Showing papers on "Pipe flow published in 1997"

A theory of particle deposition in turbulent pipe flow

Abstract: The paper describes a theory of particle deposition based formally on the conservation equations of particle mass and momentum. These equations are formulated in an Eulerian coordinate system and are then Reynolds averaged, a procedure which generates a number of turbulence correlations, two of which are of prime importance. One represents ‘turbulent diffusion’ and the other ‘turbophoresis’, a convective drift of particles down gradients of mean-square fluctuating velocity. Turbophoresis is not a small correction; it dominates the particle dynamic behaviour in the diffusion-impaction and inertia-moderated regimes.Adopting a simple model for the turbophoretic force, the theory is used to calculate deposition from fully developed turbulent pipe flow. Agreement with experimental measurements is good. It is found that the Saffman lift force plays an important role in the inertia-moderated regime but that the effect of gravity on deposition from vertical flows is negligible. The model also predicts an increase in particle concentration close to the wall in the diffusion-impaction regime, a result which is partially corroborated by an independent ‘direct numerical simulation’ study.The new deposition theory represents a considerable advance in physical understanding over previous free-flight theories. It also offers many avenues for future development, particularly in the simultaneous calculation of laminar (pure inertial) and turbulent particle transport in more complex two- and three-dimensional geometries.

Drag reduction by polymer additives in a turbulent pipe flow : numerical and laboratory experiments

Abstract: In order to study the roles of stress anisotropy and of elasticity in the mechanism of drag reduction by polymer additives we investigate a turbulent pipe flow of a dilute polymer solution. The investigation is carried out by means of direct numerical simulation (DNS) and laser Doppler velocimetry (LDV). In our DNS two different models are used to describe the effects of polymers on the flow. The first is a constitutive equation based on Batchelor's theory of elongated particles suspended in a Newtonian solvent which models the viscous anisotropic effects caused by the polymer orientation. The second is an extension of the first model with an elastic component, and can be interpreted as an anisotropic Maxwell model. The LDV experiments have been carried out in a recirculating pipe flow facility in which we have used a solution of water and 20 w.p.p.m. Superfloc A110. Turbulence statistics up to the fourth moment, as well as power spectra of various velocity components, have been measured. The results of the drag-reduced flow are first compared with those of a standard turbulent pipe flow of water at the same friction velocity at a Reynolds number of Reτ≈1035. Next the results of the numerical simulation and of the measurements are compared in order to elucidate the role of polymers in the phenomenon of drag reduction. For the case of the viscous anisotropic polymer model, almost all turbulence statistics and power spectra calculated agree in a qualitative sense with the measurements. The addition of elastic effects, on the other hand, has an adverse effect on the drag reduction, i.e. the viscoelastic polymer model shows less drag reduction than the anisotropic model without elasticity. Moreover, for the case of the viscoelastic model not all turbulence statistics show the right behaviour. On the basis of these results, we propose that the viscous anisotropic stresses introduced by extended polymers play a key role in the mechanism of drag reduction by polymer additives.

The Effects of Prandtl Numbers on Local and Average Convective Heat Transfer Characteristics in Helical Pipes

Abstract: To investigate the effects of the Prandtl number and geometric parameters on the local and average convective heat transfer characteristics in helical pipes, experiments with three different fluids-air, water, and ethylene glycol-were carried out on five uniformly heated helical pipes. The test sections were made from 22.9 mm I.D. and 10.2 mm I.D. 304 stainless steel pipes. The ratios of the pipe diameter and pitch to coil diameter (d/D and b/D) ranged from 0.0267 to 0.0884 and 0.20 to 2.56, respectively. The peripheral and average, fully developed Nusselt numbers were evaluated in the experiments. Experimental findings indicate that after two turns (X > 2) the temperature distributions along the wall are almost parallel to the linear fluid bulk temperatures, and all dimensionless peripheral wall temperatures are nearly identical, implying that both the flow and temperature distribution within the helical pipes are fully developed.

