Interfacial heat transfer during subcooled flow boiling

In order to develop a mechanistic model for the subcooled flow boiling process, the key issues which must be addressed are wall heat flux partitioning and interfacial (condensation) heat transfer. The sink term in the two-fluid models for void fraction prediction is provided by the condensation rate at the vapor-liquid interface. Low pressure subcooled flow boiling experiments, using water, were performed using a vertical flat plate heater to investigate the bubble collapse process. A high-speed CCD camera was used to record the bubble collapse in the bulk subcooled liquid. Based on the analyses of these digitized images, bubble collapse rates and the associated heat transfer rate were determined. The experimental data were in turn used to correlate the bubble collapse rate and the interfacial heat transfer rate. These correlations are functions of bubble Reynolds number, liquid Prandtl number, Jacob number, and Fourier number. The correlations account for both the effect of forced convection heat transfer and thickening of the thermal boundary layer as the vapor bubble condenses which in turn makes the condensation heat transfer time dependent. Comparison of the measured experimental data with those predicted from the correlations show that predictions are well within ±25% of the experimentally measured values. These correlations have also been compared with those available in the literature.     

Modeling of steam–water direct contact condensation using volume of fluid approach

Direct contact condensation (DCC) of steam in subcooled water has paramount importance in many heat transfer devices in different industrial areas like nuclear, thermal, chemical plants. This work aims at the exploration of underlying physics of steam–water DCC in two dimensions using ANSYS FLUENT 14.5. The volume of fluid method is utilized for performing direct simulation of the phenomenon at the phase interface. In this work, thrust is given on the modeling of the interphase heat transfer using interfacial jump approach instead of proposed empirical correlations which have different applicability limits. User-defined functions in the FLUENT software are used for evaluating the interfacial mass transfer rate, thermal gradient across the phase interface, and interface curvature. This study also emphasizes on the prediction of transient temperature field and interface characteristics under different parametric conditions (e.g., variation of water injection velocity and water temperature). Observation reveals that the present condensation model is capable of capturing the transient temperature history as well as the flow regime transition (stratified to slug flow) induced by the interfacial instability.     

Interfacial heat transfer of condensing bubble in subcooled boiling flow at low pressure

The interfacial heat transfer coefficient is an important parameter for the analysis of multi-phase flow. In subcooled boiling flow, bubbles condense through the interface of phases and the interfacial heat transfer determines the condensation rate which affects the two-phase parameters such as void fraction and local liquid temperature. Thus, the present experiments are conducted to correlate the interfacial heat transfer coefficient at low pressure in the subcooled boiling flow. The local liquid temperature is measured by microthermocouple and the bubble condensation rate is estimated by orthogonal, two-image processing. The condensate Nusselt number, which is a function of bubble Reynolds number, local liquid Prandtl number, and local Jacob number, is obtained from the experimental results. The bubble history is derived from the newly proposed correlation and the condensate Nusselt number is compared with the previous models.     

Modeling of the condensation sink term in an interfacial area transport equation

A model for the condensation sink term in an interfacial area transport equation (IATE) was developed. In the model, a bubble nucleation due to a wall surface boiling and a bubble collapse due to a condensation were assumed to be symmetric phenomena. Based on this consideration the condensing region for a subcooled condition can be divided into two regions: the heat transfer-controlled region and the inertia-controlled region. In the heat transfer-controlled region, the condensation Nusselt number approach is appropriate. On the other hand, in the inertia-controlled region, the resultant mechanical force may be balanced through an interface between a bubble and an ambient liquid. The modeled condensation sink term in an IATE in this study was evaluated against existing data which had been obtained from a bubble condensation in a subcooled water flow through a non-heated annulus. The evaluation result showed that the present model could predict the axial distribution of the interfacial area concentration accurately.     

