Development of a bluff body wake under the combined influence of curvature and pressure gradient

The present experimental investigation deals with the behaviour of a wake generated by a square cylinder developing in a curved diffuser, a curved duct, a straight duct and a straight diffuser having a same pressure gradient as in the curved diffuser. This enables a systematic study of the effects of curvature and pressure gradient on wake development. It is seen that the curvature makes the wake asymmetric; the wake half width increases on the inner side and decreases on the outer side; the inner side being the region between the centreline and the wall closer to the centre of curvature and the outer side being the region between the centreline and the other wall. It causes a higher entrainment in the inner side as compared to the outer side. An adverse pressure gradient, on the other hand, causes a higher wake growth and velocity defect but reduces the rate of decay of the velocity defect. These are not altered significantly when the curvature and pressure gradient effects are combined. The curvature enhances the Reynolds stresses and the kinetic energy on the inner side and suppresses them on the outer side which makes their profiles asymmetric. These profiles become more and more asymmetric with increase in the streamwise distance. When the effects of curvature and adverse pressure gradient are combined, the profiles become further asymmetric.Department of Aerospace Engineering     

Fluid flow in a helical pipe

Without simplifying the N-S equations of Germano's^[5], we study the flow in a helical circular pipe employing perturbation method. A third perturbation solution is fully presented. The first- second- and third-order effects of curvature κ and torsion τ on the secondary flow and axial velocity are discussed in detail. The first-order effect of curvature is to form two counter-rotating cells of the secondary flow and to push the maximum axial velocity to the outer bend. The two cells are pushed to the outer bend by the pure second-order effect of curvature. The combined higher-order (second-, third-) effects of curvature and torsion, are found to be an enlargement of the lower vortex of the secondary flow at expense of the upper one and a clockwise shift of the centers of the secondary vortices and the location of maximum axial velocity. When the axial pressure gradient is small enough or the torsion is sufficiently larger than the curvature, the location of the maximal axial velocity is near the inner bend. The equation of the volume flux is obtained from integrating the perturbation solutions of axial velocity. From the equation the validity range of the perturbation solutions in this paper can be obtained and the conclusion that the three terms of torsion have no effect on the volume flux can easily be drawn. When the axial pressure gradient is less than 22.67, the volume flux in a helical pipe is larger than that in a straight pipe.     

A numerical investigation of developing flow in an eccentric curved annulus in the presence of gravity

In this article developing incompressible viscous flow in an eccentric curved annulus in the presence of gravity is numerically studied using a second order finite difference method based on the projection algorithm to solve the governing equations including the continuity and full Navier–Stokes equations. The equations written in a bipolar–toroidal coordinate system are discretized in a three dimensional staggered grid. The effects of governing non-dimensional parameters including the eccentricity, non-dimensional curvature ratio, Dean number, Froude number, aspect ratio, and the Reynolds number on the flow field in the entrance and fully developed region are investigated. The numerical results indicate that at the small Froude numbers, the flow field distorts from the symmetrical condition due to the larger body force effect and the axial velocity formation mostly takes place at the lower half of the annulus. In addition, at the constant Froude number, by decreasing the curvature radius, the peak axial velocity and its sharp gradient appear on the outer curvature region due to the larger centrifugal forces and by increasing the eccentricity the flow rate intensifies at the wider region and weakens at the narrower region due to the larger flow resistance. Furthermore, the friction factor increases by decreasing the Froude number and increasing the Dean number.     

Electromagnetohydrodynamic flows and mass transport in curved rectangular microchannels

Curved microchannels are often encountered in lab-on-chip systems because the effective axial channel lengths of such channels are often larger than those of straight microchannels for a given per unit chip length. In this paper, the effective diffusivity of a neutral solute in an oscillating electromagnetohydrodynamic(EMHD)flow through a curved rectangular microchannel is investigated theoretically. The flow is assumed as a creeping flow due to the extremely low Reynolds number in such microflow systems. Through the theoretical analysis, we find that the effective diffusivity primarily depends on five dimensionless parameters, i.e., the curvature ratio of the curved channel, the Schmidt number, the tidal displacement, the angular Reynolds number, and the dimensionless electric field strength parameter. Based on the obtained results, we can precisely control the mass transfer characteristics of the EMHD flow in a curved rectangular microchannel by appropriately altering the corresponding parameter values.     

