Cryogenic Fluids Research Articles

CFD and experimental analysis of the coolant flow in cryogenic milling

Abstract Cryogenic cooling could improve the machining performance for hard-to-cut materials. Deployment of this modern technology for milling applications, specifically because of their severe working conditions and complicated physical phenomena inside cryogenic fluids, requires further research to become credible for industrial applications. Obtaining accurate models for coolant behavior is essential for optimum design, prediction of operational limits, and safe control of the cooling process. In this paper, Computational Fluid Dynamics (CFD) were used to determine the behavior of the liquid nitrogen (LN2) inside the coolant delivery system and the interaction of the coolant jet with the cutting area. The role of working conditions as well as nozzle geometry, formation of cavitation inside the tool, coolant pressure, and wall temperature on the efficiency of the coolant delivery were investigated in this study. Initial experimental flow measurements were used to predict the simulation setup and evaluate the results. Experimental milling tests were performed to verify the numerical findings. Cutting forces, coolant mass flow rate, temperature, and pressure were measured during the tests. A mechanistic cutting force model and the morphology of the chips were used to interpret the effect of liquid nitrogen on the cutting mechanisms. Results of this study offer three main suggestions for reliable industrial cryogenic milling: using liquid nitrogen in the range of 2–4 bar, improving the insulation of the feeding line and finding a technical solution for non-insulated parts, and increasing the quality of the liquid in the coolant mixture close to the milling head. Outcomes of this study could help to improve the cooling performance and implement a reliable industrial solution for cryogenic milling.

Theoretical and experimental approach to ball bearing frictional characteristics compared with cryogenic friction model and dry friction model

Abstract In previous studies on cryogenic ball bearings, a friction model of solid lubrication characteristics was employed with the assumption that the low dynamic viscosity of cryogenic fluids is negligible. A traction curve was then created using this dry friction model, with curve fitting being performed using a traction coefficient derived from the results of a ball-on-disk experiment with corresponding solid lubricant. However, the behavior prediction had many limitations, because the fluid characteristics in the cryogenic environment and the friction characteristics of the bearing components were not reflected. This study attempts to improve the reliability of cryogenic ball bearing dynamic analysis by proposing a hydrodynamic friction model considering the hydrodynamic effect of cryogenic fluids. A ball-on-disk experiment is conducted by simulating (1) ball-cage friction, (2) ball-inner/outer race friction, and (3) cage-inner/outer race friction characteristics. Hence, it is found that uncertainty factors causing traction coefficient fluctuation exist in certain device sections, reflecting the effect on the wear surface of friction and the hydrodynamic effect of the shear stress of the cryogenic fluid (liquid nitrogen). A dynamic experiment and cryogenic ball bearing analysis using the model considering the hydrodynamic effect are conducted and compared. From the ball bearing dynamic behavior analysis, the hydrodynamic friction model is found to predict a bearing friction coefficient that is closer to the actual value than the dry friction model. When the proposed model is applied to bearing dynamic behavior, it is possible to predict the cryogenic-bearing friction coefficient with 50% higher accuracy than the existing method.

Cryogenic Milling: Study of the Effect of CO2 Cooling on Tool Wear When Machining Inconel 718, Grade EA1N Steel and Gamma TiAl

The need for machining advanced materials has increased exponentially in recent years. Ni-based alloys, Ti-based alloys or some steel grades are commonly used in transport, energy generation or biomedicine industries due to their excellent properties that combine hardness, high temperature strength and corrosion resistance. These desirable properties make such alloys extremely difficult to machine, inducing a quick cutting tool wear that must be overcome. In the last decade, cryogenic machining has emerged in order to improve the machining of these materials. By means of cryogenic fluids such as cutting coolants, significant improvements in the life of cutting tools are obtained. However, most studies on this new technology are focused on turning processes, because of the difficulty of introducing cryogenic fluids through a rotary tool in processes such as drilling and milling. In this study, a cryogenic milling system integrated within the tool holder is used for milling Gamma TiAl, Inconel 718 and grade EA1N steel using carbon dioxide as a coolant. This system has been compared with the traditional cooling method (emulsion) in terms of tool life to check if it is possible to improve the machining operation in terms of efficiency by supplying the cryogenic coolant directly to the cutting zone. The results show that by replacing traditional pollutant cooling fluids with other more ecologically-friendly alternatives, it is possible to improve tool life by 100% and 175% in the cases of Gamma TiAl and grade EA1N steel, respectively, when using the new delivery system for the coolant.

