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A steady Newtonian fluid flow through annular region in curved pipes is studied in this paper. The flow takes place due to an axial pressure gradient and it is three-dimensional in nature. The equations governing the flow are highly coupled and nonlinear. The solutions are obtained, analytically, using a regular perturbation method. The effects of curvature ratio (δ) , Reynolds number (Re) and the radius ratio (l) on the axial velocity and stream function are presented graphically. It is observed that, along with curvature ratio and Reynolds number, radius ratio highly affects the fluid flow in annular curved pipes. [ABSTRACT FROM AUTHOR]

The bend pipe with a circular section, which is widely used in hydropower, chemical industry and other fields, is a common form in pipeline systems. However, secondary flow occurs when the fluid flows through the bend pipe, thereby affecting the stability of the pipeline system. Different bending angles have various effects. Therefore, this paper establishes 3D models of a circular bend pipe with different bending angles. The influence of bending angle on flow field distribution and downstream flow is analyzed numerically. The larger the bending angle is, the more obvious the flow distribution and even the unevenness at the elbow will be, hence resulting in poor stability. The distance required to restore flow uniformity also increases. The pressure energy loss of the bend pipe with different bending angles is investigated. Results show that with the increase in bending angle, the global pressure loss presents a trend of "increase-decrease-increase." The closer the bending angle is to 90°, the greater the influence of centrifugal force is on the flow, and the more obvious the secondary flow phenomenon will be. Aiming at the nonuniformity phenomenon, the structure optimization of a 90° bend pipe with the greatest influence is conducted. The improvement of the flow characteristics of bend pipe with different thick-diameter ratio and length-diameter ratio is compared. The deflector with a certain thickness can enhance the uniformity, safety and useful life of the bend pipe. The sharp-end length can improve the velocity uniformity to a certain extent but has minimal influence on flow characteristics compared with the thick-diameter ratio. This paper aims to study and improve the flow performance of a multi-structure bend pipe to make it suitable for more complex conditions. [ABSTRACT FROM AUTHOR]

The influences of different emergent and rigid vegetation distributions on hydrodynamic characteristics in a 180° curved open channel are experimentally investigated in this study. Experimental results show that the transverse velocity gradient generated at the vegetation and non-vegetation interface is greater for the vegetation presence on the convex bank (inner case) than the vegetation on the concave bank (outer case) with the effect of centrifugal force pointing to the concave bank. The presence of uniform distributed vegetation will weaken the secondary flow, and theoretical analysis is also developed to indicate the influential range of emergent vegetation on secondary flow over a curved channel. In addition, the peak frequency determined from the spectrum at the vegetation and non-vegetation interface along a curved channel is still associated with the Kelvin–Helmholtz (K-H) instability. Both the curved channel and presence of emergent vegetation can reduce the occurrence frequency of turbulent ejection and sweep events. [ABSTRACT FROM AUTHOR]

This article focuses on numerical simulations of the granular mixing process in a vertical cylindrical mixer with two opposed flat blades with a 45° rake angle. Computer simulations were performed by the discrete element method. The blending was examined for the blades' stirrer speeds in the range from 1.9 to 960 rpm and three different initial spatial configurations. The development of the concentration patterns and the evolution of phase interphase between different types of particles have shown that the homogenization process depends not only on the system's dynamics but also on the initial spatial distribution of particles. The dependence on the initial distribution is provided by involving primary and secondary flows in different time-scale in the homogenization process. This ability of the individual flows to engage in the mixing is granted by the mutual synergy between the direction of movements of particles located on the phase interface and the orientation of the phase interface. Because there is a significant difference between the intensity of primary and secondary flows in most cases, an improperly oriented phase interface will significantly slow down the entire rate of the homogenization process. On the other hand, during the mixing process, the phase interface expands and deforms, which gradually also allows the rest of the flows to get involved in the homogenization process. Based on the results, the basic rules have been identified for effective homogenization. As a mixing index, the relative surface of the phase interface was used. By comparing individual homogenization curves, it follows that the critical factor for the homogenization process is the centrifugal force. When it is in balance with other forces, it encourages homogenization. On the contrary, if it becomes the dominant force in the system, it causes a significant deformation of the surface, and its effect on the homogenization process is destructive. [Display omitted] • The effect of primary and secondary flows on the homogenization was analysed. • The homogenization level was determined by the relative size of a phase interface. • The centrifugal force fundamentally affects the efficiency of the mixing process. • The tangential configuration is best mixed due to the engagement of primary flows. • Secondary flows are crucial to homogenize the radial and axial configuration. [ABSTRACT FROM AUTHOR]

