Friction Factor Correlations Research Articles

Friction and Forced Convection Heat Transfer Characteristics in Tubes by Use of Helical-Wire-Coil Inserts.

This work summarizes the results of experimental investigation of convective heat transfer and friction loss characteristics of air flow in a horizontal circular copper tube of diameters 13.5/22 mm., using helical wire-coils , of diameter 1.4 mm, inserted in. The helix angle (a) of the helical-wire-coil is varied from 65° to 86.7o. The outer surface of the test tube is heated by superheated steam (degree of superheat 2:3 oC) at atmospheric pressure. During the experimental work, Reynold's number is changed from 6000 to 120000 and Prandti number is about 0.7. The heat transfer enhancement of the inserted helical-wire-coil is ranging from 30 % to 145 %. However, A quantitatively increase in hydrodynamics resistance is noticed. Correlations of Nusselt number and friction factor has been made. It was found that the nusselt number and friction factor were dependent on both Reynold's number and helix angle.

A comparative study of flow characteristics of adiabatic spiral and helical capillary tube in a CO2 transcritical system

Flow characteristics of an adiabatic spiral and a helical capillary tube in a CO2 transcritical system are numerically simulated. A homogeneous two-phase flow model is developed using the mass, energy and momentum conservation equations, taking into consideration the helical and spiral coiling effects of the capillary tubes. Friction factor and viscosity correlations are used from the available literature. Results are compared with conventional subcritical refrigerant R22. Reduction in a mass flow rate of refrigerant is more pronounced in the spiral capillary tube than helical capillary tube effect; about 18% and 11% with CO2 and R22, respectively. Length requirement with a spiral capillary tube is relatively less compared to other chosen configurations for the given mass flow rate and operating conditions.

Molecular dynamics simulation of fluid flow through nanochannels consisting of different superhydrophobic patterns

Non-equilibrium molecular dynamics simulation has been carried out to calculate the Darcy-Weisbach friction factor of water flow through the nanochannels. The nanochannel walls were decorated by different arrays of nanoscale protrusion to generate superhydrophobic surfaces. The existence of nanostructures on the channel walls leads to trapping the air inside the nanocavities and, consequently, the system transmutes to a ternary (solid-liquid-gas) system. Our goal is to study how this transmutation affects the hydrodynamics of the fluid flow. The superhydrophobic walls were comprised of longitudinal and transversal nanoridge arrangements and results are obtained for various Reynolds numbers, pillar surface fractions and relative module widths. In this contribution, we presented correlations for the Darcy-Weisbach friction factor of water flow through the nanochannels including different superhydrophobic structures. Results indicated that the relation between friction factor and Reynolds number for the flow through the nanochannels is similar to the laminar flow through channels. Our results demonstrated that the friction factor in nanochannels decreased by employing superhydrophobic structures and also the friction factor in transversal nanoridge arrangement was significantly higher than that of the longitudinal one. We found that by decreasing the percentage of surface fraction and increasing the relative module width, the friction factor decreased.

Experimental and numerical studies on novel airfoil fins heat exchanger in flue gas heat recovery system

• The novel airfoil fins heat exchanger was studied experimentally and numerically. • The novel airfoil fins channel has the best thermal–hydraulic performance. • The enhancement mechanism could be explained with field synergy principle. • Thermal-hydraulic correlations of novel airfoil heat exchanger were proposed. To improve the performance of waste heat recovery, a novel airfoil fins heat exchanger was applied to flue gas waste heat recovery. Two groups of experimental conditions were installed to test the heat effectiveness of the novel airfoil fins heat exchanger. The results showed that the heat effectiveness of the novel airfoil fins heat exchanger could reach more than 96%, which is higher than the conventional heat exchanger. The thermal–hydraulic performances of the novel airfoil channel, NACA 0020 airfoil channel and zigzag channel were investigated with the first and second laws of thermodynamics, which showed that the novel airfoil channel has the best comprehensive thermal–hydraulic performance among the three channels. The correlations of Nusselt number and friction factor of the novel airfoil fins heat exchanger were proposed for flue gas, whose maximum deviations were within ±5.0% and ±7.1%, respectively. The present work could provide guidance for the application of the novel airfoil fins heat exchanger in waste heat recovery.

