Thermo-fluid Dynamics of Two-Phase Flow, Second Edition is focused on the fundamental physics of two-phase flow. The authors present the detailed theoretical foundation of multi-phase flow ...thermo-fluid dynamics as they apply to: Nuclear reactor transient and accident analysis, Energy systems, Power generation systems, Chemical reactors and process systems, Space propulsion, Transport processes. This edition features updates on two-phase flow formulation and constitutive equations and CFD simulation codes such as FLUENT and CFX, new coverage of the lift force model, which is of particular significance for those working in the field of computational fluid dynamics, new equations and coverage of 1 dimensional drift flux models and a new chapter on porous media formulation.
The drift-flux parameters such as distribution parameter and drift velocity are critical parameters in the one-dimensional two-fluid model used in nuclear thermal-hydraulic system analysis codes. ...These parameters affect the drag force acting on the gas phase. The accurate prediction of the drift-flux parameters is indispensable to the accurate prediction of the void fraction. Because of this, the current paper conducted a state-of-the-art review on one-dimensional drift-flux correlations for various flow channel geometries and flow orientations. The essential conclusions were: (1) a channel geometry affected the distribution parameter, (2) a boundary condition (adiabatic or diabatic) affected the distribution parameter in a bubbly flow, (3) the drift velocity for a horizontal channel could be approximated to be zero, and (4) the distribution parameter developed for a circular channel was not a good approximation to calculate the distribution parameter for a sub-channel of the rod bundle. In addition to the above, the review covered a newly proposed concept of the two-group drift-flux model to provide the constitutive equation to close the modified gas mixture momentum equation of the two-fluid model mathematically. The review was also extended to the existing drift-flux correlations applicable to a full range of void fraction (Chexel-Lellouche correlation and Bhagwat-Ghajar correlation).
•Literature review on flow regime maps in vertical rod bundles has been performed.•The flow regime definitions by each researcher are detailed and compared.•Flow regime transition criteria in ...vertical rod bundles have been developed.•The newly developed model have been compared with 4 existing flow regime maps.•Some discrepancies have been discussed.
The demand of accurate prediction for two-phase flow behavior in a nuclear reactor core composed of fuel rod bundles or a heat exchanger composed of heat transfer tube bundles requires comprehensive understanding of flow regime, void fraction, heat transfer and pressure drop. In comparison with the great success in developing the two-phase flow regime transition criteria for simple geometries such as pipes, annulus and rectangular channels, limited researches have been performed for developing the flow regime transition criteria of upward two-phase flow in vertical rod bundles. In the vertical rod bundles, slug bubbles spanning the bundle casing cannot exist due to their surface instability and the two-phase flow characteristics in the vertical rod bundles are different from those in pipes, annulus or rectangular channels whose channel size are smaller than the length scale of the surface instability. This study has proposed a new flow regime transition criteria model based on the analysis on the underlying physics of the upward two-phase flow behavior in the vertical rod bundles. A reliable drift-flux correlation to predict void fraction in the vertical rod bundle developed recently has been used in modeling the flow regime transition criteria. This study has classified the flow regime into 6 distinct flow regime such as bubbly, finely dispersed bubbly, cap-bubbly, cap-turbulent, churn and annular flows. The newly developed flow regime transition criteria have been compared with existing 4 flow regime maps obtained in vertical rod bundles. The fluid systems include air-water and steam-water. A fairly good agreement with some discrepancies has been obtained between the newly developed transition criteria and the measured flow regime maps.
•Past experimental and theoretical studies on gas-liquid metal mixtures are reviewed.•Existing drift-flux correlations are evaluated with the collected experimental data.•Effects of two-phase density ...ratio and flow channel geometry on the flows are modeled.•Two-phase flow conditions and liquid metal wettability are reflected in the modeling.•A new drift-flux correlation is developed and verified for gas-liquid metal mixtures.
