Vapor Core Research Articles

A robust three-dimensional numerical model for heat transfer characteristics in sintered–grooved thin flat heat pipes

In the current research, a robust three-dimensional numerical model is developed for thin flat heat pipes (TFHPs) with a hybrid sintered–grooved wick structure. Numerical simulations for laminar incompressible flow in liquid wick and ideal gas incompressible flow in the vapor core are performed to predict temperature, pressure, and velocity profiles. The model utilized non-Darcy transport through a porous wick to determine liquid flow in the liquid-wick section. The mass flow rate of the fluid at the liquid–vapor interface is modeled using kinetic theory. Furthermore, the hybrid wick structure is modeled as an inhomogeneous porous medium. Additionally, this formulation enhances the stability and convergence of the numerical solution and accelerates the solving time. The developed model is validated with experimental data, showing very good agreement with axial wall temperatures, with a maximum error of about 2% in steady-state conditions. The numerical results, including system pressure, wall temperature, mass transfer at the liquid and vapor interface, and velocity magnitude streamlines, are investigated for a comprehensive understanding of the flow physics and performance of the hybrid wick. The results show that, at heat inputs of 5, 10, 20, and 30 W, the thermal efficiency of hybrid wick TFHP is 4.9%, 10.4%, 34.38%, and 23.3%, respectively, greater than that of the grooved wick. The TFHP with a hybrid wick indicates the best thermal efficiency at a heat input of 20 W, with a thermal resistance of 0.95 K/W.

Study of turbulent wavy annular flow inside a 3.4 mm diameter vertical channel by using the Volume of Fluid method in OpenFOAM

In annular downward flow, an annular liquid film flows at the perimeter of the channel pushed down by the gravity force and by the shear stress that the vapor core exerts on it. Depending on the working conditions, the vapor-liquid interface can be flat or rippled by waves. The knowledge of the liquid film thickness is very important for the study of annular flow condensation because the thermal resistance of the liquid is often the most important parameter controlling the heat transfer. A new approach for the simulation of annular flow is here proposed using an in-house developed transient solver based on the Volume of Fluid (VOF) adiabatic solver interIsoFoam available in OpenFOAM. With the VOF method, in addition to the standard set of equations (continuity and momentum), a transport equation related to the advection of the volume fraction scalar field has to be solved. The numerical setup consists of 2D axisymmetric domain. An adaptive mesh refinement (AMR) method is added to the solver to better capture the interface position. The k-ω SST model is used for turbulence modelling in both the liquid and vapor phases and a source term (whose magnitude is controlled by a model parameter named B) is included in the ω equation to damp the turbulence at the interface.

Influence of vapor core design on thermal and hydraulic performance of mesh-type ultra-thin vapor chamber

The mesh-type ultra-thin vapor chamber(UTVC), with an internal mesh porous structure, is a cost-effective and efficient heat transfer element for compact spaces. The design of the vapor core plays an important part in enhancing the heat transfer performance of the mesh-type UTVC within the confined space requirements. The present study proposes to design cavities in the supporting coarse mesh inside the vapor core to form a multi-scale combination of vapor channels with the mesh channels. Utilizing a numerical model that considers microporous evaporation as well as the Marangoni effect, the effects of different flow channel designs and designed channel widths on the performance of the UTVC were analyzed. The study determined the flow and heat transfer characteristics of the working medium within the mesh-type UTVC, and found that the most significant performance enhancement was achieved when the designed flow channel passed through part of the UTVC evaporation and condensation sections, reducing the thermal resistance by 17.45%. Whereas the design flow channel width has less influence on the performance of mesh-type UTVC, it satisfies the changing trend of vapor flow pressure drop and thermal resistance decreasing firstly and subsequently increasing with the expansion of the designed channel width.

