Calculation Of Friction Factor Research Articles

Direct simulation of structured wall bounded packed beds using hybrid FE/FV methods

Direct numerical simulations are conducted for regular or structured porous media represented by packed beds of spheres enclosed in square cross-section channels for different channel-to-sphere diameter ratios (Ds/dp=1 to ∞) using hybrid finite element/volume (FE/FV) methods. The hybrid flow solver methodology is based on the pressure correction or projection method, which involves a fractional step approach to obtain an intermediate velocity field by solving the original momentum equations with the matrix-free, implicit, cell-centered finite volume method. The poisson equation resulting from the fractional step approach is then solved by node based Galerkin finite element method for an auxiliary variable which is closely related to pressure and is used to update the velocity field and pressure field.The hybrid flow solver has been extended for applications in structured packed beds for both infinite and also wall bounded porous media. The packed spheres representing the porous media are shrunk by 2% dp so that there is a finite, but very small spacing between spheres and also between sphere and wall to avoid highly skewed elements. Studies are conducted to test our novel hybrid FE/FV solver for porous media flows and also to analyze wall effects in detail for regular, structured porous media in Simple Cubic (SC) configuration. Three dimensional numerical simulations are conducted for different channel to sphere diameter ratios (Ds/dp) and also for infinite porous media over wide range of Reynolds numbers (1⩽ReE⩽5000) so that the dimensionless pressure drop or friction factor dependence on the Reynolds number and Ds/dp ratio is clearly understood. Results are validated with available empirical correlations and experimental data. Friction factor correlations for random beds are suitable for structured beds only at very low Reynolds numbers (ReE⩽20), but deviate significantly beyond that due to the channeling present in regular porous media which becomes increasingly significant at higher Reynolds numbers. For structured beds, wall influence was observed to be significant on the friction factor calculation in both laminar and turbulent regimes. Compared to infinite beds, friction factors increased as the channel-to-sphere diameter ratio (Ds/dp) decreased in the entire flow regime. This is unlike the behavior for random porous media where walls have contrasting effects at lower and higher Reynolds numbers when compared to the infinite random beds. Dimensionless pressure drop and friction factor results obtained from our simulations for a wide range of ReE and Ds/dp are curve-fitted to provide generalized correlations for predicting the friction factors in Simple Cubic (SC) structured packed beds.

Very accurate explicit approximations for calculation of the Colebrook friction factor

To date, the Colebrook equation is mostly accepted as an unofficial standard for calculation of the friction factor in turbulent flow through pipes. Unfortunately, the unknown friction factor in the Colebrook equation is given implicitly. Therefore, the implicit Colebrook equation has to be solved in an iterative procedure or using some of the appropriate explicit correlations proposed by many authors. Although the iterative solution is simple and very accurate, it can cause some problems during the calculation of looped network of pipes or similar systems of pipes. Therefore, explicit approximations are favorable in these cases. Up to date, the most accurate approximations have maximal relative error of no more than 0.14% compared to the very accurate iterative solution. Here two explicit approximations are presented, based on already existing models which are improved using genetic algorithms optimization. They are with the maximal relative error of no more than 0.0083% and 0.0026%.

Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes

The implicit Colebrook–White equation is the accepted method for accurately estimating the friction factor for turbulent flow in pipes. This study reviews 28 explicit equations for approximating the friction factor to integrate both the accuracy to the implicit Colebrook–White equation and the relative computational efficiency of the explicit equations. A range of 901 Reynolds numbers were selected for the review between Re ≥ 4 ×103 and ≤ 4 × 108 and 20 relative pipe roughness values were selected between \(\varepsilon \mathord{\left/ {\vphantom {\varepsilon D}} \right.}D\ge 10^{-6}\le 10^{-1}\), thus producing a matrix of 18,020 points for each explicit equation, covering all the values to be encountered in pipeline hydraulic analysis for turbulent flow. The accuracy of the estimation of the friction factor using the explicit equations to the value obtained using the implicit Colebrook–White equation were calculated and reported as absolute, relative percentage and mean square errors. To determine the relative computational efficiency, 300 million friction factor calculations were performed using randomly generated values for the Reynolds number and the relative pipe roughness values between the limits specified for each of the explicit equations and compared to the time taken by the Colebrook–White equation. Finally, 2D and 3D contour models were generated showing both the range and magnitude of the relative percentage accuracy across the complete range of 18,020 points for each explicit equation.

