Friction Factor Values Research Articles

Evaluation of friction using double cup and spike forging test for dry-in-place coating and forming oils

The friction characteristics of lubricants were evaluated using the double cup and spike forging tests. Friction calibration curves, i.e., plots of cup height ratio vs. punch stroke and spike height vs. punch stroke, were established through finite element (FE) simulations considering various friction factor values. The friction factor of the lubricants was determined by matching the relationships of the cup height ratio and spike height with the punch stroke obtained from experiments to those obtained from the FE simulations. Under the lubricating condition of dry-in-place coating with forming oil, the results showed that different tribo-testing methods yielded different friction factors. The friction factor determined was applied in the FE simulation of a cold forging process of a claw pole.

CFD Analysis on the Heat Transfer and Fluid Flow of Solar Air Heater having Transverse Triangular Block at the Bottom of Air Duct

In this study, a two-dimensional CFD (computational fluid dynamics) analysis was performed to investigate the heat-transfer and fluid-friction characteristics in a solar air heater having a transverse triangular block at the bottom of the air duct. The Reynolds number, block height (e), pitch (P), and length (l) were chosen as design parameters. The results are validated by comparing the Nusselt number predicted by simulation with available experimental results. Renormalization-group (RNG) k - ε model with enhanced wall-treatment was selected as the most appropriate turbulence model. From the results, it was found that the presence of a transverse triangular block produces a higher Nusselt number than that of smooth air duct. The enhancement in Nusselt number varied from 1.19 to 3.37, according to the geometric conditions investigated. However, the use of transverse triangular block also results in significantly higher friction losses. The thermohydraulic performance (THPP) was also estimated and has a maximum value of 1.001 for height (e) of 20 mm, length (l) of 120 mm, and pitch (P) of 150 mm, at Reynolds number of 8000. Furthermore, in the present study, correlations of the Nusselt number and friction factor were developed as a function of geometrical conditions of the transverse triangular block and Reynolds number, which can be used to predict the value of Nusselt number and friction factor with the absolute percentage deviations of 3.29% and 7.92%, respectively.

Performance evaluation and optimization of design parameters for twisted conical strip inserts in tubular laminar flow Using Taguchi approach

Numerical simulation of flow structure and heat transfer augmentation of laminar flow in a circular tube fitted with the novel twisted conical strip inserts is investigated in this paper. The mechanism of heat transfer and the effects of geometrical parameters on thermo-hydraulic characteristics of the flow are studied through the utilization of performance evaluation criteria and performance ratio R3. In addition, the optimized cases and contribution of each parameter to heat transfer and friction factor are obtained from Taguchi analysis. The results show that higher values of Nusselt number, friction factor, and performance evaluation criteria occur due to lower pitches, lower twist angles, and non-staggered alignment. It was also observed that the Nusselt number and friction factor of the enhanced tube respectively vary in the range of 2.4–14.66 and 2.3–51.22, compared to the similar parameters of the plain tube, while performance evaluation criteria and performance ratio R3 locate in the range of 1.82–3.94 and 1.37–7.75, respectively. It was found that the twist angle is the most effective geometrical parameter on both friction factor and Nusselt number. Moreover, the effect of all investigated parameters on Nusselt number, friction factor, and performance evaluation criteria declines at higher levels of the parameters.

Evaluation of the Friction Factor Influence on the Results of Cross-Wedge Rolling Simulation in Qform Software

The paper describes the study of the friction factor influence on a workpiece shape-changing and the defects occurrence during the cross wedge rolling. The dependence between the slipping rate and the friction factor is found. Recommendations on the choice of friction scheme and friction factor values are provided.

