Two-phase flow patterns across triangular tube bundles for air–water upward flow

This paper presents flow pattern experimental results obtained during two-phase upward flow across a horizontal tube bundle. Experiments were performed for flows across a normal triangular tube bundle with 19 mm OD tubes and transversal pitch of 24 mm. Results were obtained for gas and liquid superficial velocities ranging from 0.13 to 10.00 m/s and 0.02 to 1.50 m/s, respectively. Flow patterns were identified subjectively based on visual observations through side windows, and objectively using the k-means clustering method based on signals of a differential pressure transducer and a capacitive sensor. Bubbles, large bubbles, dispersed bubbles, churn, intermittent and annular flow patterns were identified subjectively. The clustering method satisfactorily identified groups of data corresponding to the distinct flow patterns, which were compared with predictive methods available in the open literature. New predictive methods for transitions between flow patterns are proposed based on the flow patterns identified objectively. The proposed methods predicted accurately the data obtained in the present study as well as experimental results and flow pattern maps available in the open literature for distinct geometries.     

Relative Permeability Analysis of Tube Bundle Models,Including Capillary Pressure

The analytical equations for calculating two-phase flow, including local capillary pressures, are developed for the bundle of parallel capillary tubes model. The flow equations that are derived were used to calculate dynamic immiscible displacements of oil by water under the constraint of a constant overall pressure drop across the tube bundle. Expressions for averaged fluid pressure gradients and total flow rates are developed, and relative permeabilities are calculated directly from the two-phase form of Darcy's law. The effects of pressure drop and viscosity ratio on the relative permeabilities are discussed. Capillary pressure as a function of water saturation was delineated for several cases and compared to a steady-state mercury-injection drainage type of capillary pressure profile. The bundle of serial tubes model (a model containing tubes whose diameters change randomly at periodic intervals along the direction of flow), including local Young-Laplace capillary pressures, was analyzed with respect to obtaining relative permeabilities and macroscopic capillary pressures. Relative permeabilities for the bundle of parallel tubes model were seen to be significantly affected by altering the overall pressure drop and the viscosity ratio; relative permeabilities for the bundle of serial tubes were seen to be relatively insensitive to viscosity ratio and pressure, and were consistently X-like in profile. This work also considers the standard Leverett (1941) type of capillary pressure versus saturation profile, where drainage of a wetting phase is completed in a step-wise steady fashion; it was delineated for both tube bundle models. Although the expected increase in capillary pressure at low wetting-phase saturation was produced, comparison of the primary-drainage capillary pressure curves with the pseudo-capillary pressure profiles, that are computed directly using the averaged pressures during the displacements, revealed inconsistencies between the two definitions of capillary pressure.     

Updated results on hydrodynamic mass and damping estimations in tube bundles under two-phase crossflow

Flow-Induced Vibration (FIV) is the most critical dynamic issue in the design of shell-and-tube heat exchangers. This fluid-structure phenomenon may generate high amplitude vibration of tubes or structural parts, which leads to fretting wear between the tubes and supports, noise or even fatigue failure of internal components. The study of this phenomenon is more challenging if considered that two-phase crossflow exists in many shell-and-tube heat exchangers. In this framework, the analysis of the influence of void fraction and flow patterns on FIV is of particular interest. In fact, void fraction and flow patterns do affect the dynamic parameters involved in tube vibration and, hence, the current vibration mechanism. However, in spite of the importance of devices subjected to two-phase flow, FIV under these conditions have not been entirely understood. In this paper, the results of an extensive experimental campaign, aiming at validating the flow pattern maps found in open literature, are presented. For this purpose, a normal triangular (transversal pitch per diameter ratio of 1.26) tube bundle subjected to two-phase air - water vertical upward crossflow is used. Structural sensors are used to measure the tube dynamic responses and estimate parameters such as hydrodynamic mass and damping ratios, which are strongly dependent on flow conditions. Theoretical models and data previously published are compared with the present experimental results, showing good agreement.     

