Numerical simulation of hypersonic reentry flow Field with gas-phase and surface chemistry models

Numerical simulation of hypersonic reentry flow Field with gas-phase and surface chemistry models

Journal Pre-proof Numerical Simulation of Hypersonic Reentry Flow Field with Gas-phase and Surface Chemistry Models Zongshu Mei (Conceptualization) (M...

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Journal Pre-proof Numerical Simulation of Hypersonic Reentry Flow Field with Gas-phase and Surface Chemistry Models Zongshu Mei (Conceptualization) (Methodology) (Software) (Writing - review and editing), Chengying Shi (Data curation) (Writing original draft) (Supervision), Xiaobin Wang (Visualization) (Investigation) (Data curation) (Validation), Xueling Fan (Supervision) (Software) (Validation)

PII:

S2352-4928(19)30971-7

DOI:

https://doi.org/10.1016/j.mtcomm.2019.100773

Reference:

MTCOMM 100773

To appear in:

Materials Today Communications

Received Date:

28 September 2019

Revised Date:

12 November 2019

Accepted Date:

12 November 2019

Please cite this article as: Mei Z, Shi C, Wang X, Fan X, Numerical Simulation of Hypersonic Reentry Flow Field with Gas-phase and Surface Chemistry Models, Materials Today Communications (2019), doi: https://doi.org/10.1016/j.mtcomm.2019.100773

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Numerical Simulation of Hypersonic Reentry Flow Field with Gas-phase and Surface Chemistry Models Zongshu Mei1, and Chengying Shi2

School of Nuclear Engineering, Xi’an Research Institute of High-Tech, Xi’an, Shaanxi, 710025, People’s Republic of China Xiaobin Wang3

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School of Astronautics, Xi’an Jiaotong University, Xi’an, Shaanxi,710049, People’s Republic of China And Xueling Fan4

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School of Astronautics, Xi’an Jiaotong University, Xi’an, Shaanxi,710049, People’s Republic of China

Ph.D. Candidate, School of Nuclear Engineering.

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Professor, School of Nuclear Engineering.

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Ph.D. Candidate, Key Laboratory for Strength and Vibration of Mechanical Structures

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Professor, State Key Laboratory for Strength and Vibration of Mechanical Structures.

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Abstract: For the chemistry reactions of hypersonic reentry flow field, this paper focuses on combinations of the gas-phase chemistry models and the surface models. Two chemistry models named 20-species,40-reaction and 19-species,44-reaction were used to simulate the gas-phase chemistry process of hypersonic flow field in this paper; And two popular finite-rate reaction models, the Park model and the Zhluktov & Abe (ZA) model, were applied to characterize surface reactions at the wall of aircraft. In order to investigate the differences between the two gas-phase models with surface models for predicting the species distribution, six combinations were designed to characterize the chemistry reactions of reentry flow field. Results indicate that the combination of 44-reaction and Park surface chemistry model is most stable and efficient for simulation. There are two methods used to calculate the mass loss rates of ablating materials in the fluid-solid interaction. The differences of mass loss rates between the two methods were obtained by embedding the two methods into the finite element thermodynamic analysis. According to the results, the numerical differences range from 14.3% to 35.2%. Keywords: gas-phase chemistry model, hypersonic flow field, surface models, ablating materials

Nomenclature Mi

=

molecular weight of species i, kg·mol-1

Γ

=

third body efficiency = forward and backward reaction rates for reaction r, variable units

NR, Nr

= total number of gas-phase, surface reactions

NJ

=

total number of gas species

Ns

=

total number of surface species

ρ

=

density, kg·m-3

̇

=

mass production rate, kg·m-2·s-1

βr

=

temperature exponent of reaction r

A

=

pre-exponential factor, m3·kg-1·mol-1·s-1

Er

=

activation energy for the reaction r, J·kmol-1

R

=

universal gas constant, J·kmol-1·K-1

̅k

=

thermal speed(√

Φs

=

total active site density on surface phase, mol·m-2

s

=

site density exponent

T’

