Stability of detonation in a circular pipe with porous walls

Carlos Chiquete, Anatoli Tumin

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A stability analysis is carried out taking into account slightly porous walls in an idealized detonation confined to a circular pipe. The analysis is carried out using the normalmode approach and corrections are obtained to the underlying impenetrable wall case results to account for the effect of the slight porosity. The porous walls are modelled by an acoustic boundary condition for the perturbations linking the normal velocity and the pressure components and thus replacing the conventional no-penetration boundary condition at the wall. This new boundary condition necessarily complicates the derivation of the stability problem with respect to the impenetrable wall case. However, exploiting the expressly slight porosity, the modified temporal stability can be determined as a two-point boundary value problem similar to the case of a non-porous wall.

Original languageEnglish (US)
Pages (from-to)668-688
Number of pages21
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume370
Issue number1960
DOIs
StatePublished - Feb 13 2012

Fingerprint

porous walls
Detonation
detonation
Pipe
Boundary conditions
Porosity
boundary conditions
Normal Modes
Convergence of numerical methods
Two-point Boundary Value Problem
porosity
Penetration
Linking
Boundary value problems
Stability Analysis
Acoustics
boundary value problems
Perturbation
derivation
penetration

Keywords

  • Detonation
  • Linear stability
  • Normal mode
  • Porous wall

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Engineering(all)

Cite this

Stability of detonation in a circular pipe with porous walls. / Chiquete, Carlos; Tumin, Anatoli.

In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 370, No. 1960, 13.02.2012, p. 668-688.

Research output: Contribution to journalArticle

@article{ebda567c78674760924ba44d36e6674b,
title = "Stability of detonation in a circular pipe with porous walls",
abstract = "A stability analysis is carried out taking into account slightly porous walls in an idealized detonation confined to a circular pipe. The analysis is carried out using the normalmode approach and corrections are obtained to the underlying impenetrable wall case results to account for the effect of the slight porosity. The porous walls are modelled by an acoustic boundary condition for the perturbations linking the normal velocity and the pressure components and thus replacing the conventional no-penetration boundary condition at the wall. This new boundary condition necessarily complicates the derivation of the stability problem with respect to the impenetrable wall case. However, exploiting the expressly slight porosity, the modified temporal stability can be determined as a two-point boundary value problem similar to the case of a non-porous wall.",
keywords = "Detonation, Linear stability, Normal mode, Porous wall",
author = "Carlos Chiquete and Anatoli Tumin",
year = "2012",
month = "2",
day = "13",
doi = "10.1098/rsta.2011.0343",
language = "English (US)",
volume = "370",
pages = "668--688",
journal = "Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences",
issn = "0962-8428",
publisher = "Royal Society of London",
number = "1960",

}

TY - JOUR

T1 - Stability of detonation in a circular pipe with porous walls

AU - Chiquete, Carlos

AU - Tumin, Anatoli

PY - 2012/2/13

Y1 - 2012/2/13

N2 - A stability analysis is carried out taking into account slightly porous walls in an idealized detonation confined to a circular pipe. The analysis is carried out using the normalmode approach and corrections are obtained to the underlying impenetrable wall case results to account for the effect of the slight porosity. The porous walls are modelled by an acoustic boundary condition for the perturbations linking the normal velocity and the pressure components and thus replacing the conventional no-penetration boundary condition at the wall. This new boundary condition necessarily complicates the derivation of the stability problem with respect to the impenetrable wall case. However, exploiting the expressly slight porosity, the modified temporal stability can be determined as a two-point boundary value problem similar to the case of a non-porous wall.

AB - A stability analysis is carried out taking into account slightly porous walls in an idealized detonation confined to a circular pipe. The analysis is carried out using the normalmode approach and corrections are obtained to the underlying impenetrable wall case results to account for the effect of the slight porosity. The porous walls are modelled by an acoustic boundary condition for the perturbations linking the normal velocity and the pressure components and thus replacing the conventional no-penetration boundary condition at the wall. This new boundary condition necessarily complicates the derivation of the stability problem with respect to the impenetrable wall case. However, exploiting the expressly slight porosity, the modified temporal stability can be determined as a two-point boundary value problem similar to the case of a non-porous wall.

KW - Detonation

KW - Linear stability

KW - Normal mode

KW - Porous wall

UR - http://www.scopus.com/inward/record.url?scp=84856514524&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856514524&partnerID=8YFLogxK

U2 - 10.1098/rsta.2011.0343

DO - 10.1098/rsta.2011.0343

M3 - Article

C2 - 22213664

AN - SCOPUS:84856514524

VL - 370

SP - 668

EP - 688

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0962-8428

IS - 1960

ER -