Pair Of Dean Vortices Research Articles

Investigation on large fluctuation transient process of high head Pelton turbine

Abstract With the development of hydropower in southern western China, the Pelton turbine is the only choice in this ultra-high head condition which is nearly 1000 m. However, the complex coupling structure of the internal and external flow of the Pelton turbine, the change of flow pattern during the transition process, and the fluid-solid interaction of the bucket greatly increases the difficulty of accurate numerical simulation. Therefore, there are relatively few studies and applications on the transition process of the Pelton turbine. In this paper, the theoretical analysis, numerical calculation on the internal complex flow and the external characteristics of the turbine during the large fluctuation transition process are carried out in three aspects. First, the internal flow mechanism under optimized conditions is investigated, such as Dean vortex pairs, secondary flow, etc. And then analyze the influence of the flow state distribution on the jet flow. Secondly, study the instability and flow characteristics in the large fluctuation transition process of the opening and closing process of the nozzle, and predict the mechanism of the jet flow and the impact on the bucket during the dynamic process. Finally, study change of the hydraulic characteristics under the dynamic process which provides a theoretical guarantee for the safe operation of the Pelton turbine.

Critical conditions for development of a second pair of Dean vortices in curved microfluidic channels.

The centrifugal force in flow through a curved channel initiates a hydrodynamic instability that results in the development of Dean vortices, a pair of counter-rotating roll cells across the channel that deflect the high velocity fluid in the center toward the outer (concave) wall. When this secondary flow toward the concave (outer) wall is too strong to be dissipated by viscous effects, an additional pair of vortices emerges near the outer wall. Combining numerical simulation and dimensional analysis, we find that the critical condition for the onset of the second vortex pair depends on γ^{1/2}Dn (γ: channel aspect ratio; Dn: Dean number). We also investigate the development length for the additional vortex pair in channels with different aspect ratios and curvatures. The larger centrifugal force at higher Dean numbers produces the additional vortices further upstream, with the required development length being inversely proportional to the Reynolds number and increasing linearly with the radius of curvature of the channel.

Study of a toroidal-helical pipe as an innovative static mixer in laminar flows

In this paper we present the design of a novel, passive mixer, to enhance mixing and residence time distribution for promoting transport and reaction mechanisms in such devices. The goal is to understand and optimize the flow patterns for enhancing mixing in laminar flows through toroidal helical pipes, inspired by the coiled flow inverter (CFI) (Saxena and Nigam, 1984). A toroidal helix is a smooth analytical curve winding around a torus. It is characterized by three parameters: the radius of the torus’ centerline, the radius of the torus’ cross-section, and the number of turns it winds around the torus. Unlike the torus or the straight helix which have constant curvatures, the toroidal helix has a spatially oscillating curvature. We found that this causes the otherwise separated pair of Dean vortices to couple together, periodically re-orient, shrink and grow within each turn of the pipe. The resultant complex streamlines span the entire cross-section and enhances mixing via advective means. By constraining the total pipe length, a meaningful comparison of mixing efficiency within a given volume of pipe can be assessed as the torus’s cross-section radius and the number of helix turns are systematically varied. Reynolds number of up to 400 is explored with the number of turns of 3, 5, 7 and 8. The optimization study shows that the best mixing performance is achieved using a moderate number of turns. Apart from flow pattern and mixing efficiency, we also studied the pressure drop to monitor increased energy consumption and residence time distribution of the flow to monitor degree of mixing.

Flow patterns and red blood cell dynamics in a U-bend

The flow of cells in curved vessels is often accompanied by a secondary flow, which plays an important and practical role in various biomedical and bioengineering applications. However, there have been few attempts to investigate how the cells affect the development of the secondary flow in those curved microvessels. In this work, we use a particle-based model, smoothed dissipative particle dynamics, to numerically simulate the flow of red blood cells (RBCs) in a U-bend, with a diameter comparable to the RBC diameter. We first carry out three validation studies on the flow field, the cell deformation, and the cell aggregation, respectively, to establish the model predictive capability. Then, we study the formation and development of the secondary flow in a U-bend for the suspending (Newtonian) fluid, followed by exploring the disturbance of a single RBC and multiple RBCs to the secondary flow. The simulation results show that a secondary flow is developed in the U-bend for the suspending fluid, with a pair of Dean vortices. When a single RBC is suspended in the fluid, the secondary flow is disturbed, which is implemented by a transition from two to four and then back to two vortices again. This is the first time to show that cells can initiate such transition in a curved bend. When multiple RBCs are suspended in the fluid, the secondary flow becomes less likely to occur as the RBC number increases. On the contrary, the flow becomes more developed with increasing intercellular interactions.

