Interfacial Friction Factor Research Articles

Effects of Surface Tension on Two-Phase Gas-Liquid Flows in Horizontal Small Diameter Pipes

The purpose of the present study is to clarify both the surface tension and the pipe diameter effects on two-phase flows in horizontal small diameter pipes. In the experiments, four-kinds of test liquids with different fluid properties were used together with 3, 5 and 9 mm i.d. test pipes. The flow parameters studied were flow pattern, bubble size, liquid film thickness, void fraction and pressure drop, etc. The flow patterns covered were bubbly, slug, and annular flows. From the measured data, the data of interfacial friction force per unit volume, Fi, was also obtained. By comparing data obtained in different pipe and test liquid combinations, the effects of the surface tension and the pipe diameter on the flow parameters have been clarified. In addition, new correlations of mean liquid film thickness and interfacial friction factor in annular flow have been derived with some dimensionless groups.

Swirling Annular Flow in a Steam Separator

Abstract Effects of pick-off ring configuration on the separator performance of a downscaled model of a steam separator for a boiling water nuclear reactor are examined using various types of pick-off rings. The experiments are conducted using air and water. Pressure drops in a barrel and a diffuser and diameters and velocities of droplets at the exit of the barrel are measured using differential pressure transducers and particle Doppler anemometry, respectively. The separator performance does not depend on the shape of the pick-off ring but strongly depends on the width of the gap between the pick-off ring and the barrel wall. The pressure drop in the barrel is well evaluated using the interfacial friction factor for unstable film flows. Carry-under can be estimated using a droplet velocity distribution at the exit of the separator.

Gas–Liquid Interfacial Friction Factor for the Transition from Stratified to Slug Flow

Calculations based on the slug stability model and simplified stratified flow model provide predictions of the critical liquid height and the critical superficial velocities of a stratified flow for the transition to a slug flow in a horizontal pipe. Since slug flow derives from different interfacial waves patterns, previous interfacial waves model in stratified gas–liquid flows brings about the discrepancy between theoretical prediction and experimental data. A partial analysis for this behavior is given, which recognizes that the values of gas–liquid interfacial friction factor at the onset of slug flow have been underestimated, especially at high gas flows, and they should be obtained indirectly from other measured variables. Modified correlations for the interfacial friction factor are presented and better agreement between predicted and measured critical superficial velocities has been obtained.

Prediction of flow profiles and interfacial phenomena for two-phase flow in coiled tubes

The objective of the present study is to investigate the local variables and interfacial phenomena for two-phase flow in coiled tube. We believe that such information is not reported in the open literature and will be helpful for design purposes. A three-dimensional CFD model using volume of fluid (VOF) approach is presented for predicting the development of velocity fields, local and average friction factor, interfacial friction factor, phase distribution and entry length using a commercial CFD package (FLUENT 6.2). The effect of geometrical parameters (curvature ratio, λ = D c/ d; dimensionless pitch, H = p/2π R c) and operating conditions, Dean number, N De (= N Re ( d/ D c) 0.5) is also presented. The model predictions are in good agreement with the experimental dataset reported in literature [V. Czop, D. Barbier, S. Dong, Pressure in drop, void fraction and shear stress measurements in an adiabatic two-phase flow in a coiled tube, Nucl. Eng. Des. 149 (1994) 323–333; L.S. Yao, S.A. Berger, Entry flow in a coiled pipe, J. Fluid Mech. 67 (1975) 177–196; L.R. Austin, J.D. Seader, Fully developed viscous flow in coiled circular pipes, AIChE J. 19 (1973) 85–93].

Experimental Study of Interfacial Shear Stress for an Analogy Model of Evaporative Heat Transfer

In this study, we conducted measurements of an evaporative interfacial shear stress in a passive containment cooling system (PCCS). An interfacial shear stress for a counter-current flow was measured from a momentum balance equation and the interfacial friction factor for evaporation was evaluated by using experimental data. A model for the evaporative heat transfer coefficient of a vertical evaporative flat surface was developed based on an analogy between heat and momentum transfer. It was found that the interfacial shear stress increases with the Jacob number, which incorporates the evaporation rate, and the air and water Reynolds numbers. The relationship between the evaporative heat transfer and the interfacial shear stress was evaluated by using the experimental results. This relationship was used to develop a model for an evaporative heat transfer coefficient by using an analogy between heat and mass transfer. The predictions of this model were found to be in good agreement with the experimental data obtained for evaporative heat transfer by Kang and Park.

