Frictional Pressure Drop Correlations Research Articles

Frictional pressure drop of the vertically upward gas–liquid two-phase flow in an airlift pump system

Airlift pumps (ALPs) are promising in the oil and chemical industry, owing to their advantages such as a simple structure, convenient operation, wide applicability, high cost-effectiveness, environmental friendliness, safety, and reliability. However, there are few studies on the frictional pressure drop of vertically upward gas–liquid two-phase flow in ALPs. Therefore, this study presents an experimental investigation of the frictional pressure drop in the vertically upward gas–liquid two-phase flow in ALPs. Experiments were conducted in a vertical pipe with a total length of 3.245 m and a two-phase section of 2.8 m; the working pressure of the air compressor was 0.4 MPa, pipe diameter was 0.05 m, submergence ratio ranged from 0.6 to 0.85, and gas superficial velocity ranged from 0 to 4 m/s. A total of 74 sets of experimental data were obtained, and the frictional pressure drop models of 36 classical gas–liquid two-phase flows were evaluated. The results indicated that classical gas–liquid two-phase flow models significantly underestimated the experimental results. By analyzing the experimental data, visualizing the internal flow field, and performing theoretical derivations, a new frictional pressure drop correlation was established for the vertically upward gas–liquid two-phase flow in ALPs. The results demonstrated that the new model could accurately predict the frictional pressure drop of ALPs with mean percentage error, mean absolute percentage error, and root mean square percentage error values of 7.8%, 12.18%, and 25.86%, respectively.

Study of developing a condensation heat transfer coefficient and pressure drop model for whole reduced pressure ranges

This study involves the collection of data from 10 different articles to develop experimental-based models for predicting the condensation heat transfer and the frictional pressure drop. The dataset comprises a total of 1168 condensation heat transfer coefficients and 792 frictional pressure drop data. The applied operating range considered is within the reduced pressure of 0.1–0.95, mass flux ranging from 75 to 700 kg/m2s, and an inner diameter between 3.4 and 12.5 mm. We developed the models for the condensation heat transfer coefficient based on Akers et al.’s model, whose parameters are the Prandtl number, density ratio, vapor quality, and mass flux. The total error for the condensation heat transfer coefficient is ± 22.6%. The data is further categorized into two groups of the reduced pressure: Pr < 0.5 with an error of ± 22.9% and Pr > 0.5 with an error of ± 18.9%. The frictional pressure drop models were developed based on the three different ranges of the reduced pressure. The utilized non-dimensionless parameters were the two-phase multiplier (Φlo2), the Bond number (Bo), the Weber number (We), and the Martinelli parameter (Xtt), along with the regression coefficients. Regarding the frictional pressure drop correlation, the total error is ± 32.7%, and the data is divided into three segments: Pr < 0.2 with an error of ± 24.6%, 0.2 < Pr < 0.3 with an error of ± 35.6%, and an error of ± 27.8% for the reduced pressure larger than 0.3. These correlations were developed using the MATLAB regression analysis to enhance their practicality and utility.

Frictional pressure drop correlation of steam-water two-phase flow in helically coiled tubes

Helically coiled tubes are utilized as the heat transfer tubes for High-Temperature Gas-cooled Reactor (HTGR) steam generators due to their compactness, thermal expansion accommodation and high heat transfer coefficient. A clear understanding of the pressure drop characteristics is important for the design and operation of steam generators. In this study, experiments were conducted to investigate the frictional pressure drop characteristics in helically coiled tube with a very large curvature ratio of 0.109. The experiments were carried out in a steam quality range of 0.1–0.9, system pressure range of 3.5–7 MPa, mass flux range of 320–1100 kg/m2s. The results indicate that the frictional pressure drop increased with the increase of mass flux, decreased with the increase of system pressure. It first increased with the increase of steam quality, and reached a maximum value at a steam quality of approximately 0.8, then decreased until steam quality reached unity. Based on the present work and existing experimental database, 25 existing correlations are evaluated and none of them could satisfactorily fit all the data. Therefore, a new correlation based on the Martinelli and Nelson correlation was proposed. Compared with existing correlations, it has a broader range of applicability (operating pressure from 0.75 to 8 MPa, mass flux from 200 to 1100 kg/(m2·s), steam quality from 0.03 to 0.99, and curvature ratio from 0 to 0.109.), and higher accuracy (weighted mean MAPE of 8.92 % and arithmetic mean MAPE of 8.81 %). It also has better compatibility with straight tubes.