Thermal and hydrodynamic analysis of non-Newtonian nanofluid in wavy microchannel

In this study, hydrodynamic and heat transfer of non-Newtonian nanofluid behavior is investigated in a wavy microchannel with rectangular obstacles. Aluminum oxide as nanoparticles (Al2O3) with 0.5% and 1.5% volume fractions and three different diameters (25, 45 and 100 nm) are added to pure water as a base phase to form a nanofluid structure. In order to form the non-Newtonian nanofluid, 0.5% carboxy methyl cellulose (CMC) is added to the nanofluid structure. Up and down walls of microchannels at the middle section where obstacles are located have constant 50,000 W⁄m2 heat flux. Inlet temperature is constant and equal to 298 K with different Reynolds numbers varying as 5, 50, 150 and 300. Rib heights varying between 3 and 7 μm for five cases with different nanoparticle volume fractions, nanoparticle diameters and Reynolds numbers are investigated. Nusselt number, friction factor and pressure drop are studied. Results indicated that the average Nusselt number is increased by increasing the volume fraction of Al2O3 nanoparticles. Also, the results show the largest friction factor value is obtained in the case with the highest obstacle height. It is observed that MC-3 case has maximum outlet temperature, and therefore is the best case among investigated cases.

A COMMENT ON UNSTEADY–PERIODIC FLOW FRICTION FACTOR: AN ANALYSIS ON EXPERIMENTAL DATA GATHERED IN PULSATILE PIPE FLOWS

In 1940’s, Schultz- Grunow proposed that time-average value of friction factor, λ_u,ta was similar to its corresponding steady state value, λ for the presence of gradual and slow oscillations in pulsatile flows. A recent approach was available for low frequency pulsatile flows through narrow channels in transitional and turbulent regimes by Zhuang et al, in 2016 and 2017. In this analysis; extensive experimental data of λ_u,ta in fully laminar and turbulent sinusoidal flow are processed in the measured time-average Reynolds number range of 1390 ≤ Re_ta ≤ 60000 disregarding the transitional regime. The ranges of dimensionless frequency-Womersley number, √(ω') and oscillation amplitude, A_1 are 2.72 ≤ √(ω') ≤ 28 and 0.05 ≤ A_1≤ 0.96 respectively. A multiplication element is defined as Mel = Re_ta×√(ω^'). A modified friction multiplier, λ_(Mel ) which is similar to the conceptual parameter of Zhuang et al’s friction factor ratio C ( λ_Mel = λ_(u,ta)/λ ) is also referred. The correlation of λ_Mel = λ_Mel (Mel) is dependent on flow regime and the magnitude of Re_ta for the range of √(ω^') > 1.32. The proposal of Schultz-Grunow is verified irrespective of the oscillations in turbulent regime since the magnitude of λ_Mel = 1 is observed for turbulent flow cases with Re_(ta ) ≥ 35000. In laminar regime the magnitude of Re_(ta ) is governing the fact. The magnitude of λ_Mel varies in 0.589 ≤ λ_Mel ≤ 28.125 for Re_(ta ) ≤ 5000 while λ_Mel = 1 is obtained for Re_(ta ) > 5000. The graphical representation of λ_Mel = λ_Mel (Mel) can be considered as a counterpart of Moody Diagram in pulsatile fields for a significant practice.

Stability Mechanism and Repair Method of U‐Shaped Steel Reverse Arch Support in Soft Floor Roadway

This paper is aimed at the inverted arch support instability of track roadway with mining level +1100 m in Liuyuanzi Coal Mine. By means of field investigation, theoretical analysis, numerical calculation, and engineering practice, the instability reasons of inverted arch structure are expounded, the mechanical mechanism of instability of inverted arch structure is revealed, and the “sliding‐rotating beam” for the instability of inverted arch structure is put forward. Based on Fenner’s formula and mechanics principle, the equilibrium equation of “sliding‐rotating beam” is given. The results show the following: Firstly, the insufficient stiffness at the joint of the inverted arch structure and the U‐shaped steel support on the floor is the key reason for the floor instability. Secondly, when the action stress of the “sliding‐rotating beam” is less than the critical value, three kinds of instability modes of the inverted arch structure may occur, that is, sliding upward, rotating upward, or sliding‐rotating upward. Each instability criterion and critical value are also different. Considering the axisymmetric condition, the critical value calculation formula of the three modes can be simplified into one formula. Thirdly, the equivalent friction factor restricts the stability of the “sliding‐rotating beam,” and there is a “breaking point.” The relationship between the equivalent friction factor and the action stress of the “sliding‐rotating beam” is “class hyperbola.” When the equivalent friction factor is greater than the “breaking point value,” the “sliding‐rotating beam” may remain stable. Moreover, with the increase of equivalent friction factor, the action stress required for the stability of the “sliding‐rotating beam” is smaller, and it tends to be more stable. The breaking point value of equivalent friction factor is 18.6. Finally, 36U‐shaped steel round frame with bolt‐mesh‐shotcrete‐combined support is applied to improve the equivalent friction factor and the foot stiffness of U‐shaped support in roadway. After two months of on‐site implementation, the floor heave was reduced by 69.1%. In conclusion, the theoretical analysis is correct and the control method is effective.

