scholarly journals APPLICATION OF THE DEDUCTIONS FROM NAVIER STOKES EQUATIONS FOR THE DETERMINATION OF FLOW VELOCITY AND THROUGHPUT IN A GAS PIPELINE BY COMPUTATIONAL APPROACH

2019 ◽  
Vol 1 (1) ◽  
pp. 1-9
Author(s):  
Mathew Shadrack Uzoma
Keyword(s):  
Stokes Equations ◽  
Gas Pipeline ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Theoretical Treatment ◽  
Gas Pipelines ◽  
Navier Stokes Equation ◽  
Operational Conditions ◽  
Numerical Discretization ◽  
Discrete Formulation

Theoretical treatment of gas pipeline pressure-flow problem had been presented applying Navier Stokes equation reduced to their appropriate forms by applicable practical conditions. The results obtained from the theoretical analysis tally with the operating conditions of the case study pipelines. The pipelines being Shell Petroleum Development Company (SPDC) and ElfTotal Nigeria Limited. The results obtained by numerical discretization suggested that these pipelines are not optimally operated. Hence, the need to adjust the flow situation to bring pressure and flow throughput to optimal level of performance. Throughput in excess of the operating conditions could be accommodated by these operating pipelines. It is imperative that this could prevent the spread of these vital capital intensive assets. The funds so conserved could be diverted to sourcing for new gas fields to increase the nation’s strategic reserves.Purpose: The purpose of this work is to enable comparative analysis of the results of the deductions from Nervier Stokes equations with that generated by computer simulation of the discrete formulation.Methodology: Outlining the deductions and developing the discrete formulation. Computer program was developed for the discrete formulation and operational data from operating gas pipelines injected both for the deductions and computational algorithmic coding and the deduced expressions from the Nervier Stokes equations. Results obtained were compared in a bid to address line throughput subject to the operational conditions of the specified gas pipelines in this study.Findings: The output results of the Nervier Stokes deductions matched closed with operational throughput of the two gas pipelines. The numerical discretization simulation results confirmed that additional throughput far and above 1.8m3/s could still be accommodated by these gas pipelines.Unique contribution to theory, practice and policy: As earlier predicted, our existing gas pipelines are grossly under-operated. Additional capacity much more than the operational capacity could still be accommodated by these gas pipelines.

scholarly journals APPLYING DUDUCTIONS FROM NAVIER STOKES EQUATION TO FLOW SITUATIONS IN GAS PIPELINE NETWORK SYSTEM

2019 ◽  
Vol 1 (1) ◽  
pp. 10-18
Author(s):  
Mathew Shadrack Uzoma
Keyword(s):  
Stokes Equations ◽  
Optimal Level ◽  
Gas Pipeline ◽  
Navier Stokes ◽  
Network System ◽  
Gas Pipelines ◽  
Navier Stokes Equation ◽  
Flow Equations ◽  
Flow Models ◽  
Energy Equations

Navier Stokes equations are theoretical equations for pressure-flow-temperature problems in gas pipelines. Other well-known gas equations such as Weymouth, Panhandle A and Modified Panhandle B equations are employed in gas pipeline design and operational procedures at a level of practical relevance. Attaining optimality in the performance of this system entails concrete understanding of the theoretical and prevailing practical flow conditions. In this regard, Navier Stoke’s mass, momentum and energy equations had been worked upon subject to certain simplifying assumptions to deduced expressions for flow velocity and throughput in gas pipeline network system. This work could also bridge the link among theoretical, operational and optimal level of performance in gas pipelines. Purpose: The purpose of this research is to build a measure of practical relevance in gas pipeline operational procedures that would ultimately couple the missing links between theoretical flow equations such as Navier Stokes equation and practical gas pipeline flow equations. Such practical gas pipeline flow models are Weymouth, Panhandle A and Modified Panhandle B equations among others.Methodology: The approach in this regard entails reducing Narvier Stoke’s mas, momentum and energy equations to their appropriate forms by applicable practical conditions. By so doing flow models are deduced that could be worked upon by computational approach analytically or numerically to determine line throughput and flow velocity.The reduced forms of the Navier Stokes velocity and throughput equations would be applied to operating gas pipelines in Nigeria terrain. The gas pipelines are ElfTotal Nig. Ltd and Shell Petroleum Development Company (SPDC). This would enable the comparison of these gas pipelines operational data with theoretical results of Navier Stokes equations reduced to their appropriate forms.Findings: The follow up paper would employ theoretical and numerical discretization computational methods to compare theoretical and numerical discretization results to give a clue if these operating gas pipelines are operated at optimal level of performance.Unique contribution to theory, practice and policy: The reduced forms of Nervier Stokes equations applied to physical operating gas pipelines network system is considered by the researcher to be an endeavor of academic excellence that would foster clear cut understanding of theoretical and practical flow situations. It could also open up a measure of understanding to pushing a flow to attaining optical conditions in practical real life flow situations. Operating gas pipelines optimally would reduce the spread of these capital intensive assets and facilities and more so conserving our limited reserves for foreign exchange.

