Annular Flow Research Articles

Effect of annulus ratio on the residence time distribution and Péclet number in micro/milli‐scale reactors

AbstractMicro/milli‐scale annular reactor with straight and helical forms has excellent heat and mass transfer performance due to the short molecular diffusion distance and dual‐wall surface transport. The annular gap spacing is scalable by adjusting the inner and outer tube diameter. The influence of diffusion and convection effects on axial dispersion as expanding the flow scale requires further elucidation with the help of residence time distribution (RTD) curves and Péclet (Pe) numbers. The correlation of RTD characteristics with annulus ratio γ = Dh/D (ratio of annulus characteristic size to outer diameter) is investigated using computational fluid dynamics. Results show that with enlarging the straight annular gap from micro‐scale to milli‐scale, RTD characteristics exhibit opposing patterns. This can be attributed to the transition from diffusion‐dominated to convection‐dominated on momentum transfer, and the transition interval is 0.167 < γ < 0.250. Correlation equations of Pe number with Reynolds (Re) number and γ are established under diffusion‐dominated and convection‐dominated states. The symmetrically distributed secondary flow in the helical annular gap effectively elevates the Pe (Pemax > 100). Correlation equations of Pe with Re and γ are established in helical annular gaps with 0.083 < γ < 0.208 and 0.167 < γ < 0.500. The above results contribute to understanding the annular flow RTD characteristics for better applications of tube‐in‐tube reactors.

A new mechanistic model to predict liquid loading in inclined natural gas wells

Accurately predicting the critical gas velocity and inclination angle is crucial for gas field development. However, the mechanism of liquid loading remains elusive due to insufficient attention given to the multivaluedness of flow structures and phase non-uniformity. This paper theoretically studied the flow pattern and gas-liquid configuration in wellbore based on the minimum energy principle. The Kelvin-Helmholtz instability of liquid film was analyzed, and a new correlation for the interfacial friction factor was proposed based on wave properties. The results indicated that the flow pattern transitioned from stratified to annular flow as the inclination angle increased. The gas-liquid interface presented a curved shape, with the interface curvature being influenced by various factors such as fluid properties, tube diameter, inclination angle, and gas and liquid velocities. As the inclination angle increases, the critical gas velocity first increases and then decreases, reaching a peak between 44° and 59°, aligning well with experimental and conventional results. Larger tube diameter, higher liquid density, and viscosity result in a higher critical gas velocity. Waves are more prone to develop in inclined pipes, and capillary waves can break up liquid film due to instability, leading to a discontinuous flow in inclined tubes. Film instability is exacerbated by a smaller diameter, higher liquid holdup, or greater inclination angle. Finally, a new model was devised to predict liquid loading in inclined natural gas wells, demonstrating better performance than existing models. In practice, the present model can achieve real-time prediction of critical gas velocity and continuously monitor the location of liquid accumulation in gas wells over the lifespan.

Numerical investigation on dynamic flow characteristics of methane condensation in microchannels

Microchannel condensers play an essential role in cryogenic two-phase heat management systems due to their efficient heat transfer characteristics. Thus, it is worth conducting an in-depth study on microscale condensation characteristics of cryogenic fluids. This paper delves into the flow condensation process of methane in microchannels. A two-dimensional transient model with high accuracy for cryogenic fluids has been developed by combining a self-defined program for the source term of the phase transition model. The model fully considers the boundary layer thickness and accurately explores the mesh accuracy. The complete condensation flow patterns are captured for various vapor quality, mass flux, and wall subcooling degrees. The injection flow is a unique flow regime for condensation in microchannels. The decrease in wall subcooling degree and increase in mass flux leads to the separation point at the neck of the injected flow moving towards the exit, while the annular flow region is expanding and the flow pattern transition is lagging. The mass flux improves the heat transfer coefficient more significantly at high vapor quality. During injection and bubble flow, the wall shear stress and local heat transfer coefficient are subject to bouncing and oscillations, which may induce fluctuations in the upstream annular flow. The prediction performance of six classical heat transfer correlations is evaluated. The results indicate that the Nie et al. correlation has the highest comprehensive prediction accuracy with MRD and MARD of -5.00 % and 15.83 %, respectively.

