Development of a Numerical Model for Subcooled Boiling Flow

Population balance equations combined with a threedimensional two-fluid model are employed to predict bubbly flows with the presence of heat and mass transfer processes. Subcooled boiling flow belongs to this specific category of bubbly flows is considered. The MUSIG (MUltiple-SIze-Group) model implemented in CFX4.4 is further developed to account for the wall nucleation and condensation in the subcooled boiling regime. Comparison of model predictions against local measurements near the test channel exit is made for the radial distribution of the bubble Sauter diameter, void fraction and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcooling temperatures. Additional comparison using empirical relationship to determine the local bubble diameter adopted in CFX4.4 boiling model is also investigated. Good agreement is better achieved with the local radial bubble Sauter diameter, void fraction and liquid velocity profiles against measurements using the newly formulated MUSIG boiling model over the simpler boiling model of CFX4.4. However, significant weakness of the model is still evidenced in the prediction of the vapour velocity. Work is in progress to circumvent the deficiency of the model by the consideration of an algebraic slip model to account for bubble separation. INTRODUCTION The capability to predict void fraction profiles and other two-phase flow parameters in subcooled boiling flows is of considerable importance to nuclear reactor safety and of great interest to many process industries. Two-phase turbulent bubbly flows with heat and mass transfer (subcooled boiling flows belong to this specific category of bubbly flows) are encountered in many industrial applications. Bubble column reactors are extensively employed for handling processes that require large interfacial area for gas-liquid mass transfer and efficient mixing of competing gas-liquid reactions (oxidations, hydrogenations, halogenations, aerobic fermentations, etc.) that are commonly found in many chemical, petroleum, mining, food and pharmaceutical industries. Engineering systems such as industrial boilers and heat exchangers also widely employ the two-phase mixture of liquid and vapour medium for either power generation or efficient removal of extensive heat generation. Application of the population balance approach towards better describing and understanding complex industrial flow systems has received an unprecedented attention and acceptance. A population balance of any system concerns with maintaining a record for the number of entities, which for bubbly flows, bubbles, or drops, whose presence or occurrence may dictate the behaviour of the system under consideration. In addition to the motion of these entities through the state space, it is usual to encounter “birth” processes that create new entities and “death” processes that destroy existing ones. The birth and death processes may depend on the states of the entities created or destroyed with an associated phenomenology; coalescence, breakage etc. are examples of such processes. A population balance model is, therefore, formulated based on the collective phenomenology contained in the displacement of entities through their state space and the birth and death processes that terminate entities and produce new entities. With the advancement of computer technologies, the quest for improved designs has paved the trend biased towards the use of numerical simulations. Numerical methods are gradually gaining acceptance as a powerful tool for design of chemical reactors. Several studies have been conducted using the computational fluid dynamics (CFD) methodology (Krishna et al., 1999, Shimizu et al., 2000, Pohorecki et al., 2001, Olmos et al, 2001). The use of CFD and population balance models has shown to expedite a more thorough understanding of different flow regimes and further enhance the description of the bubble characteristics in the column volume for design, especially with the consideration of bubble coalescence and break-up mechanisms in the model simulations. Recently, Ramkrisha and Mahoney (2002) have highlighted a promising future towards handling two-phase flow systems using the population balance approach. Interest in the precise prediction of two-phase flow behaviours in subcooled flow boiling is of great importance to the safety analysis of nuclear reactors. Many years of extensive research work have been performed with the aim of developing and verifying various thermal-hydraulics codes, such as, TRAC, CATHARE, ATHLET and RELAP5 or its recent extension RELAP5-3D. Nevertheless, it is still not possible to apply the existing boiling models developed in these codes, which were principally developed for power reactors, to perform safety analyses for research reactors without additional developments and extensions due to the specific features of the latter. In the two-fluid model, which is the most commonly used macroscopic formulation of the thermo-fluid dynamics of the two-phase systems, the phasic interaction term appears in the field equations. These terms represent the mass, momentum and energy transfers through the interface Copyright  2003 CSIRO Australia 559 between the phases. An accurate determination of the bubble Sauter diameter is crucial as the bubble size influences the inter-phase heat and mass transfer through