Experiments on the onset of boiling entrainment from a falling liquid film with gas sheared flow

The process of droplet entrainment caused by nucleate boiling within a falling liquid film was visualized using a high-speed camera to investigate the mechanism and the onset conditions of the boiling entrainment. In the experiments, air was flowed along the liquid film to explore the potential effects of vapor core flow on the droplet generation process in diabatic annular two-phase flow. The two types of boiling entrainment mechanisms called the jet-type and the filament-type were observed in the present work. The jet-type boiling entrainment commenced at relatively low wall heat flux and produced small droplets. The filament-type was observed at higher wall heat flux and it produced larger droplets. Hence, the filament-type was supposed to have a greater impact on the liquid film flow rate in diabatic annular two-phase flow. The experimental data accumulated in this work were used to develop correlations for the onset conditions of the jet-type and filament-type boiling entrainments.

Improved flow boiling characteristics in minichannel with open-cell porous ribs

Porous metal has been proven to exhibit significant heat transfer enhancement in minichannel. Focusing on fully utilizing the advantages of porous metal in heat transfer and reducing pressure penalty, a porous ribs minichannel (PRM) heat sink employing open-cell porous copper as rib was designed and fabricated. PRM heat sink has 19 minichannels that are 1 mm in width and 2 mm in depth. Commercial open-cell porous copper with a porosity of 0.85 and 120 PPI (Pore per Inch, PPI) was selected. Flow boiling experiments were carried out with ethanol as the working fluid. The flow patterns of two heat sinks were recorded with a high speed photograph system and comparative analyzed. High-frequency periodic motion of vapor core boundary in width direction of porous ribs minichannel was recorded. This is considered a fluctuation of density wave along the channel width direction. Cooperating with capillary force, movement of vapor core boundary induces mass transfer between adjacent channels, compensating for uneven flow distribution between channels. The results show that PRM heat sink has better heat transfer performances and flow stability with a slight increment in pressure drop compared with solid ribs minichannel (SRM) heat sink. The porous ribs minichannel heat sink provides a new way to relieve flow insatiability for heat exchangers and thermal management systems.

Strategies for thermal performance improvements of polymeric thermal ground planes (TGP)

This paper presents a study on the thermal performance and enhancement techniques of polymeric thermal ground planes (TGPs). The literature features a range of polymeric TGPs that exhibit an effective thermal conductivity up to twice that of copper. However, the TGP effective thermal conductivity does not provide insight into the performance and potential improvements that could be made to a specific TGP design and configuration. Relying only on this metric can be limiting to compare different TGPs performances, since effective conductivity is affected by the device size, layout of heated and cooled zones, and the fabrication materials. In this paper, we adapted a model by connecting the TGP pumping capacity to its thermal resistance to predict the polymeric TGP thermal performances as a function of their geometry, test configuration and material used. This approach enables the development of strategies to optimize the polymeric TGPs performances and identify their limitations rather than relying on effective thermal conductivity as a benchmark for comparison. The present model considers vapor flow through a mechanical structure for the first time in TGPs. Indeed, the polymeric TGP in contrast to the metallic one requires a denser mechanical structure to support the vapor core thickness during vacuum due to the flexibility of the polymeric shell. The generated vapor pressure drop along the TGP has a dual impact on its performance as it affects both the capillary limit and vapor resistance resulting in a tradeoff between the TGP pumping capacity and thermal resistance, for a given TGP thickness. To back up the proposed model, experimental characterization was carried out on a one-step assembled polymeric TGP, to extract simultaneously the total and vapor thermal resistances. The model highlighted a trade-off in designing the vapor core and wicking structure, balancing the polymeric TGP pumping capacity and thermal resistance, for a target TGP thickness. Hence, the current study provides guidelines for defining improvement strategies for TGPs thermal performances based on the geometry and the type of material used during the fabrication process. The recommended approach also permits the identification of polymeric TGPs capabilities and limits rather than depending on the thermal metrics, which may be misleading while comparing performances.