Prediction of Pressure Gradient and Holdup in Small Eötvös Number Liquid-Liquid Segregated Flow

The segregated flow pattern, which occurs in a 26.1 mm diameter, horizontal, stainless steel test section, is investigated. Pressure gradient and in situ phase distribution data were obtained for different combinations of phase superficial velocities ranging from 0.05 m·s −1 to 0.96 m·s −1. For the current small Eötvös number liquid-liquid system ( Eo D=4.77), the dominant effect of interfacial tension and wall-wetting properties of the liquids over the gravity is considered. The approach introduces the closure relationship for the case of turbulent flow in a rough pipe, and attempts to modify the two-fluid model to account for the curved interface. In present flow rates range, wave amplitudes were found small, while interfacial mixing was observed. An adjustable definition for hydraulic diameters of two fluids and interfacial friction factor is adopted. The predicted pressure gradient and in situ phase distribution data have been compared with present experimental data and those reported in the literature.

Experimental Study of Interfacial Shear Stress for an Analogy Model of Evaporative Heat Transfer

In this study, we conducted measurements of an evaporative interfacial shear stress in a passive containment cooling system (PCCS). An interfacial shear stress for a counter-current flow was measured from a momentum balance equation and the interfacial friction factor for evaporation was evaluated by using experimental data. A model for the evaporative heat transfer coefficient of a vertical evaporative flat surface was developed based on an analogy between heat and momentum transfer. It was found that the interfacial shear stress increases with the Jacob number, which incorporates the evaporation rate, and the air and water Reynolds numbers. The relationship between the evaporative heat transfer and the interfacial shear stress was evaluated by using the experimental results. This relationship was used to develop a model for an evaporative heat transfer coefficient by using an analogy between heat and mass transfer. The predictions of this model were found to be in good agreement with the experimental data obtained for evaporative heat transfer by Kang and Park.

A Model To Predict Liquid Holdup and Pressure Gradient of Near-Horizontal Wet-Gas Pipelines

Summary A mechanistic two-fluid model with new closure relationships is proposed to predict liquid holdup and pressure gradient of stratified flow. The proposed closure relationships include correlations of wetted-wall fraction factor, liquid-wall friction factor, and interfacial-friction factor. An iterative calculation procedure is implemented to solve for liquid holdup and pressure gradient for a given set of operating conditions, pipe geometry, and fluid properties. Two sets of facilities, a small-scale facility with 51-mm internal diameter (ID) and a large-scale facility with 150-mm-ID test sections, were used to tune the model. Superficial gas and liquid velocities were varied from 5 to 25 m/s and 0.00025 to 0.03 m/s, respectively, in the small-scale facility while they were varied from 7.5 to 21 m/s and 0.005 to 0.05 m/s, respectively, in the large-scale facility. The pipe inclination angle varied from −2 to 2°. The liquid holdup was ranged between 0.003 and 0.12, emphasizing the low-liquid-loading two-phase flow. The tuned model performance was then benchmarked against the high-pressure (up to 90 bar) SINTEF-stratified flow data. The model predictions agreed well with measured values of liquid holdup and pressure gradient. The comparison between the present model and OLGA® (a commercial transient multiphaseflow simulator by Scandpower Petroleum) performance was also presented.

Two-Dimensional Modeling of the Direct ECC Bypass in the APR1400 Downcomer

In a nuclear reactor vessel downcomer incorporating the safety feature of direct vessel injection (DVI), the direct bypass of emergency core coolant (ECC) is activated during the reflood phase of a large-break loss-of-coolant accident due to momentum transfer between the downward liquid film and transverse gas. Direct ECC bypass is reportedly the major bypass mechanism of ECC, and various experiments have been performed to obtain detailed information about the ECC bypass in a DVI downcomer. In the present study, a model of the direct ECC bypass was developed based on two-dimensional two-fluid equations for the adiabatic two-phase flow to predict the ECC bypass flow rate. The direct ECC bypass fractions were calculated with various interfacial friction factor correlations, and the results were compared with the available experimental data. The values predicted by the current model showed reasonably good agreement with the experimental data at bypass fractions >40% when applying the interfacial friction factor model developed in a countercurrent flow condition. However, when the bypass fraction was <40%, models incorporating cocurrent annular flow provided better results than those with countercurrent flow. These results suggest that a transition occurs from a smooth film to a rough film as the gas flow rate increases, and hence, interfacial friction factor models that adequately incorporate this transition are necessary to predict the direct ECC bypass phenomenon.

