Improving Zielke’s Method of Simulating Frequency-Dependent Friction in Laminar Liquid Pipe Flow

1991 ◽  
Vol 113 (4) ◽  
pp. 569-573 ◽  
Author(s):  
Katsumasa Suzuki ◽  
Takayuki Taketomi ◽  
Sanroku Sato
Keyword(s):  
Method Of Characteristics ◽  
Weighting Function ◽  
Block Diagram ◽  
Computation Time ◽  
Dimensionless Time ◽  
Frequency Dependent ◽  
Transient Phenomena ◽  
Computer Storage ◽  
Calculation Process ◽  
Visual Understanding

Zielke’s technique of using a method of characteristics to simulate transient phenomena of a liquid transmission line is accurate, easy to apply to complicated systems and therefore, frequently used. However, it requires a very large amount of computation time and computer storage to simulate frequency-dependent friction in a transient liquid flow. Searching for a way to counteract these disadvantages, the authors took note of the fact that the weighting function, which is the root of the above problems, is given by exponential functions or other functions depending on dimensionless time. In order to perform mathematically equivalent calculation without approximations, they have developed a new method which requires much less computation time and computer storage than Zielke’s method. The calculation process is shown by a block diagram to facilitate visual understanding of the method.

An Efficient Method for Simulating Frequency-Dependent Friction in Transient Liquid Flow

1975 ◽  
Vol 97 (1) ◽  
pp. 97-105 ◽  
Author(s):  
A. K. Trikha
Keyword(s):  
Liquid Flow ◽  
Method Of Characteristics ◽  
Computation Time ◽  
Approximate Expression ◽  
Test System ◽  
Exact Expression ◽  
Frequency Dependent ◽  
Efficient Procedure ◽  
Liquid Line ◽  
Frequency Domains

An efficient procedure is developed for simulating frequency-dependent friction in transient laminar liquid flow by the method of characteristics. The procedure consists of determining an approximate expression for frequency-dependent friction such that the use of this expression requires much less computer storage or computation time than the use of the exact expression. The derived expression for frequency-dependent friction approximates the exact expression very well in both time and frequency domains. Calculated results for a test system are compared with the experimental results so show that the approximate expression predicts accurately the surge pressures, pressure wave distortion as well as pressure attenuation in a liquid line.

scholarly journals Particle method of characteristics (PMOC) for unsteady pipe flow

2012 ◽  
Vol 15 (3) ◽  
pp. 780-797 ◽  
Author(s):  
Yao-Hsin Hwang ◽  
Ho-Shuenn Huang ◽  
Nien-Mien Chung ◽  
Pai-Yi Wang
Keyword(s):  
Method Of Characteristics ◽  
Particle Method ◽  
Benchmark Problems ◽  
Present Formulation ◽  
Transient Effects ◽  
Piezometric Head ◽  
Transient Phenomena ◽  
Pipe Flows ◽  
Characteristic Lines ◽  
The Right

A novel particle method of characteristics (PMOC) to simulate unsteady pipe flows is introduced and validated in the present study. Contrary to the conventional method of characteristics (MOC), the present formulation is built by reallocating the computational nodes along the characteristic lines. Both the right- and left-running characteristics are accurately traced and imitated with their associated computational particles. The annoying numerical inconveniences in the fixed-grid arrangement due to incompatible Courant–Friedrichs–Lewy (CFL) condition by repeating solution interpolations is effectively eliminated. Special particles with dual states satisfying the Rankine–Hugoniot relations are deliberately imposed to emulate the shock structure. Efficacy of this formulation is verified by solving some benchmark problems with significant transient effects in pipe flows. Computational results of piezometric head and flow velocity are meticulously compared with available analytical solutions. It is concluded that the proposed PMOC will be a useful tool to replicate transient phenomena in pipe flows.

scholarly journals Marching On-In-Time Unstructured PEEC Method for Electrically Large Structures with Conductive, Dielectric, and Magnetic Media

Electronics ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 242
Author(s):  
Riccardo Torchio ◽  
Dimitri Voltolina ◽  
Paolo Bettini ◽  
Federico Moro ◽  
Piergiorgio Alotto
Keyword(s):  
Computation Time ◽  
Industrial Test ◽  
Magnetic Media ◽  
Neutral Beam Injector ◽  
Transient Phenomena ◽  
Electromagnetic Problems ◽  
Inverse Discrete Fourier Transform ◽  
Electromagnetic Devices ◽  
Vector Potentials ◽  
Fusion Applications

