Frictional Pressure Drop Correlations Research Articles

A new general correlation for frictional pressure drop during condensation inside horizontal micro-fin tubes

Experimental pressure drop data of condensation from present study and literature were collected to develop a new frictional pressure drop correlation for horizontal micro-fin tubes. The collected database contained 481 data points, covering nine refrigerants including CO2 at average saturated condensing temperatures ranging between 14 and 65°C, with mass velocities ranging from 50 to 800kg/m2s, and average vapor qualities from 0.11 to 0.91. The hydraulic diameter of micro-fin tubes varied from 2.16 to 5.67mm and was employed in the calculation of Reynolds number. The Fanning frictional factor was calculated by adopting the Churchill model with the empirically fitted relative roughness. Four existing pressure drop correlations developed for micro-fin tubes were evaluated by the database for condensation in micro-fin tubes. The correlation proposed by Cavallini et al. was the best prediction model among them, predicting 85.6% of the collected data points within the 30% error band. In addition, a new correlation based on the Martnelli parameter Xtt modified by incorporating the reduced pressure was proposed to predict the present database, which showed a good agreement. Finally, some corresponding experimental work was conducted for evaluating the reliability of the new prediction model.

Frictional pressure drop correlation for two-phase flows in mini and micro multi-channels

1029 frictional pressure drop data of two-phase flow in mini/micro multi-channels were collected from 11 literatures. This database included 8 working fluids: R134a, R22, R404a, FC-72, water, CO2, R236fa and R245fa. The channel dimension ranged from 0.109 to 2.13mm. Frictional pressure drop range of the database was from 5 to 150kPa. The applicability of 11 existing correlations developed for mini/micro single channels to mini/micro multi-channels were evaluated with the multi-channel database. Among the existing correlations, the correlation of Lee-Mudawar predicted the database with the mean absolute percentage error (MAPE) of 35.3%, the correlations of Lee-Garimella and Sun-Mishima had MAPEs within 45.0%. In the process of new correlation development, the database was divided into three categories (namely, 1: gas laminar-liquid laminar, 2: gas turbulent-liquid laminar, 3: gas turbulent-liquid turbulent) in terms of liquid Reynolds number and gas Reynolds number, since gas laminar-liquid turbulent data did not exist in the literature. The newly developed correlation was formulated by a function of the two-phase Reynolds number, Retp, the two-phase viscosity number, Nμtp, and the vapor quality, x. The correlation could predict the measured frictional pressure drop with the MAPE of 18.9%. The correlation demonstrated an excellent performance of the two-phase flow frictional pressure drop prediction in mini/micro multi-channels.

Linear stability analysis for severe slugging: sensitivity to void fraction and friction pressure drop correlations

In this paper a numerical linear stability analysis is performed on a mathematical model for the two-phase flow in a pipeline-riser system. Void fraction is a key variable, as it influences the mixture properties and slip between the phases. Friction two-phase pressure drop is also an important variable as it is necessary, for instance, to determine the pumping power in multiphase processes. For a correct prediction of the stability behaviour of a pipeline-riser flow, preventing the occurrence of severe slugging, it is important to assess the sensitivity of the system response to different void fraction and friction pressure drop correlations. Three void fraction (Bendiksen, 1984; Chexal et al., 1997; Bhagwat and Ghajar, 2014) and two friction pressure drop correlations [homogeneous and Muller-Steinhagen and Heck (1986)] are implemented. The resulting stability maps and state variables profiles for vertical risers are compared for the different correlations. For the void fraction sensitivity study, results show that the different correlations give similar stability maps, with very small differences in the near horizontal branch (low gas superficial velocities) of the stability boundary and slight differences in the near vertical branch (low liquid superficial velocities). For the friction pressure drop sensitivity study, results show that it does not affect significantly the stability maps because the mass fluxes are low and the main contribution to the total pressure drop comes from the gravitational term. The different correlations show the right experimental trend by increasing the unstable region as the equivalent buffer length in the pipeline is increased.

