Showing papers on "Pipe flow published in 2003"

Traveling waves in pipe flow

Abstract: A family of three-dimensional traveling waves for flow through a pipe of circular cross section is identified. The traveling waves are dominated by pairs of downstream vortices and streaks. They originate in saddle-node bifurcations at Reynolds numbers as low as 1250. All states are immediately unstable. Their dynamical significance is that they provide a skeleton for the formation of a chaotic saddle that can explain the intermittent transition to turbulence and the sensitive dependence on initial conditions in this shear flow.

Direct numerical simulations of turbulent channel flow with transverse square bars on one wall

Abstract: Direct numerical simulations have been carried out for a fully developed turbulent channel flow with a smooth upper wall and a lower wall consisting of square bars separated by a rectangular cavity. A wide range of of the Clauser roughness function reflects that of the form drag.

Turbulent channel flow near maximum drag reduction: simulations, experiments and mechanisms

Abstract: It is well known that the drag in a turbulent flow of a polymer solution is significantly reduced compared to Newtonian flow. Here we consider this phenomenon by means of a direct numerical simulation of a turbulent channel flow. The polymers are modelled as elastic dumbbells using the FENE-P model. In the computations the polymer model is solved simultaneously with the flow equations, i.e. the polymers are deformed by the flow and in their turn influence the flow structures by exerting a polymer stress. We have studied the results of varying the polymer parameters, such as the maximum extension, the elasticity and the concentration. For the case of highly extensible polymers the results of our simulations are very close to the maximum drag reduction or Virk (1975) asymptote. Our simulation results show that at approximately maximum drag reduction the slope of the mean velocity profile is increased compared to the standard logarithmic profile in turbulent wall flows. For the r.m.s. of the streamwise velocity fluctuations we find initially an increase in magnitude which near maximum drag reduction changes to a decrease. For the velocity fluctuations in the spanwise and wall-normal directions we find a continuous decrease as a function of drag reduction. The Reynolds shear stress is strongly reduced, especially near the wall, and this is compensated by a polymer stress, which at maximum drag reduction amounts to about 40% of the total stress. These results have been compared with LDV experiments of Ptasinski et al. (2001) and the agreement, both qualitatively and quantitatively, is in most cases very good. In addition we have performed an analysis of the turbulent kinetic energy budgets. The main result is a reduction of energy transfer from the streamwise direction, where the production of turbulent kinetic energy takes place, to the other directions. A substantial part of the energy production by the mean flow is transferred directly into elastic energy of the polymers. The turbulent velocity fluctuations also contribute energy to the polymers. The elastic energy of the polymers is subsequently dissipated by polymer relaxation. We have also computed the various contributions to the pressure fluctuations and identified how these change as a function of drag reduction. Finally, we discuss some cross-correlations and various length scales. These simulation results are explained here by two mechanisms. First, as suggested by Lumley (1969) the polymers damp the cross-stream or wall-normal velocity fluctuations and suppress the bursting in the buffer layer. Secondly, the ‘shear sheltering’ mechanism acts to amplify the streamwise fluctuations in the thickened buffer layer, while reducing and decoupling the motions within and above this layer. The expression for the substantial reduction in the wall drag derived by considering the long time scales of the nonlinear fluctuations of this damped shear layer, is shown to be consistent with the experimental data of Virk et al. (1967) and Virk (1975).

Drag reduction by polymer additives in a turbulent channel flow

Abstract: Turbulent drag reduction by polymer additives in a channel is investigated using direct numerical simulation. The dilute polymer solution is expressed with an Oldroyd-B model that shows a linear elastic behaviour. Simulations are carried out by changing the Weissenberg number at the Reynolds numbers of 4000 and 20 000 based on the bulk velocity and channel height. The onset criterion for drag reduction predicted in the present study shows a good agreement with previous theoretical and experimental studies. In addition, the flow statistics such as the r.m.s. velocity fluctuations are also in good agreement with previous experimental observations. The onset mechanism of drag reduction is interpreted based on elastic theory, which is one of the most plausible hypotheses suggested in the past. The transport equations for the kinetic and elastic energy are derived for the first time. It is observed that the polymer stores the elastic energy from the flow very near the wall and then releases it there when the relaxation time is short, showing no drag reduction. However, when the relaxation time is long enough, the elastic energy stored in the very near-wall region is transported to and released in the buffer and log layers, showing a significant amount of drag reduction.