Two-phase damping for internal flow: Physical mechanism and effect of excitation parameters

Two-phase flow induced-vibration is a major concern for the nuclear industry. This paper provides experimental data on two-phase damping that is crucial to predict vibration effects in steam generators. An original test section consisting of a tube subjected to internal two-phase flow was built. The tube is supported by linear bearings and compression springs allowing it to slide in the direction transverse to the flow. An excitation system provides external sinusoidal force. The frequency and magnitude of the force are controlled through extension springs. Damping is extracted from the frequency response function of the system. It is found that two-phase damping depends on flow pattern and is fairly proportional to volumetric fraction for bubbly flow. Measurements are completed by the processing of high-speed videos which allow to characterize the transverse relative motion of the gas phase with respect to the tube for bubbly flow. It is shown that the bubble drag forces play a significant role in the dissipation mechanism of two-phase damping.     

Studies on two-phase cross flow. Part I: Flow characteristics around a cylinder

A two-phase flow around a body has scarcely been studied until now, though the flow is used in many industrial components. The cross flows around a spacer in a fuel assembly of light water reactors (LWR) and tube supports in a steam generator are closely related to the long-term reliability and the safety. The present study has been planned to clarify the two-phase flow and heat transfer characteristics around a body including the unknown complicated flow behavior. In the first report, the flow characteristics near and behind a cylinder which was located in a vertical upward air-water bubbly flow were investigated. From the observation of the flow patterns and the measurements of the distributions of void fraction, liquid velocity and static pressure, it is revealed that the vortex flow and the change of the static pressure and liquid velocity distribution around the cylinder resulted in the large distortion of the void fraction distribution around the cylinder. The most noticeable phenomena in the wake were that the peaks of the local void fraction appeared in the vicinity of the cylinder surface near the separation point and in the wake behind the cylinder.     

加工后的双壁金属换热管在升温-降温过程中受到的力学影响

铅冷钠冷快堆核电设备中的蒸汽发生器,有着在液态金属和水之间进行热交换的作用,其换热部分由排列的换热管组成。贴合式的双壁管是一种具有高换热效率及抵抗管裂纹扩展的管材,适合于这种应用环境。这种管材的内外管间存在残余压力,这是内外管紧贴的标志。然而在经历升至高温又降温的过程后,内外管间残余压力有可能消失引起两管脱开。为了得知温度对贴合式双壁金属管的具体影响,本文设计了一种拉伸法来制备双壁管,并同时采用有限元数值模拟管的加工制备过程并得到了内外管间的残余应力,再对加温后降温的过程进行模拟,分析换热管残余应力和应变状态进行了分析的变化,并通过初步试验来进行验证。通过研究,结果表明温度变化引起的塑性变形是管间残余压力变化的主要原因。通过控制管的加工过程来控制管材加工程度的方法,可望应对温度变化对管稳定性的影响。     

Two-phase flow in inclined tubes with specific reference to condensation: A review

Tilting influences the flow patterns and thus the heat transfer and pressure drop during condensation in smooth tubes. However, few studies are available on diabatic two-phase flows in inclined tubes. The purpose of the present paper is to review two-phase flow in inclined tubes, with specific reference to condensation. Firstly, the paper reviews convective condensation in horizontal tubes. Secondly, an overview is given of two-phase flow in inclined tubes. Thirdly, a review is conducted on condensation in inclined tubes. It is shown for convective condensation in inclined tubes that the inclination angle influences the heat transfer coefficient. The heat transfer coefficient can be increased or decreased depending on the experimental conditions, and especially the flow pattern. Under certain conditions, an inclination angle may exist, which leads to an optimum heat transfer coefficient. Furthermore, this paper highlights the lack of experimental studies for the prediction of the inclination angle effect on the flow pattern, the heat transfer coefficient and the pressure drop in two-phase flows during phase change.     

Hydrodynamics of two-phase flow in vertical up and down-flow across a horizontal tube bundle

Flow patterns, void fraction and friction pressure drop measurements were made for an adiabatic, vertical up-and-down, two-phase flow of air–water mixtures across a horizontal in-line, 5×20 tube bundle with a pitch-to-diameter ratio of 1.28. The flow patterns in the cross-flow zones were obtained and flow pattern maps were constructed. The data of average void fraction were less than the values predicted by a homogenous flow model and showed a strong mass velocity effect, but were well-correlated in terms of the Martinelli parameter X_tt and liquid-only Froude number Fr_LO. The two-phase friction multiplier data could be well-correlated with the Martinelli parameter.     

