scholarly journals General Turbulent Pipe Flow Scale-Up Correlation for Rheologically Complex Fluids

1967 ◽  
Vol 7 (03) ◽  
pp. 252-258 ◽  
Author(s):  
D.L. Lord ◽  
B.W. Hulsey ◽  
L.L. Melton
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Data Analysis ◽  
Calcium Carbonate ◽  
Turbulent Flow ◽  
Scale Up ◽  
Flow Data ◽  
Cylindrical Pipe ◽  
Blasius Equation ◽  
Extensive Experimental Data

Abstract A mathematical model d1.20?p/4L = A(8v)s derived from the Blasius equation is proposed to be applicable to turbulent flow through straight cylindrical pipe for time-independent fluids which produce a diameter family of straight parallel lines on a log (d?p/4L) vs log (8v/d) plot or stress-flow diagram. Such a correlation should permit scale-up with data taken from one pipe diameter for Newtonian, inelastic non-Newtonian and viscoelastic fluids, such as dilute polymer fracturing fluids, which produce considerable frictional pressure reductions. The Newtonian diameter exponent value 1. 20 is shown to be empirically valid for turbulent non-Newtonian flow by application of numerical analysis methods. Multiple regression analysis is applied to a logarithmic linearization of the proposed model. An improved data fit results from further linearization achieved by taking linear terms from a generalized Taylor's series expansion about the multiple regression coefficients. Extensive experimental data obtained in five pipe diameters with water, sodium carboxymethylcellulose solutions, guar gum solutions, bentonite clay suspensions and calcium carbonate slurries are presented. Except for calcium carbonate slurries, which were investigated rather than time-dependent cement slurries, the fluids studied contain drilling or fracturing fluid additives. The behavior exhibited by these fluids is considered typical of most fluids encountered in drilling, cementing and fracturing operations. INTRODUCTION Considerable difficulties have been encountered in predicting turbulent flow pressure drops produced by non-Newtonian fluids flowing through straight cylindrical pipe. Correlations previously presented require extensive experimental data which represent several pipe diameters and a wide flow rate range to estimate the necessary scale-up parameters.1-7 One must implement either elaborate experimental apparatus or spend considerable time and effort to gather the se data. Presented here is a correlation method which should minimize the experimental effort and data analysis normally required by utilizing flow data taken with only one pipe diameter. Turbulent flow data (up-stream and dawn-stream pressure and volumetric flow rates) were collected for five pipe diameters through operation of a small pipeline system having an electronic data acquisition and digitizing system. A mathematical model derived from the Blasius equation was utilized to describe the functional relationship between pressure drop and the two independent variables, diameter and average flow velocity. A correlation, which should produce a valid single-pipe scale-up, resulted from a computer-implemented statistical and numerical data analysis for several time-independent non-Newtonian fluids.

scholarly journals Utilização de soluções numéricas e analíticas na descrição da secagem do eixo central de jaca

2016 ◽  
Vol 11 (3) ◽  
pp. 131 ◽  
Author(s):  
Hyago Costa Sousa ◽  
Nathan José Pereira da Silva ◽  
Emmanuel Moreira Pereira ◽  
Carlos Roberto Marinho da Silva Filho ◽  
Weysser Felipe Cândido de Souza
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Data Analysis ◽  
Mathematical Models ◽  
Analytical Solutions ◽  
Central Axis ◽  
Page Model ◽  
Different Temperatures ◽  
Best Fit ◽  
Air Exchange

<p>Objetivou-se descrever o processo de secagem do eixo central de jaca por modelos matemáticos e determinar qual modelo matemático apresentou os melhores ajustes para as características avaliadas. Foi estudado a secagem do eixo central de jaca em estufa com circulação e renovação de ar em quatro temperaturas diferentes 50, 60 70 e 80 °C utilizando modelos matemáticos para a descrição da quantidade de água no eixo central de jaca, foram utilizados frutos adquiridos no pomar do Centro de Ciências Humanas, Sociais e Agrarias, Bananeiras-PB pertencente a Universidade Federal da Paraíba. De acordo com a análise de dados o modelo de Page foi o que apresentou os melhores coeficientes de determinação e os melhores ajustes aos dados experimentais.</p><p align="center"><strong><em>Use of numerical and analytical solutions in the description of the drying of the central axis of jackfruit</em></strong></p><p><strong>Abstract</strong>: This study aimed to describe the process of drying the central axis of jackfruit by mathematical models and determine which mathematical model presented the best fit for the characteristics. This study investigated the drying of the central axis of jackfruit in an oven with circulation and air exchange at four different temperatures 50, 60, 70 and 80 ° C using mathematical models to describe the amount of water in the central axis of jackfruit, fruits were utilized acquired in orchard Humanities Center, Social and Agricultural, Bananeiras-PB belonging to the Federal University of Paraíba. According to the data analysis the Page model showed the best determination coefficients and the best fit to the experimental data.</p>

