Showing papers on "Pipe flow published in 2001"

Statistical evidence of hairpin vortex packets in wall turbulence

Abstract: The structure of velocity in the outer region of turbulent channel flow (y+ [gsim ] 100) is examined statistically to determine the average flow field associated with spanwise vortical motions. Particle image velocimetry measurements of the streamwise and wall-normal velocity components are correlated with a vortex marker (swirling strength) in the streamwise–wall-normal plane, and linear stochastic estimation is used to estimate the conditional average of the two-dimensional velocity field associated with a swirling motion. The mean structure consists of a series of swirling motions located along a line inclined at 12°–13° from the wall. The pattern is consistent with the observations of outer-layer wall turbulence in which groups of hairpin vortices occur aligned in the streamwise direction. While the observational evidence for the aforementioned model was based upon both experimental and computational visualization of instantaneous structures, the present results show that, on average, the instantaneous structures occur with sufficient frequency, strength, and order to leave an imprint on the statistics of the flow as well. Results at Reτ = 547 and 1734 are presented.

Biofluid mechanics in flexible tubes

Abstract: ▪ AbstractAlmost all vessels carrying fluids within the body are flexible, and interactions between an internal flow and wall deformation often underlie a vessel's biological function or dysfunction. Such interactions can involve a rich range of fluid-mechanical phenomena, including nonlinear pressure-drop/flow-rate relations, self-excited oscillations of single-phase flow at high Reynolds number and capillary-elastic instabilities of two-phase flow at low Reynolds number. We review recent advances in understanding the fundamental mechanics of flexible-tube flows, and discuss physiological applications spanning the cardiovascular system (involving wave propagation and flow-induced instabilities of blood vessels), the respiratory system (involving phonation, the closure and reopening of liquid-lined airways, and Marangoni flows on flexible surfaces), and elsewhere in the body (involving active peristaltic transport driven by fluid-structure/muscle interactions).

Developments in unsteady pipe flow friction modelling

Abstract: This paper reviews a number of unsteady friction models for transient pipe flow. Two distinct unsteady friction models, the Zielke and the Brunone models, are investigated in detail. The Zielke model, originally developed for transient laminar flow, has been selected to verify its effectiveness for "low Reynolds number" transient turbulent flow. The Brunone model combines local inertia and wall friction unsteadiness. This model is verified using the Vardy's analytically deduced shear decay coefficient C ∗ to predict the Brunone's friction coefficient k rather than use the traditional trial and error method for estimating k. The two unsteady friction models have been incorporated into the method of characteristics water hammer algorithm. Numerical results from the quasi-steady friction model and the Zielke and the Brunone unsteady friction models are compared with results of laboratory measurements for water hammer cases with laminar and low Reynolds number turbulent flows. Conclusions about the range of v...

A comparative study of near-wall turbulence in high and low Reynolds number boundary layers

Abstract: The present study explores the effects of Reynolds number, over three orders of magnitude, in the viscous wall region of a turbulent boundary layer. Complementary experiments were conducted both in the boundary layer wind tunnel at the University of Utah and in the atmospheric surface layer which flows over the salt flats of the Great Salt Lake Desert in western Utah. The Reynolds numbers, based on momentum deficit thickness, of the two flows were Rθ=2×103 and Rθ≈5×106, respectively. High-resolution velocity measurements were obtained from a five-element vertical rake of hot-wires spanning the buffer region. In both the low and high Rθ flows, the length of the hot-wires measured less than 6 viscous units. To facilitate reliable comparisons, both the laboratory and field experiments employed the same instrumentation and procedures. Data indicate that, even in the immediate vicinity of the surface, strong influences from low-frequency motions at high Rθ produce noticeable Reynolds number differences in the ...

Large-scale modes of turbulent channel flow: transport and structure

Abstract: Turbulent flow in a rectangular channel is investigated to determine the scale and pattern of the eddies that contribute most to the total turbulent kinetic energy and the Reynolds shear stress. Instantaneous, two-dimensional particle image velocimeter measurements in the streamwise-wall-normal plane at Reynolds numbers Re h = 5378 and 29 935 are used to form two-point spatial correlation functions, from which the proper orthogonal modes are determined. Large-scale motions – having length scales of the order of the channel width and represented by a small set of low-order eigenmodes – contain a large fraction of the kinetic energy of the streamwise velocity component and a small fraction of the kinetic energy of the wall-normal velocities. Surprisingly, the set of large-scale modes that contains half of the total turbulent kinetic energy in the channel, also contains two-thirds to three-quarters of the total Reynolds shear stress in the outer region. Thus, it is the large-scale motions, rather than the main turbulent motions, that dominate turbulent transport in all parts of the channel except the buffer layer. Samples of the large-scale structures associated with the dominant eigenfunctions are found by projecting individual realizations onto the dominant modes. In the streamwise wall-normal plane their patterns often consist of an inclined region of second quadrant vectors separated from an upstream region of fourth quadrant vectors by a stagnation point/shear layer. The inclined Q4/shear layer/Q2 region of the largest motions extends beyond the centreline of the channel and lies under a region of fluid that rotates about the spanwise direction. This pattern is very similar to the signature of a hairpin vortex. Reynolds number similarity of the large structures is demonstrated, approximately, by comparing the two-dimensional correlation coefficients and the eigenvalues of the different modes at the two Reynolds numbers.

