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Showing papers on "Pipe flow published in 2002"


Journal ArticleDOI
TL;DR: In this paper, two-phase flow patterns are visualized with a microscope for air-water and steam-water flow in circular tubes of 20, 25 and 100 μm i.d.

496 citations


Journal ArticleDOI
TL;DR: In this paper, Kattan et al. used a diabatic flow pattern map to predict two-phase flow flow and showed that the peak in the frictional pressure gradient at high vapor qualities coincided with the onset of dryout in the annular flow regime.
Abstract: Two-phase pressure drop data were obtained for evaporation in two horizontal test sections of 10.92 and 12.00 mm diameter for five refrigerants (R-134a, R-123, R-402A, R-404A and R-502) over mass velocities from 100 to 500 kg/m2 s and vapor qualities from 0.04 to 1.0. These data have then been compared against seven two-phase frictional pressure drop prediction methods. Overall, the method by Muller-Steinhagen and Heck (Muller-Steinhagen H, Heck K. A simple friction pressure drop correlation for two-phase flow in pipes. Chem. Eng. Process 1986;20:297–308) and that by Gronnerud (Gronnerud R. Investigation of liquid hold-up, flow-resistance and heat transfer in circulation type evaporators, part IV: two-phase flow resistance in boiling refrigerants. Annexe 1972-1, Bull. de l'Inst. du Froid, 1979) were found to provide the most accurate predictions while the widely quoted method of Friedel (Friedel L. Improved friction drop correlations for horizontal and vertical two-phase pipe flow. European Two-phase Flow Group Meeting, paper E2; June 1979; Ispra, Italy) gave the third best results. The data were also classified by two-phase flow pattern using the Kattan-Thome-Favrat (Kattan N, Thome JR, Favrat D. Flow boiling in horizontal tubes. Part 1: development of a diabatic two-phase flow pattern map. J. Heat Transfer 1998;120:140–7; Kattan N, Thome JR, Favrat D. Flow boiling in horizontal tubes. Part 2; new heat transfer data for five refrigerants. J Heat Transfer 1998;120:148–55; Kattan N, Thome JR, Favrat D. Flow boiling in horizontal tubes. Part 3: development of a new heat transfer model based on flow patterns. J. Heat Transfer 1998;120:156–65) flow pattern map. The best available method for annular flow was that of Muller-Steinhagen and Heck. For intermittent flow and stratified-wavy flow, the best method in both cases was that of Gronnerud. It was observed that the peak in the two-phase frictional pressure gradient at high vapor qualities coincided with the onset of dryout in the annular flow regime.

295 citations


Journal ArticleDOI
TL;DR: In this article, velocity measurements were made in two jet flows, the first exiting from a smooth contraction nozzle and the second from a long pipe with a fully developed pipe flow profile.
Abstract: Velocity measurements were made in two jet flows, the first exiting from a smooth contraction nozzle and the second from a long pipe with a fully developed pipe flow profile. The Reynolds number, based on nozzle diameter and exit bulk velocity, was the same (≃86,000) in each flow. The smooth contraction jet flow developed much more rapidly and approached self-preservation more rapidly than the pipe jet. These differences were associated with differences in the turbulence structure in both the near and far fields between the two jets. Throughout the shear layer for x<3d, the peak in the v spectrum occurred at a lower frequency in the pipe jet than in the contraction jet. For x≥3d, the peaks in the two jets appeared to be nearly at the same frequency. In the pipe jet, the near-field distributions of f(r) and g(r), the longitudinal and transverse velocity correlation functions, differed significantly from the contraction jet. The integral length scale Lu was greater in the pipe jet, whereas Lv was smaller. In the far field, the distributions of f(r) and g(r) were nearly similar in the two flows. The larger initial shear layer thickness of the pipe jet produced a dimensionally lower frequency instability, resulting in longer wavelength structures, which developed and paired at larger downstream distances. The regular vortex formation and pairing were disrupted in the shear layer of the pipe jet. The streamwise vortices, which enhance entrainment and turbulent mixing, were absent in the shear layer of the pipe jet. The formation of large-scale structures should occur much farther downstream in the pipe jet than in the contraction jet.