Efficient drilling operations in polar regions are crucial given their unique climate and surface conditions. To improve drilling efficiency, a novel technology utilizing helically coiled tubes (HCT) for transporting ice particles has been proposed. This study focuses on the gas-solid flow characteristics of ice particles within the HCT employing the Eulerian-Eulerian models of Ansys-Fluent 2022 R2. Numerical simulations were validated against experimental data, showing good agreement with a maximum error of merely 11.27%. Three distinct flow regions perpendicular to the flow direction were observed, influenced by centrifugal force and secondary flow. The inlet gas velocity, tube inner diameter, coil diameter, particle diameter, and penetration rate all affected the ice particle transport ratio (ITR) and the pressure drop in the HCT. Notably, increasing the tube inner diameter from 30 mm to 75 mm led to a remarkable 398.7% rise in the ITR, while particle diameter changes minimally affected ITR. [Display omitted] • The flow behavior of gas-solid two-phase flow in HCT is investigated. • Transportation efficiency of ice particles in HCT is discussed. • Pressure drops of gas-solid two-phase flow in HCT is analyzed. • Effect of HCT parameters and operation conditions on gas-solid flow is determined. [ABSTRACT FROM AUTHOR]

• Curve channel with periodical wave structure is proposed to enhance heat transfer. • Secondary flow in curve-wave channel generates more vortices disturbing main flow stream. • Thermal boundary layer in curve-wave channel redevelops periodically along main flow direction. • Heat transfer enhanced by curve-wave channel outweighs its pressure penalty. • The optimum wave amplitude can be obtained by evaluating the dimensionless performance factor. Flow and heat transfer in curve channel have been studied extensively due to the presence of the secondary flow induced by the centrifugal force. However, for the curved channel with small curvature, weakened centrifugal force reduces the intensity of secondary flow and heat transfer enhancement is attenuated accordingly. For sake of maintaining high heat transfer efficiency in curve channel with a wide range of curvature, periodical wave structure was introduced into the smooth-curve channel by this study. A three-dimensional model of the curve-wave structure was established and numerical simulation was carried out to explore the flow characteristics and heat transfer performance in the proposed channel. In addition, the effects of the wave amplitude on the channel performance were analyzed. The results showed that the heat transfer of smooth-curve channel can be enhanced remarkably by applying wave structure on the channel wall, and the overall performance factor indicates that the heat transfer argumentation outweighs the pressure loss penalty. It was also found that the heat transfer in the curve-wave channel can be further enhanced by increasing wave amplitude. The most effective heat transfer enhancement can be achieved based on the evaluation of the overall performance factor. [ABSTRACT FROM AUTHOR]