Cooling of power electronic devices using rectangular flat heat pipes with externally and internally cooled condenser regions

In traditional heat pipes employing external cooling, the internal flow pattern undergoes a transition to annular flow. In this stage, vapor moves through the central region of the heat pipe, while a liquid film develops on the inner wall surface. This liquid film acts as a thermal barrier, impeding the condensation of vapor within the vapor core area, which reduces the coolant's ability to condense vapor effectively. To address this issue, a rectangular flat heat pipe with an internal condenser (RFHP-IC) has been designed and tested for heat loads up to 360 W with different fill ratios. The RFHP-IC incorporates a tube-in-tube structure within the condenser section of the heat pipe, facilitating the condensation of the working fluid while maintaining a compact form factor. Results indicate that employing an internal condenser reduces thermal resistance and evaporator wall temperature by 67.5% and 20.1% respectively when compared to an external condenser. Furthermore, the RFHP-IC allows vapor to make direct contact with the cold surface of the internal condenser, increasing the condensation rate by 8.5% in comparison to an external condenser under the same heat load. The findings of this study can improve the performance, capacity, and reliability of RFHPs, making them more suitable and efficient solutions for thermal management applications.

Experimental analysis of temperature and vapor core pressure for an annular heat pipe

The main contribution of this study is the effects of the operating conditions on the internal vapor pressure and temperature in an annular screen wick heat pipe, using distilled water as the working fluid. High-resolution pressure transducers, optical fiber distributed temperature sensors, and K-type thermocouples were employed to measure the internal and external temperatures as well as the local static pressures at different axial positions of the heat pipe. Temporal and frequency analysis using a one-dimensional continuous wavelet transform was performed on the differential pressure data to characterize flow behavior and infer the flow regime occurring within the heat pipe. The heat pipe was tested in multiple orientations with respect to the horizon (θ=0°, 45°, and 90°), heat loads (25, 50, and 75 W), and condenser coolant temperatures (Tw,in= 10 °C, 20 °C, and 30 °C). To estimate the vapor-phase flow friction factor for multiple Reynolds numbers, the Lockhart–Martinelli correlation was employed. This study provides critical experimental data and analyses for complex two-phase flow behavior in an annular wick heat pipe geometry. The thermal resistance and effective thermal conductivity were estimated as a function of the heat pipe orientation and power input. The experimental investigation revealed that power input and orientation influence both the internal vapor core and external surface temperatures, as well as the local pressure response. The outcomes from this study provide a valuable database that supports the advancement of heat pipe design, modeling, and validation.

Effect of vessel dimensional ratio on heat conveyance capabilities of gravity-assisted heat pipes: Theoretical and experimental approach

This study conducts an experimental performance assessment of different gravity-assisted heat pipes, with length-to-diameter ratios ranging from 50 to 200. Process modelling is based on a mechanistic approach and complemented by a comprehensive analysis of internal entropy generation rates and convective phenomena. Findings show that increasing the dimensional ratio extends the range of the device, from 200 to 800 W to 1000–2800 W. Similarly, the temperature difference of the cooling fluid increases, achieving 5.3 °C and 15.9 °C. Nonetheless, these increment rates remain constant for all treatments, between ∼ 1.6 and 1.8 °C. Thermosyphons with L/D ≤ 50 display a linear behaviour, with an inverse Stanton-Reynolds dispersion index of 0.0089, and no dominant internal mechanism, with ranges of 0.99–4.27 kW/K for the vapour core; 0.52–4.94 kW/K for condensation and; 0.82–3.68 kW/K for evaporation, hence their separate characterization. Contrarily, for L/D ≥ 100, entropy generation rates at evaporation process is between 25 and 45% higher than the other thermally-driven processes, hence identified as the dominant mechanism inside these vessels. For all instances, condensation is the most susceptible process to external stimuli, with dispersion indexes 1.98 to 5.2 times higher than the rest. As heat flow supply rises, vapour core contribution to total entropy generation is reduced by 10–15%, entailing that external heat transfer becomes more intense than internal heat conveyance. Finally, statistical correlations were constructed to estimate inverse Stanton number and condensation vapour core temperature. For L/D ≤ 50 this estimation achieved a maximum relative error of 0.03%. For the remaining treatments, estimations achieved a maximum relative error of 14.5%.

