Frictional Pressure Gradient Research Articles

Heat transfer coefficient during condensation inside a minichannel multiport tube with R32 and R410A as working fluids

The use of microchannels and minichannels in a heat exchanger has increased in recent decades. They contribute to increasing efficiency and to reducing refrigerant charge and compactness of heat exchangers. The aim of this study is to experimentally determine the heat transfer coefficient in minichannel two-phase flow processes with the low global warming potential refrigerant R32 and to compare it with the values experimentally obtained for R410A and some of the correlations encountered in the existing literature. There are a few publications studying refrigerant R32 inside multiport minichannel tubes; this has low flammability and has been classified as A2L by ASHRAE. European air-conditioning manufacturers recommend its use instead of R410A as it has lower global warming potential (R32GWP = 675, R410AGWP = 2088). Other environmental improvements may also be considered: R32 is a monocomponent refrigerant, so recycling is easier than R410A; it is also safer according to NFPA 704 classification; and a breathing apparatus is required in the case of an accident with R410A. On the other hand, R410A flammability is lower than R32 because of the addition of R125. An installation for the study of condensation processes has been constructed at the Technical University of Cartagena, Spain. The more relevant results of heat transfer coefficient will be presented in this article. The analyzed data have been measured for R32 and R410A flowing through aluminum square multiport tubes with a hydraulic diameter of 1.16 mm, then compared. The influence of saturation temperature (or pressure), flow velocity, and vapor quality in heat transfer coefficient and frictional pressure gradient has been studied. The values considered for these variables are saturation pressure corresponding to 30°C, 35°C, 40°C, 45°C, and 50°C; flow velocities from 100 to 800 kg/(s·m2); and vapor quality from 0.05 to 0.9.

Two-phase pressure drops and flow pattern observations in 90° bends subject to upward, downward and horizontal arrangements

In this study, single-phase/two-phase frictional characteristics and flow patterns of 90° bends are experimentally investigated. The two bends have inner diameters (D) of 5.5 and 9.5mm with tube curvature ratio (2R/D) of 5.4 and 4.2, respectively. The bends are installed either an upward, horizontal or downward arrangement. For results concerned with single-phase flow, the bend friction factor (fB) is always greater than that of the straight tubes at the same liquid Reynolds number. On the other hand, the fB values for D=9.5mm with smaller curvature ratio are greater than those of D=5.5mm. The resultant two-phase frictional pressure drops of 90° bend are well predicted by the Sánchez Silva et al. [14]’s correlation. For the two-phase frictional pressure gradient, the upward arrangement is greater than that of the horizontal arrangement due to swirled motion and liquid flow reversal. The flow reversals are observed for upward flow arrangement at specific flow pattern and pressure gradient. However, no swirled motion and liquid flow reversal is seen in the downward arrangement. As mass flux and quality increase, the differences of pressure drop among the three arrangements are getting smaller due to the appreciable offset by the rising flow inertia. Meanwhile, the liquid flow reversal is more evidently observed in the large diameter bend. Flow pattern map showing the region of liquid flow reversal is shown on the diagram of the superficial gas velocity (UGS) versus superficial liquid velocity (ULS). The region for liquid flow reversal for D=9.5mm is much greater than that of D=5.5mm. For D=5mm, there is no liquid flow reversal when UGS is above 2m/s. On the other hand, the threshold value is raised to 4m/s for the 9.5mm internal diameter tube.

Simplified Explicit Flow Equations for Herschel-Bulkley Fluids in Couette-Poiseuille Flow—For Real-Time Surge and Swab Modeling in Drilling

SummarySimplified flow equations are developed for Herschel-Bulkley (HB) fluids in laminar Couette-Poiseuille (CP) flow. Such flow problems are encountered in drilling when the drillstring is moved longitudinally (surge and swab operations). The new equations give the frictional-pressure gradient explicitly as a function of the bulk-flow rate. This makes them very well-suited for applications in fast, robust dynamic models for real-time applications. Incorporating these equations in a dynamic model based on ordinary differential equations (ODEs) enables coupling with system identification and control-system theory. This is a great advantage in drilling applications where there are many uncertain parameters and few measurements. Thorough analysis of relevant analytical solutions is performed to replace the most complex (implicit) parts of the solution with simpler approximations. The accuracy of the new equations, in comparison with numerical simulations and available analytical solutions, is shown to be acceptable for most practical applications.

