Modeling and analysis of calcium bromide hydrolysis

The main focus of this paper is the modeling, simulation, and analysis of the calcium bromide hydrolysis reactor stage in the calcium–bromine thermochemical water-splitting cycle for nuclear hydrogen production. One reactor concept is to use a spray of calcium bromide into steam, in which the heat of fusion supplies the heat of reaction. Droplet models were built up in a series of steps incorporating various physical phenomena, including droplet flow, heat transfer, phase change, and reaction, separately. Given the large heat reservoir contained in a pool of molten calcium bromide that allows bubbles to rise easily, using a bubble column reactor for the hydrolysis appears to be a feasible and promising alternative to the spray reactor concept. The two limiting cases of bubble geometry, spherical and spherical-cap, are considered in the modeling. Results for both droplet and bubble modeling with COMSOL MULTIPHYSICS? are presented, with recommendations for the path forward.     

Convection and evaporation of microlayer underneath bubbles under microgravity

The multidimensional heat transfer and fluid flow in the microlayer region below a vapor bubble formed during boiling in microgravity are investigated by numerically solving the Navier–Stokes equations with the energy equation. The flow is driven by Marangoni flow due to the surface tension gradient along the bubble surface that results from the temperature gradient. The model also includes condensation and evaporation at the bubble surface. The flow field and heat transfer are calculated for microlayer thicknesses from 0.01 mm to 10 mm to investigate the effect of microlayer thickness. The results show that the velocities are small and have only a small effect on the temperature distribution as compared to the solution for pure conduction in the liquid. Natural convection is shown to have a negligible effect on heat transfer. For less than ideal evaporative heat transfer at the bubble interface, Marangoni convection caused the heat transfer to increase several percent. The flow in the microlayer is shown to agree with the lubrication analogy only for thin, relatively flat interfaces. © 2000 Scripta Technica, Heat Trans Asian Res, 30(1): 1–10, 2001     

Saturated flow boiling heat transfer and associated bubble characteristics of R-134a in a narrow annular duct

Experiments are conducted here to investigate how the channel size affects the saturated flow boiling heat transfer and associated bubble characteristics of refrigerant R-134a in a horizontal narrow annular duct. The gap of the duct is fixed at 1.0 and 2.0 mm in this study. The measured heat transfer data indicate that the saturated flow boiling heat transfer coefficient increases with a decrease in the gap of the duct. Besides, raising the imposed heat flux can cause a significant increase in the boiling heat transfer coefficients. However, the effects of the refrigerant mass flux and saturated temperature on the boiling heat transfer coefficient are milder. The results from the flow visualization show that the mean diameter of the bubbles departing from the heating surface decreases slightly at increasing R-134a mass flux. Moreover, the bubble departure frequency increases at reducing duct size mainly due to the rising shear stress of the liquid flow, and at a high imposed heat flux many bubbles generated from the cavities in the heating surface tend to merge together to form big bubbles. Correlation for the present saturated flow boiling heat transfer data of R-134a in the narrow annular duct is proposed. Additionally, data for some quantitative bubble characteristics such as the mean bubble departure diameter and frequency and the active nucleation site density are also correlated.     

Subcooled flow boiling heat transfer and associated bubble characteristics of R-134a in a narrow annular duct

Experiments are conducted here to investigate how the channel size affects the subcooled flow boiling heat transfer and associated bubble characteristics of refrigerant R-134a in a horizontal narrow annular duct. The gap of the duct is fixed at 1.0 and 2.0 mm in this study. From the measured boiling curves, the temperature undershoot at ONB is found to be relatively significant for the subcooled flow boiling of R-134a in the duct. The R-134a subcooled flow boiling heat transfer coefficient increases with a reduction in the gap size, but decreases with an increase in the inlet liquid subcooling. Besides, raising the imposed heat flux can cause a substantial increase in the subcooled boiling heat transfer coefficient. However, the effects of the refrigerant mass flux and saturated temperature on the boiling heat transfer coefficient are small in the narrow duct. Visualization of the subcooled flow boiling processes reveals that the bubbles are suppressed to become smaller and less dense by raising the refrigerant mass flux and inlet subcooling. Moreover, raising the imposed heat flux significantly increases the bubble population, coalescence and departure frequency. The increase in the bubble departure frequency by reducing the duct size is due to the rising wall shear stress of the liquid flow, and at a high imposed heat flux many bubbles generated from the cavities on the heating surface tend to merge together to form big bubbles. Correlation for the present subcooled flow boiling heat transfer data of R-134a in the narrow annular duct is proposed. Additionally, the present data for some quantitative bubble characteristics such as the mean bubble departure diameter and frequency and the active nucleation site density are also correlated.     