Linear stability analysis for severe slugging: sensitivity to void fraction and friction pressure drop correlations

Linear stability analysis for severe slugging: sensitivity to void fraction and friction pressure drop correlations

Frictional pressure drop correlation for two-phase flows in mini and micro single-channels

1521 frictional pressure drop data points were collected from 12 literatures. The database included adiabatic and diabatic systems composed of 10 working fluids. The diameter range was from 0.1 to 3mm, and the pressure drop ranged from 1.26kPa/m to 2MPa/m. 17 existing single channel two-phase pressure drop correlations including homogenous flow model and separated flow model were evaluated with the database. The comparison results showed that the correlations of Pamitran et al., Hwang and Kim, Mishima and Hibiki and Zhang et al. gave better predictions than the others. However, the performance evaluation results also showed the mean absolute errors higher than 40%. Based on the relatively large prediction error by the existing correlations, a new correlation was proposed by classifying the flow conditions into four regimes (namely, 1: gas laminar-liquid laminar, 2: gas laminar-liquid turbulent, 3: gas turbulent-liquid laminar, 4: gas turbulent-liquid turbulent). The newly developed correlation is expressed by a function of the two-phase Reynolds number, Retp, the two-phase viscosity number, Nμtp, and the gas quality, x, and was able to predict the two-phase frictional pressure drop with the mean absolute percentage error of 17.4%. The correlation demonstrated an excellent performance for predicting the two-phase frictional pressure drop in mini/micro single channels.

Condensing two-phase pressure drop and heat transfer coefficient of propane in a horizontal multiport mini-channel tube: Experimental measurements

This article reports the condensing flow heat transfer coefficient and pressure drop results of propane (R290) flowing through a square section horizontal multiport mini-channel tube made of aluminium having an internal diameter of 1.16 mm and a condensing length of 259 mm. Pressure drop and two phase flow experiments were performed at saturation temperatures of 30, 40 and 50 °C. Heat flux was varied from 15.76 to 32.25 kWm−2 and mass velocity varied from 175 to 350 kg m−2 s−1. The results show that the two-phase friction pressure gradient increases with the increase of mass velocity and vapour quality and with the decrease of saturation temperature. The heat transfer coefficients showed to increase with increases of vapour quality and mass velocity while increases of saturation temperature were observed to reduce heat transfer coefficient. The two phase frictional pressure drop correlations of Sun and Mishima and Agarwal and Garimella, and the two-phase flow heat transfer correlations of Koyama et al. and Wang et al. predicted well the experimental results.

An experimental study of flow boiling frictional pressure drop of R134a and evaluation of existing correlations

A series of experiments on flow boiling frictional pressure drop of R134a in three horizontal circular smooth copper tubes with inner diameters of 1.002, 2.168, and 4.065mm were conducted. A total of 397 experimental data points are obtained for a mass flux range of 185–935kg/m2s, a heat flux range of 18.0–35.5kW/m2, a saturation pressure range of 0.578–0.82MPa, and a vapor quality range of 0.03–1.0. The effects of mass flux, heat flux, vapor quality, saturation pressure, and diameter on the frictional pressure drop are analyzed and the results indicate that the frictional pressure drop increases with increasing mass flux, increases with vapor quality until a peak and then drops, decreases with increasing saturation pressure and hydraulic diameter, and almost keep constant with heat flux. Thirty-two existing correlations of two-phase frictional pressure drop are compared with the experimental data. The best correlation has the mean absolute deviation of 15.0%. Besides, an experimental database of flow boiling frictional pressure drop is complied, which contains 3244 data points, including 397 from the current experiments and 2847 from 27 published papers. The 32 existing correlations are evaluated with the database. The best correlation has the mean absolute deviation of 24.5%. The work provides a guide for selecting a suitable correlation for specific applications of flow boiling frictional pressure drop.

Measured and predicted frictional pressure drop for boiling zeotropic mixed refrigerants in horizontal tubes

Zeotropic mixtures are widely used in mixed refrigerant Joule–Thomson cryocoolers for various applications such as cryoprobes. Within the Joule–Thomson cycle, multicomponent mixtures exist in a two-phase condition throughout a large portion of the system. Frictional pressure drop correlations for zeotropic refrigerants operating at these conditions are necessary for designers to optimize these systems; however, there are limited experimental data on the two-phase pressure drop of these mixtures available in the open literature.This paper provides experimental data for the frictional pressure drop exhibited by a set of multicomponent zeotropic mixtures boiling in small channels over temperatures ranging from 100K to room temperature along with the sensitivity of frictional pressure drop to parameters such as mass flux, pressure, tube diameter, and mixture composition. The measured data are compared to several pressure drop correlations available in the literature and the Awad and Muzychka (definition 1) correlation (Awad and Muzychka, 2008) was able to predict the frictional pressure drop over the range of experimental data considered, with an Absolute Average Deviation (AAD) of 17%. The second best correlation is Sun and Mishima (2009) with an AAD of 18%. In addition, the Cicchitti et al. (1959), Müller-Steinhagen and Heck (1986) and Mishima and Hibiki (1996) correlations also show reasonable agreement with the experimental data. Based on our data, the Awad and Muzychka (definition 1) (Awad and Muzychka, 2008) homogeneous model is recommended for prediction of pressure drop because this correlation agrees with 81% of our data with a relative absolute error lower than 25%.