Unified model for gas-liquid pipe flow via slug dynamics: Part 1: Model development

Abstract: A unified hydrodynamic model is developed for predictions of flow pattern transitions, pressure gradient, liquid holdup and slug characteristics in gas-liquid pipe flow at all inclination angles from -90° to 90° from horizontal. The model is based on the dynamics of slug flow, which shares transition boundaries with all the other flow patterns. By use of the entire film zone as the control volume, the momentum exchange between the slug body and the film zone is introduced into the momentum equations for slug flow. The equations of slug flow are used not only to calculate the slug characteristics, but also to predict transitions from slug flow to other flow patterns. Significant effort has been made to eliminate discontinuities among the closure relationships through careful selection and generalization. The flow pattern classification is also simplified according to the hydrodynamic characteristics of two-phase flow.

Capillary driven flow in circular cylindrical tubes

Abstract: Capillary-driven flow of a perfectly wetting liquid into circular cylindrical tubes is studied. Based on an analysis of previous approaches, a comprehensive theoretical model is presented which is not limited to certain special cases. This model considers the meniscus reorientation, the dynamic contact angle as well as inertia, convective, and viscous losses inside the tube and the reservoir. The capillary-driven flow is divided into three successive phases where first inertia then convective losses and finally viscous forces counteract the driving capillary force. This leads to an initial meniscus height increase proportional to the square of time followed by a linear dependence and finally the Lucas–Washburn behavior where the meniscus height is proportional to the square root of time. The three phases are separated by two characteristic transition times which are determined by the Ohnesorge number and the inertia of the liquid. Experiments were carried out under microgravity condition in a carefully chosen range of Ohnesorge numbers and initial liquid heights to cover the complete process from the initial meniscus development to the final Lucas–Washburn behavior. Good agreement of experimental and theoretical data is found throughout the complete range of experiment parameters. The existence of all three flow regimes predicted by the theory is verified by the experiments.

Simulation of the development of karst aquifers using a coupled continuum pipe flow model

Abstract: [1] This paper is intended to provide insight into the controlling mechanisms of karst genesis based on an advanced modeling approach covering the characteristic hydraulics in karst systems, the dissolution kinetics, and the associated temporal decrease in flow resistance Karst water hydraulics is strongly governed by the interaction between a highly conductive low storage conduit network and a low-conductive high-storage rock matrix under variable boundary conditions Only if this coupling of flow mechanisms is considered can an appropriate representation of other relevant processes be achieved, eg, carbonate dissolution, transport of dissolved solids, and limited groundwater recharge Here a parameter study performed with the numerical model Carbonate Aquifer Void Evolution (CAVE) is presented, which allows the simulation of the genesis of karst aquifers during geologic time periods CAVE integrates several important features relevant for different scenarios of karst evolution: (1) the complex hydraulic interplay between flow in the karst conduits and in the small fissures of the rock matrix, (2) laminar as well as turbulent flow conditions, (3) time-dependent and nonuniform recharge to both flow systems, (4) the widening of the conduits accounting for appropriate physicochemical relationships governing calcite dissolution kinetics This is achieved by predefining an initial network of karst conduits (“protoconduits”) which are allowed to grow according to the amount of aggressive water available due to hydraulic boundary conditions The increase in conduit transmissivity is associated with an increase in conduit diameters while the conductivity of the fissured system is assumed to be constant in time The importance of various parameters controlling karst genesis is demonstrated in a parameter study covering the recharge distribution, the upgradient boundary conditions for the conduit system, and the hydraulic coupling between the conduit network and the rock matrix In particular, it is shown that conduit diameters increase in downgradient or upgradient direction depending on the spatial distribution (local versus uniform) of the recharge component which directly enters the conduit system

Transition to turbulence in particulate pipe flow.

Abstract: We investigate experimentally the influence of suspended particles on the transition to turbulence. The particles are monodisperse and neutrally buoyant with the liquid. The role of the particles on the transition depends upon both the pipe to particle diameter ratios and the concentration. For large pipe-to-particle diameter ratios the transition is delayed while it is lowered for small ratios. A scaling is proposed to collapse the departure from the critical Reynolds number for pure fluid as a function of concentration into a single master curve.

Sensitive dependence on initial conditions in transition to turbulence in pipe flow

Abstract: The experiments by Darbyshire and Mullin (J. Fluid Mech. 289, 83 (1995)) on the transition to turbulence in pipe flow show that there is no sharp border between initial conditions that trigger turbulence and those that do not. We here relate this behaviour to the possibility that the transition to turbulence is connected with the formation of a chaotic saddle in the phase space of the system. We quantify a sensitive dependence on initial conditions and find in a statistical analysis that in the transition region the distribution of turbulent lifetimes follows an exponential law. The characteristic mean lifetime of the distribution increases rapidly with Reynolds number and becomes inaccessibly large for Reynolds numbers exceeding about 2200. Suitable experiments to further probe this concept are proposed.

