An experimental study of drag on a single tube and on a tube in an array under two-phase cross flow

In this work, the drag coefficient and the void fraction around a tube subjected to two-phase cross flow were studied for a single tube and for a tube placed in an array. The drag coefficients were determined by measuring the pressure distribution around the perimeter of the tube. Single tube drag data were taken when the tube was held both rigidly and flexibly. The test tube was made of acrylic and was 2.2 cm in diameter and 20 cm in length. In the experiments, liquid Reynolds number ranged from 430 to 21,900 for the single tube and liquid gap Reynolds number ranged from 32,900 and 61,600 for the tube placed in a triangular array. Free stream void fraction was varied from 0 to 0.4. At low Reynolds numbers, the ratio of two-phase to single-phase drag coefficient is found to be a strong function of εGr/Re2. However, at high Reynolds numbers only void fraction is the important parameter. Empirical correlations have been developed for the ratio of two-phase drag on a single tube and on a tube placed in an array.     

Prediction of liquid level distribution in horizontal gas-liquid stratified flows with interfacial level gradient

A one-dimensional momentum equation has been derived based on a two-fluid model and used to predict the axial distribution of liquid level or void fraction in steady, cocurrent, gas-liquid stratified flows in horizontal circular pipes and rectangular channels. The equation is carefully formulated to incorporate the effect of interfacial level gradient. Two different critical liquid levels are found from the momentum equation and are adopted as a boundary condition to calculate the liquid level or void fraction distribution upstream of the channel exit. The predicted void fraction distributions are compared with the experimental data obtained in a rectangular channel in this work and other data reported for large-diameter pipes. Good agreement is shown for air-kerosene, air-water and stream-water stratified flows with a smooth gas-liquid interface.     

Compressible gas-liquid mixture flow at abrupt pipe enlargements

A detailed investigation was made of the flow of compressible gas-liquid mixtures through sudden enlargements in diameter of circular pipes. One-dimensional analysis shows that the dimensionless pressure rise varies with mixture void fraction and mixture momentum, while the establishment of choking conditions at the enlargement is controlled by the length of pipe downstream in which frictional pipe flow occurs. The flows were found to exhibit two characteristic modes, jet flow and submerged flow, with intermediate flows displaying unsteady oscillation between these modes. The distance to the downstream position of maximum pressure increased steadily with mixture void fraction when the upstream pipe outlet was choked, varying from 5 to 50 times the downstream pipe diameter. If the flow was not choked, this distance was much smaller and showed discrete fixed values associated with the mode of flow.

One-dimensional analysis accurately predicted maximum pressure, but when flow was choked at the enlargement the calculation was sensitive to the pressure in the region of separated flow surrounding the central jet in the enlargement. Although analysis of maximum pressure in terms of flow expansion and normal shock gave a general indication of the maximum pressure (which was thus concluded to depend on the general flow processes expected in the enlargement), accurate prediction of maximum pressures will depend on empirical knowledge of the separated flow region pressures. The maximum pressure rise was found to be in the range extending down to 0.3 of the upstream pipe outlet pressure and reduced with void fraction; it was also influenced by the enlargement area ratio. Flows in the approach and outlet pipes were found to be compressible, frictional pipe flows of the Fanno type, with somewhat reduced friction factors occurring in the outlet pipe.     

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.     

Quantitative limits of thermal and fluid phenomena measurements using the neutron attenuation characteristics of materials

Temporal and spatial resolution of the neutron radiographic technique were investigated in order to apply this technique to the visualization and measurement of thermal and fluid phenomena. The temporal resolution of three imaging methods of temporally resolved neutron radiography-static neutron radiography with a pulsed neutron beam and high frame rate neutron radiography with either a pulsed or steady neutron beam-was studied. It was determined that the temporal resolution was determined by the sensitivity and light decay time of the image detector and statistical variation of neutrons, and the resolution limits of static and dynamic imaging methods were estimated to be a few microseconds and a few hundred microseconds, respectively. An image processing method was proposed to measure flow characteristics such as void fraction. By performing an error analysis to calculate the limit value of liquid film thickness that can be measured by neutron radiography, it was determined that the limit value of a rectangular channel gap or round tube diameter should be smaller than 3.25 or 4.00 mm, respectively, for measuring the void fraction of air-water flow within an error of 10%. The void fraction measuring method was experimentally confirmed by comparing the void fraction values in a rectangular duct with a 2.4-mm gap obtained by neutron radiography with those obtained by optical and conductance probe methods. It was shown quantitatively that the measurement error decreased when consecutive frames were temporally integrated.     

