FLOW LIMITATION IN UNIFORM THICK-WALLED COLLAPSIBLE TUBES

To investigate the flow-rate limitation behaviour of the same thick-walled silicone-rubber tubes with aqueous flow as have previously been characterized by this laboratory in terms of their pressure-drop limitation behaviour, we measured how the pressure drop along the tube varied with flow rate, when both the upstream head and the external pressure were varied in such a way as to keep the transmural pressure at the upstream end to the tube at a series of constant values. Flow limitation with ‘negative effort dependence’ occurred, and it was found that the flow rate depended not just on the upstream transmural pressure but also on its history, in a hysteretic manner. Furthermore, when external pressure was being reduced to the required point, either flow limitation or absence of collapse could be obtained for the same values of upstream transmural pressure. The reductions in flow rate when flow limitation came into effect were typically much greater, relative to the flow-limited flow rates themselves, than has been reported by others using thinner tubes and lower flow rates. Large-amplitude self-excited oscillation was confined to this reducing-flow-rate transition when external pressure was being increased to set the required point, and largely confined to this transition when it was being reduced. Flow limitation was mostly associated with only small-amplitude noise-like fluctuations of the downstream pressure. The transition was analysed and explained by reference to modified control-space diagrams, which show explicitly all oscillatory and divergent instabilities as closed regions. The prominence of the transition in these results forced consideration of whether flow limitation occurs when the flow rate ceases to increase or when it becomes substantially independent of the pressure drop. In adopting the latter definition, we were led to hypothesize that the initial collapse-inducing instability is not the result of choking.     

Flow-rate limitation in a uniform thin-walled collapsible tube,with comparison to a uniform thick-walled tube and a tube of tapering thickness

Previous experiments on a tapered-thickness tube showed qualitatively different behaviour from that exhibited by a uniform thick-walled tube. To understand whether the taper or the thinner wall was responsible, similar aqueous flow-limitation experiments were conducted on a uniform thin-walled tube of the same material, with all other experimental set-up the same. As in the thick tube, there was a dramatic reduction in flow-rate when collapse and flow limitation started, but during external pressure reduction, the limited flow-rate progressively increased, so that as in the tapered-thickness tube, there was little flow-rate increase when collapse ceased. Hysteresis was thus a prominent feature of the relationship between flow-rate and pressure drop along curves of constant upstream transmural pressure. Flow-rate limitation was mainly accompanied by large-amplitude self-excited oscillation for both increasing and decreasing external pressure, to an even greater extent than in the tapered-thickness tube. Clusters of points sharing the same pair of upstream transmural pressure and upstream driving pressure values were found, indirectly implying as in the tapered-thickness tube that the flow-limited flow-rate for a given pressure drop was not uniquely determined by upstream transmural pressure. Negative effort dependence was observed in all three tubes, but in the thin tube, as in the tapered-thickness tube, it was obscured for some values of upstream transmural pressure where low-frequency single-collapse-per-cycle oscillations occurred. Thus, the qualitatively unique properties of the tapered-thickness tube appear to be confined to the relative lack of hysteresis, and the oscillatory regime in which collapse ceased before the downstream end. The rest of the observed behaviours seem to be characteristic simply of more compliant tubing.     

AQUEOUS FLOW LIMITATION IN A TAPERED-STIFFNESS COLLAPSIBLE TUBE

To find out whether the relation between flow-limited flow-rate and upstream transmural pressure was nonunique, as has been reported for air flow through a tapered-stiffness tube, and for comparison with a completed investigation of flow limitation in a uniform tube, flow limitation was observed in a tapered-stiffness tube. The tube was made by removal of material from the outside of a segment of the previous uniform tubing; thus the stiffness was on average less than that of the uniform tube. Therefore, quantitative differences in behaviour were expected, but in addition significant qualitative differences were found. Whereas in the uniform tube, large-amplitude oscillations were almost entirely confined to a transition from peak pre-collapse flow-rate to the largely pressure-drop-independent flow-limited flow-rate, the latter state here included operating points of all oscillatory types. The dramatic reduction in flow-rate at the transition was absent, and instead multiple (up to six) operating points occurred at a single value of upstream head and upstream transmural pressure. The plotting of control–space diagrams revealed a unique region of weak oscillations corresponding to the tube throat being located at an intermediate and time-varying point along the tube, with collapse as far as that point only. These oscillations were extremely variable in waveshape and frequency, often displayed intermittency, and depended sensitively on the precise operating point conditions. When in this mode, the tube upstream of the final collapse position exhibited small standing waves of area, so that up to four just-perceptible minima were seen.     