Assessment of two-phase heat transfer coefficient and critical heat flux correlations for cryogenic flow boiling in pipe heating experiments

The design and development of future cryogenic transfer systems depends on accurate correlations for modeling two-phase boiling and heat transfer at reduced temperatures in both quenching and heating configurations. The penalty for poor models translates into higher margins, increased safety factors, and an overall increase in cost. Existing correlations used in fluid/thermal design codes are based on room temperature fluids and have been shown to not accurately predict heat transfer for cryogenic fluids in the quenching configuration. This paper presents the results of a deep literature review of 40 studies conducted to gather and consolidate a database of cryogenic flow boiling data in the heating configuration. The purpose of this paper is to assess the existing correlations against the gathered experimental data. Twelve sets of cryogenic two-phase heated tube data were collected which include 872 nucleate boiling, 2250 film boiling, and 41 critical heat flux data points. The data was compared against a total of 20 heat transfer coefficient and critical heat flux correlations. As in the case of the quenching configuration, results show that existing correlations do not accurately predict cryogenic heated tube data, but the disparity between heated tube data and models is not nearly as high as in the quenching configuration.

Experimental study on the condensation characteristics of nitrogen with non-condensable gas

The non-condensable gas at the top of the main condenser of the distillation section, such as helium or neon, would lower the heat transfer efficiency and the productivity of the air separation plant. Current research mainly focuses on the study of the water vapor condensation mechanism with non-condensable gases, while those on cryogenic fluids are rare. In this work, an experimental setup was designed to study the condensation mechanism of pure nitrogen vapor and nitrogen vapor mixed with helium on the vertical plate. The experimental data of pure nitrogen vapor is in good agreement with the results calculated by the classical Nusselt model, which demonstrates that the experimental system has high reliability. The influences of the mass fraction of helium and system pressure on the condensation heat transfer coefficient are analyzed. Results show that even a very low mass fraction of helium can cause the condensation heat transfer coefficient of nitrogen vapor to decrease obviously. The deviation between the heat transfer coefficient of the nitrogen-helium mixture and pure nitrogen increases with the increases of the helium mass fraction and the decrease of system pressure. A new condensation heat transfer correlation for nitrogen with helium is developed that the deviations of most of its predictions are within 20% compared to the experimental data.

Load capacity of foil gas dynamic bearings with conical surfaces lubricated with low-viscosity cryogenic fluids

The present paper features a mathematical model of load capacity and static characteristics calculation of foil gas dynamic bearings with conical surfaces lubricated with cryogenic fluids based on equations of thermophysics, hydrodynamic and elasticity theory. Algorithmic model is presented. Original software is presented that is used to calculate load capacity and static characteristics of the bearings in question.

CFD analysis of the evaporating two-phase flow in the slug flow regime of a cryogenic fluid in a microchannel

Flow boiling in a microchannel is investigated in the present work using the multiphase CFD. Cryogenic fluid nitrogen is used as a working fluid for the CFD simulations. A single bubble is patched in the upstream of the microchannel and the bubble profile, velocity and temperature profile and the heat transfer performance is evaluated. Effect of parameters, like wall heat flux and inlet flow rate or Reynolds number, are studied. It is found that the passage of the bubble significantly alters the parabolic velocity. The passage of the bubble and the evaporation at the interface also significantly reduces the wall temperature due to the enhanced heat transfer. Heat flux does not seem to have any effect on the average heat transfer coefficient, while the heat transfer coefficient increases with the inlet flow rate. The numerical framework employed to perform this study is the open source CFD package OpenFOAM with the volume of fluid interface capturing method.

Evaluation of mass transfer correlations applying to cryogenic distillation process with non-equilibrium model

Reliable heat and mass transfer model plays a significant role on design and calculation of the distillation process. Since the cryogenic fluids of oxygen, nitrogen and argon have obviously different thermal physical properties compared to the room temperature ones, it is of great necessity to evaluate the feasibility of the existing heat and mass transfer models in the cryogenic distillation calculation. In this study, a non-equilibrium model (NEM) based on the FORTRAN compiler is implemented to investigate the actual cryogenic distillation process in a structured packing column (SPC) of the air separation unit (ASU) with capacity of 17,000 Nm3/h. The complete conservation equations for materials, mass and energy in the phases are numerically solved based on the Thomas algorithm. The commonly used mass transfer coefficient models with different diffusion coefficients, as well as the heat transfer model, are evaluated in the performance prediction of the cryogenic SPC. The multiple imports and exports of the model are validated by the limited available measurements, while the calculated distributions of the component molar fraction, temperature, pressure and flow rates along the column are compared with those from the Rate-based module of Aspen plus simulation. The comparisons verify the solving strategy and help to understand the reliability of the existing basic transfer correlations for future cryogenic distillation calculation.