Method of moments for laminar dispersion in an oscillatory flow through curved channels with absorbing walls

The unsteady dispersion of a solute, when the fluid is driven through a curved channel with absorbing walls by an imposed pulsatile pressure gradient, is studied using the method of moments. The study examines the effect of oscillatory Reynolds number, amplitude/frequency of the pressure pulsation and boundary absorption on the longitudinal dispersion. The methodology involves a set of unsteady integral moment equations obtained by applying the Aris-Barton method of moments on the convective-diffusion equation for a curved channel. Central moments are obtained from the moment equations which are solved by a finite-difference implicit scheme. The effect of curvature and boundary absorption on the effective dispersion coefficient from the initial to the stationary stage of the oscillatory flow is studied. Amplitude of the effective dispersion coefficient is found to increase with curvature and decrease with frequency of the pressure pulsation. For large Peclet number and Schmidt number, the amplitude of the dispersion coefficient can be 1.6 times that in a straight channel at large times. Also, for large times, the amplitude of the dispersion coefficient is twice the amplitude of the dispersion coefficient as α, the frequency parameter changes from 0.5 to 1.0. The axial distributions of mean concentration are determined from the first four central moments by using the Hermite polynomial representation. The effect of curvature is to delay the stationary state and also the approach to normality of the concentration distribution. The study has importance in understanding the spreading of pollutants in tidal basins and natural current fields.     

Turbulence-driven secondary flows in a curved pipe

If the torque exerted on a fluid element and the source of streamwise vorticity generation are analyzed, a turbulence-driven secondary flow is found to be possible in a curved pipe. Based on this analysis, it is found that the secondary flow is primarily induced by high anisotropy of the cross-stream turbulent normal stresses near the outer bend (furthest from the center of curvature of the bend). This secondary flow appears as a counterrotating vortex pair embedded in a Dean-type secondary motion. Recent hot-wire measurements provide some evidence for the existence of this vortex pair. To verify the formation and extent of this turbulence-driven vortex pair further, a near-wall Reynolds-stress model is used to carry out a detailed numerical investigation of a curved-pipe flow. The computation is performed specifically for a U-bend with a full developed turbulent flow at the bend entrance and a long straight pipe attached to the exit. Numerical results reveal that there are three vortex pairs in a curved pipe. The primary one is the Dean-type vortex pair. Another pair exists near the pipe core and is a consequence of local pressure imbalance. A third pair is found near the outer bend and is the turbulence-driven secondary flow. It starts to appear around 60° from the bend entrance, grows to a maximum strength at the bend exit, and disappears altogether at about seven pipe diameters downstream of the bend. On the other hand, calculations of developing laminar curved-pipe flows covering a range of pipe-to-bend curvature ratios, Reynolds number, and different inlet conditions fail to give rise to a third cell near the outer bend. Therefore, experimental and numerical evidence together lend support to the formation of a pair of turbulence-driven secondary cells in curved-pipe flows.Research supported by the Office of Naval Research under Grant No. N0014-81-K-0428 and by the David Taylor Research Center, Annapolis, Maryland, under Contract No. N00167-86-K0075.     

On the energy conversion in electrokinetic transports

Energy conversion in micro/nano-systems is a subject of current research,among which the electrokinetic energy conversion has attracted extensive attention. However, there exist two different definitions on the electrokinetic energy conversion efficiency in literature. A few researchers defined the efficiency using the pure pressure-driven flow rate, while other groups defined the efficiency based on the flow rate with the inclusion of the effect of the streaming potential field. In this work, b...     