The Dynamics of Bursting Process in Wall Turbulence

Abstract: We have examined bursting processes observed in turbulent channel flow by direct numerical simulation of the incompressible Navier-Stokes equations in a minimal flow unit. A traveling wave solution (TWS) is obtained by a shooting method. The TWS corresponds to a saddle point in a two-dimensional phase space. A low-dimensional dynamics confined to the near-wall region is proposed in terms of the TWS and its manifolds. The characteristics of the coherent structures constituting the TWS are investigated dynamically and statistically in detail. The dynamics well describes an elementary process of intermittent turbulent regeneration in wall turbulence.

The axisymmetric contraction-expansion: the role of extensional rheology on vortex growth dynamics and the enhanced pressure drop

Abstract: The flow of a polystyrene Boger fluid through axisymmetric contraction‐expansions having various contraction ratios (2 8) and varying degrees of re-entrant corner curvatures are studied experimentally over a large range of Deborah numbers. The ideal elastic fluid is dilute, monodisperse and well characterized in both shear and transient uniaxial extension. A large enhanced pressure drop above that of a Newtonian fluid is observed independent of contraction ratio and re-entrant corner curvature. Streak images, laser Doppler velocimetry (LDV) and digital particle image velocimetry (DPIV) are used to investigate the flow kinematics upstream of the contraction plane. LDV is used to measure velocity fluctuation in the mean flow field and to characterize a global elastic flow instability which occurs at large Deborah numbers. For a contraction ratio of D 2, a steady elastic lip vortex is observed while for contraction ratios of 4 8, no lip vortex is observed and a corner vortex is seen. Rounding the re-entrant corner leads to shifts in the onset of the flow transitions at larger Deborah numbers, but does not qualitatively change the overall structure of the flow field. We describe a simple rescaling of the deformation rate which incorporates the effects of lip curvature and allows measurements of vortex size, enhanced pressure drop and critical Deborah number for the onset of elastic instability to be collapsed onto master curves. Transient extensional rheology measurements are utilized to explain the significant differences in vortex growth pathways (i.e. elastic corner vortex versus lip vortex growth) observed between the polystyrene Boger fluids used in this research and polyisobutylene and polyacrylamide Boger fluids used in previous contraction flow experiments. We show that the role of contraction ratio on vortex growth dynamics can be rationalized by considering the dimensionless ratio of the elastic normal stress difference in steady shear flow to those in transient uniaxial extension. It appears that the differences in this normal stress ratio for different fluids at a given Deborah number arise from variations in solvent quality or excluded volume effects. © 2001 Elsevier Science B.V. All rights reserved.

Experiments in Turbulent Pipe Flow with Polymer Additives at Maximum Drag Reduction

Abstract: In this paper we report on (two-component) LDV experiments in a fully developed tur- bulent pipe flow with a drag-reducing polymer (partially hydrolyzed polyacrylamide) dissolved in water. The Reynolds number based on the mean velocity, the pipe diameter and the local viscosity at the wall is approximately 10000. We have used polymer solutions with three different concentrations which have been chosen such that maximum drag reduction occurs. The amount of drag reduction found is 60-70%. Our experimental results are compared with results obtained with water and with a very dilute solution which exhibits only a small amount of drag reduction. We have focused on the observation of turbulence statistics (mean velocities and turbulence intensities) and on the various contributions to the total shear stress. The latter consists of a turbulent, a solvent (viscous) and a polymeric part. The polymers are found to contribute significantly to the total stress. With respect to the mean velocity profile we find a thickening of the buffer layer and an increase in the slope of the logarithmic profile. With respect to the turbulence statistics we find for the streamwise velocity fluctuations an increase of the root mean square at low polymer concentration but a return to values comparable to those for water at higher concentrations. The root mean square of the normal velocity fluctuations shows a strong decrease. Also the Reynolds (turbulent) shear stress and the correlation coefficient between the streamwise and the normal components are drastically reduced over the entire pipe diameter. In all cases the Reynolds stress stays definitely non-zero at maximum drag reduction. The consequence of the drop of the Reynolds stress is a large polymer stress, which can be 60% of the total stress. The kinetic-energy balance of the mean flow shows a large transfer of energy directly to the polymers instead of the route by turbulence. The kinetic energy of the turbulence suggests a possibly negative polymeric dissipation of turbulent energy.