Mesoscopic numerical study of the startup characteristics of grooved heat pipe under high heat flux

The dry-out phenomenon that occurs in the evaporation section under high thermal load can lead to heat pipe startup failure, which considerably affects the safe and efficient operation of microelectromechanical systems. In this study, the startup characteristics of a grooved heat pipe are investigated with the mesoscopic lattice Boltzmann method. The focus is on the effects of wettability, inclination angle, and liquid filling volume on the evolution of the liquid supply velocity and dry-spot area. Results show that nucleate boiling can be formed by starting the heat pipe at high heat flux, and the vapor jetting generated by bubble bursting can reduce the liquid supply velocity by more than 70%. Capillary pressure can be increased, and the perturbation of bubbles to the meniscus region can be suppressed by enhancing the wettability of the capillary wick, thus promoting the return of the condensate to the evaporation section. The pressure on the liquid side in the evaporation section decreases as the inclination angle increases, which shortens the waiting time for vapor core formation and improves the stability of boiling behavior. A non-monotonic relationship exists between the liquid filling volume and heat transfer limit time of the heat pipe, which reaches the maximum only when the initial liquid layer fills the capillary wick exactly.

Experimental study on the startup of the annular wick type heat pipe using fiber optical temperature measurement technique

This study used optical fiber-distributed temperature sensors to measure the internal and external temperature distributions of a water-cooled heat pipe. The sensor technology used in this study is fiber optical distributed temperature sensing, a distributed sensing technique based on the naturally occurring Rayleigh backscatter in optical fibers. This measurement technique provides maximum spatial resolution for static and semi-static applications. Using this sensor, the temperature distribution of the heat pipe's internal, external, vapor core, and the wick was measured with a spatial resolution of 0.65 mm, a sampling frequency of 40 Hz, and a temperature resolution of 0.1 °C. Through the measured temperature distribution database, the starting phenomenon, the effective length trend, and the limitation onset were observed. From the results, it is found that a high-temperature peak appears at the evaporator if a high initial power (75 W) is imposed on the heat pipe, even after the heat pipe approaches the normal operating status. The peak is not observed in a slower startup (30 W initial power then slowly increased to 75 W). It is also found that the temperature distributions and effective condenser length of the heat pipe highly depend on the cooling conditions. There are variations in the temperature according to the radial direction of the horizontal heat pipe due to gravity. Lead and lag of the temperature evolution were observed at the onset of the operating limitations.

A study on thermal and hydraulic performance of ultra-thin heat pipe with hybrid mesh-groove wick

High power electronics require ultra-thin heat pipe (UTHP) with more efficient heat transfer capabilities to meet thermal management challenges. And the design of the wick structure is crucial to the heat transfer performance improvement of the UTHP. At the present work, a thermo-hydraulic model is proposed for UTHP with composite mesh-grooved wick structure and the potential applications of the hybrid wick with non-full coverage by mesh is analyzed. According to the different mesh coverage areas, the wick structures are classified into three types, including evaporator covered, evaporator-adiabatic section covered, and full covered. The results show the flow characteristics and thermal performance of UTHPs is closely related to mesh coverage area and vapor core thickness. The reduction in mesh coverage area causes an expansion in vapor space, the vapor velocity and the vapor pressure drop both decreases, the mass flow rises with the higher vapor-liquid circulation efficiency. The liquid pressure drop is positively related to working fluid mass flow. Moreover, a theoretical model to predict the heat transfer limit of the heat pipe with composite wick was established and verified by experimental results with a maximum error of 3.63%.