292 citations


Journal ArticleDOI
TL;DR: In this paper, the steady-state Poiseuille flow of a simple fluid in carbon nanopores under a gravitylike force is simulated using a realistic empirical many-body potential model for carbon.
Abstract: Steady-state Poiseuille flow of a simple fluid in carbon nanopores under a gravitylike force is simulated using a realistic empirical many-body potential model for carbon. Building on our previous study of slit carbon nanopores we show that fluid flow in a nanotube is also characterized by a large slip length. By analyzing temporal profiles of the velocity components of particles colliding with the wall we obtain values of the Maxwell coefficient defining the fraction of molecules thermalized by the wall and, for the first time, propose slip boundary conditions for smooth continuum surfaces such that they are equivalent in adsorption, diffusion, and fluid flow properties to fully dynamic atomistic models.

255 citations


Journal ArticleDOI
TL;DR: In this paper, the size of entrained bubbles and droplets extends over several orders of magnitude, and a significant number of bubble/droplet clusters were observed. And the increase in turbulence levels, compared to single-phase flow situations, is proportional to the number of entangled particles.

249 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated both experimentally and numerically liquid flow in microchannels with hydraulic diameters from 244 to 974 µ ma tReynolds numbers ranging from 230 to 6500 and showed that conventional theory may be used to predict successfully the flow behavior in micro-channel in the range of dimensions considered here.
Abstract: Liquid flow in microchannels is investigated both experimentally and numerically. The experiments are carried out in microchannels with hydraulic diameters from 244 to 974 µ ma tReynolds numbers ranging from 230 to 6500. The pressure drop in these microchannels is measured in situ and is also determined by correcting global measurements for inlet and exit losses. Onset of turbulence is verified by flow visualization. The experimental measurements of pressure drop are compared to numerical predictions. Results show that conventional theory may be used to predict successfully the flow behavior in microchannels in the range of dimensions considered here. Nomenclature Dh =h ydraulic diameter, µm f = Darcy friction factor H = microchannel height, µm L = microchannel length, mm l = characteristic size of eddies in turbulent flow, m P = pressure, Pa Q =v olume flow rate, m 3 /s Re =R eynolds number U =a verage velocity in microchannel, m/s u = characteristic velocity scale of eddies in turbulent flow, m/s W = microchannel width, µm x + = entrance length, mm α = aspect ratio, H/W � P = pressure difference, Pa δ = uncertainty e = dissipation rate, m 2 /s 3 η =K olmogorov length scale, m µ = fluid viscosity, N · s/m 2 ν = kinematic viscosity, m 2 /s ρ = fluid density, kg/m 3 app = apparent fd = fully developed conditions

233 citations


Journal ArticleDOI
TL;DR: In this paper, the pressure within a trapped air pocket in a rapidly filling horizontal pipe is investigated both experimentally and analytically, where the downstream end is either sealed to form a dead end or outfitted with an orifice to study the effects of air leakage on the pressure.
Abstract: The pressure within a trapped air pocket in a rapidly filling horizontal pipe is investigated both experimentally and analytically. The downstream end of the pipe is either sealed to form a dead end or outfitted with an orifice to study the effects of air leakage on the pressure. Three types of pressure oscillation patterns are observed, depending on the size of the orifice. When no air is released or orifice sizes are small, the cushioning effects of the air pocket prevents the water column from impacting on the pipe end and from generating high water hammer pressures. However, the maximum pressure experienced may still be several times the upstream driving pressure. When the orifice size is very large, the air cushioning effect vanishes and the water hammer pressure is dominant. For intermediate orifice sizes, the pressure oscillation pattern consists of both long-period oscillations (while the air pocket persists) followed by short-period pressure oscillations (once water hammer pressures dominate). Air leakage is observed to play a significant role in increasing the magnitude of the observed pressures during rapid filling, resulting in peak pressures up to 15 times the upstream head. An analytical model, capable of calculating the air pocket pressure and the peak pressure when the water column slams into the end of the pipe, is developed and results are compared with those of experiments. The model was successful in determining the amplitude of the peak pressure for the entire orifice range and was able to simulate the pressure oscillation pattern for the case of a negligible water hammer impact effect. Although the model was unable to simulate the pressure oscillation pattern for substantial air release, it was able to predict the type of pressure oscillation behavior and the peak pressure.