In view of the needs in the developments of the fast-neutron nuclear reactor, the accelerator driven nuclear reactor system, the fusion reactor and so on, this study has conducted an extensive literature survey on the past experimental and theoretical studies of the upwardly-moving gas-liquid metal two-phase flows in the vertical flow channels with various channel geometries. The experimental data of the upward gas-liquid metal two-phase flows taken in the N2-Hg (nitrogen and mercury), N2-Pb/Bi (nitrogen and lead/bismuth eutectic alloy), N2-Ga (nitrogen and gallium) and N2-Na/K(nitrogen and sodium/potassium eutectic alloy) mixtures in the vertical circular, annular and rectangular flow channels and seven available drift-flux type correlations used for the void fraction predictions in the gas-liquid metal two-phase flows have been collected. The performances of these seven drift-flux type correlations have been checked against the collected experimental data, and no available drift-flux type correlation is able to predict well the void fraction of the gas-liquid metal two-phase flows with low gas-to-liquid density ratios. So, this study has analyzed the effects of the two-phase density ratio, the flow channel size and shape, the local two-phase flow conditions and the wettability between the liquid metal and the flow channel wall surface on the two-phase flow behaviors and has proposed general mathematical expressions for the distribution parameter and the drift velocity. By fitting the experimental data, a new constitutive correlation for the distribution parameter and the drift velocity consisting of two flow-regime-independent correlation sets, which are, respectively, for the gas-liquid metal two-phase flows with the low and high wettability between the liquid metal and the flow channel wall surface, has been developed. The newly-developed drift-flux type correlation has been evaluated with the collected experimental data of the gas-liquid metal two-phase flows, and their mean relative error is 0.109. The predicted mean relative errors of the low and high wettability drift-flux type correlation sets are, respectively, 0.132 and 0.0782 for the gas-liquid metal two-phase flows with the low and high wettability between the liquid metal and the flow channel wall surface.
Thermo-fluid dynamics of two-phase flow is an important subject for various scientific and engineering fields. It plays a particularly significant role in thermal-hydraulic analysis of nuclear ...reactor transients and accidents. The topics of multiphase flow are also essential for various engineering systems related to energy, chemical engineering processes and heat transfer.Thermo-fluid Dynamics of Two-phase Flow is written for graduate students, scientists and engineers who need in depth theoretical foundations to solve two-phase problems in various technological systems.Based on the extensive research experiences focused on the fundamental physics of two-phase flow, the authors present the detailed theoretical foundation of multi-phase flow thermo-fluid dynamics.
The bubble departure characteristics are studied in flow boiling considering the available experimental data in the literature. The current bubble departure diameter and departure frequency models ...are reviewed and compared with the collected database, revealing the current modeling shortcomings in forced convective flows. Based on an energy balance approach at the heated surface, the important dimensionless groups are identified and correlated for the bubble departure diameter and departure frequency. These dimensionless groups are the Jakob number, Boiling number, density ratio, and Prandtl number. The bubble departure diameter data also suggests some effect of the flow geometry in mini-channels. The newly proposed semi-empirical models for the bubble departure diameter and departure frequency are shown based on the available database to be accurate to within + or -22% and + or -35% respectively. This work also identifies important future experimental considerations for the bubble departure characteristics including data at elevated pressures, larger Prandtl numbers, and around the boundary between mini and conventional channels.
•Database of two-phase frictional pressure drop in mini/micro single channels was established.•Homogenous flow and separated flow models of two-phase flow frictional pressure drop in single channels ...were reviewed.•A new correlation was proposed to predict two-phase frictional pressure drop in mini/micro single channels.
1521 frictional pressure drop data points were collected from 12 literatures. The database included adiabatic and diabatic systems composed of 10 working fluids. The diameter range was from 0.1 to 3mm, and the pressure drop ranged from 1.26kPa/m to 2MPa/m. 17 existing single channel two-phase pressure drop correlations including homogenous flow model and separated flow model were evaluated with the database. The comparison results showed that the correlations of Pamitran et al., Hwang and Kim, Mishima and Hibiki and Zhang et al. gave better predictions than the others. However, the performance evaluation results also showed the mean absolute errors higher than 40%. Based on the relatively large prediction error by the existing correlations, a new correlation was proposed by classifying the flow conditions into four regimes (namely, 1: gas laminar-liquid laminar, 2: gas laminar-liquid turbulent, 3: gas turbulent-liquid laminar, 4: gas turbulent-liquid turbulent). The newly developed correlation is expressed by a function of the two-phase Reynolds number, Retp, the two-phase viscosity number, Nμtp, and the gas quality, x, and was able to predict the two-phase frictional pressure drop with the mean absolute percentage error of 17.4%. The correlation demonstrated an excellent performance for predicting the two-phase frictional pressure drop in mini/micro single channels.
•Experiments to investigate the flow features in a vertical narrow rectangular channel are performed.•A database of two-group bubble local parameters in the two-phase flow is presented.•Abrupt and ...gradual axial two-group bubble evolutions at flow regime transition happen.•The two-group interfacial area transport equation (IATE) is evaluated using the narrow rectangular channel data.•The IATE evaluation results show that the cap-bubbly and slug flow prediction needs improvement.
