Some qualitative properties of the Riemann problem in gas dynamical combustion

Cheng Hsiung Hsu; Song Sun Lin

doi:10.1006/jdeq.1997.3304

Some qualitative properties of the Riemann problem in gas dynamical combustion

Cheng Hsiung Hsu, Song Sun Lin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We study the Chapman-Jouguet (CJ) model and the selfsimilar Zeldovich-von Neumann-Döring (SZND) model in chemically reacting gas flows. We discover some basic relationships among ignition temperature T_i, total chemical binding energy Q, and the adibatic exponent γ of polytropic gas. From these relations, we can determine when temperatures along the SZND burning solutions are higher than the ignition temperature T_i. We also study the all possible selfsimilar solutions for the SZND-model. From these results, we can determine when selfsimilar solutions for the CJ-model are the limits of selfsimilar solutions of the SZND model when the reaction rate tends to infinity.

Original language	English
Pages (from-to)	10-43
Number of pages	34
Journal	Journal of Differential Equations
Volume	140
Issue number	1
DOIs	https://doi.org/10.1006/jdeq.1997.3304
State	Published - 10 Oct 1997

Access to Document

10.1006/jdeq.1997.3304

Cite this

@article{7139057fac534644ab252f86c2249a93,

title = "Some qualitative properties of the Riemann problem in gas dynamical combustion",

abstract = "We study the Chapman-Jouguet (CJ) model and the selfsimilar Zeldovich-von Neumann-D{\"o}ring (SZND) model in chemically reacting gas flows. We discover some basic relationships among ignition temperature Ti, total chemical binding energy Q, and the adibatic exponent γ of polytropic gas. From these relations, we can determine when temperatures along the SZND burning solutions are higher than the ignition temperature Ti. We also study the all possible selfsimilar solutions for the SZND-model. From these results, we can determine when selfsimilar solutions for the CJ-model are the limits of selfsimilar solutions of the SZND model when the reaction rate tends to infinity.",

author = "Hsu, {Cheng Hsiung} and Lin, {Song Sun}",

note = "Funding Information: * The work was supported in part by the National Science Council of the Republic of China with Project NSC84-2121-M009-004.",

year = "1997",

month = oct,

day = "10",

doi = "10.1006/jdeq.1997.3304",

language = "???core.languages.en_GB???",

volume = "140",

pages = "10--43",

journal = "Journal of Differential Equations",

issn = "0022-0396",

number = "1",

}

TY - JOUR

T1 - Some qualitative properties of the Riemann problem in gas dynamical combustion

AU - Hsu, Cheng Hsiung

AU - Lin, Song Sun

N1 - Funding Information: * The work was supported in part by the National Science Council of the Republic of China with Project NSC84-2121-M009-004.

PY - 1997/10/10

Y1 - 1997/10/10

N2 - We study the Chapman-Jouguet (CJ) model and the selfsimilar Zeldovich-von Neumann-Döring (SZND) model in chemically reacting gas flows. We discover some basic relationships among ignition temperature Ti, total chemical binding energy Q, and the adibatic exponent γ of polytropic gas. From these relations, we can determine when temperatures along the SZND burning solutions are higher than the ignition temperature Ti. We also study the all possible selfsimilar solutions for the SZND-model. From these results, we can determine when selfsimilar solutions for the CJ-model are the limits of selfsimilar solutions of the SZND model when the reaction rate tends to infinity.

AB - We study the Chapman-Jouguet (CJ) model and the selfsimilar Zeldovich-von Neumann-Döring (SZND) model in chemically reacting gas flows. We discover some basic relationships among ignition temperature Ti, total chemical binding energy Q, and the adibatic exponent γ of polytropic gas. From these relations, we can determine when temperatures along the SZND burning solutions are higher than the ignition temperature Ti. We also study the all possible selfsimilar solutions for the SZND-model. From these results, we can determine when selfsimilar solutions for the CJ-model are the limits of selfsimilar solutions of the SZND model when the reaction rate tends to infinity.

UR - http://www.scopus.com/inward/record.url?scp=0031563742&partnerID=8YFLogxK

U2 - 10.1006/jdeq.1997.3304

DO - 10.1006/jdeq.1997.3304

M3 - 期刊論文

AN - SCOPUS:0031563742

SN - 0022-0396

VL - 140

SP - 10

EP - 43

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

Some qualitative properties of the Riemann problem in gas dynamical combustion

Abstract

Access to Document

Fingerprint

Cite this