About inverse Laplace transform of a dynamic viscosity function

Kamil Urbanowicz (Author), Anton Bergant (Author), Rafał Grzejda (Author), Michal Stosiak (Author)

Abstract

A dynamic viscosity function plays an important role in water hammer modeling. It is responsible for dispersion and decay of pressure and velocity histories. In this paper, a novel method for inverse Laplace transform of this complicated function being the square root of the ratio of Bessel functions of zero and second order is presented. The obtained time domain solutions are dependent on infinite exponential series and Calogero–Ahmed summation formulas. Both of these functions are based on zeros of Bessel functions. An analytical inverse will help in the near future to derive a complete analytical solution of this unsolved mathematical problem concerning the water hammer phenomenon. One can next present a simplified approximate form of this solution. It will allow us to correctly simulate water hammer events in large ranges of water hammer number, e.g., in oil–hydraulic systems. A complete analytical solution is essential to prevent pipeline failures while still designing the pipe network, as well as to monitor sensitive sections of hydraulic systems on a continuous basis (e.g., against possible overpressures, cavitation, and leaks that may occur). The presented solution has a high mathematical value because the inverse Laplace transforms of square roots from the ratios of other Bessel functions can be found in a similar way.

Keywords

inverzna Laplaceva transformacija;analitična rešitev;vodni udar;dinamična viskozna funkcija;dinamika tekočin;tok v cevi;Calogero–Ahmedove vrste;inverse Laplace transform;analytical solution;water hammer;dynamic viscosity function;fluid dynamics;pipe flow;Calogero–Ahmed sums;

Data

Language:	English
Year of publishing:	2022
Typology:	1.01 - Original Scientific Article
Organization:	UL FS - Faculty of Mechanical Engineering
UDC:	532.522:517.44
COBISS:	112475651
ISSN:	1996-1944
Views:	50
Downloads:	18
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	inverzna Laplaceva transformacija;analitična rešitev;vodni udar;dinamična viskozna funkcija;dinamika tekočin;tok v cevi;Calogero–Ahmedove vrste;
Type (COBISS):	Article
Pages:	str. 1-26
Volume:	ǂVol. ǂ15
Issue:	ǂiss. ǂ12
Chronology:	Jun. 2022
DOI:	10.3390/ma15124364
ID:	15711346