Calculation Of Friction Factor Research Articles

Modification and Improvement of the Churchill Equation for Friction Factor Calculation in Pipes

Modification and Improvement of the Churchill Equation for Friction Factor Calculation in Pipes

WITHDRAWN: Investigation on effectiveness calculation and interaction of friction factor of CrN-coated stainless steel: Design of experiment and surface analysis

Hydrogen valves for electric vehicles operate in a high-pressure friction environment and suffer significant wear damage; thus, application of surface treatment technology is necessary. Systematic research is needed to evaluate the effectiveness of friction factors to reduce wear damage in harsh environments of surface-treated specimens. In this investigation, CrN coating using the arc ion plating (AIP) method was applied to stainless steel, and the effectiveness of the factors (load, distance, and rotation speed) of wear damage was tested using the design of experiments method. A validity test was calculated using analysis of variance, and the calculated results were comprehensively compared with the microscopic analysis results. The analysis of variance indicated that the highest factor and lowest factor were the F-value of the load (127.49) and the rotation speed (0.66), respectively. The maximum damage depth and width increased as all friction factor conditions increased. As a result, the calculation of the effective factor of wear damage was similar between the analysis of variance and the microscopic analysis. The CrN coating layer had excellent wear resistance, and the load factor was the most effective.

Development and validation of a model for an air-to-air air conditioner

Air conditioning units are responsible for a significant amount of global warming, with demand predicted to triple by 2050. Mathematical models aid in designing energy efficient air conditioners that can contribute to climate change mitigation. This study presents a steady-state model for a air-to-air air conditioner. The proposed model can assist in reducing the number of experiments and optimizing the efficiency of air conditioning systems. It utilizes a bottom-up approach to solve for compressor, condenser, capillary tube, and evaporator sub-models. The compressor is modelled using polynomial equations to determine refrigerant mass flow rate and power consumption based on operating temperatures. Heat exchanger models are solved using finite volume approach and reliable correlations are used for void fraction, friction factor, and heat transfer coefficient calculations. The closing equations are the mass conservation, i.e. constant refrigerant charge, and the equivalence between the mass flow rate sucked by the compressor and the one that flows through the capillary tube, while the evaporating and condensing pressures are the independent variables. The capillary tube is modelled using semiempirical correlations. The model is validated against experimental data at various operating conditions and shows a ±7% agreement for predicted cooling capacity.

Experimental Investigations on the Performance of Thermosyphon Solar Flat Plate Collector using TiO2 Nanofluids

Titanium dioxide nanofluid is used in the thermosyphon solar flat plate collector at volume fractions of 0.1%, 0.3%, 0.5%, 0.7%, and 1% to test the collector’s effectiveness. The heat transfer coefficient, Nusselt number, friction factor, and pressure drop calculations were used to analyze the impact of adding nanoparticles to the working fluid. The effectiveness of the solar flat plate collector and the heat transfer coefficient are both greatly affected by the addition of titanium dioxide to the working fluid, with a tolerable rise in pressure drop. With concomitant variances of 15% and 13%, correlations were constructed for the Nusselt number and friction factor.

A Semi-empirical correlation for stratified two-phase flow friction factors

The optimal design of two-phase flow pipes depends on various variables. Pressure drop and liquid hold-up are essential parameters in the appropriate design of pipes. These parameters can be estimated by numerical simulation of pipes. However, the simulation strongly depends on both phase frictions. Frictions are commonly calculated using friction factors, and various empirical correlations have been proposed to calculate friction factors, but most of these correlations are dependent on the experimental conditions.The present study proposes a semi-empirical friction factor model by modifying an existing model in the literature for stratified two-phase flows. Experimental data from various laboratories are taken to validate the interface shear stress, velocity profile and pressure gradient. Compared with previous models, the predicted velocity profiles and shear stresses are in better agreement with the experimental data.