Effects of nanoparticle shapes on laminar forced convective heat transfer in curved ducts using two-phase model

In this study, effects of particle shape on Al2O3-water nanofluids laminar forced convection in developing and fully developed regions of a curved square duct were investigated numerically using Eulerian-Lagrangian two-phase approach. In order to improve the accuracy of the two-phase model for laminar convective heat transfer of nanofluids containing non-spherical nanoparticles, two new nanoparticle shape descriptors, flatness and elongation, were introduced. Compared with base fluid (water), nanofluids containing platelet shaped nanoparticles has the highest heat transfer enhancement, which is followed by nanofluids containing nanoparticles with cylinder, blade, sphere and brick shapes, respectively. Non-spherical nanoparticles with a suitable shape, small size and relatively high volume fraction are beneficial for enhancement of heat transfer in laminar forced convection. In developing region, a pair of Dean vortices formed and grew along the duct axis, which affected nanoparticle concentration distribution and heat and mass transfer. In fully developed region, convective heat transfer efficiencies of nanofluids are larger than 1 and vary with nanoparticle shape, size, volume fraction and Reynolds number. Enhancement of the convective heat transfer in nanofluids was attributed to the enhancement of effective thermal conductivity and effective viscosity, change of flow structure and reduction of thermal boundary layer thickness due to the presence of nanoparticles and their shapes. New correlations of Nusselt number and fraction factor with nanoparticle shape (sphericity, flatness and elongation), size and volume fraction were developed in order to predict convective heat transfer of nanofluids containing spherical and non-spherical nanoparticles.

Red blood cell motion and deformation in a curved microvessel

The flow of cells through curved vessels is often encountered in various biomedical and bioengineering applications, such as red blood cells (RBCs) passing through the curved arteries in circulation, and cells sorting through a shear-induced migration in a curved channels. Most of past numerical studies focused on the cell deformation in small straight microvessels, or on the flow pattern in large curved vessels without considering the cell deformation. However, there have been few attempts to study the cell deformation and the associated flow pattern in a curved microvessel. In this work, a particle-based method, smoothed dissipative particle dynamics (SDPD), is used to simulate the motion and deformation of a RBC in a curved microvessel of diameter comparable to the RBC diameter. The emphasis is on the effects of the curvature, the type and the size of the curved microvessel on the RBC deformation and the flow pattern. The simulation results show that a small curved shape of the microvessel has negligible effect on the RBC behavior and the flow pattern which are similar to those in a straight microvessel. When the microvessel is high in curvature, the secondary flow comes into being with a pair of Dean vortices, and the velocity profile of the primary flow is skewed toward the inner wall of the microvessel. The RBC also loses the axisymmetric deformation, and it is stretched first and then shrinks when passing through the curved part of the microvessel with the large curvature. It is also found that a pair of Dean vortices arise only under the condition of De>1 (De is the Dean number, a ratio of centrifugal to viscous competition). The Dean vortices are more easily observed in the larger or more curved microvessels. Finally, it is observed that the velocity profile of primary flow is skewed toward the inner wall of curved microvessel, i.e., the fluid close to the inner wall flows faster than that close to the outer wall. This is contrary to the common sense in large curved vessels. This velocity skewness was found to depend on the curvature of the microvessel, as well as the viscous and inertial forces.

Density-induced asymmetric pair of Dean vortices and its effects on mass transfer in a curved microchannel with two-layer laminar stream

To better understand the mass transfer and provide possible performance improvement methods for the microfluidic devices relying on the two-layer laminar flow, a computational fluid dynamics simulation is performed to investigate the phenomenon of a two-layer laminar stream passing through a curved microchannel. The results show that due to the density difference between the two fluids, asymmetric pair of Dean vortices are formed as the fluids pass through the curve. Due to the inter-stream convection, the denser fluid intrudes into the less-dense one resulting in a Γ sharp layer-interface. Furthermore, the parametric analysis helps identify ways to minimize the inter-stream mass transfer, such as increasing the density ratio, as well as reducing the Re number and aspect ratio. The study concludes that the microchannel curve can be properly designed to obtain a clear interface between two streams to fulfill the basic requirement of microfluidic devices.

