8 to ∼4.6 × 10 6 , according to the curvature. The computational domain included two consecutive and opposite bends and thus coincided with the minimum spatially repetitive unit. Heat transfer was also simulated for uniform wall heat flux conditions and a Prandtl number of 1. A complex scenario of transitions was predicted, leading from the base steady-state, top-down symmetric flow to turbulence through intermediate regimes which included steady-state asymmetric and time-periodic flows. For all curvatures, at the highest value of Re τ investigated (50) the flow was turbulent and exhibited top-down symmetric time averages. [ABSTRACT FROM AUTHOR]

The Lab On a CD (LOCD), also known as Centrifugal Microfluidics, has evolved into a sophisticated platform for performing biomedical assays due to its marvelous miniaturization and accurate simulation of biological reactions. Among the numerous applications of the LOCD is fluid mixing. In this paper a centrifugal, serpentine micromixer is simulated and reformed toward better mixing performance. The micromixer was chosen to be curved as a curved design was found to be thrice as functional and compact as a rectilinear design, mixing-wise. The two angular velocity and opening radius parameters were originally hypothesized to affect mixing performance. Effect of angular velocity was studied over a broad range starting from quite low values. It was gathered that with increasing angular velocity, mixing performance initially drops and upon reaching a minimum at a threshold angular velocity, begins to continuously increase. The threshold angular velocity was found to be the spot at which the mixing regime changes from diffusion to secondary flow. It was also realized that increasing the opening radius enhances mixing performance only insignificantly, such that it would not be a practical means of making micromixers more efficient. [ABSTRACT FROM AUTHOR]

A combined experimental and numerical investigation is carried out to study the characteristics of laminar flow and forced convection heat transfer in a square cross-section wavy “serpentine” microchannel with the upper wall insulated and other side walls held at constant temperature. Experimental measurements of convective heat transfer and pressure drop are performed for 30/70% and 10/90% by weight mixtures of glycerine/water over a range of Dean number from 0.6 to 80. Complementary three-dimensional computational fluid dynamics numerical simulations are also conducted for the same conditions. The results show that the growth of secondary-flow vortices promotes fluid mixing in the serpentine microchannel and leads to an enhancement of the convective heat transfer. As a consequence the serpentine microchannel is able to enhance the performance of heat transfer relative to a straight microchannel over the entire range of Dean number. Meanwhile, at these values of Prandtl number the relative pressure-drop losses increase with increasing Dean number. These increased pressure-drop losses are rather modest over the whole range of Dean number compared with the significant enhancement in heat transfer. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the behaviour of two non-mixing fluids flowing in a heated curved channel. In simulating this immiscible fluid flow, a multi-phase model based on VOF approach is developed for steady, turbulent, incompressible fluid flow through curved channel. The analysis examines the influence of centrifugal forces arising from channel curvature on the phase distribution and flow patterns, and their impact on the thermal characteristics. Unique flow features are identified through the interactions between the fluid phases and vortex structures of the immiscible flow in curved channels. The convective heat transfer in curved channel is appraised in relation to the behaviour of fluid components and curved channel flow parameters. Finally, the study presents a Second-Law irreversibility analysis whereby a thermal optimisation technique is developed for immiscible fluid flow through heated curved channels. [Copyright &y& Elsevier]

Scouring downstream of submerged weirs is a common problem resulting from the interaction of the three-dimensional turbulent flow field around the structures and the mobile channel bed. This paper presents the distributions of flow patterns, bed shear stresses, and turbulence structures in the approach flow and the scour hole downstream of a submerged weir. The experiments were conducted under the clear-water scour condition for an equilibrium scour hole. The experimental results show that the flow structures are considerably changed by the presence of the structure. A large recirculation zone and a flow reattachment region are formed downstream of the submerged weir. Strongly paired cellular secondary flows are observed in the scour hole. The turbulence structures ahead of the recirculation zone govern the dimensions of the scour hole. [ABSTRACT FROM AUTHOR]