A wall heat transfer model for subcooled boiling flow

High compactness, low weight and little space requirement are gaining attention as prominent design criteria in the development of modern cooling systems in many applications. The resulting demand for highest possible heat transfer rates has lead to the very promising concept of providing for a controlled transition from pure single-phase convection to subcooled boiling flow in thermally highly loaded regions. For its application in modern engineering design this approach requires a realistic modeling of the complex phenomena associated with the two-phase flow heat transfer. The present work proposes for the computation of the specific wall heat transfer rate a modified superposition model, where the total heat flux is assumed to be additively composed of a forced convective and a nucleate boiling component. Since the present model requires only local input quantities, it is well suited to CFD of geometrically very complex coolant flows, where the definition of global length or velocity scales would be impractical. The wall heat fluxes predicted by the present model were compared against experimental data which were obtained by in-house measurements with water being the working fluid. The overall agreement is very good, particularly, in the partially nucleate boiling regime, where the effect of the bulk flow rate on the heat transfer is significant. Deviations are primarily observed at higher wall superheats, where a strong two-way coupling between the motion of the liquid and the motion of the bubbles as well as considerable bubble–bubble interactions typically occur.     

Mixed Thermocapillary and Forced Convection Heat Transfer Around a Hemispherical Bubble in a Miniature Channel—A 3D Numerical Study

It has been established that for certain conditions, such as microgravity boiling, thermocapillary Marangoni flow has associated with it a significant enhancement of heat transfer. Typically, this phenomenon was investigated for the idealized case of an isolated and stationary bubble resting atop a heated solid that is immersed in a semi-infinite quiescent fluid or within a two-dimensional cavity. This article presents a three-dimensional numerical study that investigates the influence of thermal Marangoni convection on the fluid dynamics and heat transfer around a bubble during laminar flow of water in a minichannel. This mixed thermocapillary and forced convection problem is investigated for channel liquid inlet velocity of 0.01 m/s to 0.03 m/s and Marangoni numbers in the range of 10 to 300 under microgravity conditions. Three-dimensional effects become particularly important on the side and rear regions of the bubble. The thermocapillary forces accelerate the flow along almost the entire bubble interface. The hot core fluid from the heated bottom wall region is forced inward and propelled upward into the thermocapillary jet above the bubble. It can be quantified that the influence of thermocapillary flow on heat transfer enhancement shows an average increase by 40% at the downstream of the bubble and by 60% at the front and rear regions. This heat transfer enhancement depends mainly on the temperature differential as the driving potential for thermocapillary flow and bulk liquid velocity.     

Saturated flow boiling heat transfer of R-407C and associated bubble characteristics in a narrow annular duct

Experiments are conducted here to investigate how the channel size affects the R-407C saturated flow boiling heat transfer and associated bubble characteristics in a horizontal narrow annular duct. The gap of the duct is fixed at 1.0 and 2.0 mm in this study. The measured data indicate that the saturated flow boiling heat transfer coefficient increases with a decrease in the duct gap. Besides, raising the imposed heat flux can cause a significant increase in the boiling heat transfer coefficients. However, the effects of the refrigerant mass flux and saturated temperature on the boiling heat transfer coefficient are milder. The results from the flow visualization show that the mean diameter of the bubbles departing from the heating surface decreases noticeably at increasing R-407C mass flux. Moreover, the bubble departure frequency increases at reducing duct size and at a high imposed heat flux many bubbles generated from the cavities in the heating surface tend to merge together to form big bubbles. Meanwhile comparison of the present heat transfer data for R-407C with R-134a in the same duct and with some existing correlations is conducted. Furthermore, correlation for the present R-407C saturated flow boiling heat transfer data is proposed. Additionally, the present data for some quantitative bubble characteristics such as the mean bubble departure diameter and frequency and the active nucleation site density are also correlated.     