Determination of the Scalar Friction Factor for Nonspherical Particles and Aggregates Across the Entire Knudsen Number Range by Direct Simulation Monte Carlo (DSMC)

The friction factor of an aerosol particle depends upon the Knudsen number (Kn), as gas molecule–particle momentum transfer occurs in the transition regime. For spheres, the friction factor can be calculated using the Stokes–Millikan equation (with the slip correction factor). However, a suitable friction factor relationship remains sought-after for nonspherical particles. We use direct simulation Monte Carlo (DSMC) to evaluate an algebraic expression for the transition regime friction factor that is intended for application to arbitrarily shaped particles. The tested friction factor expression is derived from dimensional analysis and is analogous to Dahneke's adjusted sphere expression. In applying this expression to nonspherical objects, we argue for the use of two previously developed drag approximations in the continuum (Kn → 0) and free molecular (Kn → ∞) regimes: the Hubbard–Douglas approximation and the projected area (PA) approximation, respectively. These approximations lead to two calculable geometric parameters for any particle: the Smoluchowski radius, R S, and the projected area, PA. Dimensional analysis reveals that Kn should be calculated with PA/πR S as the normalizing length scale, and with Kn defined in this manner, traditional relationships for the slip correction factor should apply for arbitrarily shaped particles. Furthermore, with this expression, Kn-dependent parameters, such as the dynamic shape factor, are readily calculable for nonspherical objects. DSMC calculations of the orientationally averaged drag on spheres and test aggregates (dimers, and open and dense 20-mers) in the range Kn = 0.05–10 provide strong support for the proposed method for friction factor calculation in the transition regime. Experimental measurements of the drag on aggregates composed of 2–5 primary particles further agree well with DSMC results, with differences of less than 10% typically between theoretical predictions, numerical calculations, and experimental measurements. Copyright 2012 American Association for Aerosol Research

Superhydrophobic, hierarchical, plasma-nanotextured polymeric microchannels sustaining high-pressure flows

We fabricated superhydrophilic and superhydrophobic polymeric microfluidic devices with controlled hierarchical, random roughness, using plasma processing. We implemented a dye staining technique to visually demonstrate the persistence of the superhydrophobic state under flow for pressures in excess of 2.5 bar inside the microchannel. We further confirmed the stability of superhydrophobicity by pressure drop measurements, friction factor and slip length calculations under laminar flow conditions. We also compared identical rough superhydrophilic and superhydrophobic microchannels showing reduced pressure drop in the latter by as much as 22 %. Plasma etching and simultaneous nanotexturing (followed by optional fluorocarbon plasma deposition) are thus shown as an easy-to-implement method for attaining robust Cassie-state against high-pressure microchannel flows.

Forced convection heat transfer and flow characteristics in laminar to turbulent transition region in rectangular channel

Experimental investigations are performed on the forced convection heat transfer and friction characteristics in laminar to turbulent transition region in a vertical heated rectangular channel. The experiment is designed for analyzing the effect of Prandtl number on the heat transfer and friction characteristics in the transition region. Seven groups of experiments are carried out within the range of Reynolds number from 1000 to 2×104, and the Prandtl number in each group is 2.10, 2.34, 2.51, 2.69, 2.93, 3.18, and 3.45, respectively. The results show that the lower and the upper critical Reynolds number of transition region increase with the decrease of Prandtl number. However, the friction factors increase with increasing Prandtl number for a fixed Reynolds number in the transition region. In addition, the comparisons between present experimental data and classical correlations indicate that none of the existing correlations could be extended to predict the present friction and heat transfer characteristics in the transition region of the heated channel. Based on the experimental data, the empirical correlations for the calculation of friction factor and heat transfer coefficient in the rectangular channel in the flow transition region of forced circulation have been developed.