Étude tridimensionnelle des contraintes de cisaillement à la paroi dans un tube de section droite non circulaireThree-dimensional study of wall shear stresses in a tube of noncircular cross-section

This paper describes numerical solutions of the Navier–Stokes equations for incompressible steady flow through a rigid smooth straight tube with an axially uniform non-circular cross section which mimics collapsed veins at peculiar values of the transmural pressure. One of the peculiar values of the transmural pressure produces a contact of the opposite walls along a straight segment. This article deals with the space variations of the wall shear stress induced along the wetted perimeter of the cross section as well as in the streamwise direction especially in the entry length. The motivation of this study is to provide the data for experimental works on flow-subjected endothelial cell culture when the space variations of the wall shear stress are non-uniform. To cite this article: S. Naili et al., C. R. Mecanique 330 (2002) 483–490.     

Numerical study of the mechano-acoustic coupled resonance of a tube-membrane system

The acoustic behaviour of a tube is well known since antiquity, nevertheless, differences appear when a flexible element interferes this behaviour. The tube acoustic resonance is altered by the mechanic resonance of this element due to complex mechano-acoustic effects. In this paper, an experiment is designed to evaluate the response of a tube with a membrane at the end, subject to sound pressure at the open side of the tube. A baffle isolates both sides of the tube. A comprehensive numerical study is made to understand the behaviour of different parameter of the system as the tube length and those related with the membrane stiffness and mass. A proper numerical methodology has been developed and is described and justified. The study of the simple tube system is also accomplished finding that results match with the theoretical expected values with an effective length correction. Regarding the behaviour of the tube-membrane system, it is found that the membrane is not a transparent element, but its contribution as closing element is limited to a 10 dB sound pressure drop compared with the absence of membrane. The acoustic resonance of the tube is affected by the membrane resonance but a general pattern similar to the open-closed case is observed. No presence of the open-open case is found.     

Modeling Non-Darcian Single- and Two-Phase Flow in Transparent Replicas of Rough-Walled Rock Fractures

While it is generally assumed that in the viscous flow regime, the two-phase flow relative permeabilities in fractured and porous media depend uniquely on the phase saturations, several studies have shown that for non-Darcian flows (i.e., where the inertial forces are not negligible compared with the viscous forces), the relative permeabilities not only depend on phase saturations but also on the flow regime. Experimental results on inertial single- and two-phase flows in two transparent replicas of real rough fractures are presented and modeled combining a generalization of the single-phase flow Darcy’s law with the apparent permeability concept. The experimental setup was designed to measure injected fluid flow rates, pressure drop within the fracture, and fluid saturation by image processing. For both fractures, single-phase flow experiments were modeled by means of the full cubic inertial law which allowed the determination of the intrinsic hydrodynamic parameters. Using these parameters, the apparent permeability of each fracture was calculated as a function of the Reynolds number, leading to an elegant means to compare the two fractures in terms of hydraulic behavior versus flow regime. Also, a method for determining the experimental transition flow rate between the weak inertia and the strong inertia flow regimes is proposed. Two-phase flow experiments consisted in measuring the pressure drop and the fluid saturation within the fractures, for various constant values of the liquid flow rate and for increasing values of the gas flow rate. Regardless of the explored flow regime, two-phase flow relative permeabilities were calculated as the ratio of the single phase flow pressure drop per unit length divided by the two-phase flow pressure drop per unit length, and were plotted versus the measured fluid saturation. Results confirm the dependence of the relative permeabilities on the flow regime. Also the proposed generalization of Darcy’s law shows that the relative permeabilities versus fluid saturation follow physical meaningful trends for different liquid and gas flow rates. The presented model fits correctly the liquid and gas experimental relative permeabilities as well as the fluid saturation.     

