On the method of characteristics in highly compressible flows

Alan E. Vardy

On the method of characteristics in highly compressible flows

Alan E. Vardy

Civil Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

The method of characteristics (MOC) is widely used in simulations of transient liquid flows. Nearly always, the method is simplified by key assumptions that the speed of sound is (i) constant and (ii) very much larger than the fluid velocity. This paper describes how MOC can be used in transient gas flows even when these assumptions cannot reasonably be made. Examples include flows at large (but subsonic) Mach number and strongly compressible flows in long pipes with skin friction and/or heat transfer. Four formulations of the basic equations are presented and their advantages and disadvantages are explained. The simplest of these, based on pressure p, density p and velocity U, closely resembles conventional water-hammer formulations. The most powerful formulation, based on temperature T, specific entropy s and Mach number M, has special advantages in the representation of a path-line equation that is always necessary in addition to the two wave-path equations. This formulation can yield stable solutions for all subsonic flows (M < 1 ).

Original language	English
Title of host publication	Proceedings of the 14th International Conference on Pressure Surges
Editors	Sarah E. L. Jones
Place of Publication	Eindhoven
Publisher	Eindhoven University of Technology
Pages	443-457
Number of pages	15
ISBN (Print)	9789038657103
Publication status	Published - 2023
Event	14th International Conference on Pressure Surges - Eindhoven University of Technology, Eindhoven, Netherlands Duration: 12 Apr 2023 → 14 Apr 2023 https://pressuresurges14.win.tue.nl/

Conference

Conference	14th International Conference on Pressure Surges
Country/Territory	Netherlands
City	Eindhoven
Period	12/04/23 → 14/04/23
Internet address	https://pressuresurges14.win.tue.nl/

Keywords

one-dimensional
unsteady
compressible pipe-flow
momentum correction factor
energy correction factor

1 Citations
1 Conference contribution

On Boussinesq and Coriolis coefficients and implications for the Joukowsky equation
Vardy, A. E. & Tijsseling, A. S., 2023, Proceedings of the 14th International Conference on Pressure Surges. Jones, S. E. L. (ed.). Eindhoven: Eindhoven University of Technology, p. 223-338 16 p.
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Cite this

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title = "On the method of characteristics in highly compressible flows",

abstract = "The method of characteristics (MOC) is widely used in simulations of transient liquid flows. Nearly always, the method is simplified by key assumptions that the speed of sound is (i) constant and (ii) very much larger than the fluid velocity. This paper describes how MOC can be used in transient gas flows even when these assumptions cannot reasonably be made. Examples include flows at large (but subsonic) Mach number and strongly compressible flows in long pipes with skin friction and/or heat transfer. Four formulations of the basic equations are presented and their advantages and disadvantages are explained. The simplest of these, based on pressure p, density p and velocity U, closely resembles conventional water-hammer formulations. The most powerful formulation, based on temperature T, specific entropy s and Mach number M, has special advantages in the representation of a path-line equation that is always necessary in addition to the two wave-path equations. This formulation can yield stable solutions for all subsonic flows (M < 1 ).",

keywords = "one-dimensional, unsteady, compressible pipe-flow, momentum correction factor, energy correction factor",

author = "Vardy, {Alan E.}",

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year = "2023",

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T1 - On the method of characteristics in highly compressible flows

AU - Vardy, Alan E.

N1 - Copyright: © TU/ e 2023 Pressure Surges 14

PY - 2023

Y1 - 2023

N2 - The method of characteristics (MOC) is widely used in simulations of transient liquid flows. Nearly always, the method is simplified by key assumptions that the speed of sound is (i) constant and (ii) very much larger than the fluid velocity. This paper describes how MOC can be used in transient gas flows even when these assumptions cannot reasonably be made. Examples include flows at large (but subsonic) Mach number and strongly compressible flows in long pipes with skin friction and/or heat transfer. Four formulations of the basic equations are presented and their advantages and disadvantages are explained. The simplest of these, based on pressure p, density p and velocity U, closely resembles conventional water-hammer formulations. The most powerful formulation, based on temperature T, specific entropy s and Mach number M, has special advantages in the representation of a path-line equation that is always necessary in addition to the two wave-path equations. This formulation can yield stable solutions for all subsonic flows (M < 1 ).

AB - The method of characteristics (MOC) is widely used in simulations of transient liquid flows. Nearly always, the method is simplified by key assumptions that the speed of sound is (i) constant and (ii) very much larger than the fluid velocity. This paper describes how MOC can be used in transient gas flows even when these assumptions cannot reasonably be made. Examples include flows at large (but subsonic) Mach number and strongly compressible flows in long pipes with skin friction and/or heat transfer. Four formulations of the basic equations are presented and their advantages and disadvantages are explained. The simplest of these, based on pressure p, density p and velocity U, closely resembles conventional water-hammer formulations. The most powerful formulation, based on temperature T, specific entropy s and Mach number M, has special advantages in the representation of a path-line equation that is always necessary in addition to the two wave-path equations. This formulation can yield stable solutions for all subsonic flows (M < 1 ).

KW - one-dimensional

KW - unsteady

KW - compressible pipe-flow

KW - momentum correction factor

KW - energy correction factor

M3 - Conference contribution

SN - 9789038657103

SP - 443

EP - 457

BT - Proceedings of the 14th International Conference on Pressure Surges

A2 - Jones, Sarah E. L.

PB - Eindhoven University of Technology

CY - Eindhoven

T2 - 14th International Conference on Pressure Surges

Y2 - 12 April 2023 through 14 April 2023

ER -

On the method of characteristics in highly compressible flows

Abstract

Conference

Keywords

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Research output

On Boussinesq and Coriolis coefficients and implications for the Joukowsky equation

Cite this