Two-phase damping and interface surface area in tubes with vertical internal flow

Two-phase flow is common in the nuclear industry. It is a potential source of vibration in piping systems. In this paper, two-phase damping in the bubbly flow regime is related to the interface surface area and, therefore, to flow configuration. Experiments were performed with a vertical tube clamped at both ends. First, gas bubbles of controlled geometry were simulated with glass spheres let to settle in stagnant water. Second, air was injected in stagnant alcohol to generate a uniform and measurable bubble flow. In both cases, the two-phase damping ratio is correlated to the number of bubbles (or spheres). Two-phase damping is directly related to the interface surface area, based on a spherical bubble model. Further experiments were carried out on tubes with internal two-phase air–water flows. A strong dependence of two-phase damping on flow parameters in the bubbly flow regime is observed. A series of photographs attests to the fact that two-phase damping in bubbly flow increases for a larger number of bubbles, and for smaller bubbles. It is highest immediately prior to the transition from bubbly flow to slug or churn flow regimes. Beyond the transition, damping decreases. It is also shown that two-phase damping increases with the tube diameter.     

MODELLING TWO-PHASE FLOW-EXCITED DAMPING AND FLUIDELASTIC INSTABILITY IN TUBE ARRAYS

This paper reports the results of an experimental study of the flow-induced vibration of a heat exchanger tube array subjected to two-phase cross-flow of refrigerant 11. The primary concern of the research was to develop a methodology for predicting the critical flow velocities for fluidelastic instability which better characterize the physics of two-phase flows. A new method is proposed for calculating the average fluid density and equivalent flow velocity of the two-phase fluid, using a newly developed void fraction model to account for the difference in velocity between the gas and liquid phases. Additionally, damping measurements in two-phase flow were made and compared with the data of other researchers who used a variety of modelling fluids. The results show that the two-phase damping follows a similar trend with respect to homogeneous void fraction, and when normalized, agree well with the data in the literature. The fluidelastic threshold data of several researchers who used a variety of fluids, is re-examined using the proposed void fraction model, and the results show a remarkable change in trend with flow regime. The data corresponding to the bubbly flow regime shows no significant deviation from the trend established by Connors' theory. However, the data corresponding to the intermittent flow regime show a significant decrease in stability which is nearly independent of the mass-damping parameter. It is believed that the velocity fluctuations that are inherent in the intermittent flow regime are responsible for tripping the instability, causing lower than expected stability of the bundle.     

SOME ASPECTS OF HEAT-EXCHANGER TUBE DAMPING IN TWO-PHASE MIXTURES

Two-phase flow exists in many shell-and-tube heat exchangers. To avoid excessive flow-induced vibration, it is necessary to have information on damping. A simple experiment was undertaken to study the effect of several parameters such as void fraction, surface tension, tube frequency and confinement on damping in two-phase mixtures. The experiment consisted of a cantilevered tube immersed in a two-phase mixture generated by bubbling air through water. It is found that void fraction and flow regime are dominant parameters. Surface tension is also important. The results are presented in detail in the paper.     

Scaling of damping induced by bubbly flow across tubes

The damping of tubes subjected to two-phase air–water bubbly cross-flow is investigated with the use of an experimental database from several authors. A new definition of damping in stagnant flow is proposed using an extrapolation of the measured values at low dimensionless flow velocities. This approach yields values of damping substantially lower than those currently defined in the literature. They are found to vary continuously with void fraction, within the bubbly flow regime. These data are used to compare several models of the equivalent viscosity of a two-phase mixture. The effect of the flow velocity is then analysed up to fluidelastic instability. It is observed that, using scaling factors based on the characteristics of the liquid phase, fluidelastic effects of bubbly flows are closely related to those known in single-phase flows.     

Analysis of frictionless two-phase flow in tubes under centrifugal acceleration and minimum heating for choked flow

To determine the void fraction in a tube of a rotating heat exchanger, an analytical investigation was undertaken to model frictionless two-phase flow boiling. Steady, one-dimensional separated two-phase conservation equations in differential form, were first applied to a stationary system. The equations were integrated between the inlet and exit of the flow channel to yield three coupled algebraic equations. The algebraic equations were then modified to represent rotating systems. To obtain closure, the velocity ratio, mass quality and void fraction are defined as a function of pressure.

A numerical technique was used to solve the equations. Sample results are presented in a graph of mass quality versus void fraction. The graph demonstrates that a minimum heat input must be exceeded to change from a single-phase flow to saturated two-phase flow boiling. Also, the void fraction was found to increase for increasing heat input, decreasing mass flow rate, increasing inlet mass quality and decreasing pressure difference between the inlet and exit.     