213 citations


Journal ArticleDOI
TL;DR: In this paper, a developed particle-laden horizontal channel flow (length 6m, height 35mm, the length is about 170 channel heights) is presented using phase-Doppler anemometry for simultaneous determination of air and particle velocity.
Abstract: Detailed measurements in a developed particle-laden horizontal channel flow (length 6 m, height 35 mm, the length is about 170 channel heights) are presented using phase-Doppler anemometry for simultaneous determination of air and particle velocity. The particles were spherical glass beads with mean diameters in the range of 60 µm–1 mm. The conveying velocity could be varied between about 10 m/s and 25 m/s, and the particle mass loading could reach values of about 2 (the mass loading is defined as the ratio of particle to gas phase mass flow rates), depending on particle size. For the first time, the degree of wall roughness could be modified by exchanging the wall plates. The influence of these parameters and the effect of inter-particle collisions on the profiles of particle mean and fluctuating velocities and the normalised concentration in the developed flow were examined. It was shown that wall roughness decreases the particle mean velocity and enhances fluctuating velocities due to irregular wall bouncing and an increase in wall collision frequency, i.e. reduction in mean free path. Thereby, the larger particles are mainly more uniformly distributed across the channel, and gravitational settling is reduced. Both components of the particle velocity fluctuation were reduced with increasing mass loading due to inter-particle collisions and the momentum loss involved. Moreover, the effect of the particles on the air flow and the turbulent fluctuations was studied on the basis of profiles in the developed flow and turbulence spectra determined for the streamwise velocity component. In addition to the effect of particle size and mass loading on turbulence modulation, the influence of wall roughness was analysed. It was clearly shown that increasing wall roughness also results in a stronger turbulence dissipation due to two-way coupling.

190 citations


Patent
28 Aug 2002
TL;DR: In this paper, the authors present a method and apparatus for controlling fluid flow with pressure gradient fluid control, where passive fluid flow barriers are used to act as valves, thereby allowing the flow of fluids through flow paths to be regulated so as to allow fluids to be introduced via a single channel and subsequently split into multiple channels.
Abstract: Methods and apparatus are presented for controlling fluid flow with pressure gradient fluid control. Passive fluid flow barriers may be used to act as valves, thereby allowing the flow of fluids through flow paths to be regulated so as to allow fluids to be introduced via a single channel (50) and subsequently split into multiple channels (58, 60). Flow through flow paths can be regulated to allow a series of sister wells (51-53) or chambers to all fill prior to the fluid flowing beyond any one of the sister wells (51-53) or chambers. Each flow path may have multiple segments (66-69), at least one of which is designed to balance the pressure drops of the flow paths to provide uniform flow of fluids through the flow paths. The configurations of the wells (51-53) may be modified by adding vents or flow dividers to enhance fluid flushing and gas removal capability.

