Optics and Photonics Journal, 2013, 3, 90-93
doi:10.4236/opj.2013.32B023 Published Online June 2013 (http://www.scirp.org/journal/opj)
Based on Fluent Numerical Calculation of Refractive
Index on Rocket Engine Nozzle Plume
Qiangfeng Huang1, Xiong Wan1,2* Zhi min Zhang1, Huaming Zhang1,
Hengyang Shen1, Tingting Du1
1Key Laboratory of Nondestructive Testing (Ministry of Education), Nanchang, Hangkong University, Nanchang, Jiangxi, China
2Key Laboratory of Spatial Active Opto-electronic Techniques, Shanghai Institute of Technical, Physics,
Chinese Academy of Sciences, Shanghai, China
Received 2013
ABSTRACT
Numerical 2D simulation and research on internal flow field and external flow field of rocket motor nozzle using
FLUENT software. Analyze the flow condition of internal flow field and external flow field, and according to add in the
amount of the different gas components, obtain the clear distribution of contour of density flow field, pressure flow
field and various material components and so on. Simulation results agree with the results observed from the test on the
ground, and provide reference for s ol id rocket m ot or development.
Keywords: Rocket Engine Nozzle; Nozzle Plume; Fluent; Numerical Simulation
1. Introduction
The plume of the rocker motor is composed by the high
temperature, high-pressure, high-flow combustion prod-
ucts of propellan t, wh ich g o thoug h Lava l-nozzle f low b y
static state and form a supersonic gas flow on the cross
section of a nozzle. The exhaust plume of rocket motor
nozzle is composed by H2O, CO2, CO, H2 and N2 and so
on. According to design conditions of the difference,
they will make larger difference among flow field calcu-
lation, so in order to obtain the best density field contours,
here we chose the parameters of 7500 N thrust for nu-
merical calculation. In this paper, some propellant was
thermodynamically calculated, and the total temperature
and the total pressure of the gas and the mass fraction of
the ingredients of combustion resultants were obtained.
Meanwhile, the finite-rate chemical reaction model of
flow field of exhaust plume was built. Using fluent cal-
culation software solve the NS equation and the compo-
nent transport equation, so temperature field and density
field and ingredient distribution curves of the exhaust
plume were calculated, then the relationship of making
use of density field and several ingredient contents solve
the distribution of refractive index field which compare
with the experimental results again, it is available to v er-
ify the calculation method.
2. Calculation Conditions and Boundary
Condition
In order to numerical calculation which is convenient,
some rocket motor model is predigested processing. Se-
lecting the co mbustor end which is the nozzle in let is also
the gas inlet. In order to obtain higher calculation accu-
racy, the compressible, Reynolds-averaged difference N-S
equation and second order upwind are adopted to solve
the model when calculating internal flow field and nozzle
plume area. The turbulence model will adopt RNG k-

equation [1] turbulence model, and using non-equilib-
rium wall function [2] near the wall is processing. The
calculation method will adopt PISO algorithm which
must solve the pressure correction equation twice. So it
needs additional storage space to calculate the source
term in the secondary pressure correction equation. Al-
though this me t h o d invo lves more ca lc ulati ons, compar ed
to other algorithms, its speed fast, iteration converges
faster, and efficiency is very high.
2.1. Computational Domain and Boundary
Conditions
Computational domain of nozzle and flow field of plume
is shown in Figure 1. Effective length of the plume do-
main is about 10 m × 3 m. The ABHI area is the ter-
minal area of combustion chamber which is also nozzle
area, the EFGH area and the CDEHB area are plume
*Corresponding author.

Q. F. HUANG ET AL. 91
ones. The boundaries of the computational domain are
divided as following: AI area is boundary condition of
the boundary condition of the entrance of engine nozzle;
AC area is symmetrical axis of the computational domain;
CD, DEF and FG area are boundary conditions of the
exit of engine nozzle; GH and HI area are wall condi-
tions. The boundary condition of the entrance of engine
nozzle can be obtained with the thermodynamic calcula-
tion under the working conditio n of 75 00 N thru st, which
includes the total pressure 0.8 MPa, the total temperature
3040K, and the mass fraction of the ingredient of com-
bustion resultant as shown in Table 1; the total pressure
1.01325 × 105 Pa and the total temperature 300 K as
the boundary condition of the exit of engine nozzle; Vis-
cous no-slip boundary was chosen as the boundary con-
dition of the inner wall surface of engine nozzle.
2.2. Mesh Dividing of the Computational
Domain
According to the status of the gas flowing within the
nozzle, closing to the wall within the nozzle and sym-
metrical axis in plume domain are taken to mesh refine-
ment, the computational mesh needs to adopt the division
of structured mesh. The setup of computational region
and the division of computational meshes are shown in
Figure 2.
3. Numerical Computation Approach
Under normal circumstances, the relationship between
the density of plumes (ρ) and the refractive index of'
=>7??A>7 <A@97@=>7??A>7 <A@97@
=>7??A>7 <A@97@
=>7??A>7 8;97@B399 4<A;63>D
?D::7@>8539 3C8?
0/.
-
,
+
12
Figure 1. Sketch of computational domain.
Table 1. Mass fraction of the ingredients of combustion
resultant in the entrance of the nozzle.
Sequence Ingredient Mass fraction
1 H2 0.0144
2 CO2 0.0832
3 CO 0.1746
4 H2O 0.2866
5 N2 0.4160
plumes (n) can make use of the Gladstone-Dale [6] for-
mula which can be expressed as
1ii
i
nK