Numerical Simulation of Single Bubble Dynamics During Flow Boiling Conditions on a Horizontal Surface

Complete three-dimensional numerical simulations of single bubble dynamics during flow boiling conditions are carried out using the computational fluid dynamics code FLOW3D based on the volume-of-fluid method. The analyses include a numerically robust kinetic phase-change model and transient wall heat conduction. The simulation approach is calibrated by comparison with available experimental and theoretical data. It is found that the observed hydrodynamics (i.e., bubble shape, departure, and deformation) are simulated very well. The comparison with high-resolution transient temperature measurements during a heating foil experiment indicates that the modeling of the spatiotemporal heat sink distribution during bubble growth requires major attention. The simulation tool is employed for single bubble dynamics during flow boiling on a horizontal heating wall, and the agreement is excellent with published experimental data. The numerical results indicate how bulk flow velocity and wall heat transfer influence the bubble dynamics and heat transfer characteristics.     

Bubble growth,departure and the following flow pattern evolution during flow boiling in a mini-tube

In the present study, the bubble growth, departure and the following flow pattern evolution during flow boiling in the mini-tube were visualized and quantitatively investigated, along with the simultaneous measurement of the local heat transfer coefficient around a specified nucleation site. Liquid nitrogen was employed as the working fluid and the test section was a segment of vertically upward quartz glass tube with the inner diameter range of 1.3–1.5 mm, which was coated by a layer of transparent ITO film as the heater on the outer surface. The growth rates of bubbles had similar and constant growth rate in two periods of time, i.e., before and after the bubbles departing from the nucleation site, which indicated the bubble growth was primarily governed by the inertial force. The bubble departure diameter and bubble period were investigated and the corresponding correlation was obtained based on the experimental data, which showed that the tube size of the mini-tube had no notable effect on the bubble departure and the trend of the bubble departure was similar to that in macro-tubes. Whereas the following flow pattern evolution was apparently confined due to the size effect, which presented desirable heat transfer performance in mini-tubes. The heat transfer coefficients for different flow patterns along the mini-tube were obtained in terms of bubbly, slug, annular flow and the flow regimes of flow reversal and post dryout. It was found that the dominant heat transfer mechanism was the liquid film evaporation which offered desirable heat transfer capability. The heat transfer performance would be deteriorated in the post dryout regime, while flow reversal could somewhat enhance the heat transfer upstream of the nucleation site. Boiling curves around the specified nucleation site were recorded and analyzed based on the recorded flow patterns.     

Subcooled flow boiling heat transfer of R-407C and associated bubble characteristics in a narrow annular duct

An experiment is conducted here to investigate how the channel size affects the subcooled flow boiling heat transfer and the associated bubble characteristics of refrigerant R-407C in a horizontal narrow annular duct with the gap of the duct fixed at 1.0 and 2.0 mm. The measured boiling curves indicate that the temperature overshoot at ONB is relatively significant for the subcooled flow boiling of R-407C in the duct. Besides, the subcooled flow boiling heat transfer coefficient increases with a reduction in the duct gap, but decreases with an increase in the inlet liquid subcooling. Moreover, raising the heat flux imposed on the duct can cause a significant increase in the boiling heat transfer coefficients. However, the effects of the refrigerant mass flux and saturated temperature on the boiling heat transfer coefficient are slighter. Visualization of the subcooled flow boiling processes in the duct reveals that the bubbles are suppressed to become smaller and less dense by raising the refrigerant mass flux and inlet subcooling. Raising the imposed heat flux, however, produces positive effects on the bubble population, coalescence and departure frequency. Meanwhile, the present heat transfer data for R-407C are compared with the R-134a data measured in the same duct and with some existing correlations. We also propose empirical correlations for the present data for the R-407C subcooled flow boiling heat transfer and some quantitative bubble characteristics such as the mean bubble departure diameter and frequency and the active nucleation site density.     