The effect of swirling shear blade on gas-liquid flow pattern and mass transfer performance in Venturi injector

To address the challenge of low mass transfer efficiency of gas-liquid reaction in traditional reactors, this study proposes a new method to improve the gas-liquid mass transfer efficiency by integrating swirl shear blades (SSB) into Venturi injectors. The gas-liquid flow patterns in the mixing and diffusion sections between the Swirl Venturi Injector (SVI) and the Traditional Venturi Injector (TVI) was compared, and it was found that the SSB significantly reduced the proportion of annular flow while increased the proportion of mist flow. The enhancement factor αE and the acceleration factor αA are applied to evaluate the mass transfer performance. Compared to TVI, the maximum αA of SVI was 29%, and the maximum αE was 43%. This work shows great potential in efficiently capturing gas components with low solubility in the liquid phase, thereby helping to achieve the goal of green chemical engineering.

Measurement of air-water counter-current flow rates in vertical annulus using multiple differential pressure signals and machine learning

Abstract Gas–liquid counter-current flow in vertical annulus is involved in several industrial fields such as petroleum engineering. For example, in coalbed methane wells with liquid pump drainage, obtaining the real-time flow rate of gas–liquid two-phase in the annulus is crucial for the development management of coalbed methane wells. However, due to complex flow conditions, this demand is difficult to achieve through traditional flow metering means. Therefore, this paper proposes a flow prediction method based on multi-group differential pressure signals and machine learning technology. Air-water two-phase flow experiments were carried out on a vertical annulus pipeline with inner and outer diameters of 75 mm/125 mm and adjustable eccentricity. The probability density function and power spectrum density of 3 groups of differential pressure signals collected at different height intervals in the annulus were used as model inputs. A gas–liquid two-phase flow prediction model was constructed based on the artificial neural network model, and the model hyper-parameters were optimized using Bayesian optimization. The results show that on the 440-group test dataset under the combined conditions of air superficial velocity of 0.06–5.04 m s−1, water superficial velocity of 0.03–0.25 m s−1, and pipeline eccentricity of 0, 0.25, 0.5, 0.75, 1, etc. This model can achieve average prediction errors of 9.12% and 29.34% for gas and water flow rates respectively. This method can be applied to the non-throttling, non-invasive measurement of phase flow rate under the condition of annulus air-liquid counter-current flow.

P-wave velocity evolution and interpretation of seepage mechanisms during CO2 hydrate formation in quartz sands: Perspective of hydrate pore habits

The hydrate-based CO2 storage (HBCS) is a promising technology for controlling CO2 emissions. A comprehensive understanding of the hydrate pore habits and seepage mechanism of hydrate-bearing sediments (HBSs) could provide a theoretical basis for HBCS. In the study, the hydrate occurrence characteristics, water migration and P-wave velocity response during hydrate formation in quartz sands are investigated. In addition, a new theoretical equation that relates P-wave velocity to permeability is presented. The digital core of porous media containing hydrate is also established, and the seepage characteristics during hydrate formation are revealed by numerical simulation. The results show that hydrates are preferentially generated in large pores and initially appear in a non-cementing pore-filling pattern, while an annular flow path for water is formed in quartz sands during hydrate formation. The hydrate morphology is changed from a pore-filling pattern to a patchy pattern at a critical hydrate saturation of around 3–7% for quartz sands with various particle diameters. The formation sites and spatial heterogeneity of hydrates can be depicted by the evolution pattern of streamlines. The results of the experiments indicate that the new semiempirical model is effective for estimating the permeability from the P-wave velocity of HBSs. These findings offer significant theoretical and practical insights for HBCS in porous media.

Insights into two-phase flow dynamics in closed-loop pulsating heat pipes utilizing Fe3O4/water: experimental visualization study

This article discusses a focused study on visualizing the flow patterns in a two-phase pulsating heat pipe (PHP) using Fe3O4/water as the working fluid at 3 V/V% concentration. The research also aims to meticulously examine phase change phenomena in the heating section, particularly focusing on bubble formation and expansion processes. A high-speed video camera was utilized to capture dynamic insights into the behavior of the Fe3O4/water mixture. Based on the findings, a straightforward model was developed to explain bubble generation and growth in the mixture, serving as a useful reference for future PHP designs and optimizations. Visual observations also noted the stable nature of the Fe3O4/water nanofluid over a 4-day period, confirming its consistency throughout the experiments. Moreover, the impact of heat load variation on the evaporator section was assessed using controlled heat inputs ranging from 10 to 80 W. Observations on the arrangement of slugs and plugs at a 50% filling ratio revealed interesting self-adjusting flow patterns in response to increasing heat inputs, providing valuable insights into PHP operational dynamics. Notably, the oscillatory flow behavior of Fe3O4/water, the chosen working fluid, exhibited greater activity in comparison to water. This distinctive flow behavior contributed to achieving heightened thermal performance efficiency for the Fe3O4/water system, attributed to its faster attainment of the annular flow condition.