A periodic-like solution in channel flow

Abstract: We search channel flow for unsteady solutions for different Reynolds numbers and configurations by extending a shooting method which was previously used to obtain a travelling-wave solution. A general initial condition is considered. A periodic-like solution to the incompressible Navier–Stokes equations in a minimal flow unit is found. One cycle of the solution consists of two typical intervals: a single-streak period and a double-streak period. The solution seems to be periodic; however, it cannot be distinguished from a heteroclinic cycle which consists of two heteroclinic orbits connecting two single-streak solutions, because the solution is tracked only for one and half periods.

Numerical study of pulsatile flow in a constricted channel

Abstract: Pulsatile flow in a planar channel with a one-sided semicircular constriction has been simulated using direct numerical simulation and large-eddy simulation. This configuration is intended as a simple model for studying blood flow in a constricted artery. Simulations have been carried out over a range of Reynolds numbers (based on channel height and peak bulk velocity) from 750 to 2000 and a fixed non-dimensional pulsation frequency of 0.024. The results indicate that despite the simplicity of the chosen geometry, the simulated flow exhibits a number of features that have been observed in previous experiments carried out in more realistic configurations. It is found that over the entire Reynolds number range studied here, the flow downstream of the constriction is dominated by the complex dynamics associated with two shear-layers, one of which separates from the lip of the constriction and other from the opposite wall. Computed statistics indicate that for Reynolds numbers higher than about 1000, the flow transitions to turbulence downstream of the region where the separated shear layers first reattach to the channel walls. Large fluctuations in wall pressure and shear stress have also been associated with this reattachment phenomenon. Frequency spectra corresponding to velocity and pressure fluctuations have been analysed in detail and these indicate the presence of a characteristic shear-layer frequency which increases monotonically with Reynolds number. For Reynolds numbers greater than 1000, this frequency is found to be associated with the periodic formation of vortex structures in the shear-layers and the impact of this characteristic shear-layer frequency on the dynamics of the flow is described in detail.

Low-Reynolds-Number Turbulent Flows in Locally Constricted Conduits: A Comparison Study

Abstract: In numerous internal flow systems the velocity field can undergo all flow regimes, that is, from laminar, via transitional, to fully turbulent. Considering two test conduits with local constrictions, four turbulence models, with an emphasis on low-Reynolds-number (LRN) turbulence models, were compared and evaluated. The objective was to identify a readily available LRN turbulence model with which incompressible laminar-to-turbulent velocity and pressure fields in complex three-dimensional conduits can be directly computed. The comparison study revealed that the renormalization group (RNG) κ-e and Menter κ-ω models amplify the flow instabilities after tubular constrictions and hence fail to capture the laminar flow behavior at low Reynolds numbers

4D Magnetic resonance velocimetry for mean velocity measurements in complex turbulent flows

Abstract: An adaptation of a medical magnetic resonance imaging system to the noninvasive measurement of three-component mean velocity fields in complex turbulent engineering flows is described. The aim of this paper is to evaluate the capabilities of the technique with respect to its accuracy, time efficiency and applicability as a design tool for complex turbulent internal geometries. The technique, called 4D magnetic resonance velocimetry (4D-MRV), is used to measure the mean flow in fully developed low-Reynolds number turbulent pipe flow, Re=6400 based on bulk mean velocity and diameter, and in a model of a gas turbine blade internal cooling geometry with four serpentine passages, Re=10,000 and 15,000 based on bulk mean velocity and hydraulic diameter. 4D-MRV is capable of completing full-field measurements in three-dimensional volumes with sizes on the order of the magnet bore diameter in less than one hour. Such measurements can include over 2 million independent mean velocity vectors. Velocities measured in round pipe flow agreed with previous experimental results to within 10%. In the turbulent cooling passage flow, the average flow rates calculated from the 4D-MRV velocity profiles agreed with ultrasonic flowmeter measurements to within 7%. The measurements lend excellent qualitative insight into flow structures even in the highly complex 180° bends. Accurate quantitative measurements were obtained throughout the Re=10,000 flow and in the Re=15,000 flow except in the most complex regions, areas just downstream of high-speed bends, where velocities and velocity fluctuations exceeded MRV capabilities for the chosen set of scan parameters. General guidelines for choosing scanning parameters and suggestions for future development are presented.