The Marching On-In-Time (MOT) unstructured Partial Element Equivalent Circuit (PEEC) method for time domain electromagnetic problems is presented. The method allows the transient analysis of electrically large electromagnetic devices consisting of conductive, dielectric, and magnetic media coupled with external lumped circuits. By re-formulating PEEC following the Coulombian interpretation of magnetization phenomena and by using electric and magnetic vector potentials, the proposed approach allows for a completely equivalent treatment of electric and magnetic media and inhomogeneous and anisotropic materials are accounted for as well. With respect to the recently proposed Marching On-In-Time PEEC approach, based on the standard (structured) discretization of PEEC, the method presented in this paper uses a different space and time MOT discretization, which allows for a reduction in the number of the unknowns. Analytical and industrial test cases consisting in electrically large devices are considered (e.g., the model of a Neutral Beam Injector adopted in thermonuclear fusion applications). Results obtained from the simulations show that the proposed method is accurate and yields good performances. Moreover, when rich harmonic content transient phenomena are considered, the unstructured MOT–PEEC method allows for a significant reduction of the memory and computation time when compared to techniques based on Inverse Discrete Fourier Transform applied to the frequency domain unstructured PEEC approach.

Symmetry properties of the scattering matrix in 3-D electromagnetic modeling using the integral equation method

Geophysics ◽  
1992 ◽  
Vol 57 (9) ◽  
pp. 1199-1202 ◽  
Author(s):  
Zonghou Xiong
Keyword(s):  
Integral Equation ◽  
Three Dimensional ◽  
Computation Time ◽  
Integral Equation Method ◽  
Scattering Matrix ◽  
Electromagnetic Modeling ◽  
Symmetry Properties ◽  
Computer Storage ◽  
Earth Conductivity ◽  
Number Of Cells

Modeling large three‐dimensional (3-D) earth conductivity structures continues to pose challenges. Although the theories of electromagnetic modeling are well understood, the basic computational problems are practical, involving the quadratically growing requirements on computer storage and cubically growing computation time with the number of cells required to discretize the modeling body.

Efficient Methods for Numerical Modeling of Laminar Friction in Fluid Lines

2006 ◽  
Vol 128 (4) ◽  
pp. 829-834 ◽  
Author(s):  
D. Nigel Johnston
Keyword(s):  
Computational Efficiency ◽  
Method Of Characteristics ◽  
High Accuracy ◽  
Slight Reduction ◽  
Improved Method ◽  
Frequency Dependent ◽  
Transmission Line Method ◽  
Laminar Pipe Flow ◽  
Very High ◽  
High Computational Efficiency

An improved method for simulating frequency-dependent friction in laminar pipe flow using the method of characteristics is proposed. It has a higher computational efficiency than previous methods while retaining a high accuracy. By lumping the frequency-dependent friction at the ends of the pipeline, the computational efficiency can be improved further, at the expense of a slight reduction in accuracy. The technique is also applied to the transmission line method and found to give a significant improvement in accuracy over previous methods, while retaining a very high computational efficiency.

The method of characteristics for the three-dimensional unsteady magnetofluid dynamics of a multi-component medium

1966 ◽  
Vol 25 (1) ◽  
pp. 17-41 ◽  
Author(s):  
Harry Sauerwein Sauerwein
Keyword(s):  
Fluid Dynamics ◽  
Numerical Method ◽  
Method Of Characteristics ◽  
Three Dimensional ◽  
Computation Time ◽  
Hyperbolic Partial Differential Equations ◽  
Recent Experience ◽  
Local Wave ◽  
Chemically Reacting ◽  
Unsteady Problems

A general numerical method of characteristics applicable to problems in magneto-fluid dynamics as well as ordinary fluid dynamics is described. The method can be applied to unsteady three-dimensional flows of chemically reacting, non-equilibrium, multi-component media. Dissipative phenomena must be neglected in order to make the governing equations of change hyperbolic, because the method can be applied only to quasi-linear, hyperbolic, partial differential equations. Practical restrictions on computation time usually require unsteady problems to be limited to cases with short transient times although theoretically the method applies to all unsteady flows. In steady flow the local velocity must be greater than the largest local wave speed. The characteristic and compatibility equations are derived for the most general case of magnetofluid dynamics. A new finite-difference network and its corresponding equations are developed similarly. Specialization of the general method to consider simpler problems is outlined. Preliminary numerical results of calculations using the method are presented. The practicality and feasibility of utilizing the general numerical method of characteristics on presently available, electronic digital computers is evaluated in the light of recent experience in calculating multi-dimensional flows with the method.

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