scholarly journals Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 288
Author(s):  
Alexei Kushner ◽  
Valentin Lychagin
Keyword(s):  
Carbon Dioxide ◽  
Internal Structure ◽  
Stokes Equation ◽  
Hydrogen Cyanide ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

scholarly journals CAUCHY PROBLEM FOR VISCOUS SHALLOW WATER EQUATIONS WITH A TERM OF CAPILLARITY

2010 ◽  
Vol 20 (07) ◽  
pp. 1049-1087 ◽  
Author(s):  
BORIS HASPOT
Keyword(s):  
Shallow Water ◽  
Existence Of Solutions ◽  
Stokes Equations ◽  
Variable Viscosity ◽  
Water System ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Viscosity Coefficients ◽  
Global Existence Of Solutions ◽  
Dependent Viscosity

In this paper, we consider the compressible Navier–Stokes equation with density-dependent viscosity coefficients and a term of capillarity introduced formally by van der Waals in Ref. 51. This model includes at the same time the barotropic Navier–Stokes equations with variable viscosity coefficients, shallow-water system and the model introduced by Rohde in Ref. 46. We first study the well-posedness of the model in critical regularity spaces with respect to the scaling of the associated equations. In a functional setting as close as possible to the physical energy spaces, we prove global existence of solutions close to a stable equilibrium, and local in time existence of solutions with general initial data. Uniqueness is also obtained.

scholarly journals Development of Hybrid Airlift-Jet Pump with Its Performance Analysis

2018 ◽  
Vol 8 (9) ◽  
pp. 1413 ◽  
Author(s):  
Dan Yao ◽  
Kwongi Lee ◽  
Minho Ha ◽  
Cheolung Cheong ◽  
Inhiug Lee
Keyword(s):  
Boundary Conditions ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Jet Pump ◽  
Two Phase

A new pump, called the hybrid airlift-jet pump, is developed by reinforcing the advantages and minimizing the demerits of airlift and jet pumps. First, a basic design of the hybrid airlift-jet pump is schematically presented. Subsequently, its performance characteristics are numerically investigated by varying the operating conditions of the airlift and jet parts in the hybrid pump. The compressible unsteady Reynolds-averaged Navier-Stokes equations, combined with the homogeneous mixture model for multiphase flow, are used as the governing equations for the two-phase flow in the hybrid pump. The pressure-based methods combined with the Pressure-Implicit with Splitting of Operators (PISO) algorithm are used as the computational fluid dynamics techniques. The validity of the present numerical methods is confirmed by comparing the predicted mass flow rate with the measured ones. In total, 18 simulation cases that are designed to represent the various operating conditions of the hybrid pump are investigated: eight of these cases belong to the operating conditions of only the jet part with different air and water inlet boundary conditions, and the remaining ten cases belong to the operating conditions of both the airlift and jet parts with different air and water inlet boundary conditions. The mass flow rate and the efficiency are compared for each case. For further investigation into the detailed flow characteristics, the pressure and velocity distributions of the mixture in a primary pipe are compared. Furthermore, a periodic fluctuation of the water flow in the mass flow rate is found and analyzed. Our results show that the performance of the jet or airlift pump can be enhanced by combining the operating principles of two pumps into the hybrid airlift-jet pump, newly proposed in the present study.

scholarly journals NUMERICAL CALCULATION OF VELOCITY FIELDS FOR VISCO-ELASTIC MATERIALS IN CYLINDRICAL CHANNELS

2019 ◽  
pp. 19-28
Author(s):  
Ekaterina Valer'evna Fomenko ◽  
Albert Hamed-Harisovich Nugmanov ◽  
Thi Sen Nguyen ◽  
Aleksanyan Igor Yuryevich Aleksanyan
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Stokes Equations ◽  
Radiation Power ◽  
Wheat Gluten ◽  
Internal Heat ◽  
Velocity Fields ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Suggested Approach

The article touches upon the application of the numerical finite difference method for solving Navier-Stokes equation in case of one-dimensional problem of passing a cooled viscoelastic material inside circular nozzles. There have been analyzed the specific features of using the method and presented the results of its application. The object of study was not chosen at random, because viscous properties of raw gluten are variable and depend on the temperature, chemical composition and properties of the feedstock. Working not properly with the object of research (phenomenon, process), but with its model helps to characterize its properties and behavior in various situations relatively quickly and without significant costs. The need to identify patterns of internal heat and mass transfer, which is based on studying the kinetics of the process, is obvious for physic-mathematical modeling of heat and mass transfer processes of wheat gluten granulation, in particular, analyzing the mechanism of moisture removal during its drying under radiation power supply. The results of the conducted research are consistent with the available data on the subject, and the suggested approach to solving the problem of choosing rational hydrodynamic regimes has been applied due to the difficulty of experimental determining the velocity fields and problematic analyzing the system of hydrodynamic differential Navier-Stokes equations with variable proportionality ratios.