185 citations


Journal ArticleDOI
TL;DR: In this paper, a finite-volume code (CFX4.3 from AEA Technology, Pittsburgh, PA) and its user-enhanced FORTRAN programs were validated with experimental velocity data points for a single bifurcation.
Abstract: Considering oscillatory laminar incompressible three-dimensional flow in triple planar and nonplanar bifurcations representing generations three to six of the human respiratory system, air flow fields and micron-particle transport have been simulated under normal breathing and high-frequency ventilation (HFV) conditions. A finite-volume code (CFX4.3 from AEA Technology, Pittsburgh, PA) and its user-enhanced FORTRAN programs were validated with experimental velocity data points for a single bifurcation. The airflow structures and micron-particle motion in the triple bifurcations were analyzed for a representative normal breathing cycle as well as HFV condition. While both the peak inspiratory and expiratory velocity profiles for the low Womersley case (α=0.93) agree well with those of instantaneously equivalent steady-state cases, some differences can be observed between flow acceleration and deceleration at off-peak periods or near flow reversal, especially during inspiratory flow. Similarly, the basic features of instantaneous particle motion closely resemble the steady-state case at equivalent inlet Reynolds numbers. The preferential concentration of particles caused by the coherent vortical structures was found in both inhalation and exhalation; however, it is more complicated during expiration. The effects of Womersley number and non-planar geometries as well as the variations in secondary flow intensity plus pressure drops across various bifurcations under normal breathing and HFV conditions were analyzed as well. This work may elucidate basic physical insight of aerosol transport relevant in dosimetry-and-health-effect studies as well as for drug aerosol delivery analyses.

180 citations


Journal ArticleDOI
TL;DR: In this article, a simple equation is derived for expressing the drag reduction rate by spanwise wall oscillations and the relation between near-wall streamwise vortices and low and high-speed flow is scrutinized to extract the key parameters.
Abstract: Drag reduction in turbulent channel and pipe e ows by spanwise (circumferential) wall oscillations is studied numerically. The ine uence of the wall oscillation on near-wall streamwise vortices is examined. By the use of the Stokes second problem, a wall-normal distanceparameter and an acceleration parameterare obtained toestimate the drag reduction rate. A simple equation is derived for expressing the drag reduction rate by spanwise wall oscillations. The relation between near-wall streamwise vortices and low- and high-speed e uids is scrutinized to extract the key parameters. The drag reduction mechanism is analyzed in terms of the attenuation of Reynolds shear stress.

Journal ArticleDOI
TL;DR: The aerodynamic generation of sound during phonation was studied using direct numerical simulations of the airflow and the sound field in a rigid pipe with a modulated orifice to find the dominant sound production mechanism was a dipole induced by the net force exerted by the surfaces of the glottis walls on the fluid along the direction of sound wave propagation.
Abstract: The aerodynamic generation of sound during phonation was studied using direct numerical simulations of the airflow and the sound field in a rigid pipe with a modulated orifice. Forced oscillations with an imposed wall motion were considered, neglecting fluid–structure interactions. The compressible, two-dimensional, axisymmetric form of the Navier–Stokes equations were numerically integrated using highly accurate finite difference methods. A moving grid was used to model the effects of the moving walls. The geometry and flow conditions were selected to approximate the flow within an idealized human glottis and vocal tract during phonation. Direct simulations of the flow and farfield sound were performed for several wall motion programs, and flow conditions. An acoustic analogy based on the Ffowcs Williams–Hawkings equation was then used to decompose the acoustic source into its monopole, dipole, and quadrupole contributions for analysis. The predictions of the farfield acoustic pressure using the acoustic...

Journal ArticleDOI
TL;DR: In this article, a backward-facing step flow at a Reynolds number of Reh=U∞h/ν=4,660 (based on step height and freestream velocity) was measured using particle image velocimetry (PIV) measurements.
Abstract: Particle image velocimetry (PIV) measurements were carried out on a backward-facing step flow at a Reynolds number of Reh=U∞h/ν=4,660 (based on step height and freestream velocity). In-plane velocity, out-of-plane vorticity, Reynolds stress and turbulent kinetic energy production measurements in the x–y and x–z planes of the flow are presented. Proper orthogonal decomposition was performed on both the fluctuating velocity and vorticity fields of the x–y plane PIV data using the method of snapshots. Low-order representations of the instantaneous velocity fields were reconstructed using the velocity modes. These reconstructions provided insight into the contribution that the various length scales make to the spatial distribution of mean and turbulent flow quantities such as Reynolds stress and turbulent kinetic energy production. Large scales are found to contribute to the Reynolds stresses and turbulent kinetic energy production downstream of reattachment, while small scales contribute to the intense Reynolds stresses in the vicinity of reattachment.