Mixed Convective Heat Transfer Due to Forced and Thermocapillary Flow Around Bubbles in a Miniature Channel: A 2D Numerical Study

Marangoni thermocapillary convection and its contribution to heat transfer during boiling has been the subject of some debate in the literature. Currently, for certain conditions, such as microgravity boiling, it has been shown that Marangoni thermocapillary convection has a significant contribution to heat transfer. Typically, this phenomenon is investigated for the idealized case of an isolated and stationary bubble resting on a heated surface, which is immersed in a semi-infinite quiescent fluid or within a two-dimensional cavity. However, little information is available with regard to Marangoni heat transfer in miniature confined channels in the presence of a cross flow. As a result, this article presents a two-dimensional (2D) numerical study that investigates the influence of steady thermal Marangoni convection on the fluid dynamics and heat transfer around a bubble during laminar flow of water in a miniature channel with the view of developing a refined understanding of boiling heat transfer for such a configuration. This mixed convection problem is investigated under microgravity conditions for channel Reynolds numbers in the range of 0 to 500 at liquid inlet velocities between 0.01 m/s and 0.0 5m/s and Marangoni numbers in the range of 0 to 17,114. It is concluded that thermocapillary flow may have a significant impact on heat transfer enhancement. The simulations predict an average increase of 35% in heat flux at the downstream region of the bubble, while an average 60% increase is obtained at the front region of the bubble where mixed convective heat transfer takes place due to forced and thermocapillary flow.     

Saturated flow boiling heat transfer of refrigerant R-410A in a horizontal annular finned duct

An experiment is conducted here to investigate the saturated flow boiling heat transfer characteristics of ozone friendly refrigerant R-410A in a horizontal annular finned duct. Meanwhile the associated bubble characteristics in the duct are also inspected from the flow visualization. The experimental data are presented in terms of saturated flow boiling curves, boiling heat transfer coefficients and flow photos. In addition, empirical correlation equations for the saturated flow boiling heat transfer coefficient and mean bubble departure diameter are proposed. The saturated flow boiling curves show that boiling hysteresis is insignificant in the flow and the wall superheat needed for the onset of nucleate boiling is slightly affected by the refrigerant mass flux. Besides, the boiling curves are mainly affected by the imposed heat flux and refrigerant mass flux. Moreover, the measured saturated flow boiling heat transfer coefficient increases with the imposed heat flux and refrigerant mass flux. Furthermore, at a higher refrigerant mass flux the departing bubbles are smaller.     

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.     

Subcooled flow boiling heat transfer of R-134a and the associated bubble characteristics in a vertical plate heat exchanger

Subcooled flow boiling heat transfer characteristics of refrigerant R-134a in a vertical plate heat exchanger (PHE) are investigated experimentally in this study. Besides, the associated bubble characteristics are also inspected by visualizing the boiling flow in the vertical PHE. In the experiment two vertical counterflow channels are formed in the exchanger by three plates of commercial geometry with a corrugated sinusoidal shape of a chevron angle of 60°. Upflow boiling of subcooled refrigerant R-134a in one channel receives heat from the downflow of hot water in the other channel. The effects of the boiling heat flux, refrigerant mass flux, system pressure and inlet subcooling of R-134a on the subcooled boiling heat transfer are explored in detail. The results are presented in terms of the boiling curves and heat transfer coefficients. The measured data showed that the slopes of the boiling curves change significantly during the onset of nucleate boiling (ONB) especially at low mass flux and high saturation temperature. Besides, the boiling hysteresis is significant at a low refrigerant mass flux. The subcooled boiling heat transfer coefficient is affected noticeably by the mass flux of the refrigerant. However, increases in the inlet subcooling and saturation temperature only show slight improvement on the boiling heat transfer coefficient.The photos from the flow visualization reveal that at higher imposed heat flux the plate surface is covered with more bubbles and the bubble generation frequency is substantially higher, and the bubbles tend to coalesce to form big bubbles. But these big bubbles are prone to breaking up into small bubbles as they move over the corrugated plate, producing strong agitating flow motion and hence enhancing the boiling heat transfer. We also note that the bubbles nucleated from the plate are suppressed to a larger degree for higher inlet subcooling and mass flux. Finally, empirical correlations are proposed to correlate the present data for the heat transfer coefficient and the bubble departure diameter in terms of boiling, Froude, Reynolds and Jakob numbers.     