 

(1)
where Ki are a property of the gases and are also the
Gladstone-Dale constants, called as refractivity. By look-
ing up table we obtain Ki of the five main components of
plumes which are given in Table 2; αi are the mass frac-
tions of the individual components; ρ is the density of
plumes.
4. Computation Results and Analysis
In the paper, the nozzle inflow medium can be consid-
ered as the gas of ambient temperature which is treated
as idea status. Viscosity coefficient using the three-coef-
ficient Sutherland method is calculated [3]. The flow
model is numerical calculated by using FLUENT soft-
ware. Through simulated calculation solve the differen-
tial N-S equation [4], the internal field and external field
of engine motor nozzle are obtained. The distribution of
the contour of the density is shown in Figure 3; the dis-
tribution of the contour of the total pressure is shown in
Figure 4; the distribution of the contour of the tempera-
ture is shown in Figure 5; and the distribution of the
contour of axial velocity and radial velocity are shown in
Figures 6(a) and (b) respectively; the distribution of the
contour of mass fractions of five main components com-
puted are shown in Figures 7(a), (b), (c), (d) and (e)
respectively.
We can see from Figure 3 to Figure 6 that the density
and the pressure of the external field of motor plume are
higher in place of the entrance cross section of particles,
Figure 2. The setup of computational region and division of
computational meshes.
Table 2. Gladstone-Dale constants of the five main compo-
nents of plumes.
Sequence Ingredient Ki
1 H2 1.538
2 CO2 0.229
3 CO 0.267
4 H2O 0.312
5 N2 0.238

Q. F. HUANG ET AL.
92
Figure 3. The distribution of the contour of the density.
Figure 4. the distribution of the contour of the total pres-
sure.
Figure 5. the distribution of the contour of the temperature.
(a)
(b)
Figure 6. (a) the distribution of the contour of axial velocity;
(b) the distribution of the contour of radial velocity.
(a)
(b)
(c)
(d)
(e)
Figure 7. (a) the distribution of the contour of mass frac-
tions of H2; (b) the distribution of the contour of mass frac-
tions of CO2; (c) the distribution of the contour of mass
fractions of CO; (d) the distribution of the contour of mass
fractions of H2O; (e) the distribution of the contour of mass
fractions of N2.

Q. F. HUANG ET AL.
93
but reduced with air stream flowing to the vacuum; the
higher the temperature, the faster the particle’s velocity,
and with the expansion of jet flow and continue to rise,
temperature does not rise after gas flow diffuse into the
plume field; the axial velo city is the smallest o ne through
the exit cross section of motor, but radial velocity is the
biggest one, basically the distribution of velocity along
radial direction and increase constantly, and show a dif-
fusing accelerated process.
We can see from Figure 7 that the mass fractions of
the five individual components are changed constantly
with gases flowing into motor plume.
The above analysis shows that the main impact in the
motor plume flow field is that come from the diffusion of
boundary layer in the exit wall boundary of motor; plume
in vacuum diffuses very fast, and the ability of doing work
decrease greatly; the refractive index field will have an
influence with gas flow di ffusion.
5. Conclusions
This paper mainly calculated the refractive index field of
rocket motor nozzle plume, and two-dimensional axi-
symmetric Reynolds averaged NS equation was chosen
to solve; this paper that using FLUENT software carried
out numerical simulation which analyzed detailed condi-
tions and distribution characteristics of internal field and
external field of nozzle. At the same time, related fluid
flow theory was verified. This simulation provided the
data base in aspects of the design of rocket motor and
carrying out other researches for plume flow field. Other
parts need to be further study.
6. Acknowledgements
The work was supported by Chinese Natural Science
Foundation (grant 61271397), Jiangxi provincial Natural
Science Foundation (grant 20122BAB202009), Jiangxi
provincial education department Science and Technology
Foundation (grant GJJ12408) and preferentially funded
by the “Hundred Talents Plan” of the Chinese Academy
of Sciences.
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