Steady Herschel–Bulkley fluid flow in three-dimensional expansions

Abstract: In this paper we study steady flow of Herschel–Bulkley fluids in a canonical three-dimensional expansion. The fluid behavior was modeled using a regularized continuous constitutive relation, and the flow was obtained numerically using a mixed-Galerkin finite element formulation with a Newton–Raphson iteration procedure coupled to an iterative solver. Results for the topology of the yielded and unyielded regions, and recirculation zones as a function of the Reynolds and Bingham numbers and the power-law exponent, are presented and discussed for a 2:1 and a 4:1 expansion ratio. The results reveal the strong interplay between the Bingham and Reynolds numbers and their influence on the formation and break up of stagnant zones in the corner of the expansion and on the size and location of core regions.

Hydrodynamical similarities between bubble column and bubbly pipe flow

Abstract: The hydrodynamical similarities between the bubbly flow in a bubble column and in a pipe with vertical upward liquid flow are investigated. The system concerns air/water bubbly flow in a vertical cylinder of 14.9 cm inner diameter. Measurements of the radial distribution of the liquid velocity, gas fraction and the bubble velocity and size are performed using laser Doppler anemometry for the liquid velocity and a four-point optical fibre probe for the gas fraction, bubble velocity and size. The averaged gas fraction was 5.2% for the bubble column (with a superficial liquid velocity of zero) and 5.5% for the bubbly pipe flow at a superficial liquid velocity of 0.175 m s−1. From a hydrodynamical point of view, the two modes of operation are very similar. It is found that in many respects the bubbly pipe flow is the superposition of the flow in the bubble column mode and single-phase flow at the same superficial liquid velocity.The radial gas fraction profiles are the same and the velocity profiles differ only by a constant offset: the superficial liquid velocity. This means that the well-known large-scale liquid circulation (in a time-averaged sense) of the bubble column is also present in the bubbly pipe flow. For the turbulence intensities it is found that the bubbly pipe flow is like the superposition of the bubble column and the single-phase flow at the superficial liquid velocity of the pipe flow, the former being at least an order of magnitude higher than the latter. The large vortical structures that have been found in the bubble columns are also present in the bubbly pipe flow case, partly explaining the much higher ‘turbulence’ levels observed.

Propagation of unsteady disturbances in a slowly varying duct with mean swirling flow

Abstract: The propagation of unsteady disturbances in a slowly varying cylindrical duct carrying mean swirling flow is described. A consistent multiple-scales solution for the mean flow and disturbance is derived, and the effect of finite-impedance boundaries on the propagation of disturbances in mean swirling flow is also addressed.Two degrees of mean swirl are considered: first the case when the swirl velocity is of the same order as the axial velocity, which is applicable to turbomachinery flow behind a rotor stage; secondly a small swirl approximation, where the swirl velocity is of the same order as the axial slope of the duct walls, which is relevant to the flow downstream of the stator in a turbofan engine duct.The presence of mean vorticity couples the acoustic and vorticity equations and the associated eigenvalue problem is not self-adjoint as it is for irrotational mean flow. In order to obtain a secularity condition, which determines the amplitude variation along the duct, an adjoint solution for the coupled system of equations is derived. The solution breaks down at a turning point where a mode changes from cut on to cut off. Analysis in this region shows that the amplitude here is governed by a form of Airy's equation, and that the effect of swirl is to introduce a small shift in the location of the turning point. The reflection coefficient at this corrected turning point is shown to be exp (iπ/2).The evolution of axial wavenumbers and cross-sectionally averaged amplitudes along the duct are calculated and comparisons made between the cases of zero mean swirl, small mean swirl and O(1) mean swirl. In a hard-walled duct it is found that small mean swirl only affects the phase of the amplitude, but O(1) mean swirl produces a much larger amplitude variation along the duct compared with a non-swirling mean flow. In a duct with finite-impedance walls, mean swirl has a large damping effect when the modes are co-rotating with the swirl. If the modes are counter-rotating then an upstream-propagating mode can be amplified compared to the no-swirl case, but a downstream-propagating mode remains more damped.