Abstract: In order to better understand the three-dimensional non-Newtonian flow in an 180° curved duct of square cross-section, simulations were carried out considering an incompressible viscoelastic fluid, which follows the non-linear FENE-CR model, having constant shear viscosity. A fully implicit finite-volume method was used for the solution of the governing equations. Numerical simulations were performed for different Reynolds and Weissenberg numbers, and by varying the model parameters, namely the retardation ratio (β) and the extensibility (L2 ). The aim was to analyse the development and distribution of velocity field in the cross-sections along the curved channel and as a consequence to understand the variation of maximum velocity with these parameters. The results reveal complex changes with increasing extensibility and decreasing retardation parameter, which are associated to transition from one to two pairs of vortices in the secondary flow. Comparison with the literature confirms and reveals that the absence of shear-thinning delays this transition. [Copyright &y& Elsevier]

An experimental study was conducted to investigate turbulent flow through from rectangular cross-sectional area to rectangular transition duct. Three kinds of channels with different length, side angle and geometrical dimensions were designed and then flow characteristic of them were all tested. The transition duct have different inlet and outlet cross-sectional areas, outlet section is double than inlet sectional area. Measurements were made at several station along the channel and at various flow-rates, Reynolds numbers ranging from 2.105 to 6.105, in which the two-dimensional mean, local velocity and pressure were measured at the x/l = 0.20, 0.40, 0.60, 0.80, 1.00 ratio, inlet by using hot wire anemometer. Based on experimental results, different flow characteristics were obtained. According to mean and local velocity and pressure drop values, each section point of the transition duct showed various values. Friction coefficient was lowered with increasing pipe length and increasing Reynolds number. Cross flows was shown in the short pipe along length at the low Reynolds. [ABSTRACT FROM AUTHOR]

Abstract: Mechanical vapor compressor is an essential component that governs the system performance and stability in the multi-effect desalination (MED) system. The importance of improving mechanical vapor compressor''s compressing ability in enhancing the efficiency of multi-effect desalination (MED) system has been stressed for a long time. This study was aimed to investigate the influences of inlet skew angle of the impeller on performance improvement. Four designs of inlet skew angles were attempted at the first stage impeller with 8°, 10°, 15°, and 20° respectively. Three dimensional fluid flows were simplified using periodic model to reduce the computational cost and time required. A good performance was expected as which effectively reduce the losses caused by secondary flow in the flow passage of the impeller. The results show detail flow pattern on decreasing the secondary flow due to incidence angle at the impeller eye and impeller passage. The numerical solutions were performed and allowed the better design. [Copyright &y& Elsevier]

Abstract: To improve understanding of the heat transfer enhancement for shell side of a double-pipe heat exchanger with helical fins and pin fins, the three-dimensional velocity components for the shell side with and without pin fins were measured experimentally by using laser Doppler anemometer (LDA) under cylindrical coordinate system and the fluid flow characteristics, i.e., the distributions of the axial velocity, secondary flow, stream function as well as vorticity were analyzed by employing orthogonal helical coordinate system. The results showed that, for the shell side only with helical fins at large pitch, there was a pair of vortex near the upper and lower edge of the rectangular cross section; the weakest secondary flow occurred at the center. By pin fins being installed, the three-dimensional velocity components in the helical channel were strongly changed. The extra two vortices emerged at the center of the cross sections. The fluctuation of the velocity at the center of the cross sections before and behind a pin was increased sharply by the pin, especially for the situation behind a pin. [Copyright &y& Elsevier]

Abstract: This investigation presents detailed experimental measurements of an active tip-clearance control method based on tip injection in a high-turning axial turbine cascade. Besides that, numerical investigations are also conducted to study phenomena which are not easily measured in the experiments. It aims to study the influence of tip injection on tip clearance flow, with emphasis on the effects of injection locations. Detailed flow field measurements were made downstream of the cascade using a three-hole probe. Static pressure distributions were also measured on the blade surface at 50% and 97.5% span, respectively. The results suggest that tip injection can weaken tip clearance flow, reducing the tip clearance mass flow and its associated losses. Meanwhile, the heat transfer condition on the blade tip surface can be also improved significantly. It also can be found that injection chordwise location plays an important role in the redistribution of secondary flow within the cascade passage. When the same number of injection holes and injection mass flow are applied, holes located in the aft part of blade can perform much better than that in the front part. [Copyright &y& Elsevier]