Highlights • An term-by-term estimation was made of the key terms in the kinetic energy equation using detailed experimental data. • An term-by-term estimation was made of the key terms in the enstrophy equation equation using detailed experimental data. • Role of secondary flow in the transport and dissipation of kinetic energy. Abstract In sharp open-channel bends, there exists nonlinear interactions between streamwise and cross-stream velocities, which leads to the adjustment of flow energy transport, increases the energy dissipation and eventually influences the development of river bends. However, previous studies have not yet fully understood the mechanisms underlying the transport and dissipation of energy in open-channel bends. In addition, energy dissipation is directly related to the evolution of enstrophy Ω · Ω / 2. However, it has not yet received much attention in the study of the resistance in meandering rivers. To gain an insight into these mechanisms, with the aid of detailed experimental data collected in a sharp open-channel bend, this study quantified the impacts of the key terms in the kinetic energy equation and the enstrophy equation. Results show that the term related to the transport of kinetic energy by cross-stream circulation is at least an order of magnitude larger than the other terms in the kinetic energy equation, which contributes significantly to the redistribution of kinetic energy over the cross section. The term related to the production of turbulent kinetic energy in the kinetic energy equation shows the smallest order of magnitude and thus is almost negligible for the time-averaged flow field. Furthermore, over most of the measured area, the term related to the centrifugal force shows values of at least an order of magnitude larger than the other terms in the enstrophy equation, which means that this term exerts the dominant influence on the energy dissipation. The results also revealed that the transformation process is insensitive to the variations in Froude number. These results are expected to improve the understanding of the complete process of energy transformation, especially the resistance caused by secondary flow in meandering rivers. [ABSTRACT FROM AUTHOR]

Highlights • Measurements of post-dryout heat transfer in helical coils are obtained. • Curvature significantly enhances post-dryout heat transfer in helical coils. • The post-dryout heat transfer coefficient of helical coils decreases in quality. • Heat transfer correlation for post-dryout regime of helical coils is developed. Abstract Post-dryout heat transfer for steam-water flow in helical coils is experimentally investigated. The inner diameters of the helical coils are 12.5 mm and 14.5 mm, and the coil diameters range from 180 mm to 380 mm. The experimental system pressure covers the range 2–8 MP. The results indicate that the centrifugal force induced secondary flow has a great influence on post-dryout heat transfer in helical coils. In the low quality post-dryout region, because of the high redeposition rate induced by secondary flow, the heat transfer coefficient of helical coils is significantly higher than that of straight tubes. As the total droplet mass decreases with increasing quality, the heat transfer performance of helical coils decreases and continuously approaches that of straight tubes. In high quality post-dryout region, the bulk fluid in helical coils is closer to thermodynamic equilibrium state due to the secondary flow, and the heat transfer coefficient may be exceeded by straight tubes. For the effects of flow parameters, the post-dryout heat transfer performance decreases in heat flux and increases in mass flux. For system pressure, due to the change of the dominant heat transfer mechanism, the post-dryout heat transfer decreases in the low quality region but increases in the high quality region with increasing system pressure. Based on a detailed analysis of the effects of various dimensionless parameters, a new correlation containing a quality correction is proposed and provides good prediction accuracy. [ABSTRACT FROM AUTHOR]

• A microfluidic Lab-On-a-Disk device is introduced to separate cancer cells. • Active (magnetophoresis) and passive (inertial) methods are compared. • Geometrical features, including curvature and unit shape, are studied. • Optimum parameters were numerically calculated. • The curved expansion-contraction channel showed the best separation result. Cancer diagnosis has recently been at the forefront of recent medical research, with ongoing efforts to develop devices and technologies for detecting cancer in patients. One promising approach for cancer diagnosis is the detection of Circulating Tumor Cells (CTCs) in blood samples. Separating these rare cells from the diverse background of blood cells and analyzing them can provide valuable insights into the disease's stage and lethality. Here we present the design and fabrication of a centrifugal microfluidic platform on a polymeric disk that utilizes centrifugal forces for cell isolation. The separation units exploit both active and passive methods. In other words, in addition to introducing novel geometry for channels, an external magnetic field is also employed to separate the target cells from the background cells. In order for the external field to function, the CTCs must first be labeled with antibody-conjugated nanoparticles; the separation process should be then performed. Before the experimental tests, a numerical study was done to determine the optimum parameters; the angular velocity and magnetization investigations showed that 2000 rpm and 868,000 (kA/m) are the optimum conditions for the designed device to reach the efficiency of 100% for both White Blood Cells (WBCs) and CTCs. These results indicate that the passive region of the channels primarily contributes to the focusing of the target cells, and showed that the focusing effect is more pronounced in the expansion-contraction geometry compared to the zigzag geometry. Additionally, the results proved that curved channel geometries performed better than straight ones in terms of separation efficiency. However, if the separation relies solely on channel geometry, the majority of cells would be directed towards the non-target chamber, leading to suboptimal results. This is due to the direction of the forces acting on the cells. However, including an external magnetic field improves the direction of the net force and enhances the separation efficiency. Finally, the numerical and experimental results of the study were compared, and the curved expansion-contraction channel is introduced as the best geometry having 100% and ∼92% CTC separation efficiency, respectively. [ABSTRACT FROM AUTHOR]

