Average Friction Factor Research Articles

On the rotary concentrated solar collector containing twisted ribs and MgO-Ag-water nanofluid

BackgroundIncreasing the solar collectors' performance is of importance to produce higher clean energy. Twisted ribs, having a lengthy background, are beneficial fitted elements to improve mixing between the hot fluid sticking to the absorber with cold fluid flow. MethodThe combination of twisted rib and rotary wall of the tubular solar collector is seeking in the current numerical work. Further, the solar absorber is considered to be filled with a hybrid nanofluid made by water and MgO-Ag nanoparticles. The variations of the average Nusselt number, friction factor, and performance evaluation criteria for all cases are drawn. The power demand of the system to assess the current cost of the new configuration is also calculated. FindingsThe geometry with one twisted rib shows better heat transfer. Adding nanoparticles to the base fluid can improve Nusselt number 18 percent, on average. The increment in the Reynolds number causes 60 to 65 percent higher Nusselt number. The wall rotation has remained either a little aiding or an inverse effect on the heat transfer. However, this makes a lower pressure drop along the solar absorber by demanding low power, as the main advantage.

Numerical analysis and optimization design of fin-and-tube evaporator in organic Rankine cycle system for diesel engine waste heat recovery

Organic Rankine cycle (ORC) can efficiently recover exhaust heat of internal combustion engines (ICEs). Evaporator is an important component that determines how much waste heat can be recovered. Enhancing heat transfer performance and reducing flow resistance of the exhaust in the evaporator can improve not only heat-to-work conversion efficiency of the ORC system but also reduce the influence of the evaporator on the operation of the ICE. Experimental results of the combined diesel engine–organic Rankine cycle (DE–ORC) system showed that the simulation model of a fin-and-tube evaporator is established via computational fluid dynamic method. The heat transfer performance and flow state of exhaust are investigated by improving the structure of the fin-and-tube evaporator under typical working conditions of the diesel engine. In addition, genetic algorithm is used to optimize the evaporator to obtain the nonuniform structure of the evaporator. Results showed that the performance of the evaporator can be improved using a star-shaped fin and appropriately selected parameters of elliptical tube. The nonuniform structural evaporator can further enhance the heat transfer performance and reduce the influence of the ORC system on the operation of the diesel engine. The optimization results demonstrated that the area goodness factor (η) increases by 173.76% while the field synergy module average angle (θφm) and friction factor f reduces by 6.17° and 56.67%, respectively.

Heat transfer in a turbulent flow tube integrated with tori as vortex generator inserts

• Heat transfer and turbulent flow in a tube integrated with tori are simulated. • The effects of torus aspect ratio and inclination angle are evaluated. • Analyses of performance evaluation criteria and entropy generation are presented. • Thermal performance is improved by inserting tori in the heat exchanger tube. In the present study, a new design improvement of conventional smooth tubes by inserting tori is proposed to enhance heat transfer with minimal increase of frictional penalty. Heat transfer and flow characteristics in different configurations are investigated by the numerical simulations. The effects of torus aspect ratio ( AR ) and torus inclination angle ( α ) on Nusselt number, friction factor, and performance evaluation criteria (PEC) are analyzed and discussed. The variations of average entropy generation rate ( S avgen ) with AR and α are also presented. The results show that the tube integrated with tori can achieve higher average Nusselt number ( Nu ) and PEC than those of smooth tube. This is attributed to the improved fluid mixing, boundary layer disruption, and formation of vortex/swirl flow. Nu and average friction factor ( f ) increase while PEC decreases with the increase of AR . Significant enhancements of Nu and f around 1.93 to 3.36 and 4.76 to 29.05, respectively, are reported for the tori integrated tube over the smooth tube. The corresponding PEC varies from 0.94 to 1.42. All results support that torus is a favorable device for the performance improvement of tube heat exchanger.