Modeling of karst aquifer genesis: Influence of exchange flow

Abstract: [1] This paper presents a numerical model study simulating the early karstification of a single conduit embedded in a fissured system. A hybrid continuum-discrete pipe flow model (CAVE) is used for the modeling. The effects of coupling of the two flow systems on type and duration of early karstification are studied for different boundary conditions. Assuming fixed head boundaries at both ends of the conduit, coupling of the two flow systems via exchange flow between the conduit and the fissured system leads to an enhanced evolution of the conduit. This effect is valid over a wide range of initial conduit diameters, and karstification is accelerated by a factor of about 100 as compared to the case of no exchange flow. Parameter studies reveal the influence of the exchange coefficient and of the hydraulic conductivity of the fissured system on the development time for the conduit. In a second scenario the upstream fixed head boundary is switched to a fixed flow boundary at a specified flow rate during the evolution, limiting the amount of water draining toward the evolving conduit. Depending on the flow rate specified, conduit evolution may be slowed down or greatly impaired if exchange flow is considered.

Heat rejection limits of air cooled plane fin heat sinks for computer cooling

Abstract: Current desktop computers typically use fan-heat sinks for cooling the CPU, referred to as active heat sinks. This work seeks to determine the heat rejection limits for such fan-heat sinks, within specific fan and heat sink space limits. A fixed volume, 80 /spl times/ 60 /spl times/ 50 mm is chosen as the limiting dimensions, which includes the fan volume. The present work addresses plane fin heat sinks, on which a typical 60 mm fan is mounted. Both duct flow and impinging flow are considered. Analytically based models are used to predict the optimum geometry (minimum convection resistance) for plane fins with duct and impinging flow configurations. Also assessed are the effects of increased fan speed (up to 25%) and heat sink base size (33% increase) on air-cooling limits in duct and impinging flow. Tests on fan-heat sinks are done to validate the predictions. Optimization is also done for an enhanced (offset-strip) fin geometry in duct flow. The plane fin is found to outperform the enhanced geometry.

Non-Newtonian flow instability in a channel with a sudden expansion

Abstract: The paper presents a numerical investigation of instabilities occurring in non-Newtonian flows through a sudden expansion. Three non-Newtonian models, used in the literature for simulating the rheological behaviour of blood, are employed, namely the Casson, Power-Law, and Quemada models. The computations reveal that similar to Newtonian flow through a suddenly expanded channel, an instability also occurs in non-Newtonian flows. The instability is manifested by a symmetry breaking of the flow separation. The onset of the instability depends on the specific parameters involved in each model’s constitutive equation. The investigation encompasses a parametric study for each model, specifically the critical values at which transition from stable to unstable flow occurs. Due to the fact that for each of the Casson and Quemada models, two characteristic flow parameters exist, the relation between the critical values for each of these parameters is also examined.

Maximum drag reduction in a turbulent channel flow by polymer additives

Abstract: Maximum drag reduction (MDR) in a turbulent channel flow by polymer additives is studied using direct numerical simulation. An Oldroyd-B model is adopted to express the polymer stress because MDR is closely related to the elasticity of the polymer solution. The Reynolds number considered is 4000, based on the bulk velocity and the channel height, and the amount of MDR from the present study is 44%, which is in good agreement with Virk's asymptote at this Reynolds number. For ‘large drag reduction’, the variations of turbulence statistics such as the mean streamwise velocity and r.m.s. velocity fluctuations are quite different from those of ‘small drag reduction’. For example, for small drag reduction, the r.m.s. streamwise velocity fluctuations decrease in the sublayer but increase in the buffer and log layers with increasing Weissenberg number, but they decrease in the whole channel for large drag reduction. As the flow approaches the MDR limit, the significant decrease in the production of turbulent kinetic energy is compensated by the increase in energy transfer from the polymer elastic energy to the turbulent kinetic energy. This is why turbulence inside the channel does not disappear but survives in the MDR state.

Measurements and large eddy simulations of the flows in some curved flumes

Abstract: The curvature of the flow in river bends and in curved flumes leads tosecondary flow normal to the main flow direction. Reynolds averagednumerical simulations, e.g. by k-e models or RSM, fail toreproduce sufficiently the sometimes complicated secondary flow patternobserved. In the computation of the flow in a rotating annular flume both the separation of the flow from the outside wall and the turbulence energyare not reproduced correctly. For the river bend flow the reproduction of asecond counter-rotating secondary flow cell and of shear stresses of thecorrect sign, where they correspond to an observed negative eddy viscosity, proved problematic. Recently executed large eddy simulations gave better results. The computed main flow, but also the secondary flow and theturbulence energy in the rotating annular flume, hardly deviate from themeasurements. For the river bend a good reproduction of the main flow and the secondary flow is obtained, showing the second counter-rotating secondary flow cell and corre...