Drop size measurements for annular two-phase flow in a 20 mm diameter vertical tube

As part of a study on the effect of tube diameter on the mean drop size and liquid film flow rate in annular two-phase flow, data was obtained for the vertical upflow of an air-water system in a 20 mm internal diameter tube, held at a pressure of 1.5 bar and ambient temperature. This complements data taken in earlier experiments on 10 and 32 mm tubes. Increases in the superficial gas velocity caused reductions in the mean drop size whilst increasing the liquid mass flux in all but the lowest gas velocity case, caused the drop size to rise. Comparisons were made between the current drop size data and that from a 10 mm and 32 mm internal diameter tube, for similar conditions of temperature and pressure. The current drop size measurements, which fall between those from earlier work, confirm the dependence of drop size on tube diameter. The performance of several drop size correlations have been tested. Because the correlations do not account for the influence of tube diameter, they fail to predict the drop size data accurately. The influence of gas and liquid flow rate on the measured film flow rate show trends similar to those seen in data from the 10 mm and 32 mm diameter tubes. Models, to calculate the entrained liquid mass flux were tested; good predictions were given.     

Determination of slug permeability factor for pressure drop prediction of slug flow pneumatic conveying

Current models for pressure drop prediction of slug flow pneumatic conveying in a horizontal pipeline system assume some type of steady state conditions for prediction, which limits their capability for increased predictive accuracy relative to experimental data. This is partly because of the nature of slug flow pneumatic conveying system, which, as a dynamic system, never becomes stable. By utilising conservation of mass （airflow）, a dynamic pressure analysis model is proposed on the basis of the derivative of the upstream pressure behaviour. The rate of air permeation through slug, one of the important factors in the conservation model, is expressed as a function of a slug permeability factor. Other factors such as slug velocity, slug length and the fraction of stationary layer were also considered. Several test materials were conveyed in single-slug tests to verify the proposed pressure drop model, showing good agreement between the model and experimental results.     

Determination of slug permeability factor for pressure drop prediction of slug flow pneumatic conveying

Current models for pressure drop prediction of slug flow pneumatic conveying in a horizontal pipeline system assume some type of steady state conditions for prediction,which limits their capability for increased predictive accuracy relative to experimental data.This is partly because of the nature of slug flow pneumatic conveying system,which,as a dynamic system,never becomes stable.By utilising conservation of mass (airflow),a dynamic pressure analysis model is proposed on the basis of the derivative of the upstream pressure behaviour.The rate of air permeation through slug,one of the important factors in the conservation model,is expressed as a function of a slug permeability factor.Other factors such as slug velocity,slug length and the fraction of stationary layer were also considered.Several test materials were conveyed in single-slug tests to verify the proposed pressure drop model,showing good agreement between the model and experimental results.     

Effect of pressure-dependent slip on flow curve multiplicity

Various microstructural pictures for slip at polymer/solid interfaces lead to relations which have a region where multiple values of slip velocity are predicted for the same shear stress. This leads to the expectation of multivalued flow curves, which has been verified in specific cases by numerous researchers. We study the effect of pressure dependence on flow curve multiplicity using a simple multivalued slip relation to model the phenomena of hysteresis and spurt flow in polymer extrusion. A continuation technique is used to trace out the boundaries of the region of flow curve multiplicity as pressure drop and die length to diameter (L/D) ratio are changed. Results for Newtonian, shear thinning and viscoelastic constitutive equations show that, despite the multivalued nature of the slip model, multiplicity (and thus hysteresis) is absent at high L/D.  For the sake of completeness, we also carry out time-dependent simulations at constant piston speed taking fluid compressibility into account. These simulations show that oscillations in the pressure drop and exit volumetric flow rate result only if the system is operated in the multiplicity region of the steady state flow curve, in agreement with the results of similar simulations by researchers using various multivalued slip models without pressure dependence. The results demonstrate that a multivalued slip model does not guarantee multiplicity in the flow curve for the constant pressure drop operation, nor oscillations for constant piston speed operation. Received: 18 August 1997 Accepted: 30 March 1998     

On stability of elastic domain during isothermal solid-solid phase transformation in a tube configuration

Under isothermal quasi-static stretching the phasetransition of a superelastic NiTi tube involves the formation(during loading) and vanishing(in unloading) of a high strain(martensite) domain.The two events are accompanied by arapid stress drop/rise due to the formation/vanishing of domain fronts.From a thermodynamic point of view,both areinstability phenomena that occur once the system reaches itscritical state.This paper investigates the stability of a shrinking cylindrical domain in a tube configuration during unloading.The energetics and thermodynamic driving force of thecylindrical domain are quantified by using an elastic inclusion model.It is demonstrated that the two domain fronts exhibit strong interaction when they come close to each other,which brings a peak in the total energy and a sign changein the thermodynamic driving force.It is proved that suchdomain front interaction plays an important role in controlling the stability of the domain and in the occurrence of stressjumps during domain vanishing.It is also shown that the process is governed by two nondimensional length scales(thenormalized tube length and normalized wall-thickness) andthat the length scale dependence of the critical domain lengthand stress jump for the domain vanishing can be quantifiedby the elastic inclusion model.     

