About inverse Laplace transform of a dynamic viscosity function

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

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.

• Jezik: Angleški jezik
• Ključne besede: inverse Laplace transform, analytical solution, water hammer, dynamic viscosity function, fluid dynamics, pipe flow, Calogero–Ahmed sums
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FS - Fakulteta za strojništvo
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.06.2022
• Leto izida: 2022
• Št. strani: 26 str.
• Številčenje: Vol. 15, iss. 12, art. 4364
• PID: 20.500.12556/RUL-137576
• UDK: 532.522:517.44
• ISSN pri članku: 1996-1944
• DOI: 10.3390/ma15124364
• COBISS.SI-ID: 112475651
• Datum objave v RUL: 22.06.2022

URBANOWICZ, Kamil, BERGANT, Anton, GRZEJDA, Rafał in STOSIAK, Michal, 2022, About inverse Laplace transform of a dynamic viscosity function. Materials [na spletu]. 2022. Vol. 15, no. 12,  4364. [Dostopano 4 april 2025]. DOI 10.3390/ma15124364. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=137576

Gradivo je del revije

• Naslov: Materials
• Skrajšan naslov: Materials
• Založnik: MDPI
• ISSN: 1996-1944
• COBISS.SI-ID: 33588485

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.
• Začetek licenciranja: 20.06.2022

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: inverzna Laplaceva transformacija, analitična rešitev, vodni udar, dinamična viskozna funkcija, dinamika tekočin, tok v cevi, Calogero–Ahmedove vrste

Projekti

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: L2-1825
• Naslov: Modeliranje zračnih mehurjev ujetih v hidravličnih cevnih sistemih

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: P2-0162
• Naslov: Večfazni sistemi