scholarly journals SOLUTIONS IN EXPLICIT FORM FOR DETERMINING THE HYDRAULIC RESISTANCE COEFFICIENT FOR TURBULENT FLOW

2019 ◽  
Vol 9 (4) ◽  
pp. 39-46
Author(s):  
Maxim Nikolaevich NIKITIN ◽  
Tatyana Sergeevna SOLOVYOVA ◽  
Olga Vladimirovna SHLYAHTINA
Keyword(s):  
Comparative Analysis ◽  
Computational Complexity ◽  
Turbulent Flow ◽  
Iterative Solution ◽  
Resistance Coefficient ◽  
Explicit Solutions ◽  
Substitution Method ◽  
Relative Roughness ◽  
Acceptable Accuracy ◽  
Successive Substitution

A comparative analysis of explicit solutions of the Colebrook-White equation is carried out. The median values of relative deviations, coefficients of determination and computational complexities for each approximation were obtained. The results of the iterative solution of the Colebrook-White equation by successive substitution method were used as the intrinsic solution. Approximations by B. Eck and A.R. Vatankhah were identified as the most effective in terms of computational complexity. It was shown that widely used approximations by P.R.H. Blasius, A.D. Altshul and J. Nikuradze although simple, provide acceptable accuracy only within restricted ranges of Reynolds and relative roughness.

scholarly journals Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

2017 ◽  
Author(s):  
Dejan Brkić ◽  
Žarko Ćojbašić
Keyword(s):  
Turbulent Flow ◽  
Friction Factor ◽  
Iterative Solution ◽  
Good Prediction ◽  
Pipe Surface ◽  
Flow Friction ◽  
Relative Roughness ◽  
Complex Models ◽  
Transient Zone ◽  
Maximal Relative Error

Today, Colebrook’s equation is mostly accepted as an informal standard for modeling of turbulent flow in hydraulically smooth and rough pipes including transient zone in between. The empirical Colebrook’s equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of inner pipe surface (ε/D). It is implicit in unknown friction factor (λ). Implicit Colebrook’s equation cannot be rearranged to derive friction factor (λ) directly and therefore it can be solved only iteratively [λ=f(λ, R, ε/D)] or using its explicit approximations [λ≈f(R, ε/D)]. Of course, approximations carry in certain error compared with the iterative solution where the highest level of accuracy can be reached after enough number of iterations. The explicit approximations give a relatively good prediction of the friction factor (λ) and can reproduce accurately Colebrook’s equation and its Moody’s plot. Usually, more complex models of approximations are more accurate and vice versa. In this paper, numerical values of parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After this improvement computational burden stays unchanged while accuracy of approximations increases in some of the cases very significantly.

scholarly journals Comparative analysis of the geometrized histogram method and the neural network method for road markings recognition

2021 ◽  
pp. 1-22
Author(s):  
Aleksei Valerievich Podoprosvetov ◽  
Dmitry Anatolevich Anokhin ◽  
Konstantin Ivanovich Kiy ◽  
Igor Aleksandrovich Orlov
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Comparative Analysis ◽  
Computational Complexity ◽  
Video Sequences ◽  
Histogram Method ◽  
Neural Network Method ◽  
The Neural Network ◽  
Network Method ◽  
Accuracy Speed

This paper compares two approaches to determining road markings from video sequences, namely, the method of finding the markings using geometrized histograms and the method based on neural networks. An independent open dataset TuSimple is used to conduct a comparative analysis of the algorithms. Since the investigated methods have different architectures, their work is evaluated according to the following metrics: Accuracy, speed (relative FPS), general computational complexity of the algorithm (TFlops).

ROUGHNESS EFFECT OF DIFFERENT GEOMETRIES ON MICRO GAS FLOWS BY LATTICE BOLTZMANN SIMULATION

2009 ◽  
Vol 20 (06) ◽  
pp. 953-966 ◽  
Author(s):  
CHAOFENG LIU ◽  
YUSHAN NI ◽  
YONG RAO
Keyword(s):  
Surface Roughness ◽  
Lattice Boltzmann ◽  
Experimental Studies ◽  
Resistance Coefficient ◽  
Lattice Boltzmann Model ◽  
Gas Flows ◽  
Fractal Boundary ◽  
Roughness Effects ◽  
Roughness Effect ◽  
Relative Roughness

The roughness effects of the gas flows of nitrogen and helium in microchannels with various relative roughnesses and different geometries are studied and analyzed by a lattice Boltzmann model. The shape of surface roughness is simulated to be square, sinusoidal, triangular, and fractal. Numerical computations compared with theoretical and experimental studies show that the roughness geometry is an important factor besides the relative roughness in the study of the effects of surface roughness. The fractal boundary presents a higher influence on the velocity field and the resistance coefficient than other regular boundaries at the same Knudsen number and relative roughness. In addition, the effects of rarefaction, compressibility, and roughness are strongly coupled, and the roughness effect should not be ignored in studying rarefaction and compressibility of the microchannel as the relative roughness increases.