A mechanistic model in annular flow in microchannel tube for predicting heat transfer coefficient and pressure gradient

A mechanistic model that focuses on annular flow is proposed in this work. The new model predicts pressure gradient, void fraction, and heat transfer coefficient in annular flow in a microchannel tube. Six fluids, namely R32, R1234yf, R134a, R1234ze(E), R1233zd(E), and R1336mzz(Z) were tested in previous studies. The tested fluids have a wide range of properties. The results of these six fluids are reviewed and compared to models in the literature. The existing heat transfer models fail to predict the measurements accurately. The proposed model starts from the shear balance at the interface of liquid film and vapor core. The new model uses film thickness to calculate the film Reynolds number. The Film Nusselt number is then calculated. A database approach is adopted to enhance prediction accuracy. Based on the measurements in the database, the model has an MAE of 11.7%, and ME of 0.5% when predicting the heat transfer coefficient. Li and Hrnjak (2022), a flow pattern map based on the same fluids and the same facility, is used to determine the flow pattern. The model is compared to measurements from varied sources in the literature, and it also shows good accuracy. The model can also be extended to other flow patterns in a microchannel evaporator.

A novel non-destructive methodology for the analysis of deformed heat pipes

This paper presents a non-destructive methodology to analyze the influence of bend angle on the thermal performance of a sintered copper wick heat pipe. A calorimeter-based technique is used to characterize the thermal performance of a concentric tube sintered wick heat pipe under bending deformation, for a range of bend angles. It is seen that the thermal resistance of this heat pipe increases by up to 31% as the pipe was bent by 90° while its maximum heat input reduces by 29%. X-ray tomography (µ-CT) is used to obtain geometric (pipe diameter, vapor channel, etc.) and morphological (porosity, pore size distribution) data for the pipe and wick at the bend site, and this data is utilized in a thermo-fluidic model of the pipe. The methodology quantifies the local vapor and liquid pressure drops caused by deformations to the wick and vapor channel of the pipe, and their influence on the capillary pressure limit. The X-ray method revealed that, when the heat pipe was bent to 90°, there was a 23% reduction in the vapor core area, a 7% increase in the wick area, and a 48% reduction in permeability at the bend site. These geometric changes accounted for a 12% increase in the vapor phase pressure drop and a 70% increase in the liquid phase pressure drop at the bend site. When compared to the overall capillary limit the increase in liquid pressure drop demonstrated a greater contribution (12 %) in comparison to the vapor pressure drop (0.5%). In spite of the fact that the methodology presents results for a heat pipe under a specific bending case, µ-CT inspection represents a novel diagnostic tool that can underpin the optimization of heat pipe manufacture, in order to mitigate the influence of bending deformations.

Intra-Lid Multi-Core Vapor Chamber Architecture for Heterogeneous Electronic Packages: Technology Concept to Prototype Evaluation

Thermal management of future heterogeneous electronic packages with extreme heat fluxes relies on effective spreading of heat in the package lid. Intra-lid integration of vapor chambers is a promising strategy for simultaneous dissipation of large total heat loads and localized high-flux hot spots. However, conventional vapor chambers comprising a single vapor core require relatively thick evaporator wicks to prevent dry out at high total heat loads, thereby imposing a large temperature drop across the wick at the hot spot location. We recently proposed a cascaded multi-core vapor chamber (CMVC) architecture comprising a single-core vapor chamber stacked on an array of smaller footprint vapor cores having relatively thinner wicks. The multi-core array is designed to spread heat from arbitrarily distributed high-flux hot spots before they enter the top vapor chamber having a thicker wick. Then, the top vapor chamber spreads the high total heat loads to the base of the mounted heat sink. To evaluate the proposed CMVC technology, we make a weighted decision to identify an appropriate minimum viable prototype for subsequent design and testing. A reduced-order model is used to determine the dimensions and properties of the wick and vapor core that minimize the temperature drop across the down-selected multi-core vapor chamber architecture for a given power map, considering manufacturing process constraints. Finite element analysis (FEA) simulations are employed to decide a condenser wall thickness that avoids permanent deformation in the vapor chamber architecture under a mechanical load. A prototype is manufactured by a commercial vendor following these parameters and manufacturing constraints. As predicted by the thermal model, experimental characterization of this first-reported multi-core vapor chamber array prototype offers a notable reduction in temperature drop relative to a benchmark solid copper spreader, owing to attenuation of hot spots at a low temperature difference.