Hydrodynamics of two-phase flow in vertical up and down-flow across a horizontal tube bundle

Flow patterns, void fraction and friction pressure drop measurements were made for an adiabatic, vertical up-and-down, two-phase flow of air–water mixtures across a horizontal in-line, 5×20 tube bundle with a pitch-to-diameter ratio of 1.28. The flow patterns in the cross-flow zones were obtained and flow pattern maps were constructed. The data of average void fraction were less than the values predicted by a homogenous flow model and showed a strong mass velocity effect, but were well-correlated in terms of the Martinelli parameter X_tt and liquid-only Froude number Fr_LO. The two-phase friction multiplier data could be well-correlated with the Martinelli parameter.     

Effect of diameter on two-phase pressure drop in narrow tubes

The effect of tube diameter on two-phase frictional pressure drop was investigated in circular tubes with inner diameters of 0.6, 1.2, 1.7, 2.6 and 3.4 mm using air and water. The gas and liquid superficial velocity ranges were 0.01-50 m/s and 0.01-3 m/s, respectively. The gas and liquid flow rates were measured and the two-phase flow pattern images were recorded using high-speed CMOS camera. Unique flow patterns were observed for smaller tube diameters. Pressure drop was measured and compared with various existing models such as homogeneous model and Lockhart-Martinelli model. It appears that the dominant effect of surface tension shrinking the flow stratification in the annular regime is important. It was found that existing models are inadequate in predicting the pressure drop for all the flow regimes visualized. Based on the analysis of present experimental frictional pressure drop data a correlation is proposed for predicting Chisholm parameter “C” in slug annular flow pattern. For all other flow regimes Chisholm’s original correlation appears to be adequate except the bubbly flow regime where homogeneous model works well. The modification results in overall mean deviation of pressure drop within 25% for all tube diameters considered. This approach of flow regime based modification of liquid gas interaction parameter appears to be the key to pressure drop prediction in narrow tubes.     

Effects of fluid properties and pipe diameter on two-phase flow patterns in horizontal lines

Extensive new data have been obtained on the transitions between two-phase flow patterns during co-current gas liquid flow in horizontal lines. Fluid properties were varied in a systematic manner to determine the effects of liquid viscosity, liquid density, interfacial tension and gas density. Line sizes varied from 1.2 to 5 cm for most of the tests. Visual observations were supplemented by an analysis of pressure drop fluctuations and hence the present data are believed to be less subjective than most past observations.

The transition data from the present tests, as well as available literature data, were compared to the most frequently used transition line correlations. In almost all cases serious deficiencies were observed. Revised dimensionless correlations which fit present data, and those previously available, are presented.     

Downwards co-current annular flow

This paper summarizes a study of the characteristics of downwards annular two-phase flow. The measurements reported are of film thickness, wave velocity and frequency, local pressure fluctuations, pressure gradient and liquid entrainment. The most important new feature of the work is the use of continuous data recording with either on-line or off-line statistical analysis. Experiments were carried out with air-water flows in tubes of 3.18 and 3.82 cm bore. It is shown that the interfacial characteristics of the flow may require at least 5 m for full development at some flow rates and most measurements were carried out with an entrance region of this length. It is also shown that the pressure fluctuations, characteristic of this two-phase flow regime, are primarily due to pressure surges caused by disturbance waves in the system passing through the exit device. A new regime map is proposed, based on experimental evidence, in which several distinctive types of interfacial behaviour are noted.     