=

dimensionless value, ’= /1K

γer

=

Eley-Rideal reaction efficiency

γsub

=

sublimation reaction efficiency

S0

=

sticking coefficient

-p

re

) of species k, m·s-1

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kf, r, kb, r

Eer , Esub, Ead

=

energy barriers for Eley-Rideal recombination, sublimation, adsorption, J·mol-1

χk

=

mole fraction of species k

Xk

=

generalized concentration of species k

θns, k

=

fraction of active sites occupied by species k on surface phase ns

=

active site density on surface phase ns, mol·m-2

χnb, k =

mole fraction of bulk species k in bulk phase nb

Φns

=

Y, y

=

mass fraction of species in gas-phase and surface reactions



=

mass average velocity of species in gas-phase reactions

̇

=

mole production rate of species k, mol·m-2·s-1

w

=

surface-normal velocity

=

diffusion flux

-p

J

diffusion coefficient

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D

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1 Introduction

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The thermochemical process of hypersonic flow field can be divided into different aerothermal phenomenon which should be characterized by different chemical models. Earlier, Hansen [1] divided the aerothermal phenomenon into chemical and thermal equilibrium, chemical non-equilibrium and thermal equilibrium, chemical and thermal non-equilibrium based on reentry altitude. As the reentry speed is from low to high, the gas-phase chemistry models were divided into 2-species, 5-species, 7-species and 11-species reaction models, which contained only the molecular states, dissociation, and ionization of nitrogen and oxygen without C species. Obviously, Hansen’s models are not perfect for current reentry conditions, Park [2] considers the gaseous species due to surface reactions at the wall of ablating materials which are away from the surface into the gas-phase interior and extends the chemical species to 20-species. For the carbon-phenolic material with its pyrolysis gas, 20-species are considered which include: C, O, N, H, CO, C2, N2, CN, NO, O2, H2, C3, C2H, C+, H+, O+, N+, NO+, N+2 , e-. Based on the work of Park[3-5] and Candler[6], the 20-species presented by Alba[7] for carbon(graphite) material include: N2, O2, NO, CO2, CO, C2, C3, CN, NO+, N+2 , O+2 , CO+, Ar, C, N, O, N+, O+, C+, e-. Referring to Martin[8] , the 20-species conducted by Alkandry[9] for FiberForm material include: N2, O2, NO, N, O, N+2 , O+2 , NO+, N+, O+, e-, CO, CO2, C3, CN, C, C2, NCO, CO+, C+. According to the reentry speed, the chemical species and reactions can be flexibly selected. Alba chooses 11-species,23-reaction [10] gas chemistry model for a velocity of 7km/s, while 20-species,40-reaction [7] for 8500m/s. The main difference between them is that the former one has no ionization of species and the latter one does. Sometimes, there are the same number of species but different number of reactions, such as 11-species,17-reaction conducted by Hassan [11] which is different from 11-species,23-reaction conducted by Alba [10]. For the same carbon-air system, there are two different gas-phase