CFD modelling has been used to investigate the secondary flow phenomenon and its effect on grit particles carried in curved open channel flow. A CFD model was calibrated against a case study and then validated against data from a physical model with a 30○ bend. The flow was calculated by solving the full Reynolds-averaged Navier-Stokes equations and Reynolds Stress turbulence models with a finite-volume method; the air-water interaction at the free surface was simulated using a Volume of Fluid multi-phase model. The hydrodynamics of grit particles (63 to 2000 μm) moving round a bend was then modelled using Discrete Phase Modelling which was further calibrated using experimental data on grit movement from the physical model. Further parametric investigations were carried out using the numerical model on curved open channels for various angles of bend, flow rates, channel widths and radii of curvature to assess their effect on secondary flows. [ABSTRACT FROM AUTHOR]

We study theoretically the incompressible, viscous, oscillatory hydromagnetic Couette flow in a horizontal fluid-saturated highly permeable porous medium parallel-plate channel rotating about an axis perpendicular to the plane of the plates under the action of a uniform magnetic field, B0, inclined at an angle θ to the axis of rotation. The flow is generated by the non-torsional oscillation of the lower plate of the channel. The reduced unsteady momentum equations are nondimensionalized with appropriate variables. Exact solutions under specified boundary conditions are obtained using the Laplace transform method (LTM). The flow regime is found to be controlled by a rotational parameter (K2), which is the reciprocal of the Ekman number (Ek), the square of the Hartmann magnetohydrodynamic number (M2), a porous medium permeability parameter (Kp), which is the inverse of the Darcy number (Da), oscillation frequency (ω), dimensionless time (T), and magnetic field inclination (θ). The influence of these parameters on the primary (u1) and secondary (v1) velocity field is presented graphically and studied in detail. Asymptotic behavior of the solutions is also examined for several cases of the square of the Hartmann number, rotation parameter, and oscillation angular frequency. The existence of modified Hartmann boundary layers is also identified. The present study has important applications in MHD (magnetohydrodynamic) energy generator flows, chemical engineering magnetic materials processing, conducting blood flows, and process fluid dynamics. [ABSTRACT FROM AUTHOR]

Flow around a sharp open-channel bend is highly three-dimensional (3D) due to the combined effects of secondary flow, a large free surface variation and flow separation along the inner wall. Continuous vanes often used in closed curved conduits to generate a more uniform downstream flow were tested in the open channel using a 3D finite-volume model with a Reynolds stress turbulence model and the volume of fluid method for free surface prediction. The velocity field, turbulent kinetic energy and the extent of the flow separation zone were successfully validated against laboratory measurements for the no-vane case. The 3D simulations for one-vane and three-vane configurations reveal that vertical vanes are effective to reduce the secondary flow intensity and flow separation along the inner wall. The energy loss for bends with vanes is further slightly reduced compared to the no-vane case. The three-vane configuration is particularly efficient at creating uniform downstream flow. [ABSTRACT FROM AUTHOR]

Vegetation was added to a fully developed sandy point bar in the meander of a constructed stream. Significant changes in the flow structure and bed topography were observed. As expected, the addition of vegetative resistance decreased the depth-averaged streamwise velocity over the bar and increased it in the open region. In addition, the secondary circulation increased in strength but became confined to the deepest section of the channel. Over the point bar, the secondary flow was entirely outward, i.e., toward the outer bank. The changes in flow led to changes in bar shape. Although the region of the bar closest to the inner bank accumulated sediment, erosion of the bar and the removal of plants by scouring were observed at the interface between the planted bar and the open channel. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this study is to simulate flow pattern in a 90°bend experimentally and numerically. The numerical model used in this study is SSIIM 1.1. The model was used to predict the turbulence and the SIMPLE method was used to compute the pressure. For verification of the results of the numerical model the experimental data was used. The flow velocities were measured experimentally with P-EMS velocimeter. The results of the experimental data and the numerical simulation showed that the flow pattern in a channel bend is influenced widely by the secondary flow and centrifugal force. The comparison between the experimental data and the numerical model showed that SSIIM-1.1 is capable to simulate accurately the flow pattern in a 90°bend. The variations of components of velocity, streamlines, bed shear velocity and secondary flow are addressed in the study. [ABSTRACT FROM AUTHOR]