Experimental study on single- to two-phase flow and heat transfer of water in a small tube

Experimental investigation on flow boiling heat transfer in a small tube under high system pressure has been conducted in this study. The test-section is constructed with a 316L stainless steel tube. The inner diameter and heated length of the test-section are 5 mm and 930 mm, respectively. The working fluid is deionized water. The operating conditions of the experiments are as follows, the mass flux from 548 to 978 kg/(m2·s), the wall heat flux from 136 to 238 kW/m2, and the system pressure from 1.0 to 2.9 MPa. The experimental results showed that the inlet subcooling mainly affects the onset of nucleate boiling, but its impact on the heat transfer coefficient at the same vapor quality is almost negligible. The heat transfer coefficient increases with the increase of mass flux and wall heat flux, especially in the region where xe < 0.02. The average heat transfer coefficient is higher under high system pressure owing to the variation of the thermophysical properties. Additionally, the existing flow and heat transfer correlations cannot predict the flow boiling heat transfer coefficient and frictional pressure drop in the experiments accurately enough. Therefore, the new flow and heat transfer correlations are developed based on the experimental data in this paper, and the mean absolute deviation of the flow boiling heat transfer correlation and frictional pressure drop correlation are 13.3% and 12.1%, respectively.

Critical heat flux, heat transfer and pressure drop at high mass fluxes for R123 in a single microchannel

This paper presents new experimental data on pressure drop, heat transfer coefficient, and critical heat flux during flow boiling of low-pressure fluid R123 in microchannels. High mass velocities were used, above the values found in the literature in tests with this fluid. Experiments were conducted in a single smooth and horizontal microchannel, with an internal diameter of 1.1 mm and heating sections of 46 and 100 mm. The mass velocities used were between 1500 and 7500 kg/m2s. Saturation temperature ranged from 40.1 to 85.1 oC. The outlet vapor quality varied between -0.54 and 0.53 for the CHF results, between 0 and 0.5 for the pressure drop results, and between 0 and 0.35 for the HTC results, respectively. Record critical heat flux values for flow boiling of R123 in smooth microchannels were achieved, reaching 1.44 MW/m2. An analysis was made of the influence of an upstream pressure drop in avoiding instabilities during critical heat flux experiments. The highest heat transfer coefficient values during convective boiling of R123 in smooth microchannels were also obtained, with values close to 43.3 kW/m2K. The saturation temperatures used were among the highest for flow boiling of R123 in smooth microchannels found in the literature. Correlations for frictional pressure drop, heat transfer coefficient, and critical heat flux were evaluated in predicting the experimental data. An analysis was made on the influence of the void fraction correlation when estimating both the accelerational and frictional pressure drop.

ANALYSIS OF THE SINGLE-BLOW TRANSIENT TESTING TECHNIQUE FOR NONMETALLIC HEAT EXCHANGERS

For measuring the efficiency of nonmetallic heat exchangers, a mathematical model was established based on the principle of the single-blow testing technique, in which the conductive thermal resistance across nonmetallic plates of the exchangers was taken into account. The analytical solution was obtained by means of the Laplace transformation and numerical inverse transform method. The accuracy of the model was verified by comparing it with the literature. The effect of the plate Bi number on the evaluated number of transfer units (NTU) was analyzed. Based on the single-blow transient testing technique and the present model, the heat transfer performance and frictional pressure drop of four types of nonmetallic plates with different structural parameters were experimentally studied. The correlations for heat transfer and frictional pressure drop of nonmetallic heat exchange structures are established.