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chemistry models conducted by Alba [7] and Bhutta [12]. They are quite similar as 19-species,44-reaction presented by Bhutta and 20-species,40-reaction presented by Alba. It’s unknown which is better or worse among them, so it’s necessary to investigate the two models and make a comparison. In addition to the determination of species and reactions, the rate coefficients for the reactions are also not invariable but evolving with the time. Johnston [13] made modifications for the Park CO and CO2 dissociation rates based on comparisons with shock-tube radiation measurements, which was proved by Brandis [14] to improve the nonequilibrium radiance predictions compared against the standard Park gas-phase chemistry model. As parts of the energy source terms and species mass boundary of the gas-phase reactions, the surface reactions are important for the aerodynamic flow field of ablating materials. Marschall [15-16] systematically expounded the surface reaction mathematical formulas that deduced from the principle and application of surface reactions. The difficulties of surface reactions are to determine which reaction occurs and the corresponding reaction rate parameters. For carbon-air system, there are mainly two surface models: Park [17] and ZA [18] finite-rate surface kinetic models which owning themselves advantages and disadvantages. The Park model consistently overpredicted the radiative heat fluxes, which can be improved by modified nitridation efficiency [19]. ZA model is suitable for relatively low wall temperature such as 1770K, and the predictions of radiative heat fluxes are much lower than measured values at higher temperature which presumably related to the non-nitriding mechanism [7]. Since the reaction efficiency of carbon nitridation contributes directly to the surface mass loss and radiative heating, two nitridation reactions were added to ZA model by Alba [10]. The results showed that the nitridation mechanism had a minor effect compared with oxidation mechanisms. So, more researches are required to modify the carbon oxidation and nitridation reactions. In order to calculate the mass loss rates or mass flux of ablating materials, a gas-surface interaction model need to be built. There are currently at least three methods to characterize the mass loss rates. The first one was presented by Marschall [15], which summing the global mass production rates of all bulk species in bulk phases to calculate mass loss rates of ablating materials due to surface reactions. The second one from Park’s [20-21] work built mathematical formulas of mass loss rates by taking mass fraction of each species reacting with ablating materials, wall temperature and reaction probabilities of surface reactions into consideration. And the last one came from Palaninathan [22], which divided the chemical ablation into two regimes, reaction kinemics rate controlled and diffusion rate-controlled regime. Correspondingly, two mathematical formulas were built to characterize the oxidation reaction rate. Those methods always were used alone and little literature has ever compared the pros and cons between them. In this paper, the flow field was simulated by the commercial computational fluid dynamics code Fluent and user-defined functions. The mass loss rates of ablating materials were calculated by the finite element code Abaqus and user subroutines UMESHMOTION. The numerical simulation derived from a ground ablation test [23] was conducted to investigate the differences between the different chemistry models and two methods used to calculate the mass loss rates of ablating materials.

2 Methodology Gas-phase chemistry model

NR

wi 

 r 1

 d i     M  dt r

NR i





v

'' i ,r

 vi ,r ( k

NJ

'

r 1

f ,r



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The laminar finite-rate model in Fluent was used for gas-phase chemistry model as this model can ignore the effects of turbulent fluctuations. The model is exact for laminar flow field, but is generally inaccurate for turbulent flow field due to highly nonlinear Arrhenius chemical kinetics. The laminar model may, however, be acceptable for combustion with relatively slow chemistry and small turbulence-chemistry interaction, such as hypersonic flow field. Consider a system with NJ species and NR reactions, the net local production rate of species i via reaction r can be written as, '

X

i 1

 i ,r

i

NJ

 k b ,r  X

''

 i ,r

i

)

(1)

i 1

where Xi is molar concentration of species i and 'i, r and ''i, r are the stoichiometric coefficients for species i on the reactants and products. η'i, r and η''i, r are the rate exponents for species i on

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r

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the reactants and products. For a reversible reaction, the stoichiometric coefficients are equal to the rate exponents. The forward rate constant for reaction r, f, r is computed using the Arrhenius expression, k f ,r  Ar T

exp( E r / R T )

For a reversible reaction, the backward rate constant for reaction r,

(2) b, r

is computed from

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the forward rate constant using the following formula: k b ,r 

k

f ,r

(3)

Kr

na

where Kr is the equilibrium constant for the r reaction, which written by,

R

( v i ,r  v i ,r ) p a tm   )( ) i 1 RT RT

H

''

r

'

(4)

ur

K r  exp(

N

Sr

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where Patm denotes atmospheric pressure, the term within the exponential function represents the change in Gibbs free energy.

Surface chemistry model The finite-rate surface chemistry model developed in Marschall and Maclean [15-16] is a general gas-surface interaction model which can simulate the reactions between hypersonic flow field and the surface of the aircraft. The model framework allows characterization of both catalytic and surface altering reactions, such as adsorption, sublimation and recombination controlled by Eley-Rideal or Langmuir-Hinshelwood mechanism. Forward reaction rate coefficients can be specified by different formulas for different types of reactions. Several formulas of forward

reaction rates for common reactions are shown in Table 1. For the air-carbon system, two widely used surface models come from Park and Zhluktov & Abe are adopted in this paper. The Park model reaction set contains irreversible oxidation, nitridation, and sublimation/condensation. The ZA model makes use of several reaction types including Arrhenius, Eley-Rideal, adsorption/desorption besides oxidation and sublimation. The rate parameters involved in Park and ZA models provided by MacLean are shown in Table 2. There are three environments in the model system following the convention developed in Marschall and MacLean, which are the gas environment, the surface environment, and the bulk environment. The net global production rates of gas species are obtained as follows: Nr

wk  M

i

  v i 1

fi

and

bi

ki

 '  v ki   k 

Ns fi

'