Resistance characteristics of air–water two-phase flow in a rolling 3 × 3 rod bundle

Experimental investigation on ambient air–water two-phase flow in a 3×3 rod bundle subjected to rolling motion was carried out. Time-averaged and transient frictional resistance in rolling motion were studied in detailed. The results indicate that although time-averaged flow rate and frictional pressure drop in rolling rod bundle are very close to that under steady vertical condition, rolling motion induces obvious transient periodical fluctuation of frictional pressure gradient at low gas and liquid flow rate. While the periodical fluctuations become unconspicuous at high gas and liquid flow rate. In addition, the fluctuation amplitude of relative frictional gradient increases with the increasing of rolling amplitude. However, it is nearly invariable with the rolling period. The traditional correlations which are developed for non-rolling condition give poor predictions for transient frictional gradient when it fluctuates significantly. By taking into account of the influences of rolling parameters, a new correlation applied to calculate the transient frictional resistance in rolling rod bundle is achieved, showing good agreement with experimental results.

A Note on Mixture Density Using the Shannak Definition

In this study, a note on mixture density using the Shannak definition of the Froude number is presented (Shannak, B., 2009, “Dimensionless Numbers for Two-Phase and Multiphase Flow,” Proceedings of the International Conference on Applications and Design in Mechanical Engineering (ICADME), Penang, Malaysia, Oct. 11–13, 2009). From the definition of the two-phase Froude number, an expression of the two-phase density is obtained. The definition of the two-phase density can be used to compute the two-phase frictional pressure gradient using the homogeneous modeling approach in circular pipes, minichannels, and microchannels. We cannot have gas density≤two-phase density≤liquid density for 0≤mass quality≤1. Therefore, attention must be paid when using the obtained expression of the two-phase density in this note at any x value.

Support Vector Regression and Computational Fluid Dynamics Modeling of Newtonian and Non-Newtonian Fluids in Annulus With Pipe Rotation

The estimation of the pressure losses inside annulus during pipe rotation is one of the main concerns in various engineering professions. Pipe rotation is a considerable parameter affecting pressure losses in annulus during drilling. In this study, pressure losses of Newtonian and non-Newtonian fluids flowing through concentric horizontal annulus are predicted using computational fluid dynamics (CFD) and support vector regression (SVR). SVR and CFD results are compared with experimental data obtained from literature. The comparisons show that CFD model could predict frictional pressure gradient with an average absolute percent error less than 3.48% for Newtonian fluids and 19.5% for non-Newtonian fluids. SVR could predict frictional pressure gradient with an average absolute percent error less than 5.09% for Newtonian fluids and 5.98% for non-Newtonian fluids.

Effect of flow orientation on liquid–liquid slug flow in a capillary tube

• Frictional pressure drop is influenced by orientation of millichannel. • Frictional pressure drop highest for downflow orientation. • Influence of orientation most pronounced in slug flow. • Plug length increases and plug frequency decreases with increase in toluene velocity. • In-situ organic fraction highest for downflow orientation. Experiments using water and toluene have been performed to estimate the pressure drop characteristics in a 2 mm diameter 1 m long conduit. The measurements reveal a significant influence of conduit orientation on frictional pressure drop. The frictional gradient is highest for downflow followed by upflow and minimum for horizontal orientation of the test passage. The influence of orientation is more pronounced for slug flow as compared to dispersed, inverted dispersed and annular flow patterns. In order to explain these observations, an in-depth study of the slug flow pattern has been performed using image analysis. The influence of inlet phase velocities on slug characteristics namely length, frequency and velocity of toluene plugs, in-situ toluene fraction and relative slip between the phases has been investigated. The observations reveal that plug length increases with increasing toluene flow rate while its frequency increases with water flow rate. The in-situ toluene fraction increases with increasing toluene and decreasing water flow rate as expected and it is highest for downward liquid–liquid flow as compared to upward or horizontal flow for the same input conditions. This explains the significant influence of orientation on frictional pressure gradient during liquid–liquid slug flow in a 2 mm conduit.