Prediction of refrigerant void fraction in horizontal tubes using probabilistic flow regime maps

A state of the art review of two-phase void fraction models in smooth horizontal tubes is provided and a probabilistic two-phase flow regime map void fraction model is developed for refrigerants under condensation, adiabatic, and evaporation conditions in smooth, horizontal tubes. Time fraction information from a generalized probabilistic two-phase flow map is used to provide a physically based weighting of void fraction models for different flow regimes. The present model and void fraction models in the literature are compared to data from multiple sources including R11, R12, R134a, R22, R410A refrigerants, 4.26–9.58 mm diameter tubes, mass fluxes from 70 to 900 kg/m² s, and a full quality range. The present model has a mean absolute deviation of 3.5% when compared to the collected database.     

Study of two-phase flows in reduced gravity using ground based experiments

Experimental studies have been carried out to support the development of a framework of the two-fluid model along with an interfacial area transport equation applicable to reduced gravity two-phase flows. The experimental study simulates the reduced gravity condition in ground based facilities by using two immiscible liquids of similar density namely, water as the continuous phase and Therminol 59^® as the dispersed phase. We have acquired a total of eleven data sets in the bubbly flow and bubbly to slug flow transition regimes. These flow conditions have area-averaged void (volume) fractions ranging from 3 to 30% and channel Reynolds number for the continuous phase between 2,900 and 8,800. Flow visualization has been performed and a flow regime map developed which is compared with relevant bubbly to slug flow regime transition criteria. The comparison shows that the transition boundary is well predicted by the criterion based on critical void fraction. The value of the critical void fraction at transition was experimentally determined to be approximately 25%. In addition, important two-phase flow local parameters, including the void fraction, interfacial area concentration, droplet number frequency and droplet velocity, have been acquired at two axial locations using state-of-the-art multi-sensor conductivity probe. The radial profiles and axial development of the two-phase flow parameters show that the coalescence mechanism is enhanced by either increasing the continuous or dispersed phase Reynolds number. Evidence of turbulence induced particle interaction mechanism is highlighted. The data presented in this paper clearly show the marked differences in terms of bubble (droplet) size, phase distribution and phase interaction in two-phase flow between normal and reduced gravity conditions.     

Microgravity flow regime data and analysis

To utilize the advantageous properties of two-phase flow in microgravity applications, the knowledge base of two-phase flow phenomena must be extended to include the effects of gravity. In the experiment described, data regarding the behavior of two-phase flow in a conduit under microgravity conditions (essentially zero gravity) are explored. Of particular interest, knowledge of the void fraction of the gas and liquid in a conduit is necessary to develop models for heat and mass transfer, pressure drop, and wall shear. An experiment was conducted under reduced gravity conditions to collect data by means of a capacitance void fraction sensor and high speed visual imagery. Independent parameters were varied to map the flow regime regions. These independent parameters include gas and liquid volumetric flow rates and saturation pressures. Void fraction measurements were taken at a rate of 100 Hz with six sensors at two locations along the conduit. Further, statistical parameters were developed from the void fraction measurements. Statistical parameters such as variance, signal-to-noise ratio, half height value, and linear area difference were calculated and found to have characteristics allowing flow regime identification.     

The analysis of two-dimensional two-phase flow in horizontal heated tube bundles using drift flux model

This paper presents the experimental study and numerical simulation of two-dimensional two-phase flow in horizontal heated tube bundles. In the experiments, two advanced measuring systems with a single-fibre optical probe and a tri-fibre-optical-probe were developed to measure respectively the local void fraction and vapor bubble velocities among the heated tube bundles. In accordance with the internal circulation characteristics of two-phase flow in the tube bundles, a mathematical model of two-dimensional two-phase low Reynolds number turbulent flow based on the modified drift flux model and the numerical simulation method to analyze the two-phase flow structures have been developed. The modified drift flux model in which both the acceleration by gravity and the acceleration of the average volumetric flow are taken into account for the calculation of the drift velocities enables its application to the analysis of multi-dimensional two-phase flow. In the analysis the distributions of the vapor-phase velocity, liquid-phase velocity and void fraction were numerically obtained by using the modified drift flux model and conventional drift flux model respectively and compared with the experimental results. The numerical analysis results by using the modified drift flux model agree reasonably well with the experimental investigation. It is confirmed that the modified drift flux model has the capability of correctly simulating the two-dimensional two-phase flow. Received on 3 September 1998     

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.     

