scholarly journals Simulation of Transient Liquid Pipeline Flow Using the Deformable Characteristic Grid

2000 ◽  
Author(s):  
Helmut Kossatz
Keyword(s):  
Numerical Solution ◽  
Method Of Characteristics ◽  
Transient Flow ◽  
The Other ◽  
Fluid Interfaces ◽  
Conservation Of Mass ◽  
Computational Implementation ◽  
Elastic Pipeline ◽  
Eulerian Characteristic ◽  
Deforming Mesh

This study describes the numerical solution and computational implementation of the isothermal transient flow of several different compressible liquids contained in a single elastic pipeline. The method of characteristics is used to integrate the equations of conservation of mass and momentum along the deforming Eulerian characteristic mesh. Integration along the deforming mesh, which is generated as integration proceeds in time, minimizes the need for interpolation so that problem variables are accurately determined at the computed mesh points. On the other hand, since calculated mesh points are not regularly spaced in the x-t plane, interpolations among the computed points become necessary to find the value of variables at a given fixed instant of time along the length of the pipeline. The computational implementation allows for the simulation of flow across locations where there may be changes in nominal pipe diameter, valves or pumps, as well as tracking the position of fluid interfaces as different batches of fluid move along the pipeline, and results are found to be numerically accurate and stable.

Modelling solid transport in building drainage systems

1996 ◽  
Vol 33 (9) ◽  
pp. 9-16 ◽  
Author(s):  
John A. Swaffield ◽  
John A. McDougall
Keyword(s):  
Decision Making ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Water Conservation ◽  
Transient Flow ◽  
Drainage System ◽  
System Model ◽  
Flow Depth ◽  
Flow Conditions ◽  
Solid Transport

The transient flow conditions within a building drainage system may be simulated by the numerical solution of the defining equations of momentum and continuity, coupled to a knowledge of the boundary conditions representing either appliances discharging to the network or particular network terminations. While the fundamental mathematics has long been available, it is the availability of fast, affordable and accessible computing that has allowed the development of the simulations presented in this paper. A drainage system model for unsteady partially filled pipeflow will be presented in this paper. The model is capable of predicting flow depth and rate, and solid velocity, throughout a complex network. The ability of such models to assist in the decision making and design processes will be shown, particularly in such areas as appliance design and water conservation.

Influence of velocity head on filling transients in a branched pipeline

2018 ◽  
Vol 35 (7) ◽  
pp. 2502-2513 ◽  
Author(s):  
Ling Wang ◽  
Fujun Wang ◽  
Bryan William Karney ◽  
Ahmad Malekpour ◽  
Zhengwei Wang
Keyword(s):  
Method Of Characteristics ◽  
Energy Equation ◽  
Transient Flow ◽  
Numerical Results ◽  
Velocity Head ◽  
Piezometric Head ◽  
Content Type ◽  
High Point ◽  
Hydraulic Transient ◽  
Column Separation

Purpose The velocity head is usually neglected in the energy equation for a pipeline junction when one-dimensional (1D) hydraulic transient flow is solved by method of characteristics. The purpose of this paper is to investigate the effect of velocity head on filling transients in a branched pipeline by an energy equation considering velocity head. Design/methodology/approach An interface tracking method is used to locate the air–water interface during pipeline filling. The pressured pipe flow is solved by a method of characteristics. A discrete gas cavity model is included to permit the occurrence of column separation. A universal energy equation is built by considering the velocity head. The numerical method is provisionally verified in a series pipeline and the numerical results and experimental data accord well with each other. Findings The numerical results show that some differences in filling velocity and piezometric head occur in the branched pipeline. These differences arise because the velocity head in the energy equation can become an important contributor to the hydraulic response of the system. It is also confirmed that a local high point in the profile is apt to experience column separation during rapid filling. Significantly, the magnitude of overpressure and cavity volume induced by filling transients at the local high point is predicted to increase with the velocity in the pipes. Originality/value The velocity head in the energy equation for a pipeline junction could play an important role in the prediction of filling velocity, piezometric head and column separation phenomenon, which should be given more attention in 1D hydraulic transient analysis.