Effects of Roughness on Turbulent Flow in Microchannels and Minichannels

2008 ◽  
Author(s):  
Timothy P. Brackbill ◽  
Satish G. Kandlikar
Keyword(s):  
Experimental Study ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Roughness Parameter ◽  
Reynolds Numbers ◽  
Turbulent Regime ◽  
Roughness Effects ◽  
Relative Roughness ◽  
Roughness Elements ◽  
Moody Diagram

The effect of roughness ranging from smooth to 24% relative roughness on laminar flow has been examined in previous works by the authors. It was shown that using a constricted parameter, εFP, the laminar results were predicted well in the roughened channels ([1],[2],[3]). For the turbulent regime, Kandlikar et al. [1] proposed a modified Moody diagram by using the same set of constricted parameters, and using the modification of the Colebrook equation. A new roughness parameter εFP was shown to accurately portray the roughness effects encountered in laminar flow. In addition, a thorough look at defining surface roughness was given in Young et al. [4]. In this paper, the experimental study has been extended to cover the effects of different roughness features on pressure drop in turbulent flow and to verify the validity of the new parameter set in representing the resulting roughness effects. The range of relative roughness covered is from smooth to 10.38% relative roughness, with Reynolds numbers up to 15,000. It was found that using the same constricted parameters some unique characteristics were noted for turbulent flow over sawtooth roughness elements.

scholarly journals The regularities of resistance and flow in pipes and wide channels

2018 ◽  
Vol 193 ◽  
pp. 02034
Author(s):  
Ilya Bryansky ◽  
Yuliya Bryanskaya ◽  
Аleksandra Оstyakova
Keyword(s):  
Comparative Analysis ◽  
Velocity Profile ◽  
Hydraulic Resistance ◽  
Cross Section ◽  
Resistance Coefficient ◽  
Hydraulic Structures ◽  
Hydraulic Characteristics ◽  
Hydraulic Resistance Coefficient ◽  
Logarithmic Velocity Profile

The data of hydraulic characteristics of flow are required to be more accurate to increase reliability and accident-free work of water conducting systems and hydraulic structures. One of the problems in hydraulic calculations is the determination of friction loss that is associated with the distribution of velocities over the cross section of the flow. The article presents a comparative analysis of the regularities of velocity distribution based on the logarithmic velocity profile and hydraulic resistance in pipes and open channels. It is revealed that the Karman parameter is associated with the second turbulence constant and depend on the hydraulic resistance coefficient. The research showed that the behavior of the second turbulence constant in the velocity profile is determined mainly by the Karman parameter. The attached illustrations picture the dependence of logarithmic velocity profile parameters based on different values of the hydraulic resistance coefficient. The results of the calculations were compared to the experimental-based Nikuradze formulas for smooth and rough pipes.

The dispersion of matter in turbulent flow through a pipe

1954 ◽  
Vol 223 (1155) ◽  
pp. 446-468 ◽  
Keyword(s):  
Turbulent Flow ◽  
Capillary Tube ◽  
Resistance Coefficient ◽  
Mean Flow ◽  
Combined Action ◽  
Flow Through ◽  
The Mean ◽  
Coefficient Of Diffusion ◽  
Good Agreement ◽  
Made In

The dispersion of soluble matter introduced into a slow stream of solvent in a capillary tube can be described by means of a virtual coefficient of diffusion (Taylor 1953 a ) which represents the combined action of variation of velocity over the cross-section of the tube and molecluar diffusion in a radial direction. The analogous problem of dispersion in turbulent flow can be solved in the same way. In that case the virtual coefficient of diffusion K is found to be 10∙1 av * or K = 7∙14 aU √ γ . Here a is the radius of the pipe, U is the mean flow velocity, γ is the resistance coefficient and v * ‘friction velocity’. Experiments are described in which brine was injected into a straight 3/8 in. pipe and the conductivity recorded at a point downstream. The theoretical prediction was verified with both smooth and very rough pipes. A small amount of curvature was found to increase the dispersion greatly. When a fluid is forced into a pipe already full of another fluid with which it can mix, the interface spreads through a length S as it passes down the pipe. When the interface has moved through a distance X , theory leads to the formula S 2 = 437 aX ( v * / U ). Good agreement is found when this prediction is compared with experiments made in long pipe lines in America.

scholarly journals Numerical simulation of turbulent flow through Schiller’s wavy pipe

2014 ◽  
Vol 761 ◽  
pp. 241-260 ◽  
Author(s):  
G. Daschiel ◽  
V. Krieger ◽  
J. Jovanović ◽  
A. Delgado
Keyword(s):  
Turbulent Flow ◽  
Structural Changes ◽  
Stokes Equations ◽  
Resistance Coefficient ◽  
Navier Stokes ◽  
Cross Sectional ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
Pressure Resistance ◽  
Almost All

AbstractThe development of incompressible turbulent flow through a pipe of wavy cross-section was studied numerically by direct integration of the Navier–Stokes equations. Simulations were performed at Reynolds numbers of $4.5\times 10^{3}$ and $10^{4}$ based on the hydraulic diameter and the bulk velocity. Results for the pressure resistance coefficient ${\it\lambda}$ were found to be in excellent agreement with experimental data of Schiller (Z. Angew. Math. Mech., vol. 3, 1922, pp. 2–13). Of particular interest is the decrease in ${\it\lambda}$ below the level predicted from the Blasius correlation, which fits almost all experimental results for pipes and ducts of complex cross-sectional geometries. Simulation databases were used to evaluate turbulence anisotropy and provide insights into structural changes of turbulence leading to flow relaminarization. Anisotropy-invariant mapping of turbulence confirmed that suppression of turbulence is due to statistical axisymmetry in the turbulent stresses.

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