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 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 Revisiting Surface-Subsurface Exchange at Intertidal Zone with a Coupled 2D Hydrodynamic and 3D Variably-Saturated Groundwater Model

Water ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 902
Author(s):  
Zhi Li ◽  
Ben R. Hodges
Keyword(s):  
Intertidal Zone ◽  
Coastal Wetlands ◽  
High Performance ◽  
Stokes Equations ◽  
Wave Model ◽  
Surface Flow ◽  
Richards Equation ◽  
Navier Stokes ◽  
Dynamic Surface ◽  
Flow Equations

A new high-performance numerical model (Frehg) is developed to simulate water flow in shallow coastal wetlands. Frehg solves the 2D depth-integrated, hydrostatic, Navier–Stokes equations (i.e., shallow-water equations) in the surface domain and the 3D variably-saturated Richards equation in the subsurface domain. The two domains are asynchronously coupled to model surface-subsurface exchange. The Frehg model is applied to evaluate model sensitivity to a variety of simplifications that are commonly adopted for shallow wetland models, especially the use of the diffusive wave approximation in place of the traditional Saint-Venant equations for surface flow. The results suggest that a dynamic model for momentum is preferred over diffusive wave model for shallow coastal wetlands and marshes because the latter fails to capture flow unsteadiness. Under the combined effects of evaporation and wetting/drying, using diffusive wave model leads to discrepancies in modeled surface-subsurface exchange flux in the intertidal zone where strong exchange processes occur. It indicates shallow wetland models should be built with (i) dynamic surface flow equations that capture the timing of inundation, (ii) complex topographic features that render accurate spatial extent of inundation, and (iii) variably-saturated subsurface flow solver that is capable of modeling moisture change in the subsurface due to evaporation and infiltration.

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.

Essential Ingredients for the Computation of Steady and Unsteady Blade Boundary Layers

1991 ◽  
Vol 113 (4) ◽  
pp. 608-616 ◽  
Author(s):  
H. M. Jang ◽  
J. A. Ekaterinaris ◽  
M. F. Platzer ◽  
T. Cebeci
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Transitional Region ◽  
Low Reynolds Numbers ◽  
Flow Equations ◽  
Low Reynolds

Two methods are described for calculating pressure distributions and boundary layers on blades subjected to low Reynolds numbers and ramp-type motion. The first is based on an interactive scheme in which the inviscid flow is computed by a panel method and the boundary layer flow by an inverse method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier–Stokes equations with an embedded grid technique that permits accurate calculation of boundary layer flows. Studies for the Eppler-387 and NACA-0012 airfoils indicate that both methods can be used to calculate the behavior of unsteady blade boundary layers at low Reynolds numbers provided that the location of transition is computed with the en method and the transitional region is modeled properly.

Rotational and Quasiviscous Cold Flow Models for Axisymmetric Hybrid Propellant Chambers

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
Joseph Majdalani ◽  
Michel Akiki
Keyword(s):  
Rocket Engine ◽  
Navier Stokes ◽  
Mathematical Treatment ◽  
Hybrid Rocket ◽  
Mean Flow ◽  
Viscous Effects ◽  
Navier Stokes Equation ◽  
Flow Models ◽  
Hybrid Rocket Engine ◽  
Wall Injection

In this work, we present two simple mean flow solutions that mimic the bulk gas motion inside a full-length, cylindrical hybrid rocket engine. Two distinct methods are used. The first is based on steady, axisymmetric, rotational, and incompressible flow conditions. It leads to an Eulerian solution that observes the normal sidewall mass injection condition while assuming a sinusoidal injection profile at the head end wall. The second approach constitutes a slight improvement over the first in its inclusion of viscous effects. At the outset, a first order viscous approximation is constructed using regular perturbations in the reciprocal of the wall injection Reynolds number. The asymptotic approximation is derived from a general similarity reduced Navier–Stokes equation for a viscous tube with regressing porous walls. It is then compared and shown to agree remarkably well with two existing solutions. The resulting formulations enable us to model the streamtubes observed in conventional hybrid engines in which the parallel motion of gaseous oxidizer is coupled with the cross-streamwise (i.e., sidewall) addition of solid fuel. Furthermore, estimates for pressure, velocity, and vorticity distributions in the simulated engine are provided in closed form. Our idealized hybrid engine is modeled as a porous circular-port chamber with head end injection. The mathematical treatment is based on a standard similarity approach that is tailored to permit sinusoidal injection at the head end.

