Al particles additives

Accepted Manuscript Research Paper Experimental and numerical investigations on the decomposition and combustion characteristics of composite propellant with Mg/Al particles additives Min Zhu, Xiong Chen, Chang-sheng Zhou, Jin-sheng Xu, Omer Musa, Hengsheng Xiang PII: DOI: Reference:

S1359-4311(16)31904-4 http://dx.doi.org/10.1016/j.applthermaleng.2016.09.140 ATE 9165

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

30 July 2016 19 September 2016 24 September 2016

Please cite this article as: M. Zhu, X. Chen, C-s. Zhou, J-s. Xu, O. Musa, H-s. Xiang, Experimental and numerical investigations on the decomposition and combustion characteristics of composite propellant with Mg/Al particles additives, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng.2016.09.140

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Experimental and numerical investigations on the decomposition and combustion characteristics of composite propellant with Mg/Al particles additives Min Zhu, Xiong Chen*, Chang-sheng Zhou, Jin-sheng Xu, Omer Musa, Heng-sheng Xiang （School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, PR China）

Abstract Experimental and numerical works were carried out to investigate the decomposition and combustion characteristics of composite propellant with magnesium and aluminum particles additives in the near burning surface region. Experiments were performed to film the macro-structures of combustion flame, measure the constant pressure burning rates, and test the temperature distributions of combustion wave. Both of the fitted pressure-burning rate curves match well with experiment results and have good predictive capability under ramjet working conditions. A detailed combustion kinetic model was employed in the in-house computational solver to simulate this typical two-phase flow problem. The combustion phenomenon was analyzed carefully about flame structure, chemical reaction order, and an obvious "double-platform" phenomenon was observed in the temperature distributions of combustion wave on central axis. The simulation results show that on one hand higher ambient pressure restricts the diffusion of primary combustion gases, but on the other it enhances the thermal feedback effect on solid domain and helps the combustion stability of composite propellant. The influences of oxygen concentration on the combustion wave structure in axial direction are negligible before platform 1 position, while the diffusion combustion characteristics in radial direction are obviously changed.

Key words Composite propellant, Mg/Al particles additives, Two-phase flow, Computational fluid dynamics

1 Introduction Solid propellant is widely used in many propulsion systems for its obvious advantages as simplicity, reliability, and low cost compared to liquid fuel. Composite propellant is a kind of mechanical mixtures, which belongs to heterogeneous solid propellant, and its micro-structure is heterogeneous. Its basic components include oxidizing agent, polymer binder, metal particles and a small amount of other additives like curing agent, antioxidant, combustion

*Corresponding author, Tel: +86 13951981754 Email address: [email protected]

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stabilizer, plasticizer, etc [1]. From the 1940's, people found that adding energetic metal particles to composite propellant ingredient could obviously improve its density and specific impulse. Furthermore, researchers confirmed that appropriate number and size distribution of metal particles additives could help to overcome the combustion instability phenomenon caused by acoustic oscillations, and improve the performance of rocket motor in the recent decades [2]. Numerous experiments were carried out to investigate the decomposition and combustion characteristics of composite propellant, and researchers put forward a variety of hypotheses and combustion models according to respective experiment results. In the late 1950's, M. Summerfield et al. [3] proposed the famous granular diffusion flame model (GDF) based on his study on the combustion mechanisms of ammonium perchlorate (AP) based composite propellant. This GDF model belongs to gas phase reaction model. M.W. Beckstead, R. Derr and C. Price [4] carried out a large number of experiment observations on the surface structures of AP based composite propellant and presented the multiple flames model (BDP) in 1970. R. Glick and J. Condon [5, 6] proposed a small particle aggregation model in 1976. In 1974, G. Sammons et al. [7] put forward a critical AP particles size model and calculation method based on the original BDP model. C.E. Hermance [8] improved the GDF model and proposed a heterogeneous reaction model. This was the first theoretical model that considered the effects of condensation reactions and surface discontinuities of composite propellant. It was also the first model which introduced statistical concepts to analyze experiment statistics. In addition, free-radicals-cleavage model [9], neural-network model [10] and some other new decomposition and combustion models had been proposed in the recent decades. Severe difficulties were encountered by individuals attempting to conduct rigorous performance calculations for propellant systems that gave multiphase combustion products characterized by complex chemical and thermal equilibrium between 1955 and 1958. Then many scientists and organizations worked together and the Joint Army-Navy-Air Force (JANAF) Thermochemical Tables were finally pressed by M.W. Chase [11] in 1970. Thermodynamic parameters as specific heat, enthalpy and entropy can be achieved from this table. R.J. Kee et al. [12] in Sandia National Laboratories programmed a Fortran Chemical kinetics package for analyzing the gas-phase chemical and plasma kinetics in 1996, which made it possible to calculate the ideal combustion temperature and products of given components based on the principle of minimum Gibbs free energy theory. With the development of computational fluid dynamics (CFD), researchers tried to do numerical investigations on the decomposition and combustion characteristics of composite propellant. E.W. Price [13] and B.T. Chorpening [14] assumed the structure of AP/ hydroxyl-terminated polybutadiene (HTPB) propellant as a periodic sandwich model and simulated its burning surface with a simplified two-step reaction kinetic model. S. Kochevets et al. [15] modelled the two-dimensional structure of composite propellant with various particles sizes distribution based on random packs 2 / 22