Detailed measurement of heat/mass transfer and pressure drop in a rotating two-pass duct with transverse ribs

The present study investigates the convective heat/mass transfer and pressure drop characteristics in a rotating two-pass duct with and without transverse ribs. The Reynolds number based on the hydraulic diameter is kept constant at 10,000 and the rotation number is varied from 0.0 to 0.2. When rib turbulators are installed, heat/mass transfer and friction loss are respectively augmented 2.5 times and 5.8 times higher than those of the smooth duct since the main flow is turbulated by reattaching and separating on the vicinity of the duct surfaces. Differences of heat/mass transfer and pressure coefficient between leading and trailing surfaces result from the rotation of duct, so that Sherwood number ratios and pressure coefficients are high on the trailing surface in the first-pass and on the leading surface in the second-pass. In the turning region, a pair of Dean vortices shown in the stationary case transform into one large asymmetric vortex cell, and subsequently heat/mass transfer and pressure drop characteristics also change. As the rotation number increases, the discrepancies of the heat/mass transfer and the pressure coefficient enlarge between the leading and trailing surfaces.

Laminar Flow and Heat Transfer in a Periodic Serpentine Channel

AbstractThe fully developed laminar flow and heat transfer behavior in periodic serpentine circular‐section channels has been studied using computational fluid dynamics (CFD). The serpentine elements are characterised by their wavelength (2 L), channel diameter (d), and radius of curvature of bends (Rc) and results are reported for (3 < L/d < 12.5, 0.525 < Rc/d < 2.25) and Reynolds numbers up to 200. The flow is characterised by the formation of a single pair of Dean vortices after each bend, these being stronger if the bend is in the same direction as the previous bend. The vortices decay downstream of the bends, but, as the Reynolds number is increased, the flow space is increasingly dominated by these vortices. At higher values of Reynolds number (corresponding to a Dean number of about 150), a second pair of vortices develops. For Re > ∼ 200, the flow becomes unsteady. Constant wall heat flux (H2) and constant wall temperature (T) boundary conditions have been examined for a range of fluid Prandtl number (0.7 < Pr < 100). The formation of Dean vortices produces significant heat transfer enhancement relative to flow in a straight pipe, with the effect being greater at higher values of Pr. Pressure drop is also increased but to a lesser extent. The alignment of the flow with the vorticity in these structures allows significant mixing of the fluid without creating large pressure‐drop penalties. Dean vortices are also found to inhibit flow separation. These results suggest an effective method for enhancement of heat transfer in deep laminar flows.

Experimental Surface Heat Transfer and Flow Structure in a Curved Channel With Laminar, Transitional, and Turbulent Flows

Heat transfer and flow structure are described in a channel with a straight portion followed by a portion with mild curvature at Dean numbers from 100 to 1084. The channel aspect ratio is 40, radius ratio is 0.979, and the ratio of shear layer thickness to channel inner radius is 0.011. The data presented include flow visualizations, and spanwise-averaged Nusselt numbers. Also included are time-averaged turbulence structural data, time-averaged profiles of streamwise velocity, spectra of longitudinal velocity fluctuations, and a survey of the radial time-averaged vorticity component. Different flow events are observed including laminar two-dimensional flow, Dean vortex flow, wavy Dean vortex flow (in both undulating and twisting modes), splitting and merging of Dean vortex pairs, transitional flow with arrays of Dean vortex pairs, and fully turbulent flow with arrays of Dean vortex pairs. Transitional events generally first appear in the curved portion of the channel at Dean numbers less than 350 in the form of arrays of counterrotating Dean vortex pairs. At Dean numbers greater than 350, transitional events occur in the upstream straight portion of the channel but then continue to cause important variations in the downstream curved portion. The resulting Nusselt number variations with curvature, streamwise development, and Dean number are described as they are affected by these different laminar, transitional, and turbulent flow phenomena.

Comparison of Heat Transfer Augmentation Techniques

Dr. Phil Ligrani is currently of Mechanical Engineering and Director of the Convective Heat Transfer Laboratory at the University of Utah and a Fellow of the American Society of Mechanical Engineers. He has beenworking on convection heat transfer and fluid mechanics research problems since he received his Ph.D. degree from the Department of Mechanical Engineering at Stanford University in 1980. From 1979 to 1982, he was an Assistant in the Turbomachinery Department of the von Karman Institute for Fluid Dynamics, Rhode-Saint-Genese, Belgium. From 1982 to 1984, he worked in the Department of Aeronautics of the Imperial College of Science and Technology, University of London. From 1984 to 1992, he was an Associate in the Department of Mechanical Engineering of the U.S. Naval Postgraduate School. In his research, he has investigated the ultra-small-scale motions that exist near walls in turbulent boundary layers, the effects of surface roughness on turbulent boundary layers, transitional phenomena in curved channels including the development and structure of Dean vortex pairs, and innovative schemes for internal cooling and surface heat transfer augmentation, such as dimpled surfaces and swirl chambers, as well as a variety of gas turbine heat transfer and blade cooling problems. He served as Guest Editor for the journal Measurement Science and Technology from 1998 to 2000, and he will serve as Associate Technical Editor for the Journal of Heat Transfer from 2003 to 2006. He has published approximately 150 journal papers, conference papers, and book chapters. In 1995, he was presented with the Professor of the Year award at the University of Utah for outstanding classroom teaching. Some of his other activities and recognitions include a Guest Professorship in 2000 at the Institut fur Thermische Stroemungs-maschinen-Universitaet Karlsruhe, a Visiting Senior Research Fellowship from 1982 to 1983 at the Imperial College of Science and Technology-University of London, a NASA Space Act Tech Brief Award in 1991 for Development of Subminiature Multi-Sensor Hot-Wire Probes, and the Carl E. and Jessie W. Menneken Faculty Award in 1990 for Excellence in Scientific Research. E-mail: ligrani@mech.utah.edu.