Influence of jumping-droplet condensation on the properties of separated flow in an air-cooled condenser tube: An Euler-Lagrange approach

An Air-cooled condenser (ACC), which finds popularity in a steam power plant in arid areas, is usually less efficient as film condensation occurs inside the condenser tube. Recent research is directed towards eliminating the thermally insulating liquid film with the application of novel superhydrophobic surfaces. The self-cleaning property of such surfaces facilitates easy condensate drainage in the form of jumping droplets exposing favourable nucleation sites, thereby significantly promoting dropwise condensation. The present study explores the characteristics of jumping droplet condensation in finite condenser tubes using computational fluid dynamics (CFD). The wall-heat-flux for condensation is modelled here by a uniform suction boundary condition. The strength of suction is quantified by a suction Reynolds number Re s. We mainly focus on the zone corresponding to 2.3 < Re s < 10, where no previous solution exists. In a long horizontal tube, the progressive realization of a self-similar region starting from the developing regions is demonstrated. We examine the characteristics of the developing region based on the sign of the pressure gradient. The results of three-dimensional CFD simulations illustrate the variations of droplet trajectories with the inception size and coordinates of jumping droplets determined locally by the relative contributions of various force components, viz. gravity, axial drag in the vapour core, suction induced radial drag and Saffman lift. The present study also predicts the effect of pipeline inclination on condensate drainage. Ultimately, considering multiple jumps, we found that the maximum condensate emission can be obtained for small droplets (5−15 μm), while medium-sized droplets (20−50 μm) are most advantageous for isolated jumps.

Lee model based numerical scheme for steady vapor chamber simulations

Vapor chamber is a phase-change based heat spreader widely used in thermal management. Steady numerical simulation is a useful practice for vapor chamber design and optimization. In numerical simulations, assuming incompressible flow and isothermal vapor core is common to alleviate the stability issues raised at liquid-vapor interfaces because the mass/energy transfers at such interfaces are sensitive to the fluctuations of pressure, temperature, and density. It is also typical to preset a single kind of phase change behavior at a liquid-vapor interface (either condensation or evaporation). However, these assumptions could no longer be appropriate when input heat flux is high, the ratio of heating area to evaporator area is small, and/or pillars are presented. This paper presents a novel numerical scheme for vapor chamber simulations by accounting for both the flow compressibility and the temperature variations within the vapor core while applying mass/energy source terms to liquid-vapor interfaces based on the Lee model through the ghost fluid method. No preset of the phase change behavior at liquid-vapor interfaces is needed as well. The results show that, under the input heat flux from 5.6 to 38.9 W/cm2, the average temperature errors between the experiments and the simulations range from 3.0% to 5.0% for the heating area, 5.5% to 8.0% for the evaporator, and 1.4% to 3.0% for the condenser. Although these temperature errors are not exceptional, this proposed scheme is numerically stable by exhibiting good grid independence and being able to converge in 128 iterations over four million elements. Furthermore, attributed to fewer assumptions needed, this proposed scheme can simulate flow characteristics that well agree with the sense of phase change behaviors and is also applicable to other two-phase based heat spreaders (such as heat pipes) at various conditions in structure, dimension, heat input, and convergence criteria.