On the modelling of turbulent flow over low-angle sand dunes

2019 ◽  
Author(s):  
И.И. Потапов ◽  
К.С. Снигур ◽  
Г.И. Цой
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Shear Stress ◽  
Turbulent Flow ◽  
River Flow ◽  
Numerical Solutions ◽  
Control Volume ◽  
Sand Dunes ◽  
Wall Function ◽  
Wall Functions

Предложена математическая модель задачи о движении двумерного турбулентного потока жидкости в напорном канале с волнистым дном. Математическая модель включает уравнения Рейнольдса, уравнения переноса кинетической энергии и диссипации турбулентности, приведенные к квазигидродинамическому виду. Предложен алгоритм решения задачи с помощью метода контрольных объемов и метода конечных элементов. Численно решена задача о движении турбулентного потока над неподвижными пологими песчаными дюнами. Выполнено сравнение полученных расчетов с экспериментальными данными. Purpose. The aim of the paper is the development of mathematical models describing a turbulent river flow along gently sloping dunes and allowing estimation of the contribution of gently sloping dunes on the flow hydraulic resistance. Methodology. A quasi-hydrodynamic form of the classical RANS equations are used for describing the hydrodynamic flow. The standard k model is used for the turbulence viscosity while the equations have been transformed to the quasi-hydrodynamic form. A wall functions method is used for describing the flow near solid channel wall. Results. A new mathematical model for the problem of turbulent flow in a pressure channel with low-angle dunes is proposed. An algorithm for solving the problem is proposed. It is based on the control volume method and the finite element method. The problem of the turbulent flow over 6 fixed low-angle sand dunes is solved numerically. Numerical solutions are obtained with four different wall functions. A comparative analysis of the obtained solutions with the experimental data is carried out. Findings. It is shown that the proposed mathematical model describes the turbulent flow over low-angle dunes qualitatively and quantitatively. The solution obtained with the Volkov wall function provides the best agreement with the experiment. It is found out that the bed shear stress obtained in the near-wall computational cell by the wall functions method does not qualitatively agree with the experimental data for all considered wall functions. At the same time, the shear stress obtained in the next calculation cell agrees with the experimental data qualitatively and quantitatively. The average relative error of the shear stress obtained with the Volkov wall function is 6.84.

scholarly journals A Reduced Drosophila Model Whose Characteristic Behavior Scales Up

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Andrew David Irving
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Scale Up ◽  
Independent Study ◽  
Original Model ◽  
Testing Hypotheses ◽  
The Core ◽  
Characteristic Behavior ◽  
Drosophila Model ◽  
Segment Polarity

Computational biology seeks to integrate experimental data with predictive mathematical models—testing hypotheses which result from the former through simulations of the latter. Such models should ideally be approachable and accessible to the widest possible community, motivating independent studies. One of the most commonly modeled biological systems involves a gene family critical to segmentation in Drosophila embryogenesis—the segment polarity network (SPN). In this paper, we reduce a celebrated mathematical model of the SPN to improve its accessibility; unlike its predecessor our reduction can be tested swiftly on a widely used platform. By reducing the original model we identify components which are unnecessary; that is, we begin to detect the core of the SPN—those mechanisms that are essentially responsible for its characteristic behavior. Hence characteristic behavior can scale up; we find that any solution of our model (defined as a set of conditions for which characteristic behavior is seen) can be converted into a solution of the original model. The original model is thus made more accessible for independent study through a more approachable reduction which maintains the robustness of its predecessor.