Frictional factor and flow characteristics in pulsating flow with high amplitude of pulsations

Pulsating flow as a means of achieving higher heat transfer rates are of interest in many engineering applications such as industrial, environmental and biological flows. These flows are mainly characterised by superimposition of unsteady flow over a steady flow ensuring a net flow along the pipe. The forced pulsation is found to greatly affect the flow characteristics, depending upon the frequency and amplitudes of pulsations. The annular effect in which the flow near the wall is increased is explicitly observed for amplitude of pulsation greater than 0.6, resulting in the heat transfer enhancement up to 40 % for amplitude ratio of 1.8 (Sonawane and Sewatkar, 2019) [11]. The flow characteristics exhibited due to variation in amplitude ratio is absent for variation in Reynolds number and pulsation frequency. In case of heat exchangers used in the Stirling engines, the enhancement in heat transfer can bring a noticeable reduction in the size, thereby saving in the cost and space requirement. However to produce the pulsations by artificial mechanism, like the use of reciprocating pump or pulsators asks for additional amount of input energy as compared to steady flow energy. Hence it becomes necessary to know the energy lost in friction and acceleration and retardation of the fluid due to induced pulsation. Therefore, observations of effect of different amplitudes on the instantaneous and time averaged friction factor is discussed with the sole purpose of obtaining an optimised combination of the governing parameters, namely Reynolds, frequency and amplitude of pulsation for enhancing convective heat transfer for flow through pipe. It has been observed that for amplitude ratios up to 0.6, the friction factor values show a marginal decrease as compared with steady laminar flow, however for higher amplitudes, there is steep decrease in time averaged friction factors. It is also noticed that the instantaneous friction factors show high values in the latter half of pulsation cycle. The friction factor values are greatly influenced by the induced pulsation, due to which the correlations developed for steady laminar flow friction factor calculations needs to be modified.

Experimental and numerical investigation of heat loss in transition modes of buried hot fuel oil pipeline

In this research, heat transfer of fuel oil flow through the buried pipeline in three regimes, turbulent, transition, and laminar conditions are investigated. A large-scale laboratory set-up is designed for this purpose and numerical modeling was also performed to study the effect of different parameters. The simulation is based on the fluid's thermophysical properties and the results are validated using experimental data. Due to the strong dependence of viscosity and density of fuel oil on the temperature, regime changes along the pipeline happens which complicate the calculation of friction factor. Using the experiment results and choosing different numerical methods, the acceptable model of friction factor in the transition zone for the experimental pipe and the real pipeline was achieved. Numerical simulation was performed on a 107 km pipeline using a powerful computer network to achieve the results. The approach which is used to simulate laminarization shows just a 3% discrepancy with experimental data. For the real pipeline, about 30 percent of the length is in transition mode from turbulent to laminar. The diameter of 26” is chosen as the most optimal size to transform 180000 barrels per day (BPD). According to the design thickness, diameter, and length of the pipeline, the maximum safe stop time (MSST) of the pipeline is 41 hours which is the most important data in the pipeline's maintenance period. Based on the present experimental data and simulation results, the optimal depth for the least heat loss from this pipeline is 0.9 to 2.7 meters.

Accurate explicit analytical solution for Colebrook-White equation

This paper presents a direct closed form analytical solution for the implicit type equation of Colebrook-White for friction factor calculation. Based on the developed expression, the friction factor can be directly calculated given the fluid flow parameters namely the relative roughness and the Reynolds number. Obtained expression is explicit and it does not require any iterative calculation as it is built reposing on the analytical solution of a cubic equation of real coefficients. The used cubic equation is obtained through a 3rd order Taylor series expansion of the original Colebrook-White equation around an expansion point reasonably defined. The reliability of the proposed expression is proved through comparison with original Moody chart values as well as others results issued from previous approximations found in literature and the exact solution of Colebrook-White equation. The accuracy and the robustness of the established expression over other explicit correlations were emphasized. The presented closed form expression was proved to be simple, robust and accurate. Additionally it has the advantages of covering all the range of applicability of the original Colebrook-White equation.

Investigation of pressure drop in flexible ventilation ducts under different compression ratios and bending angles

Due to the large degree of freedom in terms of design and installation, flexible ventilation ducts are commonly used in ventilation systems. However, excessive use of flexible ducts may lead to greater pressure drop and higher energy consumption. This study conducted experimental measurements to characterize the pressure drop in flexible ventilation ducts with different compression ratios and bending angles. This investigation first measured the pressure drop in straight flexible ducts with four compression ratios under various airflow rates. The calculated friction factor for the straight flexible ducts was negatively associated with the compression ratio. Next, the pressure drops in single-bend flexible ducts with various bending angles from 30° to 150° were measured under various airflow rates. The calculated loss coefficient of the bend increased with the bending angle for single-bend flexible ducts. Finally, the influence of the intermediate duct length on the pressure drop across two bends was experimentally investigated. When the length of the intermediate duct was greater than eight times the inner diameter, the pressure drop across a double-bend flexible duct could be calculated from the friction factors and loss coefficients with a relative error less than 1%. The data obtained in this study can be used to calculate the total pressure loss in flexible ventilation ducting systems in buildings.