Modeling of Fluid Interaction Produced by Water Hammer

2011 ◽  
Vol 1 (1) ◽  
pp. 29-41 ◽  
Author(s):  
Kaveh Hariri Asli ◽  
Faig Bakhman Ogli Naghiyev ◽  
Soltan Ali Ogli Aliyev ◽  
Hoosein Hariri Asli
Keyword(s):  
Method Of Characteristics ◽  
Transient Flow ◽  
Practical Investigations ◽  
Computationally Efficient ◽  
Hydraulic Simulation ◽  
Computational Performance ◽  
Difference Form ◽  
Large Water ◽  
Water Transmission ◽  
Fluid Interaction

This paper compares the computational performance of two numerical methods for two models of Transient Flow. One model was defined by method of the Eulerian based expressed in a method of characteristics “MOC”, finite difference form. The other model was defined by method of Regression. Each method was encoded into an existing hydraulic simulation model. Results indicated that the accuracy of the methods was comparable but that the “MOC” was more computationally efficient for analysis of large water transmission line. Practical investigations in this article have shown mainly this tendency.

The interaction of a fibre tangle with an airflow

1967 ◽  
Vol 27 (3) ◽  
pp. 561-580 ◽  
Author(s):  
Paul A. Taub
Keyword(s):  
Unsteady Flow ◽  
Numerical Solution ◽  
Analytical Model ◽  
Method Of Characteristics ◽  
Solution Procedure ◽  
Governing Equations ◽  
Stress Strain ◽  
One Dimensional ◽  
The Method Of Characteristics ◽  
Flow Configurations

An analytical model of the interaction of a fibre tangle with an airflow is proposed. This model replaces the discrete fibres by a continuum medium with a non-linear stress-strain law. The governing equations have been examined for one-dimensional unsteady flow configurations and have been found to possess five characteristic directions.A numerical-solution procedure, based upon the method of characteristics, has been outlined and applied to the flow within a dilation chamber. A fibre sample is located at the centre of the chamber, which is alternately pressurized and depressurized.

Torsional Impact of a Stepped Shaft With a Rigid Body at One End

1973 ◽  
Vol 40 (4) ◽  
pp. 1004-1008
Author(s):  
J. A. Dalessandro
Keyword(s):  
Wave Equation ◽  
Rigid Body ◽  
Numerical Solution ◽  
Method Of Characteristics ◽  
Wave Theory ◽  
Single Step ◽  
Qualitative And Quantitative ◽  
Impact Stress ◽  
Elementary Wave ◽  
Stepped Shaft

A numerical solution of the wave equation for torsional impact of a shaft which contains a single step and a rigid body at one end is found using the method of characteristics. The results are based on discontinuous stresses and elementary wave theory at the step. An experiment verified the predicted results, but showed that the actual impact stresses will always be slightly less since they are not discontinuous, as assumed. Some qualitative and quantitative generalizations are made concerning the expected maximum impact stress.

scholarly journals NLOS Mitigation for TOA Location Based on a Modified Deterministic Model

2008 ◽  
Vol 2008 ◽  
pp. 1-4 ◽  
Author(s):  
Hong Tang ◽  
Yongwan Park ◽  
Tianshuang Qiu
Keyword(s):  
Numerical Solution ◽  
Deterministic Model ◽  
The Other ◽  
Base Stations ◽  
Line Of Sight ◽  
Time Of Arrival ◽  
Wireless Location ◽  
Scale Factors ◽  
Measured Time ◽  
Non Line Of Sight

Wireless location becomes difficult due to contamination of measured time-of-arrival (TOA) caused by non-line-of-sight. In this letter, TOA measurements seen at base stations are adjusted by scale factors, and a modified deterministic model is built. An effective numerical solution is proposed to resolve the scale factors and mobile position. A simulation comparison of four algorithms indicates that the proposed algorithm outperforms the other three algorithms.

scholarly journals Features of the Computational Implementation of the Algorithm for Estimating the Lyapunov Exponents of Systems with Delay

2019 ◽  
Vol 26 (4) ◽  
pp. 572-582
Author(s):  
Vladimir E. Goryunov
Keyword(s):  
Lyapunov Exponents ◽  
Delay Differential Equations ◽  
Logistic Equation ◽  
The Other ◽  
Numerical Estimation ◽  
Trigonometric Functions ◽  
Computational Implementation ◽  
Delay Differential ◽  
Usage Flexibility ◽  
Stable Structures

We consider the computational implementation of the algorithm for Lyapunov exponents spectrum numerical estimation for delay differential equations. It is known that for such systems, as well as for boundary value problems, it is not possible to prove the well-known Oseledets theorem which allows us to calculate the required parameters very efficiently. Therefore, we can only talk about the estimates of the characteristics in some sense close to the Lyapunov exponents. In this paper, we propose two methods of linearized systems solutions processing. One of them is based on a set of impulse functions, and the other is based on a set of trigonometric functions. We show the usage flexibility of these algorithms in the case of quasi-stable structures when several Lyapunov exponents are close to zero. The developed methods are tested on a logistic equation with a delay, and these tests illustrate the “proximity” of the obtained numerical characteristics and Lyapunov exponents.

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