Evaluation of the statistical convergence of turbulent flow data

2017 ◽  
Author(s):  
Ramon Martins ◽  
Roney Thompson ◽  
Aristeu Silveira Neto ◽  
Gilmar MOMPEAN ◽  
João Rodrigo Andrade
Keyword(s):  
Turbulent Flow ◽  
Statistical Convergence ◽  
Flow Data

The substantiation of the formalized estimation of effectiveness of technological and production systems

2018 ◽  
Vol 15 (1) ◽  
pp. 169-181
Author(s):  
M. I. Sidorov ◽  
М. Е. Stavrovsky ◽  
V. V. Irogov ◽  
E. S. Yurtsev
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Production Systems ◽  
Van Der Pol

Using the example of van der Pol developed a mathematical model of frictional self-oscillations in topochemically kinetics. Marked qualitative correspondence of the results of calculation performed using the experimental data of researchers.

scholarly journals Revisiting the Analysis of the Isochronous Mass Measurements of Uranium Fission Fragments at the ESR

2020 ◽  
Vol 227 ◽  
pp. 02012
Author(s):  
R. S. Sidhu ◽  
R. J. Chen ◽  
Yu. A Litvinov ◽  
Y. H. Zhang ◽  
Keyword(s):  
Experimental Data ◽  
Data Analysis ◽  
State Of The Art ◽  
Fission Products ◽  
Mass Measurements ◽  
Fission Fragments ◽  
Uranium Fission

The re-analysis of experimental data on mass measurements of ura- nium fission products obtained at the ESR in 2002 is discussed. State-of-the-art data analysis procedures developed for such measurements are employed.

scholarly journals Exhaust Noise Reduction by Application of Expanded Collecting System in Pneumatic Tools and Machines

Energies ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1592
Author(s):  
Dominik Gryboś ◽  
Jacek S. Leszczyński ◽  
Dorota Czopek ◽  
Jerzy Wiciak
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Noise Reduction ◽  
Sound Pressure ◽  
Acoustic Pressure ◽  
Pressure Level ◽  
Computational Results ◽  
Noise Measurements ◽  
Exhaust Noise ◽  
Collecting System

In this paper, we demonstrate how to reduce the noise level of expanded air from pneumatic tools. Instead of a muffler, we propose the expanded collecting system, where the air expands through the pneumatic tube and expansion collector. We have elaborated a mathematical model which illustrates the dynamics of the air flow, as well as the acoustic pressure at the end of the tube. The computational results were compared with experimental data to check the air dynamics and sound pressure. Moreover, the study presents the methodology of noise measurement generated in a pneumatic screwdriver in a quiet back room and on a window-fitting stand in a production hall. In addition, we have performed noise measurements for the pneumatic screwdriver and the pneumatic screwdriver on an industrial scale. These measurements prove the noise reduction of the pneumatic tools when the expanded collecting system is used. When the expanded collecting system was applied to the screwdriver, the measured Sound Pressure Level (SPL) decreased from 87 to 80 dB(A).

scholarly journals Assessment of Steady and Unsteady Friction Models in the Draining Processes of Hydraulic Installations

Water ◽  
2021 ◽  
Vol 13 (14) ◽  
pp. 1888
Author(s):  
Óscar E. Coronado-Hernández ◽  
Ivan Derpich ◽  
Vicente S. Fuertes-Miquel ◽  
Jairo R. Coronado-Hernández ◽  
Gustavo Gatica
Keyword(s):  
Mathematical Model ◽  
Turbulent Flow ◽  
Water Velocity ◽  
Experimental Facility ◽  
Governing Equations ◽  
Pressure Oscillations ◽  
Air Pocket ◽  
Friction Models ◽  
The Mathematical Model

The study of draining processes without admitting air has been conducted using only steady friction formulations in the implementation of governing equations. However, this hydraulic event involves transitions from laminar to turbulent flow, and vice versa, because of the changes in water velocity. In this sense, this research improves the current mathematical model considering unsteady friction models. An experimental facility composed by a 4.36 m long methacrylate pipe was configured, and measurements of air pocket pressure oscillations were recorded. The mathematical model was performed using steady and unsteady friction models. Comparisons between measured and computed air pocket pressure patterns indicated that unsteady friction models slightly improve the results compared to steady friction models.

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