Effects of Dean vortex pairs on surface heat transfer in curved channel flow

Heat transfer in transitional curved channel flow is investigated over a range of Dean numbers less than 300. The channel aspect ratio is 40, radius ratio is 0.979 and the ratio of boundary layer thickness to channel width is 0.011. Forced convection Nusselt numbers show the influences of Dean vortex pairs and other transitional phenomena. In particular, Nusselt numbers on the concave surface become higher than ones measured at the same streamwise location on the convex surface just after the start of curvature. Important Nusselt number increases also occur due to the twisting secondary instability as the Dean number increases from 150 to 200.

Splitting, merging and spanwise wavenumber selection of Dean vortex pairs

Splitting, merging and spanwise wavenumber selection are studied during the initial development of Dean vortex pairs in a channel with mild curvature, an aspect ratio of 40, and an inner to outer radius ratio of 0.979. Two types of splitting events, and four types of merging events are evident from flow visualizations at Dean numbers from 75 to 220. These events are described in detail along with observations that occurrances of these different events are tied to spatial and temporal variations of spanwise wavenumbers of vortex pair spacing. Also discussed are frequency spectra of different events, recurrent phenomena, and the part played by splitting and merging in laminar to turbulent transition in curved channels.

Flow Characteristics and Centrifugal Instability in a Curved Square Duct.

A numerical study is made to investigate fully developed laminar flow characteristics in a curved square duct of finite curvature ratio. It is shown that, above critical Dean numbers, a pair of Dean vortices due to centrifugal instability appears near the center of the outside wall in addition to the secondary flow vortices. A stability diagram is given in the domain of Dean number and curvature ratio. On the basis of a similarity consideration, we propose new nondimensional expressions of flow characteristics that represent a whole range of parameters inclusively. Two friction factors are proved to be different for small curvature ratio, and a correlation is developed.

Flow Visualization Studies on Secondary Flow Patterns in Straight Tubes Downstream of a 180 deg Bend and in Isothermally Heated Horizontal Tubes

Photographs are presented for secondary flow patterns in a straight tube (x/d = 0 ∼ 70) downstream of a 180 deg bend (tube inside diameter d = 2.54 cm, radius of curvature Rc = 12.7 cm) and in an isothermally heated horizontal tube (tube inside diameter d = 2.54 cm, heated length l = 46.2 cm) with free convection effects. Each test section is preceded by a long entrance length with air as the flowing fluid. For curved pipes, the Dean number range is K = 99 to 384. At the exit of the 180 deg bend, the onset of centrifugal instability in the form of an additional pair of Dean vortices near the central outer wall occurs at a Dean number of about K = 100. The developing secondary flow patterns in the thermal entrance region of an isothermally heated horizontal tube are shown for the dimensionless axial distance z = 0.8 × 10−2 to 1.83 (Re = 3134 ∼ 14) for a range of constant wall temperatures Tw = 55 ∼ 65° C with entrance air temperature at about 25° C. The secondary flow patterns shown are useful for future comparisons with predictions from numerical solutions.

Steady flow development past valve prostheses in a model human aorta—I. Centrally occluding valves

In this paper, laser-Doppler anemometry measurement of steady flow development in a model human aorta has been reported. Studies were made with uniform entry flow at the root of the aorta and our measurements showed the establishment of a pair of Dean vortices in the mid-arch region. Subsequently, the nature of flow development past centrally occluding caged ball valves in the model aorta was investigated. Our studies showed that in the ascending aorta, an asymmetric velocity profile is obtained with larger velocity gradients towards the inner wall of tertiary curvature (anatomically the left lateral wall) with centrally occluding valves. The peripheral flow past these valves prevented the development of Dean vortices in the mid-arch region. The caged ball valves at the root of the aorta had no discernible effect on the velocity profiles in the brachio-cephalic artery.