Flow pattern and flow characteristics for counter-current two-phase flow in a vertical round tube with wire-coil inserts

Flow pattern, void fraction and slug rise velocity on counter-current two-phase flow in a vertical round tube with wire-coil inserts are experimentally studied. Flow pattern and slug rise velocity are measured visually with a video camera. The void fraction is measured by the quick-closing valve method. Four kinds of coils with different coil pitches and coil diameters are used as inserts. The presence of wire-coil inserts induces disturbance into gas and liquid flows so that the shape and motion of gas slug or bubbles in a wire-coil inserted tube are quite different from those observed in a smooth tube without insert. The bubbly flow occurs in the low gas superficial velocity region in the wire-coil inserted tube, while the slug or churn/annular flow only appears in the smooth tube without insert over the all test range. The measured slug rise velocity in the wire-coil inserted tube is higher than that in the smooth tube. With modified mean flow velocity calculated with core area, the slug rise velocity in wire-coil tube inserted is in good agreement with Nicklin's correlation. The void fraction in a wire-coil inserted tube is lower than that in a smooth tube in the range of high gas superficial velocities. By introducing a simple assumption on considering the effective flowing area, the measured void fractions in a wire-coil inserted tube are in relatively good agreement with the predicted result based on the drift flux model proposed by others with the correlation for slug rise velocity given by others when the coil pitch is dense.     

Effect of bubble size on void fraction fluctuations in dispersed bubble flows

It is known that bubble size affects seriously the average void fraction in bubbly flows where buoyant velocities vary considerably with bubble size. On the contrary, there is no systematic literature report about bubble size effects on the intensity and frequency of void fraction fluctuations around the average void fraction. This work aims to provide such information. An electrical impedance technique is employed along with non-intrusive ring electrodes to register void fraction fluctuations down to 10⁻⁵. Bubble size fluctuations are estimated from high resolution optical images. Experiments are conducted in co-current upward dispersed bubble flow inside a 21 mm tube with average bubble size between ∼50 and ∼700 μm. Water and blood simulant are used as test liquids with velocity from ∼3 to ∼30 cm s⁻¹. The above resemble conditions of Decompression Sickness (DCS) in the bloodstream of human vena cava. It is found that the intensity and frequency of void fraction fluctuations vary appreciably with bubble size at constant gas and liquid flow rates. Moreover, these variations are not random but scale with bubble size. As a first step to quantify this effect, an empirical expression is derived that relates average bubble size to the ratio standard deviation/average value of void fraction.     

On the development of an objective flow regime indicator

A high intensity dual beam X-ray system was designed and constructed to make chordal-average void fraction measurements. This X-ray system employed a DC excited tube filament, full wave rectification and high voltage filtering to produce a stable photon source. The large photon flux produced by the X-ray system allowed analog linearization of the signal.A series of chordal-average void fraction measurements were made and used to generate probability density functions (PDF) and power spectral density (PSD) functions. The first four moments associated with these distributions were studied as possible flow regime indicators.The moments of the PDF indicated the various flow regime transitions. The moments of the PSD also show some flow regime transition information, but were sensitive to liquid phase velocity. The PDF variance, or second moment about the mean, was found to be the best indicator of flow regime. A variance of 0.04 appear to adequately discriminate between the bubbly, slug and annular flow regimes for low pressure air/water flow in a 2.54 cm I.D. vertical tube.     

Interfacial area concentration in gas–liquid bubbly to churn flow regimes in large diameter pipes