Frictional Pressure Drop Correlations for Single-Phase Flow, Condensation, and Evaporation in Microfin Tubes

Experimental single-phase, condensation, and evaporation (flow boiling) pressure drop data from the literature and our previous studies were collected to evaluate previous frictional pressure drop correlations for horizontal microfin tubes of different geometries. The modified Ravigururajan and Bergles correlation, by adopting the Churchill model to calculate the smooth-tube friction factor and by using the hydraulic diameter in the Reynolds number, can predict single-phase turbulent frictional pressure drop data relatively well. Eleven pressure drop correlations were evaluated by the collected database for condensation and evaporation. Correlations originally developed for condensation and evaporation in smooth tubes can be suitable for microfin tubes if the friction factors in the correlations were calculated by the Churchill model to include microfin effects. The three most accurate correlations were recommended for condensation and evaporation in microfin tubes. The Cavallini et al. correlation and the modified Friedel correlation can give good predictions for both condensation and evaporation. However, some inconsistencies were found, even for the recommended correlations.

Measurements and correlations of frictional pressure drop of TiO2/R123 flow boiling inside a horizontal smooth tube

Nanorefrigerant is one kind of nanofluids. It is the mixture of nanoparticles with refrigerants. It has better heat transfer performance than traditional refrigerants. Recently, some researches have been done about nanorefrigerants. Most of them are related to thermal conductivity of these fluids. Viscosity also deserves as much consideration as thermal conductivity. Pumping power and pressure drop depend on viscosity. In this paper, the volumetric and temperature effects over viscosity of TiO2/R123 nanorefrigerants have been studied. Numerical conditions include temperature from 300 to 325K, nanoparticle concentrations from 0.5% up to 2%, mass fluxes from 150 to 200kgm−2s−1, inlet vapor qualities from 0.2 to 0.7 and diameter of tube from 6 to 10mm. The effect of pressure drop with the increase of viscosity has also been investigated. Based on the analysis it is found that viscosity of nanorefrigerant increased accordingly with the increase of nanoparticle volume concentrations and decreases with the increment of temperature. Furthermore, pressure drop augmented significantly with the intensification of volume concentrations and vapor quality. Therefore, low volume concentrations of nanorefrigerant are suggested for better performance of a refrigeration system.

A scheme of correlation for frictional pressure drop in steam–water two-phase flow in helicoidal tubes

In the nuclear field, helically coiled tube steam generators (SGs) are considered as a primary option for different nuclear reactor projects of Generation III+ and Generation IV. For their characteristics, in particular compactness of the component design, higher heat transfer rates and better capability to accommodate thermal expansion, they are especially attractive for small-medium modular reactors (SMRs) of Generation III+.In this paper, starting from two existing databases, a new correlation is developed for the determination of the two-phase frictional pressure drop. The experimental data cover the ranges 5–65bar for the pressure, 200 to 800kg/m2s for the mass flux and 0 to 1 for the quality. Two coil diameters have been considered, namely 0.292m and 1.0m. The coil diameter in particular is crucial for a correct estimation of the two-phase frictional pressure drop. Actually, no general correlation reliable in a wide range of coil geometries is available at the moment. Starting from the noteworthy correlation of Lockhart and Martinelli, corrective parameters are included to account for the effect of the centrifugal force, introduced by the helical geometry, and the system pressure. The correlation is developed with the aim to obtain a form of general validity, while keeping as low as possible the number of empirical coefficients involved.The average relative deviation between the correlation and the experimental data is about 12.9% on the whole database, which results the best among numerous literature correlations. In addition, the new correlation is characterized by an extended range of validity, in particular for the diameter of the coil.

Pressure drop and gas holdup in air–water flow in 180° return bends

Gas–liquid flows in curved tubes are found in a number of applications, such as heat exchangers and transport pipes. The present work deals with air–water flow in 180° tube bends (curvatures of 6.1, 8.7, and 12.2) that connect two 5-m long 26-mm ID horizontal tubes. The bend lies in the vertical position and the two-phase flow can be set as upward or downward. The straight and curved segments of test section were made from borosilicate glass to enable visual access to the two-phase flow. The behavior of the static pressure upstream and downstream of the bend was measured for a wide range of flow conditions, covering the stratified, intermittent and annular flow patterns. The pressure drop and gas holdup change associated with the bend were measured for both upward and downward flows, enabling the calculation of the frictional, accelarational and gravitational components of the total pressure drop in the bend. The distribution of the phases in the bend was investigated with a high-speed camera, revealing several two-phase phenomena responsible for large variations in gas holdup between the inlet and outlet of the bend for both upward and downward flows. An assessment of the prediction methods currently available in the literature showed that correlations for gas holdup in straight tubes give inaccurate predictions of the average gas holdup in the bend for both flow orientations. Frictional pressure drop correlations for gas–liquid flows in return bends also failed to describe with reasonable accuracy the behavior of the experimental data at low gas superficial velocities for both flow orientations. The performance of the correlations improved at high mixture velocities.

