Showing papers on "Pipe flow published in 2005"

The inertio-elastic planar entry flow of low-viscosity elastic fluids in micro-fabricated geometries

Abstract: The non-Newtonian flow of dilute aqueous polyethylene oxide (PEO) solutions through micro-fabricated planar abrupt contraction-expansions is investigated. The small lengthscales and high deformation rates in the contraction throat lead to significant extensional flow effects even with dilute polymer solutions having time constants on the order of milliseconds. By considering the definition of the elasticity number, El = Wi/Re, we show that the lengthscale of the geometry is key to the generation of strong viscoelastic effects, such that the same flow behaviour cannot be reproduced using the equivalent macro-scale geometry using the same fluid. We observe significant vortex growth upstream of the contraction plane, which is accompanied by an increase of more than 200% in the dimensionless extra pressure drop across the contraction. Streak photography and video-microscopy using epifluorescent particles shows that the flow ultimately becomes unstable and three-dimensional. The moderate Reynolds numbers (0.44 ≤ Re ≤ 64) associated with these high Weissenberg number (0 ≤ Wi ≤ 548) micro-fluidic flows results in the exploration of new regions of the Re-Wi parameter space in which the effects of both elasticity and inertia can be observed. Understanding such interactions will be increasingly important in micro-fluidic applications involving complex fluids and can best be interpreted in terms of the elasticity number, El = Wi/Re, which is independent of the flow kinematics and depends only on the fluid rheology and the characteristic size of the device.

Recent progress in understanding the transition to turbulence in a pipe

Abstract: The problem of understanding the nature of fluid flow through a circular straight pipe remains one of the oldest problems in fluid mechanics. So far no explanation has been substantiated to rationalize the transition process by which the steady unidirectional laminar flow state gives way to a temporally and spatially disordered three-dimensional (turbulent) solution as the flow rate increases. Recently, new travelling wave solutions have been discovered which are saddle points in phase space. These plausibly represent the lowest level in a hierarchy of spatio-temporal periodic flow solutions which may be used to construct a cycle expansion theory of turbulent pipe flows. We summarize this success against the backdrop of past work and discuss its implications for future research.

A mathematical model for blood flow in magnetic field

Abstract: In the present study a mathematical model of biomagnetic fluid dynamics (BFD), suitable for the description of the Newtonian blood flow under the action of an applied magnetic field, is proposed. This model is consistent with the principles of ferrohydrodynamics and magnetohydrodynamics and takes into account both magnetization and electrical conductivity of blood. As a representative application the laminar, incompressible, three-dimensional, fully developed viscous flow of a Newtonian biomagnetic fluid (blood) in a straight rectangular duct is numerically studied under the action of a uniform or a spatially varying magnetic field. The numerical results are obtained using a finite differences numerical technique based on a pressure-linked pseudotransient method on a collocated grid. The flow is appreciably influenced by the application of the magnetic field and in particularly by the strength and the magnetic field gradient. A comparison of the derived results is also made with those obtained using the existing BFD model indicating the necessity of taking into account the electrical conductivity of blood.