Two-phase flow instabilities in a silicon microchannels heat sink

Two-phase flow instabilities are highly undesirable in microchannels-based heat sinks as they can lead to temperature oscillations with high amplitudes, premature critical heat flux and mechanical vibrations. This work is an experimental study of boiling instabilities in a microchannel silicon heat sink with 40 parallel rectangular microchannels, having a length of 15 mm and a hydraulic diameter of 194 μm. A series of experiments have been carried out to investigate pressure and temperature oscillations during the flow boiling instabilities under uniform heating, using water as a cooling liquid. Thin nickel film thermometers, integrated on the back side of a heat sink with microchannels, were used in order to obtain a better insight related to temperature fluctuations caused by two-phase flow instabilities. Flow regime maps are presented for two inlet water temperatures, showing stable and unstable flow regimes. It was observed that boiling leads to asymmetrical flow distribution within microchannels that result in high temperature non-uniformity and the simultaneously existence of different flow regimes along the transverse direction. Two types of two-phase flow instabilities with appreciable pressure and temperature fluctuations were observed, that depended on the heat to mass flux ratio and inlet water temperature. These were high amplitude/low frequency and low amplitude/high frequency instabilities. High speed camera imaging, performed simultaneously with pressure and temperature measurements, showed that inlet/outlet pressure and the temperature fluctuations existed due to alternation between liquid/two-phase/vapour flows. It was also determined that the inlet water subcooling condition affects the magnitudes of the temperature oscillations in two-phase flow instabilities and flow distribution within the microchannels.     

Numerical investigation of helical coil tube bundle in turbulent cross flow using large eddy simulation

A realistic five-layered helical coil tube bundle in turbulent cross flow is numerically investigated using large eddy simulation (LES). The geometry of the helical coil tube bundle, which is a 1/45 sector of a helical coil steam generator design for an advanced small modular reactor, has three counterclockwise helical layers and two clockwise helical layers stacked in alternating fashion in the radial direction. A Reynolds number of 21,800 is considered based on the mean gap velocity, diameter of the coil tube, and kinematic viscosity of the working fluid. The WALE sub-grid scale model is employed for LES to resolve scale smaller than the grid size. Additionally, LES for an ideal five-layered coil bundle model without a helical geometry is utilized to generate comparison data. Instantaneous flow fields are explored by analyzing velocity magnitude, vorticity, static pressure, and vortical structures. The detachments of vortical structures from the coil tube surface are observed by visualizing vortical structures and wall shear stress distributions simultaneously. Various turbulent statistics at multiple monitoring locations are presented with an emphasis on feature difference between realistic and ideal coil bundle models. The results of spectral analyses, including the power spectral density and continuous wavelet transform analyses, are addressed from the perspective of flow-induced vibration. The key feature of this paper is the discussion of three-dimensional effects based on the helical geometry of a coil bundle.     

Volume of fluid approach of boiling flows in concentrated solar plants

The Computational Fluid Dynamics (CFD) model proposed in this paper allows the flow patterns that evolve during progressive boiling inside large scale horizontal tubes to be simulated from the initial vapor generation stage to large vapor slugs. The volume of fluid (VOF) model was employed in combination with relatively simple hypothesis. The aim of the present work is to improve the design of receiver tubes at concentrated solar power plants with direct steam generation by simulating the evolution of flow regimes within these tubes. Despite numerous studies conducted in the past years on convective boiling, only a few made use of the VOF model to simulate large flow regime transitions. This work presents a preliminary and relatively qualitative approach to address this problem. Heat and mass transfer at the tube inner wall and at the liquid-gas interface were solved with the additional transport of two scalars. One accounts for the enthalpy field and the other represents the dispersed vapor phase of the liquid. This new phase was created at the wall surface of the liquid phase and rises up to the liquid-vapor interface. Different phenomena linked to the boiling process were taken into account: vapor creation at the wall, its transport, recondensation and the creation of large structures. This model was validated with boiling flow in a bent tube at different mass flow rates and heat fluxes, which allowed us to observe the evolution of two-phase flow patterns. Finally, numerical simulation of direct steam generation inside a concentrated solar plant receiver clearly showed the apparition and evolution of various two-phase flow patterns.     

Identification of flow regimes in vertical gas-liquid two-phase flow using differential pressure fluctuations

Differential pressure fluctuations are used to estimate flow regimes of nitrogen gas-water mixtures in a vertical pipe because the fluctuations seem to be closely connected with the flow configuration. The regimes of vertical two-phase flow are classified by the peculiar features of statistical properties of the fluctuations, which are calculated from the data of static pressures measured at four locations along the flow direction. The results show that it is possible to identify the flow pattern from the configuration of probability density functions, the order of variance and the average value of differential pressures because these statistical properties depend on a flow pattern.     