This study has experimentally investigated flow characteristics of two group bubbles in upward two-phase flows in a vertical narrow rectangular channel with 0.993 mm in gap, 40 mm in width, 2000 mm in height, and 1.94 mm in equivalent hydraulic diameter, Dh. The local measurements are performed at seven axial positions (z/Dh =52, 104, 155, 207, 415, 622, 829 (z: the axial distance from the inlet) using a high-speed camera. The database of the locally evolving parameters has been established by processing the images from the high-speed camera measurements. The measured parameters include the void fraction, interfacial area concentration (IAC), Sauter mean diameter and number density of group-1 and -2 bubbles, and gas-phase velocity of all bubbles. A total of 14 flow conditions are set at four different superficial liquid velocities ranging from 0.214 m/s to 2.08 m/s and different superficial gas velocities ranging from 0.0755 m/s to 1.70 m/s at the inlet. The observed flow regimes cover the bubbly, cap-bubbly, and slug flows. The measured void fraction ranges from 3.92 % to 42.6 %. The axially developing features of the two-phase flows are analyzed for the three flow regimes. Abrupt and gradual axial two-group bubble evolutions with intensive bubble coalescence at the flow regime transition are, respectively, observed at low and high superficial liquid velocity conditions. The newly-obtained experimental database has been used to evaluate the existing two-group interfacial area transport equation (IATE) and its corresponding source and sink models for the two-phase flow in the vertical narrow rectangular channel. Group-1 bubble IAC mean relative error of 21.1% and group-2 bubble IAC mean relative error of 33.4% have been obtained in the evaluations. The existing two-group IATE cannot satisfactorily predict the intensive bubble coalescence and the intragroup transport of the two-group bubbles at the transition from bubbly to slug flow in the vertical narrow rectangular channel. Therefore, it is necessary to improve the existing models of the intergroup and intragroup bubble interactions in the existing two-group IATE in the future.
•An issue of current 1D interfacial drag force formulation has been discussed.•A void fraction covariance correlation for a pipe has been developed.•A relative velocity covariance correlation for a ...pipe has been developed.•The covariance correlations can provide accurate 1D interfacial drag force. The covariance correlations have been validated by high-pressure pipe data.
Drift-flux parameters have been often used to formulate one-dimensional interfacial drag force in dispersed two-phase flow, which is one of key parameters to predict void fraction using one-dimensional thermal-hydraulic codes. This approach is called “Andersen approach”, which has been widely used in one-dimensional nuclear thermal-hydraulic system analysis codes such as TRACE, RELAP5 and TRAC-BF1. However, the current formulation of one-dimensional interfacial drag force ignores important void fraction covariance and relative velocity covariance when local interfacial drag force is converted to one-dimensional interfacial drag force. The impact of neglecting void fraction covariance and relative velocity covariance on one-dimensional interfacial drag force and relative velocity has been discussed in detail. In view of the importance of the drift-flux parameters, void fraction covariance and relative velocity covariance on one-dimensional formulation of the interfacial drag force, three constitutive equations have been developed for upward boiling two-phase flow in a vertical pipe. The validity of the modeled void fraction covariance and relative velocity covariance for subcooled and bulk boiling flow in a vertical pipe has been verified by boiling R12 data taken in a vertical pipe with the diameter of 19.2mm under the pressure simulating prototypic nuclear reactor thermal-hydraulic conditions. The correlation of void fraction covariance agrees with the boiling flow data in the vertical pipe with the mean absolute error, standard deviation, mean relative deviation and mean absolute relative deviation being 0.828, 3.43, 10.3% and 33.5%, respectively. The correlation of relative velocity covariance agrees with the boiling flow data in the vertical pipe with the mean absolute error, standard deviation, mean relative deviation and mean absolute relative deviation being −0.00394, 0.0663, −0.184% and 5.11%, respectively. Due to the great importance of the void fraction covariance and relative velocity covariance on one-dimensional interfacial drag force formulation, it is highly recommended to include the void fraction covariance and relative velocity covariance in the one-dimensional formulation of the interfacial drag force used in nuclear thermal-hydraulic system analysis codes.
•A systematic method to predict interfacial area concentration (IAC) is presented.•A correlation for group 1 bubble void fraction is proposed.•Correlations of IAC and bubble diameter are developed ...for group 1 bubbles.•Correlations of IAC and bubble diameter are developed for group 2 bubbles.•The newly-developed two-group IAC model compares well with collected databases.
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.
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