A new approach to study the friction-reduction characteristics of viscous/conventional slickwater in simulated pipelines and fractures

Viscous slickwater have been successfully applied as an alternative to conventional ones. However, it is still not clear whether these two types of slickwater show the same friction-reduction characteristics when migrated into pipelines and fractures. In this study, the friction-reduction performances of a conventional friction reducer (FR-800) and a highly viscous friction reducer (HVFR-900) in pipelines and fractures were tested through independently designed pipeline and visual crack modules. The corresponding λ (Darcy friction factor) values were calculated based on the friction pressure drop and used to fit a friction factor calculation model. Finally, the dynamic sand-carrying performance of the two friction reducers were obtained through a visual crack module. The results showed that, as the concentration of two friction reducers increased, the friction-reduction performance of FR-800 gradually weakened in the pipeline, while that of HVFR-900 gradually increased; meanwhile, the performances of the two chemicals varied similarly in the fractures. The λ values of FR-800 and HVFR-900 in the pipe and fractures can be calculated by using equations similar to the power-law D&M formula which is usually applied to fluids, various results mainly induced from the type of friction reducer and its concentration. Additionally, it was noted that the dynamic sand-carrying performance of viscous slickwater at a concentration of 0.60 wt% was significantly better than that of conventional slickwater.

Friction factor calculation in nanochannels comprising different wall hydrophobicities and superhydrophobic structures: Molecular dynamic simulations

A non-equilibrium molecular dynamics simulation was employed to evaluate the friction factor of water molecules confined in nanochannels composed of silicon surfaces. The investigation of water flow behavior was focused on two sets of cases. At first, two smooth silicon surfaces were used to create the wall of nanochannels. Simulation results indicated that for the studied cases, more hydrophilic walls led to higher Darcy-Weisbach friction factor of the confined water. In the second case, Nanometer-sized protrusions with the aligned and staggered nanopost arrangements were used to decorate the silicon surface to produce possibly superhydrophobic surfaces. Our results indicated that the friction factor in staggered nanopost arrangement was significantly larger than that of the aligned one. We found that for both nonopost arrangements, by increasing the Reynolds number and decreasing the percentage of pillar surface fraction, the friction factor decreased and the slip length increased. We found that employing a superhydrophobic surface in nanopost configuration, depending on pillar surface fraction, could lead to a lower friction factor than a hydrophobic surface obtained by a decrease in the wall hydrophilicity. We believe that our computational findings could shed light on the efficiency, economy improvement, and miniaturization of the nanofluidic devices.

THE PERFORMANCE OF EXPLICIT FORMULAS FOR DETERMINING THE DARCY-WEISBACH FRICTION FACTOR

ABSTRACT The Darcy-Weisbach equation is the most recommended equation for determining the pressure loss in pressurized pipes because of its wide applicability. However, one of the largest obstacles to implementing this equation is the friction factor (f) calculation. This factor can be precisely determined using the Colebrook equation, which is implicit. Thus, the objective of this study was to compare six explicit equations for calculating the Darcy-Weisbach friction factor with the implicit Colebrook equation based on the relative error. Based on the results, the equations of Vatankhah and Offor & Alabi were the most highly recommended. These six explicit formulas showed a mean relative error of less than ± 1% compared to the Colebrook equation, except for the Swamee and Jain equation, for which the laminar regime generated a mean relative error of 1.83%.