theory. M.L. Gross et al. [16] coupled the micro and meso-scale combustion models and achieved a more theoretically based and accurate description of AP/HTPB combustion flame. Most former researchers just studied the decomposition and combustion characteristics of composite propellant and proposed theoretical models in a stable condition. However, the ambient pressure in the combustion chamber varies as cruising altitude or speed changes during the working process of a ramjet. To improve the combustion efficiencies of composite propellant, researchers usually use the methods of changing the mass fraction of oxidant in its ingredient or introducing outside air into afterburning chamber to support combustion. Then the oxygen concentration in the flow field will change. Therefore, it is necessary to investigate the real decomposition and combustion characteristics of composite propellant under the actual ramjet working conditions. This paper focuses on the near burning surface region to analyze the temperature distributions of combustion wave and the conjugate heat transfer (CHT) conditions inside the solid domain. Experiments were performed on the sealed high-temperature and high-pressure laser ignition platform. The macro-structure of combustion flame was filmed with infrared imaging technique. The constant pressure burning rates were measured by constant pressure experiments with target line method. Then the experiment results were fitted based on two semi-empirical formulas and good agreements were achieved within the pressure range of ramjet working conditions. The temperature distributions of combustion wave were tested with embedded micro-thermocouple method and the burning surface temperature was obtained at the peak of temperature heating rate curve. This paper developed a reasonable and accurate in-house computational solver in Fortran language to numerically simulate the decomposition and combustion characteristics of composite propellant with magnesium (Mg) and aluminum (Al) particles additives in the near burning surface region based on a detailed combustion kinetic model with 16 components and 16 chemical reactions. This paper detailedly investigated the decomposition and combustion characteristics of composite propellant, including comparing the simulated burning surface temperature and the CHT conditions inside the solid domain with experiment results and analyzing the temperature and components distributions of combustion wave on central axis. The changes of cruising altitude and speed will obviously affect the working characteristics of ramjet. Hence, this paper mainly investigated the influences of ambient pressure and oxygen concentration changes on the decomposition and combustion characteristics of composite propellant with several computational cases.

2. Experiment instruments Experiments were carried out on the sealed high-temperature and high-pressure laser ignition platform. The schematic diagram of the experiment system is shown in Fig. 1. It mainly consists of three parts: (1) a carbon dioxide laser optical system for igniting composite propellant samples, (2) an infrared imager system for observing the macro-structure of combustion flame inside the windowed combustion chamber, (3) an embedded micro-thermocouple 3 / 22

testing system for measuring the temperature distribution of composite propellant samples on central axis under different ambient pressure and oxygen concentration conditions. This paper investigated the surface decomposition and combustion characteristics of composite propellant with 40 wt% Mg/Al particles additives, which was produced for ground direct-connected experiments of solid rocket ramjet by Xi'an Modern Chemistry Research Institute. The general components of the composite propellant ingredient are listed in Table 1. The decomposition and combustion phenomenon of composite propellant is accompanied with bright lights and lots of black smoke products. The embedded micro-thermocouple method [17] is a classical contact method to measure the temperature distributions of combustion wave, and has many advantages like wide range, high precision, fast response, etc. Its basic concept is fixing the micro-thermocouple probe position inside the composite propellant samples and then temperature signal is turned into voltage signal as the burning surface regresses during the steady combustion process to realize the temperature measurement at different positions on central axis. The experimental composite propellant were cut into samples of Φ5  20 mm3 size and were coated with high-temperature resistant insulating rubber on the surrounding sides to prevent flame over when burning, as shown in Fig. 2. The micro-thermocouple was previously embedded into the experimental sample as the literature mentioned. The positive and negative terminals were leaded out from the pole of a specially designed flange sealing screw with drilling holes on central axis. Then voltage signal was connected to the micro-thermocouple signal conditioner and was turned into digital signal by a NI data acquisition card for reading and recording in computer. The velocity in the near burning surface region is relatively slow, then the regression effects on composite propellant are not obvious, which means the ambient pressure in combustion chamber is the main reason that affects the burning rate. The burning rates can be divided into constant pressure burning rate and dynamic pressure burning rate. Z.Z. Li and B.X. Li [18] found that the pressure changes during the combustion process had obvious effects on the burning rates, and the differences between these two rates can be as large as 17% for composite propellant. When the flight state of ramjet is steady, composite propellant keeps burning under the constant pressure condition. The constant pressure experiments with target line method were carried out in this paper to measure the constant pressure burning rates of composite propellant under different ambient pressure conditions and the experiment results were useful for numerical simulation then. Compressed gases were filled in the sealed high-temperature and high-pressure combustion chamber before started doing experiments to simulate different ambient pressure and oxygen concentration conditions in the ramjet. The experiment results are listed for validating the numerical simulation results in the following sections.

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3. Mathematical models and numerical schemes Commonly, there are two mathematical models for simulating two-phase problem as two-fluid model [19, 20] based on Euler method, and particle trajectory model [21] based on Lagrange method, depending on the actual volume fraction of particles in flow field. This paper focuses on the near burning surface region of composite propellant, where has low velocity compared to the main flow field in a ramjet. Meanwhile, the composite propellant samples used in the experiments have a large mass fraction (about 40 wt%) of very fine Mg/Al particles (average initial diameter of about 20 micrometres). The temperature of composite propellant combustion flame can be higher than 3000 K, which means Mg and Al particles and their oxidation products will melt into liquid. Then these droplets have large volume fraction in the flow field compared with the characteristic parameters of some experimental and numerical study cases in literatures [22], which means it is suitable to choose two-fluid model to investigate the decomposition and combustion characteristics.