Discussion: “Correlations for Prediction of Pressure Gradient of Liquid–Liquid Flow Through a Circular Horizontal Pipe” [Dasari, A., Desamala, A. B., Ghosh, U. K., Dasmahapatra, A. K., and Mandal, T. K., 2014, ASME J. Fluids Eng., 136(7), p. 071302

The comments present an assessment of formulations for frictional pressure gradient correlation of moderately viscous lubricating oil–water two-phase flow through a horizontal pipe of 0.025 m internal diameter, which was obtained by Dasari et al. [1]. Their modified Lockhart–Martinelli correlation was(1)φW2=0.019X3+0.06X2-0.006X+1.397Recently, Muzychka and Awad [2] developed an alternative approach for predicting two-phase frictional pressure gradients using superposition of three pressure gradients: single-phase liquid, single-phase gas, and interfacial pressure gradient. Muzychka and Awad [2] obtained an expression for the two-phase frictional interfacial multiplier for the liquid phase (ϕl,i2) as follows:(2)φl,i2=φl2-1-1X2From Eq. (2), it is clear that ϕl,i2 cannot be negative because their minimum values are zero, which correspond to the case of no contribution to the pressure gradient through phase interaction (i.e., (dp/dx)f,i = 0).It should be noted that the relations of two-phase frictional multiplier for liquid with higher density (water in these comments) and liquid with lower density (lubricating oil in these comments) in two-phase liquid–liquid flow are similar to the relations of two-phase frictional multiplier for liquid and gas in two-phase gas–liquid flow. The two-phase frictional multiplier concept that was introduced by Lockhart and Martinelli [3] for the case of two-phase gas–liquid flow can be used to model the flow of two immiscible liquids such as oil and water. For example, Awad and Butt [4] presented a simple semitheoretical method for calculating the two-phase frictional pressure gradient for liquid–liquid flow in pipes using asymptotic analysis. In their analysis, Awad and Butt [4] used the two-phase frictional multiplier concept that was introduced by Lockhart and Martinelli [3] for the case of two-phase gas–liquid flow to model the flow of two immiscible liquids such as oil and water.Substituting the Dasari et al. [1] correlation, Eq. (1), into the expression of for the two-phase frictional interfacial multiplier, Eq. (2), we obtain(3)φW,i2=0.019X3-0.94X2-0.006X+0.397From Eq. (3), it is clear that the Dasari et al. [1] correlation results in negative values of the two-phase frictional interfacial multiplier in the range of the Lockhart–Martinelli parameter (X) = 0.03–1. This is impossible because its minimum value is zero.Finally, it should be noted that the empirical correlation, i.e., Eq. (1), was developed by Dasari et al. [1] for the range of the Lockhart–Martinelli parameter (X) = 0.1–20, but would not be valid for X < 0.1 as shown by the authors' Eq. (2).

Comprehensive experimental investigation of two-phase heat transfer and pressure drop with propane in a minichannel

The use of hydrocarbons as natural refrigerants inside small diameter channels allows charge minimization and therefore it may be an interesting option in the refrigerating and heat pump technology. The aim of the present experimental work is to fully characterize the thermal performance of propane (R290) in minichannels by measuring frictional pressure drop, condensation and flow boiling heat transfer coefficients inside a circular cross section horizontal minichannel with an internal diameter of 0.96 mm and a rough inner surface. Measurements of frictional pressure drop during adiabatic two-phase flow have been performed at mass velocity ranging between 200 and 800 kg m−2 s−1. Local heat transfer coefficients have been measured during condensation and during flow boiling in the mass velocity range from 100 to 1000 kg m−2 s−1. The present database, including frictional pressure gradient, condensation and vaporization heat transfer coefficients, is compared against predicting correlations available in the open literature.

Experimental study of flow patterns and pressure drops of heavy oil-water-gas vertical flow