Experimental two-phase pressure gradients during evaporation of pure and mixed refrigerants in a smooth horizontal tube. Comparison with correlations

The paper reports the results of an experimental study on pressure drop during horizontal flow boiling of refrigerants R22, R507, R404A, R134a, R407C and R410A. The test section is a smooth, horizontal, stainless steel tube (6 mm I.D., 6 m length) uniformly heated by Joule effect. The experimental tests are carried out at an almost constant evaporating pressure of 7.0 bar varying the mass flow rate in the range 280–1,080 kg/m² s. The experimental comparison clearly shown that the pressure drop of R22 is significantly higher as compared to all the other fluids. The results are compared against well-known pressure drop prediction methods. The available correlations can be used for both pure fluids and mixtures with no corrective factors, provided the mixture properties are evaluated at local compositions. The Chawla friction correlation is the best-fitting of our experimental data in combination with the heterogeneous momentum pressure drop model on the basis of the Rouhani-Axelsson void fraction correlation.     

Characteristics of HPAM dilute polymer solutions in three elongational flow situations

Previous work has shown that anomalous pressure behaviour occurs when dilute polymer solutions are subjected to elongational flows such as those existing upstream of a capillary tube entrance, of an orifice and of the stagnation point of a Pilot tube probe. Tests have been conducted with aqueous solutions of HPAM at various concentrations using the above three flow geometries. It is shown that pressure anomalies occured when critical values of the ratio between a velocity and length scale, representative of the strain rate, are exceeded. They are proportional to the power of the strain rate with an exponent larger than one. Based on previous and present results, it appears that the polymer solutions' behaviour may be characterized by three parameters: an anomalous stress magnitude, a relaxation time (inverse of the critical strain rate) and the exponent of the power law. The first two parameters depend on the polymer type, concentration and molecular weight, while the third depends only on the polymer type. The anomalous pressure is also affected by the conformation of the molecules as shown by results obtained with HPAM solutions containing varied amounts of NaCl.     

Augmented heat transfer and pressure drop of strip-type inserts in the small tubes

An experiment is carried out to investigate the characteristics of the augmentation of heat transfer and pressure drop by different strip-type inserts in small tube having an inside diameter of 2.0 mm. The effects of the imposed wall heat flux, mass flux, strip inserts with various configurations (heights, widths, pitches) on the measured augmentative heat transfer and pressure drop are examined in detail. In order to obtain insight into the fluid flow phenomena, flow visualization was also made to observe the detailed fluid flow characteristics of the present tubes inserted with strip-type inserts. In addition, comparisons are made with a plain tube having the same length, heat transfer area and experimental conditions. The measured heat transfer coefficients and pressure drops for this small pipe are also emphasized to compare with those for larger pipes. Furthermore, in order to compare results from the different configurations of strip-type inserts, several enhancement factors and performance ratios are defined to account for the effects of augmentation. Moreover, correlation equations for the heat transfer coefficient and pressure drop of the present study are proposed.The financial support extended by the National Science Council of the Republic of China through grant No. NSC-89-2212-E-230-004.     

Viscous flow of a suspension of liquid drops in a cylindrical tube

Viscous flow in a circular cylindrical tube containing an infinite line of viscous liquid drops equally spaced along the tube axis is considered under the assumption that a surface tension, sufficiently large, holds the drops in a nearly spherical shape. Three cases are considered: (1) axial translation of the drops, (2) flow of the external fluid past a line of stationary drops, and (3) flow of external fluid and liquid drops under an imposed pressure gradient. Both fluids are taken to be Newtonian and incompressible, and the linearized equations of creeping flow are used.The results show that both drag and pressure drop per sphere increase as the spacing increases at fixed radius and also increase as the radius of the drop increases. The presence of the internal motion reduces the drag and pressure gradients in all cases compared to rigid spheres, particularly for drops approaching the size of the tube.     