MODELING OF HEAT TRANSFER OF UPWARD ANNULAR FLOW IN VERTICAL TUBES

This article presents the modeling of heat transfer of upward annular flow in a smooth tube and a spirally internally ribbed tube. First, analytical models of two-phase flow dynamics and heat transfer of annular flow in flow boiling were derived from the liquid film momentum and energy equations for smooth tubes. Combined with empirical correlations for liquid droplet entrainment and deposition rates in annular flow, modeling of heat transfer of upward annular flow in the smooth tube was conducted. The predicted heat transfer coefficients of annular flow agree with the experimental results very well for the smooth tube. Based on the heat transfer model for smooth tubes, a simplified annular flow heat transfer model for the spirally internally ribbed tube was proposed by modifying the interfacial friction factor. The predicted heat transfer coefficients by the modified heat transfer model for the spirally internally ribbed tube agree with the experimental results to some extent. It is suggested that the heat transfer model for the spirally ribbed tube be further improved by modifying the correlations for liquid droplet entrainment and deposition rates in annular flow, which should describe the feature of annular flow in the spirally internally ribbed tube. Extensive experimental data are needed for this purpose.

Experimental measurement of frictional law under CCFL in porous debris

Counter-current flow limitation (CCFL) is the dominant phenomena for dryout in porous debris, which would be formed during a severe accident of a nuclear power plant. Since flow at CCFL in porous debris is far away from normal two-phase flow in a pipe, it is not clear whether the interfacial friction laws in a pipe can be applied to the CCFL in porous debris. In the present experimental research, the void fraction in porous debris is measured simultaneously with the differential pressure and flow rates for gas and liquid. The combination of these simultaneously measured data makes it possible to estimate the shear stresses and friction factors in a porous debris at CCFL. It results that the wall friction factor estimated is larger than the Ergun equation proposed for single-phase flow in a porous bed. Furthermore, the interfacial friction factor estimated is well correlated by the theoretical correlation derived here from a force balance for a hypothetical flow channel in porous debris at CCFL.

Modeling of Oil Retention in the Suction Line and Evaporator of Air-Conditioning Systems

This paper presents a general method for computing the oil retained in the suction line and evaporator of an air-conditioning system. For the suction line, a new semi-empirical correlation for the interfacial shear stress friction factor is presented. The correlation agrees closely with experimental results for conventional refrigerants and CO2 and extends to and merges with previous correlations available in the literature. The correlated friction factor is within 26% relative error as compared to experimental data. In the evaporator, oil retention volume was computed by using the Premoli et al. (1971) void fraction model and applying heat transfer and pressure drop correlations for refrigerant/oil mixtures. As a result, oil retention was predicted within 21% average relative error.

Investigation of the Noncondensable Effect and the Operational Modes of the Passive Condenser System

An experimental study is performed to investigate the effect of noncondensable gas in a passive condenser system. A vertical condenser tube is submerged in a water pool where the heat transferred from the condenser tube is removed through boiling. Data are obtained for three operational modes of the passive condenser. Degradation of the condensation with noncondensable gas is investigated. The condensation heat transfer rate is enhanced by increasing the inlet steam flow rate and the system pressure. For the condenser submerged in a saturated water pool, strong primary pressure dependency is observed. A boundary layer–based condensation model and a simple condensation model with the interfacial friction factor correlation are developed. The model predictions are compared with the pure steam data, and the agreement is satisfactory.

An assessment of the interface friction factor using the geometry of upset specimens

A new method of estimating the interface friction factor is proposed based on the bulge curvature of axially compressed cylindrical specimens. Initially, the curvature of the bulge is simulated with various interface friction factors using Marc 2000, a commercial finite element package. A calibration curve using a bulge parameter based on the maximum diameter and minimum diameter of the bulge is then developed as a function of the interface friction factor. Subsequently the bulge factor of experimentally tested specimens is obtained under various test conditions and the interface friction factor is predicted based on the calibration curves.

The influence of film structure on the interfacial friction in annular two-phase flow under microgravity and normal gravity conditions

Results for the interfacial friction factor and relative interfacial roughness on the gas-liquid interface are reported for an air-water annular flow in a small inner diameter tube (9.53 mm i.d.). The film structure was obtained through processing the time trace signal of film thickness measurements using conductance probes. The interfacial friction factor and the wave height were altered through changing the gravity level and gas Reynolds number. It was found that the wave height decreased with increasing the gas Reynolds number. The wave height in microgravity is less than half of that in normal gravity, while the friction factor was about 10% smaller in microgravity than that in normal gravity. It was shown that the annular two-phase flow friction factor decreased less dramatically as the relative interfacial roughness decreased compared to the single-phase case. It is interesting to note that the interfacial shear stress values at microgravity were very close (or even larger than) those at normal gravity. This was attributed to the thicker substrate at microgravity.