Investigation of complex flow and heat transfer mechanism in multi-tube heat exchanger with different arrangement corrugated tube

In this paper, the enhanced heat transfer performance and mechanism of a multi-tube heat exchanger (MTHX) with outward helically corrugated tubes (HCTs) are investigated by a numerical approach. Three types of tube arrangement (circle, square and triangle, indicated as CTA, STA and TSA, respectively) and four different tube spacings (1.25, 1.375, 1.5 and 1.625) are compared for Reynolds (Re) number ranging from 8900 to 89,400. Details of the coupled relationship among the multiple spiral detached vortices and turbulent pulsations are presented to explore the complex flow features. In addition, the variation trends of the average Nusselt number, friction factor, and performance index (PEC) are compared to obtain the optimum geometry parameter of the MTHX with HCTs. The results show that the rotational flow with opposite direction presents a strong overlay effect, and the circumferential velocity can reach up to 20% of the mean velocity. The non-directional turbulent pulsation only presents an overlap and strengthening effect. Besides, the secondary flow causes better heat transfer in the sub-layers, the turbulent pulsation has better heat transfer between the sub-layer and main flow region, while the rotational flow has a minor inhibiting effect on heat transfer performance. The TTA presents better interaction at the intervals of the tubes, and the Nu, f and PEC index of the TTA are all outstanding compared to the CTA and STA. The SL/Φt = 1.375–1.5 of the MTHX-TTA are suggested from the findings, and the Re should not exceed 40, 000.

The effect of off-center placement of twisted tape on flow and heat transfer characteristics in a circular tube

This study is conducted to investigate the effect of off-center placement of twisted tape on flow distribution and heat transfer in a circular tube. The effect of tape width of 20, 18, 16, 14 and 12 mm on the heat transfer performance is discussed under the same twist ratio of 2.0. The numerical analysis of the flow field, average Nusselt number, friction factor and thermo-hydraulic performance parameter of the tube are discussed with Reynolds number ranged from 2600 to 8760. The results indicate that the Nusselt number of the tube fitted with center-placed twisted tapes at various width is 7–51% higher than the plain tube, and performance in low Reynolds region was found more effective than that in high Reynolds region. The heat transfer for circular tube with twisted tape attached to the wall shows better performance than that for the tube with center-placed twisted tape. With a smaller tape width, a higher increasing ratio of Nu-wall/Nu-center is obtained. The increasing ratio for Nusselt number ranged from 3 to 18%. However, the use of twisted tape inserts is not beneficial for energy saving. The thermo-hydraulic performance parameters for convective heat transfer of helium gas flowing in a circular tube are below unity for the calculated Reynolds region.

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.

Computational analysis of gas permeability of slip flow through microannulus replete by based‐circular Sierpinski porous medium

AbstractThere are wide applications for flow in a microporous medium. In this study, a computational analysis of airflow through a porous microannulus constructed by circular‐based Sierpinski has been performed in a slip flow regime, where several parameters played an important role in the flow characteristics. These parameters are the Knudsen number, the average friction factor, radius ratio, and porosity. The impacts of these parameters on permeability and the gas flow characteristics are examined and analyzed thoroughly. The ranges of the investigated parameters are as follows (0.001 ≤ Kn ≤ 0.1 and the porosity range is 0.75 ≤ ε ≤ 0.95). The results showed that porosity has a significant impact on the velocity distribution and Darcy number. The Knudsen number has also a direct effect on the velocity distribution, while it has a positive logarithmic proportionality with a dimensionless permeability but the radius ratio does have a neglected effect on the Darcy number. Moreover, the effect of the average friction factor has an inverse proportional relationship to the Darcy number.