3.1 Governing equations of the fluid computational domain There is a constraint of the volume fraction for Euler-Eulerian two-fluid model in the fluid computational domain:

g  l  1.0

(1)

where the subscript "g" represents "the first fluid" of gaseous phase, which consists of arbitrary defined N g kinds of gas species as composition of O2 , N2 , etc. And the subscript "l" stands for "the second fluid" in liquid phase, g including N l kinds of liquid species like Mg and Al droplets and their combustion products. g   p 1g, p and

N

l   q 1l, q are the total volume fractions of these two phases, respectively. Nl

In cylindrical coordinates (r , , z ) , the conservation equations of mass, momentum and energy are expressed in the two-dimensional axisymmetric form as:

E F U E F    H  v  v  Hv  S t z r z r

(2)

where U is the original variables vector, E and F represent the inviscid flux vectors, E v and Fv stand for the viscous flux vectors, H and H v are the inviscid and viscous axisymmetric vectors, and S stands for the chemical reaction and two-phase coupling source vector. The two fluids have separate velocity and temperature fields with individual governing equations, but there is a tendency for these to equalize through mass transfer, momentum transfer and heat transfer in the source term. For gaseous phase species, these vectors in formula (2) are expressed as: 5 / 22

 g,1 g,1ug   g,1 g,1vg   g,1 g,1vg   g,1  g,1          ... ... ...        ...   g, p g, p ug   g, p g, p vg   g, p g, p vg   g, p  g, p          ... ... ...       ...  1 Ug    , Eg     u  , Fg     v  , H g     v  , r  g, Ng g, Ng g   g, Ng g, Ng g   g, Ng g, Ng g  g, Ng  g, Ng      uv   uv    u  2 g g g g g g g g  g ( g ug  pg )       g g g    uv    ( v2  p )     g  g vg  g g vg2 g g g g g g g g         g (  g Eg  pg )ug  g ( g Eg  pg )vg  g ( g Eg  pg )vg   g  g Eg 

Eg,v

H g,v

c c     g,1 g Dg,1 g,1 g,1  g Dg,1 g,1     z r     ... ...         c c     g, p g Dg, p g, p g, p g Dg, p g, p     z r     ... ...   , Fg,v   ,   cg, Ng  cg, Ng   g, Ng  g Dg, Ng   g, Ng  g Dg, Ng  z r         g g, zz g g, zr     g g, zr g g, rr         g (ug g, zz  vg g, zr  qg, z )  g (ug g, zr  vg g, rr  qg, r ) 

(3)

mg,1   cg,1       D   g,1 g g,1 ...   r     m ... g, p       ...   cg, p   g, p g Dg, p     mg, Ng r    1   ... Ng    , Sg    r m u  F    g  gl, p g gl ,z g g z cg, Ng    p 1  g, Ng  g Dg, Ng     r N   g     mgl, p vg  Fgl ,r g g, zr      p 1   g ( g, rr   g, )    Ng      mgl, p Eg, p  ( Fgl ,z ug  Fgl ,r vg )  Qgl  g (ug g, zr  vg g, rr  qg, r )   p 1 

g where g , p is the density of the p th gaseous species, and g   p 1 g, p is the total density consisting of all kinds

N

of gaseous species in control volume. ug and vg are the velocity components of gaseous species in z and r directions, respectively. pg is local pressure and Eg is total gaseous energy per unit mass. cg, p  g, p / g is the mass fraction of the p th gaseous species and mg, p is its mass production rate due to chemical reactions that will be discussed later in section 3.2. mgl, p , Fgl,z , Fgl,r and Qgl are the inter-phase coupling terms. Ng

g, p

p 1

M g, p

pg  

RuTg

(4) 6 / 22

Ng

g Eg   g ( 

Tg

Tg ,0

p 1

cp

Ng

Tg , p

M g, p

dTg  hg,0 p )  RuTg 

g, p

p 1 M g, p



1 g (ug2  vg2 ) 2

(5)

where Ru  8.314 J  mol-1  K-1 is the gas constant. M g, p is the relative molecular mass of the p th gaseous species as shown in the following Table 2 and Tg is the gaseous phase temperature. cpTg , p is the specific heat at constant pressure,

hTg , p is the enthalpy and sT , p is the entropy at temperature Tg . hg,0 p is the heat of formation at reference temperature g

Tg0  298.15 K . cpT , p  Ru (a1, p  a2, pTg  a3, pTg 2  a4, pTg 3  a5, pTg 4 )

(6)

g

hTg , p 

sTg , p 

RuTg

a2, p

a3, p

a4, p

a5, p

Tg 4  a6, pTg 1 )

(7)

a3, p 2 a4, p 3 a5, p 4 Ru (a1, p ln Tg  a2, pTg  Tg  Tg  Tg  a7, p ) M g, p 2 3 4

(8)

M g, p

(a1, p 

2

Tg 

3

Tg 2 

4

Tg 3 

5

where these coefficients ai , p , i=1,...,7 can be obtained from thermodynamic data file of the chemical kinetics package [12] or from NASA thermochemical polynomial data [23]. Besides, the viscous stress components  g,ij and heat flux terms q x and q y in formulas (3) are expressed as following:

 g, zz 

u v v 2 g (2 g  g  g ) 3 z r r

(9)

 g, rr 

v u v 2 g (2 g  g  g ) 3 r z r

(10)

 g, zr  g (

ug r

 g,  2g

qg, z  g

qg, r  g



vg z

(11)

