Based on Fluent Numerical Calculation of Refractive Index on Rocket Engine Nozzle Plume

doi:10.4236/opj.2013.32B023

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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

Email: *[email protected]

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/.

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









(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.

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.

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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