Feedback Control of Turbulence

1994 ◽  
Vol 47 (6S) ◽  
pp. S3-S13 ◽  
Author(s):  
Parviz Moin ◽  
Thomas Bewley
Keyword(s):  
Feedback Control ◽  
Turbulent Flows ◽  
Systems Approach ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Flow Equations ◽  
Active Feedback ◽  
Active Feedback Control ◽  
Mathematical Techniques

A brief review of current approaches to active feedback control of the fluctuations arising in turbulent flows is presented, emphasizing the mathematical techniques involved. Active feedback control schemes are categorized and compared by examining the extent to which they are based on the governing flow equations. These schemes are broken down into the following categories: adaptive schemes, schemes based on heuristic physical arguments, schemes based on a dynamical systems approach, and schemes based on optimal control theory applied directly to the Navier-Stokes equations. Recent advances in methods of implementing small scale flow control ideas are also reviewed.

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.

Rotordynamic Coefficients of Labseals for Turbines: Comparing CFD Results With Experimental Data on a Comb-Grooved Labyrinth

2005 ◽  
Author(s):  
Joachim Schettel ◽  
Martin Deckner ◽  
Klaus Kwanka ◽  
Bernd Lu¨neburg ◽  
Rainer Nordmann
Keyword(s):  
Stokes Equations ◽  
Labyrinth Seal ◽  
Navier Stokes ◽  
Test Rig ◽  
Navier Stokes Equations ◽  
Detailed Model ◽  
Identification Methods ◽  
Rotating Speed ◽  
Flow Models ◽  
Rotordynamic Coefficients

The main goal of this paper is to improve identification methods for rotordynamic coefficients of labseals for turbines. This aim was achieved in joint effort of the Technische Universita¨t Mu¨nchen, working on experimental identification methods for rotordynamic coefficients, the University of Technology, Darmstadt, working on prediction methods, and Siemens AG, realizing the results. The paper focuses on a short comb-grooved labyrinth seal. Short labseals, amongst others the above mentioned comb-grooved labyrinth, were examined. by means of a very accurately measuring test rig. The rotor was brought into statically eccentric positions relative to the stator, in order to measure the circumferential pressure distribution as a function of pressure, rotating speed and entrance swirl. The data collected were used to validate results obtained with a numerical method. The theoretical approach is based on a commercial CFD tool, which solves the Navier Stokes equations using numerical methods. As a result, a detailed model of the flow within the test rig is produced. The efforts of computation here are greater than when compared with the likewise wide-spread Bulk flow models, however improved accuracy and flexibility is expected. As the validation of the model is successful, it could then be used to gain further insight in the flow within the seal, and to understand the results better. This showed that rotordynamic coefficients of labseals gained from different test rigs are not necessarily comparable.

Numerical Study of the Effect of Inlet Constriction on Bubble Growth During Flow Boiling in Microchannels

2005 ◽  
Author(s):  
Abhijit Mukherjee ◽  
Satish G. Kandlikar
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Flow Boiling ◽  
Navier Stokes ◽  
Channel Cross Section ◽  
Vapor Bubbles ◽  
Reversed Flow ◽  
Cross Sectional ◽  
Parallel Microchannels ◽  
Energy Equations

Flow boiling through microchannels is characterized by nucleation of vapor bubbles on the channel walls and their rapid growth as they fill the entire channel cross-section. In parallel microchannels connected through a common header, formation of vapor bubbles often results in flow maldistribution that leads to reversed flow in certain channels. The reversed flow is detrimental to the heat transfer and leads to early CHF condition. One way of eliminating the reversed flow is to incorporate flow restrictions at the channel inlet. In the present numerical study, a nucleating vapor bubble placed near the restricted end of a microchannel is numerically simulated. The complete Navier-Stokes equations along with continuity and energy equations are solved using the SIMPLER method. The liquid-vapor interface is captured using the level set technique. The results show that with no restriction the bubble moves towards the nearest channel outlet, whereas in the presence of a restriction, the bubble moves towards the distant but unrestricted end. It is proposed that channels with increasing cross-sectional area may be used to promote unidirectional growth of the vapor plugs and prevent reversed flow.

Sign in / Sign up

Export Citation Format

Share Document