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Convolution integral in transient pipe flow

100%

Urbanowicz K. , Zarzycki Z.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2012

tom Vol. 16, No 3-4

277--291

This paper is devoted to the modeling of hydraulic losses during transient flow of liquids in pressure lines. Unsteady pipe wall shear stress is presented in the form of a convolution integral of liquid acceleration and a weighting function. The weighting function depends on the dimensionless time and the Reynolds number. In its first revision (Zielke W 1968 J. ASME 90 109) it had a complex and inefficient mathematical structure (featured power growth of computational time). Therefore, further work aimed at developing the so-called efficient models for correct estimation of hydraulic resistance with simultaneous linear loading of the computer's operating memory was needed. The work compared the methods of numerical solving of the convolution integral known from the literature (classic by Zielke W 1968 J. ASME 90 109 and Yardy A E and Brown J M B 2010 J. Hydratd. Eng. 136 (7) 453 and efficient by Trikha A K 1975 J. Fluids Eng. p. 97. Kagawa T et at. 1983 Trans. Jpn. Soc. Mech. Eng. 49 (447) 2638 and Schohl G A 1993 J. Fluids Eng. 115 420). The comparison highlighted the level of usefulness of the analyzed models in simulating the water hammer and revealed the demand for further research for the improvement of efficiency of the solutions.

Analytical expressions for effective weighting functions used during simulations of water hammer

100%

Urbanowicz K.

Journal of Theoretical and Applied Mechanics

2017

tom Vol. 55 nr 3

1029--1040

For some time, work has been underway aimed at significant simplification of the modelling of hydraulic resistance occurring in the water hammer while maintaining an acceptable error. This type of resistance is modelled using a convolution integral, among others, from local acceleration of a liquid and a certain weighting function. The recently completed work shows that during efficient calculations of the convolution integral, the effective weighting function used does not have to be characterised by large convergence with a classical function (according to Zielke during laminar flow and to Vardy-Brown during turbulent flow). However, it must be a sum of at least two or three exponential expressions so that the final results of the simulation could be considered as satisfactory. In this work, it has been decided to present certain analytical formulas using which it will be possible to determine the coefficients of simplified effective weighting functions in a simple direct way.

Inverse Laplace transforms using convolution integral

75%

Jha B. K. , Ajibade A. O.

International Journal of Applied Mechanics and Engineering

2008

tom Vol. 13, no 4

1119-1123

In the present article, the convolution theorem is used to obtain the inverse Laplace-transforms of some Laplace-transforms functions. Although the inverse Laplace-transforms of these functions are available in the works of Abramowitz and Stegun (1965), Carlslaw and Jaeger (1952), Churchill (1972), Miles (1971) and Özisik (1980), they require integration of complementary-error-function for computational purposes. The results presented in this article are directly applicable in many branches of science where time-dependent initial and boundary conditions are frequently occurring.

Computer simulation of the electromechanical systems using convolution integral

63%

Moroz V.

Zeszyty Naukowe. Elektrotechnika / Uniwersytet Technologiczno-Przyrodniczy w Bydgoszczy

2009

tom z. 14

17-24

The method of the computer simulation of the electromechanical systems using the recurrent equations based on the convolution integral approximations is presented in the paper.

W artykule przedstawiono metodę symulacji komputerowej układu elektromechanicznego z wykorzystaniem równań rekurencyjnych opartych na aproksymacji całki splotu.