Development and assessment of performance of artificial neural networks for prediction of frictional pressure gradients during two-phase flow

This paper presents a discussion on several possibilities to predict the frictional pressure gradient during two-phase flow, with both the application of artificial intelligence and the implementation of conventional correlations and predictive methods. To this purpose, a huge database of approximately 8000 data points has been collected from 49 sources available in scientific literature, including 23 working fluids and the following ranges of parameters: mass fluxes from 32.7 to 2000 kg/m2s, saturation temperatures from -190°C to +120°C (reduced pressures from 0.021 to 0.780), tube diameters from 0.5 to 14.0 mm.This consolidated database has been used to train several artificial neural networks (ANNs), by using only two hidden layers (shallow neural networks) and evaluating the effect of: training and testing datasets choice (either test data included or outside the training domain), the number of neurons for each hidden layer (from 1 to 50), the type of output (either dimensional or non-dimensional), the type and number (from 1 to 22) of input parameters.The best results (MAPE of 16.8% and 88% of data within ±30%) have been obtained by using the liquid-only two-phase multiplier ΦLO2 as non-dimensional output and 12 mixed input parameters. Compared to the statistics of well-established literature correlations for frictional pressure drop (best MAPE of 22% and 73% of data points predicted within a ±30% error range, provided by Mauro et al. mechanistic method), the ANN demonstrates therefore a higher general accuracy. However, the use of Artificial Neural Networks does not guarantee a physical trend, which is instead preserved with conventional prediction methods.

Evaluation of frictional pressure drop correlations for air-water and air-oil two-phase flow in pipeline-riser system

Accurate prediction of the frictional pressure drop is important for the design and operation of subsea oil and gas transporting system considering the length of the pipeline. The applicability of the correlations to pipeline-riser flow needs evaluation since the flow condition in pipeline-riser is quite different from the original data where they were derived from. In the present study, a comprehensive evaluation of 24 prevailing correlation in predicting frictional pressure drop is carried out based on experimentally measured data of air-water and air-oil two-phase flows in pipeline-riser. Experiments are performed in a system having different configuration of pipeline-riser with the inclination of the downcomer varied from −2° to −5° to investigated the effect of the elbow on the frictional pressure drop in the riser. The inlet gas velocity ranges from 0.03 to 6.2 m/s, and liquid velocity varies from 0.02 to 1.3 m/s. A total of 885 experimental data points including 782 on air-water flows and 103 on air-oil flows are obtained and used to access the prediction ability of the correlations. Comparison of the predicted results with the measured data indicate that a majority of the investigated correlations under-predict the pressure drop on severe slugging. The result of this study highlights the requirement of new method considering the effect of pipe layout on the frictional pressure drop.

Boiling heat transfer and pressure drop of R290 in a micro-fin tube

The present study focuses on the analysis of heat transfer and pressure drop of R290 in a horizontal micro-fin tube. In this regard, experiments were conducted, and flow patterns, heat transfer coefficient, and friction pressure drop were analyzed under various conditions. A wide range of conditions was studied, including saturation pressures ranging from 0.215 to 0.415 MPa, mass fluxes ranging from 70 to 190 kg m−2 s−1, heat fluxes in the range of 10.6–73.0 kW m−2, and vapor qualities from 0 to 0.96. The performed analyses revealed four flow patterns, including bubbly flow, plug flow, slug flow, and annular flow. It is found that the onset of dry-out occurs when the liquid film thickness is equal to the fin height and occurs earlier at high heat fluxes and low saturation pressures. The maximum heat transfer coefficient and friction pressure drop occur at the onset of dry-out, and the heat transfer coefficient exhibits a significant correlation with the heat flux. The obtained results were verified using the heat transfer correlation of Cavallini and the friction pressure drop correlation of Rollman, where the average relative deviation (ARD) was −24.01% and −8.65%, respectively.

Effects of Pipe Inclination on Global Two-Phase Flow Parameters

Inclined two-phase flow geometries can be found in advanced nuclear reactor systems, such as the helical coil steam generators being considered for use in current integral steam generator designs. While this geometry includes inclination and centrifugal effects coupled together on two-phase flow, there have been limited studies to separate these effects to develop robust models. The majority of two-phase flow research is conducted on vertical channels, with recent work being conducted in a horizontal orientation and limited work in inclined pipes. In the current work, experiments are conducted in an adiabatic two-phase flow test facility to investigate the inclination effect on an air-water flow in straight pipes near atmospheric pressure. The pipe is made of clear acrylic with an inner diameter of 25.4 mm. The inclination of the flow loop can be adjusted in increments of 0.1 deg. Measurement capabilities are included to obtain local two-phase flow parameters such as void fraction, interfacial area concentration, bubble velocity, and Sauter-mean diameter using a local multisensor conductivity probe, local two-phase flow static pressure and pressure drop using a pressure transducer, and flow visualization using a high-speed video camera system. The experimental studies performed in the current work demonstrate how changes in inclination angle can affect the gas distribution flow regime transition and two-phase frictional pressure drop. Based on these experimental results, existing correlations for frictional pressure drop are evaluated, and the modified Lockhart-Martinelli correlation is found to predict the two-phase frictional pressure drop for inclined two-phase flows. This method agrees with experimental data within 7% on average.