Experimental investigation on turbulent flow in a square-sectioned 90-degree bend

The development of steady, turbulent flow in a 90° section of a curved square duct was studied at a Reynolds number of 4 × 10⁴ by hot-wire anemometer. The curved duct has a cross-section measuring 80 × 80 mm and a curvature radius ratio of 4 and is connected with a long, straight duct at its both ends. The longitudinal and lateral components of mean and fluctuating velocities, and the Reynolds stresses were measured by the method of rotating a probe with an inclined hot-wire. The velocity fields of the primary and secondary flows, and the Reynolds stress distributions in the cross-section were illustrated in the form of contour map. The development of the primary flow was found to be connected with a strong pressure gradient near the outer and inner wall and a secondary flow induced in the cross-section of the bend by a pressure difference between the outer and inner wall and a centrifugal force acting on the fluid; the fluid is accelerated near the inner wall and decelerated near the outer wall between the bend angle ϕ ≅ 0° and ϕ ≅ 30°, but an increase and decrease of the fluid velocity are reversed between ϕ ≅ 30° and ϕ ≅ 90°. The fluctuating velocity correlations, i.e. the Reynolds stresses follow a complicated progress according to the complex development of the primary flow. The results obtained can be available to verify various types of turbulence models and to develop new models. Received: 10 May 1999/Accepted: 15 March 2000     

Laser-Doppler measurements of laminar and turbulent flow in a pipe bend

Laser-Doppler measurements are reported for laminar and turbulent flow through a 90° bend of circular cross-section with mean radius of curvature equal to 2.8 times the diameter. The measurements were made in cross-stream planes 0.58 diameters upstream of the bend inlet plane, in 30, 60 and 75° planes in the bend and in planes one and six diameters downstream of the exit plane. Three sets of data were obtained: for laminar flow at Reynolds numbers of 500 and 1093 and for turbulent flow at the maximum obtainable Reynolds number of 43 000. The results show the development of strong pressure-driven secondary flows in the form of a pair of counter-rotating vortices in the streamwise direction. The strength and character of the secondary flows were found to depend on the thickness and nature of the inlet boundary layers, inlet conditions which could not be varied independently of Reynolds number. The quantitative anemometer measurements are supported by flow visualization studies. Refractive index matching at the fluid-wall interface was not used; the measurements consist, therefore, of streamwise components of mean and fluctuating velocities only, supplemented by wall pressure measurements for the turbulent flow. The displacement of the laser measurement volume due to refraction is allowed for in simple geometrical calculations. The results are intenden for use as benchmark data for calibrating flow calculation methods.     

Experimental investigation on turbulent flow through a circular-sectioned 180° bend

The steady, developing turbulent flow in a circular-sectioned 180° bend has been investigated. The bend had a radius of 104 mm and a curvature radius ratio of 4.0 with long, straight upstream and downstream pipes. Measurements of the longitudinal, radial and circumferential components of mean velocity, and corresponding components of the Reynolds stress were obtained with a hot wire anemometer at a Reynolds number of 6×10⁴ and at various longitudinal stations. The velocity fields of the primary and secondary flows and the Reynolds stresses were illustrated in the form of contour map or vector diagram. Moreover, the mean quantities characterizing the bend flow, i.e., the deflection of the primary flow in the cross section, the intensity of the secondary flow and the turbulence energy, were shown in a graphic form against the longitudinal distances. In the section upstream from a bend angle of about 60°, both the flows through the 180° and the 90° bend are closely similar in their behavior. In the section from the bend angle of 90°, the high-velocity regions, however, occur near the upper and lower walls as a result of strong secondary flow and the turbulence with high level emerges in the central region of the bend. Just behind the bend exit, an additional pair of vortices appears in the outer part of the cross section owing to the transverse pressure difference. In the downstream tangent, the flow returns slowly to the proper flow in a straight pipe, but it needs a longer distance for recovery than in the 90° bend. Received: 23 April 1998/Accepted: 24 April 1999     

纳米粒子在方管中传输与沉降的研究

采用有限体积法离散并应用Simple方法对方截面弯曲管道内的纳米粒子传输和沉降进行了数值计算,结果表明Reynolds数和Schmidt数是影响纳米粒子传输和沉降的重要参数。粒子较小时,弯管中轴向速度较大的区域就是粒子的高浓度区域,沉降增强因子最大值出现在外弯侧的中心位置;粒子较大时,截面浓度的梯度值降低,沉降增强因子趋于平均,此时整个截面的粒子平均沉降。弯曲作用对于粒子较大且Dean数也较大时的影响更加明显。     

