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.

Nonlinear waves in compacting media

1986 ◽  
Vol 164 ◽  
pp. 429-448 ◽  
Author(s):  
Victor Barcilon ◽  
Frank M. Richter
Keyword(s):  
Mathematical Model ◽  
Solitary Waves ◽  
Nonlinear Waves ◽  
Nonlinear Interaction ◽  
Phase Speed ◽  
Governing Equations ◽  
One Dimensional ◽  
The Earth ◽  
Permanent Shape ◽  
The Mathematical Model

An investigation of the mathematical model of a compacting medium proposed by McKenzie (1984) for the purpose of understanding the migration and segregation of melts in the Earth is presented. The numerical observation that the governing equations admit solutions in the form of nonlinear one-dimensional waves of permanent shape is confirmed analytically. The properties of these solitary waves are presented, namely phase speed as a function of melt content, nonlinear interaction and conservation quantities. The information at hand suggests that these waves are not solitons.

Analysis of High Pressure Transients in Water Hydraulic Pipeline Using Matlab/Simulink

2014 ◽  
Vol 621 ◽  
pp. 311-316
Author(s):  
Tian Yang Zhao ◽  
Dan Jiang ◽  
Song Yu ◽  
Jie Wang ◽  
Ping Yang
Keyword(s):  
Mathematical Model ◽  
High Pressure ◽  
Turbulent Flow ◽  
Weighting Function ◽  
Viscous Friction ◽  
Dynamic Friction ◽  
Matlab Simulink ◽  
Pressure Transients ◽  
Water Hydraulic ◽  
The Mathematical Model

Based on the continuity equation and the motion equation of fluid dynamics, a mathematical model of high pressure transients in water hydraulic pipeline is presented. In the model, the friction item is consist of steady friction item and dynamic friction item, using the Darcy-Weisbach equation to solve steady viscous friction item and using four exponential terms instead of weighting function to solve dynamic friction item. By finite difference method accompanied with Matlab/Simulink, an example of high pressure turbulent flow in water hydraulic pipeline is configured so as to simulate the dynamic characteristics of pressure transients. The comparison between the observed result and the simulation result shows the mathematical model of high pressure transients in water hydraulic pipeline with turbulent flow is reasonable.

Implicit Bidiagonal Numerical Scheme for Simulation of 2D Flood Waves

2011 ◽  
Vol 356-360 ◽  
pp. 2293-2296
Author(s):  
Guang Cai Sun
Keyword(s):  
Mathematical Model ◽  
Numerical Scheme ◽  
Open Channel ◽  
Water Velocity ◽  
Dam Break ◽  
Rectangular Cylinder ◽  
Predictor Corrector ◽  
The Mathematical Model ◽  
Depth Water ◽  
Flood Waves

This paper is concerned with a mathematical model for numerical simulation of 2D flood waves due to partial dam-break. The governing water equations are solved by an implicit bidiagonal numerical scheme, based on the MacCormack’s predictor-corrector technique. The mathematical model is used to compute 2D flood waves due to partial instantaneous symmetrical dam-break in a rectangular open channel with a rectangular cylinder barrier downstream. Results, in terms of water velocity vectors and contours of water depth, water surface, following dam-break phenomena, are investigated in the two-dimensional problems.

Fractional Order Thermoelastic Waves of Cylindrical Gold Nano-Beam

2013 ◽  
Author(s):  
Hamdy M. Youssef ◽  
Khaled A. Elsibai ◽  
Alaa A. El-Bary
Keyword(s):  
Mathematical Model ◽  
Fractional Order ◽  
Thermal Load ◽  
Laplace Transforms ◽  
Thermal Waves ◽  
Governing Equations ◽  
Elastic Parameters ◽  
The Impact ◽  
The Mathematical Model ◽  
Thermoelastic Waves

In this work, a mathematical model of cylindrical nano-beam with constant elastic parameters with fractional order heat conduction will be constructed. The governing equations of the mathematical model will be taken when the beam is quiescent first. Laplace transforms techniques will be used to get the general solution for any set of boundary conditions. The solution will be obtained for a certain model when the beam is subjected to thermal load. Inversion of Laplace transforms will be obtained numerically, and the results will be presented graphically with some comparisons to study the impact of thermal load and the effect of the fractional order parameter on the speed of progress of mechanical and thermal waves through the beam.