)

ug vg vg 2  g (   ) r 3 z r r

vg

Tg z Tg r

Ng

 g  Dg, p hg, p p 1

Ng

 g  Dg, p hg, p p 1

cg, p z cg, p r

(12)

(13)

(14)

where Dg , p is the mass diffusivity of the p th gaseous species, defined as:

Dg, p 

1  X g, p

D i j

(15)

g, ij

7 / 22

where Dg,ij is binary diffusivity, X g, p is mole fraction.  g is dynamic viscosity and g is thermal conductivity coefficient, which are determined using values from NASA thermodynamic data [24]. For liquid phase species, viscosity and partial pressure are ignored, therefore the vectors in formula (2) are expressed as:

 l,1  l,1ul   l,1  l,1vl   l,1  l,1vl   l,1  l,1          ... ... ...        ...   l, q l, q ul   l, q  l, q vl   l, p  l, p vl   l, q  l, q          ... ... ...       ...  1 Ul   , El   , Fl   , Hl    ,   r l, Nl  l, Nl vl  l, Nl  l, Nl ul  l, Nl  l, Nl vl  l, Nl  l, Nl     u2   uv   uv   u   l l l   l l l l   l l l l   l l l  2  l  l vl   l  l ul vl   l  l vl2   l  l vl   E         l l l   l  l El ul   l  l El vl   l  l El vl 

0 0 ... ...     0 0     ... ... E l,v    , Fl,v    , H l,v 0 0     0 0 0 0      0   0 

(16)

ml,1     ...   0   ml, p ...   ...     0   ml, Ng     ...  Ng    , Sl   0    mgl, p ug  Fgl ,z  l l g z     p 1 0   Ng 0    mgl, p vg  Fgl ,r     p 1  0     Ng    mgl, p Eg  ( Fgl ,z ug  Fgl ,r vg )  Qgl   p 1 

l where l,q is the average density of the q th liquid species in control volume and l   q 1 l ,q is the total density

N

consisting of all kinds of liquid species. ul and vl are the velocity components of liquid species in z and r directions, respectively. El is total liquid energy per unit mass. The exchanges of mass, momentum and energy between the two fluids are realized by the terms of source vectors. Where mgl, p is the mass production rate of gaseous species that react with Mg and Al droplets. Fgl,z and Fgl,r respectively stand for the inter-phase friction components in z and r directions. Qgl is the thermal transfer consists of heat conduction Qgl,conduction and thermal radiation Qgl,radiation .

mg, p , O2 and O mgl, p   , else 0

(17)

Fgl ,z  Cf g l 1gl V (ul  ug )

(18)

8 / 22

where V

Fgl ,r  Cf g l 1gl V (vl  vg )

(19)

Qgl  Qgl,conduction  Qgl,radiation  Ct C p g l 1gl (Tl  Tg )+l l 1 0 (Tl 4  Tg 4 )

(20)

is the characteristic "slip" velocity which is equal to the absolute value of the differences between the

mainstream velocities of the two fluids. l is the Prandtl mixing length and  0  5.67 108 J  s-1  m-2  K-4 is the Stefan-Boltzmann constant. 1/ 2

V = (ul  ug )2  (vl  vg )2 

(21)

l  C3 4 k 3 2 

(22)

where the constants employed in the above formulas include Cf  0.05 , Ct  0.05 and C  0.09 . The k   shear stress transport (SST) model proposed by F.R. Menter [25] is selected in the solver to describe the turbulence of gaseous phase within the fluid computational domain. It is a two-equation, eddy viscosity, first-order Reynolds-average Navier–Stokes (RANS) model. This model is chosen because of its good behavior in adverse pressure gradients, separating flows, and recirculation areas compared with other two equation models.

3.2 Combustion kinetic model Previous experimental investigations indicated that AP starts to decompose when temperature arrives at 443 K and its combustion phenomenon at high temperature is very violent as what called "deflagration" [26]. HTPB is a kind of high polymer, which starts to decompose later than AP and its decomposition temperature is about 623 K. D.Y. Zhang et al. [27] found that there are over 40 combustion products for HTPB binder. Therefore, we need to make some simplified assumptions as following in order to do numerical simulation investigations: (1) the composite propellant components of AP and HTPB absorb heat and warm up inside the solid domain. They are first starting condensed phases reactions and decompose into the corresponding gas phase products. AP deflagrates on composite propellant burning surface and the chemical formula of its reaction is 4NH4ClO4=5O2+2N2+6H2O+4HCl . Meanwhile, HTPB mainly decomposes into its single molecule based element as butadiene ( C4H6 ) [28]. The decomposition products are added into the flow field according to the conservation law and then continue to react according to the combustion kinetic model. (2) Mg and

Al particles do not react with AP or HTPB binder. Then they will not affect the condensed phase reaction process, but are added into the flow field with the regression of composite propellant burning surface. This paper considers that these two kind of metal particles only react with oxygen and produced the corresponding oxide as magnesia ( MgO ) and alumina ( Al2O3 ). 9 / 22