Patent
12 Jun 2002
TL;DR: In this article, a technique for controlling fluid production in a deviated wellbore is described, where a plurality of flow control valves are disposed at spaced apart positions along the length of the flow pipe.
Abstract: A technique for controlling fluid production in a deviated wellbore is disclosed. The technique utilizes a flow pipe the interior of which is in hydraulic communication with the earth's surface. A plurality of flow control valves are disposed at spaced apart positions along the length of the flow pipe. The flow control valves are used to regulate flow along intervals of the flow pipe.

Journal ArticleDOI
TL;DR: In this paper, a series of numerical simulations of small spherical bubbles seeded in a turbulent channel flow at average volume fractions of up to 8% were performed and it was shown that even for relatively large bubbles, an initial transient drag reduction can occur as bubbles disperse into the flow.
Abstract: While turbulent drag reduction through the injection of micro-bubbles into a turbulent boundary layer is well established in experiments, there is a lack of corresponding supporting evidence from direct numerical simulations. Here we report on a series of numerical simulations of small bubbles seeded in a turbulent channel flow at average volume fractions of up to 8%. These results show that even for relatively large bubbles, an initial transient drag reduction can occur as bubbles disperse into the flow. Relatively small spherical bubbles will produce a sustained level of drag reduction over time.

Journal ArticleDOI
TL;DR: In this article, the minimum of the system free energy is combined with a model for drop size in dense dispersions to predict the critical conditions for phase inversion in oil-water flow systems.

Patent
Edward J. Zisk1
22 Jan 2002
TL;DR: In this paper, the authors present a fluid flow annulus within the production tube inside of the downhole sand screen, where fluid passing through the screen is required to flow along the annulus to find a flow aperture into an interior flow bore.
Abstract: Apparatus and methods are disclosed for actively controlling the flow of hydrocarbon fluids from a producing formation at the downhole sand screen. A preferred embodiment of the invention provides a fluid flow annulus within the production tube inside of the screen. In a first flow control configuration, fluid passing through the screen is required to flow along the annulus to find a flow aperture into an interior flow bore. A static flow control device within the annulus between the sand screen and a first flow aperture dissipates flow energy by forcing the flow through a restricted area that helically winds about the flow annulus. Dissipation of the flow energy increases the pressure reduction from the screen into the production bore and reduces the flow velocity. In a second flow control configuration, flow control structure within the flow annulus obstructs all flow along the annulus. A third flow control configuration removes all flow restrictions within the flow annulus.

Journal ArticleDOI
TL;DR: In this article, a numerical method capable of simulating viscoelastic free surface flow of an Oldroyd-B fluid was developed for the computation of the non-Newtonian extra-stress components on rigid boundaries.
Abstract: This work is concerned with the development of a numerical method capable of simulating viscoelastic free surface flow of an Oldroyd-B fluid. The basic equations governing the flow of an Oldroyd-B fluid are considered. A novel formulation is developed for the computation of the non-Newtonian extra-stress components on rigid boundaries. The full free surface stress conditions are employed. The resulting governing equations are solved by a finite difference method on a staggered grid, influenced by the ideas of the marker-and-cell (MAC) method. Numerical results demonstrating the capabilities of this new technique are presented for a number of problems involving unsteady free surface flows.

Journal ArticleDOI
TL;DR: In this paper, a successful application of ultrasound Doppler velocimetry in liquid sodium flows is described, where the velocity profiles modified to a M-shape owing to the effect of an inhomogeneous magnetic field is investigated.
Abstract: A successful application of ultrasound Doppler velocimetry in liquid sodium flows is described. To obtain sufficient Doppler signals, different problems had to be solved: the transmission of the ultrasonic beam through the channel wall made of stainless steel, the acoustic coupling between the transducer and the channel wall, and the wetting of the inner surface of the wall by the liquid metal, respectively. A sodium flow in a square duct exposed to a transverse magnetic field is investigated. In accordance with the existing knowledge about MHD channel flows, we found that the velocity profiles modified to a M-shape owing to the effect of an inhomogeneous magnetic field.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the constant-wall-temperature convective heat transfer characteristics of a model gaseous flow in two-dimensional micro and nano-channels under hydrodynamically and thermally fully developed conditions.
Abstract: We investigate the constant-wall-temperature convective heat-transfer characteristics of a model gaseous flow in two-dimensional micro and nano-channels under hydrodynamically and thermally fully developed conditions Our investigation covers both the slip-flow regime 0≤Kn≤01, and most of the transition regime 01