Experimental investigations of gas–liquid two-phase flow in a horizontal mini pipe: Flow regime, void friction, and frictional pressure drops

Experimental studies of air–water two-phase flows in a mini tube with an inner diameter of 3.12 mm have been conducted in terms of the flow pattern, void fraction, and pressure gradients. The fluid velocities range from 0.065 to 21.78 m/s and from 0.109 to 1.835 m/s, respectively. A right-angle prism is applied to capture images simultaneously from two perpendicular directions. Three-dimensional gas–liquid interfaces are reconstructed with the obtained images from two directions. The gas void fraction is investigated using this method, which is experimentally validated with the quick closing valves method. Three flow patterns are obtained in the present work, which is bubbly, slug, and annular flows. The Probability Density Functions of the cross-sectional void fraction show that the intermittent flow has two peaks and the annular flow has only one peak. Volumetric void fraction is affected by the flow pattern and the flow rate. However, at very high gas velocities, volumetric void fraction is independent of the liquid rate. A new frictional pressure drop correlation is proposed based on the experimental data.

The Development of Empirical Correlations to Understand the Frictional Behavior of Aqueous Biomass Slurry Flows in Vertical Pipes

Highlights The frictional pressure drop correlation of agricultural residue-water slurry flows in vertical pipes is developed. Multiple linear regression with the backward elimination method was used in RStudio to obtain the optimal model. Some regression coefficients differ for different types of biomass feedstocks. The predicted pressure drops agree well with the experimental data within a 95% CI. Empirical models for the onset velocity of drag reduction of different particle sizes of biomass are proposed. Abstract. Large-scale biofuel production at levels equivalent to conventional oil refineries using long-distance pipeline hydro-transport of biomass can be a cleaner alternative to fossil fuels when it comes to economics and traffic congestion associated with the overland transportation of biomass. The transport of aqueous slurries of several saturated mass concentrations (5%-40%) and four particle sizes (from &amp;lt;3.2-19.2 mm) of two types of agricultural residue biomass (ARB) feedstock (corn stover and wheat straw) was studied through a vertical test section of a 29 m long, 50 mm diameter closed circuit pipeline facility, and frictional pressure drops were recorded at different flow rates (0.5-4.3 m s-1). A framework was developed in RStudio (4.0.5) to analyze the experimentally obtained frictional pressure drops of biomass slurries through a multiple linear regression approach using a backward elimination method and Akaike information criterion. An empirical model was proposed to predict slurry frictional pressure drop in terms of slurry velocity, slurry solid mass concentration, particle aspect ratio, and feedstock type. The model satisfactorily predicted the frictional pressure drops of both feedstocks of biomass-water slurry flows through pipes within a 95% confidence interval. The correlations introduced for onset velocities of drag reduction in terms of slurry solid mass concentrations seemed helpful to interpret the transition points of the corresponding slurries in vertical upward flows through pipes. The empirical correlation developed in this research could help select biomass slurry pumps and pipe dimensions when designing a typical long distance pipeline network for biofuel production at the commercial level. Keywords: Agricultural biomass wastes, Frictional loss prediction, Numerical model, Onset velocity correlation, Regression coefficients, Upward pipe flow.

Experimental study and general correlation for frictional pressure drop of two-phase flow inside microfin tubes

The adiabatic pressure drop in a microfin tube with an outside diameter of 3.5 mm was experimentally studied herein. The experiments were conducted using R1234yf as a working fluid at saturation temperatures of 20 °C and 30 °C with varying mass velocities from 50 to 300 kg m−2s−1 and vapor qualities ranging from 0.1 to 0.9. The effects of experimental conditions were analyzed and discussed with present and previous data. A new two-phase flow frictional pressure drop correlation has been developed using the data with tube diameter of 2.5–9.52 mm, mass velocity of 50–1000 kg m−2s−1, and many kinds of refrigerants. The proposed correlation predicts the experimental data of other researchers with mean deviation of 17.6%.