Nonlinear dynamics and conformational changes of linear entangled polymers using the Rolie-Poly model with an “effective” maximum contour length

The extended Rouse-CCR tube model for linear entangled polymers recently proposed by the authors (Kabanemi and Hétu, J Non Newtonian-Fluid Mech 160:113–121, 2009), designed to capture the progressive changes in the average internal structure (kinked state) of polymer chains, is here used to analyze, by means of a time-dependent three-dimensional finite element method, chain segment dynamics, pressure drop, and stability of flow through a 4:1:4 constriction in a tube. The model predicts an enhancement of the pressure drop in the stretch-dominated flow regime, which is also observed experimentally. This excess pressure drop was not associated with the onset of flow instability. The model also predicts kinked configurations within chain segments in the entry section to the constriction tube, at the inception of flow, and prior to the development of upstream vortices. It is also shown how these kinked configurations within chain segments influence pressure drop transients.     

A single segment differential tube model with interchain tube pressure effect

We develop a single segment differential tube model including interchain tube pressure effect (ITPE) [G. Marrucci, G. Ianniruberto, Interchain pressure effect in extensional flows of entangled polymers, Macromolecules 36 (2004) 3934–3942], able to describe the non-linear behaviour of entangled linear polymers. The model accounts for the effect of flow on the tube length and diameter. It is presented in two versions, depending on which tube dimension is assumed to deform affinely. The classical relaxation mechanisms, i.e., reptation, stretch dynamics, convective constraint release (CCR), as well as finite extensibility, are incorporated in a simple manner; hence the model allows an explicit comparison of the relative importance of various effects. A striking result is the insignificance of finite extensibility and the detrimental influence of CCR for moderately entangled systems when ITPE is taken into account. For highly entangled systems, CCR regains importance to avoid the well-known shear stress instability. The proposed model is able to make quantitative predictions of steady elongational and shear data for monodisperse melts, while transient values are less accurate but within experimental errors.     

Studies on two-phase co-current air/non-Newtonian shear-thinning fluid flows in inclined smooth pipes

In this work, co-current flow characteristics of air/non-Newtonian liquid systems in inclined smooth pipes are studied experimentally and theoretically using transparent tubes of 20, 40 and 60 mm in diameter. Each tube includes two 10 m long pipe branches connected by a U-bend that is capable of being inclined to any angle, from a completely horizontal to a fully vertical position. The flow rate of each phase is varied over a wide range. The studied flow phenomena are bubbly flow, stratified flow, plug flow, slug flow, churn flow and annular flow. These are observed and recorded by a high-speed camera over a wide range of operating conditions. The effects of the liquid phase properties, the inclination angle and the pipe diameter on two-phase flow characteristics are systematically studied. The Heywood–Charles model for horizontal flow was modified to accommodate stratified flow in inclined pipes, taking into account the average void fraction and pressure drop of the mixture flow of a gas/non-Newtonian liquid. The pressure drop gradient model of Taitel and Barnea for a gas/Newtonian liquid slug flow was extended to include liquids possessing shear-thinning flow behaviour in inclined pipes. The comparison of the predicted values with the experimental data shows that the models presented here provide a reasonable estimate of the average void fraction and the corresponding pressure drop for the mixture flow of a gas/non-Newtonian liquid.     

Flow condensation heat transfer characteristics of hydrocarbon refrigerants and dimethyl ether inside a horizontal plain tube

Flow condensation heat transfer coefficients (HTCs) and pressure drop of R22, propylene, propane, DME and isobutane are measured on a horizontal plain tube. The main test section in the experimental flow loop is made of a plain copper tube of 8.8 mm inner diameter and 530 mm length. The refrigerant is cooled by passing cold water through the annulus surrounding the test section. Tests are performed at a fixed refrigerant saturation temperature of 40 ± 0.2 °C with mass fluxes of 100, 200, and 300 kg/m² s and heat flux of 7.3–7.7 kW/m². The heat transfer and pressure drop data are obtained in the vapor quality range of 10–90%. Test results show that for a given mass flux the flow condensation HTCs of propylene, propane, DME and isobutane are higher than those of R22 by up to 46.8%, 53.3%, 93.5% and 61.6%, respectively. Also well-known correlations developed based upon conventional fluorocarbon refrigerants predict the present data within a mean deviation of 33%. Finally, the pressure drop increases as the mass flux and quality increase and isobutane shows the highest pressure drop due to its lowest vapor pressure among the fluids tested.