Effect of aspect ratio and inlet manifold shape on the laminar-to-turbulent transition of gas flow in rectangular microchannels

A combined experimental and numerical study on the laminar-to-turbulent transition in microchannels using gas flow is presented. The effects of two geometric parameters, namely aspect ratio (height to width) of microchannels and inlet manifold shape, are considered on the value assumed by the critical Reynolds number linked to the laminar-to-turbulent transition. To study the effect of aspect ratio, seven rectangular microchannels having an aspect ratio between 0.25 and 1.04 are micro-milled in PMMA plastic with a constant length of 100 mm. Four rectangular microchannels with different inlet shapes, namely sudden contraction, rounded entrance, V shape and bellmouth, are fabricated to analyze the effects of inlet shape. Pressure loss analyses are then performed for all 11 microchannels by evaluating both average and semi-local friction factors. The Reynolds number in correspondence of which the transition takes place is determined by observing the trend of the friction factor. In parallel, numerical simulations using an intermittency-based transitional turbulence model are also performed and results are compared with the experiments. Experimental and numerical results have demonstrated that both of the investigated geometrical characteristics (aspect ratio and inlet manifold shape) play an important role on the range of the Reynolds number between the onset of transition and the onset of fully turbulent regime for gas microflows. Experimental critical Reynolds numbers show a good agreement with the predictions of the conventional theory and are in the range of 1863–3470 for all the tested microchannels. The role of gas compressibility on the laminar-to-turbulent transition is also discussed.Graphic abstract

Optimization of a Wavy Microchannel Heat Sink with Grooves

In this study, a wavy microchannel heat sink with grooves using water as the working fluid is proposed for application to cooling microprocessors. The geometry of the heat sink was optimized to improve heat transfer and pressure loss simultaneously. To achieve optimization goals, the average friction factor and thermal resistance were used as the objective functions. Three dimensionless parameters were selected as design variables: the distance between staggered grooves, groove width, and groove depth. A modified Latin hypercube sampling (LHS) method that combines the advantages of conventional LHS and a three-level full factorial method is also proposed. Response surface approximation was used to construct surrogate models, and Pareto-optimal solutions were obtained with a multi-objective genetic algorithm. The modified LHS was proven to have better performance than the conventional LHS and full factorial methods in the present optimization problem. A representative optimal design showed that both the thermal resistance and friction factor improved by 1.55% and 3.00%, compared to a reference design, respectively.

Experimental investigation on thermo-hydraulic performance of triangular cross-corrugated flow passages

Heat exchangers made of corrugated flow passages generally have better thermo-hydraulic performance compared to parallel flow passages. The corrugation angle (β), corrugation pattern, and the ratio of depth to pitch (hch/Pch) are critical geometrical parameters influencing the heat transfer and pressure drop in corrugated flow passages. This paper experimentally investigates heat transfer and pressure drop characteristics of triangular-shaped cross-corrugated flow passages for the range of 25° < β < 75° and 0.13 < hch/Pch < 0.36. Experiments are performed using representative compact heat exchangers in a small-scale test facility. This study also reports the effects of plate geometry on heat transfer and pressure drop and provides correlations for the average Nusselt number and friction factor. A detailed comparison of test data with relevant literature is also presented. Results of this study will be useful to manufactures and designers for developing high-performance heat exchangers.

Numerical study of thermal and dynamic structure of a laminar flow in solar collector

This paper reports a numerical study of laminar fluid flow and thermal performances along a solar collector. This technique is used to improve the heat transfer in outlet of the system. The numerical model based on the finite volume method and the SIMPLE Algorithm is applied for the solution of the mass, momentum and energy governing equations. In our mathematical formulation, the terms of convection and diffusion are discretized respectively by center and quick schemes. In this work, we consider that the working fluid is transparent, at most the upper solid surface contributes to radiation exchanges and lower solid is assumed to be insulated. Results are analyzed in terms of velocity, temperature fields, average Nusselt numbers and friction factor for various positions of the shoulder in the solar collector.

Hydrodynamic analysis of nanofluid’s convective heat transfer in channels with extended surfaces

The effects of nanoparticles (NPs) on heat transfer in extended surface channels have been analyzed using a two-component (TC) model. The results show that unlike the single-component model, the TC model leads to more accurate predictions of the system’s heat transfer performance as a result of the direct influence of the NPs’ distribution on the hydrodynamics. It is found that the average Nusselt number varies non-monotonically with the block’s heights, and the trend is explained by the interplay between heat transfer mechanisms and the hydrodynamics. A similar non-monotonic trend observed in the case of the friction factor has been explained by the variations of the concentration- and temperature-dependent viscosity of the nanofluids. A guideline for an optimum design based on the combination of the variation of average Nusselt number and friction factor with respect to the geometrical parameters has also been presented.

