ERRATUM TO “CHARACTERISTICS OF PRESSURE DROP AND CORRELATION OF FRICTION FACTORS FOR SINGLE-PHASE FLOW IN ROLLING HORIZONTAL PIPE”

This is the erratum to the article [zhang Jin-hong, Yan Chang-qi, Gao Pu-zhen, Journal of Hydrodynamics, 2009, 21(5)]. The Fig.5 is corrected.

CHARACTERISTICS OF PRESSURE DROP AND CORRELATION OF FRICTION FACTORS FOR SINGLE-PHASE FLOW IN ROLLING HORIZONTAL PIPE

Gas-liquid two-phase flow occurs increasingly in some dynamic devices operating in the oceanic condition. The relative data are limited with respect to flow characteristics, so the present study is to investigate systematically single-phase pressure drop, and to develop the theory for frictional factor under the roiling condition. Using deionized water as the test fluid, a series of experiments of single-phase flow were conducted in pipe with the inner diameter of 34.5 ram. The test section was horizontally settled on the rolling apparatus, and its regularity was similar to simple harmonic motion. It is found that the pressure drop during rolling motion fluctuate with the change of the rolling period and rolling angle, which is significantly different from fluid motion in a steady state. By the contrast between experiment results and stable-state theory values, existing correlations can not predict present frictional factor very well. Therefore, in the present article, the single-phase frictional factor is correlated with the Reynolds number for rolling motion, and its computated results agree well with experimental data.

Pipes with Trapezoidal Cut Twisted Tape Inserts in the Laminar Flow Regime:Nusselt Number and Friction Coefficient Analysis

The thermal behavior of pipes with a twisted tape inside(used to enhance heat transfer through the tube wall)is studied in the laminar flow regime.Oil is used as the work fluid with the corresponding Reynolds Number spanning the interval 200–2000.It is found that in such conditions the‘Nusselt Number’(Nu)gradually increases with reducing the tape twist ratio,whereas the friction factor is detrimentally affected by the presence of the tape(as witnessed by the comparison with the companion case where a plain tube is considered).In particular,it is shown that the heat transfer efficiency can be improved by nearly 69%if tape inserts with a relatively low twist ratio are used.On the basis of these findings,it is concluded that loose fit tape inserts are superior to tight fit tapes in terms of heat transfer and ease of replacement.

Analysis of Friction and Heat Transfer Characteristics of Tubes with Trapezoidal Cut Twisted Tape Inserts

The thermo-hydraulic properties of circular tubes with a twisted tape inside(used accordingly to induce turbulence and enhance heat transfer through the tube wall)are described for Reynolds Numbers ranging from 830 to 1990.Tapes twisted with the three distinct twist ratios are considered,namely,6,4.4 and 3.Air is used as the working fluid in several tests.For the sake of comparison,the standard tube with no insert is also examined.It is shown that in the presence of the twisted tape,the‘frictional factor’,‘Nusselt Number’and the‘thermal performance factor’are much higher than those obtained for the plain tube.Moreover,the tapes having the lowest twist ratio,i.e.,3,are more effective than the others in terms of heat transfer augmentation.The‘thermal performance factor’is greater than one for all the twisted tapes used in the experiments,which confirms the enhanced performances of the heat exchanger and the related savings in terms of total energy.

Friction factor correlation for airflow through broken rocks and its applications in mine ventilation

The Atkinson equation along with its friction factor is commonly used to estimate pressure requirement in mine ventilation.However,friction factor correlation of flow through broken rock,typically found in blasted stope,gob,rock pit or block caving rock deposits,etc.,is currently unavailable.Also,it is impractical to conduct direct measurements of flow resistance in an inaccessible broken rock zone.This paper aims to develop a new friction factor correlation of flow through broken rock that can be used directly in Atkinson equation.The proposed correlation is valid for broken rocks with diameter between 0.04 and 1.2 m and porosity ranging from 0.23 to 0.7.

An Accurate and Computationally Efficient Explicit Friction Factor Model

The implicit Colebrook equation has been the standard for estimating pipe friction factor in a fully developed turbulent regime. Several alternative explicit models to the Colebrook equation have been proposed. To date, most of the accurate explicit models have been those with three logarithmic functions, but they require more computational time than the Colebrook equation. In this study, a new explicit non-linear regression model which has only two logarithmic functions is developed. The new model, when compared with the existing extremely accurate models, gives rise to the least average and maximum relative errors of 0.0025% and 0.0664%, respectively. Moreover, it requires far less computational time than the Colebrook equation. It is therefore concluded that the new explicit model provides a good trade-off between accuracy and relative computational efficiency for pipe friction factor estimation in the fully developed turbulent flow regime.