the interfacial area concentrations and momentum drag terms. Another consideration dominating the boiling process as observed in Lee et al. (2002) is the occurrence of large bubbles due to the competing mechanisms of bubble coalescence and condensation. The importance of coalescence and break-up of bubbles in bubble column reactors has been studied rather extensively through population balance approach in recent times due to the improved computer resources. Along similar development of models to consider bubble coalescence and break-up processes, a transport equation for the interfacial area has been considered by Kocamustafaogullari and Ishii (1995), Wu et al. (1998) and Hibiki et al. (2002) to handle twophase turbulent bubbly flows. Here, the approach is to treat the bubbles as multiple type of groups not as a number of subdivided bubble classes having different discrete diameters covering the range of bubble sizes in the column volume. In an attempt to predict the transition of bubbly to slug or churnturbulent flow regimes, Hibiki and Ishii (2000) proposed a two-group interfacial transport equations, which accounted bubbles belonging to spherical/distorted bubble group and cap/slug bubble group. Although considerable efforts have been invested to develop more sophisticated models for bubble migration, attention of the transport processes is still very much focused on isothermal bubbly flow problems. Such flows greatly simplify the formulation of mathematical models where the heat and mass transfer processes can be safely neglected. In a boiling flow, heterogeneous bubble nucleation occurs within small pits and cavities at the heated surface where these nucleation sites are activated when the temperature of the surface exceeds the saturation temperature of the liquid at the local pressure. Bubbles subsequently detach from the heated surface due to the forces acting on them in the axial and normal directions, which include buoyancy, drag, lift, surface tension, capillary force pressure force, excess pressure force and the inertia of the surrounding liquid. If, at the same location, the temperature of the bulk fluid remains below saturation, the process is known as subcooled flow boiling. Because the bulk liquid remains mainly subcooled, bubbles migrated from the heated surface are condensed and the rate of collapse is dependent on the extent of the liquid subcooling. The interfacial contribution between the vapour and liquid due to heat and mass are characterised by temperature difference (subcooling), wall nucleation and condensation respectively. Subcooled boiling flows therefore behave very differently from isothermal bubbly flows though a number of boiling experiments have confirmed some similarities in particular the presence of coalescence and break-up of bubbles inherently evidenced in both. Experimentally, there has been an enormous interest in understanding the complex processes associated with bubbly flows with heat and mass transfer such as subcooled boiling flows. These experiments (Zeitoun and Shoukri, 1996, Bonjour and Lallemand, 2001, Prodanovic et al., 2002, Lee et al., 2002, Gopinath et al., 2002) have shed light to some interesting detail information on local bubble behaviour and size along the boiling channel volume. Observations made during experiments using high-speed photography (see Figure 1) revealed that large bubble sizes were present away from the heated wall not at the heated geometric boundary. The vapour bubbles, relatively small when detached from the heated surface, were seen to increase in size due to bubble coalescence confirming the observations of Prodanovic et al. (2002). As they migrated towards the centre of the flow channel, their sizes decreased due to the increased condensation as they migrated towards the opposite end of the unheated wall of the annular channel. This was further confirmed by experimental observations of Gopinath et al. (2002) (Figure 2), which illustrates a bubble gradually being condensed in a subcooled liquid away from the heated surface. Key observations are the significant coalescence visualised near the heater wall and condensation towards the unheated side. Also, detached bubbles originated from the surface cervices were found sliding or traveling close to the surface of the heater causing more coalescence. These fundamental observations have not been well modelled. In our comprehensive review on axial void fraction distribution in channels, good agreement has been achieved against a wide range experimental data by improvements made to the boiling flow model in the generic CFD code CFX4.4 (Tu and Yeoh, 2002). Further investigation in Yeoh et al. (2002) revealed significant weakness of the model predictions against local radial measurements of Lee et al. (2002) for subcooled boiling flow. This was evidenced in the prediction of bubble size distribution, local void fraction and liquid and vapour velocities. It was concluded that the determination of the local bubble size based only on the local liquid subcooling and pressure was insufficient to accurately represent the bubble coalescence and condensation. In the two-fluid approach as aforementioned, the phasic interaction term appears in the field equations. These terms represent the Figure 1: Significant bubble coalescence observed in the vicinity of the heated wall of an annular channel (Lee et al., 2002).