Numerical investigation of flow and heat transfer in axially-finned in-line tube banks

ABSTRACT Numerical analysis of heat and fluid flow over tube bank heat exchangers with axial fins is performed in this work. Finite volume method is used to solve the governing equations numerically. Simulations are carried out in the range of 400–1500 Reynolds number. To ensure the numerical model reliability, unfinned in-line tube bank is simulated and compared with results from the literature. It is shown that the results are in accordance with the experimental studies in the literature. Heat transfer and pressure loss computations are carried out for four different axial and transversal pitch ratios; namely, and , and , and , and . Air and water are used as working fluids for determined mass flow rates where Prandtl numbers are 0.7 and 7, respectively. Moreover, velocity streamlines and temperature contours along the flow field are given. Effects of axial () and transversal () pitch ratios and fin lengths on the average Nusselt number and friction factor are also presented in graphical forms. It is found that the maximum average Nusselt number is observed at Re = 1500 for the pitch ratios of and where fin length equals to 2D mm. Besides, adding axial-fins to in-line tube bank results in a decrement in friction factors.

Effect of Addition of Montmorillonite and Indium Composite Powder on Tribological Properties of 45 Steel Friction Pairs

The oil soluble modified montmorillonite (MMT)/indium (In) composite nanoscale powders were prepared into four disperse systems by adding 1%, 2%, 3% and 4% to the base oil respectively. The friction properties of the 45 steel samples were tested by MMU-10G friction and wear testing machine, and the surface composition of the samples was analyzed by SEM and EDX. The mechanism that affects the tribological properties is compared and analyzed. The results show that the wear weight loss of the sample added with MMT/In nano powder is smaller than that in the base oil, and the average friction factor of the sample with 3% additions is 43.14% ,lower than that of the base oil, and the total wear is negative weightlessness.EDX analysis showed that the surface of the friction specimen was composed of Mg, Al and In repair membranes. The main mechanism of anti friction and friction reduction is that the composite powder will form a repair film on the surface of the friction pair during the friction process, and the repair layer can reduce the friction, compensate for the wear and play the role of resisting wear and reducing the effect of friction. With the increase of adding amount, the repair layer is gradually improved and the tribological performance is enhanced. But if the amount of addition is too high, the micro cutting and furrow effect of a large number of hard particles on the matrix and the new film will be greater than the compensation effect of the repair film, making the antiwear and antifriction properties decrease.

General Correlations for Laminar Flow Friction Loss and Heat Transfer in Plain Rectangular Plate-Fin Cores

Abstract New generalized correlations for predicting the average fanning friction factor f and average Nusselt number Nu for laminar flow in plain plate-fin compact cores of rectangular cross section are presented. These are based on extended experimental data, as well as three-dimensional computational simulations, obtained for a broad range of fin density and geometrical attributes. The results indicate that while the fully developed forced convection scales only with the interfin channel cross-sectional ratio α (fin spacing by fin height), the entrance region hydrodynamic and thermal performance is additionally a function of the fin-core length L, flow Reynolds number Re, and fluid Prandtl number Pr. The developing flow and convection is further shown to scale as: (fRe)∼(L/dhRe)1/2, and Nu ∼(L/dhRe)1/2Pr1/3ϕ(α), where f, Re, and Nu are all based on the hydraulic diameter dh of the interfin flow channel. Generalized correlations for both (fRe) and Nu are developed by the corresponding scaling of the forced convection behavior and asymptotic matching of the entrance or developing flow (short fin-core flow length) and the fully developed flow (large fin-core flow length) region performance. Finally, the predictions from these correlations are found to be within ±15% of all available experimental data for air, water, and glycol (0.71 ≤ Pr ≤ 10), and fin cores with 0 &amp;lt; α ≤ 1.