Analysis of heat transfer in grooved plain carbon steel tube for solar applications

A computational fluid dynamics study is conducted in pressure drop and thermal performance of a plain material tube and plain material tube enriched with square, circular and trapezoidal internal grooves. The computational fluid dynamics (CFD) is an authoritative method to evaluate the thermal properties for high Reynolds number condition in water heating using solar energy. A transition in flow from laminar to turbulent condition there prevails an enhancement in Nusselt number (Nu), thermal performance and pressure drop. However, for turbulent flow condition an increase in flow rate and Reynolds number (Re) the value of friction factor decreases for plain material tube and internal grooved tubes. The computational fluid dynamics results indicates that trapezoidal shaped grooving tubes attains the maximum value of drop in pressure, thermal performance and Nusselt number as compared to plain material tube and other grooved tubes pertaining to turbulent flow condition of Re from 5500 to 11500. The output signifies that the highest enhanced value of reduction in pressure attained in trapezoidal, circular and square grooving tubes are 68%, 65% and 63%. The CFD results also indicate that the highest value of increase of heat transfer rate (Q) is attained in trapezoidal grooved tube as 27%. The enhancement in Q value pertaining to circular and square grooved tubes are 21% and 14%.

Relevancy and comparison of friction factor equations for gravel bed in bedload regime

The friction coefficient f value is a dominant term in the open channel flow calculation. In this study, eight empirical flow resistance equations in a gravel bed are selected to calculate friction factor under bed load regime. To check the relevancy of these equations, 1,392 flume data are selected with measure values of friction factor in uniform and non-uniform bed materials. We used a friction evaluation approach based on the integration of velocity profiles with two types of equations under well-defined conditions. The first type based on relative depth R/D and the second type concern equations that depend on slope value S, Froude number Fr and Reynolds number Re. In this article, we have used each equation whatever conditions and fields of use. In the second step, friction coefficient f was calculated according to application conditions of each equation while maintaining same formula without change. We concluded that Ferro's (2018) equation is best one that estimates friction coefficient value with a mean normalised error of 12% for all dataset, in both cases.

Geometric Optimization of a Gas Turbine Blade Cooling Passage using CFD

This work focuses on the rib-turbulated cooling which is a category of impingement cooling and aims at optimizing the geometry of rib-roughened cooling passage of a gas turbine blade. CFD analysis is carried out using Ansys/Fluent to solve the steady RANS equations. Computational domain consists of a long rectangular channel with the length of the channel being 9 times its height. Ratios of rib width, rib height and rib pitch to hydraulic diameter of the channel are taken as 0.1, 0.1 and 1.2, respectively. Numerical simulations are performed to analyze the performance of various rib shapes for Reynolds number, based upon the hydraulic diameter, in a range of 5000 to 50,000. Uniform heat flux of 800 W/m2 is applied to the ribbed wall. Incompressible air is used as the cooling fluid. Turbulent flow conditions are applied to the channel geometry with k-ω turbulence model. The effect of rib cross-section and rib pitch to rib width ratio on the heat transfer and friction factor is observed. The 2D CFD analysis revealed that the presence of ribs has significant effect on thermo-hydraulic performance of the cooling channel. Introducing square ribs in a smooth channel caused the Nusselt number to increase by two-folds. The highest value of Nusselt number was achieved by incorporating right-angle triangular ribs which caused the Nusselt number to increase by further 8%, as compared to the square ribs, and an increase in friction factor of 2.5%. The lowest value of friction factor was observed in semicircular ribs (2.95% less than the square ribs), however, the Nusselt number also decreased by 1.5%, as compared to square ribs. Decreasing rib pitch to rib width ratio increased both the Nusselt number and friction factor for all the cases. For square ribs, decreasing this ratio from 15 to 9 resulted in the rise of Nusselt number by 50% and increase in friction factor by 54%.