[Display omitted] • Two-phase liquid–liquid flow and interaction mechanism in coiled flow invertor (CFI) over a wide range of parameters. • Effect of oil-phase fraction, inlet velocity and CFI orientation on liquid–liquid two-phase flow in CFI. • Oil-fraction have little influence on overall vorticity spectrum of the mixture, however a significant effect on the individual phases vorticity. • The change in CFI orientation (horizontal and vertical) enhanced surface area-to-volume ratio by ≈32%. The present study deals with the numerical investigation of void fraction and flow patterns for liquid–liquid (oil–water) two-phase flow through a coiled flow inverter (CFI) with different flow conditions and geometrical orientations (horizontal and vertical). A CFI comprising 90° bends between two consecutive helical coils, and works on complete flow inversion due to directional change in centrifugal force. The velocity and phase distribution profiles for liquid–liquid two-phase flow in CFI are analysed by varying Reynolds and Dean numbers from 637−5033 and 202–1592, respectively. The orientation significantly influences overall friction factor based on mixture at low inlet velocities, while at higher inlet velocity it is nearly similar despite of CFI orientation. The inherent mechanism of vorticity distribution, to predict fluid rotational motion, is also reported for each phase in CFI. The change in CFI orientation resulted into an increase in the surface area(interface)-to-volume ratio of oil by ≈32%. [ABSTRACT FROM AUTHOR]

In the article, attention is focused on a secondary flow in the narrow gap of a magnetic fluid shaft seal, and the secondary flow and circumferential speed of the magnetic fluid are numerically evaluated with variation in magnetic fluid plug shape such as angle of the polar head and seal clearance to be varied, using a spectral finite difference method with a new mapped function. Moreover, the maximum pressure drop is calculated in several patterns of equilibrium magnetic fluid plug, and the influence of the centrifugal force is also discussed. [ABSTRACT FROM AUTHOR]

A numerical study is conducted on the fully-developed laminar flow of an incompressible viscous fluid in a square duct rotating about a perpendicular axis to the axial direction of the duct. At the straight duct, the rotation produces vortices due to the Coriolis force. Generally two vortex cells are formed and the axial velocity distribution is distorted by the effect of this Coriolis force. When a convective force is weak, two counter-rotating vortices are shown with a quasi-parabolic axial velocity profile for weak rotation rates. As the rotation rate increases, the axial velocity on the vertical centreline of the duct begins to flatten and the location of vorticity center is moved near to wall by the effect of the Coriolis force. When the convective inertia force is strong, a double-vortex secondary flow appears in the transverse planes of the duct for weak rotation rates but as the speed of rotation increases the secondary flow is shown to split into an asymmetric configuration of four counter-rotating vortices. If the rotation rates are increased further, the secondary flow restabilizes to a slightly asymmetric double-vortex configuration. Also, a numerical study is conducted on the laminar flow of an incompressible viscous fluid in a 90°-bend square duct that rotates about axis parallel to the axial direction of the inlet. At a 90°-bend square duct, the feature of flow by the effect of a Coriolis force and a centrifugal force, namely a secondary flow by the centrifugal force in the curved region and the Coriolis force in the downstream region, is shown since the centrifugal force in curved region and the Coriolis force in downstream region are dominant respectively.

