Navier-Stokes solutions for accelerating pipe flow : a review of analytical models

Urbanowicz, Kamil (author), Bergant, Anton (author), Stosiak, Michal (author), Deptuła, Adam (author), Karpenko, Mykola (author)

This paper reviews analytical solutions for the accelerated flow of an incompressible Newtonian fluid in a pipeline. This problem can be solved in one of two ways according to the (1) imposed pressure gradient or (2) flow rate. Laminar accelerated flow solutions presented in a number of publications concern cases where the two driving mechanisms are described by simple mathematical functions: (a) impulsive change; (b) constant change; (c) ramp change, etc. The adoption of a more complex and realistic description of the pressure gradient or flow rate will be associated with a profound mathematical complexity of the final solution. This is particularly visible with the help of the universal formula derived by several researchers over the years and discussed in this paper. In addition to the solutions strictly defined for laminar flow, an interesting extension of this theory is the theory of underlying laminar flow for the analysis of turbulent accelerated pipe flows (TULF model developed by García García and Alvariño). The TULF model extends the Pai model developed more than 60 years ago, which has been previously used for steady flows only. The discussed solutions extend the theory of analytical solutions of simplified two-dimensional Navier–Stokes equations and can be used not only to study the behavior of liquids during accelerating pipe flow but they can also be used to test the accuracy of commercial CFD codes.

• Language: English
• Keywords: Navier–Stokes equations, analytical solutions, accelerated flow, pipe flow
• Work type: Article
• Typology: 1.02 - Review Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: 30 str.
• Numbering: Vol. 16, iss. 3, art. 1407
• PID: 20.500.12556/RUL-144242
• UDC: 621.22
• ISSN on article: 1996-1073
• DOI: 10.3390/en16031407
• COBISS.SI-ID: 140793091
• Publication date in RUL: 06.02.2023

Record is a part of a journal

• Title: Energies
• Shortened title: Energies
• Publisher: Molecular Diversity Preservation International
• ISSN: 1996-1073
• COBISS.SI-ID: 518046745

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: Navier-Stoksove enačbe, analitične rešitve, pospešujoč tok, cevni tok, kanalski tok

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: L2-1825
• Name: Modeliranje zračnih mehurjev ujetih v hidravličnih cevnih sistemih

• Funder: ARRS - Slovenian Research Agency
• Project number: P2-0162
• Name: Večfazni sistemi