Determination of separated region in a curved tube

The formation of atherosclerosis in a curved aorta is closely related to the existence of separated vortex region. This paper deals with the steady laminar motion of an incompressible Newtonian fluid through a curved tube with circular cross-section whose curvature is small and whose curvature gradient is not too large. Using the momentum integral method and the approximation of quasi-constant curvature, an equation which determines the location of separation and reattachment is derived. From this equation the earliest point of separation and the corresponding critical Reynolds number are obtained, and the relation between the position of separation and reattachment and Reynolds number R_e for different azimuthal angle are revealed. It is concluded that the separation first emerges at the position whose curvature gradient has the maximum absolute value. With increasing R_e, the separation region extends in the direction of mainstream, azimuthal angle and radius vector, and then forms a three-dimensional separated vortex, which gradually enlarges in all three directions with the increase of Reynolds number. The theoretical results also very clearly demonstrate the following striking experimental fact: if a symmetrical curved tube exhibits a separated vortex at the outside of the upstream, then it must have another one symmetrically placed at the inside of its downstream.     

Evolution of turbulence characteristics from straight to curved pipes

Fully developed, statistically steady turbulent flow in straight and curved pipes at moderate Reynolds numbers is studied in detail using direct numerical simulations (DNS) based on a spectral element discretisation. After the validation of data and setup against existing DNS results, a comparative study of turbulent characteristics at different bulk Reynolds numbers Re_b = 5300 and 11,700, and various curvature parameters κ = 0, 0.01, 0.1 is presented. In particular, complete Reynolds-stress budgets are reported for the first time. Instantaneous visualisations reveal partial relaminarisation along the inner surface of the curved pipe at the highest curvature, whereas developed turbulence is always maintained at the outer side. The mean flow shows asymmetry in the axial velocity profile and distinct Dean vortices as secondary motions. For strong curvature a distinct bulge appears close to the pipe centre, which has previously been observed in laminar and transitional curved pipes at lower Re_b only. On the other hand, mild curvature allows the interesting observation of a friction factor which is lower than in a straight pipe for the same flow rate.All statistical data, including mean profile, fluctuations and the Reynolds-stress budgets, is available for development and validation of turbulence models in curved geometries.     

Modeling low Reynolds number incompressible flows with curved boundaries using SPH

In this paper, a method that can be used to model low Reynolds number incompressible flows with curved boundaries using SPH was presented. In contrast to that usually used for the flows with flat and straight boundaries, the hydrostatic pressure gradient is treated as a variable body force in this method, and thus, it can be applied to simulate the flows with curved boundaries. Three numerical examples of low Reynolds number incompressible flows, including Poiseuille flow, flow in a section of blood vessel with a local expansion, and flow between inclined plates were calculated to test the method. The results obtained with the proposed method were in good agreement with the analytical solutions. It implies that the method presented in this paper can be successfully used to simulate low Reynolds number incompressible flows not only with flat and straight boundaries but also with curved boundaries. Copyright © 2011 John Wiley & Sons, Ltd.     

PRESSURE AND PRESSURE GRADIENT IN AN AXISYMMETRIC RIGID VESSEL WITH STENOSIS

Based on an improvement of the Karman-Pohlhausen's method, using nonlinear polynomial fitting and numerical integral, the axial distributions of pressure and its gradient in an axisymmetric rigid vessel with stenosis were obtained, and the distributions related to Reynolds number and the geometry of stenotic vessel were discussed. It shows that with the increasing of stenotic degree or Reynolds number, the fluctuation of pressure and its gradient in stenotic area is intense rapidly, and negative pressure occurs subsequently in the diverging part of stenotic area. Especially when the axial range of stenosis extends, the flow of blood in the diverging part will be more obviously changed. In higher Reynolds number or heavy stenosis, theoretical calculation is mainly in accordance with nast experiments.     