Heat transfer coefficients of additively manufactured tubes with internal pin fins for supercritical carbon dioxide cycle recuperators

This paper describes the measurement of convective heat transfer coefficients and friction factors for sCO2 flowing in additively manufactured tubes with internal pin fins at the US DOE’s National Energy Technology Laboratory in Morgantown, WV. The measurement procedures were validated by conducting benchmark tests with smooth stainless-steel tube and comparing the results with published correlations for Nusselt number (Nu) and friction factor. Over Reynolds numbers (ReD) ranging from 5 × 104 to 2.5 × 105, measured Nu was within 5% of the Dittus-Boelter correlation and measured friction factors were within 5% of the McAdams correlation for smooth tube flow.The candidate pin fin patterned pipes were additively manufactured (AM) at the Oak Ridge National Laboratory. The pins were circular or elliptical in cross-section and were printed at a 30° angle relative to the inner wall (to meet AM constraints). The pin arrangement was helical to promote enhanced heat transfer due to swirl flow. Pin length to diameter aspect ratio was 1.33, 2, and 8, while the pin diameter to tube diameter ratio was 0.188, 0.125, and 0.063. Tests were performed for ReD varying from 6.9 × 104 to 2.2 × 105 and at conditions equivalent to the low pressure (LP) outlet (8.69 MPa, 361 K) and the high pressure (HP) inlet (20.7 MPa, 350 K) of the low temperature recuperator (LTR) in an indirect sCO2 cycle. The Wilson plot technique was utilized to measure the bulk heat transfer coefficients.For the best performing design (tube A, pin length to tube diameter ratio: 1.33, pin diameter to tube diameter ratio: 0.19), the local heat transfer coefficient increased by 136% relative to the Dittus-Boelter correlation at the LTR low pressure outlet and 194% at the LTR high pressure inlet. These correspond to a 282% and a 271% increase in the product of the heat transfer coefficient and surface area (adjusted for fin efficiency) product, respectively. Large pressure drops across the test articles were observed. For Tube Design A, the average friction factor, across the range of ReD considered, was significantly larger than the McAdams correlation at both the LTR LP outlet and the LTR HP inlet. A thermal performance factor was utilized to express the ratio of material required to build a finned heat exchanger relative to a finless heat exchanger with the same heat duty and pumping power. Tube Design A was estimated to decrease the required heat exchanger material by 13%.

Investigation of Forced Convection Enhancement and Entropy Generation of Nanofluid Flow through a Corrugated Minichannel Filled with a Porous Media.

Corrugating channel wall is considered to be an efficient procedure for achieving improved heat transfer. Further enhancement can be obtained through the utilization of nanofluids and porous media with high thermal conductivity. This paper presents the effect of geometrical parameters for the determination of an appropriate configuration. Furthermore, the optimization of forced convective heat transfer and fluid/nanofluid flow through a sinusoidal wavy-channel inside a porous medium is performed through the optimization of entropy generation. The fluid flow in porous media is considered to be laminar and Darcy–Brinkman–Forchheimer model has been utilized. The obtained results were compared with the corresponding numerical data in order to ensure the accuracy and reliability of the numerical procedure. As a result, increasing the Darcy number leads to the increased portion of thermal entropy generation as well as the decreased portion of frictional entropy generation in all configurations. Moreover, configuration with wavelength of 10 mm, amplitude of 0.5 mm and phase shift of 60° was selected as an optimum geometry for further investigations on the addition of nanoparticles. Additionally, increasing trend of average Nusselt number and friction factor, besides the decreasing trend of performance evaluation criteria (PEC) index, were inferred by increasing the volume fraction of the nanofluid (Al2O3 and CuO).