An evaluation of selected friction factor correlations and results for the pressure drop through random and structured packed beds of uniform spheres

The focus in the paper is on an evaluation of the friction factors as a function of the modified Reynolds number for the pressure drop through randomly and structured packed beds consisting only of uniform sized spheres. In the evaluation of the friction factor for large aspect ratio randomly packed beds it is confirmed that the use of the Ergun correlation should be avoided and that the KTA correlation should be employed to predict the friction factor. The effect of the wall for small aspect ratio randomly packed beds as predicted by the Eisfeld and Schnitzlein correlation is also evaluated and it is suggested that the use of the correlation be restricted to aspects ratios of D/dp>2. The combination between the Eisfeld and Schnitzlein and KTA correlations should also be investigated. An evaluation is also provided for the friction factor results for selected structured packed beds. A correlation is proposed to predict the friction factor for offset simple cubic, hexagonal close packed, simple cubic and body-centred cubic packed beds. It is recommended that the friction factors for structured packed beds should be studied in more detail to develop a sound understanding of the effect of the packing structure on the pressure drop through a packed bed.

Experimental exergy analysis of a printed circuit heat exchanger for supercritical carbon dioxide Brayton cycles

Abstract Exergy analysis could improve the quality of energy in the printed circuit heat exchanger. However, most of the current researches were carried out based on the first law of thermodynamics, which only focus on heat transfer, pressure drop, and heat transfer rate of the heat exchanger. There are no reports about experimental analysis of the printed circuit heat exchanger using the exergy analysis. Therefore, in this study, experimental exergy analysis of a printed circuit heat exchanger used as a recuperator for the supercritical carbon dioxide Brayton cycle is introduced. In the tests, the zigzag channels are adopted for the current heat exchanger to achieve higher heat transfer capability. The maximum running temperature and pressure in the experiments are 715.2 K and 22.5 MPa, respectively. The Reynolds number varies from 3212 to 23888. Pressure drops and temperatures are measured at the inlet and outlet of both sides. The effects of the inlet temperatures and Reynolds numbers on the exergy loss and efficiency of the printed circuit heat exchanger are investigated. The results show that the low Reynolds number and high inlet temperature on the cold side have positive effects on the exergy efficiency. New Nusselt number and friction factor correlations are developed according to the test results.

Investigation of Pressure Drop Calculation for Twisted Tape Swirl Tubes by Conventional Channel Flow Correlations with Fusion Applications

Twisted tape inserts are commonly used for heat transfer enhancement in fusion applications. Although these devices have been extensively studied, existing correlations relating friction factor to Reynolds number and system geometry are applicable only for tight-fitting inserts and cannot account for system roughness and fouling. In this work, we examine pressure losses in twisted tapes of various twist ratios using both a typical twisted tape correlation and a newer formulation that incorporates conventional channel flow correlations. We study flows down to a Reynolds number of 4000 and find that the channel flow treatment predicts experimental outcomes well for turbulent conditions, like those expected in the ITER divertor. For calculations at low Reynolds numbers (expected during start-up and show-down of the divertor), we propose that channel flow correlations be merged with twisted tape correlations. This new, merged correlation is seen to be applicable across all Reynolds numbers observed, although it predicts small divergences among tape pitches at low Reynolds numbers that are not clearly reflected in our experimental data. Experimental and legacy data show that conventional channel flow friction factor correlations can be used under this formulation for pressure drop predictions at Reynolds number above 15 000. We suggest the use of this twisting channel treatment for loose-fitting inserts and systems in which fouling and roughness may be of concern, allowing existing straight channel models to be used for twisted tape pressure drop calculations.