Experimental investigation on line chill-down process by liquid argon

The cryogenic line chill-down process is an essential part of the cryogenic system application. As the heat transfer characteristics during the transient cooling down are highly affected by the fluid properties, universal heat transfer correlations, which are valid for the chill-down process with various kinds of cryogenic fluid, are required in many industries. This paper investigates cryogenic line chill-down process by using a 7 m long stainless steel horizontal pipe. Liquid argon is selected as the working fluid to examine the fluid property effects. The histories of the wall temperature, pressure, and mass flow rate are measured during the chill-down process. The heat transfer characteristics of liquid argon are analyzed and compared with those of chill-down process with liquid nitrogen. At the same time, the empirical correlations for the critical heat flux, critical heat flux temperature, and minimum heat flux temperature, which can well estimate the parameters for both of liquid nitrogen and liquid argon cases, are suggested. As a result, the critical heat flux is estimated with the mean absolute error (MAE) of 14.8%. The critical heat flux temperature and minimum heat flux temperature are predicted with the MAE of 3.4% and 1.9%, respectively. The empirical correlations are essential to construct a numerical model for simulating the cryogenic line chill-down process.

Design and numerical investigation to visualize the fluid flow and thermal characteristics of non-axisymmetric convergent nozzle

In this paper, numerical simulations are conducted to visualize the fluid flow and thermal characteristics of a non-axisymmetric convergent nozzle. The novel design methodology is based on curve-fitting approach. The curves used for designing the nozzle are based on a combination of fifth and third order polynomial at upper and lower surfaces respectively. The computations are performed using commercially available computational fluid dynamics (CFD) tool ANSYS CFX®. Firstly, mesh independence analysis are carried out. Then, numerical simulation is further validated for medium and low-pressure helium by comparing it with the available experimental data. Thereafter, an exhaustive analysis is carried out to compare the fluid flow behavior inside the nozzle for two cryogenic fluids, nitrogen and helium at three different inlet pressure and temperature. The fluid flow pattern, pressure, velocity, Prandtl number, static enthalpy, Reynolds number, eddy viscosity, etc. are identified at various positions. The Mach number and temperature at the outlet of the nozzle is the key feature of this analysis which satisfies the criteria for a nozzle which is used for the high, medium and low-pressure turbine. The analysis provides a better understanding of the further improvement of the design methodology or performed an experiment. The designed nozzle has a tremendous effect on the fluid flow behavior and suitable for impulse type turbine with a small amount of reaction used in a turboexpander. The work proposes a new design methodology for designing a non-axisymmetric airfoil convergent nozzle of rectangular cross-section.

Simulation of boil-off losses during transfer at a LH2 based hydrogen refueling station

Losses along the LH2 pathway are intrinsic to the utilization of a cryogenic fluid. They occur when the fluid is transferred between 2 vessels (liquefaction plant to trailer, trailer to station storage, station storage to pump or compressor, then possibly onto fuel cell electric vehicles …) and when it is warmed up due to heat transfer with the environment. Those losses can be estimated with good accuracy using thermodynamic models based on the conservation of mass and energy, provided that the thermodynamic states are correctly described. Indeed, the fluid undergoes various changes as it moves along the entire pathway (2 phase transition, sub-cooled liquid phase, super-heated warming, non-uniform temperature distributions across the saturation film) and accurate equations of state and 2 phase behavior implementations are essential. The balances of mass and energy during the various dynamics processes then enable to quantify the boil-off losses. In this work, a MATLAB code previously developed by NASA to simulate rocket loading is used as the basis for a LH2 transfer model. This code implements complex physical phenomena such as the competition between condensation and evaporation and the convection vs. conduction heat transfer as a function of the relative temperatures on both sides of the saturated film. The original code was modified to consider real gas equations of state, and some semi-empirical relationships, such as between the heat of vaporization and the critical temperature, were replaced by a REFPROP equivalent expression, assumed to be more accurate. Non-constant liquid temperature equations were added to simulate sub-cooled conditions. The model shows that under environmental heat transfer only the liquid phase of a LH2 vessel would experience cooling, while the boil-off is mainly a result of evaporation from the saturation film onto the vapor phase. Under the conditions assumed for this work, it was also concluded that the actual LH2 density was lower than the corresponding saturation density given by the working pressure of the vessel. During a bottom fill transfer, for example from a LH2 trailer to an on-site stationary vessel, it is shown that the boil-off losses are due to the compression of the vapor phase (“pdV” force). The model indicates that the magnitude of those losses is not dependent on the regulated pressure in the receiving vessel but is rather a function of the initial pressure in the vessel, amounting to more than 12% of losses for a vessel initially at 100 psia. At last, the model is used to estimate the amount of vapor H2 vented when depressurizing a LH2 trailer following a LH2 delivery.