Lift-off of a single particle in Newtonian and viscoelastic fluids by direct numerical simulation

Abstract: In this paper we study the lift-off to equilibrium of a single circular particle in Newtonian and viscoelastic fluids by direct numerical simulation. A particle heavier than the fluid is driven forward on the bottom of a channel by a plane Poiseuille flow. After a certain critical Reynolds number, the particle rises from the wall to an equilibrium height at which the buoyant weight just balances the upward thrust from the hydrodynamic force. The aim of the calculation is the determination of the critical lift-off condition and the evolution of the height, velocity and angular velocity of the particle as a function of the pressure gradient and material and geometric parameters. The critical Reynolds number for lift-off is found to be larger for a heavier particle whereas it is lower for a particle in a viscoelastic fluid. A correlation for the critical shear Reynolds number for lift-off is obtained. The equilibrium height increases with the Reynolds number, the fluid elasticity and the slip angular velocity of the particle. Simulations of single particle lift-off at higher Reynolds numbers in a Newtonian fluid by Choi & Joseph (2001) but reported here show multiple steady states and hysteresis loops. This is shown here to be due to the presence of two turning points of the equilibrium solution.

Pressure-driven laminar flow in tangential microchannels: an elastomeric microfluidic switch.

Abstract: This paper describes laminar fluid flow through a three- dimensional elastomeric microstructure formed by two microfluidic channels, fabricated in layers that contact one another face-to-face (typically at a 90 degrees angle), with the fluid flows in tangential contact. There are two ways to control fluid flow through these tangentially connected microchannels. First, the flow profiles through the crossings are sensitive to the aspect ratio of the channels; the flow can be controlled by applying external pressure and changing this aspect ratio. Second, the flow direction of an individual laminar stream in multiphase laminar flow depends on the lateral position of the stream within the channel; this position can be controlled by injecting additional streams of fluid into the channel. We describe two microfluidic switches based on these two ways for controlling fluid flow through tangential microchannels and present theoretical arguments that explain the observed dependence of the flow profiles on the aspect ratio of the channels.

A numerical comparison between the multiple-scales and finite-element solution for sound propagation in lined flow ducts

Abstract: An explicit, analytical, multiple-scales solution for modal sound transmission through slowly varying ducts with mean flow and acoustic lining is tested against a numerical finite-element solution solving the same potential flow equations. The test geometry taken is representative of a high-bypass turbofan aircraft engine, with typical Mach numbers of 0.5–0.7, circumferential mode numbers m of 10–40, dimensionless wavenumbers of 10–50, and both hard and acoustically treated inlet walls of impedance Z = 2 − i. Of special interest is the presence of the spinner, which incorporates a geometrical complexity which could previously only be handled by fully numerical solutions. The results for predicted power attenuation loss show in general a very good agreement. The results for iso-pressure contour plots compare quite well in the cases where scattering into many higher radial modes can occur easily (high frequency, low angular mode), and again a very good agreement in the other cases.

The second-law analysis of mixed convection in rectangular ducts

Abstract: The rate of entropy generation, S˙′G[W/mK], is examined both theoretically and numerically for forced and mixed convection in a rectangular duct heated at the bottom. Under fully-developed flow conditions S˙′G is expressed in terms of relevant non-dimensional hydrodynamic and thermal parameters. Numerically, it is demonstrated that S˙′G is a single, effective parameter to examine both thermal and hydrodynamic fields and their variations.

Experimental study of chaotic advection regime in a twisted duct flow

Abstract: The generation of Lagrangian chaos has been studied experimentally in a twisted duct flow, a configuration representing a three-dimensional steady open flow in which various signatures of Lagrangian chaos are documented. The twisted duct consists of four 90∘ bends of square cross-section; the plane of curvature of each bend is at 90∘ to that of its neighbors. Dean roll-cells, generated by centrifugal forces and the geometrical perturbation due to the change in curvature plane, are the source of the irregular trajectories of the fluid particles. The Eulerian nature of the flow was investigated using a laser Doppler velocimeter (LDV). From the Eulerian point of view, the flow is completely regular. We show by laser-induced fluorescence (LIF) visualization that many characteristics of a Lagrangian chaotic system are present in this flow: − strong stretching and folding of material lines and surfaces; − sensitivity to initial conditions; − exponential growth of stretching in some flow regions. It is also shown that in some regions of the flow stretchings grow linearly with space, indicating non-chaotic behavior. Due to the chaotic nature of the flow, an equalization of the fly-time of fluid particles was observed during their passage through the twisted duct.