Reynolds number effects in a turbulent pipe flow for low to moderate Re

Abstract: We present in this paper high resolution, two-dimensional LDV measurements in a turbulent pipe flow of water over the Reynolds number range 5000–25000. Results for the turbulence statistics up to the fourth moment are presented, as well as power spectra in the near-wall region. These results clearly show that the turbulence statistics scaled on inner variables are Reynolds-number dependent in the aforementioned range of Reynolds numbers. For example, the constants in the dimensionless logarithmic mean-velocity profile are shown to vary with Reynolds number. Our conclusion that turbulence statistics depend on the Reynolds number is consistent with results found in other flow configurations, e.g., a channel flow. Our results for the pipe flow, however, lead nevertheless to quite different tendencies.

The axisymmetric and plane cases of a gas phase steadily displacing a Newtonian liquid—A simultaneous solution of the governing equations

Abstract: The flow induced by a long bubble steadily displacing a liquid confined by two closely located parallel plates or by a cylindrical tube of small diameter is numerically analyzed. The technique employed solves the complete set of governing equations simultaneously. The present analysis encompasses, and also extends, the whole range of Capillary values previously studied with various numerical techniques. The results shown uncover a type of recirculating flow pattern that appears to have been overlooked before. The effects of the inertial forces on the liquid flow rate are also assessed.

Numerical simulations of laminar flow over a 3D backward‐facing step

Abstract: A numerical investigation of laminar flow over a three-dimensional backward-facing step is presented with comparisons with detailed experimental data, available in the literature, serving to validate the numerical results. The continuity constraint method, implemented via a finite element weak statement, was employed to solve the unsteady three-dimensional Navier–Stokes equations for incompressible laminar isothermal flow. Two-dimensional numerical simulations of this step geometry underestimate the experimentally determined extent of the primary separation region for Reynolds numbers Re greater than 400. It has been postulated that this disagreement between physical and computational experiments is due to the onset of three-dimensional flow near Re ≈ 400. This paper presents a full three-dimensional simulation of the step geometry for 100⩽ Re⩽ 800 and correctly predicts the primary reattachment lengths, thus confirming the influence of three-dimensionality. Previous numerical studies have discussed possible instability modes which could induce a sudden onset of three-dimensional flow at certain critical Reynolds numbers. The current study explores the influence of the sidewall on the development of three-dimensional flow for Re greater than 400. Of particular interest is the characterization of three-dimensional vortices in the primary separation region immediately downstream of the step. The complex interaction of a wall jet, located at the step plane near the sidewall, with the mainstream flow reveals a mechanism for the increasing penetration (with increasing Reynolds number) of three-dimensional flow structures into a region of essentially two-dimensional flow near the midplane of the channel. The character and extent of the sidewall-induced flow are investigated for 100⩽Re⩽ 800. © 1997 John Wiley & Sons, Ltd.

Drop formation in viscous flows at a vertical capillary tube

Abstract: Drop formation at the tip of a vertical, circular capillary tube immersed in a second immiscible fluid is studied numerically for low-Reynolds-number flows using the boundary integral method. The evolution and breakup of the drop fluid is considered to assess the influences of the viscosity ratio λ, the Bond number B, and the capillary number C for 10−2⩽λ⩽10, 10−2⩽C⩽1, and 0.1⩽B⩽5. For very small λ, breakup occurs at shorter times, there is no detectable thread between the detaching drop and the remaining pendant fluid column, and thus no large satellite drops are formed. The distance to detachment increases monotonically with λ and changes substantially for λ>1, but the volume of the primary drop varies only slightly with λ. An additional application of the numerical investigation is to consider the effect of imposing a uniform flow in the ambient fluid [e.g., Oguz and Prosperetti, J. Fluid Mech. 257, 111 (1993)], which is shown to lead to a smaller primary drop volume and a longer detachment length, as ...

Scaling of the mean velocity profile for turbulent pipe flow

Abstract: An experimental investigation was conducted to determine the scaling of the mean velocity profile for a fully developed, smooth pipe flow. Measurements of the mean velocity profiles and static pressure gradients were performed at 26 different Reynolds numbers between $31\ifmmode\times\else\texttimes\fi{}{10}^{3}$ and $35\ifmmode\times\else\texttimes\fi{}{10}^{6}$. The profiles indicate two overlap regions: one which scales as a power law and one which scales as a log law, where the log law is only evident when the Reynolds number exceeds approximately $300\ifmmode\times\else\texttimes\fi{}{10}^{3}$. It is proposed that the velocity scales for the inner and outer regions are different, which is contrary to commonly accepted beliefs.