Thermohydraulic performance and second law analysis of a tube embedded with multiple helical tape inserts

ABSTRACT The present investigation deals with the analysis of the heat exchanger tube by inserting the multiple helical tape geometry to determine the heat transfer, friction factor, thermal performance, and entropy generation experimentally. The helical tapes designed for current investigation are analyzed in terms of geometrical parameters namely number of tape (1,2,3), twist ratio (2,3,4), and width ratio (0.4). The experiments are conducted in the range of Reynolds number lying in turbulent region from 5000 to 29000. The experimentation affirms an enhancement of the thermal performance. The experimental data reveal that there is 3.95 times enhancement in the heat transfer for twist ratio of 2 and number of tapes of 3. The thermal performance factor is enhanced by 1.23 times over smooth tube for the twist ratio of 2 and number of tapes of 1. It is observed that the maximum heat transfer enhancement is found for low and high values of twist ratio and number of tapes, respectively. The rate of entropy generation is less for the tube equipped with helical tape inserts for all possible cases than smooth tube. The minimum entropy generation value of 0.27 is observed for twist ratio of 2 and number of tapes 3. The developed empirical correlations for Nusselt number, friction factor, and thermal performance factor are in good agreement with experimental results.

Augmentation of laminar flow heat transfer in annular flat tubes by means of helical screw-tape inserts in the inner tube.(Dept.M)

The heat transfer characteristics and friction factor in horizontal double pipes of flat tubes with full length helical screw element of different twist ratio and helical screw inserts with different spacer length are investigated. Cold and hot water are used as working fluid in tube side and shell side respectively. The experiments covered a range of Reynolds numbers 5.7*102 ≤ Re ≤ 1.31*103. The effect of spacer length and twist ratio on the heat transfer augmentation and friction factor on heat transfer have been presented separately. The study shows that, Nusslet number (Nu) and friction factor (f) decrease with the increase of spacer length (S) and twist ratio (Y) for flat tube. The comparison between the data of present plain circular tube with that of previous plain circular tubes showed good agreement but the data of present plain flat tube showed a higher in heat transfer and pressure drop than that of plain circular tube. The correlations of average Nusselt number and friction factor with Re, S and Y are presented.

A detailed review on research, technology, configurations and application of wire ribs as artificial roughness in rectangular solar air heater duct

Use of artificial roughness in the duct of solar air heater (SAH) has been an interesting area of research during the last few decades. In present review article a holistic view about application of circular shape wire ribs as roughness element and its different geometry on the absorber plate of SAH duct for performance enhancement has been done. This article, reported in details numerous experimental as well as analytical studies for rib roughened SAHs which have been carried out by different researchers positively. Correlations for heat transfer and friction factor, developed by various investigators for different artificially roughened solar air heaters (SAHs) geometry have been reported in chronological order and in well tabulated form. The roughness and operating parameters into which investigators have obtained their maximum performances of SAHs have also been presented separately in the table. Effects of various rib roughness parameters on heat transfer and fluid flow process are also discussed in details.

A model to calculate the pressure loss of Newtonian and non-Newtonian fluids flow in coiled tubing operations

The coiled tubing is a system consisting of a long, continuous and flexible steel pipe used in many processes, especially in the oil industry. As the fluid flow in curved pipes generates significant energy dissipation compared to a straight pipe, it is essential to predict the pressure drop to obtain the pumping pressure to be used in the operation and optimize process control. In this work, the pressure drop in the flow of Newtonian and non-Newtonian fluids was evaluated in a pilot unit and a mathematical model was developed to simulate the pressure drop along the coiled tube. Water and an aqueous solution of xanthan gum, with rheological power-law parameters similar to those observed in cement slurries, were used in experimental tests. The experimental unit is 375 m long divided into 8 layers with pressure measurements in each layer where fluids were pumped at different volumetric flow rates and curvature ratios. A mathematical model was proposed to calculate the pressure drop assuming the existence of a sequential pumping of different fluids along the coiled tubing, with different curvature ratios and internal tube diameters. The mathematical modeling could predict the pilot experiments for Newtonian fluids and, based on the results obtained in the laboratory, the parameters of a friction factor correlation for non-Newtonian fluids present in the literature were re-estimated. A case study of a real well abandonment operation with a coiled tubing system was used to validate the proposed modeling. The developed software was used to simulate the real conditions, where a good approximation to the field data was observed, with a percentage error between the experimental and calculated values below 7%.