[X k]

v ki

Ns

 k bi  [ X k ]

k 1

''

v ki

k 1

  

(5)

are the forward and backward rate coefficients for reaction i. X is the

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where

''

generalized species concentration for species k in a gas, surface, or bulk phase which can be written as follows [15], X

 k

k

s u r fa c e p h a s e

X

b u lk p h a s e

X

 

k

k

P RT ns ,k

  ns ,k 

(6)

ns

-p

gas  phase

  nb ,k

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where in the gas-phase, the generalized species concentration is in units of mole·m-3 which related to species partial pressure. The generalized species concentration for surface species represents the local concentration within its surface phase with units in mole·m-2. The generalized species concentration is equal to the mole fraction of species k in the bulk phase, which is dimensionless.

Interaction between gas-phase and surface chemistry model

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The coupling of the two thermochemical models is mainly achieved by the mass conservation and the energy balance at the wall. The mass conservation is mainly characterized by the rates of diffusion of gaseous species away from the surface into the gas-phase interior and the rate that the entire mixture is convected away from the surface due to bulk production exactly balances the rate of production from surface reactions of that species in the infinitely thin control volume at the surface at any instant time[16]. Considering the consumption and production of the species at the wall, the mass fraction of the species at the wall is calculated by the mass flux balance of the corresponding species,   w Dk yk

w

  w v w y k ,w  M k w k

(7)

where the first term denotes the diffusion of the gas species and the second term denotes the mass flux away from surface into gas-phase interior. While the last one denotes the production or consumption rate due to surface reactions. In the gas-phase reactions, the mass conversation of species is given by,  t

(  Yi )    (  v Yi )     J i  R i  S i

(8)

where Ri is the net production rate of species i in the gas phase reactions and Si is the mass flux of

gas species that inpours from surface reactions. The energy conversation of gas-phase reactions interior is written by, ( g E ) t

     (  g E  P )        T    

 i

 h i J i  (   )   S h  S w 

(9)

where Sh is the release heat due to gas-phase reactions and Sw is the release heat due to surface reactions. Energy balance on an ablative surface is given by, q C O N V  q D IF F  q R A D  IN  m ( h w  h c s )  q R A D  O U T  q C O N D

In this balanced system, the leaving energy fluxes include the radiation q̇

AD-OU

(10) away from the

surface and the conduction q̇ COND into the materials. The inputting energy fluxes involve the

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conduction 𝑞̇ 𝐶𝑂𝑁𝑉 , the inward radiation 𝑞̇ 𝑅𝐴𝐷−𝐼𝑁 and the species diffusion 𝑞̇ 𝐷𝐼𝐹𝐹 . The remaining two terms ṁ hcs and ṁ hw represent the reaction enthalpy flux and ablation mass ejector heat flux due to surface reactions.

3 Result and discussion

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Using the above models to simulate the hypersonic reentry flow field, the reentry conditions were derived from a hypersonic impulse facility, the X-2 expansion tube as shown in Fig.3 which came from the University of Queensland. The tunnel conditions used for these tests were equivalent to a flight speed of 8.6 km/s and the freestream parameters in detail are shown in Table 3. In the fluid dynamics section, the turbulence model in Fluent selects the k-ω SST model, which has the advantage of being insensitive to the parameters of the incoming flow and better stability of calculation near the wall. This model can be used to calculate the problem of a wide range of inflow velocity and separation due to reverse pressure gradient.