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.     

Numerical investigation of subcooled flow boiling in segmented finned microchannels

Bubble growth behavior and heat transfer characteristics during subcooled flow boiling in segmented finned microchannels have been numerically investigated. Simulations have been performed for a single row of segmented finned microchannel and predicted results are compared with experimental investigations. Onset of nucleation, formation of bubbles, their growth and movements have been investigated for different values of applied heat flux. Mechanism of bubble expansion without clogging resulting in enhanced heat transfer in segmented finned microchannels has been explained. Temperature and pressure fluctuations during subcooled flow boiling condition have been investigated. It is observed that at high heat flux, thin liquid film trapped between the bubble and channel wall is evaporated leading to localized heating effect. Predicted flow patterns are similar to experimental results. However, simulations over predict the bubble growth rate and heat transfer coefficient.     

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.     

OPTICAL MEASUREMENT OF MICROSCALE TRANSPORT PROCESSES IN DROPWISE CONDENSATION

The optimum use of interfacial free-energy gradients to control fluid flow in small regions naturally leads to simpler passive heat transfer systems. In this context, "passive" refers to the natural pressure field for fluid flow due to changes in the intermolecular force field resulting from an imposed nonisothermal temperature field. Although the particular constrained vapor bubble (CVB) discussed can be viewed as a large version of a wickless heat pipe, it is a much more general heat transfer concept. Herein, it is an ideal system for the optical study of microscale transport processes in droplet condensation due to interfacial phenomena. This article concerns the movement of a single condensed ethanol sessile drop into a concave liquid film. The intermolecular force is found to be much larger than the gravitational force and dominates condensate removal. A dimensionless force balance for viscous shear stress demonstrates the effect of changes in the contact angle and curvature. A dimensionless difference in free energy is identified as the cause of spontaneous condensate removal.     

Simulation of heat transfer with the growth and collapse of a cavitation bubble near the heated wall

The growth and collapse behaviors of a single cavitation bubble near a heated wall and its effect on the heat transfer are numerically investigated. The present study is designed to reveal the mechanism of cavitation enhanced heat transfer from a microscopic perspective. In the simulation, the time-dependent Navier-Stokes equations are solved in an axisymmetric two-dimensional domain. The volume of fluid (VOF) method is employed to track the liquid-gas interface. It is assumed that the gas inside the bubble is compressible vapor, and the surrounding liquid is incompressible water. Mass transfer between two phases is ignored. The calculated bubble profiles were compared to the available experimental data, and a good agreement was obtained. Then, the relationship among bubble motion, flow field and surface heat transfer coefficient was analyzed. On this basis, the effects of such factors as the initial distance between the bubble and the wall, the initial vapor pressure and the initial bubble nucleus size on the heat transfer enhancement are discussed. The present study is helpful to understand the heat transfer phenomenon in presence of cavitation bubble in liquid.     

Interaction of two cavitation bubbles in a tube and its effects on heat transfer

When two cavitation bubbles exist in a confined space, the interaction between the bubbles significantly affects the characteristics of bubble dynamic behaviors. In this paper, a three-dimensional (3D) model is established to study the growth and collapse of two cavitation bubbles in a heated tube and its effects on heat transfer. The liquid and gas phases throughout the calculation domain are solved by a set of Navier-Stokes equations. It is assumed that the gas inside the bubble is compressible vapor, and the surrounding liquid is incompressible water. The mass transfer between two phases is ignored. The calculated bubble profiles were compared to the available experimental data, and a good agreement has been achieved. Then, the relationship among the bubble motion, flow field and pressure distributions was analyzed. On this basis, the effects of bubble interaction on the heat transfer between the wall surface and sounding liquid were discussed. It is found that heat transfer in the centre wall region is enhanced owing to the vortex flow and micro-jet induced by the bubble contraction and collapse. In contrast, the highest surface temperature appears in the surrounding region, which is mainly attributed to the thermal resistance induced by the bubble. The present study is helpful to understand the heat transfer phenomenon with cavitation in the liquid.