A stainless steel apparatus of 18.5 m high and 0.05 m in inner diameter is developed, with the heavy oil from Lukeqin Xinjiang oil field as the test medium, to carry out the orthogonal experiments for the interactions between heavy oil-water and heavy oil-water-gas. With the aid of observation windows, the pressure drop signal can be collected and the general multiple flow patterns of heavy oil-water-gas can be observed, including the bubble, slug, churn and annular ones. Compared with the conventional oil, the bubble flows are identified in three specific flow patterns which are the dispersed bubble (DB), the bubble gas-bubble heavy oil, and the bubble gas-intermittent heavy oil (Bg – Io). The slug flows are identified in two specific flow patterns which are the intermittent gas-bubble heavy oil (Ig – Bo) and the intermittent gas-intermittent heavy oil (Ig – Io). Compared with the observations in the heavy oil-water experiment, it is found that the conventional models can not accurately predict the pressure gradient. And it is not water but heavy oil and water mixed phase that is in contact with the tube wall. So, based on the principle of the energy conservation and the kinematic wave theory, a new method is proposed to calculate the frictional pressure gradient. Furthermore, with the new friction gradient calculation method and a due consideration of the flow characteristics of the heavy oil-water-gas high speed flow, a new model is built to predict the heavy oil-water-gas pressure gradient. The predictions are compared with the experiment data and the field data. The accuracy of the predictions shows the rationality and the applicability of the new model.

The effect of surfactants on air–water annular and churn flow in vertical pipes. Part 2: Liquid holdup and pressure gradient dynamics

In this paper, we study the effect of surfactants on both the liquid holdup and the dynamics of the pressure gradient in annular and churn flow in vertical pipes. This effect is linked to the influence of the surfactants on the morphology of the air–water interface, which is studied in a related paper (van Nimwegen et al., 2014). The experimental results, obtained using a vertical flow loop with a 5cm internal diameter at ambient pressure, show three different effects of the surfactants on the measured quantities, depending on the air and water flow rates. (i) At large air flow rates, in the annular flow regime for air–water flow, the surfactants increase the pressure gradient; this is solely due to the increase of the frictional pressure gradient, caused by the larger interfacial stress between the foamy waves overlaying the foam substrate along the wall and the gas core. (ii) At low air flow rates and low water flow rates, in the churn flow regime for air–water flow, the surfactants decrease significantly both the average pressure gradient and the pressure gradient fluctuations. While the frictional pressure gradient increases, the liquid holdup decreases by more than a factor of two; the foam suppresses the flooding waves, making the flow much more regular, leading to the small pressure gradient fluctuations. Furthermore, there exists an optimum surfactant concentration for decreasing the average pressure gradient and the pressure gradient fluctuations. (iii) At low air and high water flow rates, in the churn flow regime for air–water flow, the average pressure gradient and the pressure gradient fluctuations are both somewhat decreased by the surfactants.

Pressure drop during condensation of R134a flowing inside a multiport minichannel

This paper is a continuation of the authors’ previous work on the condensation of R134a flowing inside a multiport minichannel (Sakamatapan et al., 2013) [22]. The pressure drop’s characteristics during condensation were investigated in an experiment for R134a flowing inside a multiport minichannel. The pressure drop characteristics were observed under mass flux range of 345–685kg/m2, heat flux of 15–25kW/m2, and saturation temperature of 35–45°C. Two types of multiport minichannels having 14 channels, one with a 1.1mm hydraulic diameter and another with 8 channels with a 1.2mm hydraulic diameter, were designed as a counter flow tube in a tube heat exchanger. The results showed that the total pressure drop is dominated by the frictional pressure drop. The frictional pressure gradient increased with the augmentation of mass flux and vapor quality, but the increase of the saturation temperature and channel size play an important role in the decrease of frictional pressure gradient. On the other hand, the heat flux had an insignificant effect on the frictional pressure gradient. Moreover, the miniscale correlations were conducted to predict the frictional pressure gradient, and it was found that only the multiport minichannel correlations gave a reasonable result. A new two-phase friction factor correlation was proposed using the equivalent Reynolds number concept to predict the frictional pressure gradient during condensation.

Bounds on Two-Phase Frictional Pressure Gradient and Void Fraction in Circular Pipes