Gas Pipeline Hydraulics

Abstract: GAS PROPERTIES Mass and Weight Volume Density, Specific Weight, and Specific Volume Specific Gravity Viscosity Ideal Gases Real Gases Natural Gas Mixtures Pseudo-Critical Properties from Gas Gravity Impact of Sour Gas on Non-Hydrocarbon Components Compressibility Factor Heating Value Summary Problems References PRESSURE DROP DUE TO FRICTION Bernoulli's Equation Flow Equations General Flow Equation Effect of Pipe Elevations Average Pipe Segment Pressure Velocity of Gas in a Pipeline Erosional Velocity Reynolds Number of Flow Friction Factor Colebrook-White Equation Transmission Factor Modified Colebrook-White Equation American Gas Association (AGA) Equation Weymouth Equation Panhandle A Equation Panhandle B Equation Institute of Gas Technology (IGT) Equation Spitzglass Equation Mueller Equation Fritzsche Equation Effect of Pipe Roughness Comparison of Flow Equations Summary Problems References PRESSURE REQUIRED TO TRANSPORT Total Pressure Drop Required Frictional Effect Effect of Pipeline Elevation Effect of Changing Pipe Delivery Pressure Pipeline with Intermediate Injections and Deliveries Series Piping Parallel Piping Locating Pipe Loop Hydraulic Pressure Gradient Pressure Regulators and Relief Valves Temperature Variation and Gas Pipeline Modeling Line Pack Summary Problems References COMPRESSOR STATIONS Compressor Station Locations Hydraulic Balance Isothermal Compression Adiabatic Compression Polytropic Compression Discharge Temperature of Compressed Gas Horsepower Required Optimum Compressor Locations Compressors in Series and Parallel Types of Compressors-Centrifugal and Positive Displacement Compressor Performance Curves Compressor Station Piping Losses Compressor Station Schematic Summary Problems References PIPE LOOPS VERSUS COMPRESSION Purpose of a Pipe Loop Purpose of Compression Increasing Pipeline Capacity Reducing Power Requirements Looping in Distribution Piping Summary Problems References PIPE ANALYSIS Pipe Wall Thickness Barlow's Equation Thick-Walled Pipes Derivation of Barlow's Equation Pipe Material and Grade Internal Design Pressure Equation Class Location Mainline Valves Hydrostatic Test Pressure Blowdown Calculations Determining Pipe Tonnage Summary Problems References THERMAL HYDRAULICS Isothermal versus Thermal Hydraulics Temperature Variation and Gas Pipeline Modeling Review of Simulation Model Reports Summary Problems References TRANSIENT ANALYSIS AND CASE STUDIES Unsteady Flow Case Studies Summary Problems References VALVES AND FLOW MEASUREMENTS Purpose of Valves Types of Valves Material of Construction Codes for Design and Construction Gate Valve Ball Valve Plug Valve Butterfly Valve Globe Valve Check Valve Pressure Control Valve Pressure Regulator Pressure Relief Valve Flow Measurement Flow Meters Venturi Meter Flow Nozzle Summary Problems References PIPELINE ECONOMICS Components of Cost Capital Costs Operating Costs Determining Economic Pipe Size Summary Problems References APPENDIX A: UNITS AND CONVERSIONS APPENDIX B: PHYSICAL PROPERTIES OF VARIOUS GASES APPENDIX C: PIPE PROPERTIES-US CUSTOMARY SYSTEM OF UNITS APPENDIX D: GASMOD OUTPUT REPORT APPENDIX E: SUMMARY OF FORMULAS INDEX

Friction factors for pipe flow of xanthan-based concentrates of fire fighting foams

Abstract: In this paper we develop a friction factor correlation to predict the pressure drop during pumping and induction of concentrates of fire fighting foams containing around 1% of xanthan gum. Such concentrates are highly elastic, display small yield stress and exhibit significant thinning upon shearing. We demonstrate that in the turbulent regime, the Blasius equation normally used for Newtonian fluids seems to correlate well the friction factor with the Metzner-Reed Reynolds number. Our development provides an example of how the methodology used to develop the friction factor correlation can be applied to analyse a set of experimental data to verify its internal consistency. The friction factors developed in the paper can be applied to other foam concentrates that include a similar content of xanthan gum in their formulation, to predict pressure drop as a function of a flow rate and pipe diameter, provided that there exists an appropriate viscosity model. Subsequently, the paper presents experimental measurements of apparent viscosity for one foam concentrate and develops relevant viscosity models. We observe that the rheology of the concentrate is governed by the behaviour of xanthan gum. Although, the foam concentrate considered in the article is yield pseudo plastic (i.e., it follows the Herschel-Bulkley model), for the shear stresses normally encountered during pipe flow, the viscosity of the material can be described by a power law model. Over the temperature range of between 0 and 40 o C, the apparent viscosity displays only a weak dependence on temperature. Subsequent calculations of pressure drop with temperature demonstrate minor variation in pressure drop with temperature, but only in the turbulent flow regime. This suggests that induction systems intended to operate under widely varying temperature conditions should be designed to function in the turbulent flow regime.