A new correlation of two-phase frictional pressure drop for condensing flow in pipes

The calculation of two-phase frictional pressure drop for condensing flow in pipes is essential in many areas. Although numerous studies concerning this issue have been conducted, an accurate correlation is still required. In this paper, an overall survey of correlations and experimental investigations of two-phase frictional pressure drop is carried out. There 525 experimental data points of 9 refrigerants are gathered from literature, with hydraulic diameter from 0.1 to 10.07mm, mass flux from 20 to 800kg/m2s, and heat flux from 2 to 55.3kW/m2. The 29 existing correlations are evaluated against the experimental database, among which the best one has a mean absolute relative deviation (MARD) of 25.2%. Based on all the experimental data, a new correlation which has an MARD of 19.4% is proposed, improving significantly the prediction of two-phase frictional pressure drop for pipe condensing flow.

Flow-pattern-based correlations for pressure drop during flow boiling of ethanol–water mixtures in a microchannel

This paper constitutes an experimental investigation into the pressure drop during flow boiling of ethanol–water mixtures in a diverging microchannel with artificial cavities. Similar to boiling curves, the experimental results reveal that the single-phase and boiling two-phase flow pressure drops are significantly influenced by the molar fraction. The single-phase pressure drop for water demonstrates the smallest as the water viscosity is smaller than that of ethanol–water mixtures. During flow boiling, in general, two-phase flow pressure drop at a given wall superheat for the mixture with molar fraction of 0.1 is the highest, due to the higher boiling heat flux resulted from the Marangoni effect. Based on the correlation development of boiling heat transfer coefficient in the previous study, two flow-pattern-based empirical correlations for the two-phase frictional pressure drop are proposed in the terms of nondimensional parameters, such as boiling number, Weber number, and Marangoni number. The proposed correlations are similar to the empirical correlation for boiling heat transfer coefficient with different numerical values of the coefficients and exponents. Different values of flow-pattern-based constant are obtained for different flow patterns. The constants for annular flow and liquid film breakup are the same. It may be due to the major mechanism of the two-phase flow is liquid film evaporation for these two flow types. The overall mean absolute errors of the proposed correlations are 13.7% and 11.6%, respectively. More than 90% of the experimental data can be predicted within a ±25% error band. Such an excellent agreement confirms that the proposed correlations may predict the Marangoni effect on the two-phase flow pressure drop during flow boiling of binary mixtures in a microchannel.

Numerical study of the pressure drop phenomena in wound woven wire matrix of a Stirling regenerator

Friction pressure drop correlation equations are derived from a numerical study by characterizing the pressure drop phenomena through porous medium of both types namely stacked and wound woven wire matrices of a Stirling engine regenerator over a specified range of Reynolds number, diameter and porosity. First, a finite volume method (FVM) based numerical approach is used and validated against well known experimentally obtained empirical correlations for a misaligned stacked woven wire matrix, the most widely used due to fabrication issues, for Reynolds number up to 400. The friction pressure drop correlation equation derived from the numerical results corresponds well with the experimentally obtained correlations with less than 5% deviation. Once the numerical approach is validated, the study is further extended to characterize the pressure drop phenomena in a wound woven wire matrix model of a Stirling engine regenerator for a diameter range from 0.080 to 0.110mm and a porosity range from 0.472 to 0.638 within the same Reynolds number range. Thus, the new correlation equations are derived from this numerical study for different flow configurations of the Stirling engine regenerator. The results indicate flow nature and complex geometry dependent friction pressure drop characteristics within the present Stirling engine regenerator system. It is believed that the developed correlations can be applied with confidence as a cost effective solution to characterize and hence to optimize stacked and woven Stirling engine efficiency in the above specified ranges.