A BUBBLE MECHANISTIC MODEL FOR SUBCOOLED BOILING FLOW PREDICTIONS

Population balance equations combined with a three-dimensional two-fluid model are employed to predict subcooled boiling flow at low pressure in a vertical annular channel. The MUSIG (Multiple-Size-Group) model implemented in CFX4.4 is extended to account for the wall nucleation and condensation in the subcooled boiling regime. Comparison of model predictions against local measurements is made for the void fraction, bubble Sauter diameter, interfacial area concentration, bubble population density, and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcooling temperatures. Good agreement is achieved with the local radial void fraction, bubble Sauter diameter, interfacial area concentration, bubble population density, and liquid velocity profiles against measurements. However, further improvement is needed for the accurate prediction of the vapor velocity using the present bubble mechanistic model. A proposal to include an algebraic slip model to account for bubble separation in the MUSIG boiling model is presented.     

Numerical Simulation on Collapse of Vapor Bubble Using Particle Method

In this paper, the collapse of a void bubble filled with vapor content is numerically investigated using a novel moving particle semi-implicit with meshless advection by flow-directional local grid (MPS-MAFL) method. The interfacial velocity, collapse time, bubble shape variation, peak pressure, rebound bubble radius, and other interesting parameters were obtained and are discussed profoundly. The vapor bubble undergoes several cycles of oscillation with reduced amplitude during the whole collapse process, which is similar to cavitation bubble collapse. The computational results show that the bubble collapse time is linearly proportional to the initial bubble size, which agrees with the Rayleigh equation. The minimum rebound bubble radius ratio is less affected by initial bubble size for a large bubble. Comparison work was also conducted against experimental data by Board and Kimpton. The comparison revealed that the MPS method supplied with an adiabatic compression assumption for vapor content is more suitable to evaluate the collapse behaviors of a low-pressure vapor bubble. This work is helpful for further application of the moving particle semi-implicit with meshless advection using flow-directional local grid (MPS-MAFL) method to solving complicated bubble dynamics.     

Experimental investigation of bubble behaviors in subcooled flow boiling

The experimental investigation on vapor bubble growth is performed for analyzing subcooled boiling in a vertical annular channel with inner heating surface and upward water flow under atmospheric pressure. Bulk liquid mass flux ranges from 79 kg/m2s to 316 kg/m2s, and subcooling is from 40 K to 60 K. The bubble behaviors from inception to collapse are captured by High-speed photography. The performance of bubble growth recorded by the high-speed photography is given in this paper. The bubble behaviors, effect of the bubble slippage on the heat transfer, and various forces acting on the bubble are discussed.     

Microbubble return phenomena during subcooled boiling on small wires

An experimental investigation was conducted to explore the characteristics of subcooled boiling on microwires of 25 and 100 μm diameter. Microbubbles were observed to return to the wire surface after detachment, with two types of bubble return identified, i.e., isolated bubble return, and bubble return with liquid–vapor trailing jets. The former mode of bubble return occurred when isolated small bubbles (of less than 50 μm diameter) were generated from bubble collapse, while in the latter mode, a larger bubble (of up to 200 μm in diameter) at the end of a liquid–vapor jet issuing from the wire departed and then returned to the wire surface. The numerical simulations conducted show that the isolated bubble return is caused by large temperature gradients in the vicinity of the wire which lead to Marangoni flows and result in a strong thrust force driving the bubble back to the wire. Existence of large temperature gradients close to the microwire surface was demonstrated by experimental measurements, confirming numerical predictions. The numerical model accounts for the influence of noncondensable gas on the vapor saturation temperature as well as the interfacial condensation coefficient. The presence of noncondensable gas facilitates bubble return.     