Frictional pressure drop correlation for condensation of refrigerants in microchannel heat exchangers

ABSTRACT Condensation of HFC refrigerants in microchannel heat exchangers has gained a lot of interest recently due to high heat transfer coefficient, small size, and reduced refrigerant inventory. Additionally, these microchannel heat exchangers can be conveniently used for extensive ranges of temperature and pressure. Even though numerous research studies have been conducted on the two-phase frictional pressure drop for condensing flows in microchannels, the efforts are continuing to get more experimental data that can be used to develop an accurate frictional pressure drop correlation. The present paper uses 384 experimental data points, which the authors have obtained during the condensation of refrigerants, R134a and R410A, inside multiport rectangular microchannels with hydraulic diameters ranging from 0.66 to 1 mm, at average saturation temperatures of 30°C to 40°C, mass fluxes of 200 to 600 kg/m2s, and average vapor qualities ranging from 0.05 to 0.83. A frictional pressure drop correlation for condensing flows through microchannels has been developed, and the resulting correlation agrees with the experimental data with an MAE of 11.58% and predicts the data almost within the 20% error band. Experimental data were compared with 10 well-known frictional pressure drop correlations from the literature, and it was found that these correlations either over-predict or under-predict the data.

New generalized flow boiling heat transfer and frictional pressure drop correlations for R32

The objective of this study is to establish generalized correlations for R32 flow boiling heat transfer and frictional pressure drop in horizontal channels with wide ranges of geometric and flow parameters. In the paper, two consolidated databases for heat transfer and frictional pressure drop were amassed from open literatures, which involved R32 as working fluid. The heat transfer database consisted of 1509 data points from 10 sources, with hydraulic diameters of 1−6.3mm, while the pressure drop database included 496 data points from 8 sources, which covered hydraulic diameters of 0.643−6mm. New heat transfer coefficient correlation and frictional pressure drop correlation were developed based on prediction technique of dimensionless parameter analysis considering the governing force effect. Moreover, five existing flow boiling heat transfer empirical correlations and four existing frictional pressure drop correlations were also introduced to perform assessment. The validation results showed that all of the selected heat transfer correlations had poor results of mean absolute errors (MAE) and significantly high maximum absolute errors (MAX). The new heat transfer coefficient correlation provided superior prediction accuracy with MAE of 14.59% and 90.85% of data within ±30% error bands. In addition, the new pressure drop correlation exhibited the best performance, which yielded MAE of 17.86%. The two new correlations had broad application range and satisfactory prediction accuracy, which were applicable to analyze the heat transfer and pressure drop performance of heat exchangers with refrigerant R32.

Boiling Heat Transfer and Visualization for R717 in a Horizontal Smooth Mini-tube

The paper presents an experimental and theoretical investigation on the two-phase flow boiling heat transfer with ammonia (R717) as the refrigerant in a horizontal smooth mini-tube with inner diameter of 3mm. The experimental data were obtained in the following condition, the heat flux density is 10∼30 kW · m − 2 , the mass flux is 40∼200 kg · m − 2 · s − 1 , the saturation temperature is -10∼10 ℃, and the range of vapor quality is 0.1 ∼1. The experimental results show that the heat transfer coefficient before dryout phenomenon increases and gradually reaches a peak with the increase of vapor quality, but occurs heat transfer deterioration after dryout phenomenon. Combined with the transform of flow patterns, the effect of mass flux, heat flux density, and saturation temperature on the heat transfer coefficient and friction pressure drop are analyzed. The theoretical gas phase flow velocity of ammonia is much higher than other refrigerants, and the flow boiling heat transfer for ammonia is more dependent on convective boiling. The existing correlations of two-phase flow are compared with the measured data of ammonia. According to the experimental and comparative results, Kew and Conwell correlation and Müller-Steinhagen and Heck correlation were updated respectively, and new boiling heat transfer correlation and frictional pressure drop correlation were obtained.