Experimental Study on the Effect of Localized Blockages on the Friction Factor of a 61-Pin Wire-Wrapped Bundle

Abstract The thermal-hydraulic behavior of the flow in rod bundles has motivated numerous experimental and computational investigations. Previous studies have identified potential for accumulation of debris within the small subchannels of typical wire-wrapped assemblies with subsequent total or partial blockage of subchannel coolant flow. A test campaign was conducted to study the effects of localized blockages on the bundle averaged friction factor of a tightly packed wire-wrapped rod bundle. Blockages were installed within the bundle, and fluid pressure drop was measured across one wire pitch for a Reynolds number range of 500–17,200. The Darcy–Weisbach friction factor of the perturbed rod bundle geometry was compared with that of the unblocked bundle, as well as with the predictions of a well-established friction factor correlation. Differing effects based on blockage size and location for various flow regimes were studied. A number of conclusions can be made about the effects of the blockages on the friction factor, such as an increasing effect of the blockage on friction factor with an increase in Reynolds number, a change in flow behavior in the turbulent transition flow regime near Reynolds number 3000, differences in effect on friction factor for different types of subchannel blockage, and a nonlinear trend in friction factor variation with flow area impeded for edge subchannels. To this end, all data and quantified uncertainty produced in this study are made available for comparison and validation of advanced computational tools.

Average Friction Factors of Choked Gas Flow in Microtubes

A micro-tube passage is a basic and important element in the design of micro heat exchangers and for this reason during the last decade a series of investigations have been made with the aim to clarify the main scaling effects playing an important role in microtubes. In this paper, a combined analysis of numerically and experimentally obtained average friction factors in microtubes under the situation of under-expanded (choked) gas flow is presented. The working fluid (nitrogen) passes through the microtube and discharges into the atmosphere under an increasing inlet pressure. Experiments and numerical computations are performed for microtubes with 249 and 528.9 mm in diameter, by varying the aspect ratio (i.e. length/diameter) from 100 to 200. The numerical methodology to solve the governing equations is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. In order to capture the under-expansion characteristics of the flow during choking, the computational domain is extended in the downstream region beyond the microtube outlet. Both experimental and numerical results were obtained for a wide range of Mach number and Reynolds number. In the previous study, it was demonstrated how the outlet Mach number can be expressed as a function of the tube diameter under choked conditions. In this paper, a data reduction procedure for the estimation of the average friction factor between the inlet and the outlet of the microtube is proposed for choked flows in which the outlet gas temperature and pressure are obtained by using the outlet Mach number calculated numerically as a function of the microtube diameter. It is demonstrated how this data reduction method allows an accurate calculation of the average friction factors in microtubes by using a limited number of parameters which are easy to measure. The results obtained in this way are in good agreement with the numerical predictions as well as with the most common empirical correlations.

Identification of Gas Flow Regimes in Adiabatic Microtubes by means of Wall Temperature Measurements

There exists the laminar flow, transitional flow, turbulent flow and choked flow regimes in a microtube gas flow. Development of a non-invasive identification method of the flow regimes within a microdevice is expected. This paper demonstrated how the internal gas flow regimes can be identified by measuring the distribution of the external wall temperature of the microchannel along the flow direction. A series of experiments were conducted by using nitrogen as working fluid through a stainless steel micro-tube with an inner diameter of 523 µm and a fused silica micro-tube having a diameter of 320 µm. The experiments were performed by fixing the back pressure at the exit of the microchannel at the atmospheric value and by varying the inlet pressure in order to modify the gas flow regime. In order to measure the external wall temperature along the microtube, two or three bare type-K thermocouples with a diameter of 50 µm were attached to the micro-tube external surface by using a high conductivity epoxy. In the case of the microtube having a diameter of 523 µm, local pressures were measured at three local pressure ports along the microtube. The pressure ports were placed on the opposite side of the tube wall where three thermocouples were attached. The microtube external wall was thermally insulated with foamed polystyrene to prevent heat gain or loss from the surrounding. The experimental results show that the wall temperature decreases in the laminar flow regime, increases in the transitional flow regime, decreases in the turbulent flow regime and it stays nearly constants in the choked flow regime. The behavior of the average Fanning friction factor and the local Mach number can be explained by identifying the flow regime. It is clarified that the microtube external wall temperature is a reliable indicator of the flow regime.