scholarly journals Simulation of aeromechanics of the grinding process in a centrifugal mill

2020 ◽  
Vol 8 (2) ◽  
pp. 59-66
Author(s):  
I.A. Ostashko ◽  
◽  
A.P. Naumenko ◽  
Keyword(s):  
Gas Dynamics ◽  
Heterogeneous Medium ◽  
Stokes Equations ◽  
Flow Path ◽  
Navier Stokes ◽  
Maximum Diameter ◽  
Navier Stokes Equation ◽  
Crushed Material ◽  
Centrifugal Mill

The article discusses aeromechanical processes in a centrifugal mill at different speeds of rotation in order to establish the regularities of the kinematics of the flow of a heterogeneous medium in the grinding chamber of the mill, its interaction with the working body and the classification of the crushed material when removed from the grinding chamber. The study of gas dynamics of processes in the flow path of a centrifugal mill has been carried out. The trajectories of streams, velocity and pressure fields were investigated. The influence of various factors on the efficiency of the classification and the maximum diameter of particles removed from the grinding chamber was revealed. The regularities of the movement of a heterogeneous medium, its interaction with the working body and the classification of the crushed material when removed from the grinding chamber were established, the gas dynamics of processes in the flow path of a centrifugal mill was studied. The main way to increase the speed of air flows is to increase the flow of transport air, which in turn affects the aerodynamics of the processes in the grinding chamber of the mill, productivity and grinding time of the material. Processes of gas dynamics in a compressed medium of the flow path of a centrifugal mill were described by a system of non-stationary Navier-Stokes equations of continuity, energy and equation of state in approximation of the turbulence model. Analysis of the results of mathematical modeling of processes in the working chamber showed that the air flow carries out a complex rotational movement in the transverse and longitudinal sections with the formation of local zones of increased turbulence. As a result of numerical modeling and analysis of the results, factors have been identified that make it possible to intensify the process of material grinding. The flows have a pronounced ballistic trajectory. They start their movement from the center of the bottom of the grinding chamber and move along the walls of the chamber while rotating in a spiral and moving down the wall of the hollow shaft. It is observed that the point of separation of the flows rotating in the lower part of the grinding chamber and the flows moving in the upper part is on 60% of the height of the chamber. Keywords: modeling, centrifugal mill, finite element method, Navier-Stokes equation.

The Onset of Turbulence: Insights Into the Navier-Stokes Equations

2017 ◽  
Author(s):  
Carl E. Rathmann
Keyword(s):  
Stokes Equations ◽  
Direct Consequence ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Fluid Behavior ◽  
Onset Of Turbulence ◽  
And Mathematics ◽  
High Reynolds

For well over 150 years now, theoreticians and practitioners have been developing and teaching students easily visualized models of fluid behavior that distinguish between the laminar and turbulent fluid regimes. Because of an emphasis on applications, perhaps insufficient attention has been paid to actually understanding the mechanisms by which fluids transition between these regimes. Summarized in this paper is the product of four decades of research into the sources of these mechanisms, at least one of which is a direct consequence of the non-linear terms of the Navier-Stokes equation. A scheme utilizing chaotic dynamic effects that become dominant only for sufficiently high Reynolds numbers is explored. This paper is designed to be of interest to faculty in the engineering, chemistry, physics, biology and mathematics disciplines as well as to practitioners in these and related applications.

ON THE ASYMPTOTIC ANALYSIS OF THE BGK MODEL TOWARD THE INCOMPRESSIBLE LINEAR NAVIER–STOKES EQUATION

2010 ◽  
Vol 20 (08) ◽  
pp. 1299-1318 ◽  
Author(s):  
A. BELLOUQUID
Keyword(s):  
Asymptotic Analysis ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Uniqueness Theorems ◽  
Bgk Model ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Stokes Systems ◽  
Global Strong Solutions

This paper deals with the analysis of the asymptotic limit for BGK model to the linearized Navier–Stokes equations when the Knudsen number ε tends to zero. The uniform (in ε) existence of global strong solutions and uniqueness theorems are proved for regular initial fluctuations. As ε tends to zero, the solution of BGK model converges strongly to the solution of the linearized Navier–Stokes systems. The validity of the BGK model is critically analyzed.

Large-frequency global regularity for the incompressible Navier–Stokes equation

1999 ◽  
Vol 129 (5) ◽  
pp. 903-912
Author(s):  
Joel D. Avrin
Keyword(s):  
Boundary Conditions ◽  
Global Regularity ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Dirichlet Boundary Conditions ◽  
Navier Stokes ◽  
Thin Domains ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Incompressible Navier Stokes Equation

We obtain global existence and regularity of strong solutions to the incompressible Navier–Stokes equations for a variety of boundary conditions in such a way that the initial and forcing data can be large in the high-frequency eigenspaces of the Stokes operator. We do not require that the domain be thin as in previous analyses. But in the case of thin domains (and zero Dirichlet boundary conditions) our results represent a further improvement and refinement of previous results obtained.

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