Analysis of Frictional Pressure Drop Correlations of Refrigerant Two-Phase Flow in Mini-Channel

Analysis of Frictional Pressure Drop Correlations of Refrigerant Two-Phase Flow in Mini-Channel

Experimental Investigation on Adiabatic Two-Phase Frictional Pressure Drop of R1234ze(E) and R134a in a Horizontal Minichannel

Abstract R1234ze(E) has been created as an environmentally friendly substitution of R134a. An experimental investigation on adiabatic two-phase frictional pressure drop inside a 1.88 mm horizontal minichannel with R1234ze(E) and R134a was conducted. The saturation pressure and mass flux ranged within 0.6–0.9 MPa and 450–900 kg/(m2 s). Based on the 299 measured data points, the influences of various factors, including saturation pressure, mass flux, and the like, are examined detailedly. Larger mass flux brings about larger frictional pressure drop, and vapor quality performs the same function, but saturation pressure works inversely. The frictional pressure drops between R1234ze(E) and R134a present no significant differences. The experimental data are compared against 23 predictive models, among which the one from Xu and Fang (2013, “A New Correlation of Two-Phase Frictional Pressure Drop for Condensing Flow in Pipes,” Nucl. Eng. Des., 263, pp. 87–96) gives the best accuracy. In addition, a database including 3150 experimental adiabatic two-phase frictional pressure drop data points is derived from the current study and 29 published literature. Based on the database, the 23 models are assessed, and the most effective one is from Müller-Steinhagen and Heck (1986, “A Simple Friction Pressure Drop Correlation for Two-Phase Flow in Pipes,” Chem. Eng. Process., 20(6), pp. 297–308). This work can provide guidance for choosing appropriate two-phase frictional pressure drop models under adiabatic conditions.

Effect of Ambient Temperature Variation on Pressure Drop During Condensation in Long Inclined Tubes

Abstract Two-phase flow pressure drop during condensation of steam inside inclined tube heat exchangers was investigated over a wide range of ambient temperature. The ambient temperature changes from 3 to 45 °C, the steam mass flux varies from 3 to 18 kg/(m2 · s), vapor quality ranges from 0.51 to 0.86. 608 data points were experimentally obtained and compared with eight commonly used correlations from the available literatures. Frictional pressure drop increases with increasing temperature difference and fan speed. For the full experimental dataset, the best overall performing correlation was obtained by using the Wallis correlation (MAPE = 17.60%, NRMSE = 14.87%). For cold ambient temperatures, (Tamb &amp;lt; 20 °C, N = 298), the best overall performing correlation was obtained by using the Carey correlation (MAPE = 11.02%, NRMSE = 14.71%). For hot ambient temperatures (Tamb &amp;gt; 30 °C, N = 196), the Lockhart and Martinelli correlation has shown the best performance (MAPE = 16.84%, NRMSE = 20.45%). An improved two-phase frictional pressure drop correlation based on the Wallis correlation (Wallis, 1969, One Dimensional Two-Phase Flow, McGraw-Hill, New York) is proposed.

On instantaneous pressure surges and time averaged pressure drop in intermittent regime of two-phase flow

Vigorous aeration and instantaneous pressure fluctuations associated with intermittent flow cause severe erosion-corrosion in the piping systems which lead to material degradation or wall thinning and leakages. Sometimes, this phenomenon results in catastrophic failures and hazards in transportation pipelines for industries such as petroleum, nuclear, geothermal and chemical. Present analysis is on the instantaneous pressure surges associated with the intermittent flow patterns and the two-phase frictional pressure drop. Experiments are carried out for three distinct sub-regimes of intermittent flow namely; Plug, Less Aerated Slug (LAS) and Highly Aerated Slug (HAS) flow. Instantaneous pressure fluctuation and time averaged pressure drop along the pipe length are reported for 350 combinations of inlet flow conditions (in term of ReSL and ReSG) of intermittent flow regime. Combined images of captured visual observations and measured instantaneous pressure fluctuations are demonstrated in terms of their influence on erosion and corrosion in detail. The obtained results are compared with the existing models for estimation of two-phase pressure drop proposed by earlier researchers. Large deviations between the experimental results and existing pressure models signify the need of separate correlation for two-phase frictional pressure drop for intermittent flow regime. In this direction, a unified correlation for prediction of two-phase frictional pressure drop for intermittent flow regime is proposed. The measured experimental results and obtained correlation for pressure drop will help in avoiding the erosion-corrosion in piping system. Also, database presented in this paper will aid to the effective and safe design of piping systems for petroleum, nuclear, geothermal and chemical industries.