Journal ArticleDOI
TL;DR: In this paper, a 3D stochastic fracture network model was built and validated for a gneissic rock mass based on the fracture data mapped from scanline surveys at the site.

Journal ArticleDOI
TL;DR: The linearized NavierStokes equations play a central role in describing the unsteady motion of a viscous fluid inside a porous tube and asymptotic solutions of these equations have been found.
Abstract: The linearized NavierStokes equations play a central role in describing the unsteady motion of a viscous fluid inside a porous tube. Asymptotic solutions of these equations have been found and here...

Journal ArticleDOI
TL;DR: In this article, the effect of rotation on heat transfer in a rectangular channel (aspect ratio = 4:1) with dimples was investigated. But the results were limited to two different surface configurations, including a smooth duct and a dimpled duct with a depth-to-print diameter (δ/Dp ) ratio of 0.3.
Abstract: As the world of research seeks ways of improving the efficiency of turbomachinery, attention has recently focused on a relatively new type of internal cooling channel geometry, the dimple. Preliminary investigations have shown that the dimple enhances heat transfer with minimal pressure loss. An investigation into determining the effect of rotation on heat transfer in a rectangular channel (aspect ratio = 4:1) with dimples is detailed in this paper. The range of flow parameters includes Reynolds number (Re = 5000–40000), rotation number (Ro = 0.04–0.3) and inlet coolant-to-wall density ratio (Δρ/ρ = 0.122). Two different surface configurations are explored, including a smooth duct and dimpled duct with dimple depth-to-print diameter (δ/Dp ) ratio of 0.3. A dimple surface density of 10.9 dimples/in2 was used for each of the principal surfaces (leading and trailing) with a total of 131 equally spaced hemispherical dimples per surface; the side surfaces are smooth. Two channel orientations of β = 90° and 135° with respect to the plane of rotation are explored to determine channel orientation effect. Results show a definite channel orientation effect, with the trailing-edge channel enhancing heat transfer more than the orthogonal channel. Also, the dimpled channel behaves somewhat like a 45° angled rib channel, but with less spanwise variations in heat transfer.Copyright © 2002 by ASME

Journal ArticleDOI
TL;DR: In this article, a two-dimensional serpentine duct model is designed to produce controlled separated flow in two configurations, in which the flow is either completely separated or has a separation bubble.
Abstract: Active control of separation in a duct flow is achieved using an array of fluidic actuators based on synthetic-jet technology. A two-dimensional serpentine duct model is designed to produce controlled separated flow in two configurations, in which the flow is either completely separated or has a separation bubble. An array of synthetic-jet actuators is placed within the separated flow domain in the diffuser section downstream of the onset of separation. Actuation leads to complete flow attachment up to U in =75 m/s (M≃0.2) and to partial reattachment up to U in = 105 m/s (M≃0.3)