Two-phase flow pattern identification using continuous hidden Markov model

This paper presents a new method for identifying two-phase flow regimes from the instantaneous local fluid phase signals using continuous hidden Markov model (CHMM). CHMM is known to be a very strong pattern identifier. Air–water two-phase flows were realized in a transparent vertical tube. The tube length was 2 m, and its inner diameter was 19 mm. The instantaneous local fluid phase signals were collected using a single step index multimode optical fiber probe located at the center and mid-length of the tube. Signal features required in CHMM implementation were extracted using an innovative method. Various aspects of hidden Markov modeling and their effects on the results were studied. The flow pattern results are in very good agreement with photographs of the flow captured during the experiments. In sum, the results show that hidden Markov model has a good potential in identifying two-phase flow patterns.     

Photoelastic determination of stresses in the tube plate of a 70-mw steam generator

This article describes the examination, by three-dimensional photoelasticity, of the tube plate of a sodium steam generator. The tube plate is flat on the side of the tube bundle (121 tubes) and spherical (concave) on the other side. The photoelastic model was made by precision casting, there being no glued joints at the points which are important from the point of view of stresses, such as the tube-tube plate junctions. Both the stress distribution along important sections and the stress concentrations in different types of tube-tube plate junctions due to the internal pressure were determined. The investigation described in this article was carried out in the framework of the Association—Euratom TNO/RCN on Fast Reactors, on behalf of the TNO—Neratoom Sodium Technology Project.     

Relative Permeability Analysis of Tube Bundle Models

The analytical solution for calculating two-phase immiscible flow through a bundle of parallel capillary tubes of uniform diametral probability distribution is developed and employed to calculate the relative permeabilities of both phases. Also, expressions for calculating two-phase flow through bundles of serial tubes (tubes in which the diameter varies along the direction of flow) are obtained and utilized to study relative permeability characteristics using a lognormal tube diameter distribution. The effect of viscosity ratio on conventional relative permeability was investigated and it was found to have a significant effect for both the parallel and serial tube models. General agreement was observed between trends of relative permeability ratios found in this work and those from experimental results of Singhal et al. (1976) using porous media consisting of mixtures of Teflon powder and glass beads. It was concluded that neglecting the difference between the average pressure of the non-wetting phase and the average pressure of the wetting phase (the macro-scale capillary pressure) – a necessary assumption underlying the popular analysis methods of Johnson et al. (1959) and Jones and Roszelle (1978) – was responsible for the disparity in the relative permeability curves for various viscosity ratios. The methods therefore do not account for non-local viscous effects when applied to tube bundle models. It was contended that average pressure differences between two immiscible phases can arise from either capillary interfaces (micro-scale capillary pressures) or due to disparate pressure gradients that are maintained for a flow of two fluids of viscosity ratio that is different from unity.     

A semi-empirical model of two-phase flow of refrigerant-134a through short tube orifices

Measurements were conducted on Refrigerant-134a flowing through short tube orifices with length-to-diameter (L/D) ratios ranging from 5 to 20. Both two-phase and subcooled liquid flow conditions entering the short tube were examined for upstream pressures ranging from 896 to 1448 kPa and for qualities as high as 10% and subcoolings as high as 13.9°C. Data were analyzed as a function of the main operating variables and tube geometry. Semi-empirical models for both single- and two-phase flow at the inlet of the short tubes were developed to predict the mass flow of Refrigerant-134a through short tube orifices.

Choked flow conditions for Refrigerant-134a were typically established when downstream pressures were reduced below the saturation pressure corresponding to the inlet temperature. The flow rate strongly depended on the upstream pressure and upstream subcooling/quality. The mass flow also depended on cross-sectional area and short tube length. The mass flow model utilized a modified orifice equation that formulated the mass flow as a function of normalized operating variables and short tube geometry. For a two-phase flow entering the short tube, the modified orifice equation was corrected using a theoretically derived expression that related the liquid portion of the mass flow under two-phase conditions to a flow that would occur if the flow were a single-phase liquid. It was found that for sharp-edged short tubes with single- and two-phase flow, approximately 95% of the measured data and model's prediction were within ±15% of each other.