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Procedia Engineering 00 (2014) 000–000
www.elsevier.com/locate/procedia
“APISAT2014”, 2014 Asia-Pacific International Symposium on Aerospace Technology,
APISAT2014
A Numerical Study of the Flow Dynamics of Through-type Pintle
Nozzles with Large Scale Separation Flow
Ki-Yeon Jeonga, Jun-Young Heoa, Hong-Gye Sungb,*
a
Department of Aerospace and Mechanical Engineering, Korea Aerospace University, Gyeonggi-do, 412-791, South Korea
b
School of Aerospace and Mechanical Engineering, Korea Aerospace University, Gyeonggi-do, 412-791, South Korea
Abstract
A numerical study of the flow dynamics of through-type pintle nozzle has been analyzed. Two-equation turbulence models, namely
the low Reynolds k-e models with compressibility corrections proposed by Sarkar are evaluated and compared with experimental
results. The flow dynamics is analyzed with a mass flow inlet condition in order to provide the same boundary condition used in a
cold flow test. In order to investigate the pintle movement effects, the sliding mesh method was applied and the pintle velocity is
set at 0.1m/s. Performance characteristics of through-type pintle nozzle are derived comparing nozzle wall pressure and thrust.
© 2014 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA).
Keywords: Pintle Nozzle; Separation Flow; Burning Rate
1. Introduction
The Combination of different burning rate propellants, fracturing of the wall barrier between grains, and the pintle
stroke in a nozzle can be employed as a technique to change thrust level during a solid motor operation[1,3]. Among
them, the pintle nozzle is the most effective control method, especially for continuous change[4,6]. However, sudden
movement of the pintle usually induces the rapid change of flow fields; pressure oscillations in the combustor, shock
train and flow separation in the nozzle, and so on[7,8]. The shock train and flow separation to the pintle position in
* Corresponding author. Tel.: +82-10-5275-9196; fax: 02-3158-5769.
E-mail address: [email protected]
1877-7058 © 2014 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA).
Author name / Procedia Engineering 00 (2014) 000–000
2
the nozzle are a highly unsteady phenomena which may cause flow instability and hysteresis of thrust[9]. So the
precious capture of shock and flow separation for the pintle stroke is a very important factor for the prediction of
pressure and thrust of the motor. Through previous studies, a suitable turbulence model is selected[10,12]. The object
of this research is comparing to reacting/non-reacting characteristics of the solid motor with through-type pintle nozzle.
Nomenclature
At
Nozzle Throat Area
P
Pc
Static Pressure
Chamber Pressure
P"d "
Pk
Pressure Dilatation
Production of Kinetic Energy
T
Ck
Static Temperature
Turbulent Time Scale Parameter
Ce 1 , Ce 2
Turbulent Energy Dissipation Parameter
Cm
Turbulent Viscosity Parameter
k
Turbulent Kinetic Energy
M
Mach Number
Turbulent Mach Number
Mt
R
t
Tturb
u
Specific Gas Constant
Time
Turbulent Time Scale
y+
Velocity
Volume
Spatial Coordinate
Dimensionless Wall Distance
a1 , a 2 , a 3
Model Constants for Compressible Correction of
g
d ij
Specific Heat Ratio
ec
eS
Compressible Dissipation
m
Molecular Viscosity
Turbulent Viscosity
V
x
mt
r
Kronecker Delta
Dissipation Rate
s k ,s e
Density
Model Constants
t ij
Viscous Stress Tensor
k - e Model
Author name / Procedia Engineering 00 (2014) 000–000
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2. Numerical method
2.1. Governing equation
The Favre-averaged governing equation based on conservation of mass, momentum, and energy for a compressible
flow can be written as:
¶ r ¶ r u°j
+
=0
¶t
¶x j
(1)
(
°°
¶ t ij - r u "j ui"
¶ r u°i ¶ r ui u j + pd ij
+
=
¶t
¶x j
¶x j
(
)
)
(2)
° + p u°
¶ u°i t ij - r h"ui" ¶ q
° ¶ rE
j
¶r E
+
=
- j
¶t
¶x j
¶x j
¶x j
((
) )
(
)
(3)
2.2. Turbulence closure & compressibility corrections model
To account for the important features in high-speed flow, the combined model of compressible-dissipation and
pressure-dilatation proposed by Sarkar [13,15] and the low Reynolds number k - e model was used in this study.
The turbulent kinetic energy and its dissipation rate are calculated from the turbulence transport equation as follows:
Low-Reynolds k - e Turbulent Model
°
m
¶ rk ¶ r u j k
¶ ææ
+
=
çç ç m + i
¶t
¶x j
¶x j è è
sk
(
)
ö ¶k
÷
ø ¶x j
°
¶ re s ¶ r u j e s
m
¶ ææ
+
=
çç ç m + i
¶t
¶x j
¶x j è è
se
(
)
ö
" "
÷÷ + Pk - r ( e s + e c ) + p d
ø
ö ¶e s
÷
ø ¶x j
(
)
ö Ce 1 Pk - Ce 2 re s
+L
÷÷ +
Tturb
ø
(4)
(5)
e c = a1M t2e s
(6)
p"d " = -a 2 Pk M t2 + a 3 re s M t2
(7)
Where
ec
and
p"d " represent compressible-dissipation and pressure-dilatation, respectively. The closure
coefficients for the compressible corrections are:
Sarkar’s Model
Author name / Procedia Engineering 00 (2014) 000–000
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a1 = 1.0,
F ( M t ) = M t2
(8)
2.3. Numerical scheme
Dual time stepping and LU-SGS are applied for time integration, and the control volume method is used to
integrate inviscid fluxes represented by AUSMPW+ and MUSCL and viscous fluxes by central difference. In order
to obtain a stable numerical result in a wide range of Mach number and variants of cell size, the precondition
technique is applied. The code is parallelized using an MPI library to accelerate the calculation.