Experimental Investigation of Spherical Particles Settling in Annulus Filled with Rising-Bubble-Containing Newtonian Fluids

During the drilling of ultra-deep wells, gas kick often occurs, influenced by the complex void pressure profile. The accurate description of particle settling behavior in the gas–liquid mixture is of great significance to effectively deal with gas kicks and ensure drilling safety. In this study, the gas–liquid two-phase annulus flow with different gas volume fractions is created through the transparent annular pipe, constant pressure air pump, and gas flowmeter. High-speed photography is used to record and analyze the sedimentation of particles in gas–liquid mixtures. This study is based on 288 tests. The main parameters in this experiment include the particle Reynolds number, the gas fraction, and liquid viscosity. The effects of wall and gas fraction on the drag coefficient were analyzed. The correlation of particle terminal settling velocity was established. The results obtained show a correlation with average absolute errors (AAE) of 10.7%. This study reveals the settling characteristics of particles in the annular gas–liquid mixed flow, provides an accurate terminal settling velocity prediction explicit formula, and provides guidance for the calculation of bottom hole pressure under the condition of gas kick.

AERODYNAMIC IMPACT OF SECONDARY AIR INJECTION FLOWRATES ON THE MAIN ANNULUS FLOW FIELD FOR A TRANSONIC HIGH-PRESSURE TURBINE STAGE

Abstract In this study, the influence of secondary air blowing on the main annulus flow field of a transonic high-pressure turbine (HPT) was investigated experimentally and numerically. The experimental setup was a single-stage, unshrouded turbine with a blading consistent with modern HPTs. The entire testing campaign was conducted in a full annular, rotating, continuous turbine test rig at the Japan Aerospace Exploration Agency (JAXA), which realized the most faithful matching unrivalled of both the primary and secondary stream similarity parameters to reality. An elaborate secondary air system implemented in the hardware enabled it to mimic all the dominant coolant/purge streams representative of advanced hot sections: the full coverage film-cooling on stator and rotor airfoils, disk wheelspace purge air blown forward and aft of the rotor, and coolant injection through the over-tip casing. Detailed three-dimensional flow field measurements for various secondary air flowrates were performed by traversing a pneumatic thermometric combination probe downstream of the rotor. A complete set of numerical simulations was run concurrently with the testing to determine how well they captured the flow physics, particularly the interaction of the ejected secondary streams with the primary flow. The JAXA in-house code, UPACS, and its best practice settings, based on past verification and validation efforts, were employed and not intentionally tuned to better fit the data.

Interfacial area concentration correlation for boiling steam-water two-phase flows in annulus flow channels

The investigation of boiling two-phase flows in annulus flow channels has garnered increasing significance given its extensive utilization in various heating devices and its crucial contribution as a fundamental basis for comprehending boiling two-phase flow behavior in intricate flow channels, such as rod bundle flow channels. Accurate modeling of Interfacial Area Concentration (IAC) in boiling steam-water two-phase flows is essential for enhancing the predictive performance of the two-fluid model in simulating complex two-phase behaviors in a diverse range of practical boiling systems. The present study evaluates the predictive performance of seven representative IAC correlations using available typical experimental IAC data from boiling steam-water two-phase flows in annulus flow channels. Although some representative IAC correlations exhibit favorable predictive performance for specific experimental databases, none of the reviewed existing correlations consistently maintain acceptable predictive performance across all collected experimental data. In order to enhance the accuracy and reliability of IAC predictions under boiling flow conditions, a novel IAC correlation has been proposed grounded in physical-based considerations to effectively model the IAC contributions of small (group-1) and large (group-2) bubbles in boiling steam-water two-phase flows in annulus flow channels. The newly proposed two-group bubble IAC correlation has been validated through the examination of 303 boiling steam-water data obtained from annulus flow channels, demonstrating satisfactory predictive performance with the mean relative error of 0.216. Moreover, the applicability of the newly proposed IAC correlation to rod bundle flow channels has been evaluated using 53 boiling steam-water data taken from a 3 × 3 rod bundle flow channel, yielding a favorable prediction result with a mean relative error of 0.173. The anticipated improvement in the accuracy of predicting IAC for steam-water two-phase flows through the newly proposed correlation is expected to provide a scientific foundation for enhancing the performance and safety of thermal systems.