Compressible Fluid Flow

Abstract: The equations of steady one-dimensional compressible flow some fundamental aspects of compressible flow one-dimensional isentropic flow normal shock waves oblique shock waves expansion waves - Prandtl-Meyer flow variable area flow adiabatic flow with friction flow with heat addition generalized quasi one-dimensional flow numerical analysis of one-dimensional flows aerodynamic heating an introduction to two-dimensional compressible flow hypersonic flow high temperature flows low density flows.

Two Types of Nonlinear Pressure-Drop Versus Flow-Rate Relation Observed for Saturated Porous Media

Abstract: Previous reports of experiments performed with water (Fand et al., and Kececioglu and Jiang) indicated that beyond the Forchheimer regime the rate of change of the hydrostatic pressure gradient along a porous medium suddenly decreases. This abnormal behavior has been termed transition to turbulence in a porous medium. We investigate the relationship between the hydrostatic pressure gradient of a fluid (air) through a porous medium and the average seepage fluid velocity. Our experimental results, reported here, indicate an increase in the hydrostatic pressure rate beyond a certain transition speed, not a decrease. Physical arguments based on a consideration of internal versus extemal incompressible viscous flow are used to justify this distinct behavior, a consequence of the competition between a form dominated transition and a viscous dominated transition. We establish a criterion for the viscous dominated transition from consideration of the results of three porous media with distinct hydraulic characteristics. A theoretical analysis based on the semivariance model validation principle indicates that the pressure gradient versus fluid speed relation indeed departs from the quadratic Forchheimer-extended Darcy flow model, and can be correlated by a cubic function of fluid speed for the velocity range of our experiments.

Computation of energy dissipation in transient flow

Abstract: A new model for the computation of unsteady friction losses in transient flow is developed and verified in this study. The energy dissipation in transient flow is estimated from the instantaneous velocity profiles. The ratio of the energy dissipation at any instant and the energy dissipation obtained by assuming quasi-steady conditions defines the energy dissipation factor. This is a nondimensional, time-varying parameter that modifies the friction term in the transient flow governing equations. The model was verified for laminar and turbulent flows and the comparison of measured and computed pressure heads shows excellent agreement. This model can be adapted to an existing transient program that uses the well-known method of characteristics for the solution of the continuity and momentum equations.

Gas-Liquid Stratified-Wavy Flow in Horizontal Pipelines

Abstract: Gas-liquid stratified-wavy flow with low liquid loading is common in natural gas transmission pipelines and offshore gas pipelines. This specific case of two-phase pipe flow has been studied experimentally and theoretically in the present paper. The interfacial behavior during air-kerosene stratified-wavy flow in a 77.9-mm-dia 420-m-long pipeline was observed carefully. The gas-liquid interface usually exhibits a concave downward curved configuration. The liquid film-wetted wall fraction, liquid holdup, and pressure drop were also measured. A mechanistic double-circle model and a correlation for interfacial friction factor, required as a closure relationship in the model, have been developed. The new model gives significantly improved predictions for both liquid holdup and pressure drop during gas-liquid stratified-wavy flow in horizontal pipelines.

Shear flow of wormlike micelles in pipe and cylindrical Couette geometries as studied by nuclear magnetic resonance microscopy

Abstract: The nonlinear viscosity of the wormlike surfactant system cetyl pyridinium chloride/sodium salicylate (60 mM/100 mM in water) has been investigated in both pipe and cylindrical Couette geometries, using nuclear magnetic resonance to image both velocity and diffusion In pipe flow we observe transitions from Newtonian to non-Newtonian viscosity, to spurt, to unstable flow, and then to a regime where fluctuations are rapid on the timescale of a few milliseconds In the Couette cell we observe apparent slip at the inner wall as well as a high shear rate band located away from the wall in the body of the fluid The banding phenomenon, which has its counterpart in the pipe flow, is consistent with double valuedness in the stress versus rate of strain relationship for this fluid

Comparison Of Ecn And Eis Measurement For Corrosion Monitoring Under Multiphase Flow Conditions