An improved semi-empirical friction model for gas-liquid two-phase flow in horizontal and near horizontal pipes

Pressure drop and liquid hold-up are two very important fluid flow parameters in design and control of multiphase flow pipelines.Friction factors play an important role in the accurate calculation of pressure drop.Various empirical and semi-empirical closure relations exist in the literature to calculate the liquid-wall,gas-wall and interfacial friction in two-phase pipe flow.However most of them are empirical correlations found under special experimental conditions.In this paper by modification of a friction model available in the literature,an improved semiempirical model is proposed.The proposed model is incorporated in the two-fluid correlations under equilibrium conditions and solved.Pressure gradient and velocity profiles are validated against experimental data.Using the improved model,the pressure gradient deviation from experiments diminishes by about 3%;the no-slip condition at the interface is satisfied and the velocity profile is predicted in better agreement with the experimental data.

Sticking-up Behaviors and Surface Friction of IF Electrogalvanized Sheet Steel in Forming

X-ray diffraction (XRD), ball-disc friction and wearing machine and draw-bead test were introduced to investigat the strcusture and workability of IF sheet steel electrogalvanized deposits prepared from sulphate solution system. It was shown that the picking-up of the zinc coating on die strengthened with the increasing of friction factor which was originally affected by the coating's structure. Duing forming, (00X) planes (X= 2, 4) preferential orientation of zinc deposits increased, which resulted in enhanc ing the coating's friction behaviors. Therefore, the forming mechanism of electrogalvedzed deposit was demonstrated that both friction and the stricking -up behaviors of the coating are intensified simultaneously and affect each other.

Investigation into the Computational Costs of Using Genetic Algorithm and Simulated Annealing for the Optimization of Explicit Friction Factor Models

Research reports show that the accuracies of many explicit friction factor models, having different levels of accuracies and complexities, have been improved using genetic algorithm (GA), a global optimization approach. However, the computational cost associated with the use of GA has yet to be discussed. In this study, the parameters of sixteen explicit models for the estimation of friction factor in the turbulent flow regime were optimized using two popular global search methods namely genetic algorithm (GA) and simulated annealing (SA). Based on 1000 interval values of Reynolds number (Re) in the range of and 100 interval values of relative roughness () in the range of , corresponding friction factor (f) data were obtained by solving Colebrook-White equation using Microsoft Excel spreadsheet. These data were then used to modify the parameters of the selected explicit models. Although both GA and SA led to either moderate or significant improvements in the accuracies of the existing friction factor models, SA outperforms the GA. Moreover, the SA requires far less computational time than the GA to complete the corresponding optimization process. It can therefore be concluded that SA is a better global optimizer than GA in the process of finding an improved explicit friction factor model as an alternative to the implicit Colebrook-White equation in the turbulent flow regime.

Numeric Study on Skin Friction Reduction of Engine Oil-WS2 Nanofluid by MRT Lattice Boltzman Method

New lubricants use nanoparticles like WS2 to improve lubrication performance.The aim of the present study is to determine numerically the skin friction of nanofluid on moving surfaces in a lubricating system.The base fluid is 5W-30 engine oil and the nano-additive is WS2 nanoparticles.This numerical study is based on the multiple-relaxation-time Lattice Boltzmann method(MRT-LBM).The two-dimensional nine-velocity(D2Q9)model is adopted to simulate the nanofluid flow confined by two moving surfaces.The parameters considered are the nanoparticle concentration􀟮and the flow Reynolds number Re.The results obtained show a reduction of skin friction factor when we increase the nanoparticle concentration.

CFD analysis of Al_(2)O_(3)-syltherm oil nanofluid on parabolic trough solar

In this paper,in order to improve the performance of a linear parabolic collector,the thermal effects of using Al_(2)O_(3)-syltherm oil nanofluid with different concentrations and new flange-shaped turbulators are investigated.The simulation was performed by ANSYS-FLUENT-18.2 commercial software using Realizable k-εtwo-equation turbulence model.In accordance with the results,it was realized that increasing the volume fraction of nanoparticles(to 5%)and number of turbulators causes the heat transfer coefficient(h)of the fluid to elevate and ultimately the uniform temperature is created in the absorber.For instance,at a flow rate of 4.5kg/s and an inlet temperature of 350 K,the value of h increases by about 8.5%by changing the number of turbulators from 10 to 15 sets.On the other hand,the results indicate that by changing the arrangement of the turbulators,the heat transfer efficiency of the collector can be increased by 5%for 350 K,3.5%for 450 K and 1%for 550 K inlet temperature.