Analysis of stability and internal flow mechanisms in spiral annular flow with different swirlers

Spiral annular flow within ducts is widely utilized in modern industry, with the swirler serving as a critical component in generating such flow patterns. The structure of the swirler significantly influences the generation and stability of the spiral annular flow. This study selected four different swirler structures with outstanding performance from previous research and analyzed their characteristics through visual image processing combined with numerical simulations. By analyzing the amplitude information of the wave fluctuations in the annular swirling flow liquid film under different operating conditions using probability density functions, it was found that the swirler A(Flat-vane swirler) and swirler B(Flat-vane swirler with hub) produced smaller fluctuations in the annular swirling flow liquid film, indicating better stability compared to the swirler C(Arc-vane swirler) and swirler D(Spiral-vane swirler), which exhibited poor performance. Combining the numerical simulation results with the analysis of the internal mechanism of the swirlers, it was discovered that within the swirler A and swirler B, the fluid between the swirler vanes experienced a larger pressure gradient, resulting in phenomena such as “jump” and “pull” under this pressure gradient. This, in turn, contributed to the generation of greater tangential velocity and radial pressure gradient after the fluid exited the swirler. Due to the influence of the swirler structure, the swirler A and swirler B did not completely separate the fluid region into four independent spaces. Instead, in the central connection area of the rear section of the swirler, the gas phase components aggregated earlier, greatly promoting the downstream generation of spiral annular flow. This study analyzed the two-phase flow process and mechanism inside the swirler, filling a gap in previous research and providing important references for the optimization and selection of swirlers.

Effect of tip clearance on non-synchronous propagating flow disturbances of compressor rotors under high aerodynamic loading conditions

The complex tip flow instability and its induced non-synchronous vibration have become significant challenges, especially as aerodynamic loading continues to increase. This study investigates the effects of tip clearance on non-synchronous propagating flow disturbances of compressor rotors under high aerodynamic loading conditions by conducting full-annulus unsteady numerical simulations with three typical tip clearance values for a 1-1/2 stage transonic compressor. The non-synchronous aerodynamic excitation frequency, circumferential mode characteristics, and annular unstable flow structures are analyzed under near stall conditions. The results show that the total pressure ratio and normalized mass flow parameters first increase and then decrease as the tip clearance increases from 0.5%C (where C represents the tip chord length) to 2%C under high aerodynamic loading conditions, instead of constantly decreasing. For the 0.5%C tip clearance case, the traveling large-scale tornado-like separation vortices cause a low non-synchronous aerodynamic excitation frequency and severe pressure fluctuations. The periodic shedding and reattachment processes of the rotor blades separated by 2 – 3 pitches result in 19 dominant mode orders in the circumferential direction. As the tip clearance increases from 1%C to 2%C, the difference of tip flow structures in each blade passage is significantly weakened, and the dominant mode order of the disturbance is equal to the rotor blade-passing number. The pressure fluctuation is mainly caused by cross-channel tip leakage flow, and the aerodynamic excitation frequency exhibits evident broadband hump characteristics, which has been reported as a rotating instability phenomenon.

Energy Efficient Downsizing of Ribbed Confinements for Heat Exchange Applications

Abstract Downsizing double-pipe heat exchangers is possible by deploying ribs on the two sides of the heat exchangers. The shape of these ribs, along with two key geometric variables – pitch and height, are crucial in the selection of energy-efficient rib configurations. This is because, the enhancement in heat transfer performance comes at the cost of increased pressure drop. Thus, the goal of this three-dimensional numerical investigation is to identify favourable rib shapes and explore the effect of truncation on triangular ribs, something which is missing from existing literature. Truncation is expected to greatly affect the performance of triangular ribs, either adversely or favorably. To explore this conclusively, an unbiased and exhaustive analysis is carried out by comparing the performance of confinements with modified and regular triangular ribs, keeping plain confinements as the baseline. Furthermore, the effects of two principal design variables – rib height and rib pitch are explored for each shape. Separate results are presented for the inner and outer confinements of the double-pipe heat exchangers (pipes and annuli) to allow for the extrapolation of results for a wide range of applications employing internal flows in pipes and annuli. A phenomenological model is developed to classify the thermo-hydraulic performance of each confinement and identify optimal geometrical configuration and identify best performing design(s). Once optimal rib pitch-height combinations are identified, performance at this optimal combination is evaluated at different Reynolds numbers, spanning from 10,000 to 30,000.