The Development Lengths of Laminar Pipe and Channel Flows

Abstract: The authors’ research work into fully developed pulsating and oscillating laminar pipe and channel flows raised questions regarding the development length of the corresponding steady flow. For this development length, i.e., the distance from the entrance of the pipe to the axial position where the flow reaches the parabolic velocity profile of the Hagen-Poiseuille flow, a wide range of contradictory data exists. This is shown through a short review of the existing literature. Superimposed diffusion and convection, together with order of magnitude considerations, suggest that the normalized development length can be expressed as L∕D=C0+C1Re and for Re→0 one obtains C0=0.619, whereas for Re→∞ one obtains C1=0.0567. This relationship is given only once in the literature and it is presumed to be valid for all Reynolds numbers. Numerical studies show that it is only valid for Re→0 and Re→∞. The development length of laminar, plane channel flow was also investigated. The authors obtained similar results to those for the pipe flow: L∕D=C0′+C1′; Re, where C0′=0.631 and C1′=0.044. Finally, correlations are given to express L∕D analytically for the entire Re range for both laminar pipe and channel flows.

Granular slumping on a horizontal surface

Abstract: We report the results of an experimental investigation of the flow induced by the collapse of a column of granular material (glass beads of diameter d) over a horizontal surface. Two different setups are used, namely, a rectangular channel and a semicircular tube, allowing us to compare two-dimensional and axisymmetric flows, with particular focus on the internal flow structure. In both geometries the flow dynamics and the deposit morphologies are observed to depend primarily on the initial aspect ratio of the granular column a=Hi∕Li, where Hi is the height of the initial granular column and Li its length along the flow direction. Two distinct regimes are observed depending on a: an avalanche of the column flanks producing truncated deposits for small a and a column free fall leading to conical deposits for large a. In both geometries the characteristic time scale is the free fall of the granular column τc=Hi∕g. The flow initiated by Coulomb-like failure never involves the whole granular heap but remains localized in a surface layer whose size and shape depend on a and vary in both space and time. Except in the vicinity of the pile foot where the flow is pluglike, velocity profiles measured at the side wall are identical to those commonly observed in steady granular surface flows: the velocity varies linearly with depth in the flowing layer and decreases exponentially with depth in the static layer. Moreover, the shear rate is constant, γ=0.3g∕d, independent of the initial aspect ratio, the flow geometry, position along the heap, or time. Despite the rather complex flow dynamics, the scaled deposit height Hf∕Li and runout distance ΔL∕Li both exhibit simple power laws whose exponents depend on a and on the flow geometry. We show that the physical origin of these power laws can be understood on the basis of a dynamic balance between acceleration, pressure gradient, and friction forces at the foot of the granular pile. Two asymptotic behaviors can be distinguished: the flow is dominated by friction forces at small a and by pressure forces at large a. The effect of the flow geometry is determined primarily by mass conservation and becomes important only for large a.

Computational study of turbulent laminar patterns in couette flow.

Abstract: Turbulent-laminar patterns near transition are simulated in plane Couette flow using an extension of the minimal-flow-unit methodology. Computational domains are of minimal size in two directions but large in the third. The long direction can be tilted at any prescribed angle to the streamwise direction. Three types of patterned states are found and studied: periodic, localized, and intermittent. These correspond closely to observations in large-aspect-ratio experiments.

Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows

Abstract: The properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows are explored both experimentally and theoretically. Available highquality data reveal a dynamically relevant four-layer description that is a departure from the mean profile four-layer description traditionally and nearly universally ascribed to turbulent wall flows. Each of the four layers is characterized by a pre­ dominance of two of the three terms in the governing equations, and thus the mean dynamics of these four layers are unambiguously defined. The inner normalized physical extent of three of the layers exhibits significant Reynolds-number dependence. The scaling properties of these layer thicknesses are determined. Particular signi­ ficance is attached to the viscous/Reynolds-stress-gradient balance layer since its thickness defines a required length scale. Multiscale analysis (necessarily incomplete) substantiates the four-layer structure in developed turbulent channel flow. In parti­ cular, the analysis verifies the existence of at least one intermediate layer, with its own characteristic scaling, between the traditional inner and outer layers. Other information is obtained, such as (i) the widths (in order of magnitude) of the four layers, (ii) a flattening of the Reynolds stress profile near its maximum, and (iii) the asymptotic increase rate of the peak value of the Reynolds stress as the Reynolds num ber approaches infinity. Finally, on the basis of the experimental observation that the velocity increments over two of the four layers are unbounded with increasing Reynolds num ber and have the same order of magnitude, there is additional theore­ tical evidence (outside traditional arguments) for the asymptotically logarithmic character of the mean velocity profile in two of the layers; and (in order of magnitude) the mean velocity increments across each of the four layers are determined. All of these results follow from a systematic train of reasoning, using the averaged momentum balance equation together with other minimal assumptions, such as that the mean velocity increases monotonically from the wall.

A new friction factor relationship for fully developed pipe flow

Abstract: The friction factor relationship for high-Reynolds-number fully developed turbulent pipe flow is investigated using two sets of data from the Princeton Superpipe in the range 31×10^3 ≤ ReD ≤ 35×10^6. The constants of Prandtl’s ‘universal’ friction factor relationship are shown to be accurate over only a limited Reynolds-number range and unsuitable for extrapolation to high Reynolds numbers. New constants, based on a logarithmic overlap in the mean velocity, are found to represent the high-Reynolds-number data to within 0.5%, and yield a value for the von Karman constant that is consistent with the mean velocity profiles themselves. The use of a generalized logarithmic law in the mean velocity is also examined. A general friction factor relationship is proposed that predicts all the data to within 1.4% and agrees with the Blasius relationship for low Reynolds numbers to within 2.0%.

The subgrid-scale models based on coherent structures for rotating homogeneous turbulence and turbulent channel flow

Abstract: The subgrid-scale (SGS) models based on the coherent structure in grid-scale flow fields are proposed and are applied to (non-)rotating homogeneous turbulences and turbulent channel flows The eddy viscosity is modeled by a coherent structure function (CSF) with a fixed model-parameter The CSF is defined as the second invariant normalized by the magnitude of a velocity gradient tensor and plays a role of wall damping The probability density function of the CSF is non-Gaussian showing an intermittency effect The model parameter is locally determined, and it is always positive and has a small variance These models satisfy a correct asymptotic behavior to a wall for incompressible flows It is shown that the SGS models with an energy-decay suppression function which indicates also a pseudo-backscatter are consistent with the asymptotic material frame indifference in a rotating frame Since the CSF characterizing turbulent flows has relation to the SGS energy dissipation, the present SGS models are applicable not only to (non-)rotating homogeneous and shear turbulences but also to laminar flows The proposed models have almost the same performance as the dynamic Smagorinsky model for (non-)rotating homogeneous turbulences and turbulent channel flows, but these models do not need to average or clip the model parameter, use an explicit wall-damping function, or change the fixed-parameter, so that they are suitable for engineering applications of large-eddy simulation

A comparison between snapshot POD analysis of PIV velocity and vorticity data

Abstract: Proper orthogonal decomposition (POD) was performed on both the fluctuating velocity and vorticity fields of a backward-facing step (BFS) flow at Reynolds numbers of 580 and 4,660 The data was obtained from particle image velocimetry (PIV) measurements The vorticity decomposition captured the fluctuating enstrophy more efficiently than the equivalent velocity field decomposition for a given number of modes Coherent structures in the flow are also more easily identifiable using vorticity-based POD A common structure of the low-order vorticity POD modes suggests that a large-scale similarity, independent of the Reynolds number, may be present for the BFS flow The POD modes obtained from a vorticity-based decomposition would help in determining a basis for constructing simplified vortex skeletons and low-order flow descriptions based on the vorticity of turbulent flows