Friction factor calculation for turbulent flow in annulus with temperature effects

Purpose The purpose of this paper is to present a new friction factor equation for practical use, including fluid temperature, pipe diameter ratio and inner pipe rotation effects. Design/methodology/approach A friction factor relationship is developed by applying Buckingham’s Theorem of dimensional analysis. Then, the formula is calibrated using experimental data conducted at Izmir Katip Celebi University flow loop. Moreover, the effects of fluid temperature, inner pipe rotation and pipe diameter ratio on friction factor are investigated experimentally. Findings Satisfactory agreements are obtained between proposed formula and experiments. The experimental results indicate that major variable parameters affecting friction factor is Reynolds number. Pipe rotation has negligible effect on friction factor at high Reynolds number. Prandtl number is one of the important parameters affecting the friction factor. Moreover, as the pipe diameter ratio is decreased, friction factor increases. Originality/value Determining fluid behavior of fluids under high temperature is especially important for deep wells during drilling. Temperature drastically changes fluid properties and flow characteristics in wells. These changes have a remarkable effect on pressure losses. However, since the temperature is considered constant in the calculation of the pressure loss, problems can be encountered in most systems. Friction factor is one of the important parameters for determining pressure loss in closed conduits. The originality of this work is to propose a new friction factor equation for practical use, including fluid temperature, pipe diameter ratio and inner pipe rotation effects.

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.

EFFECT OF ARTIFICIAL CAVITIES ON HEAT TRANSFER AND FLOW CHARACTERISTICS MICROCHANNEL

An experimental investigation was conducted to study single-phase fluid flow and heat transfer in a copper micro channel. To investigate the effect of artificial cavities on fluid flow and single phase heat transfer in micro channel heat sink, two model of straight micro channel recognized as two models (model -1and model -2) were designed and manufactured ,where model-1 have smooth bottom surface while Model-2 have 47 artificial cavities distributed uniformly at the bottom surface along the micro channel length. The two models having the same nominal dimension of 300?m height and 300?m depth while the real dimension value are 367 ?m for width and 296 ?m for depth .De-ionized water was used as the working fluids. Experimental test was conducted at 30?C inlet temperature with Reynolds numbers range from 700 to 2200 covering laminar flow conditions. The experiments were conducted with horizontal micro channel under both adiabatic (for friction factor calculation) and diabatic (for Nusselt number calculation) conditions. The results indicated that the experimental Darcy friction factor can be predicted well with conventional scale fanning friction factor correlations for developing flow in laminar region by shah and London (1978) correlation for two models. Also, the experimental Nusselt number Agree well with each correlation of shah and London (1978) and Mirmanto correlation in laminar region.

Influence of corrugation topology on thermohydraulic performance of cold dielectric counter cooled high temperature superconducting cable

Fluid flow, pressure drop and heat transfer across the long length cold dielectric counter cooled High Temperature Superconducting (HTS) cables are significantly influenced by the different corrugation (rectangular, circular and triangular) topologies. Thus, in this present work, thermal and hydraulic characteristics of turbulent LN2 flow in counter cooled HTS cable with various corrugation topologies are computationally investigated. The 2-D axisymmetric model of HTS cable with counter flow cooling system is considered by changing the corrugation shapes for Reynolds number ranging from 3.0 × 104 to 6.0 × 104. Heat flux from ambient temperature on outer corrugated pipe and heat generation from A.C. losses in the HTS tapes are also considered in the present simulations. In addition, distribution of the velocity, temperature and turbulent kinetic energy (TKE) of liquid nitrogen (LN2) in the HTS cable with various corrugations are estimated using computational fluid dynamics (CFD) technique. Finite volume method is adapted to solve the governing equations (continuity, momentum and energy) using Semi-Implicit Pressure Linked Equations (SIMPLE) scheme with k−ε turbulence model and enhanced wall treatment. The results reveal that the corrugation topologies (rectangular, circular and triangular) have significant effect on heat transfer and pressure drop. The corrugated pipes with different topologies exhibit different friction factors due to the variations in the contact of wall surfaces with the LN2. Moreover, the calculated friction factors for all the three corrugation topologies are compared with the experimental results available in the literature. Further, the results of temperature difference between outlet and inlet temperatures of LN2 are validated with the available experimental measurements. Finally, it was concluded that the effect of heat flux and AC Losses on cooling capacity and heat transfer is found to be significant as compared that on friction factor and pumping power.