Heat absorption effect of magneto-natural convection flow in vertical concentric annuli with influence of radial and induced magnetic field

This paper aims to study the natural convective magneto-hydrodynamic flow of fluid through vertical concentric annuli with iso-flux heating under the conditions of constant internal heat absorption and an induced magnetic field. By solving the set of dimensionless coupled governing equations, we were able to obtain exact expressions for the temperature field, velocity field, and induced magnetic field. We also managed to derive the formulas for skin friction, mass flux, and induced current density. We also examined the effects of non-dimensional parameters on skin friction and mass flux. For easy comprehension and interpretation, the results are provided graphically and in tabular form. The heat absorption parameter, the induced current density, the induced magnetic field, and velocity exhibit a negative trend as the Hartmann number (Ha) value increases. The induced magnetic field has the effect of raising both the induced current density and velocity profile. It is found that, when a fluid absorbs heat, the heat absorption parameter experiences reverse flow. For the heat-absorbing fluids, the radii ratio has the effect of increasing velocity, induced magnetic field, and induced current density. The numerical values of skin friction and mass flux at cylindrical walls increase (decrease) with increasing heat absorption parameter and generally it has decreasing tendency with increasing Hartmann number

Calcium carbonate scale thickness prediction in annular three-phase flow using gamma-ray densitometry and artificial neural networks

This study presents a methodology based on gamma-ray densitometry for predicting calcium carbonate (CaCO3) scale thickness in pipelines of three-phase systems (oil, salty water, and gas) in the petroleum industry. Both concentric and eccentric scale thicknesses were calculated using analytical equations and artificial neural networks. The artificial neural networks were trained using a backpropagation algorithm with data acquired from the Monte Carlo N-Particle (MCNP6) computer code. The model utilized to achieve the supervised training of the network consisted of three 1¼ × ¾″ NaI(Tl) detectors positioned 120° apart around the pipe. Results demonstrate that the networks successfully predicted over 96 % of both concentric and eccentric cases of CaCO3 scale thickness with a relative error within 10%.

Model establishment and flow field simulation analysis of high torque screw motor in ultra-deep well

Abstract To explore the distribution law of the flow field in the inner annular flow channel of the stator-rotor of the high-torque screw drill tool and determine the key performance parameters of the tool under different drilling fluid densities and flow rates, a physical model for fluid simulation was established with the 7/8 head screw motor as the research object to study the distribution law of the flow field and the output torque of the rotor at different flow rates and densities, and a comparative analysis was made with the actual test. The results show that the pressure of the internal flow channel is mainly concentrated at the entrance of the flow channel and the wall of the flow channel. The flow rate in the thick fluid domain is high, the flow rate in the thin fluid domain is low, and the flow rate in the thinnest area is about zero. The relationship between displacement pressure drop and output torque presents a positive correlation. When displacement increases, the output torque of the screw increases, and the relationship between displacement and torque presents a linear increase. The torque and displacement of fluid simulation under ideal conditions are larger than the actual test parameters. In the actual test, the drilling fluid temperature and experimental equipment factors affect the performance of the screw motor. In the process of fluid simulation, the setting of boundary conditions should refer to the real situation as much as possible to improve the accuracy of simulation results. The difference between fluid simulation and actual test parameter values is small and the trend is the same, so fluid simulation can guide practical application and reduce cost to a certain extent.

Analysis of Bubble-Flow Characteristics in Scavenge Pipe and Establishment of a Flow-Prediction Model

In the modern aerospace industry, the importance of a lubrication system is self-evident for aero-engines, and the aero-engine bearing chamber return line is an even more challenging environment, as it involves a complex two-phase flow. The designer of the scavenge pipe needs to have an accurate understanding of the flow conditions in the scavenge pipe. This paper establishes a visual scavenge pipe test system. The flow direction was vertical flow, the test temperature was 370 k, and a high-speed camera was used to take high-definition flow photographs, which can observe the three main flow types: bubble flow, slug flow, and annular flow. Code program was created to analyze many pictures taken to obtain the apparent flow rate and perimeter of bubbles in the pipe under different flow conditions and to explore the gas–liquid two-phase flow in the scavenge pipe. A support vector machine (SVM) was used for data regression prediction, and the converted velocities of the gas–oil phases were inputted as eigenvalues to obtain the predicted values of bubble-flow velocity. The bubble-flow analysis prediction model established in this paper has a good prediction effect with root mean square error RMSE = 0.0172, which can more objectively and accurately describe the bubble-flow characteristics in the scavenge pipe.