Simple rules are developed for obtaining rational bounds for two-phase frictional pressure gradient and void fraction in circular pipes. The bounds are based on turbulent-turbulent flow assumption. Both the lower and upper bounds for frictional pressure gradient are based on the separate cylinders formulation. For frictional pressure gradient, the lower bound is based on the separate cylinders formulation that uses the Blasius equation to represent the Fanning friction factor while the upper bound is based on the separate cylinders equation that represents well the Lockhart-Martinelli correlation for turbulent-turbulent flow. For void fraction, the lower bound is based on the separate cylinders formulation that uses the Blasius equation to predict the Fanning friction factor while the upper bound is based on the Butterworth relationship that represents well the Lockhart-Martinelli correlation. These two bounds are reversed in the case of liquid fraction (1-α). For frictional pressure gradient, the model is verified using published experimental data of two-phase frictional pressure gradient versus mass flux at constant mass quality. The published data include different working fluids such as R-12, R-22, and Argon at different mass qualities, different pipe diameters, and different saturation temperatures. The bounds models are also presented in a dimensionless form as two-phase frictional multiplier (ϕ l and ϕ g) versus Lockhart-Martinelli parameter ( X) for different working fluids such as R-12, R-22, and air-water and steam mixtures. For void fraction, the bounds models are verified using published experimental data of void fraction versus mass quality at constant mass flow rate. The published data include different working fluids such as steam, R-12, R-22, and R-410A at different pipe diameters, different pressures, and different mass flow rates. It is shown that the published data can be well bounded for a wide range of mass fluxes, mass qualities, pipe diameters, and saturation temperatures.

REVIEW AND MODELING OF TWO-PHASE FRICTIONAL PRESSURE GRADIENT AT MICROGRAVITY CONDITIONS

First, a detailed review of two-phase frictional pressure gradient at microgravity conditions is presented. Then, a simple semi-theoretical method for calculating two-phase frictional pressure gradient at microgravity conditions using asymptotic analysis is presented. Two-phase frictional pressure gradient is expressed in terms of the asymptotic single-phase frictional pressure gradients for liquid and gas flowing alone. In the present model, the two-phase frictional pressure gradient for x ≅ 0 is nearly identical to single-phase liquid frictional pressure gradient. Also, the two-phase frictional pressure gradient for x ≅ 1 is nearly identical to single-phase gas frictional pressure gradient. The proposed model can be transformed into either a two-phase frictional multiplier for liquid flowing alone (φl2) or two-phase frictional multiplier for gas flowing alone (φg2) as a function of the Lockhart-Martinelli parameter, X. Comparison of the asymptotic model with experimental data at microgravity conditions is presented.Copyright © 2010 by ASME

A Robust Asymptotically Based Modeling Approach for Two-Phase Flows

A simple semitheoretical method for calculating two-phase frictional pressure gradient in horizontal circular pipes using asymptotic analysis to develop a robust compact model is presented. Two-phase frictional pressure gradient is expressed in terms of the asymptotic single-phase frictional pressure gradients for liquid and gas flowing alone. The proposed model can be transformed into either a two-phase frictional multiplier for liquid flowing alone (ϕl2) or two-phase frictional multiplier for gas flowing alone (ϕg2) as a function of the Lockhart-Martinelli parameter, X. Single-phase friction factors are calculated using the Churchill model which allows for prediction over the full range of laminar-transition-turbulent regions and allows for pipe roughness effects. The proposed model is compared against published data to show the asymptotic behavior. Comparison with other existing correlations for two-phase frictional pressure gradient such as the Chisholm correlation, the Friedel correlation, and the Müller-Steinhagen and Heck correlation, is also presented. Comparison with experimental data for both ϕl and ϕl versus X is also presented. At the end of the paper, the present asymptotic model is also extended to minichannels and microchannels.

Modeling of Interfacial Component for Two-Phase Frictional Pressure Gradient at Microscales

A simple approach for calculating the interfacial component of frictional pressure gradient in two-phase flow at microscales is presented. This approach is developed using superposition of three pressure gradients: single-phase liquid, single-phase gas, and interfacial pressure gradient. The proposed model can be transformed in two different ways: first, two-phase interfacial multiplier for liquid flowing alone ([Formula: see text]) as a function of two-phase frictional multiplier for liquid flowing alone ([Formula: see text]) and the Lockhart-Martinelli parameter, X, and, second, two-phase interfacial multiplier for gas flowing alone (ϕ g, i2) as a function of two-phase frictional multiplier for gas flowing alone (ϕ g2) and the Lockhart-Martinelli parameter, X. This proposed model allows for the interfacial pressure gradient to be easily modeled. Comparisons of the proposed model with experimental data for microchannels and minichannels and existing correlations for both ϕ l and ϕ g versus X are presented.