Study on interfacial friction in the inverted annular film boiling regime

The interfacial friction factor is an important closure model in the two-fluid model for the inverted annular film boiling (IAFB) regime. Almost all the interfacial friction factor correlations used in IAFB modeling were obtained based on experimental data from annular two-phase flows. This paper first reviews the interfacial friction factor models/correlations used in IAFB modeling. A laminar vapor film model is then derived for the smooth IAFB region based on a laminar flow assumption. Experimental data obtained from subcooled and low-quality film boiling experiments in the literature are reduced to calculate the interfacial friction factor by solving one-dimensional two-fluid momentum equations for the liquid and vapor phases. The trend of the interfacial friction factor indicates that the transition from the smooth to wavy IAFB regions occurs at a void fraction range of 0.2 to 0.4. Comparisons between the laminar vapor film model and corresponding experimental data and nine correlations in the literature indicate that the laminar vapor film model appears to provide the lower bound of the interfacial friction factor in the smooth IAFB region. Two interfacial friction factor correlations from the literature are recommended for the smooth and wavy IAFB regions based on the analysis. It can be concluded that the interfacial friction factor in the smooth IAFB region is dependent on the gas Reynolds number and vapor film thickness, while in the wavy IAFB region, it is primarily dependent on the amplitude of the interfacial waves.

Investigation on thermal performance of different wire coil twisted tape inserts in a tube circulated with water

This study gives the combined outcome of twisted tapes (TT) and perforated twisted tapes (PTT) with twist ratios of (TRS) 3, 4 and 5 and wire coils (WC) coil ratios (CR) of 3 and 4 in a circular tube, where water has been circulated as the working fluid. The convective heat transfer coefficient (h) and friction factor (f) characteristics are examined in the turbulent flow regime (3000 ≤ Re ≤ 16,000) in order to obtain the thermal performance. These characteristics obtained with the combined effect of TT and PTT associated with WC in a plain tube are 65.06%–101.13%, 75.67%–177.81% and 2.75%–30%, 9%–28% respectively when compared with the circular tube. These enhancements are due to reversed flow caused by wire coils with swirling and impinging flow from the twisted tapes. In addition, high turbulence is created while the fluid is passing through the perforations of PTT. With the wire coil at TR = 3 and CR = 3, the maximum thermal enhancement factor at stable pumping power is 2.03 and 2.66 for TT and PTT, respectively. For all wire coils, twisted tapes and plain tubes, the correlations of Nusselt number and friction factor are established.

RETRACTED: Development of correlations for Nusselt number and friction factor of packed bed solar thermal energy storage system having spheres with pores as packing elements

Solar energy is an emerging alternative of fossil fuels to fulfill the global energy demand as it is available in plenty and eco-friendly in behaviour. However, solar energy systems requires storage unit due to its intermittent nature. The packed bed storage system (PBSS) as storage unit is considered to be a feasible option for solar thermal energy systems having operating temperature range under 100°C. The heat transfer and pressure drop within PBSS are influenced by shape of packing element as convective heat transfer coefficient is a function of it. Under the current study, correlations are developed for Nusselt number as well as friction factor using the results obtained through experimental investigation for the PBSS built up of spherical shaped packing elements having pores on the surface. The developed correlations are the function of Reynolds number, ratio of pore diameter to sphere diameter (d/D), perforation index (PI) and ratio of pore depth to sphere diameter (t/D) within range of 200 to 800, 0.066 to 0.2, 0.06 to 0.22 and 0.05 to 0.2, respectively. Values obtained from the developed correlations are compared with the values obtained through experimentations and it is found that the correlations for Nusselt number and friction factor can predict the values with mean absolute deviation of 6.7% and 7.5%, respectively. These correlations may be helpful for the researchers working in the same research area and manufacturers developing the low temperature solar thermal energy systems. This study may also be useful to investigate the effect of similar shape of packing elements in latent heat based PBSSs.