Forced flow cooling of high field, REBCO-based, fusion magnets using supercritical hydrogen, helium, and neon

Rare Earth Barium Copper Oxide (REBCO) High Temperature Superconductor (HTS) tapes are being considered for the Toroidal Field (TF) magnets of a highly compact, high field fusion reactor operating at magnetic fields as high as 21 T and operating temperatures in the range of 10–30 K. Due to the increase in range of operating conditions made available through HTS tapes, a new set of cryogenic fluids are being considered for forced flow cooling. The present study investigates helium, hydrogen, and neon as a forced flow coolant for REBCO HTS tapes used in a highly compact, high-field reactor design. Four design criteria are considered, including current sharing temperature, fluid inlet temperature, cable pressure drop (dP), and operating pressure. From these simulations, neon is removed from consideration due to its high required pressure drop and low temperature margins with respect to the current sharing limit. Helium and hydrogen are then compared, with hydrogen producing the highest overall heat transfer rate at its optimum operating condition (1.5 MPa/15 K). A compromise across inlet temperature, dP, and operating pressure is found when helium has a minimum initial temperature of 10 K and an inlet pressure of 2.0 MPa. For the current design, helium is selected as a coolant due its acceptable cable pressure drop, required cooling load, and system complexity inherent to a forced-flow cryogenic system.

A Study on Safety Assessment of Leakage of Small LNG Storage Facility Considering Numerical Simulation of Rollover Phenomena Using Vapor-Liquid Equilibrium at Cryogenic Fluid Interface

The share of natural gas as an energy source is gradually increasing, and natural gas has an important role as major energy source role that consumes more than 15% of the total energy consumption. In case of LNG, there is an increasing demand due to the advantage of cleanliness, convenience and economy of natural gas and also, demand for the small LNG storage facilities for fuel supplying LNG fuelled vessels, LNG cars and buses is increasing rapidly. In this study, we analyze the rollover case, which is the biggest LNG leakage accident in small LNG storage facility, by using Vapor- Liquid Equilibrium at the cryogenic fluid interface. Using this calculated results, we evaluate the accident impact by prediction and analysis of leakage damage in small LNG storage facility and examine the safety assessment for facilities to be constructed in the future.

Experimental study of thermal-crack characteristics on hot dry rock impacted by liquid nitrogen jet

Liquid nitrogen jet fracturing is a novel stimulation technology, which is expected to be suitable for hot dry rock (HDR) reservoirs. Due to the large temperature difference between hot rock and cryogenic fluid, a great number of thermal cracks would be created during fracturing process, which is conductive to improve the penetration capacity of formation. In this study, a set of experiments were conducted to investigate the characteristics of thermal cracks. In these experiments, granite specimens with temperatures ranging from 200 ℃ to 300 ℃ were impacted by the low-pressure liquid nitrogen jet. The complexity and connectivity of cracks were quantitatively analyzed by a fractal method. The permeability and ultrasonic velocity of the granite specimens were tested in order to evaluate the damage conditions caused by thermal stress. Additionally, scanning electron microscope was adopted to analyze the microscopic characteristics of the thermal cracks. The results show that the heating process has a slight effect on thermal-crack generation compared with the liquid-nitrogen impact. The cracks mainly concentrate in the region near the impingement surface, due to the large temperature gradient there. The impacted rock breaks as the effects of tensile stress and shear stress. With an increase of initial rock temperature, the number of thermal cracks increases, and a more complex crack-network is formed in each specimen. Transient pulse evaluation and ultrasonic velocity measurements indicate that the impact of liquid nitrogen jet can improve the permeability and cause the damage of hot rock noticeably. This study demonstrates the important effect of thermal stress on crack generation during liquid nitrogen jet fracturing for HDR reservoirs, and the results shed light on the exploitation of HDR energy.