Abstract: This paper provides an analysis on cooling tower fouling data taken in seven 15.54mm I.D. helically ribbed, copper tubes at R e =16,000. The geometric parameters include number of rib starts, helix angle, and height. A series of semi-theoretical fouling correlations as a function of the product of area indexes and efficiency indexes are developed. The mass transfer coefficient is calculated by the Von-Karman analogy. The wall shear stress is obtained from the pressure drop. The correlations and the analyses can be used directly to assess the fouling potential of helical-rib in actual cooling water systems. [Copyright &y& Elsevier]

Abstract: Secondary flows are always present when a turbulent Newtonian fluid flows through a square duct. We show that they are suppressed in surfactant solutions at maximum drag reduction. This result confirms the one-dimensional behaviour of such flows, which is caused by the alignment of the micelles. [Copyright &y& Elsevier]

In the present study, it will be shown that at vanishingly small Reynolds numbers the extensional behavior of a fluid has a strong effect on its kinematics when flowing through a tapered slit die. To show this, the Cauchy equations of motion were simplified using the creeping flow approximation. Assuming the flow to be steady, laminar, two-dimensional, and incompressible, the governing PDEs were reduced to a set of coupled ODEs using a series solution in terms of the powers of 1/r. Two different constitutive equations, both incorporating an extensional parameter, were used in the analysis: (i) the Giesekus model and (ii) the Simplified Phan-Thien-Tanner (SPTT). An analytical solution was found for each fluid model clearly depicting the strong influence of the extensional parameter on the flow becoming non-radial within the channel. [ABSTRACT FROM AUTHOR]

In order to unravel the main flow and secondary flow characteristics and the role of turbulence in a curved single-bend open-channel flow, large-eddy simulations (LES) and Reynolds-averaged numerical simulations (RANS) were carried out and compared with experiments of the flow through a strongly bent laboratory flume. Turbulence was found to play an important role with respect to processes that are important in natural rivers. The strength of the curvature-induced secondary flow in the core of the flow domain, which is the most typical feature of curved open-channel flow, depends on the turbulence. Turbulence is especially important in the flow regions near the banks. Only the LES model is able to resolve accurately the boundary layer detachment and the formation of an internal shear layer at the inner bank as well as the outer-bank cell of secondary flow, whereas the RANS model is unable to reproduce these processes. Turbulence also conditions the magnitude of the bed shear stress, as indicated by the considerable overestimations of the bed shear stress by the RANS model as compared with the LES model. As a result, only LES properly reproduces the experimentally measured overall friction losses over the bend, whereas RANS overestimates these losses. The large scales of turbulence play an essential role in generating these flow processes by means of their interaction with the mean secondary flow structures, whereas small-scale turbulence is merely dissipative and does not play a dynamic role with respect to the time-averaged flow pattern. This implies that the simulated flow field is rather insensitive to the sub-grid model in the LES computation. [ABSTRACT FROM AUTHOR]

Abstract: The laminar flow of power-law and yield-stress fluids in 180° curved channels of rectangular cross section was studied experimentally and numerically in order to understand the effect of rheological fluid behavior on the Dean instability that appears beyond a critical condition in the flow. This leads to the apparition of Dean vortices that differ from the two corner vortices created by the channel wall curvature. Flow visualizations showed that the Dean vortices develop first in the near-wall zone on the concave (outer) wall, where the shear rate is higher and the viscosity weaker; then they penetrate into the centre of the channel cross section where power-law fluids have high viscosity and Bingham fluids are unyielded in laminar flow. Based on the complete formation on the concave wall of the new pairs of counter-rotating vortices (Dean vortices), the critical value of the Dean number decreases as the power-law index increases for the power-law fluids, and the Bingham number decreases for the Bingham fluids. For power-law fluids, a diagram of critical Dean numbers, based on the number of Dean vortices formed, was established for different axial positions. For the same flow conditions, the critical Dean number obtained using the axial velocity gradient criterion was smaller then that obtained with the visualization technique. [Copyright &y& Elsevier]