Thermohydraulic characteristics of inline and staggered angular cut baffle inserts in the turbulent flow regime

In the present work, heat transfer and pressure drop characteristics in flow through a tube with inline and staggered baffles having angular cut at the edge are reported for various operating conditions. An experimental test rig is designed and developed to investigate heat transfer and pressure drop behavior for different conditions. Effects of different geometrical parameters, i.e., pitch ratios, baffle arrangement and cutting angle of baffles on heat transfer rate and pressure drop characteristics, have been investigated for turbulent flow regime. Reynolds number ranging from 10,000 to 52,000 has been considered in the present study. The maximum heat transfer rate has been observed for staggered arrangement with pitch ratio of 0.1 and cutting angle of 60°, while minimum heat transfer rate has been observed for inline arrangement with pitch ratio of 0.2 and cutting angle of 30°. Empirical correlations for Nusselt number and friction factor have been developed as a function of geometrical and flow parameters. The deviations between experimental and predicted values of Nusselt number and friction factor for staggered arrangements have been observed as ± 10%, ± 4%, respectively, whereas for inline arrangement the deviation has been observed as ± 12%, ± 5%, respectively. Results from empirical correlations are well agreed with the experimental data.

Heat transfer evaluation of a micro heat exchanger cooling with spherical carbon-acetone nanofluid

In this article, we experimentally measured the convective heat transfer of a micro-channel heat sink cooling with carbon-acetone nanofluid (NF), which potentially is a cost-effective nano-suspension with plausible heat transfer characteristics. The heat transfer and fluid flow characteristics including heat transfer coefficient (HTC), friction factor (FF), pressure drop value (PD), and the thermo-hydraulic performance (THP) was quantified. The structure and morphology of the nanoparticles (NPs) were characterised. It was found that carbon-acetone NF can enhance the HTC value by ~73%. Also, a small increase in the FF and PD values were reported due to the augmentation of particle-fluid friction forces and viscosity. The value of PD was augmented by 18.3% at Re~1400 at wt.% = 0.1. The THP value was increased by 69% despite an increase in the PD of the system. It was identified that the promotion of heat transfer was due to the micro-scale phenomena such as Brownian motion and thermophoresis. Also, reduction in the thermal boundary layer inside the micro-channel further contributed to the promotion of heat transfer within the micro-channel.

Enhanced heat transfer in pin fin heat sink working with nitrogen gas–water two-phase flow: variable pin length and longitudinal pitch

In the current study, thermal–hydraulic characteristics of nitrogen gas–water two-phase flow through a plate–pin fin heat sink are investigated experimentally. Water flow through the smooth case, i.e., heat sink without pin fin, is considered as baseline. Four new models of the pin fin with variable longitudinal pitch and pin length having low-to-high and high-to-low arrangements are proposed. They are named for short as LP–LH, LP–HL, PL–LH, and PL–HL. The results indicate that in all heat sinks, the Nusselt number values of the two-phase flow in comparison with those of the single-phase flow are higher, but the friction factor values of the two-phase flow in comparison with those of the single-phase flow are lower. Also, the friction factor and the Nusselt number of both the single-phase flow and the two-phase flow in the heat sinks with pin fin are greater than those in the heat sink without pin fin. The highest values of the Nusselt number are recorded for PL–HL at water mass flow rate of 0.0093 kg s−1 and gas volume flow rate of 0.8 L min−1. At these flow rates in PL–HL, the Nusselt number of the two-phase flow is increased about 45.6% relative to the single-phase flow.