Large-eddy simulation of low frequency oscillations of the Dean vortices in turbulent pipe bend flows

Abstract: Large-eddy simulations are performed to investigate turbulent flows through 90° pipe bends that feature unsteady flow separation, unstable shear layers, and an oscillation of the Dean vortices Single bends with curvature radii of one- and three-pipe diameters are considered at the Reynolds number range 5000–27 000 The numerically computed distributions of the time-averaged velocities, Reynolds stress components, and power spectra of the velocities are validated by comparison with particle image velocimetry measurements The power spectra of the overall forces onto the pipe walls are determined The spectra exhibit a distinct peak in the high frequency range that is ascribed to vortex shedding at the inner side of the bends and shear layer instability At the largest Reynolds number the spectra also exhibit an oscillation at a frequency much lower than that commonly observed at vortex shedding from separation It turns out that the associated flow pattern is similar to the swirl switching phenomenon earl

Cavitation in flow through a micro-orifice inside a silicon microchannel

Abstract: Hydrodynamic cavitation in flows through a micro-orifice entrenched in a microchannel has been detected and experimentally investigated. Microfabrication techniques have been employed to design and develop a microfluidic device containing an 11.5μm wide micro-orifice inside a 100.2μm wide and 101.3μm deep microchannel. The flow of de-ionized water through the micro-orifice reveals the presence of multifarious cavitating flow regimes. This investigation divulges both similarities and differences between cavitation in micro-orifices and cavitation in their macroscale counterparts. The low incipient cavitation number obtained from the current experiments suggests a dominant size scale effect. Choking cavitation is observed to be independent of any pressure or velocity scale effects. However, choking is significantly influenced by the small stream nuclei residence time at such scales. Flow rate choking leads to the establishment of a stationary cavity. Large flow and cavitation hysteresis have been detected a...

Direct numerical simulations of turbulent flow over a permeable wall using a direct and a continuum approach

Abstract: A direct numerical simulation (DNS) has been performed of turbulent channel flow over a three-dimensional Cartesian grid of 30×20×9 cubes in, respectively, the streamwise, spanwise, and wall-normal direction. The grid of cubes mimics a permeable wall with a porosity of 0.875. The flow field is resolved with 600×400×400 mesh points. To enforce the no-slip and no-penetration conditions on the cubes, an immersed boundary method is used. The results of the DNS are compared with a second DNS in which a continuum approach is used to model the flow through the grid of cubes. The continuum approach is based on the volume-averaged Navier–Stokes (VANS) equations [ S. Whitaker, “The Forchheimer equation: a theoretical development,” Transp. Porous Media 25, 27 (1996) ] for the volume-averaged flow field. This method has the advantage that it requires less computational power than the direct simulation of the flow through the grid of cubes. More in general, for complex porous media one is usually forced to use the VANS equations, because a direct simulation would not be possible with present-day computer facilities. A disadvantage of the continuum approach is that in order to solve the VANS equations, closures are needed for the drag force and the subfilter-scale stress. For porous media, the latter can often be neglected. In the present work, a relation for the drag force is adopted based on the Irmay [ “Modeles theoriques d’ecoulement dans les corps poreux,” Bulletin Rilem 29, 37 (1965) ] and the Burke–Plummer model [ R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena (Wiley, New York, 2002) ], with the model coefficients determined from simulations reported by W. P. Breugem, B. J. Boersma, and R. E. Uittenbogaard [“Direct numerical simulation of plane channel flow over a 3D Cartesian grid of cubes,” Proceedings of the Second International Conference on Applications of Porous Media, edited by A. H. Reis and A. F. Miguel (Evora Geophysics Center, Evora, 2004), p. 27 ]. The results of the DNS with the grid of cubes and the second DNS in which the continuum approach is used, agree very well.

Vortex-Generator Model and Its Application to Flow Control

Abstract: A new vortex-generator model is introduced, the jBAY model, which provides an efficient method for computational-fluid-dynamics (CFD) simulation of flow systems with vortex-generator arrays. The ...