Assessment of ansys-fluent Code for Computation of Two-Phase Flow Characteristics: A Comparative Study of Water–Air and Silicone Oil–Air in a Vertical Pipe

Abstract The study aimed to assess the flow characteristics of water–air and silicone oil–air in a vertical upward pipe, utilizing computational fluid dynamics (CFD) simulations with the volume of fluid (VOF) model. Structured meshes with various resolutions were employed to ensure mesh independence, and the k–ε realizable model addressed turbulence. Simulations were conducted in a vertical pipe with a diameter of 67 mm, while varying superficial gas velocities. The investigation focused on the impact of superficial gas velocity on flow patterns, radial void fractions, void fraction time series, probability density functions (PDFs), and mean void fractions. Results indicated a transition in flow patterns with increasing superficial gas velocities: water–air shifted from cap-bubbly to churn flow, and silicone oil–air transitioned from bubbly to annular flow. Notably, annular flow was observed in silicone oil even at low gas velocity. Substantial alterations were observed in radial void fraction profiles corresponding to changing flow patterns. Void fraction time series showed higher fluctuations for water compared to silicone oil, and PDFs identified regimes. Mean void fraction consistently demonstrated higher values for silicone oil compared to water across all flow conditions. The CFD results were validated against experiments, demonstrating good agreement. Furthermore, the validated model was applied to predict pressure drops and liquid velocities between the two systems. Silicone oil exhibited lower pressure drops compared to water. Significant differences in liquid velocities were observed between the two systems at 0.05 m/s and 5.71 m/s, emphasizing the impact of fluid properties.

Drift-flux correlation for bubbly to annular two-phase flows under microgravity conditions

In light of the substantial importance of accurate void fraction predictions for the engineering design and safety evaluation of two-phase systems utilized in space-related applications, this study is dedicated to the investigation of the drift-flux correlation specifically for microgravity conditions. The present study has collected 458 experimental void fraction data taken in microgravity bubbly to annular flows. The analysis of the collected experimental data evident that (1) the distribution parameters vary with the flow conditions, and (2) the drift velocities under microgravity conditions are exceedingly small. However, the distribution parameter models of the reviewed existing drift-flux correlations fail to accurately capture the variation of distribution parameters with flow conditions under microgravity conditions. Moreover, there is a lack of a simple yet effective way to model the drift velocity of microgravity two-phase flow. To overcome the above weaknesses, a new drift-flux correlation has been proposed by (1) taking the flow condition effect on the variation of asymptotic distribution parameters into consideration, and (2) employing the concept of effective body acceleration and considering the decay of drift velocity in annular flow. The newly proposed drift-flux correlation has been evaluated by checking against the collected data and shows good predictive ability.

Thermal hydraulic behavior of a large dimension hybrid heat pipe/oscillating heat pipe

Similar to the layout of an oscillating heat pipe (OHP), a quartz hybrid heat pipe (HHP) with an inner diameter of 5 mm, exceeding 59.7 % of the capillary threshold of OHP, was designed. The detailed thermal hydraulic behavior of fluid in the HHP has been revealed. It was found that the HHP undergoes a heat transfer mode transition from phase change to pulsating flow. It is also means that the liquid slugs can be dynamically and stably formed if the heat input is sufficient. The single bubble growth and the multi-bubble coalescence are two ways to form the intermittent flow. In addition, as the main flow pattern in low filling ratio (FR), the formation of annular flow is closely concerned in the behaviors of fluid. Moreover, the higher the FR is, the clearer the contour of slug flow is. At the same time, the oscillating motion can be formed easily at a high FR, resulting in a better performance of HHP in lower heat load. However, as the heat input increases, HHP with a 60 % filling ratio exhibits lower thermal resistance, achieving a minimum value of 0.08 °C/W at 100 W.