Annular liquid film thermohydraulic and intermittent dryout in microchannel flow boiling

The annular flow regime in microchannels is commonly described as the steady flow of a vapor core with a surrounding liquid film along the channel length. However, limited studies have suggested temporal discontinuity in the liquid film coverage of the microchannel wall. The lack of experimental tools to directly interrogate the liquid flow characteristics and the local surface heat flux has resulted in proliferation of different hypotheses concerning the physics of this process. Surface de-wetting due to high shear stresses at the vapor–liquid interface and liquid film instability and rupture due to perturbation growth at the vapor–liquid interface have been suggested as the underlaying causes of this phenomenon. In this study, a recently developed microsensor array capable of measuring the surface local heat flux and liquid film thickness and velocity is utilized to decipher thermohydraulic characteristics of the annular flow regime and intermittent dryout with unprecedented details. The studies are conducted in a 600 μm square cross-section microchannel using FC-72 as the test fluid at 70–80% exit vapor quality. The results show that liquid film thinning because of evaporation rather than de-wetting and film rupture is responsible for intermittent surface dryout. Studies at different mass and heat fluxes suggest that for a given surface heat flux, there is a mass flux threshold above which intermittent surface dryout vanishes. Furthermore, the experimental liquid and vapor flow velocities and liquid film thickness are used to calculate the liquid–vapor interfacial shear stress. The results suggest that under the studied conditions, the liquid–vapor interfacial shear stress has little impact on the surface intermittent dryout. This study enhances predictable and reliable design and operation of two-phase heat sinks at high exit vapor qualities.

Application of the depth-averaged liquid film model to the annular flow regime in BWR fuel assemblies

The flow regime found in the downstream half of the BWR assembly can be described as an annular film flow with a central core of vapour with suspended droplets. This study presents the application of the fluid film model available in STAR-CCM+ to analyze the interplay between the vapour flow and the liquid film dynamics. The film model, based on depth-averaged equations, can be used to simulate film depth and velocity over complex geometries. Built on sound mathematical basis and applied to a wide variety of areas, the fluid film model, however, has not been widely used to study annular flow in nuclear fuel assemblies. Applying this model to a simplified geometry of a single rod with different gaps, the basic relationship between the vapour velocity, liquid film thickness and velocity distribution along the circumference of the rod is clarified. The minimum vapour velocity required to transport a liquid film along the surface of a fuel rod of a specific length against gravity was found using first-principles force balances. The model was then applied to a real, but simplified assembly geometry where the resulting flow pattern was primarily affected by the presence of part length rods. The minimum velocity required to transport a liquid film along the fuel rods in the assembly against gravity was found to be close to the range of velocities obtained using sub-channel codes. Strong circumferential variation in the wall shear across a short arc-length was observed for some fuel rods. The variation in wall shear also results in a corresponding variation in film velocity and film thickness and presumably has a strong impact on the local heat and mass-transfer characteristics. Cross flow from high resistance regions in the assembly towards lower resistance regions has a strong impact in terms of variations in the film thickness on the rods that are the furthest away from the low resistance paths.The modelling palette for the depth-averaged film model contains several features that can extend the validity of the modelling used in this study, such as the presence of droplets in the vapour core, deposition of droplets on to the film, heat transfer and boiling, and the influence of spacers in disrupting the liquid film. These features were not considered in this study and remain avenues for future work. The use of time-averaged turbulence modelling results in damping of unsteadiness of the vapour flow and perturbations in the film thickness. For better estimates of unsteady effects use of turbulence models such as the Large Eddy Simulation method is recommended. Current state-of-the-art in predicting dispersed annular flow using liquid film models is limited to single rods. The generalized depth-averaged film model can be applied to complex geometries including the effect of spacers.

Void fraction and pressure gradient model for an adiabatic symmetric annular developed flow with entrainment

This paper presents a new method for the evaluation of the pressure gradient during annular two-phase flow in the presence of entrainment, based on the momentum balance on the liquid film trapped between the wall and the vapor core. The entrained liquid fraction, together with the atomization/deposition rates and shear stresses, are considered with the use of closure equations, in which the interfacial shear stress is calibrated by means of an experimental database. Through the resolution of a simple iterative procedure, the outcomes of the method are both pressure gradient and void fraction. The accuracy of the present model is tested with independent experimental databases from the literature, showing a very good agreement also with respect to existing available methods for pressure gradient and void fraction.