A nonlinear turbulence model for numerical solution of uniform channel flow is presented. Turbulent stresses are evaluated from a nonlinear mixing length model that relates turbulent stresses to quadratic products of the mean rate of strain and the mean vorticity. The definition of the mixing length, based on a three-dimensional integral measure of boundary proximity, eliminates the need for solution of additional transport equations for the turbulence quantities. Experimental data from the literature for closed and open-channel flows are utilized to validate the model. The model produced the secondary flow vortices successfully. Velocity field and wall shear stresses affected by secondary flow vortices are accurately computed. Bulging of velocity contour lines toward the corners and dipping phenomena of maximum velocity are successfully simulated. [ABSTRACT FROM AUTHOR]

Abstract: We present an experimental analysis of pressure-driven flow in a high (62:1) aspect ratio microchannel having a repeated herringbone surface pattern. The velocity field is determined at the groove–channel interface and at the midplane of the channel using microscopic particle image velocimetry. At Reynolds numbers of 0.08, 0.8 and 8, we observe secondary flow patterns consisting of counter-rotating flow cells aligned in the streamwise direction. The strength of this secondary flow is inhibited by fluid inertia when . The resulting flow structure can be viewed as splitting one wide channel into multiple smaller channels without the use of solid boundaries. [Copyright &y& Elsevier]

A three-dimensional numerical model was used to examine the turbulent flow field and associated sediment transport due to a series of barbs (submerged groynes) in a channel bend. Model results were in good agreement with measured laboratory data and adequately simulated the important features of sediment transport. Statistical comparison of the predicted and measured equilibrium bed geometry found average regression coefficients of determination of 0.77 and 0.72 for the 90° and 135° channels, respectively. The predicted velocity data followed expected trends. The capability of a three-dimensional numerical model to simulate sediment transport through bend sections of a channel containing barbs was verified. This included the simulation of the effects of different arrangements of barb groups and an analysis of the data to determine the relation of the flow field to associated scour and deposition in a complex fluvial environment. These novel results are useful for improved analyses of the bank-protection capabilities of these structures and for the development and improvement of design guidelines. [ABSTRACT FROM AUTHOR]

For transverse mixing problems in open channels, the effect of secondary currents on a tracer cloud is to disperse and mix the tracer in three dimensions more rapidly than would be the case if transverse turbulent diffusion were acting alone. Transverse mixing of this kind is difficult to simulate using two-dimensional depth-averaged mixing models which typically requires the specification of an equivalent dispersivity combining the effects of vertical shear dispersion and horizontal turbulent diffusion. In this paper, a two-dimensional vertically averaged and moment (VAM) equation technique for describing the transverse mixing mechanics of passive tracer vertical shear dispersion in approximately uniform curved open channel flow is detailed. An analytical expression is generated and compared to previous works in the literature describing the longitudinal development and asymptotic value of transverse dispersivity due to secondary current vertical shear dispersion. This expression is shown to describe the changing value of dispersivity even within the advective zone where traditional two-dimensional models cannot be applied. Distributions of depth-averaged concentration generated from numerical simulations of the VAM equations are compared to other higher fidelity computational results. The practical value of this VAM analysis framework is discussed relative to the potential for implementation in modern river modeling software packages. [ABSTRACT FROM AUTHOR]