In this paper, a comprehensive numerical study is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a rotating curved rectangular duct of small curvature. Numerical calculations are carried out by using a spectral method, and covering a wide range of the Taylor number 0 ≤ Tr ≤ 2000 for the Dean numbers Dn = 500 and 1000. A temperature difference is applied across the vertical sidewalls for the Grashof number Gr = 100, where the outer wall is heated and the inner wall cooled. The rotation of the duct about the center of curvature is imposed, and the effects of rotation ( Coriolis force ) on the unsteady flow characteristics are investigated. It is found that the unsteady flow undergoes in the scenario ‘ Chaotic → multi-periodic → periodic → steady-state’ , if Tr is increased in the positive direction. Contours of secondary flow patterns and temperature profiles are also obtained at several values of Tr , and it is found that there exist two- and multi-vortex solutions for the unsteady flow if the duct rotation is involved in the present cases. [ABSTRACT FROM AUTHOR]

The nature of three-dimensional flow in submarine channel bends is poorly understood, largely due to the absence of detailed data from natural channels. Herein, data from density-driven flows in a large reservoir on the Huanghe (Yellow) River are presented showing the spatio-temporal variation of flow around a subaqueous bend. The data demonstrate for the first time that reversed helical flow, relative to that found in river channel bends, can occur from the centrifugal forcing of flow, even when the Coriolis force acts in the opposite direction. The data also suggest that reversed helical flow fields in submarine channels may be more frequent than currently estimated, notably for bends where Coriolis and centrifugal forces combine in the same direction. In addition, this study provides the first field evidence suggesting that sinuous submarine channels can exhibit an asymmetry in helical flow orientation between left and right-turning bends, which will have major implications for the morphodynamics of submarine channels, their resultant patterns of sedimentation and, ultimately, the distribution of depositional units across submarine fan systems. [ABSTRACT FROM AUTHOR]

Abstract: Rotating microchannels are integral part of centrifugally actuated miniaturized microfluidic devices, which have important applications in chemical analysis and biomedical diagnostics. As the field of centrifugal microfluidics continues to evolve, it is becoming imperative to understand the fundamental principles of fluid flow inside microchannels under the influence of centrifugal and Coriolis forces. These forces arise as a consequence of expressing the governing equations in rotating Eulerian reference frame and change the flow pattern significantly from the symmetric parabolic profile of a non-rotating channel. In this paper, we have summarized the recent advances in the area of fluid flow and heat trans er applications in radially rotating microchannels. A review of experimental and numerical studies available in the current literature is performed and issues with the applicability of analytical correlations for conventional macro-sized channels to describe the microscale flow phenomena have been discussed. From this state of the art review, it is evident that further systematic investigations are needed for a clear understanding of the transport mechanism associated with the flow and heat transfer inside rotating microchannels. [Copyright &y& Elsevier]

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: A numerical study using the lattice Boltzmann method has been carried out for flow through a rotating straight channel with a rectangular cross section. With different forces applied, the secondary flow exhibits two-cell states, four-cell states or six-cell states at a range of low rotational Reynolds number, however, within which only the two-cell states have been commonly reported. In addition to the force-dependent flow transition, a time-dependent flow transition of the secondary flow among two-cell states, four-cell states and six-cell states is also discovered during flow development. These newly found flow transitions and their regulations by force application have been analyzed. Based on numbers of case studies, it is found that a dimensionless number, the ratio of the driving pressure gradient to the centrifugal force, regulates such flow transitions. This study not only releases new phenomena of flow transition, but also indicates new applications in flow control, particle separation and heat transfer. [Copyright &y& Elsevier]

In this study, confined swirling flows of an aqueous surfactant solution due to a rotating disk in a cylindrical casing were investigated using a sectional flow visualization technique and a two-component laser Doppler velocimetry system. The concentrations of aqueous surfactant solutions (C14TASal) are 0.4 wt %, 0.8 wt %, and 1.2 wt %. Rheological properties such as shear viscosity and first normal stress difference of the surfactant solution were measured with a rheometer The patterns of secondary flow were classified using the Reynolds and elasticity numbers. We revealed that the projection formed near the center of the rotating disk moved up and down at a constant frequency for C14TASal 0.8 wt % and 1.2 wt %, which has not been reported as far as we know. The effects of the Reynolds number elasticity number and aspect ratio on the velocity profiles were clarified. It was also found that the region of rigid body rotation existed at the higher Reynolds number tested for C14TASal 0.4 wt %. [ABSTRACT FROM AUTHOR]