Numerical Investigation of a Solar Air Heater (SAH) with Triangular Artificial Roughness Having a Curved Top Corner

In the present study, numerical investigation of two-dimensional incompressible air flow through a solar air heater (SAH) with a triangular artificial roughness having a curved top corner is performed using ANSYS Fluent 15.0 based finite volume method. The geometrical parameters of the triangular ribs having a curved top corner such as the roughness height ratio (e/D = 0.021, 0.03 and 0.042) and the roughness pitch ratio (p/e =7.14, 10.70, 14.28 and 17.86) have been investigated for a varied Reynolds number between 3800 to 18000. Flow and energy governing equations were solved with the accosiation of two transport equation for the turbulence kinetic energy k and the dissipation rate ɛ. The RNG k-ε turbulent model have been selected to be the more appropriate turbulence model for the present study. Results indicates that the values of Nusselt number and friction factor strongly depend on the roughness relative height e/D, relative pitch p/e and the value of Re number. The best solar air heater performance could be obtained for e/D=0.042 and p/e=7.14.

Investigation of the Combined Effects of Temperature and Large-Scale Tortuosity on Friction-Factor Profile in Straight Inclined Sections

Summary This paper studies the implicit effects of temperature and wellbore tortuosity on the mechanical friction factor in torque-and-drag models applied to straight inclined sections. Experimental work was performed to measure the variation of viscosity and density of a water-based-mud (WBM) sample with respect to temperature and pressure. The effect of wellbore tortuosity was accounted for by means of the dogleg-severity (DLS) filter, which is presented in the paper. Experimentally obtained parameters were included in an algorithm for friction-factor-profile back calculation using a selected torque-and-drag model. A field case is presented to show this approach. The calculated friction factors were compared with those obtained by using the original torque-and-drag model and the averaged friction-factor values provided by the field operator, and the deviation mechanisms were discussed. Comparing the obtained results, we concluded that pressure and temperature, accounted for through variation in fluid buoyancy with depth, affect friction factor just marginally for rotation off-bottom and negligibly for tripping operations. The unplanned large-scale tortuosity affects the ultimate friction factor more significantly. The magnitude of the studied effects would greatly depend on the wellbore conditions. By including additional parameters in the traditional torque-and-drag models, researchers and engineers would be able to evaluate the effects of these parameters on the friction-factor estimation. It can help to estimate the range of friction forces during the planning phase and explain abnormal trends in post-run analysis.

The influence of tip clearance and shape of pin fins on the heat transfer performance and friction factor in aluminum silicon alloy heat exchanger

In this article, the coupled heat transfer model was applied to investigate the effect of the tip clearance and shape of pin fins on the heat transfer performance and friction factor in the high temperature region of aluminum silicon alloy heat exchanger. The tip clearance ranged from 1 mm to 8 mm, and the shape of pin fins was the circular, drop-A and drop-B. The results showed that as the tip clearance increases, the outlet flue gas temperature increases, while the Nusselt number, the pressure loss and the friction factor decreases. For the circular pin fin, the difference of outlet flue gas temperature between it and drop-A was very slight, but both were higher than drop-B. In addition, circular pin fin had the minimum values of pressure loss friction factor. Comprehensively considering the heat transfer performance and friction factor, the thermo-hydraulic performance of circular pin fin with the tip clearance of 4 mm was superior to other cases.

Performance evaluation and optimization of solar assisted air heater with discrete multiple arc shaped ribs

Abstract Solar air heater is widely used for heating and drying applications. Many techniques have been used to improve the performance of a solar air heater but the most common technique is surface roughness in which ribs are provided over the absorber plate. In the present article, multiple-arc shaped (three arcs) rib roughness is provided on the underside of absorber plate. The impacts of different roughness elements i.e. number of gaps (ranged from 1 to 3), relative gap width (0.5 to 1.5) and relative gap position (0.3 to 0.9) are examined for fixed range of flow parameter on the performance of a single glazed duct solar air heater. To investigate the optimized thermal performance of solar air heater, response surface methodology was used for the design of experiments using analysis of variance. Remarkable improvement in thermal performance of solar air heater is observed by varying roughness parameters but it leads to increase in pumping power of solar air heater. Additionally, a generalized quadratic correlation for Nusselt number and friction factor is also developed based on the analysis of variance which show percentage deviation of ± 6.15% and ± 5.74% in comparison to experimentally estimated value of Nusselt number and friction factor respectively. The optimum thermo hydraulic performance calculated is 3.85 at relative gap width, relative gap position and number of gaps of 1, 0.6, and 3, respectively.