Concentration of Samples in Microfluidic Structure Using Joule Heating Effects

2009 ◽  
Author(s):  
Zhengwei Ge ◽  
Chun Yang
Keyword(s):  
Mathematical Model ◽  
Joule Heating ◽  
Electroosmotic Flow ◽  
Scaling Analysis ◽  
Analyte Concentration ◽  
Governing Equations ◽  
Sample Concentration ◽  
Heating Effects ◽  
Concentration Enhancement ◽  
The Mathematical Model

Microfluidic concentration is achieved using temperature gradient focusing (TGF) in a microchannel with a step change in cross-section. A mathematical model is developed to describe the complex TGF processes. The proposed mathematical model includes a set of governing equations for the applied electric potential, electroosmotic flow field, Joule heating induced temperature field, and sample analyte concentration distributions as well. Scaling analysis was conducted to estimate time scales so as to simplify the mathematical model. Numerical computations were performed to obtain the temperature, velocity and sample concentration distributions. Experiments were carried out to study the effects of applied voltage, buffer concentration, and channel size on sample concentration in the TGF processes. These effects were analyzed and summarized using a dimensionless Joule number that was introduced in this study. In addition, Joule number effect in the PDMS/PDMS microdevice was compared with the PDMS/Glass microdevice. A more than 450-fold concentration enhancement was obtained within 75 seconds in the PDMS/PDMS microdevice. Overall, the numerical simulations were found in a reasonable agreement with the experimental results.

scholarly journals Analysis of Sub-Atmospheric Pressures during Emptying of an Irregular Pipeline without an Air Valve Using a 2D CFD Model

Water ◽  
2021 ◽  
Vol 13 (18) ◽  
pp. 2526
Author(s):  
Aris D. Hurtado-Misal ◽  
Daniela Hernández-Sanjuan ◽  
Oscar E. Coronado-Hernández ◽  
Héctor Espinoza-Román ◽  
Vicente S. Fuertes-Miquel
Keyword(s):  
Water Column ◽  
Model Simulation ◽  
Water Velocity ◽  
Column Length ◽  
Cfd Model ◽  
Air Pocket ◽  
Pressure Water ◽  
Air Valve ◽  
Experimental Values ◽  
The Mathematical Model

Studying sub-atmospheric pressure patterns in emptying pipeline systems is crucial because these processes could cause collapses depending on the installation conditions (the underground pipe covering height, type, fill, and pipeline stiffness class). Pipeline studies have focused more on filling than on emptying processes. This study presents an analysis of the following variables: air pocket pressure, water velocity, and water column length during the emptying of an irregular pipeline without an air valve by two-dimensional computational fluid dynamics (2D CFD) model simulation using the software OpenFOAM. The mathematical model predicts the experimental values of the study variables. Water velocity vectors are also analysed within the experimental facility, assessing the sensitivity of the drain valve to different openings and changes in water column length during the hydraulic phenomenon.

THE MATHEMATICAL MODEL OF CALCULATION OF THE THRUST CONICAL FOIL BEARINGS

2020 ◽  
Vol 3 ◽  
pp. 3-10
Author(s):  
А.Yu. KORNEYEV ◽  
A.V. SYTIN ◽  
А.V. KUZAVKA ◽  
E.V. MISHCHENKO
Keyword(s):  
Mathematical Model ◽  
Turbulent Flow ◽  
Reynolds Equation ◽  
Lubricant Layer ◽  
Conical Part ◽  
Method Of Calculation ◽  
Foil Bearings ◽  
The Mathematical Model ◽  
Elastic Elements ◽  
Unified Method

The question of creating a unified method of calculation for the thrust and conical part of the combined thrust conical foil bearings. Mathematical model for calculating the turbulent flow of a lubricant in the conical and thrust parts of foil bearings. The design of the bearing and foil, the function of the gap in the lubricant layer of the bearing, the Reynolds equation and the equation of deformations of elastic elements are presented.