Investigation of two phase heat transfer and pressure drop of propane in a vertical circular minichannel

This article reports the flow boiling heat transfer and pressure drop results of propane in a vertical circular stainless steel minichannel having an internal diameter of 1.70mm and a heated length of 245mm. Two phase heat transfer and pressure drop experiments have been performed at saturation temperatures of 23, 33 and 43°C. Heat flux is varied from 5 to 280kW/m2 and mass flux is varied from 100 to 500kg/m2s. The results show that the two phase frictional pressure drops, as expected, are increased with the increase of mass flux, vapour qualities and with the decrease of saturation temperature. The heat transfer coefficients are showed to increase with the increase of heat flux and saturation temperature while the influence of mass flux and vapour quality is observed as insignificant. After incipience of dryout, the decrease in heat transfer coefficient and also the two phase frictional pressure drop, especially at higher mass fluxes, is observed. The two phase frictional pressure drop correlations of Müller-Steinhagen and Heck and Friedel and two phase flow heat transfer correlations of Cooper and Liu and Winterton well predicted the experimental results.

Evaluation of frictional pressure drop correlations for two-phase flow in pipes

The calculation of frictional pressure drop for two-phase flow in pipes is required by a variety of design practices. In the past six decades, many correlations for two-phase frictional pressure drop were proposed, and some evaluations were provided. However, both the correlations and the experimental data included in the existing evaluation literature are limited, which makes the evaluation results inconsistent and inaccurate. This work conducts a comprehensive survey of correlations and experimental investigations of two-phase frictional pressure drop. There are 29 correlations reviewed, and 3480 experimental data points are obtained from the open literature, with the experimental range of hydraulic diameters from 0.0695 to 14mm, and mass flux from 8 to 6000kg/m2s. The reviewed correlations are evaluated against the experimental data, and two correlations which can present the most agreeable predictions are found.

A new correlation of two-phase frictional pressure drop for evaporating flow in pipes

The calculation of two-phase frictional pressure drop for evaporating flow in pipes is required in many fields. Although plenty of studies associated with this issue have been carried out, an accurate correlation is still needed. In this paper, a comprehensive survey of correlations and experimental investigations of two-phase frictional pressure drop is conducted. The 2622 experimental data points of 15 refrigerants are obtained, with hydraulic diameter from 0.81 to 19.1 mm, mass flux from 25.4 to 1150 kg m−2 s−1, and heat flux from 0.6 to 150 kW m−2. There are 29 existing correlations evaluated against the experimental database. It is found that the best correlation has a mean absolute relative deviation (MARD) of 28.5%. Based on the experimental database, a new correlation is proposed, which has an MARD of 25.2%, improving remarkably the prediction of two-phase frictional pressure drop for pipe evaporating flow, especially for micro-channels.

Experimental investigation on frictional pressure drop of water in vertical rectangular channel

Experimental investigation on saturated flow boiling frictional pressure drop was made during a phase-change process with water. The outlet pressure ranged from 12.1 to 16.1MPa, mass fluxes from 500 to 1501kg/(m2s), heat flux from 737 to 1211kW/m2, and average quality in test section from 0.05 to 0.38. The rectangular channel had the following dimensions: gap size 2mm, width 40mm, and heated length 1000mm. The experiments were performed with the channel oriented uprightly.Analysis of the experimental data showed that the effects of pressure, mass flux, and quality on frictional pressure drop agreed with those of a conventional channel. Seven state-of-the-art correlations for conventional channel or rectangular channel were evaluated, but they failed to predict the experimental data. According to the results, the quality was an important parameter on predicting frictional pressure drop for steam–water fluid. The Nconf (Nconf=(1/Dh)(4σ/(g(ρl−ρg))) could not offer any advantage for the present experiment condition. A new correlation for two-phase frictional pressure drop in rectangular channel was developed on the basis of C coefficient method, all the data were within ±15% of error of prediction. The mean deviation was 3.4%.

Evaluation of using two-phase frictional pressure drop correlations for normal gravity to microgravity and reduced gravity

The calculation of two-phase frictional pressure drop (TPFPD) is required by two-phase systems operating under microgravity and reduced gravity. There are a large number of correlations for the TPFPD in tubes under normal gravity. However, it is hard to find out a TPFPD correlation obtained from microgravity and/or reduced gravity conditions, and thus people have to use TPFPD correlations for normal gravity to calculate TPFPD under microgravity and reduced gravity. It is necessary to evaluate the feasibility of such practice. This paper offers a comprehensive review of the TPFPD correlations for normal gravity and an up-to-data survey of the TPFPD experimental study under microgravity and reduced gravity. There are 23 TPFPD correlations for normal gravity reviewed and 135 experimental data under microgravity obtained from the literature. These experimental data are used to evaluate the reviewed TPFPD correlations. It is found that the smallest mean absolute relative deviation (MARD) of the correlations is greater than 34%. Using TPFPD correlations for normal gravity to reduced gravity and microgravity may be acceptable for the first approximation, but correlations intended for microgravity and reduced gravity are needed and more experiments are desired to obtain more data with high accuracy.