Numerical simulation of circulation in gas-liquid column reactors: isothermal, bubbly, laminar flow

The gas-liquid flow inside a circular, isothermal column reactor with a vertical axis has been studied using numerical simulations. The flow is assumed to be in the laminar, bubbly flow regime which is characterized by a suspension of discrete air bubbles in a continuous liquid phase such as glycerol water. The mathematical formulation is based on the conservation of mass and momentum principle for the liquid phase. The gas velocity distribution is calculated via an empirically prescribed relative velocity as a function of void fraction. The interface viscous drag forces are prescribed empirically. For some cases a profile shape is assumed for the void ratio distribution. The influence of various profile shapes is investigated. The results are compared with those where the void ratio distribution is calculated from the conservation of mass equation. The mathematical model has been implemented by modifying a readily available computer code for single-phase newtonian fluid flows. The numerical discretization is based on a finite volume approach. The predictions show a good agreement with measurements. The circulation pattern seems not to be so sensitive to the actual shape of the void fraction profiles, but the inlet distribution of it is important. A significantly different flow pattern results when the void fraction distribution is calculated from the transport equation, as compared to those with a priori prescribed profiles. When the void fraction is uniformly distributed over the whole distributor plate, no circulation is observed. Calculations also show that even the two-phase systems with a few discrete bubbles can be simulated successfully by a continuum model.     

Continuum thermo-mechanical model for homogeneous liquid–gas flows with internal surface tension effects

This work presents a rational thermodynamic model which consistently incorporates internal surface tension effects in homogeneous and isothermal two-component two-phase flows, without appealing to additional kinematical variables to describe its microstructure. The liquid and gaseous phases are regarded as a pseudo-fluid whose constitutive behavior is obtained from two thermodynamic potentials—the Helmholtz free energy and a pseudo-potential of dissipation. The structure of the flow is assumed to be described solely by the void fraction, which is treated as an internal variable. The constraint associated with it is regarded as a material property, being an effective part of the constitutive equations. Surface tension is taken by the model into account by adding a suitable extra term, with dependence on the void fraction, in the Helmholtz free energy. The capability of the proposed model in properly describing pertinent physical phenomenon is demonstrated by comparing the analytical predictions of sound speeds in the medium with available experimental data.     

Propagation of a pressure wave in two-phase flow with very high void fraction

An experimental and theoretical study of a finite amplitude pressure wave propagating through a two-phase media of about 0.9999–0.99999 void fraction is performed. This two-phase media consists of many parallel liquid films in a gas. The films are perpendicular to the wave propagation direction and result in a two-phase fluid of extremely high void fraction. Experiments are done in a vertical shock tube and show that the shock wave is broken down into an initial sharply rising wave and a second gradually rising wave. The velocity of the first wave agrees well with the theoretical prediction assuming an adiabatic thermal equilibrium change, which approaches the gas sonic velocity in the two-phase flow in the low void fraction region. The second wave is caused by the complex reflection and destruction of the waves.     

Analysis of the characteristic lengths in the bubble and slug flow regimes generated in a capillary T-junction

We present an analysis of the geometry of the continuous and disperse phases in the bubble and slug flow regimes in air–water mixtures generated in a capillary T-junction of 1  mm internal diameter. Bubble size dispersion is very low in the considered flow patterns. The concept of unit cell is used to identify two characteristic lengths of the two-phase flow, namely, the unit cell length and the bubble length. The relationship between these lengths and the gas and liquid superficial velocities, gas mean velocity, bubble generation frequency and volume average void fraction is analysed. We conclude that in the considered configuration the unit cell and bubble lengths can be predicted either by the ratio of the gas–liquid superficial velocities or the volume average void fraction.     

Mass flow rate measurements in gas–liquid flows by means of a venturi or orifice plate coupled to a void fraction sensor

Two-phase flow measurements were carried out using a resistive void fraction meter coupled to a venturi or orifice plate. The measurement system used to estimate the liquid and gas mass flow rates was evaluated using an air–water experimental facility. Experiments included upward vertical and horizontal flow, annular, bubbly, churn and slug patterns, void fraction ranging from 2% to 85%, water flow rate up to 4000 kg/h, air flow rate up to 50 kg/h, and quality up to almost 10%. The fractional root mean square (RMS) deviation of the two-phase mass flow rate in upward vertical flow through a venturi plate is 6.8% using the correlation of Chisholm (D. Chisholm, Pressure gradients during the flow of incompressible two-phase mixtures through pipes, venturis and orifice plates, British Chemical Engineering 12 (9) (1967) 454–457). For the orifice plate, the RMS deviation of the vertical flow is 5.5% using the correlation of Zhang et al. (H.J. Zhang, W.T. Yue, Z.Y. Huang, Investigation of oil–air two-phase mass flow rate measurement using venturi and void fraction sensor, Journal of Zhejiang University Science 6A (6) (2005) 601–606). The results show that the flow direction has no significant influence on the meters in relation to the pressure drop in the experimental operation range. Quality and slip ratio analyses were also performed. The results show a mean slip ratio lower than 1.1, when bubbly and slug flow patterns are encountered for mean void fractions lower than 70%.     