The influences of wave height on the interfacial friction in annular gas–liquid flow under normal and microgravity conditions

In this paper, results for the interfacial friction factor and relative interfacial roughness on the gas–liquid interface are reported for an air–water annular flow in a small inner diameter tube (9.525 mm i.d.). The film structure was obtained through processing the time trace signal of film thickness that was measured using conductance probe technique. The interfacial friction factor and the relative interfacial roughness were altered through changing the gas mass flow rate. Changing gravity level was another way to alter the friction factor and roughness. It was found that wave height, hence the relative interfacial roughness (defined by the wave height measured from the substrate surface) decreased with increasing the gas Reynolds number. The roughness in microgravity is less than half of that in normal gravity, while the friction factor was about 10% smaller in microgravity than that in normal gravity. It was reasoned that the friction factor in annular two-phase flow decreased less significantly with the decrease of the relative interfacial roughness than that in single-phase flow, which could be explained by the flat wave shape in annular flow. The values of the interfacial shear stress at microgravity were also compared to those calculated at normal gravity. Based on the results, some similarities and differences between the single-phase flow and the gas core in annular flow were highlighted and discussed.

ANALYSIS OF INTERFACIAL AND MASS TRANSFER EFFECTS ON FORCED CONVECTION IN GAS-LIQUID ANNULAR TWO-PHASE FLOW

In a gas-liquid annular two-phase flow one of the main factors influencing the determination of heat transfer rates is the average thickness of the liquid film. A model to accurately represent the heat transfer in such situations has to be able of determining the average liquid film thickness to within a reasonable accuracy. A typical physical aspect in gas-liquid annular flows is the appearance of interface waves, which affect heat, mass and momentum transfers. Existing models implicitly consider the wave effects in the momentum transfer by an empirical correlation for the interfacial friction factor. However, this procedure does not point out the difference between interface waves and the natural turbulent effects of the system. In the present work, the wave and mass transfer effects in the theoretical estimation of average liquid film thickness are analyzed, in comparison to a model that does not explicitly include these effects, as applied to the prediction of heat transfer rates in a thermally developing flow situation.

FRICTION FACTORS IN TWO PHASE HORIZONTAL PIPE FLOW

Methods for prediction of gas wall, liquid wall and interfacial friction factors for two phase horizontal co-current pipe flow are discussed critically after being checked against reliable data obtained under a wide range of conditions. The use of equivalent diameters and the Blasius relation were shown to be valid for estimation of the gas wall friction. Prediction of liquid wall and interfacial friction factors proved to be more difficult but estimation improved if consideration was given to the effects of liquid holdup and interfacial liquid shape

Momentum Balance for Two‐Phase Horizontal Pipe Flow Part 1: Friction Factors

AbstractEstimations of gas wall, liquid wall and interfacial friction factors for two‐phase horizontal co‐current pipe flow are discussed critically after being checked against reliable data obtained under a wide range of conditions. The use of equivalent diameters and the Blasius relation were shown to be valid for estimation of the gas wall friction. Prediction of liquid wall and interfacial friction factors proved to be more difficult but estimation improved if consideration was given to the effects of liquid holdup and interfacial liquid shape.

Analysis of experiments for in-tube steam condensation in the presence of noncondensable gases at a low pressure using the RELAP5/MOD3.2 code modified with a non-iterative condensation model

The standard RELAP5/MOD3.2 code is modified using non-iterative modeling, which is a mechanistic model developed for easy engineering application to simulate steam condensation in the presence of noncondensable gases in a tube. To predict the liquid-side heat transfer coefficients in the modified RELAP5/MOD3.2 code, Nusselt’s correlation is used for the condensation in a vertical tube and Kim’s correlation, correlated with the Froude number is used for the condensation in a horizontal tube. In the modified code, the wall friction in a vertical tube is calculated using the two-phase friction factor correlation proposed by Collier and the interfacial friction factor is calculated using the empirical power-law relationship of Choi. Both the standard and the modified RELAP5/MOD3.2 codes are used to simulate two kinds of vertical in-tube experiments and a horizontally stratified in-tube experiment involving the condensation phenomenon in the presence of noncondensable gases. Two vertical in-tube experiments, Passive Containment Cooling System (PCCS) condensation and reflux condensation experiments, provide data on the steady-state behaviors with a typical flow, pressure and air mass fraction conditions likely to be seen in a condensing tube of PCCS and in a U-tube of a steam generator in a mid-loop operation. The horizontally stratified in-tube experiment represents the direct-contact condensation phenomena in a hot leg of a nuclear reactor. The modeling capabilities of the modified code as well as the standard code for steam condensation in the presence of noncondensable gases are assessed using these three KAIST condensation experiments. The modified code gives a better prediction for the data of the three condensation experiments than that of the standard code. Simulation results of PCCS and reflux condensation experiments show that the local heat transfer coefficients are predicted well with the modified code but in the standard version of the code they are under-predicted by the default model and over-predicted by the alternative model. The modified code predicts well the experimental void fraction using the two-phase wall friction factor correlation. Simulation results of the horizontally stratified condensation experiments show that the modified code predicts the interfacial heat transfer coefficient better than that of the standard code.