2.4. Sliding mesh mechanism
In order to investigate the pintle movement effects, the sliding mesh method was studied. The sliding mesh
mechanism is shown in Fig. 1.
Fig. 1. Sliding mesh mechanism
An initial state, the bottom and upper blocks are met. By moving the bottom block, one grid point of the upper
block follows the bottom block. When one grid passes the next grid, the moving grid of the upper block is set at an
initial state and the next grid of the moving grid follows the bottom block. Since this causes it to go through an
existing grid, the grid of the bottom block disappears.
3. Model description and Boundary condition
Schematics of the pintle nozzle and boundary conditions are shown in Fig. 2. There are approximately 50~55K
total grid points, and the first cell height along the inside of the nozzle is approximately y+ = 1, imposing on
approximately five cells in the boundary layer. Several boundary conditions are applied for this study; the mass flow
rate inlet boundary condition of the chamber, the constant pressure outflow boundary conditions for subsonic flow,
switched to extrapolation for the supersonic flow, and a no-slip and adiabatic wall boundary condition on the nozzle
and pintle walls. Along the nozzle axis, the ax symmetric boundary condition is specified.
Fig. 2. Schematics of pintle nozzle and grid system with boundary conditions
Author name / Procedia Engineering 00 (2014) 000–000
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4. Results
4.1. Sliding mesh mechanism result
The sliding mesh mechanism is compared with the commercial code, Fluent. It leads to a generation of a
discontinuous boundary since the interpolation was considered. However, the in-house sliding mesh mechanism code
shows an improved result because conformal grids are maintained regardless of the mesh movement.
(a)
(b)
Fig. 3. X-velocity contour; (a) Fluent (b) In-house code
Stream wise velocity and temperature are compared at the location of pintle tip. The position of data extraction is
represented at Fig. 4.
Fig. 4. Data extraction location of pintle tip
(a)
(b)
Fig. 5. (a) Temperature distribution (b) x-velocity distribution
Figure 5 indicates that the distributions of temperature and x-velocity show differences in continuity of the
pintle sliding interface, although the flow structure is similar to both codes. Consequently, the discontinuous boundary
in the mass and energy conservation leads to poor pintle performance.
Author name / Procedia Engineering 00 (2014) 000–000
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4.2. Performance characteristics of pintle stroke
(a)
(b)
(c)
(d)
(e)
Fig. 6. Flow structures (a) 0 mm (b) 10 mm (c) 20 mm (d) 30 mm (e) 40 mm
No change in flow structure was observed at position 0 and 10mm (Fig. 6.(a) and (b)). It implies that an area of
nozzle throat was not changed. As pintle moves to position at 20mm (Fig. 6.(c)), new nozzle throat is formed at an
inclined part of the pintle. This nozzle throat area affects the combustion chamber pressure, and it shows that air with
constant mass flow rate flows into the combustor. At 30 mm of the pintle position (Fig. 6.(d)), it is observed that
shockwaves, generated at pintle slope hit the nozzle wall and lead to flow disturbance. And also generation of a large
separation region was captured at the nozzle exit wall (Fig. 6.(e))
Fig. 7. Nozzle wall pressure distribution
Author name / Procedia Engineering 00 (2014) 000–000
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Figure 7 shows the pressure distribution of the nozzle wall at each position of pintle. When 40 mm of the pintle
position, the nozzle wall pressure is restored by the separated flow.
Fig. 8. Thrust variation of momentum & pressure
& e + ( Pe - Pa ) Ae
F = mV
(9)
Equation (9) indicates that thrust of the rocket, and it consists of momentum and pressure. Figure. 8 shows thrust,
momentum and pressure at each position of pintle. The thrust, momentum and pressure values are normalized with
initial thrust at 0 mm. The pressure term has a negative value since the pintle nozzle is operated over-expansion
condition. From 0 to 40 mm, the tendency of thrust and momentum is similar. Furthermore, the maximum difference
of thrust is 20%. The position of the pintle at the 40 mm, the pressure term shows the largest variation due to the effect
of the separation flow. At the same time, thrust and momentum are the biggest term due to the highest chamber
pressure.
5. Conclusions
The numerical study of the flow dynamics of the through-type pintle nozzle has been conducted. The flow dynamics
of pintle nozzle in cold flow condition is analyzed with a mass flow inlet condition in order to provide the same
boundary condition. The in-house sliding mesh mechanism code shows an improved result because conformal grids
are maintained. At each position of pintle, the structure of flow and shockwaves are different. As pintle moves to
downstream, intense shockwaves are generated. Due to the shockwaves, pressure term is the largest. At the same time,
the thrust and momentum term is biggest due to the highest chamber pressure.
6. Acknowledgement
This work was supported by Defense Acquisition Program Administration and Agency for Defense Development
under the contract UD140023GD.
Author name / Procedia Engineering 00 (2014) 000–000
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