Dynamic Behavior of Bubble Interface During Boiling

A brief review with discussions is conducted for some pertinent works, done and ongoing in the Laboratory of Phase-Change and Interfacial Phenomena at Tsinghua University, on interfacial behavior of vapor bubbles and interfacial transport phenomena during liquid nucleation boiling. From a sequence of experimental investigations, some new phenomena, particularly, the visually observed interfacial transport phenomena or processes including jet-like flows, bubble interaction and spatial scale effect, were described in this article. The interfacial effects and transport phenomena associated with surface tension gradients caused by temperature and concentration variations were theoretically analyzed to reveal the marked influence on bubble interfacial shape and dynamic behavior, the bubble dynamics including nucleation, bubble motion and coalescence. Several theoretical models and methods were proposed to describe the dynamic characteristics and explain the physics of interfacial phenomena/processes. The spe     

On the transition from partial to fully developed subcooled flow boiling

The subject of the present study is to relate the boiling heat transfer process with experimentally observed bubble behaviour during subcooled flow boiling of water in a vertical heated annulus. It presents an attempt to explain the transition from partial to fully developed flow boiling with regard to bubble growth rates and to the time that individual bubbles spend attached to the heater surface.Within the partial nucleate boiling region bubbles barely change in size and shape while sliding a long distance on the heater surface. Such behaviour indicates an important contribution of the microlayer evaporation mechanism in the overall heat transfer rate. With increasing heat flux, or reducing flow rate at constant heat flux, bubble growth rates increase significantly. Bubbles grow while sliding, detach from the heater, and subsequently collapse in the bulk fluid within a distance of 1-2 diameters parallel to the heater surface. This confirms that bubble agitation becomes a leading heat transfer mode with increasing heat flux. There is however, a sharp transition between the two observed bubble behaviours that can be taken as the transition from partial to fully developed boiling. Hence, this information is used to develop a new model for the transition from partial to fully developed subcooled flow boiling.     

Wall heat flux partitioning during subcooled forced flow film boiling of water on a vertical surface

Subcooled flow film boiling experiments were conducted on a vertical flat plate, 30.5 cm in height, and 3.175 cm wide with forced convective upflow of subcooled water at atmospheric pressure. Data have been obtained for mass fluxes ranging from 0 to 700 kg/m²s, inlet subcoolings ranging from 0 to 25 °C and wall superheats ranging from 200 to 400 °C. Correlations for wall heat transfer coefficient and wall heat flux partitioning were developed as part of this work. These correlations derive their support from simultaneous measurements of the wall heat flux, fluid temperature profiles, liquid side heat flux and interfacial wave behavior during steady state flow film boiling. A new correlation for the film collapse temperature was also deduced by considering the limiting case of heat flux to the subcooled liquid being equal to the wall heat flux. The premise of this deduction is that film collapse under subcooled conditions occurs when there is no net vapor generation. These correlations have also been compared with the data and correlations available in the literature.     

Interface Shape and Marangoni Effect Around aBubble Within the Thermal Boundary Layer

INTRoDUCTIoNDuetohighheattransferperformancecharacter-izedbysmalltemPeraturedifferencesandhighheatfluxes,transportprocesseswithphasechange,espe-ciallyboilingandcondensationprocessesarewidelyemployedinnumerousenergyconversionandtrans-portsystems,heatingand/orcoolingdevices,andaerospaceaPplications.Priortotheutilizationofboil-ingprocessesinspaceapplications,suchasspacecraftthermalcontrol,additionalunderstandingofboilingheattransferbehaviorisneeded.Becauselargedmer-encesekistinthefiuiddensiti…     

The effect of motion on bubble collapse

The effects of constant and radius-dependent translational bubble velocity on the collapse rate of a single bubble in a single and two-component system, either pure or containing non-condensables, are analysed and compared. A quasi steady-state in a potential or modified potential flow field is assumed.An attempt is then made to analyse the combined effects of bubble rise velocity and main stream cross flow in forced convection surface boiling in slightly subcooled water. The results are in excellent agreement with available experimental data for most of the condensation process. Ideas for farther improvements are explored, and a general framework for analyzing bubble collapse in a flow field has been suggested.     