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A. Different chemistry models

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In order to make a comparison between the two similar gas-phase chemistry models of 20-species,40-reaction[7] and 19-species,44-reaction[12]and the two frequently used surface models, The gas phase reactions and surface reactions were combined into four thermochemical reaction models: 40-reaction with Park surface model(Park_40), 44-reaction with Park surface model(Park_44), 40-reaction with ZA surface model(ZA_40), 44_reaction with ZA surface model(ZA_44). In order to make a benchmark reference, two gas-phase chemistry models, named Pure_40 and Pure_44 respectively, were designed without surface reactions. Calculating the hypersonic flow field represented by the four thermochemical reaction models, it was expected to gain the contours of species distribution and the species distribution curves along the stagnation line. In order to obtain the complete species distribution contours, the model in Fig.3(b) was extended. The expanded model was shown in Fig. 4. According to the species distribution contours in Fig. 5, the two-dimensional model can exactly reflect the spatial distribution of each species. Among the four species, the distribution of C+ was mainly concentrated at the stagnation point and near the wall, while the distribution of CO,

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CN, O was extended to the area outside the wall. As to the maximum concentration spatial distribution, CO was significantly different from other species, with a lower concentration near the stagnation point and a larger concentration at the end of the wall, indicating that the lower temperature at the end of the wall was more conducive to CO generation than the high temperature at the stagnation point. CO also existed at the inner part of the wall, indicating that the temperature activating formation reaction of CO is lower than other species. According to the distribution curves of species mass fraction, CN and CO had the highest values at the wall due to the surface reactions, and the concentrations of C+ and O decreased or decreased slightly at the wall. Comparing the mass fraction curves under those models, it can be seen that when the gas-phase chemistry model was 44-reaction, the mass fractions of C+, CO and O obtained were similar with the surface kinetic models of Park and ZA at the wall. Numerically, the mass fraction of each species with surface chemistry model was slightly higher than the mass fraction of the pure gas-phase reaction without surface chemistry model at the wall. As to the CN, the mass fraction calculated by the Park_44 with nitriding reaction was 1.8 times as much as that by the ZA_44 model without nitriding reaction, while the latter one was similar but slightly higher with the Pure_44 model. The concentration trends of the four species in the gas-phase reaction zone were similar, indicating that surface reactions have little effect on the gas-phase reaction under the 44-reaction. When the gas-phase reaction was represented by 40-reaction model, the results of species CO, CN and C+ calculated by different surface chemistry models were quite different. It can be seen that the species mass fraction curves obtained by the Park_40 model agreed with the curves obtained by the Pure_40 model, indicating that in the 40-reaction model, the Park surface reactions have little effect on the gas-phase reactions and only can significantly increase the concentration of CN or slightly increase the concentration of species C+, CO, O at the wall. The mass fraction curves obtained by ZA_40 were different from the curves obtained by Park_40 and Pure_40, which were not only at the wall but also in the gas-phase reaction zone. It can be concluded that the ZA model affects species concentration both at the wall and in the gas-phase reaction zone. Although there was no carbon nitridation in the ZA model, the mass fraction of CN obtained by ZA model was higher than that by the pure gas-phase model at the wall. The mass fraction of CN with ZA_44 model was 10% higher than that with Pure_44 model and was about 5 times higher with ZA_40 than that with Pure_40. Although there was no direct nitridation reaction, the ZA model can still increase the concentration of CN during ablation which indicates that the ZA model without nitridation can compensate for the nitridation reaction among the gas-phase reactions. The concentration of C+ obtained by ZA_40 model was higher than that by Park_40 model at the wall. In the gas-phase reaction zone, the C+ concentration with ZA_40 model was significantly higher than that with Park_40 model, which indicating that the ZA surface chemistry model has a greater influence on the C+ concentration in the gas-phase reaction zone. In general, the concentrations of species obtained with the surface chemistry models are more likely to converge when the gas-phase reactions represented by 44-reaction model but more divergent by 40-reaction model. With the Park surface model, the mass fraction curves of species C+, CO and CN in both gas-phase models agreed well with each other in the initial segment of the shock layer while becoming different closer to the wall. When the surface reactions model was represented by ZA model, the species concentration varied greatly in both the trend and the numerical value. It can be seen that the Park_44 model is more stable in simulating hypersonic flow field.