Abstract: A simple and efficient method to improve morphological predictions using depth-averaged tidal models is presented. The method includes the contribution of secondary flows in sediment transport using the computed flow field from a depth-averaged model. The method has been validated for a case study using the 3D POLCOMS model and ADCP data. The enhanced depth-averaged tidal model along with the SWAN wave model are applied to morphological prediction around the Lleyn Peninsula and Bardsey Island as a case study in the Irish Sea. Due to the presence of a headland in this area two asymmetrical tidal eddies are developed in which the cyclonic eddy is stronger as a result of Coriolis effects. The results show that the enhanced model can effectively predict formation of sand banks at the centre of cyclonic eddies, while the depth-averaged model, due to its inability to accommodate secondary flow, is inadequate in this respect. [Copyright &y& Elsevier]

Two contrasting mechanisms, created by channel curvature which strongly affect longitudinal dispersion of solutes in rivers are examined. In natural channels the large cross-sectional variability of the primary velocity component tends to increase longitudinal dispersion by providing a large difference between adjacent fast and slow moving zones of fluid. By contrast secondary circulation tends to decrease longitudinal dispersion by enhancing transverse mixing. A series of tests have been carried out in a very large flume containing a meandering water-formed sand bed channel to measure the longitudinal dispersion coefficient at various locations around a meander. These experimental observations are compared with experimental data obtained from meandering channels with smooth, fixed sides and regular cross-sectional shapes. All the data has been compared against predictions from two current modeling approaches. Finally, the significance of the two competing mechanisms in curved channels is discussed with regard to their relative influence on longitudinal mixing. [ABSTRACT FROM AUTHOR]

Abstract: A method based on computational fluid dynamics (CFD) for the characterization of static mixers using the factor, helicity and the rate of striation thinning is presented. These measures were found to be well-suited for the characterization of static mixers as they reflect the pressure drop, the formation of secondary flow, i.e. vortices, and their effect on the mixing process. Two commercial static mixers, the Kenics KM and Lightnin Series 45, have been characterized. In the mixers investigated, secondary flow is formed in the flow at the element intersections and due to the curvature of the mixer elements. The intensity of the vortices is higher in the Lightnin than the Kenics mixer due to edges in the middle of the Lightnin mixer elements. The formation of vortices affects the factor by an increase in the power requirement, and the rate of striation thinning by an increase in the stretching of the striations. The formation of vortices was observed at a Reynolds number of 10 in both mixers with aspect ratios of 1.5. However, the intensity of the vortices was greater in the Lightnin than the Kenics mixer, which was observed in not only the magnitude of the helicity, but also the factor, rate of striation thinning and the distribution of striation thickness. The distribution in striation thickness is shifted towards thin striations as the flow rate is increased from below to above the Reynolds numbers of which vortices were first observed, but some striations still pass the mixer elements almost unaffected, which can be seen in the skewness of the distribution of the striation thickness, which shifts from being negative to positive. [Copyright &y& Elsevier]

Abstract: CFD simulations have been carried out to describe pervaporation of organic–water mixtures with a tubular membrane. The calculated density and temperature profiles have been compared with experiments. The profiles have been measured by ultrasound computer tomography (UCT) for pervaporation of pure water and an ethanol–water mixture. Good agreement between the measured and calculated density and temperature profiles has been found. Several flow patterns have been detected depending on the density ratio between the non-permeating and the permeating component in the mixture. For light organic–water mixtures an inversion point has been found at the membrane surface below which the flow moves downwards and above which the flow moves upwards. The inversion point is caused by the opposite effects of water concentration and temperature on the mixture density and consequently on the natural convection. For heavy organic–water mixtures the inversion point disappears and the flow on the membrane surface is only downward. The flux through the membrane tube increases as the density ratio increases. For the design of multi-tubular pervaporation modules, the results suggest that for separation of heavy organic–water mixtures the flux is maximized with a squared configuration. On the other hand, a triangular configuration is preferred for dewatering of light organic–water mixtures. [Copyright &y& Elsevier]