The numerical simulation method has been used to study the characteristics of two-phase flow field in many literatures. In 1971, A. Mellor et al. [29] carried out a study on the gaseous phase combustion model of Mg particles. S. Gallier et al. [30] conducted a research about the gaseous phase combustion model of Al particles in 2011. G. Cheng et al. [31] compared the differences between a simplified and detailed combustion kinetic models. They found that the flow field results based on combustion kinetic model #2 which considered multiple forward and backward reaction steps had better agreements with the experimental results of real rocket motor. This paper selected the two-fluid model with a detailed combustion kinetic model (16 species and 16 chemical reactions) as shown in the following Table 2 and Table 3 to simulate the two-phase flow problem in the near burning surface region of composite propellant burning surface. In the realistic combustion process, the general formulas of a combustion kinetic model with I elementary chemical reactions are defined as: Ng  Nl

 k 1

vki X k

Ng  Nl

 k 1

vki X k ,

i  1,..., I

(23)

Then the mass production rate of arbitrary species is: Ng  Nl I  Ng  Nl    mk  M k  (vki  vki )  kf ,i  ( k )vki  kb,i  ( k )vki  , k  1,..., ( N g  N l ) Mk M k  i 1 k 1 k 1 

(24)

where the subscripts "f" and "b" stand for "forward" and "backward" chemical reactions, respectively. The forward reaction rate constants for the i th reaction are calculated with Arrhenius formula: ni (  Ei / RT ) kf ,i  AT e i

(25)

where the values of Ai , ni and Ei / R can be obtained from Table 3, and T  TgTl is the root-mean-square temperature of two phases. Besides, the backward reaction rates kb,i are calculated with the equilibrium constants keq,i of chemical reactions as following: kb,i 

kf , i

(26)

keq,i

GRpuT ,T ,i  GR0uT ,T ,i  RuT ln keq ,i GR0uT ,T ,i 

Ng  Nl

 (v  v )(h k 1

ki

ki

k T

 TsTk )

When an arbitrary chemical reaction reaches the equilibrium, the minimum Gibbs free energy term 10 / 22

(27)

(28)

GRpuT ,T ,i  0 ,

0 and then the formula (27) becomes ln keq ,i   GR T ,T ,i / RuT , which only has a relationship with T . The values of u

enthalpy and entropy are calculated with the above formulas (7-8) for different species at a known temperature.

3.3 Governing equations of the solid computational domain The CHT modular was added into the computational solver to calculate the boundary temperature TB at the burning surface position and the temperature distribution inside the solid domain. The basic theory of CHT modular is that fluid and solid domains are thermal coupled by ensuring the equivalent heat flux and boundary temperature at the interface. The two-dimensional axisymmetric form of solid phase governing equations which considering mass pyrolysis is shown as following:

s cs

Ts  T T T h  1  (s s )  (s s )  (s s )  s r s t z z r r r r r

(29)

where  s , cs Ts and hs respectively express the density, specific heat, temperature and energy of unit mass in composite propellant. s stands for the thermal conductivity and the last item in formula (29) stands for the energy change of solid phase which is caused by surface regression in the combustion process. r is the burning rate of composite propellant under the designed conditions of computational cases. Thermophysical properties of the composite propellant samples used in experiments and numerical simulation are given in Table 4.

3.4 Boundary conditions Dummy cells were generated for each boundary grid cell at the physical domain for treating the boundary conditions as transparent as possible. The purpose of the dummy cells is to simplify the computation of the fluxes and gradients along the boundaries. This is achieved by the possibility of extend the stencil of the spatial discretization scheme beyond the physical boundaries. For viscous surface, which was defined as no-slip boundary, the velocity and normal pressure gradients of the solid wall are zero, expressed as:

u2  u1 g,wall  g,wall  u2l,wall  u1l,wall v   v  2g,wall 1g ,wall ,    v2l,wall  v1l,wall  p2g,wall  p1g,wall

(30)

For central axis, which was defined as slip boundary, the normal velocity component and pressure gradients of the solid wall are zero, expressed as:

11 / 22

u2  u1 g,axis  g,axis v  v  2g,axis 1g,axis  0 ,   p2g,axis  p1g,axis

 u2l,axis  u1l,axis   v2l,axis  v1l,axis  0

(31)

For farfield, which was defined as constant pressure outlet boundary, the velocity components are nearly zero and the pressure is stable as designed for experiments for different cases, expressed as:

ug,  0   ul,  0 ,  vg,  0 vl,  0    pg,  pdesigned

(32)

3.5 Numerical schemes The third-order MUSCL upwind scheme [32] was utilized to discretize the convection terms and the central difference scheme was selected to discretize the viscosity terms. The computational solver used the Van Albada limiter [33] to prevent the numerical oscillation in break fields. The values on the grid cells surface are calculated with the following formula:

u

i

1 2

s

s s s   ui  (1  )(ui  ui 1 )  (1  )(ui 1  ui )  4 3 3 

(33)

2(ui  ui 1 )(ui 1  ui )  106 (ui  ui 1 ) 2  (ui 1  ui ) 2  106

(34)

The AUSMPW+ scheme [34, 35] was selected to split fluxes and the explicit third-order Runge-Kutta method [36] was adopted in time advance modular for quick convergence.

3.6 Solver validation The accuracy and reliability of the numerical algorithm was validated by comparison with two classical test cases: (1) "Sod's Shock Tube" and (2) "Shock-induced Combustion". It is obvious in Fig. 3 that the calculated results of the first test case match well with the theory results at the discontinuity position of flow field. The second test case in Fig. 4 shows that the solver can achieve good agreements with the experimental results which have violent H-O chemical reactions. The backward chemical reactions have great influences on the numerical simulation results and cannot be ignored.