B. Mass loss rate of ablating materials There are two main methods, named Method_1 and Method_2 in the paper, for calculating the mass loss rates of ablating materials. Method_1 was to solve the equation shown in (11) based on the reaction formulas and reaction rates of bulk carbon in the surface model: Nb

m c   c

w

nb

 



(11)

M k wk

n b 1 k 1

kTw

m1   C O

2 m O kTw 2

2 m O

kTw

m3  C N

C

M

O

(12)

M 2

M

2

C O2

N

M

C

M

N

re

2 m N

O

M

-p

m2  2CO

O

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Method_2 calculated specific mass loss formulas of the gaseous species reacting with carbon at the wall based on the concentrations of species proved by the chemistry reactions, wherein the carbon sublimation products (C2(g), C3(g)) were neglected due to the low concentration, the specific model [20] are shown as below:

(13)

(14)

According to the research of Chen and Milos [17], βi can be expressed as:

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 O  0 .6 3 e x p (  1 1 6 0 / T w )  O  0 .5 2

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 N  0 .3

m c  m 1  m 2  m 3   c w

(15) (16) (17) (18)

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The mass loss rates of bulk carbon materials in the hypersonic flow field were calculated by finite element thermodynamic code Abaqus with user subroutines UMESHMOTION. The flow field chemistry model chose Park_44 and Park_40 models respectively in order to make a comparison. The ablating materials is C/C composites and the composite density, specific heat, and heat conductivity coefficient are taken as 2780 kg/m3, 828.63 J/(kg·K), and 18.8 W/(m·K). It can be seen from the Fig.6 that when the gas-phase reaction model was fixed, the two methods for calculating the curves of mass loss rates had the same trend. In 40-reaction model, the mass loss rates increased with time in both methods, but the change was small. One reason for this phenomenon was that the surface reactions tended to be balance in a short time so as to gas-phase reactions in 40-reaction model, so the mass loss rates of bulk carbon changed little with time. Maximum mass loss rate happened at the stagnation point where mass loss rate obtained by the Method_2 was 25% higher than that by Method_1. The mass loss rates of the two methods gradually increased with time, and tended to be fixed at a certain range in 44-reaction model. At the time of 5μs, 10μs, 15μs, 20μs, the stagnation point

mass loss rate calculated by Method_2 was 35.2%, 16.8%, 12.2%, and 14.3% higher than that by Method_1 respectively. In general, the mass loss rates calculated by 40-reaction model get to be balance faster compared with those by 44-reaction model, and the mass loss rates calculated by the Method_2 are higher than those by the Method_1 which range from 14.3% to 35.2%.

4 In conclusion

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In this paper, the differences between the several combinations of gas-phase chemistry models and the surface models are studied. The following conclusions can be drawn by comparison: Firstly, the Park surface model only affects species concentrations at the wall, while the ZA model affects species concentrations both at the wall and in the gas-phase reactions zone. Secondly, although there is no nitridation reaction of carbon in ZA model, those reactions in ZA model can compensate for the nitridation reactions among the gas-phase reactions, thereby increasing the CN concentration. Thirdly, compared with other combinations, Park_44 model is most stable in calculating the species distribution of hypersonic flow field; Fourthly, the mass loss rates calculated by 40-reaction get to be balance faster than that by 44-reaction; Fifth. the mass loss rates calculated by the Method_2 are higher than that by the Method_1 which range from 14.3% to 35.2%. By comparing the similarities and differences of different combinations of gas-phase chemistry reactions and surface models, it provides references for model selection and optimization. What needs to be improved in the future is to extend the comparison of different chemistry models to the modified C/C composites which has great practical value.

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Conflicts of Interest

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The authors declare that there are no conflicts of interest regarding the publication of this paper.

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Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 1171101165).

CRediT authorship contribution statement Mei Zongshu: Conceptualization, Methodology, Software, Writing,

Reviewing and Editing. Shi Chengying: Data curation, Writing, Original draft preparation, Supervision. Wang Xiaobin: Visualization, Investigation, Data curation, Validation.

References

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Fan Xueling: Supervision, Software, Validation.