Experimental Study of Forced Convection Heat Transfer through Porous Media inside a Rectangular Duct of Fully Developed Region

This prospective study was designed to experimentally investigate the effects of inserting copper mesh in fully developed turbulent flow on the flow and heat transfer characteristics. Experimental work includes designing and manufacturing the test section of rectangular duct with dimensions of (30*3*40 cm) with aspect ratio and hydraulic diameter of 10 and 5.45 mm respectively. A constant heat flux ranged (1.5*102 – 1.8*102 W/m2) was applied to the lower surface of duct with Reynolds number range (3.3*104 – 4.8*104). The porosity rang of (0.98 – 0.99). Also, the effects of porous height ratio (full and partial filling) were considered and considered air as working fluid. The results indicate that inserting mesh wire leads to enhance heat transfer coefficient and increase pressure drop. Taken together, these results show that the obtained values of performance enhancement criteria (PEC) ranged (1.01 -1.98 ), the enhancement in heat transfer coefficient is 315% duo to wire mesh insert. Also, from obtained results empirical correlation for friction factor and Nusselt number were suggested.

Thermal performance assessment of self-rotating twisted tapes and Al2O3 nanoparticle in a circular pipe

Heat transfer devices are widely encountered in many chemical applications. This study aims at developing an effective method of heat transfer enhancement by using self-rotating twisted tapes (SRTTs) and Al 2 O 3 nanoparticles. The results indicate the heat transfer performance is rapidly improved with the highest heat transfer multiplier of 2.08. In view of the practical importance of the heat transfer devices in various thermal engineering fields including chemical and nuclear engineering, this study aims at developing an effective method of heat transfer enhancement by using self-rotating twisted tapes (SRTTs) and Al 2 O 3 nanoparticles. The effect of the self-rotating twisted tapes and Al 2 O 3 nanoparticles on the thermal performance was comprehensively investigated in a circular pipe. The experimental results indicated the heat transfer rate was effectively improved by SRTTs in comparison of plain tube. In addition, the heat transfer multiplier with SRTTs decreased from 1.38 to 1.08 with the Reynolds number increasing from 19,322 to 64,407, while the friction factor multiplier decreased from 1.61 to 1.32. Besides, the results indicated that the employment of Al 2 O 3 nanoparticles and SRTTs demonstrated superior thermal performance to the single SRTTs. As Reynolds number increases from 19,322 to 64,407, the heat transfer multiplier decreased from 2.08 to 1.18 in the mass concentration of 3.0% and from 1.38 to 1.08 in mass concentration of 0.0%. Finally, the new heat transfer and friction factor correlations considering the combined effect of Al 2 O 3 nanoparticle and SRTTs were developed within 10% deviation of experimental values.

Thermal-hydraulic performance of compressed humid air flowing in a recuperator

A novel heat exchanger unit structure was adopted to improve the thermal–hydraulic performance of compressed humid air and high-temperature flue-gas in a megawatt (MW) grade humid air turbine (HAT) cycle. Staggered airfoil fin channels and rectangular straight fin channels were projected for the compressed humid air and flue-gas, respectively. A three-dimensional model of the heat exchanger unit structure was built to simulate the heat transfer and flow of flue-gas and compressed humid air under different moisture content, mass flow-rate, and inlet temperature of humid air. The thermal–hydraulic performances of staggered airfoil channels were contrasted with that of straight and zigzag channels. The results showed that the airfoil channel has the best comprehensive thermal–hydraulic performance. Heat transfer and friction factor correlations were proposed to predict thermal–hydraulic performances of the compressed humid air flowing in the airfoil channel. The effects of moisture content on the heat transfer and flow characteristics were quantitatively described using correlations. The moisture content of the humid air is the main influence factor on heat transfer performance. In present study, the results and correlations can provide guidance for the design and application of recuperator structures with airfoil fins for the MW grade HAT cycle.