Gene expression programming analysis of implicit Colebrook–White equation in turbulent flow friction factor calculation

Estimating head losses due to friction in closed pipes is an important task in the solution of many practical problems in the different branches of the engineering profession. The hydraulic design and analysis of water distribution systems are two prime examples. Many consider the Darcy–Weisbach equation to be the most fundamentally sound method for evaluating head losses due to friction in closed pipe conduits. The implicit Colebrook–White equation has been widely used to estimate the friction factor for turbulent fluid-flow in Darcy–Weisbach equation. A fast, accurate, and robust resolution of the Colebrook–White equation is, in particular, necessary for scientific intensive computations. For instance, numerical simulations of pipe flows require the computation of the friction coefficient at each grid point and for each time step. For long-term simulations of long pipes, the Colebrook–White equation must therefore be solved a huge number of times and hence this is the main reason for attempting to develop an accurate explicit relationship that is a reasonable approximation for the Colebrook–White equation. This paper examines the potential of genetic programming (GP) based technique in estimating flow friction factor in comparison with the most currently available explicit alternatives to the Colebrook–White equation. The performance of the gene expression programming (GEP), a variant of GP, was compared with most available approximations using some statistic parameters for error estimation. The comparison test results reveal that by using GEP, the friction factor can be identified precisely.

Thermal performance and pressure drop analysis of nanofluids in turbulent forced convective flows

In this research the enhancement of nanofluids convective heat transfer through a circular tube with a constant heat flux condition in the turbulent flow regime is numerically studied. All of the nanofluid properties depend on temperature and nanoparticle volume concentration. The incompressible and steady-state forms of continuity, Navier–Stokes and energy equations have been solved using finite volume approach with the SIMPLER algorithm. In order to demonstrate the validity and precision of the numerical procedure, calculated friction factors and Nusselt numbers have been compared with the experimental data and the well-known correlations. To attain the best prediction, the different turbulence models are examined and it has been observed that the best model to predict the near wall treatment is based on enhanced wall function in the κ–ɛ turbulence model. The effects of nanoparticle concentration (1–10% Al2O3) in EG/water mixture, Reynolds and Prandtl numbers on the heat transfer rate have been investigated. A dimensionless effectiveness quantity has been defined to measure the thermal performance of nanofluid in comparison with the base fluid with the same Reynolds number. But for a fixed pumping power, due to more increase of viscosity, the nanofluids heat transfer coefficient has been decreased by adding nanoparticle concentration. From the results, it can be deduced that for a fixed Reynolds number, increasing the particle concentration enhances convective heat transfer rate considerably. Moreover, there is a large pressure drop and pumping power when using nanofluids instead of base fluid with the same Reynolds number. Thus using nanofluids may be not a good candidate for the practical applications in turbulence region, in which an increase in pumping power is an important problem.

Distribution Analysis of Freight Transportation with Gravity Model and Genetic Algorithm

The application of a gravity model in freight modeling work on both short-haul and long-haul trips is discussed. A commodity-based gravity model was developed to assess the distribution of freight by long-haul trucks in southeastern Virginia. Although gravity models have been used extensively in transportation studies, little work has been done to address the special characteristics of freight transportation, such as the definition of friction factors and the differences between long-haul and short-haul trips. Results of a recent study of these and similar problems provide valuable insight into freight distribution modeling. A new calibration method that used a genetic algorithm was applied, various commodities were modeled, and the impact of the commodities on the accuracy of the gravity model was studied. Both travel time and travel distance were tested to generate the impedance for friction factors; results showed that for commodity-based long-haul models, travel times were more appropriate for friction factor calculations. In addition, results showed that the gamma function was more suitable than the exponential function for friction factor calculations. Extensive analyses of the causes of variation between observed values and the gravity model outputs are provided. The analyses and conclusions may help modelers better understand characteristics specific to freight transportation and can promote model constructions with greater accuracy and efficiency.