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[1] Hansen, C. F., Heims, S. P., A Review of the Thermodynamic, Transport, and Chemical Reaction Rate Properties of High-Temperature Air,’’ NACA TN 4359, July 1958. [2] Park, C., Jaffe, R.L., and Partridge, H., “Chemical-Kinetic Parameters of Hyperbolic Earth Entry,” 38th Aerospace Sciences Meeting and Exhibit, AIAA Paper 2000-0210, 2000. [3] Park, C., Nonequilibrium Hypersonic Aerothermodynamics, Wiley, New York, 1990, pp.324-328. [4] Park, C., Howe, J.T., and Jaffe, R.L., “Review of Chemical Kinetic Problems of Future NASA Missions, 2: Mars Entries,” Journal of Thermophysics and Heat Transfer, Vol.8, No.6,1994, pp.9-23. [5] Park, C., “Review of Chemical Kinetic Problems of Future NASA Missions,1: Earth Entries,” Journal of Thermophysics and Heat Transfer, Vol.7, No.3,1993, pp.385-398. [6] Candler, G.V.,” Nonequilibrium Process in Hypervelocity Flow: An Analysis of Carbon Ablation Models,” 50th AIAA Aerospace Sciences Meeting, AIAA Paper 2012-0724, Jan.2012. [7] Alba, C.R., Greedyke, R. B., Lewis, S.W., et al. Numerical Modeling of Earth Reentry Flow with Surface Ablation. Journal of Spacecraft and Rockets,2016. [8] Martin, A., Boyd, I.D., Cozmuta, I., et al. Chemistry model for ablating carbon-phenolic material during atmospheric re-entry. 48th AIAA Aerospace Sciences Meeting, AIAA 2010-1175, Jan.2010. [9] Alkandry, H., Farbar, E.D., Boyd, I.D., Evaluation of Finite-Rate Surface Chemistry Models for Simulation of the Stardust Reentry Capsule.43rd AIAA Thermophysics Conference, AIAA 2012-2874, June 2012. [10] Alba, C. R., Greedyke, R.B., Marschall J., Development of a Nonequilibrium Finite-Rate Ablation Model for Radiating Earth Reentry Flows. Journal of Spacecraft and Rockets,2016. [11] Basil Hassan, David W. Kuntz, and Donald L. Potter. Coupled Fluid/Thermal Prediction of Ablating Hypersonic Vehicles. American Institute of Aeronautics and Astronautics, Inc,1997. [12] Bhutta, B.A., Daywitt, J.E., Rahaim, J.J., et al. A new technique for the computation of severe reentry environments. AIAA Meeting Papers on Disc, June 1996.

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[13] Johnston, C.O., Brandis, A.M., Sutton, K., “Shock Layer Radiation Modeling and Uncertainty for Mars Entry,” 43rd AIAA Thermophysics Conference, AIAA Paper 2012-2866, June 2012. [14] Brandis, A.M., Johnston, C.O., Cruden, B.A., et al. “Investigation of Nonequilibrium Radiation for Mars Entry,” 51st AIAA Aerospace Sciences Meeting, AIAA Paper 2013-1055, Jan.2013. [15] Marschall, J., and Maclean, M., “Finite-Rate Surface Chemistry Model, Ⅰ: Formulation and Reaction System Examples,” 42nd AIAA Thermophysics Conference, AIAA Paper 2011-3783, June 2011. [16] MacLean, M., Marschall, J., and Driver, D. M., “Finite-Rate Surface Chemistry Model, Ⅱ: Coupling to Viscous Navier-Stokes Code,” 42nd AIAA Thermophysics Conference, AIAA Paper 2011-3784, June 2011. [17] Chen, Y., and Milos, F.S., “Finite-Rate Ablation Boundary Conditions for a Carbon-Phenolic Heat-Shield,” 37th AIAA Thermophysics Conference, AIAA Paper 2004-2270, June-July 2004. [18] Zhluktov, S.V., and Abe, T., “Viscous Shock-Layer Simulation of Airflow Past Ablating Blunt Body with Carbon Surface,” Journal of Thermophysics and Heat Transfer, Vol.52, No.6, Jan.-March 1999, pp.50-59. [19] Suzuki, T., Fujita, K., and Sakai, T., “Graphite Nitridation in Lower Surface Temperature Regime,” 47th AIAA Aerospace Sciences Meeting, AIAA Paper 2009-0260, Jan.2009. [20] Park, C., and Ahn, H.K., “Stagnation-Point Heat Transfer Rates for Pioneer-Venus Probes,” Journal of Thermophysics and Heat Transfer, Vol.13, No.1, 1999, pp.33-41. [21] Park, C., “Calculations of Stagnation-Point Heating Rates Associated with Stardust Vehicle,” Journal of spacecraft and Rockets, Vol.44, No.1, 2007, pp.24-32. [22] Palaninathan, R., Behavior of Carbon-Carbon Composite under Intense Heating. International Journal of Aerospace Engineering, 2010. [23] Zander, F., Morgan, R.G., Sheikh, U., Buttsworth, D.R., and Teakle, P.R., “Hot-Wall Reentry Testing in Hypersonic Impulse Facilities,” AIAA Journal, Vol.51, No.2, Feb.2013, pp.476-484.