This study performed a survey on existing correlations for interfacial area concentration (IAC) prediction and collected an IAC experimental database of two-phase flows taken under various flow conditions in large diameter pipes. Although some of these existing correlations were developed by partly using the IAC databases taken in the low-void-fraction two-phase flows in large diameter pipes, no correlation can satisfactorily predict the IAC in the two-phase flows changing from bubbly, cap bubbly to churn flow in the collected database of large diameter pipes. So this study presented a systematic way to predict the IAC for the bubbly-to-churn flows in large diameter pipes by categorizing bubbles into two groups (group 1: spherical or distorted bubble, group 2: cap bubble). A correlation was developed to predict the group 1 void fraction by using the void fraction for all bubble. The group 1 bubble IAC and bubble diameter were modeled by using the key parameters such as group 1 void fraction and bubble Reynolds number based on the analysis of Hibiki and Ishii (2001, 2002) using one-dimensional bubble number density and interfacial area transport equations. The correlations of IAC and bubble diameter for group 2 cap bubbles were developed by taking into account the characteristics of the representative bubbles among the group 2 bubbles and the comparison between a newly-derived drift velocity correlation for large diameter pipes and the existing drift velocity correlation of Kataoka and Ishii (1987) for large diameter pipes. The predictions from the newly-developed two-group IAC correlation were compared with the collected experimental data in gas–liquid bubbly to churn flow regimes in large diameter pipes and their mean absolute relative deviations were obtained to be 28.1%, 54.4% and 29.6% for group 1, group 2 and all bubbles respectively.     

The influence of tube bundle geometry on cross-flow boiling heat transfer and pressure drop

An experimental investigation was performed to compare the boiling heat transfer coefficients and two-phase pressure drops from a square inline and a staggered tube bundle having the same tube pitch-to-diameter ratio (P/D = 1.30) and from two square inline tube bundles having different pitch-to-diameter ratios (P/D = 1.30 and 1.70). Except at the highest heat fluxes the heat transfer coefficients generally were higher in the staggered tube bundle than in the inline tube bundle and higher in the larger P/D tube bundle than in the smaller. As the heat flux increased, the differences decreased. The differences were attributed to the tradeoff between nucleation and convection. The staggered tube bundle had higher pressure drops than the inline bundle except at low mass velocities; the larger pressure drop in the staggered bundle was attributed to the combination of a larger void fraction and a larger friction multiplier, with the frictional component dominating at higher mass velocities. Comparing the inline tube bundle pressure drops, it was concluded that the larger P/D bundle had a larger void fraction than the smaller P/D tube bundle; no conclusions could be drawn regarding the relative magnitude of the two-phase fraction multiplier.     

Experimental analysis of local void fractions measurements for boiling hydrocarbons in complex geometry

The present paper is part of a research program on two-phase flows and heat transfer studies in tube bundles. An experimental study was carried out to analyse the void fraction for vertical two-phase flows. Boiling across a horizontal tube bundle for three hydrocarbons (n-pentane, propane and iso-butane) under saturated conditions is investigated. The experiments were performed on a tube bundle with 45 plain copper tubes of 19.05 mm outside diameter in a staggered configuration with a pitch to diameter ratio of 1.33. An optical probe has been developed to determine the local void fraction at the minimum cross section between the tubes.     

Time-resolved two-dimensional X-ray densitometry of a two-phase flow downstream of a ventilated cavity

To measure the void fraction distribution in gas–liquid flows, a two-dimensional X-ray densitometry system was developed. This system is capable of acquiring a two-dimensional projection with a 225 cm² area of measurement through 21 cm of water. The images can be acquired at rates on the order of 1 kHz. Common sources of error in X-ray imaging, such as X-ray scatter, image distortion, veiling glare, and beam hardening, were considered and mitigated. The measured average void fraction was compared successfully to that of a phantom target and found to be within 1 %. To evaluate the performance of the new system, the flow in and downstream of a ventilated nominally two-dimensional partial cavity was investigated and compared to measurements from dual-tip fiber optical probes and high-speed video. The measurements were found to have satisfactory agreement for void fractions above 5 % of the selected void fraction measurement range.     

An investigation of void fraction in liquid slugs for horizontal and inclined gas—liquid pipe flow

The void fraction in liquid slugs has been determined for air—water fiow in horizontal and near-horizontal pipes by a newly-developed conductance probe technique. A semi-empirical correlation has been developed and compared with the present measurements and available data. This correlation predicts reasonably well the observed effects of diameter, inclination and physical properties.     

An experimental study on developing air-water two-phase flow along a large vertical pipe: effect of air injection method

The flow structure in a developing air-water two-phase flow was investigated experimentally along a large vertical pipe (inner diameter, D_h: 0.48 m, ratio of length of flow path L to D_h: about 4.2). Two air injection methods (porous sinter injection and nozzle injection) were adopted to realize an extremely different flow structure in the developing region. The flow rate condition in the test section was as follows: superficial air velocity: 0.02–0.87 m/s (at atmospheric pressure) and superficial water velocity: 0.01–0.2 0.01–0.2 m/s, which covers the range of bubbly to slug flow in a small-scale pipe (D_h about 0.05 m).