Extensive study on laminar free film condensation from vapor–gas mixture

The dimensionless velocity component method was successfully applied in a depth investigation of laminar free film condensation from a vapor–gas mixture, and the complete similarity transformation of its system of governing partial differential equations was conducted. The set of dimensionless variables of the transformed mathematical model greatly facilitates the analysis and calculation of the velocity, temperature and concentration fields, and heat and mass transfer of the film condensation from the vapor–gas mixture. Meanwhile, three difficult points of analysis related to the reliable analysis and calculation of heat and mass transfer for the film condensation from the vapor–gas mixture were overcome. They include: (i) correct determination of the interfacial vapor condensate saturated temperature; (ii) reliable treatment of the concentration-dependent densities of vapor–gas mixture, and (iii) rigorously satisfying the whole set of physical matching conditions at the liquid–vapor interface. Furthermore, the critical bulk vapor mass fraction for condensation was proposed, and evaluated for the film condensation from the water vapor–air mixture, and the useful methods in treatment of temperature-dependent physical properties of liquids and gases were applied. With these elements in place, the reliable results on analysis and calculation of heat and mass transfer of the film condensation from the vapor–gas mixture were achieved.The laminar free film condensation of water vapor in the presence of air was taken as an example for the numerical calculation. It was confirmed that the presence of the non-condensable gas is a decisive factor in decreasing the heat and mass transfer of the film condensation. It was demonstrated that an increase of the bulk gas mass fraction has the following impacts: an expedited decline in the interfacial vapor condensate saturation temperature; an expedited decrease in the condensate liquid film thickness, the condensate liquid velocity, and the condensate heat and mass transfer. It was found that an increase of the wall temperature will increase the negative effect of the non-condensable gas on heat and mass transfer of the film condensation from the vapor–gas mixture.     

The evaluation of the diffuse interface method for phase change simulations using OpenFOAM

In the present study, a new solver named phaseChangeHeatFoam is implemented on the OpenFOAM cfd package to simulate boiling and condensation. The solver is capturing the interface between two immiscible phases with a color function volume of fluid (CF‐VOF) method. The two fluids (vapor and liquid) are assumed Newtonian and incompressible. The surface tension is modeled with continuous surface force (CSF) which is improved with a Lafaurie filter to suppress the spurious current. The mass flux across the interface in the phase change process is determined by either Lee or Tanasawa mass transfer models. Additionally, the slight variation of saturation temperature with local pressure is considered with the simplified Clausius–Clapeyron relation. The coupled velocity pressure equation is solved using the PIMPLE algorithm. The new solver is validated and examined with (i) Stefan problem, (ii) two‐dimensional film boiling, (iii) the film condensation on a horizontal plate, (iv) the laminar film condensation over a vertical plate, and (v) bubble condensation in subcooled boiling. The present study shows the capability of a diffuse interface method in accurate simulation of the phase change process and it is expected to be instructive for further numerical studies in this area.     

Zero‐flux zone model analysis of a single bubble in boiling liquid

We start from a bubble, the basic unit of boiling, to explore liquid boiling. Research indicates that the heat and mass transfer between liquid and vapor is the determinant factor of boiling heat transfer. We have analyzed interfacial vaporization and condensation of a single bubble in boiling liquid based on a zero‐flux zone model. We have deduced the expression of zero‐flux angle and discussed the relationship between zero‐flux zone and the other parameters in order to comprehend the mechanism of boiling heat transfer. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(4): 249–256, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10026     

An investigation of direct condensation of steam jet in subcooled water

The direct contact condensation phenomenon, which occurs when steam is injected into the subcooled water, has been experimentally investigated. Two plume shapes in the stable condensation regime are found to be conical and ellipsoidal shapes depending on the steam mass flux and the liquid subcooling. Divergent plumes, however, are found when the subcooling is relatively small. The measured expansion ratio of the maximum plume diameter to the injector inner diameter ranges from 1.0 to 2.3. By means of fitting a large amount of measured data, an empirical correlation is obtained to predict the steam plume length as a function of a dimensionless steam mass flux and a driving potential for the condensation process. The average heat transfer coefficient of direct contact condensation has been found to be in the range 1.0∼3.5 MW/m²−°C. Present results show that the magnitude of the average condensation heat transfer coefficient depends mainly on the steam mass flux. By using dynamic pressure measurements and visual observations, six regimes of direct contact condensation have been identified on a condensation regime map, which are chugging, transition region from chugging to condensation oscillation, condensation oscillation, bubbling condensation oscillation, stable condensation, and interfacial oscillation. The regime boundaries stable condensation, and interfacial oscillation condensation. The regime boundaries are quite clearly distinguishable except the boundaries of bubbling condensation oscillation and interfacial oscillation condensation.     