Numerical Study on Flow and Heat Transfer Performance of Natural Gas in a Printed Circuit Heat Exchanger During Transcritical Liquefaction

Abstract The main cryogenic heat exchanger is a core piece of equipment in the liquefaction of natural gas. The printed circuit heat exchanger is gradually becoming a primary choice for the main cryogenic heat exchanger, because it has good pressure resistance, high efficiency, and compactness. In this work, a numerical simulation is conducted to examine the local flow and heat transfer characteristics of natural gas in the printed circuit heat exchanger during trans-critical liquefaction. It is found that the heat flux density reaches a minimum value and the heat transfer is the worst when the temperature difference between the hot and cold sides is the smallest. Owing to the large variations in physical properties of trans-critical natural gas, the local pressure drop exhibits an upward parabolic shape along the flow direction, and the pressure drop reaches a minimum value near the pseudo-critical point. Finally, the friction factor and heat transfer correlations for natural gas during trans-critical liquefaction are fitted.

Forced Convection Heat Transfer in Circular Meso-Tubes.(Dept.M)

Convection heat transfer of water flow inside a circular meso-channel was investigated experimentally. To perform this experimental study, an experimental test rig was designed and constructed. Test section was shell and tube heat exchanger. It consists of seven meso scale circular tubes surrounded by a saturated steam to perform its outer surface at constant temperature, Water flows inside these tubes in steady flow and pulsating flow. The ranges tested for pulsation frequencies are 0.5 Hz to 5 Hz and Reynolds number is of 200 to 5000. Four values of inner diameters was tested in this study ; 0.25, 0.35, 0.52 and 0.7 mm. Experimental measurements for mass flow rate, temperature, pressure, pressure drop and pulsation frequency are taken to perform the required analysis. Therefore, the average value of convection heat transfer coefficient and friction factor for different operating parameters are computed The experimental results show that, the friction factor in the studied operating range decreases as Reynolds number increases but its values are deviated from those reported in conventional tubes due to the small dimensions of the meso-tubes. The friction factor decreases with decreasing tube diameter. Also, Nusselt number increases with increasing Reynolds number for pulsating flow and steady flow. For pulsating flow, Nusselt number takes lower values than steady flow for the same conditions in the studied operating ranges. Comparison between the obtained experimental results with the previous data and the classical correlations for conventional tubes was done and the disagreement among the researchers was still. Two empirical correlations for both friction factor and Nusselt number were obtained in the range of the studied operating parameters.

Experimental and numerical thermal performance analysis with exergy destruction on nanofluid flow in tube with double strip helical screw inserts

Experimental and numerical analysis is arranged with exergy destruction to evaluate thermal performance of system on nanofluid flow in tube with single and double strip helical screw inserts at different values of twist ratio in laminar flow regime. CFD analysis has occurred on the fluent workbench of ANSYS software. The Nusselt number attained enhancement with the flow of nanofluid in double strip helical screw inserts as compared with single strip helical screw inserts at decreasing values of twist ratio and increasing values of Reynolds number. Maximum enhancement of 421% is found with Nusselt number in the flow of nanofluid in tube with double strip helical screw insert at 1.5 of twist ratio and lower value of Reynolds number as compared with the flow of water in plain tube. Common correlations of Nusselt number and friction factor are generated. Exergy destruction number is attained less than one value for both types of inserts at different values of twist ratio and Reynolds number, whereas attained lower value with the flow of nanofluid in tube with double strip helical screw insert at twist ratio of 1.5 and low value of Reynolds number. Heat transfer enhancement number is attained more than one value for both types of inserts with different values of twist ratio and Reynolds number, whereas double strip helical screw inserts attained maximum value at twist ratio of 1.5 in the range of Reynolds number. Therefore, double strip helical screw inserts are the best inserts as compared with single strip helical screw inserts to compact the size of heat exchangers, whereby size of many thermal applications could be compact such as solar water heater, electronic cooling devices, automobile radiator, power plants etc.