Revisiting the Estimation of Colebrook Friction Factor: A Comparison between Artificial Intelligence Models and C-W based Explicit Equations

Application of Colebrook-White (C-W) relation for calculating Darcy-Weisbach (D-W) friction factor has been widely accepted in literature. However, its implicit formation made it unsuitable in practice. The main aim of this study is to investigate the computational accuracy of friction factor calculation in pressurized flows. Based on the number of recursive steps exploited for calculating friction factor, forty C-W based explicit equations available in the literature are classified into one-step, two-step, three-step, and four-step models. In favour of improving the accuracy of such estimation, two new explicit equations are proposed. The performances of these forty two explicit equations are compared with that of artificial neural network (ANN) and genetic programming (GP) using both global and local criteria while the results of C-W formula are considered as benchmarks. The results indicate that the accuracy of the best and worst ones among these forty four models differ order of magnitudes from one another. Furthermore, the first proposed equation outperformed others based on all eleven considered criteria. Moreover, GP and ANN results are found to be comparable with the best one-step explicit equations. Finally, the results demonstrate that explicit equations with higher recursive steps do not necessarily yield to closer estimations to implicit C-W formula comparing with all of equations with lower number of steps even though the best n-step explicit formula yields to better results than the best (n-1)-step one based on the global criteria.

Research on the influence mechanism of friction factor of gear based on mathematical statistics principle

This paper first introduces the development status of gear friction factor research. Secondly, the advantage of the experimental method based on mathematical statistics is discussed. In addition, the mathematical statistics principle is used to design the orthogonal experiment to verify the existing formula of gear friction factor calculation. The correlation of each parameter was studied according to the experimental data. The deficiency of calculation formula is analysed and the prospect of future research is put forward.

Calculation of Friction Factors and Nusselt Numbers for Twisted Elliptical Tube Heat Exchangers Using Nek5000

Twisted elliptical tube geometries for heat exchanger design are expected to offer significant enhancement in heat transfer with a marginal increase in frictional losses. The presented work focuses on computational fluid dynamics (CFD) simulations of heated molten salt flows through twisted elliptical tube geometries at low modified Froude numbers. The objectives of this work are to evaluate the available correlations at low Froude numbers and to determine the impact of using a small gap to resolve contact points. The spectral element CFD code Nek5000 was used for all simulations, which were performed in periodic domains of triangular and square unit cells surrounding a single tube through a complete twist using an explicit filtering large eddy simulation (LES) method. The simulation methodology was validated by comparing to the experimental data of Tan et al. Excellent agreement was observed for this comparison. The Dzyubenko correlation for transitional flow was evaluated for a range of Froude numbers. This correlation demonstrated good agreement with LES results at high modified Froude number. As Froude number was decreased toward the bounds of the correlation, the agreement worsened. Cases were then simulated at low Froude number, testing the effects of tube spacing. It was determined that the laminar case for the square unit cell is the most affected by increasing gap size, which should be minimized to mitigate the effect. In the triangular unit cell, the laminar flow regime is also more significantly impacted by increasing gap size compared to the turbulent flow regime which was only marginally impacted.

A Comparison of Data Reduction Methods for Average Friction Factor Calculation of Adiabatic Gas Flows in Microchannels.

In this paper, a combined numerical and experimental approach for the estimation of the average friction factor along adiabatic microchannels with compressible gas flows is presented. Pressure-drop experiments are performed for a rectangular microchannel with a hydraulic diameter of 295 μm by varying Reynolds number up to 17,000. In parallel, the calculation of friction factor has been repeated numerically and results are compared with the experimental work. The validated numerical model was also used to gain an insight of flow physics by varying the aspect ratio and hydraulic diameter of rectangular microchannels with respect to the channel tested experimentally. This was done with an aim of verifying the role of minor loss coefficients for the estimation of the average friction factor. To have laminar, transitional, and turbulent regimes captured, numerical analysis has been performed by varying Reynolds number from 200 to 20,000. Comparison of numerically and experimentally calculated gas flow characteristics has shown that adiabatic wall treatment (Fanno flow) results in better agreement of average friction factor values with conventional theory than the isothermal treatment of gas along the microchannel. The use of a constant value for minor loss coefficients available in the literature is not recommended for microflows as they change from one assembly to the other and their accurate estimation for compressible flows requires a coupling of numerical analysis with experimental data reduction. Results presented in this work demonstrate how an adiabatic wall treatment along the length of the channel coupled with the assumption of an isentropic flow from manifold to microchannel inlet results in a self-sustained experimental data reduction method for the accurate estimation of friction factor values even in presence of significant compressibility effects. Results also demonstrate that both the assumption of perfect expansion and consequently wrong estimation of average temperature between inlet and outlet of a microchannel can be responsible for an apparent increase in experimental average friction factor in choked flow regime.