Abstract: Electrochemical Noise (ECN) and Electrochemical Impedance Spectroscope (EIS) measurements were made simultaneously in a 75 mm I.D., 10 m long acrylic pipeline using salt-water/carbon dioxide mixtures. Full pipe flow was studied for liquid velocities of 0.5, 0.75, 1.1, 1.5 m/s and slug flow for Froude numbers 4, 6 and 9. Experiments were carried out at a constant pressure of 136 kPa and temperature of 40 C. ECN data were measured with a fast auto zero resistance ammeter. The ECN technique is able to detect changes in flow regime, showing distinct differences between full pipe flow and slug flow. The choice of sampling rate when using ECN is very important. For slug flows, sampling rates as high as 100 Hz are necessary to include most of the transients in the flow. Distinct differences can be seen in the Fast Fourier Transforms where dominant frequencies exist which correspond to possible bubble action in the slug body. EIS can be used to measure corrosion rate in multiphase flows. It does show an increase in the corrosion rate with liquid flow rates for full pipe flow and Froude numbers for stationary slug flow. A simple statistical analysis of ECN response gives a correlation withmore » corrosion rate. These show ECN could be a very powerful tool for determining corrosion rate and corrosion mechanism in multiphase flow.« less

Applying hypothesis of self-similarity for flow-resistance law of small-diameter plastic pipes

Abstract: In this paper the writer reports the results of an investigation carried out to test the applicability of the self-similarity hypothesis for determining the flow-resistance law in small-diameter plastic pipes. The incomplete self-similarity (ISS) hypothesis is applied for establishing both the flow-resistance law and the velocity distribution. The analysis shows that the head loss per unit length can be accurately estimated using a theoretical approach based on the ISS hypothesis for the velocity profile in a circular smooth pipe. A new relationship between the Γ coefficient of the power-velocity profile and the flow Reynolds number, based on previous measurements carried out in plastic polyethylene (PE) pipes with nominal diameter equal to 16, 20, and 25 mm and for flow Reynolds numbers ranging from 3,037 to 36,112, is also established.

Residence time distribution in twisted pipe flows: helically coiled system and chaotic system

Abstract: This study compares residence time distributions in a helically coiled tube and a spatially chaotic system. The chaotic system consists of an array of bends, the plane of curvature of each one makes a 90° angle with that of its neighbors. Chaotic trajectories are obtained by the switch in the symmetry plane of the Dean vortices which appear in the bends. Mixing in the two configurations is compared by modeling the residence time distributions, experimentally determined by means of a two-measurement-point technique, using the axial dispersion plug-flow model. For Reynolds numbers greater than 2500, axial dispersion in the chaotic system is more than 20% less than in a helically coiled tube having the same number of bends. The decrease in axial dispersion is due to the generation of chaotic trajectories, which also contribute to an increase in transverse dispersion. Thus, the chaotic curved pipes system appears very promising in producing good mixing, especially in a laminar flow regime.

Flow near the permeable boundary of a porous medium: An experimental investigation using LDA

Abstract: Fluid flow at the interface of a porous medium and an open channel is the governing phenomenon in a number of processes of industrial importance. Traditionally, this has been modeled by applying the Brinkman’s modification of Darcy’s law to obtain the velocity profile in terms of an additional parameter known as the “apparent viscosity” or the “slip coefficient”. To test this ad hoc approach, a detailed experimental investigation of the flow was conducted using Laser Doppler Anemometry (LDA) in the close vicinity of the permeable boundary of a porous medium. The porous medium used in the experiments consisted of a network of continuous glass strands woven together in a random fashion.

The Lift on a Tank-Treading Ellipsoidal Cell in a Shear Flow

Abstract: The lift on a strongly non-spherical vesicle in a bounded shear flow is studied in the case the membrane moves with a velocity, which is a linear function of the coordinates. The magnitude of the induced drift is calculated as a function of the axes lengths, of the distance from the wall, and of the ratio of the cell to the solvent viscosity. It appears that the main mechanism for lift, in the presence of tank-treading motions, is the fixed orientation of the vesicle with respect to the flow. Tank-treading vesicles in suspensions, flowing through narrow gaps under small Reynolds number conditions: Re = Lv/ν< 1 (with L the gap width, v the flow velocity and ν the viscosity) migrate away from the walls, with a velocity that is ${\cal O}({\rm Re}^{-1})$ larger than predicted by inertia.