Numerical modeling investigation on turbulent oscillatory flow over a plane rough bed composed by randomly arrayed particles

A three-dimensional numerical model is established to simulate the turbulent oscillatory boundary layer over a fixed and rough bed composed by randomly arrayed solid spheres based on the lattice Boltzmann method and the large eddy simulation model.The equivalent roughness height,the location of the theoretical bed and the time variation of the friction velocity are investigated using the log-fit method.The time series of turbulent intensity and Reynolds stress are also investigated.The equivalent roughness height of cases with Reynolds numbers of 1×10^4–6×10^4 is approximately 2.81 d（grain size）.The time variation of the friction velocity in an oscillatory cycle exhibits sinusoidal-like behavior.The friction factor depends on the relative roughness in the rough turbulent regime,and the pattern of solid particles arrayed as the rough bed in the numerical simulations has no obvious effect on the friction factor.

Thermal performance assessment of self-rotating twisted tapes and Al_(2)O_(3) nanoparticle in a circular pipe

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 selfrotating twisted tapes(SRTTs)and Al_(2)O_(3) nanoparticles.The effect of the selfrotating twisted tapes and Al2O3 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 Al2O3 nanoparticle and SRTTs were developed within 10%deviation of experimental values.

High-precision Thickness Setting Models for Titanium Alloy Plate Cold Rolling without Tension

Due to its highly favorable physical and chemical properties,titanium and titanium alloy are widely used in a variety of industries.Because of the low output of a single batch,plate cold rolling without tension is the most common rolling production method for titanium alloy.This method is lack of on-line thickness closed-loop control,with carefully thickness setting models for precision.A set of high-precision thickness setting models are proposed to suit the production method.Because of frequent variations in rolling specification,a model structural for the combination of analytical models and statistical models is adopted to replace the traditional self-learning method.The deformation resistance and friction factor,the primary factors which affect model precision,are considered as the objectives of statistical modeling.Firstly,the coefficient fitting of deformation resistance analytical model based on over-determined equations set is adopted.Additionally,a support vector machine（SVM）is applied to the modeling of the deformation resistance and friction factor.The setting models are applied to a 1450 plate-coiling mill for titanium alloy plate rolling,and then thickness precision is found consistently to be within 3%,exceeding the precision of traditional setting models with a self-learning method based on a large number of stable rolling data.Excellent application performance is obtained.The proposed research provides a set of high-precision thickness setting models which are well adapted to the characteristics of titanium alloy plate cold rolling without tension.

Experimental Investigation and Prediction Model of the Loads Exerted by Oblique Internal Solitary Waves on FPSO

By using a 30-meter-long wave flume equipped with a double-plate wave maker,a series of depression ISWs were generated in a density stratified two-layer fluid and the forces exerted by oblique internal solitary waves(ISWs)on fixed FPSO model had been measured.According to the laboratory experiments,a numerical flume taken the applicability of KdV,eKdV and MCC ISWs theories in consideration was adopted to study the force components.Based on the experimental data and the force composition,the simplified prediction model was established.It was shown that the horizontal and transversal loads consisted of two parts:the Froude−Krylov force that could be calculated by integrating the dynamic pressure induced by ISW along the FPSO wetted surface,as well as the viscous force that could be obtained by multiplying the friction coefficient Cfx(C_(fy)),correction factor K_(x)(K_(y))and the integration of particle tangential velocity along the FPSO wetted surface.The vertical load was mainly the vertical Froude−Krylov force.Based on the experimental results,a conclusion can be drawn that the friction coefficient Cf and correction factor K were regressed as a relationship of Reynolds number Re,Keulegan-Carpenter number KC,upper layer depth h1/h and ISW accident angleα.Moreover,the horizontal friction coefficient Cfx yielded the logarithmic function with Re,and transversal friction coefficient C_(fy)obeyed the exponent function with Re,while the correction factors K_(x)and K_(y)followed power function with KC.The force prediction was also performed based on the regression formulae and pressure integral.The predicted results agreed well with the experimental results.The maximum forces increase linearly with the ISWs amplitude.Besides,the upper layer thickness had an obvious influence on the extreme value of the horizontal and transversal forces.