On the use of area-averaged void fraction and local bubble chord length entropies as two-phase flow regime indicators

In this work, the use of the area-averaged void fraction and bubble chord length entropies is introduced as flow regime indicators in two-phase flow systems. The entropy provides quantitative information about the disorder in the area-averaged void fraction or bubble chord length distributions. The CPDF (cumulative probability distribution function) of void fractions and bubble chord lengths obtained by means of impedance meters and conductivity probes are used to calculate both entropies. Entropy values for 242 flow conditions in upward two-phase flows in 25.4 and 50.8-mm pipes have been calculated. The measured conditions cover ranges from 0.13 to 5 m/s in the superficial liquid velocity j _f and ranges from 0.01 to 25 m/s in the superficial gas velocity j _g. The physical meaning of both entropies has been interpreted using the visual flow regime map information. The area-averaged void fraction and bubble chord length entropies capability as flow regime indicators have been checked with other statistical parameters and also with different input signals durations. The area-averaged void fraction and the bubble chord length entropies provide better or at least similar results than those obtained with other indicators that include more than one parameter. The entropy is capable to reduce the relevant information of the flow regimes in only one significant and useful parameter. In addition, the entropy computation time is shorter than the majority of the other indicators. The use of one parameter as input also represents faster predictions.     

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.     

Numerical simulation of streamwise fluidelastic instability of tube bundles subjected to two-phase cross flow

This work aims to develop and validate a numerical model to simulate the flow-structure interaction in tube bundles subjected to two-phase flow. The model utilizes a mixture multiphase module in which a drift flux formulation is used to account for the slip between the phases. Two methods of numerical flow-structure interaction are used to predict the onset of fluidelastic instability (FEI) in the streamwise direction for a two-phase air–water flow mixture in parallel triangular tube bundles. These models are the hybrid analytical-flow field model and the direct numerical flow/structure coupling model. This work investigates the effects of void fractions in the range of 20% to 80% and several pitch-to-diameter ratios (P/D) in the range of 1.3 to 1.7. The results of the fluidelastic forces and the stability threshold are validated against the experimental data available in the literature and show an excellent agreement. The streamwise FEI threshold shows a significant dependency on the pitch-to-diameter ratio while the void fraction exhibits a lesser effect. Generally, the stability threshold increases as the pitch-to-diameter ratio increases. The model that was developed paves the way for devising of more reliable prediction tools for FEI in steam generators.     

Fluidelastic instability study in a rotated triangular tube array subject to two-phase cross-flow. Part I: Fluid force measurements and time delay extraction

Fluidelastic instability is a key issue in steam generator tube bundles subjected to cross-flow. The extension to two-phase flow of the existing theoretical models, developed and tested mostly for single phase flow, is investigated in this paper. The time delay is one of the key parameter for modeling fluidelastic instability, especially the damping controlled mechanism. The direct measurement of the time delay between the tube motion and the fluid force faces certain difficulties in two-phase flow since the high turbulence due to the interaction of the two components of the flow may increase the randomness of the measured force. To overcome this difficulty, an innovative method for extracting the time delay inherent to the quasi-steady model for fluidelastic instability is proposed in this study.Firstly, experimental measurements of unsteady and quasi-static fluid forces (in the lift direction) acting on a tube subjected to air–water two-phase flow were conducted. The unsteady fluid forces were measured by exciting the tube using a linear motor. These forces were measured for a wide range of void fractions, flow velocities and excitation frequencies. The experimental results showed that the unsteady fluid forces could be represented as single valued function of the reduced flow velocity. It was also found that for a given frequency, the unsteady fluid force phase was weakly dependent on the void fraction for the range of flow velocities considered.The time delay was determined by equating the unsteady fluid forces with the quasi-steady forces. The results given by this innovative method of measuring the time delay in two-phase flow were consistent with theoretical expectations. The time delay could be expressed as a linear function of the convection time and the time delay parameter was determined for void fractions ranging from 60% to 90%.