Developments In Smooth Wall Turbulent Duct Flows

Abstract: An experimental investigation into the fully developed, turbulent flow in circular pipes and high aspect ratio rectangular ducts (channels) was undertaken. A review of the literature revealed that there is a need for more accurate duct flow measurements, despite the large number of studies already completed. Thus, a new, high quality channel flow apparatus has been carefully designed and constructed. For the fully developed flow, all measureable turbulence statistics at the centre of the channel are presented. Measurements are recorded using hot-wire and pitot tube anemometry, with an insistence on the highest accuracy. All results are analysed with the intention of providing a better physical understanding of turbulent flows. An existing pipe flow apparatus — most recently employed by Henbest (1983) — is used to check the applicability of common pitot corrections by comparison with hotwire data. It is found that applying the MacMillan (1956) and turbulence intensity corrections gives good agreement between measurements. Velocity profiles measured at the centre of the channel display the expected logarithmic scaling. These also highlight a significant difference between pipe and channel flow velocity profiles; that is, pipe flow has a much larger wake. This observation has been observed, but not explained in the literature. It was postulated that the difference is due to an increased number of eddies contributing to the outer flow in the pipe. Evidence supporting this claim is found from the attached eddy hypothesis. Recent literature has provided predictions of the turbulence intensities in boundary layers, based on the attached eddy hypothesis. These predictions are compared and extended to channel flow measurements for the first time. In the analysis of flow structure, the auto-correlation of streamwise velocity fluctuations is an often neglected statistic. It is shown here that channel flow auto-correlation measurements

Application of the augmented Lagrangian method to steady pipe flows of Bingham, Casson and Herschel-Bulkley fluids

Abstract: The augmented Lagrangian method is applied to the steady flow problems of Bingham, Casson and Herschel–Bulkley fluids in pipes of circular and square cross-sections. The plug flow velocity, the flow rate, the flow pattern, the velocity profile, the locations of yielded/unyielded surfaces, the stopping criteria and the friction factor are presented and compared with one another. The numerical strategy based on variational inequalities is shown to be realised easily and applicable extensively.

Reynolds number effects in the outer layer of the turbulent flow in a channel with rough walls

Abstract: Turbulent channel flow measurements for two different rough surfaces have been compared with a smooth reference case. A range of Reynolds numbers, Reτ∊⟨360,6000⟩, has been investigated using hot-wire anemometry. Reynolds stresses and third-order moments are shown to be very little affected by the substantially different wall conditions outside 5k, where k is the characteristic length scale of the roughness. In this region, a reasonably good collapse with Reynolds number is demonstrated when scaling with friction velocity is used. This contrasts some of the rough-wall investigations previously published for boundary layers and channels with only one rough wall. It is believed that the differences observed are due to the differences in boundary conditions and that symmetrically roughened channel flows and flows in rough-wall pipes may be better candidates for the Townsend’s wall similarity hypothesis than asymmetrical flows.

The DS2V/3V Program Suite for DSMC Calculations

Abstract: There is a need for general purpose DSMC codes that can be readily applied by non‐specialist users to a wide variety of practical problems. The specifications that should be met by such programs are outlined and the currently available programs are noted. The DS2V program for two‐dimensional and axially‐symmetric flows and the DS3V program for three‐dimensional flows are described in some detail. The “V” in the program names is to indicate the interactive visual characteristic of the programs. Both programs run in a time‐accurate mode and the flow sampling may be of the unsteady flow or, if a steady flow is established at sufficiently large times, of the steady flow. The gas model includes internal degrees of freedom, gas phase chemical reactions, and surface reactions. The initial state may include flow discontinuities that permit the study of shock tube flows and free shear flows. Solid surfaces may move in their own plane, a typical application being a rotating body in an axially‐symmetric flow. Alternatively, a surface may move in a normal direction to generate a moving shock wave for diffraction studies. Flow boundaries may be arbitrary combinations of solid surfaces and specified flows. Other options include periodic boundaries and constant pressure boundaries that have been developed especially for MEMS applications.