3.7 Physical model and computational grids The research problem can be simplified into a two-dimensional axisymmetric model, which consists of fluid and

12 / 22

solid domains. The diameter of the composite propellant sample is DCP  5 mm . The length of the fluid domain in axial direction is as large as 80 times of DCP and about 40 times in radial direction, then the surrounding boundaries can be regarded as farfield. The burning surface is defined at z  0 m position. The physical model and computational grids are shown in Fig. 5. The grids near the wall were refined to 1105 m to make y   1 for ensuring calculation accuracy. And grids away from the walls were built based on the "Exponential" mesh law with a ratio of 1.05. The total mesh number of the computational domain is 19968. The conditions of all the computational cases for numerical simulation and analysis in this paper are described in Table 5. The two variables include ambient pressure and oxygen concentration, and the standard reference cases are "case 3" and "case 7".

4. Results and discussions This section presents the experiment and numerical simulation results of the decomposition and combustion characteristics of composite propellant with energetic particles additives in the near burning surface region. Meanwhile, we discuss the composite propellant decomposition and combustion mechanisms and the influences of different ambient pressure and oxygen concentration conditions. This section consists of three parts: (1) detailedly analyzing the decomposition and combustion phenomenon under the standard designed condition of case 3, (2) fitting the experiment burning rates with two semi-empirical formulas and investigating the ambient pressure effects, (3) analyzing the influence of oxygen concentration on combustion characteristics.

4.1 Flame shape, combustion wave structure and chemical reaction order This part analyzed the detailed decomposition and combustion characteristics of composite propellant by comparing the numerical simulation results with experiment results under the standard designed condition of case 3.

4.1.1 Analysis of flame shape in the near burning surface region The temperature contour of flow field under case 3 condition is shown in Fig. 6 and the highest temperature is about 3592 K. It is obvious that the shape of combustion flame seems like a jet flow along the axial direction, and its diffusion motion along the radial direction is relatively weak. The height of the main flame on central axis is about 10 times of DCP , which has good agreements with the experimental photo taken by infrared imaging technique as shown in Fig. 7.

4.1.2 The temperature distribution of combustion wave on central axis 13 / 22

The CHT modular in the solver can calculate the temperature distribution of combustion wave on central axis in a coupled way. The shape of the combustion temperature curve is a typical "∫" structure, which has very large temperature rising gradient at the burning surface position as shown in Fig. 8. The temperature rises from 298 to over 3500 K in a rather short distance. The temperature keeps stable of over 3500 K and maintains a distance about 4 times of DCP . Then the temperature of flow field decreases gradually away from the burning surface and finally reaches the farfield temperature of 298 K. The temperature distribution of the fluid domain on central axis has an obvious "double-platform" phenomenon, which is also found in the other cases. The reason leads to the first platform is that the heat release of chemical reactions and the heat dissipation have just reaches the equilibrium within this distance. Q.L. Yan et al. [33] found the same phenomenon in his experimental study on the combustion characteristics of double-base propellant, as the defined "steady combustion stage". The second platform has seldom been mentioned before in former literatures. There is high possibility that this phenomenon takes place here because of the diffusion combustion. The original oxidizing gases from composite propellant ingredient are totally consumed before platform 2. Then the primary combustion products will mix with the external environment gases. The mixtures of combustion gases continue to react and then cause the second platform phenomenon. The CHT condition inside the solid domain is shown in Fig. 9 and the temperature distribution at burning surface position in radial direction is shown in Fig. 10. The temperature rising gradient along the axial direction is very large, while the temperature along the radial direction is comparatively uniform. The burning surface temperature TB is about 1044 K from simulation results. The temperature distribution on central axis is measured by embedded micro-thermocouple method in the sealed high-temperature and high-pressure laser ignition platform and the temperature rising rate can be calculated by taking derivative of experiment results with respect to time. The largest rising rate takes place at the burning surface position according to the CHT characteristics as shown in Fig. 11. The experimental burning surface temperature TB is about 1000 K. Considering the time lag and heat loss problem of this experiment method, the numerical simulation results have good agreements with experiment results. We can say that the 4.4% difference is acceptable.

4.1.3 Analysis of chemical reactions order The decomposition and combustion of composite propellant lead to temperature rising in flow field. The power source is originally stored as chemical energy in propellant, and then heat released with the chemical reactions among multiple components. Figs. 12(a-h) represent the mass fraction contours of several major reaction species in the combustion flow field under case 3 condition. By comparing a series of these simulation results, we find that the fastest 14 / 22

chemical reactions, which take place in the near burning surface region of combustion flame, are the deflagration of AP and the combustion of Mg droplets, as shown in Figs. 12(a) and (g). These two species are totally consumed in a rather short distance from the burning surface. These two combustion reactions release a large amount of heat and the thermal feedback to the solid domain helps keep a stable temperature on the burning surface which can ensure the steady combustion. Then the oxidation combustion process of hydride (H2 ,H,OH,H2 O) is shown in Figs. 12(b-d). The particular characteristic of this process is that the forward and backward chemical reactions are both very violent. The synthesis reaction rates are mainly controlled by the slowest reaction as C4H6+2O2=4CO+3H2 . The burning rates of carbide (CO,CO2 ) are relatively slow and are restricted by the concentration of the oxidizing gas components as shown in Figs. 12(e-f). However, as the ingredient is fuel-rich and the decomposition oxidizing gases have been totally consumed in the near burning surface region, then the carbide combustion mainly reacts with the afterburning oxygen in the farfield, which belongs to diffusion reactions. Lots of incompletely burnt carbides can be observed in the form of black smokes and keep diffusing outwards in experiments through the open window. In the most external part of the main flame, only few Al particles react with oxidizing gases and generate Al2O3 as shown in Fig. 12(h). Its chemical reaction rate is the slowest and it needs a large amount of high-temperature oxidizing gases to support combustion. However, the Al particles cannot burn completely under the restrictions of oxidized cap and agglomeration effects. Meanwhile, its combustion efficiency has great relationship with external environment conditions.