Laminar flow and heat transfer of water/NDG nanofluid on tube banks with rhombic cross section with different longitudinal arrangements

In present numerical study, water/NDG (nitrogen-doped graphene) nanofluid flow in different arrangements of rhombic tube banks is investigated in a two-dimensional space. Water/NDG nanofluid is considered in mass fractions of 0, 1, 2, 4 and 6% and Re numbers of 10, 100 and 450 as cooling fluid. The arrangements of tube banks are considered as ET (equilateral triangle), RS (rotated square) and ES (equal spacing) arrangements. Results revealed that the enhancement of mass fraction causes heat transfer enhancement which is due to the increase in thermal conductivity coefficient of cooling nanofluid compared to base fluid. The increase in Re causes the enhancement of average Nu which is due to better mixture of fluid layers with the enhancement of fluid velocity in higher Re which causes the reduction in temperature gradients among fluid layers away from tubes and homogeneous temperature distribution in these areas. Among investigated arrangements, RS has the highest Nu. Also, ET arrangement, compared to ES arrangement, has higher Nu. In all of the studied arrangements, the increase in Re causes the reduction in friction factor and the maximum values of friction factor are related to RS and ET arrangements, respectively.

Experimental study on the air-side thermal-flow performance of additively manufactured heat exchangers with novel fin designs

We introduce novel fin designs for finned tube heat exchangers which enhance the conduction heat transfer within the fin and the convective heat transfer along the fin surface simultaneously. Oval tubes with circular plain fins (CPF), circular integrated pin fins (CIPF) and a serrated integrated pin fins (SIPF) were additively manufactured via Selective Laser Melting (SLM) and their heat transfer and flow characteristics studied in a flow channel for different Reynolds number between 1800 and 7800 as well as fin spacing values between 6mm and 16mm. From the experiments an improvement of Nusselt number and a reduction of friction factor was found for all fin designs when fin spacing increases. CIPF showed a higher Nusselt number compared to CPF at all Reynolds numbers and fin spacing values. The highest Nusselt number as well as moderate friction factor values were found for the SIPF design. However, for SIPF the fin efficiency of 30.3% is lowest due to the high heat dissipation along the fin surface. In order to evaluate the thermal and flow performance three parameters were studied: the performance evaluation criterion, the volumetric heat flux density and the global performance. CIPF gives a higher performance evaluation criterion compared to CPF and SIPF performs best compared to the other fin designs. Highest volumetric heat flux density of 2.72kWm³K was achieved with CIPF at lowest fin spacing. Small differences in the global performance criterion between the fin designs and for various fin spacing were observed. The SIPF design is of advantage, if the required surface area, the material cost and the weight of the finned tube heat exchanger are relevant. From the experimental results a heat transfer correlation that includes Nusselt number, Reynolds number, Prandtl number, fin spacing and fin design has been derived.

CFD modeling of immiscible liquids turbulent dispersion in Kenics static mixers: Focusing on droplet behavior

The present study is concerned with the computational fluid dynamics (CFD) simulation of turbulent dispersion of immiscible liquids, namely, water–silicone oil and water–benzene through Kenics static mixers using the Eulerian–Eulerian and Eulerian–Lagrangian approaches of the ANSYS Fluent 16.0 software. To study the droplet size distribution (DSD), the Eulerian formulation incorporating a population balance model (PBM) was employed. For the Eulerian–Lagrangian approach, a discrete phase model (DPM) in conjunction with the Eulerian approach for continuous phase simulation was used to predict the residence time distribution (RTD) of droplets. In both approaches, a shear stress transport (SST) k − ω turbulence model was used. For validation purposes, the simulated results were compared with the experimental data and theoretical values for the Fanning friction factor, Sauter mean diameter and the mean residence time. The reliability of the computational model was further assessed by comparing the results with the available empirical correlations for Fanning friction factor and Sauter mean diameter. In addition, the influence of important geometrical and operational parameters, including the number of mixing elements and Weber number, was studied. It was found that the proposed models are capable of predicting the performance of the Kenics static mixer reasonably well.