Pressurization in sanitary sewer conduit atmosphere is modeled using computational fluid dynamics techniques. The modeling approach considers both turbulent and laminar flow regimes. The turbulent model takes into consideration the turbulence-driven secondary currents associated with the sewer headspace and hence the Reynolds equations governing the air flow field are closed with an anisotropic closure model which comprises the use of the eddy viscosity concept for the turbulent shear stresses and semiempirical relations for the turbulent normal stresses. The resulting formulations are numerically integrated. The turbulent model outputs are verified with experimental data reported in the literature. Satisfactory agreement is obtained between numerical simulations and experimental data. Mathematical formulas and curves as functions of longitudinal pressure gradient, wastewater velocity, and sewer headspace geometry are developed for the cross-sectional average streamwise velocity. [ABSTRACT FROM AUTHOR]

This paper investigates the thermal fluid-flow transport phenomena in an axially rotating passage in which twin concentric orifices of different radii are installed. Emphasis is placed on the effects of pipe rotation and orifice configuration on the flow and thermal fields, i.e. both the formation of vena contracta and the heat-transfer performance behind each orifice. The governing equations are discretized by means of a finite-difference technique and numerically solved for the distributions of velocity vector and fluid temperature subject to constant wall temperature and uniform inlet velocity and fluid temperature. It is found that: (i) for a laminar flow through twin concentric orifices in a pipe, axial pipe rotation causes the vena contracta in the orifice to stretch, resulting in an amplification of heat-transfer performance in the downstream region behind the rear orifice, (ii) simultaneously the heat transfer rate in the area between twin orifice is intensified by pipe rotation, (iii) the amplification of heat transfer performance is affected by the front and rear orifice heights. Results may find applications in automotive and rotating hydraulic transmission lines and in aircraft gas turbine engines. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The effect of a traveling sonic wave on a convective flow in a horizontal layer with a fixed linear temperature distribution on the boundaries is investigated. Convective rolls with axes parallel to the basic flow (lengthwise rolls) are considered. On the basis of a weakly nonlinear analysis, it is shown that the lengthwise rolls appear smoothly and the regular flows are stable near the stability threshold. A direct numerical simulation is performed. Secondary near-critical flow regimes and regimes corresponding to finite supercriticalities are investigated. [ABSTRACT FROM AUTHOR]

Abstract: Submarine channels have long been considered analogous to meandering fluvial channels due to their similar planform geometry, and this has given rise to strong analogies in terms of the fluid dynamics of these channel types. However, there is a paucity of direct measurements detailing the structure of velocity or sediment concentration, and nothing is known about the structure of secondary flow, within submarine channels. Within fluvial channels, secondary circulation has been shown to be an important control of erosion, deposition, lateral sediment transport and overall bend stability. This paper presents a series of experiments in which saline gravity currents flowed through a submerged, fixed-form, sinuous channel model. Ultrasonic Doppler velocity profiling provided high-resolution, three-dimensional visualisation of flow fields, thereby allowing the first quantitative visualisation of velocity profiles and secondary flows of a saline gravity current within a sinuous submarine channel. The same model was also used to measure the structure of flow within a subaerial channel, thereby providing a detailed comparison between a submarine and fluvial channel. The data reveal that secondary flow cells in submarine channels are best developed at bend apexes and that the basal component of the flow cell moves from the inside to the outside of the bend, in a reversed direction to that expected from models of fluvial bend flow. These results are of prime importance when assessing the validity of comparisons between submarine and fluvial channels, and the role of secondary flow cells in the migration and evolution of meander bends. This work demonstrates that the fundamental flow processes controlling the evolution and migration of submarine and fluvial channels may be very different, and suggest that the form and evolution of submarine channels may also show different properties to their fluvial counterparts. [Copyright &y& Elsevier]