New explicit correlations for turbulent flow friction factor

Two new correlations of single-phase friction factor for turbulent pipe flow are shown in this paper. These two formulas are actually explicit approximations of iterative Colebrook's relation for calculation of flow friction factor. Calculated friction factors are valid for whole turbulent flow including hydraulically smooth and rough pipes with special attention on transient zone of turbulence between them. Hydraulically smooth regime of turbulence does not occur only in total absence of roughness of inner pipe surface, but also, four new relations for this theoretical regime are presented. Some recent formulas for turbulent flow friction calculation are also commented.

Newly developed friction factor correlation for pipe flow and flow assurance

The purpose of this research is to present petroleum and chemical engineers with a new, practical, and fundamental equation that accurately determines the friction losses in traditional and modern piping systems. The results of this study begin with a necessary mathematical and historical review of determining pipe friction factors under smooth and rough conditions. These formulas provided a base for a statistical evaluation of the calculated friction factors associated with rough and smooth pipes. A new formula is developed, making it easy to calculate explicitly without carrying out rigorous iterative methods. Our new friction factor correlation was based on the nonlinear multivariable surface fitting tool in MATLAB. The final equation correlates the friction factor to the Reynolds number and relative roughness by means of simple logarithmic and exponential functions. The validation and accuracy of the model was tested by using statistical analysis and comparison to other existing correlations. The Ghanbari–Farshad–Rieke’s correlation generates superior results over the existing standard friction factor equations. Key words: Friction factor, piping, relative roughness, Reynolds’ number.

A new explicit equation for accurate friction factor calculation of smooth pipes

Calculation of friction factor for smooth pipes in fully developed flow is important for heat transfer applications. Many different coefficients in the Prandtl equation (Prandtl, L., 1949. Führer durch die Strömungslehre. F. Vieweg & S, Braunschweig.), or PKN correlation [Kakac, S., Shah, R.K., Aung, W., 1987. Handbook of Single-Phase Convective Heat Transfer. John Wiley & Sons; Rohsenow, W.M., Hartnett, J.P., Cho, Y.I., 1998. Handbook of Heat Transfer. McGraw-Hill Professional.], are cited in the literature. This report reviews these coefficients and presents the original Prandtl equation based on the Fanning friction factor. In addition, a new explicit equation is presented to approximate the PKN correlation. This equation yields a more accurate approximation than the existing ones.

Closure to the Discussion of “Computer-based analysis of explicit approximations to the implicit Colebrook–White equation in turbulent flow friction factor calculation” by Dejan Brkić

Closure to the Discussion of “Computer-based analysis of explicit approximations to the implicit Colebrook–White equation in turbulent flow friction factor calculation” by Dejan Brkić

Closure to “Discussion: ‘A Novel Explicit Equation for Friction Factor in Smooth and Rough Pipes’ ” (2011, ASME J. Fluids Eng., 133, p. 015501)

The discussion made by Tajadura and Gonzales (1) necessitates the clarification of the comments about our paper (2). The same notation and comment numbers are used here, to respond to the following comments.It should be expected that the three equations, which were proposed for the calculation of friction factor, should give almost the same results. Otherwise, we should be in doubt about the correctness of a formula that gives different results.The new equation presented in Ref. 2 can be used for turbulent flows and there is no limitation comparing to other classical equations.The study given by Avci and Karagoz (2) presents a new approach to obtain the friction factor explicitly, depending on surface roughness and Reynolds number. It gives an alternative way for friction factor calculation. It is not a pure empirical equation and the derivation of this formula was also given in this paper.Actually, a new formula must be compared with experimental data rather than other empirical formulas. Therefore, in our paper, the proposed formula is compared with experimental data taken from literature. Detailed information on the experiments and experimental results including “Princeton superpipe” can be found in related literature and is not given here.