A note on the mixture viscosity using the Shannak definition

In this study, a note on the mixture viscosity using the Shannak definition is presented [Shannak, B. A., 2008. Frictional pressure drop of gas liquid two-phase flow in pipes. Nucl. Eng. Des. 238, 3277–3284]. From his definition of the two-phase Reynolds number (Re(2ph)), an expression of the two-phase viscosity (μ(2ph)) is obtained. This expression of the two-phase viscosity (μ(2ph)) satisfies the following important limiting conditions: i. at x=0, μ(2ph)=μf, and at x=1, μ(2ph)=μg. This definition of the two-phase viscosity (μ(2ph)) can be used to compute the two-phase frictional pressure gradient using the homogeneous modeling approach in circular pipes, minichannels and microchannels. By plotting μ(2ph)/μf versus x for air–water system at atmospheric conditions using the Shannak definition as well as the other most commonly used formulas of the two-phase viscosity (μ(2ph)) in gas–liquid two-phase flows such as McAdams et al. (1942), Cicchitti et al. (1960), and Awad and Muzychka (2008) (Definition 1, Definition 2, Definition 3, and Definition 4), it is clear that the Shannak definition of the two-phase viscosity gives μ(2ph)>μf at low x. This is impossible because we must have μg<μ(2ph)<μf for 0<x<1. Therefore, attention must be taken when using the Shannak definition of the two-phase viscosity at low x.

Effects of void fraction correlations on pressure gradient separation of air–water two-phase flow in vertical mini rectangular ducts

Effects of void fraction correlations on pressure gradient separation of air–water two-phase flow in vertical rectangular ducts were investigated experimentally under ambient temperature and pressure. The superficial gas and liquid velocities ranged from 0.58 to 32 m/s and from 0.16 to 3.8 m/s respectively. The results indicate that although the void fraction correlation has great influence on gravitational pressure gradient of slug flow, churn flow and annular flow, it nearly has no influence on that of bubbly flow. For the separating frictional pressure gradient, the void fraction correlation nearly has no effect on bubbly flow and annular flow, while it has significant influence on that of slug flow and churn flow. The correlations of kβ type and drift-flux type are more compatible with each other than the slip ratio and general type, when they are applied to separate the frictional component from the total pressure gradient. The drift velocity correlation of Jones and Zuber (1979) agrees well with Ishii (1977) for bubbly flow, slug flow and churn flow, so it is recommended for pressure gradient separation in vertical mini rectangular duct. Furthermore, the void fraction correlation has less influence on the pressure gradient separation as the duct size decreases.

Two-phase adiabatic frictional pressure gradients for R410A and CO2 in a macro channel: Experiments and a simplified predictive method for annular flow from low to medium reduced pressures

The use of refrigerants at evaporating temperatures much higher than those of the refrigeration field is an emerging need in the industry related to energy conversion systems, such as Organic Rankine Cycles and cascade heat pumps for sanitary hot water production.In this work the effect of reduced pressure is experimentally investigated for two-phase adiabatic frictional pressure gradients for CO2 and R410A in a wide range of reduced pressure (0.19–0.52 for R410A and 0.57–0.64 for CO2) and mass flux (150–500kgm−2s−1) in a adiabatic horizontal smooth tube of 6.00mm of inner diameter, collecting 1214 new data points. A simplified phenomenological method for annular flow was proposed and validated with the present and existing databases by the same authors and independent databases for several fluids (CO2, R410A, R134a and also the new fluid R1234ze(E)).

Pressure Drop During Condensation in Microchannels

The paper reports calculations of friction pressure gradient for the special case of laminar annular flow condensation in microchannels. This is the only flow regime permitting theoretical solution without having recourse to experimental data. Comparisons are made with correlations based on experimental data for R134a. The correlations differ somewhat among themselves with the ratio of highest to lowest predicted friction pressure gradient typically around 1.4 and nearer to unity at high quality. The friction pressure gradients given by the laminar annular flow solutions are in fair agreement with the correlations at high quality and lower than the correlations at lower quality. Attention is drawn to the fact that the friction pressure gradient cannot be directly observed and its evaluation from measurements requires estimation of the nondissipative momentum or acceleration pressure gradient. Methods used to estimate the nondissipative pressure gradient require quality and void fraction together with equations which relate these and whose accuracy is difficult to quantify. Quality and void fraction can be readily found from the laminar annular flow solutions. Significant differences are found between these and values from approximate equations.