A Modified Low-Reynolds-Number k-ω Model for Recirculating Flows

Abstract: A modified form of Wilcox's low-Reynolds-number k-ω model (Wilcox) is proposed for predicting recirculating flows. The turbulent diffusion for the specific dissipation rate, ω, is modeled with two parts: a second-order diffusion term and a first-order cross-diffusion term. The model constants are re-established. The damping functions are redevised, which reproduce correct near-wall asymptotic behaviors, and retain the mechanism describing transition as in the original model. The new model is applied to channel flow, backward-facing step flow with a large expansion ratio (H/h = 6), and recirculating flow in a ventilation enclosure. The predictions are considerably improved

Water Bioengineering Techniques: for Watercourse Bank and Shoreline Protection

Abstract: Preface to Fourth Edition.Chapter 1 Properties of Fluids.Chapter 2 Fluid Statics.Chapter 3 Fluid Flow Concepts and Measurements.Chapter 4 Flow of Incompressible Fluids in Pipelines.Chapter 5 Pipe Network Analysis.Chapter 6 Pump-pipeline System Analysis and DesignChapter 7 Boundary Layers on Flat Plates and in Ducts.Chapter 8 Steady Flow in Open Channels.Chapter 9 Dimensional Analysis, Similitude and Hydraulic Models.Chapter 10 Ideal Fluid Flow and Curvilinear Flow.Chapter 11 Gradually Varied Unsteady Flow from Reservoirs.Chapter 12 Mass Oscillations and Pressure Transients in Pipelines.Chapter 13 Unsteady Flow in Channels.Chapter 14 Uniform in Loose-boundary Channels.Chapter 15 Hydraulic Structures.Answers.Index.Conversion Table.

Evaluating Pressure Losses in Drip-Irrigation Lines

Abstract: In this paper an experimental investigation was carried out to deduce an evaluating procedure of local losses due to the protrusion of emitter barbs into the flow in drip-irrigation lines. Local losses corresponding to different pipe-on line emitter systems were measured for different Reynolds number values. Each pipe-emitter system was characterized by an obstruction index (OI) summarizing the reduction of cross-sectional area of the pipe due to the emitter connection. A power relationship between a characteristic value of the α coefficient, expressing the local losses amount as a fraction of the kinetic height, and the corresponding OI index was deduced. Two evaluating procedures of OI were also compared: an analysis of photographs of the connections obtained by dissecting the pipe at the emitters and the use of a caliper to measure emitter protrusion dimensions. Only the first procedure makes it possible to obtain an estimating criterion of the α coefficient because it takes into account both the characteristics of the emitter connection and the deformation of the pipe surrounding the stem.

Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method

Abstract: A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.

Stability of viscoelastic flow around periodic arrays of cylinders

Abstract: Low Reynolds number flow of Newtonian and viscoelastic Boger fluids past periodic square arrays of cylinders with a porosity of 0.45 and 0.86 has been studied. Pressure drop measurements along the flow direction as a function of flow rate as well as flow visualization has been performed to investigate the effect of fluid elasticity on stability of this class of flows. It has been shown that below a critical Weissenberg number (Wec), the flow in both porosity cells is a two-dimensional steady flow, however, pressure fluctuations appear above Wec which is 2.95±0.25 for the 0.45 porosity cell and 0.95±0.08 for the higher porosity cell. Specifically, in the low porosity cell as the Weissenberg number is increased above Wec a transition between a steady two-dimensional to a transient three-dimensional flow occurs. However, in the high porosity cell a transition between a steady two-dimensional to a steady three-dimensional flow consisting of periodic cellular structures along the length of the cylinder in the space between the first and the second cylinder occurs while past the second cylinder another transition to a transient three-dimensional flow occurs giving rise to time- dependent cellular structures of various wavelengths along the length of the cylinder. Overall, the experiments indicate that viscoelastic flow past periodic arrays of cylinders of various porosities is susceptible to purely elastic instabilities. Moreover, the instability observed in lower porosity cells where a vortex is present between the cylinders in the base flow is amplifieds spatially, that is energy from the mean flow is continuously transferred to the disturbance flow along the flow direction. This instability gives rise to a rapid increase in flow resistance. In higher porosity cells where a vortex between the cylinders is not present in the base flow, the energy associated with the disturbance flow is not greatly changed along the flow direction past the second cylinder. In addition, it has been shown that in both flow cells the instability is a sensitive function of the relaxation time of the fluid. Hence, the instability in this class of flows is a strong function of the base flow kinematics (i.e., curvature of streamlines near solid surfaces), We and the relaxation time of the fluid.