Rheology and fluid dynamics properties of sugarcane juice

The sugarcane juice is a relatively low-cost agricultural resource, abundant in South Asia, Central America and Brazil, with vast applications in producing ethanol biofuel. In that way, a good knowledge of the rheological properties of this raw material is of crucial importance when designing and optimizing unit operations involved in its processing. In this work, the rheological behavior of untreated (USCJ, 17.9 °Brix), clarified (CSCJ, 18.2 °Brix) and mixed (MSCJ, 18.0 °Brix) sugarcane juices was studied at the temperature range from 277K to 373K, using a cone-and-plate viscometer. These fluids were found to present a Newtonian behavior and their flow curves were well-fitted by the viscosity Newtonian model. Viscosity values lied within the range 5.0×10−3Pas to 0.04×10−3Pas in the considered temperature interval. The dependence of the viscosity on the temperature was also successfully modeled through an Arrhenius-type equation. In addition to the dynamic viscosity, experimental values of pressure loss in tube flow were used to calculate friction factors. The good agreement between predicted and measured values confirmed the reliability of the proposed equations for describing the flow behavior of the clarified and untreated sugarcane juices.

Thermo-hydraulic characterization of a louvered fin and flat tube heat exchanger

In the present study, a whole heat exchanger with a hydraulic diameter of 2.3 mm is tested, which is a minichannel heat exchanger according to the Kandlikar classification. This is a louvered fin and flat tube heat exchanger currently used in car cooling systems, also known as radiator. A glycol–water mixture (60/40 in volume) circulates through the tubes at flows ranging from 100 to 7800 l/h and at a supply temperature of 90 °C. This fluid is cooled with ambient air at a temperature of 20 °C and at frontal air velocities varying between 0.5 and 7 m/s. The thermohydraulic performance of the heat exchanger is compared with the classical correlations given in the literature for the heat transfer and the friction factor calculation. On the glycol–water side the heat exchanger is characterized for Reynolds numbers from 30 to 8000. A first comparison is carried out with the correlations available in the literature with a purely predictive model by obtaining a predictive value with a systematic under prediction lower than 10%. In a second step a semi-empirical model is considered to identify the experimental heat transfer coefficients for this application.

A Simple Model for Turbulent Boundary Layer Momentum Transfer on a Flat Plate

AbstractA simple model is presented for turbulent momentum transfer on a flat plate. The proposed model is based on some polynomial velocity profiles in a laminar sublayer as well as in a fully developed boundary layer and two integral boundary layer equations. The model could be used for the calculation of boundary layer thickness, velocity profile and skin friction factor on the flat plate. The calculated results are in very good agreement with other proposed empirical correlations.

Alternative Sizing Methodology for Compact Heat Exchangers of the Spiral Type

A rapid sizing methodology for compact heat exchangers of the spiral plate type is presented. The methodology allows for the determination of the exchanger geometry such that full pressure drop utilization is achieved on both streams. This is done by considering plate width and plate spacing as continuous variables. The resulting values are the basis for selecting the final exchanger dimensions according to standard dimensions. The design approach makes use of empirical correlations for the calculation of heat transfer coefficient and friction factor based on average curvature. The approach is demonstrated using two case studies.

Computer-based analysis of explicit approximations to the implicit Colebrook–White equation in turbulent flow friction factor calculation

The implicit Colebrook-White equation has been widely used to estimate the friction factor for turbulent fluid-flow in rough-pipes. In this paper, the state-of-the-art review for the most currently available explicit alternatives to the Colebrook-White equation, is presented. An extensive comparison test was established on the 20x500 grid, for a wide range of relative roughness (@e/D) and Reynolds number (R) values (1x10^-^6=<@e/D=<5x10^-^2; 4x10^3=

Discussion of “Turbulent Flow Friction Factor Calculation Using a Mathematically Exact Alternative to the Colebrook–White Equation” by Jagadeesh R. Sonnad and Chetan T. Goudar

Discussion of “Turbulent Flow Friction Factor Calculation Using a Mathematically Exact Alternative to the Colebrook–White Equation” by Jagadeesh R. Sonnad and Chetan T. Goudar