Figure captions Fig.1 Schematic diagram of mass conservation Fig.2 Schematic diagram of energy conservation

Fig.3 X-2 test facility: (a) Schematic diagram of X-2 test facility; (b) Numeral model for X-2

Fig.4 Expanded model with mesh for X-2 flow field

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Fig.5 Mass fraction of species i along the stagnation line: (a) i=C+;(b) i=CN;(c) i=CO;(d) i=O

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Fig.6 Mass loss rate as a function of distance from the stagnation point: (a)method_1, Park_40;(b) Method_1, Park_44;(c) Method_2, Park_40;(d) Method_2, Park_44

Table Table 1 Forward reaction rate

Reaction Type

Rate Formula

0: Arrhenius (Arrh)

k

f

1: Adsorption (Ads)

k

f

k

3: Sublimation (Sub)

k

 v    4

 v    4

f

E   exp    R T  

'

vs s

vs s

  S 0T 

'

   er T 

  v    vs  4 s RT 

f

A,  , E

 E ad  exp     RT 

'

su b

S 0 ,  , E ad

 E er  exp     RT 

T

'

 er ,  , E er

 E su b  exp    RT  

 su b ,  , E su b

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2: Eley-Rideal(E-R)

 AT

Specified Parameters

Table 2 Park and ZA model surface reactions and rate parameters

2

O2 +2(s)+2C(b)→2CO+2(s)

3

N+(s)+C(b)→CN+(s)

E(kJ/mol)

E-R

0.63

0

9.644

E-R

0.50

0

0

0

0

4

3(s)+3C(b)→C3 +3(s)

1

775.81

5

C3 +3(s)→3(s)+3C(b)

1

O+(s)↔O(s)

2

N+(s)↔N(s)

-p

O+(s)+C(b)→CO+(s)

βi

re

1

S0 /γ0 /A

Type

E-R

0.30 5.19×10

E-R

0.10

0

0

Ads

1.0

0

0

Ads

1.0

0

0

1

256.07

0

118.06

0

0

1

332.56

0

16.63

1

332.56

2O(s)↔O2 +2(s)

Arrh

3.58×10

4

O2 +(s)↔O+O(s)

E-R

1.0

CO2+(s)↔CO+O(s)

E-R

0.9

5 6 7

13

Arrh

3

O(s)+C(b)↔CO+(s)

Arrh

2.08×10

O+O(s)+C(b)↔CO2 +(s)

E-R

0.8

ur

Zhluktov & Abe model

Reaction

lP

Park model

Nr

na

Model

13

9

17

2O(s)+C(b)↔CO2 +2(s)

Arrh

3.58×10

9

C+(s)↔(s)+C(b)

E-R

0.24

0

0

10

C2 +2(s)↔2(s)+2C(b)

E-R

0.5

0

0

11

C3 +3(s)↔3(s)+3C(b)

E-R

0.023

0

0

12

N2 +(s)↔N+N(s)

E-R

1.0

0

636.85

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Table 3 Parameters of freestream conditions in X-2

Parameter

Value

Pressure

847Pa

Temperature

2040K

Velocity

8500m/s

1.45×10-3kg/m3

Density 𝑦𝑁2

0.751

𝑦𝑂2

0.225

𝑦𝑁𝑂

8.53×10-3

𝑦𝐶𝑂 𝑦𝐶𝑂2

1.26×10-5

𝑦𝐴𝑟

0.013

𝑦𝑂

2.37×10-3

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4.65×10-4