No air slugs occupying the flow path were recognized in this experiment regardless of the air injection methods even under the condition where slug flow is realized in the small-scale pipe. In the lower half of the test section, the axial distribution of sectional differential pressure and the radial distribution of local void fraction showed peculiar distributions depending on the air injection methods. However, in the upper half of the test section, the effects of the air injection methods are small in respect of the shapes of the differential pressure distribution and the phase distribution. The comparison of sectional void fraction near the top of the test section with Kataoka's correlation indicated that the distribution parameter of the drift-flux model should be modeled including the effect of D_h and the bubble size distribution is affected by the air injection methods. The bubble size distribution is considered to be affected also by L/D_h based on comparison of results with Hills' correlation.     

Bubbly-to-cap bubbly flow transition in a long-26 m vertical large diameter pipe at low liquid flow rate

The concurrent upward two-phase flow of air and water in a long vertical large diameter pipe with an inner diameter (D) of 200 mm and a height (z) of 26 m (z/D = 130) was investigated experimentally at low superficial liquid velocities from 0.05009 to 0.3121 m/s and the superficial gas velocities from 0.01779 to 0.5069 m/s. The resultant void fractions range from 0.03579 to 0.4059. According to the observations using a high speed video camera, the flow regimes of bubbly, developing cap bubbly and fully-developed cap bubbly flows prevailed in the flows. The developing cap bubbly flow appeared as a flow regime transition from bubbly to fully-developed cap bubble flow in the vertical large diameter pipe. The developing cap bubbly flow changes gradually and lasts for a long time period and a wide axial region in the flow direction, in contrast to a sudden transition from bubbly to slug flows in a small diameter pipe. The analysis in this study showed that the flow regime transition depends not only on the void fraction but also on the axial distance in the flow and the pipe diameter. The axial flow development brings about the transition to happen in a lower void fraction flow and the increase of pipe diameter causes the transition to happen in a higher void fraction flow. The measured void fraction showed an N-shaped axial changing manner that the void fraction increases monotonously with axial position in the bubbly flow, decreases non-monotonously with axial position in the developing cap bubbly flow, and increases monotonously again with axial position in the fully-developed cap bubbly flow. The temporary void fraction decrease phenomenon in the transition region from bubbly to cap bubbly flow can be attributed to the formation of medium to large cap bubbles and their gradual growth into the maximum size of cap bubble and/or cluster of large cap bubbles in the developing cap bubbly flow. In order to predict the N-shaped axial void fraction changing behaviors in the flow regime transition from bubbly to cap bubbly flow, the existing 12 drift flux correlation sets for large diameter pipes are reviewed and their predictabilities are studied against the present experimental data. Although some drift flux correlation sets, such as those of Clark and Flemmer (1986) and Hibiki and Ishii (2003), can predict the present experimental data with reasonable average relative deviations, no drift flux correlation set for distribution parameter and drift velocity can give a reliable prediction for the observed N-shaped axial void fraction changing behaviors in the region from bubbly to cap bubbly flow in a vertical large diameter pipe.     

Vertical, Bubbly, Cross-Flow Characteristics over Tube Bundles

Two-phase flow over tube bundles is commonly observed in shell and tube-type heat exchangers. However, only limited amount of data concerning flow pattern and void fraction exists due to the flow complexity and the difficulties in measurement. The detailed flow structure in tube bundles needs to be understood for reliable and effective design. Therefore, the objective of this study was to clarify the two-phase structure of cross-flow in tube bundles by PIV. Experiments were conducted using two types of models, namely in-line and staggered arrays with a pitch-to-diameter ratio of 1.5. Each test section contains 20 rows of five 15 mm O.D. tubes in each row. The experiment’s data were obtained under very low void fraction (α<0.02). Liquid and gas velocity data in the whole flow field were measured successfully by optical filtering and image processing. The structures of bubbly flow in the two different configurations of tube bundles were described in terms of the velocity vector field, turbulence intensity and void fraction.     

