Experimental analysis of the effect of bed-load movement on flow hydraulic characteristics

In this study, the effect of bed-load movement on mean flow characteristics was evaluated in two rigid rectangular flumes. The experiments consisted of creating flow conditions carrying sediments with mean diameters of D50 = 0.5, 0.6, and 2.84 mm over both smooth and rough beds. Various sediment concentrations were injected at the upstream end of the flume at non-deposit injection rates to study the effect of various concentrations on flow resistance. The effect of sediment movement on flow resistance was examined by comparing the results with those of clear water flows (without sediment injection on both smooth and rough beds). The results showed that the sediment transport in maximum injection rate may increase the friction factor up to 50 and 58 percent for smooth bed, and up to about 75 and 80 percent in rough bed with mean diameter of 0.5 and 0.6 mm. Besides, for D50 = 2.84 mm, the friction factor decreased in smooth bed and increased up to 50 percent in rough bed. In general, it can be concluded that bed-load transport can be increased by the flow friction factor. The results also showed that bed-loads may decrease the average velocity and increase shear velocity with extraction of momentum from the flow, which both of mentioned factors may increase the flow friction factor. Raising the bed-load concentration in the flow may increase the elevation of the friction factor, approaching a constant value after reaching to the aggregation threshold and generation of bed forms.

EXCEL VBA-BASED USER DEFINED FUNCTIONS FOR HIGHLY PRECISE COLEBROOK’S PIPE FLOW FRICTION APPROXIMATIONS: A COMPARATIVE OVERVIEW

This review paper gives Excel functions for highly precise Colebrook’s pipe flow friction approximations developed by users. All shown codes are implemented as User Defined Functions – UDFs written in Visual Basic for Applications – VBA, a common programming language for MS Excel spreadsheet solver. Accuracy of the friction factor computed using nine to date the most accurate explicit approximations is compared with the sufficiently accurate solution obtained through an iterative scheme which gives satisfying results after sufficient number of iterations. The codes are given for the presented approximations, for the used iterative scheme and for the Colebrook equation expressed through the Lambert W-function (including its cognate Wright ω-function). The developed code for the principal branch of the Lambert W-function has additional and more general application for solving different problems from variety branches of engineering and physics. The approach from this review paper automates computational processes and speeds up manual tasks.

Excel VBA-Based User Defined Functions for Highly Precise Colebrook’s Pipe Flow Friction Approximations: A Comparative Overview

This review paper gives Excel functions for highly precise Colebrook’s pipe flow friction approximations developed by users. All shown codes are implemented as User Defined Functions – UDFs written in Visual Basic for Applications – VBA, a common programming language for MS Excel spreadsheet solver. Accuracy of the friction factor computed using nine to date the most accurate explicit approximations is compared with the sufficiently accurate solution obtained through an iterative scheme which gives satisfying results after sufficient number of iterations. The codes are given for the presented approximations, for the used iterative scheme and for the Colebrook equation expressed through the Lambert W-function (including its cognate Wright ω-function). The developed code for the principal branch of the Lambert W-function has additional and more general application for solving different problems from variety branches of engineering and physics. The approach from this review paper automates computational processes and speeds up manual tasks.

An Experimental Study of Thermohydraulic Processes in the Model of a Fuel Assembly with Micro Fuel Elements

The test section design of the TVS-MEI experimental setup intended for studying the hydrodynamics and heat transfer in a fuel assembly with micro fuel elements is developed, and the setup hydraulic circuit is modernized. The setup process characteristics correspond to the operational parameters of VVER-1000 reactor plants (a pressure up to 16 MPa and coolant temperature up to 350°C). The internal heat release in the bed of metal pebbles is obtained by high-frequency induction heating. A technology for compacting the test section made of high-strength alundum ceramics and a special clamping device for holding the bed were developed. The fuel assemblies with micro fuel elements have the outer geometrical parameters fully identical with those of the conventional assemblies with fuel rods. A technology for installing, wiring, and sealing thermocouples in the test section has been developed. Experimental studies aimed at determining the pressure loss and flow friction coefficient for a cylindrical pebble bed were carried with the following coolant operating parameters: P = (2--7) MPa and G = (0.05--0.5) kg/s. In processing the obtained experimental results, the dependences of pressure loss on the coolant mass velocity and the pebble bed flow friction on the Reynolds number were identified and plotted. The first experimental data on the temperature distribution in the pebble bed are obtained. The main objective of the experiments was to determine the possibility of heating the considered test section by using the chosen method.

Experimental Observation of a Regression Dependence for Hydrodynamic Performance of the Regular Packing

The investigational studies of regression dependence of the new efficient regular packing bed’s flow friction on gas velocity and liquid spray rate has been carried out. The tests were made by the procedure of a complete two-factor experiment. On account of experiment design matrix, there are four tests to be made to determine the regression dependence. It is found that the packing bed’s flow friction builds up along with increase of superficial gas velocity and liquid spray rate. The regression dependence that puts packing bed’s flow friction in touch with superficial gas velocity and liquid spray rate is procured. The specific dependence is valid for air velocity 1.21-3.12 m/sec and liquid spray rate 0.0080-0.0304 m3/(m2 sec). The conclusion on significance of regression dependencies has been made in terms of Student’s t-test. The sufficiency of regression equation has been inspected via the Fisher’s criterion. The resulting regression equation can be utilized in the design and engineering process of absorbers with the shock-spray packing.

Experimental analysis and ANN prediction on performances of finned oval-tube heat exchanger under different air inlet angles with limited experimental data

A high accuracy of experimental correlations on the heat transfer and flow friction is always expected to calculate the unknown cases according to the limited experimental data from a heat exchanger experiment. However, certain errors will occur during the data processing by the traditional methods to obtain the experimental correlations for the heat transfer and friction. A dimensionless experimental correlation equation including angles is proposed to make the correlation have a wide range of applicability. Then, the artificial neural networks (ANNs) are used to predict the heat transfer and flow friction performances of a finned oval-tube heat exchanger under four different air inlet angles with limited experimental data. The comparison results of ANN prediction with experimental correlations show that the errors from the ANN prediction are smaller than those from the classical correlations. The data of the four air inlet angles fitted separately have higher precisions than those fitted together. It is demonstrated that the ANN approach is more useful than experimental correlations to predict the heat transfer and flow resistance characteristics for unknown cases of heat exchangers. The results can provide theoretical support for the application of the ANN used in the finned oval-tube heat exchanger performance prediction.

Suitability for coding of the Colebrook’s flow friction relation expressed by symbolic regression approximations of the Wright-ω function

This article analyses a form of the empirical Colebrook’s pipe flow friction equation given originally by the Lambert W-function and recently also by the Wright ω-function. These special functions are used to explicitly express the unknown flow friction factor of the Colebrook equation, which is in its classical formulation given implicitly. Explicit approximations of the Colebrook equation based on approximations of the Wright ω-function given by an asymptotic expansion and symbolic regression were analyzed in respect of speed and accuracy. Numerical experiments on 8 million Sobol’s quasi-Monte points clearly show that also both approaches lead to approximately the same complexity in terms of speed of execution in computers. However, the relative error of the developed symbolic regression-based approximations is reduced significantly, in comparison with the classical basic asymptotic expansion. These numerical results indicate promising results of artificial intelligence (symbolic regression) for developing fast and accurate explicit approximations.