4.2 Influences of ambient pressure When the flight state is steady, composite propellant keeps burning under a constant pressure condition. We did constant pressure experiments with target line method to test the constant pressure burning rates of composite propellant under different ambient pressure conditions. The experiment results are shown in Table 6. Fitting the experiment results in Table 6 with two different semi-empirical formulas. According to the Vielle burning rate formula as r  ap n , the fitted parameter a  2.98898 , and the pressure index n  0.29682 . The experiment results and the fitted curve are shown in Fig. 13(a). According to the Summerfield burning rate formula as

1/ r  a / p  b / p1 3 , the fitted parameter a  0.00264 and b  0.33329 . The experiment results and the fitted curve are shown in Fig. 13(b). Comparing these two fitted curves, it is obvious that both of the semi-empirical formulas agree well with the experiment results and have good predictive capability to estimate the burning rates within the pressure 15 / 22

range of ramjet working conditions. This paper carried out numerical simulations about the decomposition and combustion characteristics of composite propellant under five different ambient pressure conditions of 0.10, 0.35, 0.60, 0.85 and 1.10 MPa as computational cases 1-5 by the in-house Fortran solver. The temperature distributions of the combustion wave on central axis of these five cases are shown in Fig. 14. All of these five temperature distribution curves on central axis have an obvious "double-platform" phenomenon. The difference is that as the pressure rises from 0.10 to 1.10 MPa, the length of platform 1 turns shorter and platform 2 is nearly totally disappeared. There are mainly two reasons for the former phenomenon of platform 1: (1) higher pressure restricts the diffusion movement of combustion gases, (2) higher absolute concentration of oxidizing gases leads to shorter distance from the burning surface that combustion components are totally consumed. The highest temperature in platform 1 is larger as the pressure rises in the flow field when composite propellant burns steadily. However, the variation of temperature distribution in platform 2 is not monotonic and it is affected complicatedly by diffusion movement and local concentration distribution of combustion components. The temperature on the burning surface is also affected by ambient pressure. The basic reason is that different heat feedbacks lead to different heat fluxes on composite propellant burning surface and then the burning rates are changed under different ambient pressure conditions at the same time.

4.3 Influences of oxygen concentration This paper performed numerical simulations about the combustion characteristics of three different oxygen concentration conditions of 10.0%, 23.2% and 35.0% as computational cases 6-8 under the standard ambient pressure condition of 0.60 MPa. The influences of environmental oxygen concentration changes on the combustion characteristics of composite propellant is mainly reflected in the outside diffusion zone of the combustion flame, and higher oxygen concentration is obviously beneficial for the secondary afterburning of the primary combustion products as shown in Figs. 15(a-c). Then the temperature distributions of combustion wave on central axis for these three cases are shown in Fig. 16. It is obvious that the temperature distributions along the axial direction from the burning surface to the platform 1 position are completely consistent, where oxygen concentration has little effect, by comparing these three simulated temperature distribution results under different oxygen concentration conditions. It is not until the platform 2 position that the temperature distributions start changing which means that the outside oxygen concentration has almost no effect on temperature distribution of the main combustion flame in the near burning surface region under the same pressure condition. Then the burning rates and surface temperature have little changes among these cases 6-8. From the analyses of these three simulated cases, we found that the flame diffuses mainly along the axial direction 16 / 22

in lower oxygen concentration environment and has longer length. The diffusion combustion characteristics along the radial direction is obviously enhanced and its radial structure is thicker with the increase of oxygen concentration. We came to the conclusion that higher oxygen concentration induces the primary combustion products to start burning in the position where is closer to the surface and leads to the above combustion phenomenon in constant pressure environment.

5. Conclusions This paper investigated the decomposition and combustion characteristics of composite propellant with Mg/Al particles additives in the near burning surface region with an in-house Fortran solver based on two-fluid model. Experiment results were helpful in validating numerical simulation results. The combustion phenomenon was analyzed carefully about flame structure, chemical reaction order, and an obvious "double-platform" phenomenon was observed in the temperature distributions of combustion wave on central axis. On one hand higher ambient pressure restricts the diffusion of primary combustion gases, but on the other it enhances the thermal feedback effect on solid domain and helps the combustion stability of composite propellant. The influences of oxygen concentration on the combustion wave structure in axial direction are negligible before platform 1 position, while the diffusion combustion characteristics in radial direction are obviously changed.

Acknowledge This research was supported by the Fundamental Research Funds for the Central Universities (No. 30915118805).

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List of Tables Table 1. The general components of composite propellant ingredient. Table 2. The 16 species in combustion kinetic model with relative molecular weights. Table 3. The 16 chemical reactions in combustion kinetic model with parameters for calculating forward reaction rates. Table 4. Thermophysical properties of the composite propellant samples. Table 5. Numerical simulation cases description. Table 6. The constant pressure burning rates in different ambient pressure cases.