Prediction of developing turbulent flow in 90°‐curved ducts using linear and non‐linear low‐Re k–ε models

This paper reports the outcome of applying two different low‐Reynolds‐number eddy‐viscosity models to resolve the complex three‐dimensional motion that arises in turbulent flows in ducts with 90^° bends. For the modelling of turbulence, the Launder and Sharma low‐Re k–ε model and a recently produced variant of the cubic non‐linear low‐Re k–ε model have been employed. In this paper, developing turbulent flow through two different 90^° bends is examined: a square bend, and a rectangular bend with an aspect ratio of 6. The numerical results indicate that for the bend of square cross‐section the curvature induces a strong secondary flow, while for the rectangular cross‐section the secondary motion is confined to the corner regions. For both curved ducts, the secondary motion persists downstream of the bend and eventually slowly disappears. For the bend of square cross‐section, comparisons indicate that both turbulence models can produce reasonable predictions. For the bend of rectangular cross‐section, for which a wider range of data is available, while both turbulence models produce satisfactory predictions of the mean flow field, the non‐linear k–ε model returns superior predictions of the turbulence field and also of the pressure and friction coefficients. Copyright © 2006 John Wiley & Sons, Ltd.     

A criterion for detection of the onset of Dean instability in Newtonian fluids

Dean instability for Newtonian fluids in laminar secondary flow in 180° curved channels was studied experimentally and numerically. The numerical study used Fluent CFD code to solve the Navier–Stokes equations, focusing on flow development conditions and the parameters influencing Dean instability. An accurate criterion based on the radial gradient of the axial velocity was defined that allows detection of the instability threshold, and this criterion is used to optimize the grid geometry. The effects on Dean instability of the curvature ratio (from 5.5 to 20) and aspect ratio (from 0.5 to 12) are studied. In particular, we show that the critical value of the Dean number decreases with the increasing duct curvature ratio. The variation of the critical Dean number with duct aspect ratio is less regular.In the experimental study, flows were visualized in several tangential positions of a 180° curved channel with aspect ratio 8 and curvature ratio 10. The flow is hydrodynamically developed at the entrance to the curved channel. The critical Dean number is detected and the development of secondary flow vortices by additional counter-rotating vortex pairs is observed. A diagram of different critical Dean numbers is established.     

Large Eddy Simulations of convergent–divergent channel flows at moderate Reynolds numbers

The paper is focused on the study of fully turbulent channel flows, using Large Eddy Simulations (LES), in order to address the effects of adverse pressure gradient regions. Analyses of the effects of streak instabilities, which have been shown to be relevant in such regions, are extended to moderate Reynolds numbers. The work considers two different channel geometries in order to further separate influences from wall curvature, flow separation and adverse pressure gradients. Turbulent kinetic energy and Reynolds stress budgets are investigated at separation and re-attachment points. The numerical approach used in the present work is based on the incompressible Navier–Stokes equations, which are solved by a pseudo-spectral methodology for structured grids. Wall-resolved LES calculations are performed using the WALE subgrid scale model. The study shows that the streak instability mechanism persists at higher Reynolds numbers with and without wall curvature in the adverse pressure gradient regions. Moreover, the observed effects are also present regardless of the existence of flow separation regions. Finally, the study of turbulent kinetic energy budgets indicates that, independently of the flow condition, there are well-defined patterns for such turbulent properties at separation and re-attachment points.     

A Lattice Boltzmann model with high Reynolds number in the presence of external forces to describe microfluidics

We present here a lattice Boltzmann model with high Reynolds number in the presence of external force fields to describe electrokinetic phenomena in microfluidics, by considering pressure as the only external force for liquid flow. Our results from a 9-bit square lattice Boltzmann model are in excellent agreement with experimental data in pressure-driven microchannel flow that could not be fully described by electrokinetic theory. The difference between the predicted and experimental Reynolds numbers from pressure gradients are well within 5%. Our results suggest that the lattice Boltzmann model described here is an effective computational tool to predict the more complex microfluidic systems that might be problematic using conventional methods.     

环形截面螺旋管道内二次流动特性的研究

从曲线柱坐标系下的N-S方程出发,以曲率和挠率为小参数,采用摄动法求解了环形截面螺旋管道内的黏性流动,给出了完全二阶摄动解,结果表明：当挠率为零时,二次流表现为上下对称的四个涡;当挠率不为零,涡的对称性遭到破坏,二次涡的强度和个数受De数和环形截面内外径之比δ的影响,轴向速度最大值在De数较小时靠近管道的内侧,随着De数的增加,其最大值向外侧移动。