Model inference using the Akaike information criterion for turbulent flow of non-Newtonian crude oils in pipelines

The friction factor is a crucial parameter in calculating frictional pressure losses. However, it is a decisive challenge to estimate, especially for turbulent flow of non-Newtonian fluids in pipes. The objective of this paper is to examine the validity of friction factor correla- tions adopting a new informative-based approach, the Akaike information criterion （AIC） along with the coeffi- cient of determination （R2）. Over a wide range of measured data, the results show that each model is accurate when it is examined against a specific dataset while the E1-Emam et al. （Oil Gas J 101：74-83, 2003） model proves its supe- riority. In addition to its simple and explicit form, it covers a wide range of flow behavior indices and generalized Reynolds numbers. It is also shown that the traditional belief that a high R2 means a better model may be mis- leading. AIC overcomes the shortcomings of R2 as a trade between the complexity of the model and its accuracy not only to find a best approximating model but also to develop statistical inference based on the data. The authors present AIC to initiate an innovative strategy to help alleviate several challenges faced by the professionals in the oil and gas industry. Finally, a detailed discussion and models＇ ranking according to AIC and R2 is presented showing the numerous advantages of AIC.Keywords Friction factor - Pipeline Information theory Non-Newtonian Turbulent

Flow stress and tribology size effects in scaled down cylinder compression

Microforming is an effective method to manufacture small metal parts.However,macro forming can not be transferred to microforming directly because of size effects.Flow stress and tribology size effects were studied.Scaled down copper T2 cylinder compression was carried out with the lubrication of castor oil and without lubrication.The results show that the flow stress decreases with decreasing the initial specimen diameter in both lubrication conditions,and the flow stress decreases by 30 MPa with the initial specimen diameter decreasing from 8 mm to 1 mm.The friction factor increases obviously with decreasing the initial specimen diameter in the case of lubricating with castor oil,and the friction factor increases by 0.11 with the initial specimen diameter decreasing from 8 mm to 1 mm.However,the tribology size effect is not found in the case without lubrication.The reasons of the flow stress and tribology size effects were also discussed.

A new model for predicting the critical liquid-carrying velocity in inclined gas wells

Based on the assumption of gas-liquid stratified flow pattern in inclined gas wells,considering the influence of wettability and surface tension on the circumferential distribution of liquid film along the wellbore wall,the influence of the change of the gas-liquid interface configuration on the potential energy,kinetic energy and surface free energy of the two-phase system per unit length of the tube is investigated,and a new model for calculating the gas-liquid distribution at critical conditions is developed by using the principle of minimum energy.Considering the influence of the inclination angle,the calculation model of interfacial friction factor is established,and finally closed the governing equations.The interface shape is more vulnerable to wettability and surface tension at a low liquid holdup,resulting in a curved interface configuration.The interface is more curved when the smaller is the pipe diameter,or the smaller the liquid holdup,or the smaller the deviation angle,or the greater gas velocity,or the greater the gas density.The critical liquid-carrying velocity increases nonlinearly and then decreases with the increase of inclination angle.The inclination corresponding to the maximum critical liquid-carrying velocity increases with the increase of the diameter of the wellbore,and it is also affected by the fluid properties of the gas phase and liquid phase.The mean relative errors for critical liquid-carrying velocity and critical pressure gradient are 1.19%and 3.02%,respectively,and the misclassification rate is 2.38%in the field trial,implying the new model can provide a valid judgement on the liquid loading in inclined gas wells.

AN APPROXIMATE ANALYTICAL SOLUTION OF THE LAMINAR BOUNDARY LAYER EQUATIONS

Using the pressure gradient as the new variable instead of. the ordinary longitudinal coordinate x, Liu transformed the ordinary laminar boundary equations into a new form. On this base Liu obtained the frictional stress factor by using the graphical method.In this paper the same variable replacement as in [1] is used and an approximate analytical solution of the laminar boundary layer equations by the series method is obtained. The author also obtains a formula of frictional stress factor. For the case of the main function without the term of constant, the author makes a further simplification. The error of the frictional stress factor obtained by the author is still less than 10%, compared with that of [1].

Determination of Airways Resistance, Volumetric Efficiency and Development of Ventilation Model of Rosh Pinah Zinc Mine Namibia

A quantitative technique was conducted at Rosh Pinah Zinc mine, Namibia with its main purpose to determine airways resistance which is a function of the parameters;roughness of the airways and the friction factor. The 32 branch points (i.e. a-ag) that stand for ventilation circuit have been selected. Data collected includes, length and width of airways, air velocity;air density, and roughness of the airways which were used to determine coefficient of frictions, friction factors and airway resistances. A ventilation model was developed. In order to improve the current ventilation model, airways resistance of the mine was determined and simulated in a modified model using VentSimTM software. An average total airways resistance of 0.32027 Ns2/m8 has been achieved for Rosh Pinah mine. It should be pointed out that, as the mine advances its production faces deeper, this value would increases suddenly. Simulation revealed that as much as 34.4 m3/s of air can be received at the production faces, compared to the measured received amount of 19.3 m3/s. Therefore, volumetric efficiency of the mine was improved from 29.3% to 68.3%. It was also noticed that after importing the resistance values into the model together with other parameters, the model was greatly improved and no cause for concern.