Background: Computational fluid dynamics tools are useful for their ability to model patient specific data relevant to the genesis and progression of atherosclerosis, but unavailable to measurement tools. The sensitivity of the physiologically relevant parameters of wall shear stress (WSS) and the oscillatory shear index (OSI) to secondary flow in the inlet velocity profiles was investigated in three realistic models of the carotid bifurcation. Method of Approach: Secondary flow profiles were generated using sufficiently long entrance lengths, to which curvature and helical pitch were added. The differences observed were contextualized with respect to effect of the uncertainty of the models' geometry on the same parameters. Results: The effects of secondary velocities in the inlet profile on WSS and OSI break down within a few diameters of the inlet. Overall, the effect of secondary inlet flow on these models was on average more than 3.5 times smaller than the effect of geometric variability, with 13% and 48% WSS variability induced by inlet secondary flow and geometric differences, respectively. Conclusions. The degree of variation is demonstrated to be within the range of the other computational assumptions, and we conclude that given a sufficient entrance length of realistic geometry, simplification to fully developed axial (i.e., Womersley) flow may be made without penalty. Thus, given a choice between measuring three components of inlet velocity or a greater geometric extent, we recommend effort be given to more accurate and detailed geometric reconstructions, as being of primary influence on physiologically significant indicators. [ABSTRACT FROM AUTHOR]

Abstract: Streamwise vorticity in viscous, compressible, steady flow about aircraft is analysed on the basis of the steady Reynolds-averaged Navier–Stokes equations. It is shown, that streamwise vorticity can develop in the presence of stream-normal vorticity and can be non-negligible only inside e.g. boundary layers, shock layers, viscous (turbulent) wakes, jet exhausts and propeller slipstreams, but also along streamlines leaving such viscous and heat conduction dominated flow regions on their downstream side (e.g. downstream of shock layers). However, the actual development of streamwise vorticity then still depends on such local flow characteristics as e.g. streamline curvature and streamline convergence or divergence. Two illustrative examples are discussed. [Copyright &y& Elsevier]

Abstract: The secondary flow in a curved duct of square cross-section is investigated experimentally using a visualization method. Three walls of the duct (except the outer wall) rotate around the center of curvature and an azimuthal pressure gradient is imposed. Photographs of the flow in a cross-section at 180° downstream from the curved duct entrance are taken by changing the flux (Dean number) at a constant rotational speed (Taylor number) of the duct walls. Several types of secondary flow are detected. The variation of the flow patterns with change of flow parameters is compared with that of numerical calculations and is found to be in good agreement. The diagram showing types of secondary flow patterns in the Taylor–Dean number plane is obtained. [Copyright &y& Elsevier]

To improve navigation conditions for barges passing through river channels, many submerged weirs (SWs) have been installed along the bendways of many waterways by the U.S. Army Corps of Engineers. This paper presents results from three-dimensional numerical simulations that were conducted to study the helical secondary current (HSC) and the near-field flow distribution around one SW. The simulated flow fields around a SW in a scale physical model were validated using experimental data. The three-dimensional flow fields around a SW, the influence of the SW on general HSC, and the implication of effectiveness of submerged weirs to realign the flow field and improve navigability in bendways were analyzed. The numerical simulations indicated that the SW significantly altered the general HSC. Its presence induced a skewed pressure difference cross its top and a triangular-shaped recirculation to the downstream side. The over-top flow tends to realign toward the inner bank and therefore improves conditions for navigation. [ABSTRACT FROM AUTHOR]

This paper investigates the mechanism of the dip phenomenon whereby the location of the maximum velocity appears below the free surface vis-à-vis the secondary currents in open-channel flows. It is found that the classical log law gives a good description of the velocity distribution in the inner region if the local shear velocity is introduced into the dimensionless distance, i.e., u*(z)y/v. In the outer region, where the maximum velocity occurs at some distance below the free surface in a vertical plane, it is found that the velocity deviation from the log law is linearly proportional to the logarithmic distance ln(1-y/h) from the free surface. To this end, the study proposes a dip-modified log law for the velocity distribution in smooth uniform open channel flows. This new law is capable of describing the dip phenomenon, and is applicable to the velocity profile in the region from the near bed to just below the free surface, and transversely, from the center line to the near-wall region of the channel. The dip-modified log law consists of two logarithmic distances, one from the bed ln(u*(z) y/v), and the other from the free surface ln(1 -y/h), respectively, and a dip-correction factor a. The latter is the only parameter that needs to be determined and an empirical equation for a has been proposed in this study. The dip-modified log law has been verified using published experimental data for smooth rectangular open channels and the agreement between the measured and computed velocity profiles is good. [ABSTRACT FROM AUTHOR]