Measurement of bubble size, velocity and concentration in flashing flow behind a sudden constriction

In the present paper the results of investigations in flashing flow behind a sudden constriction in vertical upflow are described. Flow visualization, laser-Doppler and phase-Doppler anemometry have been used to measure local bubble and fluid velocities, local bubble sizes and void fractions. The measurements were performed in the midplane of a two-dimensional channel with a 2:1 stepwise constriction.It was found that bubble nucleation takes place in the recirculation zone immediately behind the constriction, which is the location of the lowest static pressure. These bubbles are transported downstream by the mean flow field, while undergoing further growth. No additional nucleation was observed downstream of the recirculation zone. A periodic, cloudwise behaviour of the bubble formation was found which could be explained by the interaction between the bubble growth and the mean flow field. This interaction results in strong disturbances of the mean flow field, which show up as an increase of the fluctuating bubble velocity by a factor of 3 compared to single-phase measurements in a region of 10 step heights behind the constriction. However, these fluctuations appear more like a periodic change in the mean velocity rather than a higher turbulence level. The measured arithmetic mean bubble diameters rise from approx. 50 μm in the recirculation region to about 70–80 μm 50 step heights downstream. Maximum local bubble number density and void fraction were found to be 160001/cm³ and 0.8%, respectively.     

Incorporating truncated fractal distribution into Maxwell model to quantify thermal conductivity and its uncertainty in heterogeneous multiparticle systems

An approach is developed to examine the mean and uncertainty of thermal conductivity of a heterogeneous multiparticle system, where the particle concentration or void fraction is treated as a truncated fractal distribution. The truncated fractal distribution is then integrated into the Maxwell model, which is equivalent to a cell model in which the multiparticle system is conceptualized as a spherical fluid cell that envelopes a solid particle. The developed mean thermal conductivity is compared with four experimental data sets of liquid-saturated media from the literature. The effect of fractal characteristics is quantified and discussed. Incorporating particle concentration or void fraction truncated fractal distribution can better capture scatters in the experimental results. The thermal conductivity and its standard deviation decrease with increasing fractal dimensions. When the void fraction is truncated fractal, the uncertainty increases mostly in the low mean void fraction range and drops more quickly with the increasing mean void fraction compared to the case where the particle concentration is truncated fractal. In a typical case of multiparticle system when the solid particles are more conductive than the fluid, the faster increase rate of standard deviation with the ratio of solid over fluid conductivities occurs when the mean void fraction is smaller.     

Bubble and liquid turbulence characteristics of bubbly flow in a large diameter vertical pipe

The bubble and liquid turbulence characteristics of air–water bubbly flow in a 200 mm diameter vertical pipe was experimentally investigated. The bubble characteristics were measured using a dual optical probe, while the liquid-phase turbulence was measured using hot-film anemometry. Measurements were performed at six liquid superficial velocities in the range of 0.2–0.68 m/s and gas superficial velocity from 0.005 to 0.18 m/s, corresponding to an area average void fraction from 1.2% to 15.4%. At low void fraction flow, the radial void fraction distribution showed a wall peak which changed to a core peak profile as the void fraction was increased. The liquid average velocity and the turbulence intensities were less uniform in the core region of the pipe as the void fraction profile changed from a wall to a core peak. In general, there is an increase in the turbulence intensities when the bubbles are introduced into the flow. However, a turbulence suppression was observed close to the wall at high liquid superficial velocities for low void fractions up to about 1.6%. The net radial interfacial force on the bubbles was estimated from the momentum equations using the measured profiles. The radial migration of the bubbles in the core region of the pipe, which determines the shape of the void profile, was related to the balance between the turbulent dispersion and the lift forces. The ratio between these forces was characterized by a dimensionless group that includes the area averaged Eötvös number, slip ratio, and the ratio between the apparent added kinetic energy to the actual kinetic energy of the liquid. A non-dimensional map based on this dimensionless group and the force ratio is proposed to distinguish the conditions under which a wall or core peak void profile occurs in bubbly flows.     

Interfacial measurements in stratified types of flow. Part II: Measurements for R-22 and R-410A

A new optical void fraction measurement system has been coupled to a flow boiling test facility to obtain dynamic and time-averaged void fractions in a horizontal tube. A series of evaporation tests have been run for two refrigerants. R-22 was tested under mass velocity conditions of 70, 100, 150 and 200 kg/m² s and R-410A for 70, 150, 200 and 300 kg/m² s in a 13.6 mm diameter glass tube. Using our newly developed image processing system, about 227 000 images have been analyzed in this study to provide the same number of dynamic void fraction measurements. From these images, 238 time-averaged void fraction values have been obtained for vapor qualities from 0.01 to 0.95. These experimental points show very good agreement with the horizontal version of the Rouhani–Axelsson drift flux void fraction model.