21 / 22

List of Figures Fig. 1. The schematic diagram of the sealed high-temperature and high-pressure laser ignition platform. Fig. 2. Experimental composite propellant samples. Fig. 3. Solver validation by "Sod's Shock Tube" test case [37] (x is a non-dimensional length variable and p is a non-dimensional pressure variable). Fig. 4. Solver validation by "Shock-induced Combustion" test case [38] (x/r is a non-dimensional length variable). Fig. 5. Physical model and computational grids. Fig. 6. The temperature contour of flow field under case 3 condition. Fig. 7. The experimental photo taken by infrared imaging technique. Fig. 8. The temperature distribution of combustion wave on central axis. Fig. 9. The conjugate heat transfer condition inside the solid domain. Fig. 10. The temperature distribution at burning surface position in radial direction. Fig. 11. The experimental temperature distribution and its rising rate (derivative curve). Fig. 12. The mass fraction contours of several major reaction species in the combustion flow field under case 3 condition (a) O2 , (b) C4H6 , (c) H2 , (d) H2O , (e) CO , (f) CO2 , (g) MgO , (h) Al2O3 . Fig. 13. Experimental constant pressure burning rates and fitted curves based on (a) Vielle formula, (b) Summerfield formula. Fig. 14. The temperature distribution of combustion wave on central axis for cases 1-5 under different ambient pressure conditions. Fig. 15. The temperature contours of flow field for cases 6-8 under different oxygen concentration conditions (a) case 6, (b) case 7, (c) case 8. Fig. 16. The temperature distributions of combustion wave on central axis for cases 6-8 under different oxygen concentration conditions.

22 / 22

Table 1. The general components of composite propellant ingredient.

Components Type Mass fraction

AP

HTPB

Mg

Al

Others

Oxidizing

Polymer

Metal combustion

Metal combustion

Curing agent,

agent

binder

agent

agent

adhesive, etc.

40.0 wt%

15.9 wt%

20.0 wt%

20.0 wt%

4.10 wt%

Table 2. The 16 species in combustion kinetic model with relative molecular weights.

No.

Chemical formula

Relative molecular weight

No.

Chemical formula

Relative molecular weight

1

O2

32

9

HCl

36.5

2

N2

28

10

Mg

24

3

C4H6

54

11

MgO

40

4

NH4ClO4

117.5

12

OH

17

5

CO

28

13

O

16

6

CO2

44

14

H

1

7

H2

2

15

Al

27

8

H2O

18

16

Al2O3

102

Table 3. The 16 chemical reactions in combustion kinetic model with parameters for calculating forward reaction rates.

No.

Equations of chemical reaction

A

n

1

C4H6+2O2=4CO+3H2

8.80 1011

0

1.52 104

2

H2+O2=2OH

1.70 1013

0

2.41104

3

OH+H2=H2O+H

2.19 1013

0

2.59 103

4

2OH=O+H2O

6.02 1012

0

5.50 102

5

O+H2=H+OH

1.80 1010

1.0

4.48 103

6

H+O2=O+OH

1.22 1017

-0.91

8.37 103

7

O+H+M=OH+M

1.00 1016

0

0

8

2O+M=O2+M

2.55 1018

-1.0

5.94 104

9

2H+M=H2+M

5.00 1015

0

0

10

H+OH+M=H2O+M

8.40 1021

-2.0

0

11

CO+OH=H+CO2

4.00 1012

0

4.03 103

12

CO+O2=CO2+O

3.00 1012

0

2.50 104

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E/R

13

CO+O+M=CO2+M

6.00 1013

0

0

14

Mg+O2=MgO+O

4.44 1012

0.5

1.54 104

15

Mg+O+M=MgO+M

1.90 1014

0.5

0

4Al+3O2=2Al2O3

9.70 10

0

8.06 101

16

13

(Units are in seconds, moles, cubic centimeter, joules and degrees Kelvin. All third body efficient M are equal to 1, except for N2 .)

Table 4. Thermophysical properties of the composite propellant samples.

parameter

value

unit

s

1700

kg/m3

cs

1300

J/kg  K

s

1.3

W/m  K

Table 5. Numerical simulation cases description.

variables

1. Ambient pressure

2. Oxygen concentration

case No.

p /MPa

mass fraction (O2/N2)

case 1

0.10

0.232/0.768

case 2

0.35

0.232/0.768

case 3

0.60

0.232/0.768

case 4

0.85

0.232/0.768

case 5

1.10

0.232/0.768

case 6

0.60

0.100/0.900

case 7

0.60

0.232/0.768

case 8

0.60

0.350/0.650

Table 6. The constant pressure burning rates in different ambient pressure cases.

p /MPa

0.10

0.35

0.60

0.85

1.10

r /mm/s

1.3029

2.4707

2.6426

2.7438

3.0100

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Highlights 

Performed experiments to measure the combustion characteristics of Mg/Al based composite propellant.



Developed an in-house solver to simulate the two-phase flow problem with a detailed combustion kinetic model.



Analyzd carefully about the combustion flame structure and chemical reaction order.



Found an obvious "double-platform" phenomenon in temperature distributions of combustion wave.



Ambient pressure and oxygen concentration have different great influences on combustion characteristics.

25 / 25