Breaking up is hard to do: Global cartography and topography of Pluto's mid-sized icy Moon Charon from New Horizons

The 2015 New Horizons flyby through the Pluto system produced the first high-resolution topographic maps of Pluto and Charon, the most distant objects so mapped. Global integrated mosaics of the illuminated surface of Pluto's large icy moon Charon have been produced using both framing camera and line scan camera data (including four-color images at up to 1.47 km pixel scales), showing the best resolution data at all areas of the surface. Digital elevation models (DEMs) with vertical precisions of up to ∼0.1 km were constructed for ∼40% of Charon using stereo imagery. Local radii estimates for the surface were also determined from the cartographic control network solution for the LORRI framing camera data, which validate the stereo solutions. Charon is moderately cratered, the largest of which is ∼250-km across and ∼6 km deep. Charon has a topographic range over the observed hemisphere from lowest to highest of ∼19 km, the largest topographic amplitude of any mid-sized icy body (including Ceres) other than Iapetus. Unlike Saturn's icy moons whose topographic signature is dominated by global relaxation of topography and subsequent impact cratering, large-scale tectonics and regional resurfacing dominate Charon's topography. Most of Charon's encounter hemisphere north of the equator (Oz Terra) is broken into large polygonal blocks by a network of wide troughs with typically 3–6 km relief; the deepest of these occur near the illuminated pole and are up to 13 km deep with respect to the global mean radius, the deepest known surfaces on Charon. The edge of this terrain is defined by large tilted blocks sloping ∼5° or so, the crests of which rise to 5 or 6 km above Charon mean, the highest known points on Charon. The southern resurfaced plains, Vulcan Planitia, consist of rolling plains, locally fractured and pitted, that are depressed ∼1 km below the mean elevation of the disrupted northern terrains of Oz Terra that comprise much of the northern hemisphere (but ∼2–2.5 km below the surfaces of the blocks themselves). These plains roll downward gently to the south with a topographic range of ∼5 km. The outer margins of Vulcan Planitia along the boundary with Oz Terra form a 2-3-km-deep trough, suggesting viscous flow along the outer margins. Isolated massifs 2–4 km high, also flanked by annular moats, lie within the planitia itself. The plains may be formed from volcanic resurfacing of cryogenic fluids, but the tilted blocks along the outer margins and the isolated and tilted massifs within Vulcan Planitia also suggest that much of Charon has been broken into large blocks, some of which have been rotated and some of which have foundered into Charon's upper “mantle”, now exposed as Vulcan Planitia, a history that may be most similar to the disrupted terrains of Ariel.

Experimental study on dynamic behavior of ball bearing cage in cryogenic environments, Part II: Effects of cage mass imbalance

Abstract We studied the dynamic behavior of a ball bearing cage submersed in a cryogenic fluid and rotating at high speed as a function of the mass imbalance of the cage under various rotational speeds and light load conditions. The results include the whirling motions and distribution of whirling frequencies of the cage, the ball bearing torque, and the wear loss of the ball bearing elements for varying rotational speeds and mass imbalance conditions. The whirling motion of the cage tended to increase with the increase of the mass imbalance, and the influence of the mass imbalance was apparent with the increase of inner race speed. For all mass imbalance conditions, the whirling amplitude decreased with the increase of the inner race speed owing to the influence of the hydraulic force of liquid nitrogen. In addition, the standard deviation of the whirling frequency of the cage increased with the increase of the inner race speed. In particular, when the inner race rotational speed was 11,000 rpm, the standard deviation tended to increase markedly with increasing mass imbalance. The wear loss of the cage increased with the increase of the mass imbalance, and the wear loss at the bottom part of the cage increased owing to an abnormal motion caused by intermittent collision of the cage. The experimental results obtained under various mass imbalance conditions are consistent with existing interpretive literature and demonstrate the importance of the mass imbalance of the cage.

