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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: [email protected]
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