Numerical analysis of the dynamics of moving vapor bubbles

Bubbles have been observed rapidly sweeping along very fine heated wires during subcooled nucleate boiling with jet flows emanating from the tops of the vapor bubbles. This paper analyzes the physical mechanisms driving the bubble and the jet flows from the tops of these moving bubbles. The flows are analyzed by numerically solving the governing equations for the velocity and temperature distributions around the bubble and the heated wire as the bubble moves along the wire. The bubble motion is due to the non-uniform temperature distribution in the liquid and in the wire caused by the bubble as it moves along the wire. The flow is driven by the horizontal Marangoni flow induced by the temperature difference across the bubble which thrusts the bubble forward. Comparisons with experimental observations suggest that the condensation heat transfer at the bubble interface is restricted by non-condensable gases that increases the surface temperature gradient and the resulting Marangoni flow.     

On the rise paths of single vapor bubbles after the departure from nucleation sites in subcooled upflow boiling

A photographic study was carried out for the subcooled flow boiling of water to elucidate the rise characteristics of single vapor bubbles after the departure from nucleation sites. The test section was a transparent glass tube of 20 mm in inside diameter and the flow direction was vertical upward; liquid subcooling was parametrically changed within 0–16 K keeping system pressure and liquid velocity at 120 kPa and 1 m/s, respectively. The bubble rise paths were analyzed from the video images that were obtained at the heat flux slightly higher than the minimum heat flux for the onset of nucleate boiling. In the present experiments, all the bubbles departed from their nucleation sites immediately after the inception. In low subcooling experiments, bubbles slid upward and consequently were not detached from the vertical heated wall; the bubble size was increased monotonously with time in this case. In moderate and high subcooling experiments, bubbles were detached from the wall after sliding for several millimeters and migrated towards the subcooled bulk liquid. The bubbles then reversed the direction of lateral migration and were reattached to the wall at moderate subcooling while they collapsed due to the condensation at high subcooling. It was hence considered that the mechanisms of the heat transfer from heated wall and the axial growth of vapor volume were influenced by the difference in bubble rise path. It was observed after the inception that bubbles were varied from flattened to more rounded shape. This observation suggested that the bubble detachment is mainly caused by the change in bubble shape due to the surface tension force.     

Effect of an interfacial shear stress on steam condensation in the presence of a noncondensable gas in a vertical tube

Experimental and analytical studies were performed to examine local condensation heat transfer coefficients in the presence of a noncondensable gas inside a vertical tube. The experimental data for pure steam and steam/nitrogen mixture bypass modes were compared to study the effects of noncondensable nitrogen gas on annular film condensation phenomena. The condenser tube had a relatively small inner diameter of 13 mm. The experimental results demonstrated that the local heat transfer coefficients increased as the inlet steam flow rate increased and the inlet nitrogen mass fraction decreased. The results obtained using steam/nitrogen mixtures with a low inlet nitrogen mass fraction were similar to those obtained using pure steam. Therefore, the effects of noncondensable gas on steam condensation were weak in the small-diameter condenser tube because of interfacial shear stress. A new correlation based on dimensionless shear stress and noncondensable gas mass fraction variables was developed to evaluate the condensation heat transfer coefficient inside a vertical tube with noncondensable gas, irrespective of the condenser tube diameter. A theoretical model using a heat and mass transfer analogy and simple models using four empirical correlations were developed and compared with the experimental data obtained under various experimental conditions. The predictions of the theoretical model and the simple model based on a new correlation were in good agreement with the experimental results.