Experimental study on dynamic behavior of ball bearing cage in cryogenic environments, Part I: Effects of cage guidance and pocket clearances

Abstract In cryogenic environments, it is not possible to apply oil or grease to ball bearings, owing to the extreme temperature conditions. Thus, polytetrafluoroethylene (PTFE) cages are used as solid lubricants in such environments, because PTFE has a low coefficient of friction. PTFE cages increase the rotational stability of the ball bearings by reducing the frictional force of the rolling elements. In addition, design parameters such as the cage guidance and ball-pocket clearances significantly affect the stability of the ball bearings. In this study, the dynamic behavior of a ball bearing cage submerged in a cryogenic fluid was investigated for different cage clearances and rotation speeds. For experimental verification, a test rig was designed to realize a cryogenic environment. The test rig could be driven to 11,000 rpm using a DC motor and provided loads of up to 20 kN using a pneumatic cylinder. A metal ring was employed to measure the cage whirling amplitude using a fiber optic displacement sensor. The parameters considered included the cage whirling amplitude, ball bearing torque, and cage wear. The effects of the clearances and rotation speed on the cage stability and performance were analyzed using the probability density function of the cage whirling frequency, and the standard deviation of this function decreased as the outer guidance clearance decreased. In addition, the cage wear loss increased with decreasing cage ball-pocket clearance, owing to the collisions between the balls and cage pocket. The experimental results agreed partially with the existing theory and demonstrated that the cage instability increased as the cage guidance clearance increased.

Modeling of Cryogenic Liquefied Natural Gas Ambient Air Vaporizers

The ambient air vaporizer (AAV) technology is a promising option for vaporization of cryogenic fluids including liquefied natural gas (LNG). In this study, the heat transfer between ambient air and cryogenic LNG under supercritical conditions has been studied by using computational fluid dynamics (CFD). The process of regasification was first analyzed from the thermodynamics standpoint. In the absence of actual data for LNG, the empirical correlations and experimental data for supercritical flows of water and carbon dioxide were used to validate the CFD model. The model was then used to investigate the supercritical flow of LNG inside AAV. Operating conditions such as air flow velocity and operating pressure were studied. Furthermore, optimization of fin configurations including the number of fins, fin length, and fin thickness was also investigated. The methodology and results discussed in this study are of critical importance for designing AAV.

Quench Detection Utilizing Stray Capacitances

Fast detection of the occurrence of a quench in a high-field superconducting magnet is required in order to avoid damage due to overheating of the coil's spot when the quench initiated. This problem is particularly challenging for high temperature superconductor (HTS) magnets due to the low normal zone propagation velocity. As a result, quench detection is one of the factors presently limiting the application of HTS coils. Here, a method based on the measurement of the variation of the stray capacitances between the magnet's elements is proposed. Upon quench initiation, the capacitances between the elements and the coil vary due to multiple effects, including cryogenic fluid boil-off, variation of the dielectric properties of the insulation material, and thermal expansion, which locally changes the distance between coil and metal parts. Results from the first application of this method on a small-scale HTS coil are reported and discussed. Advantages and limitations of this technique with respect to state of the art quench detection methods are discussed.

Evaluation of the approach based on the concept of hyperbolicity breaking for prediction of flooding velocity of both room temperature and cryogenic fluids

The theoretical approach for the prediction of flooding velocity based on the concept of hyperbolicity breaking was evaluated in the counter-current two-phase flow. Detailed mathematical derivations of neutral stability condition together with the correlation of the void fraction are presented. The flooding velocity is obtained by assuming that the wavelength at flooding is proportional to the wavelength of the fastest-growing wave at Helmholtz instability. Some available experimental data for different fluid pair flow in inclined tubes is adopted for comparison with the theoretical calculations, which includes the data of water/air, aqueous oleic acid natrium solution/air, Aq. butanol 2%/air and kerosene/air in the published papers, as well as the liquid nitrogen/vapor nitrogen by the present authors. The comparison of flooding velocity proves that the approach can predict the flooding velocity with accepted accuracy for the water/air and liquid nitrogen/vapor nitrogen flow if the tube diameter is greater than 9 mm. While the diameter is smaller than 9 mm, regardless of the inclinations and the fluid pairs, the error becomes larger relative to the cases of diameter larger than 9 mm. The calculations for small diameter cases also fail to predict the critical liquid velocity at which the flooding velocity of gas reaches the maximum value, as revealed by the experiments. The reasons for the increased errors were qualitatively explained.