High Cycle Fatigue Cracks at Radial Fan Impellers Caused by Aeroelastic Self-Excited Impeller Vibrations: Part 2 — Mechanism and Mathematical Model

1999 ◽  
Author(s):  
Alexander Ni
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
High Cycle Fatigue ◽  
Dynamic Behaviour ◽  
Fatigue Cracks ◽  
Model Fit ◽  
Acoustic Properties ◽  
Cycle Fatigue ◽  
Pressure Oscillations ◽  
The Mathematical Model

Abstract The radial impeller of the main fan of hydrogen cooled generator has been noted to sustain fatigue failure. Experimental data pointed out to the impeller selfexcitation as the cause of the failure. According to the mechanism and the mathematical model suggested in the paper the impeller selfexcitation is due to the feedback between the natural impeller vibrations and the acoustic field in the side room adjacent to the impeller. The impeller vibrations induce the pressure oscillations in the side room that in turn influence the impeller. Under special conditions of the fan dynamic behaviour and the acoustic properties of the fan side room this feedback leads to the selfexcitation. The suggested mechanism and the model fit all the experimental data. Their validity has been also later confirmed by the maintaince experience of other similar machines.

scholarly journals Statistical Analysis of the Mathematical Model of Entropy Generation of Magnetized Nanofluid

Inventions ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 32 ◽  
Author(s):  
Munawwar Ali Abbas ◽  
Ibrahim Hussain
Keyword(s):  
Mathematical Model ◽  
Reynolds Number ◽  
Statistical Analysis ◽  
Entropy Generation ◽  
Concentration Profile ◽  
Perturbation Technique ◽  
Governing Equations ◽  
Friction Forces ◽  
Long Wavelength ◽  
The Mathematical Model

This investigation introduces a mathematical model of entropy generation for Magnetohydrodynamic (MHD) peristaltic wave of nanofluid. The governing equations have been created by the supposition of low Reynolds number and long wavelength estimation. The scientific arrangement has been procured with the help of perturbation technique. The concentration profile, temperature profile, pressure distribution and friction forces are shown graphically for some important parameters. Further, the eventual outcomes of connection between the entropy generation and some various parameters have been plotted by means of correlation and regression. It is fundamental to find the affectability of each parameter on entropy generation.

scholarly journals Effect of Ventricular Elasticity Due to Congenital Hydrocephalus

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2087
Author(s):  
Hemalatha Balasundaram ◽  
Senthamilselvi Sathiamoorthy ◽  
Shyam Sundar Santra ◽  
Rifaqat Ali ◽  
Vediyappan Govindan ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Cerebrospinal Fluid ◽  
Perturbation Technique ◽  
Current Model ◽  
Governing Equations ◽  
Symmetric Flow ◽  
Cerebrospinal Fluid Flow ◽  
Flow Transport ◽  
Brain Biomechanics ◽  
The Mathematical Model

Cerebrospinal fluid (CSF) is a symmetric flow transport that surrounds brain and central nervous system (CNS). Congenital hydrocephalusis is an asymmetric and unusual cerebrospinal fluid flow during fetal development. This dumping impact enhances the elasticity over the ventricle wall. Henceforth, compression change influences the force of brain tissues. This paper presents a mathematical model to establish the effects of ventricular elasticity through a porous channel. The current model is good enough for immediate use by a neurosurgeon. The mathematical model is likely to be a powerful tool for the better treatment of hydrocephalus and other brain biomechanics. The non-linear dimensionless governing equations are solved using a perturbation technique, and the outcome is portrayed graphically with the aid of MATLAB.

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