Journal of the Korean Society of Propulsion Engineers Vol. 19, No. 2, pp. 29-37, 2015 29

Nomenclature

PDE : pulse detonation engine

GFM : ghost fluid method

Research Paper DOI: http://dx.doi.org/10.6108/KSPE.2015.19.2.029

-

a a a, *

Numerical Analysis of Detonation of Kerosene-Air Mixture

and Solid Structure

Younghun Lee a Min-cheol Gwak a Jai-ick Yoh a, *

a Department of Mechanical and Aerospace Engineering, Seoul National University, Korea* Corresponding author. E-mail: jjyoh@snu.ac.kr

ABSTRACT

This paper presents a numerical investigation on detonation of a kerosene-air mixture in the copper

tube and the structural response associated with combustion instability in liquid rocket engine. A

single step Arrehnius rate law and Johnson-Cook strength model are used to describe the chemical

reaction of kerosene-air mixture detonation and the plastic deformation of the copper tube. The

changes of flow field and tube stress which are induced by plastic deformation, are investigated on

the different tube thicknesses and nozzle configurations.

.

1 ,

Johnson-Cook .

.

Key Words: Kerosene(), Detonation(), Multi-material(), Liquid Rocket Engine

(), Plastic Deformation()

Received 24 December 2014 / Revised 8 March 2015 / Accepted 13 March 2015Copyright The Korean Society of Propulsion EngineerspISSN 1226-6027 / eISSN 2288-4548[ 2014 (2014. 12. 17-19,

) .]

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License(http://creativecommons.org /licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

30

C-J : Champman-Jouguet

e : total energy density

p : pressure

R : gas constant

u : velocity

Yi : mass fraction of the reactant mixture

: strain

: cauchy stress tensor

: deviatoric stress tensor

: level

r : r-axis in 2-D cylindrical domain

z : z-axis in 2-D cylindrical domain

1.

,

.

[1].

,

[2].

,

PDE(Pulse Detonation Engine)

.

PDE ,

.

,

[3-6].

,

[9]

.

, PDE

-

,

.

1

[4,8]

, -

GFM(Ghost Fluid Method)

,

.

.

PDE

,

.

2.

2.1

-

433 K

,

. -

1 2

, Eq. 1-5 2

.

(1)

19 2 2015. 4.-

31

(2)

(3)

(4)

(5)

, = 0, = 1 , -

, = 1, = 0

, .

, ur, uz, P, e, Yi , r z

, , ,

.

1

.

Eq. 6 1

. ,

[6].

exp (6)

,

(Hook)

Eq. 7

.

(7-1)

(7-2)

(7-3)

, ij, G, , DijP (spin

tensor), , ,

. = 1 ( = 0) (

) [7].

3 Conves

ENO scheme, 3 R-K

method, 2 FDM

.

2.2

,

. ,

Eq. 8 9 Mie-Grueisen

,

Johnson-Cook [7].

if

(8)

ln

(9)

32

, 0, a0, s, c0, A, B, n

Tm, T0, p, 0 ,

, , .

Johnson-Cook 1

, 1

[7].

2.3

Eulerian

, hybrid particle level set

. Eq. 10 level set

, =0

19 2 2015. 4.-

33

Fig. 2 Schematic of a 2D problem setup for tube.

Fig. 2

(4 mm X 30 mm) .

- 2

mm X 30 mm

C-J 2

.

(: 0.12 mm, : 0.2

mm)

.

, , ,

, , ,

(Xboundary=0.95X1+0.05X0) .

X1

36 bar

X0 1 bar[6].

- ,

1

, Mie-Gruneisen EOS,

Johnson-Cook

[7] .

. Fig.

3 1/15, 1/50, 1/100 mm

. 1/50 mm

Fig. 3 Pressure profiles of three different mesh sizes

(1/15, 1/50, and 1/100 mm).

1/100 mm von Neumann spike C-J

1/50 mm

. 1/50 mm 1

- (0.1 ~0.2

mm) 5 ~ 10

, 0.2

mm 10 [4]

.

3.3

,

0.2 mm

. Fig. 4

.

2 s

2 s

.

18 s 2 s

. 20 mm

.

,

34

Fig. 4 Pressure histories of a rigid tube(2D cylindrical

model).

,

.

C-J 2

(3.5 MPa) .

von Neumann

spike 2.8 MPa .

Fig. 5

.

.

,

. ,

0.12 mm

0.2 mm

.

Fig. 6 0.12 mm

. , Fig. 6(a)

Fig. 5 Snapshots of density [unit: kg/m3] in a rigid

tube, where arrows indicate the propagation

direction.

Fig. 6 Snapshots of density [unit: kg/m3] in a tube.

19 2 2015. 4.-

35

Fig. 7 Schematic of a 2D problem setup for nozzle.

Fig. 8 Snapshots of density [unit: kg/m3] in gas

phase and r-axis stress [unit: Pa] in solid

phase.

.

Fig.

6(b)

.

0.85

Fig. 9 r-axis stress [unit: MPa] at solid region.

.

rigid ,

.

3.4

.

Fig. 7 .

0.2

mm ,

45 60

2 mm, 1.5 mm,

2.5 mm .

Fig. 8 .

,

.

,

Fig. 9 .

36

4.

-

.

-

,

hybrid particle level-set

GFM .

,

,

.

PDE

.

.

-

,

.

2015 BK21

(No.

2013073861) ,

.

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- ABSTRACT1. 2. 3. 4. References