Journal ArticleDOI
TL;DR: In this article, the effects of pipe flow on storm runoff generation and the roles of bedrock groundwater in rainfall-runoff phenomena in a steep headwater catchment in central Japan were examined.
Abstract: [1] It has been suggested that pipe flow and bedrock groundwater play important roles in storm runoff generation. We examined the effects of pipe flow on storm runoff generation and the roles of bedrock groundwater in rainfall-runoff phenomena in a steep headwater catchment in central Japan. Measurements of pore water pressures, pipe flow, and streamflow showed that when the total rainfall amount was 70 mm, the dominant runoff process shifted to pipe flow. Temperature measurements indicated four key points: (1) During base flow conditions (streamflow 0.2 mm h−1) the source of pipe flow was the same as the streamflow; (3) the transient groundwater at the upper hillslope was commonly dominated by the preevent soil water; and (4) only after the large storms with wet antecedent conditions, was water emerging from the bedrock and mixing with preevent soil water in the transient saturated area at the upper hillslope. Both the hydrometric and temperature measurements indicated that once pipe flow occurs, the contributing area of streamflow extended to upper hillslope, and the transient groundwater at the upper hillslope was delivered to the stream via preferential flow paths, shortcutting the normal mixing process through the soil matrix.

Journal ArticleDOI
TL;DR: In this paper, the authors present a visual, interactive, open-source numerical model that calculates steady state flow of magma and gas in vertical eruptive conduits and contains user-friendly utilities for quickly determining physical, thermodynamic, and transport properties of silicate melts, H2O gases, and melt-gas-crystal mixtures.
Abstract: [1] Numerical models that calculate the fluid dynamics of explosive volcanic eruptions have been used with increasing frequency to understand volcanic processes and evaluate volcanic hazards. Yet those who develop such models rarely make them publicly available so that they can be verified, used, and possibly improved by other scientists. In this paper I present a visual, interactive, open-source numerical model that calculates steady state flow of magma and gas in vertical eruptive conduits and contains user-friendly utilities for quickly determining physical, thermodynamic, and transport properties of silicate melts, H2O gases, and melt-gas-crystal mixtures. The model represents an advance over previously published conduit models by incorporating a non-Arrhenian viscosity relation for hydrous silicate melts, a relation between viscosity and volume fraction of gas that depends on Capillary number, and adiabatic temperature changes in the mixture using established thermodynamic relations for melts and H2O gas, respectively. Volcanologists who have not had access to conduit models have frequently approximated conduit flow using an analytical equation for incompressible, laminar, Newtonian pipe flow, which predicts that the mass flux is proportional to the fourth power of conduit radius and inversely proportional to mixture viscosity. The model presented here, which is not much more difficult to use than a back-of-the-envelope calculation, shows that the pipe-flow approximation significantly overestimates the sensitivity of mass flux to both conduit radius and mixture viscosity. Results from the model also show that viscous heating in the lower conduit, which is not considered in most other models, may increase the mass flux of large silicic eruptions by several percent and decrease the viscosity of the mixture at the fragmentation depth by a few tens of percent.

Journal ArticleDOI
TL;DR: In this paper, a direct numerical simulation is performed for a turbulent concentric annular pipe flow at Re D h =8900 for two radius ratios (R 1 / R 2 = 0.1 and 0.5).

Journal ArticleDOI
TL;DR: In this paper, a double pulse particle image velocimetry (PIV) system was used to clarify the spatial velocity distribution of surfactant solution flow in a two-dimensional channel.

Journal ArticleDOI
TL;DR: In this paper, the authors considered the flow of a third-grade fluid in a pipe with heat transfer and presented approximate analytical solutions for each case using perturbations, which were compared with the finite difference solutions given in Massoudi and Christie (Int. Non-Linear Mech. 30 (1995) 687-699) and within admissible parameter range, a close match was achieved.
Abstract: The flow of a third-grade fluid in a pipe with heat transfer is considered. Constant viscosity, Reynold's model viscosity and Vogel's model viscosity cases are treated separately. Approximate analytical solutions are presented for each case using perturbations. The criteria for which the solutions are valid are determined for the dimensionless parameters involved. The analytical solutions are contrasted with the finite difference solutions given in Massoudi and Christie (Int. J. Non-Linear Mech. 30 (1995) 687–699) and within admissible parameter range, a close match is achieved.

Journal ArticleDOI
TL;DR: In this article, the authors proposed a flow model based on the measured characteristic of the discharge coefficient versus the square root of the Reynolds number given by Merritt and proposed a single empirical flow formula for small pressure differences and the conventional square root law for turbulent conditions.