The need for eco-friendly and energy saving processes which are substantially compact and give higher efficiency has led to the concept of process intensification (PI). Curved microchannel is such innovative device, which has potential for the intensification of processes currently carried out in conventional straight or T-type microchannels. Curved microchannels utilize the benefits of centrifugal force to its advantage. The present study deals with the numerical simulation of the Taylor flow in curved microchannels, particularly on gas and liquid slugs with varying curvature ratios (i.e., coil to tube , 10, 20 and 30). The three-dimensional, unsteady slug flow development in the curved microchannel was carried out using control volume finite difference method (CVFDM). The gas and liquid slug lengths at various operating and fluid conditions were obtained. The slug flow development for different inlet conditions and geometries (premixed feed, T-type and Y-type inlets) was also studied in the curved microchannels. It was found that for low curvature ratio , the phenomenon of flow reversal and slug freezing takes place due to centrifugal and buoyancy forces. For the similar process conditions, with an increase in curvature ratio to 5 and 10, the phenomenon of flow reversal and slug freezing observed was very minor. The non-uniformity in the slug formation was observed for low curvature ratio as compared to the higher curvature ratios. Further the influence of surface tension, viscosity and wall adhesion was studied on slug flow development in the curved microchannels. From the results it was observed that the surface tension, viscosity and wall adhesion have significant influence on slug flow development in curved microchannels. [Copyright &y& Elsevier]

Abstract: A numerical study is performed to examine the characteristics of fluid flow and convective heat transfer in a helical square duct rotating at a constant angular velocity about the center of curvature. Due to the combined effects of rotation (the Coriolis force), torsion and curvature (the centrifugal force), the flow behaviors become very complicated. A wide range of parameters is covered in this work. The variations of flow structure and temperature distribution with the force ratio F (the ratio of the Coriolis force to the centrifugal force) and the torsion are examined in details. The effects of rotation and torsion on the friction factor and Nusselt number are also studied at length. And also multiple solutions for a rotating toroidal square duct have been obtained. Certain hitherto unknown flow patterns are found. The present work shows both the nature of flow behaviors and the characteristics of heat transfer in a rotating helical square duct. [Copyright &y& Elsevier]

In the present study, the flow in a rotating helical pipe with an elliptical cross section is considered. The axes of the elliptical cross section are in arbitrary, directions. Using the perturbation method, the Navier-Stokes equations in a rotating helical coordinate system are solved. The combined effects of rotation, torsion, and geometry on the characteristics of secondary flow and fluid particle trajectory are discussed. Some new and interesting conclusions are obtained, such as how the number of secondary flow cells and the secondary flow intensity depends on the ratio of the Coroilis force to the centrifugal force. The results show that the increase of torsion has the tendency to transfer the structure of secondary flow into a saddle flow and that the incline angle a increases or decreases the secondary flow intensity depending on the resultant force between the Corilois force and centrifugal force. [ABSTRACT FROM AUTHOR]

When a temperature-induced variation of fluid density occurs in a rotating curved pipe, the Coriolis force, the centrifugal-type buoyancy force and the centrifugal force will contribute to the generation of the secondary flow. The interaction of these body forces complicates the characteristics of flow and heat transfer. A numerical study is performed to examine the combined effects of rotation (Coriolis force), curvature (centrifugal force) and heating/cooling (centrifugal-type buoyancy force), and solutions are obtained for a wide range of parameters. The combined effects of these comparable order of magnitude forces on the flow structure, temperature distribution, friction factor and Nusselt number are examined in detail. Present works show the natures of the flow and heat transfer in rotating curved pipes. [Copyright &y& Elsevier]